From 84ef783f53d25d671b41b521e730740397896d65 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan Date: Wed, 24 Jul 2024 15:27:30 -0400 Subject: [PATCH 01/71] rename --- src/OrdinaryDiffEq.jl | 2 +- src/alg_utils.jl | 5 +- src/algorithms.jl | 10 +- src/algorithms/explicit_rk_pde.jl | 1230 + src/caches/extrapolation_caches.jl | 1704 + src/caches/feagin_caches.jl | 248 + src/caches/firk_caches.jl | 18 +- src/caches/low_storage_rk_caches.jl | 3839 ++ src/caches/rkc_caches.jl | 348 + src/caches/rkn_caches.jl | 683 + src/caches/ssprk_caches.jl | 1265 + src/caches/symplectic_caches.jl | 419 + src/caches/verner_caches.jl | 258 + src/dense/verner_addsteps.jl | 1323 + src/integrators/controllers.jl | 2 +- src/integrators/integrator_interface.jl | 4 +- .../extrapolation_perform_step.jl | 3639 ++ src/perform_step/feagin_rk_perform_step.jl | 1288 + src/perform_step/firk_perform_step.jl | 8 +- .../low_storage_rk_perform_step.jl | 842 + src/perform_step/rkc_perform_step.jl | 1296 + src/perform_step/rkn_perform_step.jl | 1821 + src/perform_step/ssprk_perform_step.jl | 1707 + src/perform_step/symplectic_perform_step.jl | 2025 + src/perform_step/verner_rk_perform_step.jl | 1284 + src/rkc_utils.jl | 276 + src/tableaus/feagin_tableaus.jl | 2650 ++ src/tableaus/firk_tableaus.jl | 8 +- src/tableaus/rkc_tableaus.jl | 37731 ++++++++++++++++ src/tableaus/rkn_tableaus.jl | 2472 + src/tableaus/symplectic_tableaus.jl | 807 + src/tableaus/verner_tableaus.jl | 3894 ++ .../algconvergence/ode_extrapolation_tests.jl | 242 + test/algconvergence/ode_feagin_tests.jl | 53 + test/algconvergence/ode_firk_tests.jl | 8 +- .../ode_low_storage_rk_tests.jl | 1567 + test/algconvergence/ode_ssprk_tests.jl | 534 + test/algconvergence/rkc_tests.jl | 97 + test/algconvergence/symplectic_tests.jl | 102 + 39 files changed, 75678 insertions(+), 31 deletions(-) create mode 100644 src/algorithms/explicit_rk_pde.jl create mode 100644 src/caches/extrapolation_caches.jl create mode 100644 src/caches/feagin_caches.jl create mode 100644 src/caches/low_storage_rk_caches.jl create mode 100644 src/caches/rkc_caches.jl create mode 100644 src/caches/rkn_caches.jl create mode 100644 src/caches/ssprk_caches.jl create mode 100644 src/caches/symplectic_caches.jl create mode 100644 src/caches/verner_caches.jl create mode 100644 src/dense/verner_addsteps.jl create mode 100644 src/perform_step/extrapolation_perform_step.jl create mode 100644 src/perform_step/feagin_rk_perform_step.jl create mode 100644 src/perform_step/low_storage_rk_perform_step.jl create mode 100644 src/perform_step/rkc_perform_step.jl create mode 100644 src/perform_step/rkn_perform_step.jl create mode 100644 src/perform_step/ssprk_perform_step.jl create mode 100644 src/perform_step/symplectic_perform_step.jl create mode 100644 src/perform_step/verner_rk_perform_step.jl create mode 100644 src/rkc_utils.jl create mode 100644 src/tableaus/feagin_tableaus.jl create mode 100644 src/tableaus/rkc_tableaus.jl create mode 100644 src/tableaus/rkn_tableaus.jl create mode 100644 src/tableaus/symplectic_tableaus.jl create mode 100644 src/tableaus/verner_tableaus.jl create mode 100644 test/algconvergence/ode_extrapolation_tests.jl create mode 100644 test/algconvergence/ode_feagin_tests.jl create mode 100644 test/algconvergence/ode_low_storage_rk_tests.jl create mode 100644 test/algconvergence/ode_ssprk_tests.jl create mode 100644 test/algconvergence/rkc_tests.jl create mode 100644 test/algconvergence/symplectic_tests.jl diff --git a/src/OrdinaryDiffEq.jl b/src/OrdinaryDiffEq.jl index a0204c73a0..b832c88f8c 100644 --- a/src/OrdinaryDiffEq.jl +++ b/src/OrdinaryDiffEq.jl @@ -415,7 +415,7 @@ export FunctionMap, Euler, Heun, Ralston, Midpoint, RK4, ExplicitRK, OwrenZen3, FRK65, PFRK87, RKM, MSRK5, MSRK6, Stepanov5, SIR54, QPRK98, PSRK4p7q6, PSRK3p6q5, PSRK3p5q4 -export RadauIIA3, RadauIIA5, RadauIIA7 +export RadauIIA3, RadauIIA5, RadauIIA9 export ImplicitEuler, ImplicitMidpoint, Trapezoid, TRBDF2, SDIRK2, SDIRK22, Kvaerno3, KenCarp3, Cash4, Hairer4, Hairer42, SSPSDIRK2, Kvaerno4, diff --git a/src/alg_utils.jl b/src/alg_utils.jl index cb7c0cc5b7..3c4e3ece28 100644 --- a/src/alg_utils.jl +++ b/src/alg_utils.jl @@ -176,7 +176,7 @@ qmin_default(alg::DP8) = 1 // 3 qmax_default(alg::Union{OrdinaryDiffEqAlgorithm, DAEAlgorithm}) = 10 qmax_default(alg::CompositeAlgorithm) = minimum(qmax_default.(alg.algs)) qmax_default(alg::DP8) = 6 -qmax_default(alg::Union{RadauIIA3, RadauIIA5, RadauIIA7}) = 8 +qmax_default(alg::Union{RadauIIA3, RadauIIA5, RadauIIA9}) = 8 function has_chunksize(alg::OrdinaryDiffEqAlgorithm) return alg isa Union{OrdinaryDiffEqExponentialAlgorithm, @@ -441,7 +441,7 @@ alg_order(alg::TanYam7) = 7 alg_order(alg::TsitPap8) = 8 alg_order(alg::RadauIIA3) = 3 alg_order(alg::RadauIIA5) = 5 -alg_order(alg::RadauIIA7) = 7 +alg_order(alg::RadauIIA9) = 9 alg_order(alg::ImplicitEuler) = 1 alg_order(alg::RKMK2) = 2 alg_order(alg::RKMK4) = 4 @@ -580,6 +580,7 @@ alg_adaptive_order(alg::Rosenbrock32) = 2 alg_adaptive_order(alg::RadauIIA3) = 1 alg_adaptive_order(alg::RadauIIA5) = 3 +alg_adaptive_order(alg::RadauIIA9) = 7 alg_adaptive_order(alg::ImplicitEuler) = 0 alg_adaptive_order(alg::Trapezoid) = 1 diff --git a/src/algorithms.jl b/src/algorithms.jl index cf3182d624..abeea83bdb 100644 --- a/src/algorithms.jl +++ b/src/algorithms.jl @@ -1007,10 +1007,10 @@ year={1999}, publisher={Elsevier} } -RadauIIA7: Fully-Implicit Runge-Kutta Method +RadauII97: Fully-Implicit Runge-Kutta Method An A-B-L stable fully implicit Runge-Kutta method with internal tableau complex basis transform for efficiency. """ -struct RadauIIA7{CS, AD, F, P, FDT, ST, CJ, Tol, C1, C2, StepLimiter} <: +struct RadauIIA9{CS, AD, F, P, FDT, ST, CJ, Tol, C1, C2, StepLimiter} <: OrdinaryDiffEqNewtonAdaptiveAlgorithm{CS, AD, FDT, ST, CJ} linsolve::F precs::P @@ -1024,7 +1024,7 @@ struct RadauIIA7{CS, AD, F, P, FDT, ST, CJ, Tol, C1, C2, StepLimiter} <: step_limiter!::StepLimiter end -function RadauIIA7(; chunk_size = Val{0}(), autodiff = Val{true}(), +function RadauIIA9(; chunk_size = Val{0}(), autodiff = Val{true}(), standardtag = Val{true}(), concrete_jac = nothing, diff_type = Val{:forward}, linsolve = nothing, precs = DEFAULT_PRECS, @@ -1032,7 +1032,7 @@ function RadauIIA7(; chunk_size = Val{0}(), autodiff = Val{true}(), new_W_γdt_cutoff = 1 // 5, controller = :Predictive, κ = nothing, maxiters = 10, smooth_est = true, step_limiter! = trivial_limiter!) - RadauIIA7{_unwrap_val(chunk_size), _unwrap_val(autodiff), typeof(linsolve), + RadauIIA9{_unwrap_val(chunk_size), _unwrap_val(autodiff), typeof(linsolve), typeof(precs), diff_type, _unwrap_val(standardtag), _unwrap_val(concrete_jac), typeof(κ), typeof(fast_convergence_cutoff), typeof(new_W_γdt_cutoff), typeof(step_limiter!)}(linsolve, @@ -1046,7 +1046,7 @@ function RadauIIA7(; chunk_size = Val{0}(), autodiff = Val{true}(), controller, step_limiter!) end -TruncatedStacktraces.@truncate_stacktrace RadauIIA7 +TruncatedStacktraces.@truncate_stacktrace RadauIIA9 ################################################################################ diff --git a/src/algorithms/explicit_rk_pde.jl b/src/algorithms/explicit_rk_pde.jl new file mode 100644 index 0000000000..20fbeadeae --- /dev/null +++ b/src/algorithms/explicit_rk_pde.jl @@ -0,0 +1,1230 @@ +#Low Storage Explicit Runge-Kutta Methods + +@doc explicit_rk_docstring( + "A fourth-order, five-stage explicit low-storage method of Carpenter and Kennedy +(free 3rd order Hermite interpolant). Fixed timestep only. Designed for +hyperbolic PDEs (stability properties).", + "CarpenterKennedy2N54", + references = "@article{carpenter1994fourth, + title={Fourth-order 2N-storage Runge-Kutta schemes}, + author={Carpenter, Mark H and Kennedy, Christopher A}, + year={1994} + }", + extra_keyword_description = """- `williamson_condition`: allows for an optimization that allows fusing broadcast expressions with the function call `f`. However, it only works for `Array` types. + """, + extra_keyword_default = "williamson_condition = true") +Base.@kwdef struct CarpenterKennedy2N54{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() + williamson_condition::Bool = true +end +# for backwards compatibility +function CarpenterKennedy2N54(stage_limiter!, + step_limiter! = trivial_limiter!; + williamson_condition = true) + CarpenterKennedy2N54(stage_limiter!, step_limiter!, False(), williamson_condition) +end + +@doc explicit_rk_docstring( + "A fourth-order, six-stage explicit low-storage method. Fixed timestep only.", + "SHLDDRK64", + references = "D. Stanescu, W. G. Habashi. + 2N-Storage Low Dissipation and Dispersion Runge-Kutta Schemes for Computational + Acoustics. + Journal of Computational Physics, 143(2), pp 674-681, 1998. + doi: https://doi.org/10.1006/jcph.1998.5986 + }", + extra_keyword_description = """- `williamson_condition`: allows for an optimization that allows fusing broadcast expressions with the function call `f`. However, it only works for `Array` types. + """, + extra_keyword_default = "williamson_condition = true") +Base.@kwdef struct SHLDDRK64{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() + williamson_condition::Bool = true +end +# for backwards compatibility +function SHLDDRK64(stage_limiter!, + step_limiter! = trivial_limiter!; + williamson_condition = true) + SHLDDRK64(stage_limiter!, step_limiter!, False(), williamson_condition) +end + +@doc explicit_rk_docstring("TBD", "SHLDDRK52") +Base.@kwdef struct SHLDDRK52{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function SHLDDRK52(stage_limiter!, step_limiter! = trivial_limiter!) + SHLDDRK52(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring("TBD", "SHLDDRK_2N") +Base.@kwdef struct SHLDDRK_2N{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function SHLDDRK_2N(stage_limiter!, step_limiter! = trivial_limiter!) + SHLDDRK_2N(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring("Low-Storage Method +6-stage, fourth order low-stage, low-dissipation, low-dispersion scheme. +Fixed timestep only.", "HSLDDRK64", + references = "D. Stanescu, W. G. Habashi. + 2N-Storage Low Dissipation and Dispersion Runge-Kutta Schemes for Computational + Acoustics. + Journal of Computational Physics, 143(2), pp 674-681, 1998. + doi: https://doi.org/10.1006/jcph.1998.5986 + }", + extra_keyword_description = """- `williamson_condition`: allows for an optimization that allows fusing broadcast expressions with the function call `f`. However, it only works for `Array` types. + """, + extra_keyword_default = "williamson_condition = true") +struct HSLDDRK64{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread + williamson_condition::Bool + function HSLDDRK64(stage_limiter! = trivial_limiter!, step_limiter! = trivial_limiter!; + williamson_condition = true) + Base.depwarn("HSLDDRK64 is deprecated, use SHLDDRK64 instead.", :HSLDDRK64) + SHLDDRK64(stage_limiter!, step_limiter!, thread; + williamson_condition = williamson_condition) + end +end + +@doc explicit_rk_docstring( + "7-stage, third order low-storage low-dissipation, low-dispersion scheme for +discontinuous Galerkin space discretizations applied to wave propagation problems. +Optimized for PDE discretizations when maximum spatial step is small due to +geometric features of computational domain. Fixed timestep only.", + "DGLDDRK73_C", + references = "T. Toulorge, W. Desmet. + Optimal Runge–Kutta Schemes for Discontinuous Galerkin Space Discretizations + Applied to Wave Propagation Problems. + Journal of Computational Physics, 231(4), pp 2067-2091, 2012. + doi: https://doi.org/10.1016/j.jcp.2011.11.024", + extra_keyword_description = """- `williamson_condition`: allows for an optimization that allows fusing broadcast expressions with the function call `f`. However, it only works for `Array` types. + """, + extra_keyword_default = "williamson_condition = true") +Base.@kwdef struct DGLDDRK73_C{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() + williamson_condition::Bool = true +end +# for backwards compatibility +function DGLDDRK73_C(stage_limiter!, step_limiter! = trivial_limiter!; + williamson_condition = true) + DGLDDRK73_C(stage_limiter!, + step_limiter!, + False(), + williamson_condition) +end + +@doc explicit_rk_docstring( + "8-stage, fourth order low-storage low-dissipation, low-dispersion scheme for +discontinuous Galerkin space discretizations applied to wave propagation problems. +Optimized for PDE discretizations when maximum spatial step is small due to +geometric features of computational domain. Fixed timestep only.", + "DGLDDRK84_C", + references = "T. Toulorge, W. Desmet. + Optimal Runge–Kutta Schemes for Discontinuous Galerkin Space Discretizations + Applied to Wave Propagation Problems. + Journal of Computational Physics, 231(4), pp 2067-2091, 2012. + doi: https://doi.org/10.1016/j.jcp.2011.11.024", + extra_keyword_description = """- `williamson_condition`: allows for an optimization that allows fusing broadcast expressions with the function call `f`. However, it only works for `Array` types. + """, + extra_keyword_default = "williamson_condition = true") +Base.@kwdef struct DGLDDRK84_C{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() + williamson_condition::Bool = true +end +# for backwards compatibility +function DGLDDRK84_C(stage_limiter!, step_limiter! = trivial_limiter!; + williamson_condition = true) + DGLDDRK84_C(stage_limiter!, + step_limiter!, + False(), + williamson_condition) +end + +@doc explicit_rk_docstring( + "8-stage, fourth order low-storage low-dissipation, low-dispersion scheme for +discontinuous Galerkin space discretizations applied to wave propagation problems. +Optimized for PDE discretizations when the maximum spatial step size is not +constrained. Fixed timestep only.", + "DGLDDRK84_F", + references = "T. Toulorge, W. Desmet. + Optimal Runge–Kutta Schemes for Discontinuous Galerkin Space Discretizations + Applied to Wave Propagation Problems. + Journal of Computational Physics, 231(4), pp 2067-2091, 2012. + doi: https://doi.org/10.1016/j.jcp.2011.11.024", + extra_keyword_description = """- `williamson_condition`: allows for an optimization that allows fusing broadcast expressions with the function call `f`. However, it only works for `Array` types. + """, + extra_keyword_default = "williamson_condition = true") +Base.@kwdef struct DGLDDRK84_F{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() + williamson_condition::Bool = true +end +# for backwards compatibility +function DGLDDRK84_F(stage_limiter!, step_limiter! = trivial_limiter!; + williamson_condition = true) + DGLDDRK84_F(stage_limiter!, + step_limiter!, + False(), + williamson_condition) +end + +@doc explicit_rk_docstring( + "12-stage, fourth order low-storage method with optimized stability regions for +advection-dominated problems. Fixed timestep only.", + "NDBLSRK124", + references = "Jens Niegemann, Richard Diehl, Kurt Busch. + Efficient Low-Storage Runge–Kutta Schemes with Optimized Stability Regions. + Journal of Computational Physics, 231, pp 364-372, 2012. + doi: https://doi.org/10.1016/j.jcp.2011.09.003", + extra_keyword_description = """- `williamson_condition`: allows for an optimization that allows fusing broadcast expressions with the function call `f`. However, it only works for `Array` types. + """, + extra_keyword_default = "williamson_condition = true") +Base.@kwdef struct NDBLSRK124{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() + williamson_condition::Bool = true +end +# for backwards compatibility +function NDBLSRK124(stage_limiter!, step_limiter! = trivial_limiter!; + williamson_condition = true) + NDBLSRK124(stage_limiter!, + step_limiter!, False(), + williamson_condition) +end + +@doc explicit_rk_docstring( + "13-stage, fourth order low-storage method with optimized stability regions for +advection-dominated problems. Fixed timestep only.", + "NDBLSRK134", + references = "Jens Niegemann, Richard Diehl, Kurt Busch. + Efficient Low-Storage Runge–Kutta Schemes with Optimized Stability Regions. + Journal of Computational Physics, 231, pp 364-372, 2012. + doi: https://doi.org/10.1016/j.jcp.2011.09.003", + extra_keyword_description = """- `williamson_condition`: allows for an optimization that allows fusing broadcast expressions with the function call `f`. However, it only works for `Array` types. + """, + extra_keyword_default = "williamson_condition = true") +Base.@kwdef struct NDBLSRK134{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() + williamson_condition::Bool = true +end +# for backwards compatibility +function NDBLSRK134(stage_limiter!, step_limiter! = trivial_limiter!; + williamson_condition = true) + NDBLSRK134(stage_limiter!, + step_limiter!, False(), + williamson_condition) +end + +@doc explicit_rk_docstring( + "14-stage, fourth order low-storage method with optimized stability regions for +advection-dominated problems. Fixed timestep only.", + "NDBLSRK144", + references = "Jens Niegemann, Richard Diehl, Kurt Busch. + Efficient Low-Storage Runge–Kutta Schemes with Optimized Stability Regions. + Journal of Computational Physics, 231, pp 364-372, 2012. + doi: https://doi.org/10.1016/j.jcp.2011.09.003", + extra_keyword_description = """- `williamson_condition`: allows for an optimization that allows fusing broadcast expressions with the function call `f`. However, it only works for `Array` types. + """, + extra_keyword_default = "williamson_condition = true") +Base.@kwdef struct NDBLSRK144{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() + williamson_condition::Bool = true +end +# for backwards compatibility +function NDBLSRK144(stage_limiter!, step_limiter! = trivial_limiter!; + williamson_condition = true) + NDBLSRK144{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, False(), + williamson_condition) +end + +@doc explicit_rk_docstring("Low-Storage Method +6-stage, fourth order low-storage, low-dissipation, low-dispersion scheme. +Fixed timestep only.", "CFRLDDRK64", + references = "M. Calvo, J. M. Franco, L. Randez. A New Minimum Storage Runge–Kutta Scheme + for Computational Acoustics. Journal of Computational Physics, 201, pp 1-12, 2004. + doi: https://doi.org/10.1016/j.jcp.2004.05.012") +Base.@kwdef struct CFRLDDRK64{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function CFRLDDRK64(stage_limiter!, step_limiter! = trivial_limiter!) + CFRLDDRK64(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +7-stage, fourth order low-storage low-dissipation, low-dispersion scheme with maximal accuracy and stability limit along the imaginary axes. +Fixed timestep only.", + "TSLDDRK74", + references = "Kostas Tselios, T. E. Simos. Optimized Runge–Kutta Methods with Minimal Dispersion and Dissipation + for Problems arising from Computational Acoustics. Physics Letters A, 393(1-2), pp 38-47, 2007. + doi: https://doi.org/10.1016/j.physleta.2006.10.072") +Base.@kwdef struct TSLDDRK74{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function TSLDDRK74(stage_limiter!, step_limiter! = trivial_limiter!) + TSLDDRK74(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +4-stage, third order low-storage scheme, optimized for compressible Navier–Stokes equations. +", "CKLLSRK43_2") +Base.@kwdef struct CKLLSRK43_2{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function CKLLSRK43_2(stage_limiter!, step_limiter! = trivial_limiter!) + CKLLSRK43_2{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations. +", "CKLLSRK54_3C") +Base.@kwdef struct CKLLSRK54_3C{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function CKLLSRK54_3C(stage_limiter!, step_limiter! = trivial_limiter!) + CKLLSRK54_3C{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +9-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations. +", "CKLLSRK95_4S") +Base.@kwdef struct CKLLSRK95_4S{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function CKLLSRK95_4S(stage_limiter!, step_limiter! = trivial_limiter!) + CKLLSRK95_4S{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +9-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations. +", "CKLLSRK95_4C") +Base.@kwdef struct CKLLSRK95_4C{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function CKLLSRK95_4C(stage_limiter!, step_limiter! = trivial_limiter!) + CKLLSRK95_4C{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +9-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations. +", "CKLLSRK95_4M") +Base.@kwdef struct CKLLSRK95_4M{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function CKLLSRK95_4M(stage_limiter!, step_limiter! = trivial_limiter!) + CKLLSRK95_4M{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations. +", "CKLLSRK54_3C_3R") +Base.@kwdef struct CKLLSRK54_3C_3R{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function CKLLSRK54_3C_3R(stage_limiter!, step_limiter! = trivial_limiter!) + CKLLSRK54_3C_3R{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations. +", "CKLLSRK54_3M_3R") +Base.@kwdef struct CKLLSRK54_3M_3R{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function CKLLSRK54_3M_3R(stage_limiter!, step_limiter! = trivial_limiter!) + CKLLSRK54_3M_3R{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations. +", "CKLLSRK54_3N_3R") +Base.@kwdef struct CKLLSRK54_3N_3R{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function CKLLSRK54_3N_3R(stage_limiter!, step_limiter! = trivial_limiter!) + CKLLSRK54_3N_3R{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +8-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations. +", "CKLLSRK85_4C_3R") +Base.@kwdef struct CKLLSRK85_4C_3R{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function CKLLSRK85_4C_3R(stage_limiter!, step_limiter! = trivial_limiter!) + CKLLSRK85_4C_3R{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +8-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations. +", "CKLLSRK85_4M_3R") +Base.@kwdef struct CKLLSRK85_4M_3R{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function CKLLSRK85_4M_3R(stage_limiter!, step_limiter! = trivial_limiter!) + CKLLSRK85_4M_3R{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +8-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations. +", "CKLLSRK85_4P_3R") +Base.@kwdef struct CKLLSRK85_4P_3R{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function CKLLSRK85_4P_3R(stage_limiter!, step_limiter! = trivial_limiter!) + CKLLSRK85_4P_3R{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations. +", "CKLLSRK54_3N_4R") +Base.@kwdef struct CKLLSRK54_3N_4R{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function CKLLSRK54_3N_4R(stage_limiter!, step_limiter! = trivial_limiter!) + CKLLSRK54_3N_4R{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations. +", "CKLLSRK54_3M_4R") +Base.@kwdef struct CKLLSRK54_3M_4R{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function CKLLSRK54_3M_4R(stage_limiter!, step_limiter! = trivial_limiter!) + CKLLSRK54_3M_4R{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "6-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.", + "CKLLSRK65_4M_4R") +Base.@kwdef struct CKLLSRK65_4M_4R{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function CKLLSRK65_4M_4R(stage_limiter!, step_limiter! = trivial_limiter!) + CKLLSRK65_4M_4R(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +8-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.", + "CKLLSRK85_4FM_4R") +Base.@kwdef struct CKLLSRK85_4FM_4R{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function CKLLSRK85_4FM_4R(stage_limiter!, step_limiter! = trivial_limiter!) + CKLLSRK85_4FM_4R(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "CKLLSRK75_4M_5R: Low-Storage Method +7-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.", + "CKLLSRK75_4M_5R") +Base.@kwdef struct CKLLSRK75_4M_5R{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function CKLLSRK75_4M_5R(stage_limiter!, step_limiter! = trivial_limiter!) + CKLLSRK75_4M_5R{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +3-stage, second order (3S) low-storage scheme, optimized the spectral difference method applied to wave propagation problems.", + "ParsaniKetchesonDeconinck3S32", + references = "Parsani, Matteo, David I. Ketcheson, and W. Deconinck. + Optimized explicit Runge--Kutta schemes for the spectral difference method applied to wave propagation problems. + SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. + doi: https://doi.org/10.1137/120885899") +Base.@kwdef struct ParsaniKetchesonDeconinck3S32{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function ParsaniKetchesonDeconinck3S32(stage_limiter!, step_limiter! = trivial_limiter!) + ParsaniKetchesonDeconinck3S32{typeof(stage_limiter!), typeof(step_limiter!), False}( + stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +8-stage, second order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.", + "ParsaniKetchesonDeconinck3S82", + references = "Parsani, Matteo, David I. Ketcheson, and W. Deconinck. + Optimized explicit Runge--Kutta schemes for the spectral difference method applied to wave propagation problems. + SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. + doi: https://doi.org/10.1137/120885899") +Base.@kwdef struct ParsaniKetchesonDeconinck3S82{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function ParsaniKetchesonDeconinck3S82(stage_limiter!, step_limiter! = trivial_limiter!) + ParsaniKetchesonDeconinck3S82{typeof(stage_limiter!), typeof(step_limiter!), False}( + stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +5-stage, third order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.", + "ParsaniKetchesonDeconinck3S53", + references = "Parsani, Matteo, David I. Ketcheson, and W. Deconinck. + Optimized explicit Runge--Kutta schemes for the spectral difference method applied to wave propagation problems. + SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. + doi: https://doi.org/10.1137/120885899") +Base.@kwdef struct ParsaniKetchesonDeconinck3S53{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function ParsaniKetchesonDeconinck3S53(stage_limiter!, step_limiter! = trivial_limiter!) + ParsaniKetchesonDeconinck3S53{typeof(stage_limiter!), typeof(step_limiter!), False}( + stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +17-stage, third order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.", + "ParsaniKetchesonDeconinck3S173", + references = "Parsani, Matteo, David I. Ketcheson, and W. Deconinck. + Optimized explicit Runge--Kutta schemes for the spectral difference method applied to wave propagation problems. + SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. + doi: https://doi.org/10.1137/120885899") +Base.@kwdef struct ParsaniKetchesonDeconinck3S173{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function ParsaniKetchesonDeconinck3S173(stage_limiter!, step_limiter! = trivial_limiter!) + ParsaniKetchesonDeconinck3S173{typeof(stage_limiter!), typeof(step_limiter!), False}( + stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +9-stage, fourth order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.", + "ParsaniKetchesonDeconinck3S94", + references = "Parsani, Matteo, David I. Ketcheson, and W. Deconinck. + Optimized explicit Runge--Kutta schemes for the spectral difference method applied to wave propagation problems. + SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. + doi: https://doi.org/10.1137/120885899") +Base.@kwdef struct ParsaniKetchesonDeconinck3S94{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function ParsaniKetchesonDeconinck3S94(stage_limiter!, step_limiter! = trivial_limiter!) + ParsaniKetchesonDeconinck3S94{typeof(stage_limiter!), typeof(step_limiter!), False}( + stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +18-stage, fourth order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.", + "ParsaniKetchesonDeconinck3S184", + references = "Parsani, Matteo, David I. Ketcheson, and W. Deconinck. + Optimized explicit Runge--Kutta schemes for the spectral difference method applied to wave propagation problems. + SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. + doi: https://doi.org/10.1137/120885899") +Base.@kwdef struct ParsaniKetchesonDeconinck3S184{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function ParsaniKetchesonDeconinck3S184(stage_limiter!, step_limiter! = trivial_limiter!) + ParsaniKetchesonDeconinck3S184{typeof(stage_limiter!), typeof(step_limiter!), False}( + stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +10-stage, fifth order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.", + "ParsaniKetchesonDeconinck3S105", + references = "Parsani, Matteo, David I. Ketcheson, and W. Deconinck. + Optimized explicit Runge--Kutta schemes for the spectral difference method applied to wave propagation problems. + SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. + doi: https://doi.org/10.1137/120885899") +Base.@kwdef struct ParsaniKetchesonDeconinck3S105{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function ParsaniKetchesonDeconinck3S105(stage_limiter!, step_limiter! = trivial_limiter!) + ParsaniKetchesonDeconinck3S105{typeof(stage_limiter!), typeof(step_limiter!), False}( + stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "Low-Storage Method +20-stage, fifth order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.", + "ParsaniKetchesonDeconinck3S205", + references = "Parsani, Matteo, David I. Ketcheson, and W. Deconinck. + Optimized explicit Runge--Kutta schemes for the spectral difference method applied to wave propagation problems. + SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. + doi: https://doi.org/10.1137/120885899") +Base.@kwdef struct ParsaniKetchesonDeconinck3S205{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function ParsaniKetchesonDeconinck3S205(stage_limiter!, step_limiter! = trivial_limiter!) + ParsaniKetchesonDeconinck3S205{typeof(stage_limiter!), typeof(step_limiter!), False}( + stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "A third-order, five-stage explicit Runge-Kutta method with embedded error estimator +designed for spectral element discretizations of compressible fluid mechanics.", + "RDPK3Sp35", + references = "Ranocha, Dalcin, Parsani, Ketcheson (2021) + Optimized Runge-Kutta Methods with Automatic Step Size Control for + Compressible Computational Fluid Dynamics + [arXiv:2104.06836](https://arxiv.org/abs/2104.06836)") +Base.@kwdef struct RDPK3Sp35{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function RDPK3Sp35(stage_limiter!, step_limiter! = trivial_limiter!) + RDPK3Sp35{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, False()) +end + +@doc explicit_rk_docstring( + "A third-order, five-stage explicit Runge-Kutta method with embedded error estimator +using the FSAL property designed for spectral element discretizations of +compressible fluid mechanics.", + "RDPK3SpFSAL35", + references = "Ranocha, Dalcin, Parsani, Ketcheson (2021) + Optimized Runge-Kutta Methods with Automatic Step Size Control for + Compressible Computational Fluid Dynamics + [arXiv:2104.06836](https://arxiv.org/abs/2104.06836)") +Base.@kwdef struct RDPK3SpFSAL35{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function RDPK3SpFSAL35(stage_limiter!, step_limiter! = trivial_limiter!) + RDPK3SpFSAL35{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "A fourth-order, nine-stage explicit Runge-Kutta method with embedded error estimator +designed for spectral element discretizations of compressible fluid mechanics.", + "RDPK3Sp49", + references = "Ranocha, Dalcin, Parsani, Ketcheson (2021) + Optimized Runge-Kutta Methods with Automatic Step Size Control for + Compressible Computational Fluid Dynamics + [arXiv:2104.06836](https://arxiv.org/abs/2104.06836)") +Base.@kwdef struct RDPK3Sp49{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function RDPK3Sp49(stage_limiter!, step_limiter! = trivial_limiter!) + RDPK3Sp49{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, False()) +end + +@doc explicit_rk_docstring( + "A fourth-order, nine-stage explicit Runge-Kutta method with embedded error estimator +using the FSAL property designed for spectral element discretizations of +compressible fluid mechanics.", + "RDPK3SpFSAL49", + references = "Ranocha, Dalcin, Parsani, Ketcheson (2021) + Optimized Runge-Kutta Methods with Automatic Step Size Control for + Compressible Computational Fluid Dynamics + [arXiv:2104.06836](https://arxiv.org/abs/2104.06836)") +Base.@kwdef struct RDPK3SpFSAL49{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function RDPK3SpFSAL49(stage_limiter!, step_limiter! = trivial_limiter!) + RDPK3SpFSAL49{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "A fifth-order, ten-stage explicit Runge-Kutta method with embedded error estimator +designed for spectral element discretizations of compressible fluid mechanics.", + "RDPK3Sp510", + references = "Ranocha, Dalcin, Parsani, Ketcheson (2021) + Optimized Runge-Kutta Methods with Automatic Step Size Control for + Compressible Computational Fluid Dynamics + [arXiv:2104.06836](https://arxiv.org/abs/2104.06836)") +Base.@kwdef struct RDPK3Sp510{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function RDPK3Sp510(stage_limiter!, step_limiter! = trivial_limiter!) + RDPK3Sp510{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, False()) +end + +@doc explicit_rk_docstring( + "A fifth-order, ten-stage explicit Runge-Kutta method with embedded error estimator +using the FSAL property designed for spectral element discretizations of +compressible fluid mechanics.", + "RDPK3SpFSAL510", + references = "Ranocha, Dalcin, Parsani, Ketcheson (2021) + Optimized Runge-Kutta Methods with Automatic Step Size Control for + Compressible Computational Fluid Dynamics + [arXiv:2104.06836](https://arxiv.org/abs/2104.06836)") +Base.@kwdef struct RDPK3SpFSAL510{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function RDPK3SpFSAL510(stage_limiter!, step_limiter! = trivial_limiter!) + RDPK3SpFSAL510{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, + step_limiter!, + False()) +end + +#SSP Optimized Runge-Kutta Methods + +@doc explicit_rk_docstring("TBD", + "KYK2014DGSSPRK_3S2") +Base.@kwdef struct KYK2014DGSSPRK_3S2{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function KYK2014DGSSPRK_3S2(stage_limiter!, step_limiter! = trivial_limiter!) + KYK2014DGSSPRK_3S2(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "A second-order, two-stage explicit strong stability preserving (SSP) method. +Fixed timestep only.", + "SSPRK22", + references = "Shu, Chi-Wang, and Stanley Osher. + Efficient implementation of essentially non-oscillatory shock-capturing schemes. + Journal of Computational Physics 77.2 (1988): 439-471. + https://doi.org/10.1016/0021-9991(88)90177-5") +Base.@kwdef struct SSPRK22{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function SSPRK22(stage_limiter!, step_limiter! = trivial_limiter!) + SSPRK22(stage_limiter!, + step_limiter!, False()) +end + +@doc explicit_rk_docstring( + "A third-order, three-stage explicit strong stability preserving (SSP) method. +Fixed timestep only.", + "SSPRK33", + references = "Shu, Chi-Wang, and Stanley Osher. + Efficient implementation of essentially non-oscillatory shock-capturing schemes. + Journal of Computational Physics 77.2 (1988): 439-471. + https://doi.org/10.1016/0021-9991(88)90177-5") +Base.@kwdef struct SSPRK33{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function SSPRK33(stage_limiter!, step_limiter! = trivial_limiter!) + SSPRK33(stage_limiter!, + step_limiter!, False()) +end + +@doc explicit_rk_docstring( + "A third-order, five-stage explicit strong stability preserving (SSP) method. +Fixed timestep only.", + "SSPRK53", + references = "Ruuth, Steven. + Global optimization of explicit strong-stability-preserving Runge-Kutta methods. + Mathematics of Computation 75.253 (2006): 183-207") +Base.@kwdef struct SSPRK53{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function SSPRK53(stage_limiter!, step_limiter! = trivial_limiter!) + SSPRK53(stage_limiter!, + step_limiter!, False()) +end + +@doc explicit_rk_docstring("TBD", + "KYKSSPRK42") +Base.@kwdef struct KYKSSPRK42{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function KYKSSPRK42(stage_limiter!, step_limiter! = trivial_limiter!) + KYKSSPRK42(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "A third-order, five-stage explicit strong stability preserving (SSP) low-storage method. +Fixed timestep only.", + "SSPRK53_2N1", + references = "Higueras and T. Roldán. + New third order low-storage SSP explicit Runge–Kutta methods + arXiv:1809.04807v1.") +Base.@kwdef struct SSPRK53_2N1{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function SSPRK53_2N1(stage_limiter!, step_limiter! = trivial_limiter!) + SSPRK53_2N1(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "A third-order, five-stage explicit strong stability preserving (SSP) low-storage method. +Fixed timestep only.", + "SSPRK53_2N2", + references = "Higueras and T. Roldán. + New third order low-storage SSP explicit Runge–Kutta methods + arXiv:1809.04807v1.") +Base.@kwdef struct SSPRK53_2N2{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function SSPRK53_2N2(stage_limiter!, step_limiter! = trivial_limiter!) + SSPRK53_2N2(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "A third-order, five-stage explicit strong stability preserving (SSP) low-storage method. +Fixed timestep only.", + "SSPRK53_H", + references = "Higueras and T. Roldán. + New third order low-storage SSP explicit Runge–Kutta methods + arXiv:1809.04807v1.") +Base.@kwdef struct SSPRK53_H{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function SSPRK53_H(stage_limiter!, step_limiter! = trivial_limiter!) + SSPRK53_H(stage_limiter!, + step_limiter!, False()) +end + +@doc explicit_rk_docstring( + "A third-order, six-stage explicit strong stability preserving (SSP) method. +Fixed timestep only.", + "SSPRK63", + references = "Ruuth, Steven. + Global optimization of explicit strong-stability-preserving Runge-Kutta methods. + Mathematics of Computation 75.253 (2006): 183-207") +Base.@kwdef struct SSPRK63{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function SSPRK63(stage_limiter!, step_limiter! = trivial_limiter!) + SSPRK63(stage_limiter!, + step_limiter!, False()) +end + +@doc explicit_rk_docstring( + "A third-order, seven-stage explicit strong stability preserving (SSP) method. +Fixed timestep only.", + "SSPRK73", + references = "Ruuth, Steven. + Global optimization of explicit strong-stability-preserving Runge-Kutta methods. + Mathematics of Computation 75.253 (2006): 183-207") +Base.@kwdef struct SSPRK73{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function SSPRK73(stage_limiter!, step_limiter! = trivial_limiter!) + SSPRK73(stage_limiter!, + step_limiter!, False()) +end + +@doc explicit_rk_docstring( + "A third-order, eight-stage explicit strong stability preserving (SSP) method. +Fixed timestep only.", + "SSPRK83", + references = "Ruuth, Steven. + Global optimization of explicit strong-stability-preserving Runge-Kutta methods. + Mathematics of Computation 75.253 (2006): 183-207") +Base.@kwdef struct SSPRK83{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function SSPRK83(stage_limiter!, step_limiter! = trivial_limiter!) + SSPRK83(stage_limiter!, + step_limiter!, False()) +end + +@doc explicit_rk_docstring( + "A third-order, four-stage explicit strong stability preserving (SSP) method.", + "SSPRK43", + references = """Optimal third-order explicit SSP method with four stages discovered by + + - J. F. B. M. Kraaijevanger. + "Contractivity of Runge-Kutta methods." + In: BIT Numerical Mathematics 31.3 (1991), pp. 482–528. + [DOI: 10.1007/BF01933264](https://doi.org/10.1007/BF01933264). + + Embedded method constructed by + + - Sidafa Conde, Imre Fekete, John N. Shadid. + "Embedded error estimation and adaptive step-size control for + optimal explicit strong stability preserving Runge–Kutta methods." + [arXiv: 1806.08693](https://arXiv.org/abs/1806.08693) + + Efficient implementation (and optimized controller) developed by + + - Hendrik Ranocha, Lisandro Dalcin, Matteo Parsani, David I. Ketcheson (2021) + Optimized Runge-Kutta Methods with Automatic Step Size Control for + Compressible Computational Fluid Dynamics + [arXiv:2104.06836](https://arxiv.org/abs/2104.06836)""") +Base.@kwdef struct SSPRK43{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function SSPRK43(stage_limiter!, step_limiter! = trivial_limiter!) + SSPRK43(stage_limiter!, + step_limiter!, False()) +end + +@doc explicit_rk_docstring( + "A third-order, four-stage explicit strong stability preserving (SSP) method.", + "SSPRK432", + references = "Gottlieb, Sigal, David I. Ketcheson, and Chi-Wang Shu. + Strong stability preserving Runge-Kutta and multistep time discretizations. + World Scientific, 2011. + Example 6.1") +Base.@kwdef struct SSPRK432{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function SSPRK432(stage_limiter!, step_limiter! = trivial_limiter!) + SSPRK432(stage_limiter!, + step_limiter!, False()) +end + +@doc explicit_rk_docstring( + "A third-order, four-step explicit strong stability preserving (SSP) linear multistep method. +This method does not come with an error estimator and requires a fixed time step +size.", + "SSPRKMSVS43", + references = "Shu, Chi-Wang. + Total-variation-diminishing time discretizations. + SIAM Journal on Scientific and Statistical Computing 9, no. 6 (1988): 1073-1084. + [DOI: 10.1137/0909073](https://doi.org/10.1137/0909073)") +Base.@kwdef struct SSPRKMSVS43{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function SSPRKMSVS43(stage_limiter!, step_limiter! = trivial_limiter!) + SSPRKMSVS43(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "A second-order, three-step explicit strong stability preserving (SSP) linear multistep method. +This method does not come with an error estimator and requires a fixed time step +size.", + "SSPRKMSVS32", + references = "Shu, Chi-Wang. + Total-variation-diminishing time discretizations. + SIAM Journal on Scientific and Statistical Computing 9, no. 6 (1988): 1073-1084. + [DOI: 10.1137/0909073](https://doi.org/10.1137/0909073)") +Base.@kwdef struct SSPRKMSVS32{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function SSPRKMSVS32(stage_limiter!, step_limiter! = trivial_limiter!) + SSPRKMSVS32(stage_limiter!, + step_limiter!, + False()) +end + +@doc explicit_rk_docstring( + "A third-order, nine-stage explicit strong stability preserving (SSP) method. + +Consider using `SSPRK43` instead, which uses the same main method and an +improved embedded method.", + "SSPRK932", + references = "Gottlieb, Sigal, David I. Ketcheson, and Chi-Wang Shu. + Strong stability preserving Runge-Kutta and multistep time discretizations. + World Scientific, 2011.") +Base.@kwdef struct SSPRK932{StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqAdaptiveAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function SSPRK932(stage_limiter!, step_limiter! = trivial_limiter!) + SSPRK932(stage_limiter!, + step_limiter!, False()) +end + +@doc explicit_rk_docstring( + "A fourth-order, five-stage explicit strong stability preserving (SSP) method. +Fixed timestep only.", + "SSPRK54", + references = "Ruuth, Steven. + Global optimization of explicit strong-stability-preserving Runge-Kutta methods. + Mathematics of Computation 75.253 (2006): 183-207.") +Base.@kwdef struct SSPRK54{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function SSPRK54(stage_limiter!, step_limiter! = trivial_limiter!) + SSPRK54(stage_limiter!, + step_limiter!, False()) +end + +@doc explicit_rk_docstring( + "A fourth-order, ten-stage explicit strong stability preserving (SSP) method. +Fixed timestep only.", + "SSPRK104", + references = "Ketcheson, David I. + Highly efficient strong stability-preserving Runge–Kutta methods with + low-storage implementations. + SIAM Journal on Scientific Computing 30.4 (2008): 2113-2136.") +Base.@kwdef struct SSPRK104{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm + stage_limiter!::StageLimiter = trivial_limiter! + step_limiter!::StepLimiter = trivial_limiter! + thread::Thread = False() +end +# for backwards compatibility +function SSPRK104(stage_limiter!, step_limiter! = trivial_limiter!) + SSPRK104(stage_limiter!, + step_limiter!, False()) +end diff --git a/src/caches/extrapolation_caches.jl b/src/caches/extrapolation_caches.jl new file mode 100644 index 0000000000..34bb50d377 --- /dev/null +++ b/src/caches/extrapolation_caches.jl @@ -0,0 +1,1704 @@ +@cache mutable struct AitkenNevilleCache{ + uType, + rateType, + arrayType, + dtType, + uNoUnitsType +} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + tmp::uType + k::rateType + utilde::uType + atmp::uNoUnitsType + fsalfirst::rateType + dtpropose::dtType + T::arrayType + cur_order::Int + work::dtType + A::Int + step_no::Int + u_tmps::Array{uType, 1} + k_tmps::Array{rateType, 1} +end + +@cache mutable struct AitkenNevilleConstantCache{dtType, arrayType} <: + OrdinaryDiffEqConstantCache + dtpropose::dtType + T::arrayType + cur_order::Int + work::dtType + A::Int + step_no::Int +end + +function alg_cache(alg::AitkenNeville, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + utilde = zero(u) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + cur_order = max(alg.init_order, alg.min_order) + dtpropose = zero(dt) + T = Array{typeof(u), 2}(undef, alg.max_order, alg.max_order) + # Array of arrays of length equal to number of threads to store intermediate + # values of u and k. [Thread Safety] + u_tmps = Array{typeof(u), 1}(undef, Threads.nthreads()) + k_tmps = Array{typeof(k), 1}(undef, Threads.nthreads()) + # Initialize each element of u_tmps and k_tmps to different instance of + # zeros array similar to u and k respectively + for i in 1:Threads.nthreads() + u_tmps[i] = zero(u) + k_tmps[i] = zero(rate_prototype) + end + # Initialize lower triangle of T to different instance of zeros array similar to u + for i in 1:(alg.max_order) + for j in 1:i + T[i, j] = zero(u) + end + end + work = zero(dt) + A = one(Int) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + step_no = zero(Int) + AitkenNevilleCache(u, uprev, tmp, k, utilde, atmp, fsalfirst, dtpropose, T, cur_order, + work, A, step_no, u_tmps, k_tmps) +end + +function alg_cache(alg::AitkenNeville, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + dtpropose = zero(dt) + cur_order = max(alg.init_order, alg.min_order) + T = Array{typeof(u), 2}(undef, alg.max_order, alg.max_order) + @.. broadcast=false T=u + work = zero(dt) + A = one(Int) + step_no = zero(Int) + AitkenNevilleConstantCache(dtpropose, T, cur_order, work, A, step_no) +end + +@cache mutable struct ImplicitEulerExtrapolationCache{uType, rateType, QType, arrayType, + dtType, JType, WType, F, JCType, + GCType, uNoUnitsType, TFType, UFType, + sequenceType} <: + OrdinaryDiffEqMutableCache + uprev::uType + u_tmps::Array{uType, 1} + u_tmps2::Array{uType, 1} + utilde::uType + tmp::uType + atmp::uNoUnitsType + k_tmps::Array{rateType, 1} + dtpropose::dtType + T::arrayType + A::Int + step_no::Int + du1::rateType + du2::rateType + J::JType + W::WType + tf::TFType + uf::UFType + linsolve_tmps::Array{rateType, 1} + linsolve::Array{F, 1} + jac_config::JCType + grad_config::GCType + sequence::sequenceType #support for different sequences + stage_number::Vector{Int} # stage_number[n] contains information for extrapolation order (n - 1) + + Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n - 1) + n_curr::Int # Storage for the current extrapolation order + n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter + sigma::Rational{Int} # Parameter for order selection + res::uNoUnitsType # Storage for the scaled residual of u and utilde + + #Stepsizing caches + work::Array{QType, 1} + dt_new::Array{QType, 1} + + # Values to check overflow in T1 computation + diff1::Array{uType, 1} + diff2::Array{uType, 1} +end + +@cache mutable struct ImplicitEulerExtrapolationConstantCache{QType, dtType, arrayType, TF, + UF, sequenceType} <: + OrdinaryDiffEqConstantCache + Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n) + dtpropose::dtType + T::arrayType + n_curr::Int + n_old::Int + A::Int + step_no::Int + sigma::Rational{Int} + + tf::TF + uf::UF + + sequence::sequenceType #support for different sequences + stage_number::Vector{Int} + + #Stepsizing caches + work::Array{QType, 1} + dt_new::Array{QType, 1} +end + +function alg_cache(alg::ImplicitEulerExtrapolation, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + dtpropose = zero(dt) + #cur_order = max(alg.init_order, alg.min_order) + QType = tTypeNoUnits <: Integer ? typeof(qmin_default(alg)) : tTypeNoUnits # Cf. DiffEqBase.__init in solve.jl + Q = fill(zero(QType), alg.max_order + 1) + n_curr = alg.init_order + n_old = alg.init_order + T = Array{typeof(u), 2}(undef, alg.max_order + 1, alg.max_order + 1) + for i in 1:(alg.max_order + 1) + for j in 1:i + T[i, j] = zero(u) + end + end + A = one(Int) + step_no = zero(Int) + tf = TimeDerivativeWrapper(f, u, p) + uf = UDerivativeWrapper(f, t, p) + sequence = generate_sequence(constvalue(uBottomEltypeNoUnits), alg) + stage_number = Vector{Int}(undef, alg.max_order + 1) + + for n in 1:length(stage_number) + s = zero(eltype(sequence)) + for i in 1:n + s += sequence[i] + end + stage_number[n] = 2 * Int(s) - n + 7 + end + sigma = 9 // 10 + work = fill(zero(eltype(Q)), alg.max_order + 1) + dt_new = fill(zero(eltype(Q)), alg.max_order + 1) + ImplicitEulerExtrapolationConstantCache(Q, dtpropose, T, n_curr, n_old, A, step_no, + sigma, tf, uf, sequence, stage_number, work, + dt_new) +end + +function alg_cache(alg::ImplicitEulerExtrapolation, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + u_tmp = zero(u) + u_tmps = Array{typeof(u_tmp), 1}(undef, Threads.nthreads()) + + u_tmps[1] = u_tmp + for i in 2:Threads.nthreads() + u_tmps[i] = zero(u_tmp) + end + + u_tmps2 = Array{typeof(u_tmp), 1}(undef, Threads.nthreads()) + + for i in 1:Threads.nthreads() + u_tmps2[i] = zero(u_tmp) + end + + utilde = zero(u) + tmp = zero(u) + k_tmp = zero(rate_prototype) + k_tmps = Array{typeof(k_tmp), 1}(undef, Threads.nthreads()) + + k_tmps[1] = k_tmp + for i in 2:Threads.nthreads() + k_tmps[i] = zero(rate_prototype) + end + + #cur_order = max(alg.init_order, alg.min_order) + dtpropose = zero(dt) + T = Array{typeof(u), 2}(undef, alg.max_order + 1, alg.max_order + 1) + # Initialize lower triangle of T to different instance of zeros array similar to u + for i in 1:(alg.max_order + 1) + for j in 1:i + T[i, j] = zero(u) + end + end + A = one(Int) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + step_no = zero(Int) + + du1 = zero(rate_prototype) + du2 = zero(rate_prototype) + + if DiffEqBase.has_jac(f) && !DiffEqBase.has_Wfact(f) && f.jac_prototype !== nothing + W_el = WOperator(f, dt, true) + J = nothing # is J = W.J better? + else + J = false .* _vec(rate_prototype) .* _vec(rate_prototype)' # uEltype? + W_el = zero(J) + end + + W = Array{typeof(W_el), 1}(undef, Threads.nthreads()) + W[1] = W_el + for i in 2:Threads.nthreads() + if W_el isa WOperator + W[i] = WOperator(f, dt, true) + else + W[i] = zero(W_el) + end + end + + tf = TimeGradientWrapper(f, uprev, p) + uf = UJacobianWrapper(f, t, p) + linsolve_tmp = zero(rate_prototype) + linsolve_tmps = Array{typeof(linsolve_tmp), 1}(undef, Threads.nthreads()) + + for i in 1:Threads.nthreads() + linsolve_tmps[i] = zero(rate_prototype) + end + + linprob = LinearProblem(W[1], _vec(linsolve_tmps[1]); u0 = _vec(k_tmps[1])) + linsolve1 = init(linprob, alg.linsolve, alias_A = true, alias_b = true) + #Pl = LinearSolve.InvPreconditioner(Diagonal(_vec(weight))), + #Pr = Diagonal(_vec(weight))) + + linsolve = Array{typeof(linsolve1), 1}(undef, Threads.nthreads()) + linsolve[1] = linsolve1 + for i in 2:Threads.nthreads() + linprob = LinearProblem(W[i], _vec(linsolve_tmps[i]); u0 = _vec(k_tmps[i])) + linsolve[i] = init(linprob, alg.linsolve, alias_A = true, alias_b = true) + #Pl = LinearSolve.InvPreconditioner(Diagonal(_vec(weight))), + #Pr = Diagonal(_vec(weight))) + end + + res = uEltypeNoUnits.(zero(u)) + grad_config = build_grad_config(alg, f, tf, du1, t) + jac_config = build_jac_config(alg, f, uf, du1, uprev, u, du1, du2) + sequence = generate_sequence(constvalue(uBottomEltypeNoUnits), alg) + cc = alg_cache(alg, u, rate_prototype, uEltypeNoUnits, uBottomEltypeNoUnits, + tTypeNoUnits, uprev, uprev2, f, t, dt, reltol, p, calck, Val(false)) + diff1 = Array{typeof(u), 1}(undef, Threads.nthreads()) + diff2 = Array{typeof(u), 1}(undef, Threads.nthreads()) + for i in 1:Threads.nthreads() + diff1[i] = zero(u) + diff2[i] = zero(u) + end + ImplicitEulerExtrapolationCache(uprev, u_tmps, u_tmps2, utilde, tmp, atmp, k_tmps, + dtpropose, T, A, step_no, + du1, du2, J, W, tf, uf, linsolve_tmps, linsolve, + jac_config, grad_config, sequence, cc.stage_number, + cc.Q, cc.n_curr, cc.n_old, cc.sigma, res, cc.work, + cc.dt_new, diff1, diff2) +end + +struct extrapolation_coefficients{T1, T2, T3} + # This structure is used by the caches of the algorithms + # ExtrapolationMidpointDeuflhard() and ExtrapolationMidpointHairerWanner(). + # It contains the constant coefficients used to extrapolate the internal discretisations + # in their perfom_step! function and some additional constant data. + + subdividing_sequence::T1 # subdividing_sequence[n] is used for the (n -1)th internal discretisation + + # Weights and Scaling factors for extrapolation operators + extrapolation_weights::T2 + extrapolation_scalars::T3 + + # Weights and scaling factors for internal extrapolation operators (used for error estimate) + extrapolation_weights_2::T2 + extrapolation_scalars_2::T3 +end + +function create_extrapolation_coefficients(T, + alg::Union{ExtrapolationMidpointDeuflhard, + ExtrapolationMidpointHairerWanner, + ImplicitDeuflhardExtrapolation, + ImplicitHairerWannerExtrapolation}) + # Compute and return extrapolation_coefficients + + @unpack min_order, init_order, max_order, sequence = alg + + # Initialize subdividing_sequence: + if sequence == :harmonic + subdividing_sequence = BigInt.(1:(max_order + 1)) + elseif sequence == :romberg + subdividing_sequence = BigInt(2) .^ (0:max_order) + else # sequence == :bulirsch + subdividing_sequence = [n == 0 ? BigInt(1) : + (isodd(n) ? BigInt(2)^((n + 1) ÷ 2) : + 3 * BigInt(2)^(n ÷ 2 - 1)) for n in 0:max_order] + end + + # Compute nodes corresponding to subdividing_sequence + nodes = BigInt(1) .// subdividing_sequence .^ 2 + + # Compute barycentric weights for internal extrapolation operators + extrapolation_weights_2 = zeros(Rational{BigInt}, max_order, max_order) + extrapolation_weights_2[1, :] = ones(Rational{BigInt}, 1, max_order) + for n in 2:max_order + distance = nodes[2:n] .- nodes[n + 1] + extrapolation_weights_2[1:(n - 1), n] = extrapolation_weights_2[1:(n - 1), + n - 1] .// distance + extrapolation_weights_2[n, n] = 1 // prod(-distance) + end + + # Compute barycentric weights for extrapolation operators + extrapolation_weights = zeros(Rational{BigInt}, max_order + 1, max_order + 1) + for n in 1:max_order + extrapolation_weights[n + 1, (n + 1):(max_order + 1)] = extrapolation_weights_2[n, + n:max_order] // + (nodes[n + 1] - nodes[1]) + extrapolation_weights[1, n] = 1 // prod(nodes[1] .- nodes[2:n]) + end + extrapolation_weights[1, max_order + 1] = 1 // + prod(nodes[1] .- nodes[2:(max_order + 1)]) + + # Rescale barycentric weights to obtain weights of 1. Barycentric Formula + for m in 1:(max_order + 1) + extrapolation_weights[1:m, m] = -extrapolation_weights[1:m, m] .// nodes[1:m] + if 2 <= m + extrapolation_weights_2[1:(m - 1), m - 1] = -extrapolation_weights_2[1:(m - 1), + m - 1] .// + nodes[2:m] + end + end + + # Compute scaling factors for internal extrapolation operators + extrapolation_scalars_2 = ones(Rational{BigInt}, max_order) + extrapolation_scalars_2[1] = -nodes[2] + for n in 1:(max_order - 1) + extrapolation_scalars_2[n + 1] = -extrapolation_scalars_2[n] * nodes[n + 2] + end + + # Compute scaling factors for extrapolation operators + extrapolation_scalars = -nodes[1] * [BigInt(1); extrapolation_scalars_2] + + # Initialize and return extrapolation_coefficients + extrapolation_coefficients(Int.(subdividing_sequence), + T.(extrapolation_weights), T.(extrapolation_scalars), + T.(extrapolation_weights_2), T.(extrapolation_scalars_2)) +end + +function create_extrapolation_coefficients(T, alg::ImplicitEulerBarycentricExtrapolation) + # Compute and return extrapolation_coefficients + + @unpack min_order, init_order, max_order, sequence = alg + + # Initialize subdividing_sequence: + if sequence == :harmonic + subdividing_sequence = BigInt.(1:(max_order + 1)) + elseif sequence == :romberg + subdividing_sequence = BigInt(2) .^ (0:max_order) + else # sequence == :bulirsch + subdividing_sequence = [n == 0 ? BigInt(1) : + (isodd(n) ? BigInt(2)^((n + 1) ÷ 2) : + 3 * BigInt(2)^(n ÷ 2 - 1)) for n in 0:max_order] + end + + # Compute nodes corresponding to subdividing_sequence + nodes = BigInt(1) .// subdividing_sequence + + # Compute barycentric weights for internal extrapolation operators + extrapolation_weights_2 = zeros(Rational{BigInt}, max_order, max_order) + extrapolation_weights_2[1, :] = ones(Rational{BigInt}, 1, max_order) + for n in 2:max_order + distance = nodes[2:n] .- nodes[n + 1] + extrapolation_weights_2[1:(n - 1), n] = extrapolation_weights_2[1:(n - 1), + n - 1] .// distance + extrapolation_weights_2[n, n] = 1 // prod(-distance) + end + + # Compute barycentric weights for extrapolation operators + extrapolation_weights = zeros(Rational{BigInt}, max_order + 1, max_order + 1) + for n in 1:max_order + extrapolation_weights[n + 1, (n + 1):(max_order + 1)] = extrapolation_weights_2[n, + n:max_order] // + (nodes[n + 1] - nodes[1]) + extrapolation_weights[1, n] = 1 // prod(nodes[1] .- nodes[2:n]) + end + extrapolation_weights[1, max_order + 1] = 1 // + prod(nodes[1] .- nodes[2:(max_order + 1)]) + + # Rescale barycentric weights to obtain weights of 1. Barycentric Formula + for m in 1:(max_order + 1) + extrapolation_weights[1:m, m] = -extrapolation_weights[1:m, m] .// nodes[1:m] + if 2 <= m + extrapolation_weights_2[1:(m - 1), m - 1] = -extrapolation_weights_2[1:(m - 1), + m - 1] .// + nodes[2:m] + end + end + + # Compute scaling factors for internal extrapolation operators + extrapolation_scalars_2 = ones(Rational{BigInt}, max_order) + extrapolation_scalars_2[1] = -nodes[2] + for n in 1:(max_order - 1) + extrapolation_scalars_2[n + 1] = -extrapolation_scalars_2[n] * nodes[n + 2] + end + + # Compute scaling factors for extrapolation operators + extrapolation_scalars = -nodes[1] * [BigInt(1); extrapolation_scalars_2] + + # Initialize and return extrapolation_coefficients + extrapolation_coefficients(Int.(subdividing_sequence), + T.(extrapolation_weights), T.(extrapolation_scalars), + T.(extrapolation_weights_2), T.(extrapolation_scalars_2)) +end + +function create_extrapolation_coefficients(T::Type{<:CompiledFloats}, + alg::ImplicitEulerBarycentricExtrapolation) + # Compute and return extrapolation_coefficients + + @unpack min_order, init_order, max_order, sequence = alg + + max_order > 15 && + error("max_order > 15 not allowed for Float32 or Float64 with this algorithm. That's a bad idea.") + + # Initialize subdividing_sequence: + if sequence == :harmonic + subdividing_sequence = [ + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 21 + ] + extrapolation_weights = T[-1.0 -2.0 -3.0 -4.0 -5.0 -6.0 -7.0 -8.0 -9.0 -10.0 -11.0 -12.0 -13.0 -14.0 -15.0 -16.0; + 0.0 4.0 24.0 96.0 320.0 960.0 2688.0 7168.0 18432.0 46080.0 112640.0 270336.0 638976.0 1.490944e6 3.44064e6 7.86432e6; + 0.0 0.0 -27.0 -324.0 -2430.0 -14580.0 -76545.0 -367416.0 -1.653372e6 -7.08588e6 -2.9229255e7 -1.1691702e8 -4.55976378e8 -1.741000716e9 -6.528752685e9 -2.410616376e10; + 0.0 0.0 0.0 256.0 5120.0 61440.0 573440.0 4.58752e6 3.3030144e7 2.2020096e8 1.38412032e9 8.30472192e9 4.798283776e10 2.68703891456e11 1.46565758976e12 7.81684047872e12; + 0.0 0.0 0.0 0.0 -3125.0 -93750.0 -1.640625e6 -2.1875e7 -2.4609375e8 -2.4609375e9 -2.255859375e10 -1.93359375e11 -1.571044921875e12 -1.221923828125e13 -9.1644287109375e13 -6.6650390625e14; + 0.0 0.0 0.0 0.0 0.0 46656.0 1.959552e6 4.7029248e7 8.46526464e8 1.269789696e10 1.67612239872e11 2.011346878464e12 2.2412150931456e13 2.35327584780288e14 2.35327584780288e15 2.259144813890765e16; + 0.0 0.0 0.0 0.0 0.0 0.0 -823543.0 -4.6118408e7 -1.452729852e9 -3.389702988e10 -6.5251782519e11 -1.0962299463192e13 -1.66261541858412e14 -2.327661586017768e15 -3.0550558316483204e16 -3.8018472571623546e17; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.6777216e7 1.207959552e9 4.831838208e10 1.41733920768e12 3.401614098432e13 7.07535732473856e14 1.3207333672845312e16 2.2641143439163392e17 3.6225829502661427e18; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -3.87420489e8 -3.486784401e10 -1.725958278495e12 -6.213449802582e13 -1.817434067255235e15 -4.579933849483192e16 -1.0304851161337183e18 -2.119855096046506e19; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0e10 1.1e12 6.6e13 2.86e15 1.001e17 3.003e18 8.008e19; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.85311670611e11 -3.7661140520652e13 -2.692771547226618e15 -1.3822893942429973e17 -5.701943751252363e18 -2.007084200440832e20; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 8.916100448256e12 1.390911669927936e15 1.1683658027394662e17 7.010194816436797e18 3.364893511889663e20; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -3.02875106592253e14 -5.512326939979005e16 -5.37451876647953e18 -3.726333011425807e20; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.1112006825558016e16 2.3335214333671834e18 2.6135440053712454e20; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -4.378938903808594e17 -1.0509453369140625e20; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.8446744073709552e19] + extrapolation_weights_2 = T[-2.0 -12.0 -48.0 -160.0 -480.0 -1344.0 -3584.0 -9216.0 -23040.0 -56320.0 -135168.0 -319488.0 -745472.0 -1.72032e6 -3.93216e6; + 0.0 18.0 216.0 1620.0 9720.0 51030.0 244944.0 1.102248e6 4.72392e6 1.948617e7 7.794468e7 3.03984252e8 1.160667144e9 4.35250179e9 1.607077584e10; + 0.0 0.0 -192.0 -3840.0 -46080.0 -430080.0 -3.44064e6 -2.4772608e7 -1.6515072e8 -1.03809024e9 -6.22854144e9 -3.598712832e10 -2.01527918592e11 -1.09924319232e12 -5.86263035904e12; + 0.0 0.0 0.0 2500.0 75000.0 1.3125e6 1.75e7 1.96875e8 1.96875e9 1.8046875e10 1.546875e11 1.2568359375e12 9.775390625e12 7.33154296875e13 5.33203125e14; + 0.0 0.0 0.0 0.0 -38880.0 -1.63296e6 -3.919104e7 -7.0543872e8 -1.05815808e10 -1.3967686656e11 -1.67612239872e12 -1.867679244288e13 -1.9610632065024e14 -1.9610632065024e15 -1.882620678242304e16; + 0.0 0.0 0.0 0.0 0.0 705894.0 3.9530064e7 1.245197016e9 2.905459704e10 5.5930099302e11 9.396256682736e12 1.42509893021496e14 1.995138502300944e15 2.618619284269989e16 3.2587262204248755e17; + 0.0 0.0 0.0 0.0 0.0 0.0 -1.4680064e7 -1.056964608e9 -4.227858432e10 -1.24017180672e12 -2.976412336128e13 -6.19093765914624e14 -1.1556416963739648e16 -1.9811000509267968e17 -3.169760081482875e18; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.44373768e8 3.099363912e10 1.53418513644e12 5.523066491184e13 1.61549694867132e15 4.071052310651726e16 9.159867698966385e17 1.884315640930228e19; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -9.0e9 -9.9e11 -5.94e13 -2.574e15 -9.009e16 -2.7027e18 -7.2072e19; 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+ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0231987972010274e22] + extrapolation_scalars = T[-1.0, 0.5, -0.16666666666666666, 0.041666666666666664, + -0.006944444444444444, 0.0008680555555555555, + -7.233796296296296e-5, 4.521122685185185e-6, + -1.8838011188271604e-7, 5.886878496334876e-9, + -1.226433020069766e-10, 1.9163015938590095e-12, + -1.9961474936031345e-14, 1.5594902293774489e-16, + -8.122344944674213e-19, 3.1727909940133645e-21] + extrapolation_scalars_2 = T[-0.5, 0.16666666666666666, -0.041666666666666664, + 0.006944444444444444, -0.0008680555555555555, + 7.233796296296296e-5, -4.521122685185185e-6, + 1.8838011188271604e-7, -5.886878496334876e-9, + 1.226433020069766e-10, -1.9163015938590095e-12, + 1.9961474936031345e-14, -1.5594902293774489e-16, + 8.122344944674213e-19, -3.1727909940133645e-21] + end + extrapolation_coefficients(subdividing_sequence, + extrapolation_weights, extrapolation_scalars, + extrapolation_weights_2, extrapolation_scalars_2) +end + +function create_extrapolation_coefficients(T::Type{<:CompiledFloats}, + alg::Union{ExtrapolationMidpointDeuflhard, + ExtrapolationMidpointHairerWanner, + ImplicitDeuflhardExtrapolation, + ImplicitHairerWannerExtrapolation}) + # Compute and return extrapolation_coefficients + + @unpack min_order, init_order, max_order, sequence = alg + + max_order > 15 && + error("max_order > 15 not allowed for Float32 or Float64 with this algorithm. That's a bad idea.") + + # Initialize subdividing_sequence: + if sequence == :harmonic + subdividing_sequence = [ + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 21 + ] + extrapolation_weights = T[-1.0 -1.3333333333333333 -1.5 -1.6 -1.6666666666666667 -1.7142857142857142 -1.75 -1.7777777777777777 -1.8 -1.8181818181818181 -1.8333333333333333 -1.8461538461538463 -1.8571428571428572 -1.8666666666666667 -1.875 -1.8823529411764706; + 0.0 5.333333333333333 38.4 204.8 975.2380952380952 4388.571428571428 19114.666666666668 81555.91111111111 343170.32727272727 1.4298763636363635e6 5.915044102564103e6 2.433618145054945e7 9.970459794285715e7 4.0712710826666665e8 1.6579836988235295e9 6.737203601568627e9; + 0.0 0.0 -72.9 -1499.6571428571428 -21088.928571428572 -253067.14285714287 -2.79006525e6 -2.9219592436363637e7 -2.9584837341818184e8 -2.925972923916084e9 -2.8449861733434067e10 -2.7311867264096704e11 -2.596334381793193e12 -2.449162486354648e13 -2.2960898309574828e14 -2.141777720860745e15; + 0.0 0.0 0.0 1872.4571428571428 83220.31746031746 2.3967451428571427e6 5.6940854303030305e7 1.214738225131313e9 2.422001138107972e10 4.613335501158042e11 8.50611193356378e12 1.5311001480414803e14 2.7059443139242895e15 4.7143563158147624e16 8.120422362168969e17 1.3858854164768373e19; + 0.0 0.0 0.0 0.0 -77504.96031746031 -6.341314935064935e6 -3.236712831439394e8 -1.3278821872571873e10 -4.80171683784965e11 -1.6005722792832168e13 -5.043469942533053e14 -1.525755612867142e16 -4.4766093502525523e17 -1.2827711003647664e19 -3.607793719775906e20 -9.995618963881296e21; + 0.0 0.0 0.0 0.0 0.0 4.711650077922078e6 6.393346721118882e8 5.260811016234965e10 3.4090055385202573e12 1.9175656154176447e14 9.826959789128542e15 4.7169406987817e17 2.15773437679608e19 9.515608601670712e20 4.078117972144591e22 1.708360692331116e24; + 0.0 0.0 0.0 0.0 0.0 0.0 -3.952348909376457e8 -8.263044119869713e10 -1.0248756909925902e13 -9.846844874242534e14 -8.108603230469998e16 -6.022558357283822e18 -4.1560671463889437e20 -2.715297202307443e22 -1.7009177076954297e24 -1.0307396968759164e26; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.3741255122091064e10 1.3338509797230594e13 2.371290630618772e15 3.221627130440662e17 3.711314454267642e19 3.8230073464151254e21 3.6330154661690406e23 3.249405137443117e25 2.772825717284793e27; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -6.174193142616171e12 -2.6321560239574205e15 -6.449440297701669e17 -1.1940678036887662e20 -1.8574538823517637e22 -2.5642554640188345e24 -3.245385821648838e26 -3.845504022726303e28; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.082508822446903e15 6.237312738860727e17 2.041302350899874e20 4.99971155510259e22 1.0207744425001122e25 1.837393996500202e27 3.015210660923408e29; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.30788366240374e17 -1.748372388422729e20 -7.448430618928414e22 -2.355293074113417e25 -6.165659032955555e27 -1.4147218829987503e30; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 5.87960511179021e19 5.723442800021062e22 3.1065086459191243e25 1.2426034583676497e28 4.089940525827236e30; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.7640007344435631e22 -2.1641022343595773e25 -1.4694640618129094e28 -7.307458985088932e30; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6.155890364150897e24 9.361198795139813e27 7.828458512415587e30; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.472332709198601e27 -4.593753679027078e30; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.1322357960170301e30] + extrapolation_weights_2 = T[-4.0 -28.8 -153.6 -731.4285714285714 -3291.4285714285716 -14336.0 -61166.933333333334 -257377.74545454545 -1.0724072727272727e6 -4.436283076923077e6 -1.8252136087912086e7 -7.477844845714286e7 -3.053453312e8 -1.2434877741176472e9 -5.052902701176471e9; + 0.0 64.8 1333.0285714285715 18745.714285714286 224948.57142857142 2.480058e6 2.5972971054545455e7 2.6297633192727274e8 2.6008648212587414e9 2.5288765985274727e10 2.4277215345863736e11 2.3078527838161714e12 2.1770333212041316e13 2.0409687386288734e14 1.9038024185428845e15; + 0.0 0.0 -1755.4285714285713 -78019.04761904762 -2.2469485714285714e6 -5.338205090909091e7 -1.138817086060606e9 -2.2706260669762238e10 -4.325002032335664e11 -7.974479937716044e12 -1.4354063887888878e14 -2.5368227943040215e15 -4.41970904607634e16 -7.612895964533408e17 -1.299267577947035e19; + 0.0 0.0 0.0 74404.76190476191 6.087662337662337e6 3.107244318181818e8 1.2747668997668997e10 4.609648164335664e11 1.536549388111888e13 4.8417311448317306e14 1.4647253883524564e16 4.29754497624245e17 1.2314602563501758e19 3.4634819709848696e20 9.595794205326044e21; + 0.0 0.0 0.0 0.0 -4.580770909090909e6 -6.215753756643356e8 -5.114677376895105e10 -3.314310940228028e12 -1.8642999038782656e14 -9.553988683874972e15 -4.585914568259986e17 -2.0977973107739664e19 -9.251286140513193e20 -3.964836917362797e22 -1.6609062286552515e24; + 0.0 0.0 0.0 0.0 0.0 3.8716887275524473e8 8.094410566402983e10 1.0039598605641701e13 9.64588885640085e14 7.943121531888978e16 5.899649003053539e18 4.071249449523863e20 2.659882973688924e22 1.6662051014159312e24 1.0097041928580407e26; + 0.0 0.0 0.0 0.0 0.0 0.0 -4.3057798010808395e10 -1.3130095581648865e13 -2.3342392145153535e15 -3.1712892065275264e17 -3.65332516591971e19 -3.763272856627389e21 -3.5762495995101494e23 -3.198633182170568e25 -2.729500315452218e27; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6.097968535917206e12 2.59966027057523e15 6.369817577976957e17 1.1793262258654482e20 1.8345223529400134e22 2.532597989154405e24 3.205319330023544e26 3.7980286644210397e28; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0716837342224339e15 -6.174939611472119e17 -2.0208893273908753e20 -4.949714439551565e22 -1.010566698075111e25 -1.8190200565352e27 -2.9850585543141743e29; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.2888102437061885e17 1.733923029840723e20 7.38687334108603e22 2.3358278420959505e25 6.114703173179063e27 1.4030299666103307e30; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -5.838774520736112e19 -5.6836966694653606e22 -3.0849356692113527e25 -1.233974267684541e28 -4.061538161064547e30; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.753562860275258e22 2.1512968956947278e25 1.4607690081927147e28 7.2642195828103e30; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -6.124482760252167e24 -9.313437576797262e27 -7.788517397556324e30; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.461344563824385e27 4.57333699600918e30; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.1278129999388386e30] + extrapolation_scalars = T[-1.0, 0.25, -0.027777777777777776, 0.001736111111111111, + -6.944444444444444e-5, 1.9290123456790124e-6, + -3.936759889140842e-8, 6.151187326782565e-10, + -7.594058428126624e-12, 7.594058428126623e-14, + -6.276081345559193e-16, 4.358389823304995e-18, + -2.5789288895295828e-20, 1.3157800456783586e-22, + -5.8479113141260385e-25, 2.2843403570804838e-27] + extrapolation_scalars_2 = T[-0.25, 0.027777777777777776, -0.001736111111111111, + 6.944444444444444e-5, -1.9290123456790124e-6, + 3.936759889140842e-8, -6.151187326782565e-10, + 7.594058428126624e-12, -7.594058428126623e-14, + 6.276081345559193e-16, -4.358389823304995e-18, + 2.5789288895295828e-20, -1.3157800456783586e-22, + 5.8479113141260385e-25, -2.2843403570804838e-27] + elseif sequence == :romberg + subdividing_sequence = [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256, + 512, + 1024, + 2048, + 4096, + 8192, + 16384, + 32768 + ] + extrapolation_weights = T[-1.0 -1.3333333333333333 -1.4222222222222223 -1.4447971781305116 -1.4504630494172979 -1.451880901860521 -1.452235451531305 -1.4523240943593299 -1.4523462554044868 -1.4523517956869105 -1.4523531807588372 -1.4523535270269017 -1.4523536135939228 -1.4523536352356785 -1.4523536406461173 -1.452353641998727; + 0.0 5.333333333333333 28.444444444444443 121.36296296296297 493.15743680188126 1980.3655501377505 7929.205565360925 31724.5675171852 126906.01579724405 507631.8090356717 2.0305349820189304e6 8.122147673959353e6 3.248859844172289e7 1.2995440151277749e8 5.19817613796996e8 2.07927046293387e9; + 0.0 0.0 -91.02222222222223 -1941.8074074074075 -33140.17975308642 -538659.4296374682 -8.652349112921841e6 -1.3857291091506496e8 -2.2177080072599993e9 -3.54854939788296e10 -5.677765672441477e11 -9.084459730370057e12 -1.4535149430390788e14 -2.325624463334606e15 -3.720999363124215e16 -5.953599069714284e17; + 0.0 0.0 0.0 5917.889241622575 504993.2152851264 3.4474203496797964e7 2.241370436871182e9 1.4401024799097037e11 9.225665310201598e12 5.905867660750885e14 3.77998601491761e16 2.4192279640364677e18 1.5483118033241417e20 9.909204991428803e21 6.341892706539483e23 4.05881157410929e25; + 0.0 0.0 0.0 0.0 -1.5209207425057925e6 -5.1914094677531046e8 -1.4176008786611145e11 -3.6866623485688414e13 -9.474866810815984e15 -2.4279369357326935e18 -6.217036386624773e20 -1.591658462098873e23 -4.074707838080507e25 -1.0431291857706623e28 -2.670413262277438e30 -6.836259581321538e32; + 0.0 0.0 0.0 0.0 0.0 1.5589452477944808e9 2.1284799116553977e12 2.3248676581708025e15 2.4184528070774876e18 2.486207422190278e21 2.5483650380553205e24 2.6101630458060033e27 2.6729701040532997e30 2.7371631523457504e33 2.8028657600863993e36 2.870137275504677e39; + 0.0 0.0 0.0 0.0 0.0 0.0 -6.386999060908798e12 -3.4881530871309916e16 -1.5239973381214444e20 -6.341377114357268e23 -2.607614058456583e27 -1.069122783562139e31 -4.380196305334128e34 -1.7942379182565492e38 -7.349310654759861e41 -3.010289127531343e45; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0465098000284594e17 2.2861355418221703e21 3.995311436502874e25 6.649821721972122e29 1.0937793665786103e34 1.7937998718897874e38 2.93967940527153e42 4.816664723480877e46 7.891743901406595e50; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -6.858511278043386e21 -5.993058601571351e26 -4.189451610800854e31 -2.7891799442838834e36 -1.835085270122301e41 -1.2038170852496654e46 -7.891262227584487e50 -5.171933283225826e55; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.7979244390088466e27 6.284201388527134e32 1.7571900680469942e38 4.679485289631606e43 1.2315095760466199e49 3.231484209329825e54 8.473210620642257e59; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.8852622144842938e33 -2.635787615753444e39 -2.948078543974702e45 -3.140352413792322e51 -3.305811498811932e57 -3.46978305819599e63; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7.907364732522996e39 4.422118870277351e46 1.9784224923818425e53 8.429821331796452e59 3.549588914822444e66; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.3266357401568573e47 -2.9676339154575293e54 -5.310787755579382e61 -9.051452272305827e68; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 8.902901879036164e54 7.966181752074431e62 5.702415016525277e70; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.389854534525231e63 -8.553622556652643e71; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.5660867693856473e72] + extrapolation_weights_2 = T[-4.0 -21.333333333333332 -91.02222222222223 -369.86807760141096 -1485.274162603313 -5946.904174020694 -23793.4256378889 -95179.51184793304 -380723.8567767538 -1.522901236514198e6 -6.091610755469514e6 -2.4366448831292167e7 -9.746580113458312e7 -3.89863210347747e8 -1.5594528472004025e9; 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+ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.0269737017532947e20 -1.0674622648776207e24 -3.279244077704051e27 -8.791712994944155e30 -2.1606513856374756e34 -5.159530537984771e37; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.1022516982215851e24 8.126681320648103e27 4.438251558583284e31 2.0451463181951773e35 8.935380607282608e38; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -7.659880204931148e27 -1.6135647078547534e32 -1.9827483130119208e36 -2.126313710861715e40; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.665360734159382e32 4.911348648324117e36 1.0729004833885644e41; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -4.62766803500927e36 -3.8992995301161535e41; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.023990816545532e41] + extrapolation_weights_2 = T[-4.0 -28.8 -153.6 -691.2 -2949.12 -12133.522285714285 -49304.47151020408 -198597.0320970458 -797503.3759504899 -3.1955613533737888e6 -1.279474027704696e7 -5.120118384423134e7 -2.0485474874331778e8 -8.195079172733225e8 -3.27823175648077e9; + 0.0 64.8 1333.0285714285715 15996.342857142858 167525.33610389612 1.6082432265974027e6 1.5001588640001683e7 1.3715738185144395e8 1.2453620011260173e9 1.1252211963115074e10 1.0149291456038025e11 9.143291305850092e11 8.233484963636221e12 7.411946024407464e13 6.671667636089105e14; + 0.0 0.0 -1755.4285714285713 -50556.34285714286 -1.0785353142857142e6 -1.941363565714286e7 -3.313260485485714e8 -5.45268011325649e9 -8.862768945991501e10 -1.427959416193316e12 -2.2936948112658125e13 -3.6762941531523006e14 -5.887820469721143e15 -9.424603291176736e16 -1.508304765056309e18; + 0.0 0.0 0.0 55987.2 4.606946742857143e6 2.2113344365714285e8 9.263480985201038e9 3.557176698317199e11 1.327244552700053e13 4.853922935588765e14 1.7629065526851648e16 6.37135168217509e17 2.29873754256621e19 8.283544552215128e20 2.9837150424218233e22; + 0.0 0.0 0.0 0.0 -5.020091644675325e6 -5.783145574665974e8 -4.9349508903816315e10 -3.5531646410747744e12 -2.4256270616403794e14 -1.5967556428626954e16 -1.0381446211373969e18 -6.690587991889685e19 -4.2987683787890434e21 -2.755996478533553e23 -1.765561927831622e25; + 0.0 0.0 0.0 0.0 0.0 5.661016157622857e8 1.863283032451866e11 3.577503422307583e13 5.994594825452124e15 9.207697651894463e17 1.3742209159491396e20 2.0102888827598844e22 2.920484310307798e24 4.221989553536732e26 6.093053013029727e28; + 0.0 0.0 0.0 0.0 0.0 0.0 -1.9484826341819125e11 -8.978607978310253e13 -3.0646981899298996e16 -8.826330786998111e18 -2.410176726902951e21 -6.346339632896457e23 -1.6504512467519928e26 -4.254701731487095e28 -1.0934750300970127e31; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 8.539308868165419e13 1.1242610075573214e17 8.63432453804023e19 5.787195268551182e22 3.555652772997846e25 2.1226815194136454e28 1.2420719290740417e31 7.217771758563227e33; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.1639991919747662e17 -2.145483310647889e20 -2.929299880137918e23 -3.3745534619188814e26 -3.685912261338597e29 -3.882213417199601e32 -4.0384879128506835e35; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.0260939388619086e20 1.0669989566029343e24 3.277820794684214e27 8.787897147290099e30 2.1597136029180146e34 5.157291158410993e37; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.1019825938030739e24 -8.124697267591304e27 -4.437168001073864e31 -2.0446470148948364e35 -8.933199117876534e38; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7.6590490547353e27 1.6133896248786405e32 1.9825331710508737e36 2.126082991058019e40; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.66525908860676e32 -4.911048883391968e36 -1.07283499873992e41; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.627542501479674e36 3.8991937548467816e41; + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -4.023929415318473e41] + extrapolation_scalars = T[-1.0, 0.25, -0.027777777777777776, 0.001736111111111111, + -4.8225308641975306e-5, 7.535204475308642e-7, + -5.232780885631001e-9, 2.0440550334496098e-11, + -3.548706655294462e-14, 3.465533843060998e-17, + -1.5041379527174468e-20, 3.672211798626579e-24, + -3.9846048162180767e-28, 2.4320097755237285e-32, + -6.597248740027475e-37, 1.0066602691692314e-41] + extrapolation_scalars_2 = T[-0.25, 0.027777777777777776, -0.001736111111111111, + 4.8225308641975306e-5, -7.535204475308642e-7, + 5.232780885631001e-9, -2.0440550334496098e-11, + 3.548706655294462e-14, -3.465533843060998e-17, + 1.5041379527174468e-20, -3.672211798626579e-24, + 3.9846048162180767e-28, -2.4320097755237285e-32, + 6.597248740027475e-37, -1.0066602691692314e-41] + end + extrapolation_coefficients(subdividing_sequence, + extrapolation_weights, extrapolation_scalars, + extrapolation_weights_2, extrapolation_scalars_2) +end + +function generate_sequence(T, alg::ImplicitEulerExtrapolation) + # Compute and return extrapolation_coefficients + + @unpack min_order, init_order, max_order, sequence = alg + + # Initialize subdividing_sequence: + if sequence == :harmonic + subdividing_sequence = BigInt.(1:(max_order + 1)) + elseif sequence == :romberg + subdividing_sequence = BigInt(2) .^ (0:max_order) + else # sequence == :bulirsch + subdividing_sequence = [n == 0 ? BigInt(1) : + (isodd(n) ? BigInt(2)^((n + 1) ÷ 2) : + 3 * BigInt(2)^(n ÷ 2 - 1)) for n in 0:max_order] + end + + subdividing_sequence +end + +function generate_sequence(T::Type{<:CompiledFloats}, alg::ImplicitEulerExtrapolation) + # Compute and return extrapolation_coefficients + + @unpack min_order, init_order, max_order, sequence = alg + + # Initialize subdividing_sequence: + if sequence == :harmonic + subdividing_sequence = Int.(1:(max_order + 1)) + elseif sequence == :romberg + subdividing_sequence = Int(2) .^ (0:max_order) + else # sequence == :bulirsch + subdividing_sequence = [n == 0 ? Int(1) : + (isodd(n) ? Int(2)^((n + 1) ÷ 2) : 3 * Int(2)^(n ÷ 2 - 1)) + for n in 0:max_order] + end + + subdividing_sequence +end + +@cache mutable struct ExtrapolationMidpointDeuflhardConstantCache{QType, + extrapolation_coefficients +} <: + OrdinaryDiffEqConstantCache + # Values that are mutated + Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n + alg.min_order - 1) + n_curr::Int # Storage for the current extrapolation order + n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter + + # Constant values + coefficients::extrapolation_coefficients + stage_number::Vector{Int} # stage_number[n] contains information for extrapolation order (n + alg.min_order - 1) +end + +function alg_cache(alg::ExtrapolationMidpointDeuflhard, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + # Initialize cache's members + QType = tTypeNoUnits <: Integer ? typeof(qmin_default(alg)) : tTypeNoUnits # Cf. DiffEqBase.__init in solve.jl + + Q = fill(zero(QType), alg.max_order - alg.min_order + 1) + n_curr = alg.init_order + n_old = alg.init_order + sequence_factor = alg.sequence_factor + + coefficients = create_extrapolation_coefficients(constvalue(uBottomEltypeNoUnits), alg) + stage_number = Vector{Int}(undef, alg.max_order - alg.min_order + 1) + for n in 1:length(stage_number) + s = zero(eltype(coefficients.subdividing_sequence)) + for i in 1:(alg.min_order + n) + s += coefficients.subdividing_sequence[i] + end + stage_number[n] = sequence_factor * Int(s) - alg.min_order - n + 3 - sequence_factor + end + + # Initialize cache + ExtrapolationMidpointDeuflhardConstantCache(Q, n_curr, n_old, coefficients, + stage_number) +end + +@cache mutable struct ExtrapolationMidpointDeuflhardCache{uType, uNoUnitsType, rateType, + QType, extrapolation_coefficients +} <: OrdinaryDiffEqMutableCache + # Values that are mutated + utilde::uType + u_temp1::uType + u_temp2::uType + u_temp3::Array{uType, 1} + u_temp4::Array{uType, 1} + tmp::uType # for get_tmp_cache() + T::Array{uType, 1} # Storage for the internal discretisations obtained by the explicit midpoint rule + res::uNoUnitsType # Storage for the scaled residual of u and utilde + + fsalfirst::rateType + k::rateType + k_tmps::Array{rateType, 1} + + # Constant values + Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n + alg.min_order - 1) + n_curr::Int # Storage for the current extrapolation order + n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter + coefficients::extrapolation_coefficients + stage_number::Vector{Int} # Stage_number[n] contains information for extrapolation order (n + alg.min_order - 1) +end + +function alg_cache(alg::ExtrapolationMidpointDeuflhard, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + # Initialize cache's members + utilde = zero(u) + u_temp1 = zero(u) + u_temp2 = zero(u) + u_temp3 = Array{typeof(u), 1}(undef, Threads.nthreads()) + u_temp4 = Array{typeof(u), 1}(undef, Threads.nthreads()) + + for i in 1:Threads.nthreads() + u_temp3[i] = zero(u) + u_temp4[i] = zero(u) + end + + tmp = zero(u) + T = Vector{typeof(u)}(undef, alg.max_order + 1) + for i in 1:(alg.max_order + 1) + T[i] = zero(u) + end + res = uEltypeNoUnits.(zero(u)) + + fsalfirst = zero(rate_prototype) + k = zero(rate_prototype) + k_tmps = Array{typeof(k), 1}(undef, Threads.nthreads()) + for i in 1:Threads.nthreads() + k_tmps[i] = zero(rate_prototype) + end + + cc = alg_cache(alg::ExtrapolationMidpointDeuflhard, u, rate_prototype, uEltypeNoUnits, + uBottomEltypeNoUnits, tTypeNoUnits, uprev, uprev2, f, t, dt, reltol, p, + calck, Val(false)) + # Initialize cache + ExtrapolationMidpointDeuflhardCache(utilde, u_temp1, u_temp2, u_temp3, u_temp4, tmp, T, + res, fsalfirst, k, k_tmps, cc.Q, cc.n_curr, + cc.n_old, cc.coefficients, cc.stage_number) +end + +@cache mutable struct ImplicitDeuflhardExtrapolationConstantCache{QType, + extrapolation_coefficients, + TF, UF} <: + OrdinaryDiffEqConstantCache + # Values that are mutated + Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n + alg.min_order - 1) + n_curr::Int # Storage for the current extrapolation order + n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter + + # Constant values + coefficients::extrapolation_coefficients + stage_number::Vector{Int} # stage_number[n] contains information for extrapolation order (n + alg.min_order - 1) + + tf::TF + uf::UF +end + +@cache mutable struct ImplicitDeuflhardExtrapolationCache{uType, QType, + extrapolation_coefficients, + rateType, JType, WType, F, JCType, + GCType, uNoUnitsType, TFType, + UFType} <: + OrdinaryDiffEqMutableCache + # Values that are mutated + utilde::uType + u_temp1::uType + u_temp2::uType + u_temp3::Array{uType, 1} + u_temp4::Array{uType, 1} + tmp::uType # for get_tmp_cache() + T::Array{uType, 1} # Storage for the internal discretisations obtained by the explicit midpoint rule + res::uNoUnitsType # Storage for the scaled residual of u and utilde + + fsalfirst::rateType + k::rateType + k_tmps::Array{rateType, 1} + + # Constant values + Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n + alg.min_order - 1) + n_curr::Int # Storage for the current extrapolation order + n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter + coefficients::extrapolation_coefficients + stage_number::Vector{Int} # Stage_number[n] contains information for extrapolation order (n + alg.min_order - 1) + + du1::rateType + du2::rateType + J::JType + W::WType + tf::TFType + uf::UFType + linsolve_tmps::Array{rateType, 1} + linsolve::Array{F, 1} + jac_config::JCType + grad_config::GCType + # Values to check overflow in T1 computation + diff1::Array{uType, 1} + diff2::Array{uType, 1} +end + +function alg_cache(alg::ImplicitDeuflhardExtrapolation, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + # Initialize cache's members + QType = tTypeNoUnits <: Integer ? typeof(qmin_default(alg)) : tTypeNoUnits # Cf. DiffEqBase.__init in solve.jl + + Q = fill(zero(QType), alg.max_order - alg.min_order + 1) + n_curr = alg.init_order + n_old = alg.init_order + + coefficients = create_extrapolation_coefficients(constvalue(uBottomEltypeNoUnits), alg) + stage_number = Vector{Int}(undef, alg.max_order - alg.min_order + 1) + + #== + Work calculation in Deuflhard is referenced from here: https://link.springer.com/article/10.1007/BF01418332 + A[1] := CJAC + CLR + (N[1] + 1)(CF + CS) + A[J] := A[J-1] - N[J]*(CF + CS) + CLR + CS J = 2, 3, 4..... + CF = 1; CJ = n*CF ; CS = CLR = 0 + n = Dimension of the jacobian (particularly gaussian decomposition of I - hJ (n,n) matrix) + Since we are using 4*N sequence and doing 4*N - 1 Computations + A[J] := A[J-1] - (4*N[J] - 1)*(CF + CS) + CLR + CS J = 2, 3, 4..... + ===# + for n in 1:length(stage_number) + s = zero(eltype(coefficients.subdividing_sequence)) + for i in 1:(alg.min_order + n) + s += coefficients.subdividing_sequence[i] + end + stage_number[n] = 4 * Int(s) - alg.min_order - n - 1 + end + + #Update stage_number by the jacobian size + jac_dim = rate_prototype isa Union{CompiledFloats, BigFloat} ? 1 : + sum(size(rate_prototype)) + stage_number = stage_number .+ jac_dim + + tf = TimeDerivativeWrapper(f, u, p) + uf = UDerivativeWrapper(f, t, p) + ImplicitDeuflhardExtrapolationConstantCache(Q, n_curr, n_old, coefficients, + stage_number, tf, uf) +end + +function alg_cache(alg::ImplicitDeuflhardExtrapolation, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + utilde = zero(u) + u_temp1 = zero(u) + u_temp2 = zero(u) + u_temp3 = Array{typeof(u), 1}(undef, Threads.nthreads()) + u_temp4 = Array{typeof(u), 1}(undef, Threads.nthreads()) + + for i in 1:Threads.nthreads() + u_temp3[i] = zero(u) + u_temp4[i] = zero(u) + end + + tmp = zero(u) + T = Vector{typeof(u)}(undef, alg.max_order + 1) + for i in 1:(alg.max_order + 1) + T[i] = zero(u) + end + res = uEltypeNoUnits.(zero(u)) + + fsalfirst = zero(rate_prototype) + k = zero(rate_prototype) + k_tmps = Array{typeof(k), 1}(undef, Threads.nthreads()) + for i in 1:Threads.nthreads() + k_tmps[i] = zero(rate_prototype) + end + + cc = alg_cache(alg::ImplicitDeuflhardExtrapolation, u, rate_prototype, uEltypeNoUnits, + uBottomEltypeNoUnits, tTypeNoUnits, uprev, uprev2, f, t, dt, reltol, p, + calck, Val(false)) + + du1 = zero(rate_prototype) + du2 = zero(rate_prototype) + + if DiffEqBase.has_jac(f) && !DiffEqBase.has_Wfact(f) && f.jac_prototype !== nothing + W_el = WOperator(f, dt, true) + J = nothing # is J = W.J better? + else + J = false .* _vec(rate_prototype) .* _vec(rate_prototype)' # uEltype? + W_el = zero(J) + end + + W = Array{typeof(W_el), 1}(undef, Threads.nthreads()) + W[1] = W_el + for i in 2:Threads.nthreads() + if W_el isa WOperator + W[i] = WOperator(f, dt, true) + else + W[i] = zero(W_el) + end + end + tf = TimeGradientWrapper(f, uprev, p) + uf = UJacobianWrapper(f, t, p) + linsolve_tmp = zero(rate_prototype) + linsolve_tmps = Array{typeof(linsolve_tmp), 1}(undef, Threads.nthreads()) + + for i in 1:Threads.nthreads() + linsolve_tmps[i] = zero(rate_prototype) + end + + linprob = LinearProblem(W[1], _vec(linsolve_tmps[1]); u0 = _vec(k_tmps[1])) + linsolve1 = init(linprob, alg.linsolve, alias_A = true, alias_b = true) + #Pl = LinearSolve.InvPreconditioner(Diagonal(_vec(weight))), + #Pr = Diagonal(_vec(weight))) + + linsolve = Array{typeof(linsolve1), 1}(undef, Threads.nthreads()) + linsolve[1] = linsolve1 + for i in 2:Threads.nthreads() + linprob = LinearProblem(W[i], _vec(linsolve_tmps[i]); u0 = _vec(k_tmps[i])) + linsolve[i] = init(linprob, alg.linsolve, alias_A = true, alias_b = true) + #Pl = LinearSolve.InvPreconditioner(Diagonal(_vec(weight))), + #Pr = Diagonal(_vec(weight))) + end + grad_config = build_grad_config(alg, f, tf, du1, t) + jac_config = build_jac_config(alg, f, uf, du1, uprev, u, du1, du2) + + diff1 = Array{typeof(u), 1}(undef, Threads.nthreads()) + diff2 = Array{typeof(u), 1}(undef, Threads.nthreads()) + for i in 1:Threads.nthreads() + diff1[i] = zero(u) + diff2[i] = zero(u) + end + + ImplicitDeuflhardExtrapolationCache(utilde, u_temp1, u_temp2, u_temp3, u_temp4, tmp, T, + res, fsalfirst, k, k_tmps, cc.Q, cc.n_curr, + cc.n_old, cc.coefficients, cc.stage_number, + du1, du2, J, W, tf, uf, linsolve_tmps, linsolve, + jac_config, grad_config, diff1, diff2) +end + +@cache mutable struct ExtrapolationMidpointHairerWannerConstantCache{QType, + extrapolation_coefficients +} <: + OrdinaryDiffEqConstantCache + # Values that are mutated + Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n - 1) + n_curr::Int # Storage for the current extrapolation order + n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter + + # Constant values + coefficients::extrapolation_coefficients + stage_number::Vector{Int} # stage_number[n] contains information for extrapolation order (n - 1) + sigma::Rational{Int} # Parameter for order selection + + #Stepsizing caches + work::Array{QType, 1} + dt_new::Array{QType, 1} +end + +function alg_cache(alg::ExtrapolationMidpointHairerWanner, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + # Initialize cache's members + QType = tTypeNoUnits <: Integer ? typeof(qmin_default(alg)) : tTypeNoUnits # Cf. DiffEqBase.__init in solve.jl + + Q = fill(zero(QType), alg.max_order + 1) + n_curr = alg.init_order + n_old = alg.init_order + sequence_factor = alg.sequence_factor + + coefficients = create_extrapolation_coefficients(constvalue(uBottomEltypeNoUnits), alg) + stage_number = Vector{Int}(undef, alg.max_order + 1) + for n in 1:length(stage_number) + s = zero(eltype(coefficients.subdividing_sequence)) + for i in 1:n + s += coefficients.subdividing_sequence[i] + end + stage_number[n] = sequence_factor * Int(s) - n + 3 - sequence_factor + end + sigma = 9 // 10 + + work = fill(zero(eltype(Q)), alg.max_order + 1) + dt_new = fill(zero(eltype(Q)), alg.max_order + 1) + # Initialize the constant cache + ExtrapolationMidpointHairerWannerConstantCache(Q, n_curr, n_old, coefficients, + stage_number, sigma, work, dt_new) +end + +@cache mutable struct ExtrapolationMidpointHairerWannerCache{uType, uNoUnitsType, rateType, + QType, + extrapolation_coefficients} <: + OrdinaryDiffEqMutableCache + # Values that are mutated + utilde::uType + u_temp1::uType + u_temp2::uType + u_temp3::Array{uType, 1} + u_temp4::Array{uType, 1} + tmp::uType # for get_tmp_cache() + T::Array{uType, 1} # Storage for the internal discretisations obtained by the explicit midpoint rule + res::uNoUnitsType # Storage for the scaled residual of u and utilde + + fsalfirst::rateType + k::rateType + k_tmps::Array{rateType, 1} + + # Constant values + Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n - 1) + n_curr::Int # Storage for the current extrapolation order + n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter + coefficients::extrapolation_coefficients + stage_number::Vector{Int} # stage_number[n] contains information for extrapolation order (n - 1) + sigma::Rational{Int} # Parameter for order selection + + #Stepsizing caches + work::Array{QType, 1} + dt_new::Array{QType, 1} +end + +function alg_cache(alg::ExtrapolationMidpointHairerWanner, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + # Initialize cache's members + utilde = zero(u) + u_temp1 = zero(u) + u_temp2 = zero(u) + u_temp3 = Array{typeof(u), 1}(undef, Threads.nthreads()) + u_temp4 = Array{typeof(u), 1}(undef, Threads.nthreads()) + + for i in 1:Threads.nthreads() + u_temp3[i] = zero(u) + u_temp4[i] = zero(u) + end + tmp = zero(u) + T = Vector{typeof(u)}(undef, alg.max_order + 1) + for i in 1:(alg.max_order + 1) + T[i] = zero(u) + end + res = uEltypeNoUnits.(zero(u)) + fsalfirst = zero(rate_prototype) + k = zero(rate_prototype) + k_tmps = Array{typeof(k), 1}(undef, Threads.nthreads()) + for i in 1:Threads.nthreads() + k_tmps[i] = zero(rate_prototype) + end + + cc = alg_cache(alg, u, rate_prototype, uEltypeNoUnits, uBottomEltypeNoUnits, + tTypeNoUnits, uprev, uprev2, f, t, dt, reltol, p, calck, Val(false)) + + # Initialize the cache + ExtrapolationMidpointHairerWannerCache(utilde, u_temp1, u_temp2, u_temp3, u_temp4, tmp, + T, res, fsalfirst, k, k_tmps, + cc.Q, cc.n_curr, cc.n_old, cc.coefficients, + cc.stage_number, cc.sigma, cc.work, cc.dt_new) +end + +@cache mutable struct ImplicitHairerWannerExtrapolationConstantCache{QType, + extrapolation_coefficients, + TF, UF} <: + OrdinaryDiffEqConstantCache + # Values that are mutated + Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n - 1) + n_curr::Int # Storage for the current extrapolation order + n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter + + # Constant values + coefficients::extrapolation_coefficients + stage_number::Vector{Int} # stage_number[n] contains information for extrapolation order (n - 1) + sigma::Rational{Int} # Parameter for order selection + + tf::TF + uf::UF + + #Stepsizing caches + work::Array{QType, 1} + dt_new::Array{QType, 1} +end + +function alg_cache(alg::ImplicitHairerWannerExtrapolation, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + # Initialize cache's members + QType = tTypeNoUnits <: Integer ? typeof(qmin_default(alg)) : tTypeNoUnits # Cf. DiffEqBase.__init in solve.jl + + Q = fill(zero(QType), alg.max_order + 1) + n_curr = alg.init_order + n_old = alg.init_order + + coefficients = create_extrapolation_coefficients(constvalue(uBottomEltypeNoUnits), alg) + #==Work Calculation (A[J] denotes Jth order work) + Default values are used from https://github.com/luchr/ODEInterface.jl/blob/master/src/Seulex.jl#L393-L399 + + ║ WKFCN │ estimated works (complexity) │ 1.0 ║ + ║ WKJAC │ for a call to │ 5.0 ║ + ║ WKDEC │ WKFCN: right-hand side f │ 1.0 ║ + ║ WKSOL │ WKJAC: JACOBIMATRIX │ 1.0 ║ + ║ WKROW │ WKDEC: LU-decomposition │ 2.0 ║ + ║ │ WKSOL: Forward- and Backward subst. │ ║ + ║ | WKROW: Tot. work in one iteration | ║ + ╚════════════╧═════════════════════════════════════╧═════════╝ + WKROW = WKFCN + WKSOL + A[1] = WKJAC + (N[1] + 1)* WKROw + WKDEC + A[J] = A[J - 1] + N[J]* WKROW + WKDEC + + Since we are using 4*N Sequence and only performing 4*N - 1 computations, The modified Work Equation becomes: + A[J] = A[J - 1] + (4*N[J] - 1)* WKROW + WKDEC + ==# + stage_number = Vector{Int}(undef, alg.max_order + 1) + for n in 1:length(stage_number) + s = zero(eltype(coefficients.subdividing_sequence)) + for i in 1:n + s += coefficients.subdividing_sequence[i] + end + stage_number[n] = 8 * Int(s) - n + 3 + end + sigma = 9 // 10 + + # Initialize the constant cache + tf = TimeDerivativeWrapper(f, u, p) + uf = UDerivativeWrapper(f, t, p) + work = fill(zero(eltype(Q)), alg.max_order + 1) + dt_new = fill(zero(eltype(Q)), alg.max_order + 1) + ImplicitHairerWannerExtrapolationConstantCache(Q, n_curr, n_old, coefficients, + stage_number, sigma, tf, uf, work, + dt_new) +end + +@cache mutable struct ImplicitHairerWannerExtrapolationCache{uType, uNoUnitsType, rateType, + QType, + extrapolation_coefficients, + JType, WType, F, JCType, + GCType, TFType, UFType} <: + OrdinaryDiffEqMutableCache + # Values that are mutated + utilde::uType + u_temp1::uType + u_temp2::uType + u_temp3::Array{uType, 1} + u_temp4::Array{uType, 1} + tmp::uType # for get_tmp_cache() + T::Array{uType, 1} # Storage for the internal discretisations obtained by the explicit midpoint rule + res::uNoUnitsType # Storage for the scaled residual of u and utilde + + fsalfirst::rateType + k::rateType + k_tmps::Array{rateType, 1} + + # Constant values + Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n - 1) + n_curr::Int # Storage for the current extrapolation order + n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter + coefficients::extrapolation_coefficients + stage_number::Vector{Int} # stage_number[n] contains information for extrapolation order (n - 1) + sigma::Rational{Int} # Parameter for order selection + + du1::rateType + du2::rateType + J::JType + W::WType + tf::TFType + uf::UFType + linsolve_tmps::Array{rateType, 1} + linsolve::Array{F, 1} + jac_config::JCType + grad_config::GCType + # Values to check overflow in T1 computation + diff1::Array{uType, 1} + diff2::Array{uType, 1} + + #Stepsizing caches + work::Array{QType, 1} + dt_new::Array{QType, 1} +end + +function alg_cache(alg::ImplicitHairerWannerExtrapolation, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + # Initialize cache's members + utilde = zero(u) + u_temp1 = zero(u) + u_temp2 = zero(u) + u_temp3 = Array{typeof(u), 1}(undef, Threads.nthreads()) + u_temp4 = Array{typeof(u), 1}(undef, Threads.nthreads()) + + for i in 1:Threads.nthreads() + u_temp3[i] = zero(u) + u_temp4[i] = zero(u) + end + tmp = zero(u) + T = Vector{typeof(u)}(undef, alg.max_order + 1) + for i in 1:(alg.max_order + 1) + T[i] = zero(u) + end + res = uEltypeNoUnits.(zero(u)) + fsalfirst = zero(rate_prototype) + k = zero(rate_prototype) + k_tmps = Array{typeof(k), 1}(undef, Threads.nthreads()) + for i in 1:Threads.nthreads() + k_tmps[i] = zero(rate_prototype) + end + + cc = alg_cache(alg, u, rate_prototype, uEltypeNoUnits, uBottomEltypeNoUnits, + tTypeNoUnits, uprev, uprev2, f, t, dt, reltol, p, calck, Val(false)) + + du1 = zero(rate_prototype) + du2 = zero(rate_prototype) + + if DiffEqBase.has_jac(f) && !DiffEqBase.has_Wfact(f) && f.jac_prototype !== nothing + W_el = WOperator(f, dt, true) + J = nothing # is J = W.J better? + else + J = false .* _vec(rate_prototype) .* _vec(rate_prototype)' # uEltype? + W_el = zero(J) + end + + W = Array{typeof(W_el), 1}(undef, Threads.nthreads()) + W[1] = W_el + for i in 2:Threads.nthreads() + if W_el isa WOperator + W[i] = WOperator(f, dt, true) + else + W[i] = zero(W_el) + end + end + + tf = TimeGradientWrapper(f, uprev, p) + uf = UJacobianWrapper(f, t, p) + linsolve_tmp = zero(rate_prototype) + linsolve_tmps = Array{typeof(linsolve_tmp), 1}(undef, Threads.nthreads()) + + for i in 1:Threads.nthreads() + linsolve_tmps[i] = zero(rate_prototype) + end + + linprob = LinearProblem(W[1], _vec(linsolve_tmps[1]); u0 = _vec(k_tmps[1])) + linsolve1 = init(linprob, alg.linsolve, alias_A = true, alias_b = true) + #Pl = LinearSolve.InvPreconditioner(Diagonal(_vec(weight))), + #Pr = Diagonal(_vec(weight))) + + linsolve = Array{typeof(linsolve1), 1}(undef, Threads.nthreads()) + linsolve[1] = linsolve1 + for i in 2:Threads.nthreads() + linprob = LinearProblem(W[i], _vec(linsolve_tmps[i]); u0 = _vec(k_tmps[i])) + linsolve[i] = init(linprob, alg.linsolve, alias_A = true, alias_b = true) + #Pl = LinearSolve.InvPreconditioner(Diagonal(_vec(weight))), + #Pr = Diagonal(_vec(weight))) + end + grad_config = build_grad_config(alg, f, tf, du1, t) + jac_config = build_jac_config(alg, f, uf, du1, uprev, u, du1, du2) + + diff1 = Array{typeof(u), 1}(undef, Threads.nthreads()) + diff2 = Array{typeof(u), 1}(undef, Threads.nthreads()) + for i in 1:Threads.nthreads() + diff1[i] = zero(u) + diff2[i] = zero(u) + end + + # Initialize the cache + ImplicitHairerWannerExtrapolationCache(utilde, u_temp1, u_temp2, u_temp3, u_temp4, tmp, + T, res, fsalfirst, k, k_tmps, + cc.Q, cc.n_curr, cc.n_old, cc.coefficients, + cc.stage_number, cc.sigma, du1, du2, J, W, tf, + uf, linsolve_tmps, + linsolve, jac_config, grad_config, diff1, diff2, + cc.work, cc.dt_new) +end + +@cache mutable struct ImplicitEulerBarycentricExtrapolationConstantCache{QType, + extrapolation_coefficients, + TF, UF} <: + OrdinaryDiffEqConstantCache + # Values that are mutated + Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n - 1) + n_curr::Int # Storage for the current extrapolation order + n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter + + # Constant values + coefficients::extrapolation_coefficients + stage_number::Vector{Int} # stage_number[n] contains information for extrapolation order (n - 1) + sigma::Rational{Int} # Parameter for order selection + + tf::TF + uf::UF + + #Stepsizing caches + work::Array{QType, 1} + dt_new::Array{QType, 1} +end + +function alg_cache(alg::ImplicitEulerBarycentricExtrapolation, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + # Initialize cache's members + QType = tTypeNoUnits <: Integer ? typeof(qmin_default(alg)) : tTypeNoUnits # Cf. DiffEqBase.__init in solve.jl + + Q = fill(zero(QType), alg.max_order + 1) + n_curr = alg.init_order + n_old = alg.init_order + sequence_factor = alg.sequence_factor + + coefficients = create_extrapolation_coefficients(constvalue(uBottomEltypeNoUnits), alg) + + stage_number = Vector{Int}(undef, alg.max_order + 1) + for n in 1:length(stage_number) + s = zero(eltype(coefficients.subdividing_sequence)) + for i in 1:n + s += coefficients.subdividing_sequence[i] + end + stage_number[n] = 2 * sequence_factor * Int(s) - n + 7 + end + sigma = 9 // 10 + + work = fill(zero(eltype(Q)), alg.max_order + 1) + dt_new = fill(zero(eltype(Q)), alg.max_order + 1) + # Initialize the constant cache + tf = TimeDerivativeWrapper(f, u, p) + uf = UDerivativeWrapper(f, t, p) + ImplicitEulerBarycentricExtrapolationConstantCache(Q, n_curr, n_old, coefficients, + stage_number, sigma, tf, uf, work, + dt_new) +end + +@cache mutable struct ImplicitEulerBarycentricExtrapolationCache{uType, uNoUnitsType, + rateType, QType, + extrapolation_coefficients, + JType, WType, F, JCType, + GCType, TFType, UFType} <: + OrdinaryDiffEqMutableCache + # Values that are mutated + utilde::uType + u_temp1::uType + u_temp2::uType + u_temp3::Array{uType, 1} + u_temp4::Array{uType, 1} + tmp::uType # for get_tmp_cache() + T::Array{uType, 1} # Storage for the internal discretisations obtained by the explicit midpoint rule + res::uNoUnitsType # Storage for the scaled residual of u and utilde + + fsalfirst::rateType + k::rateType + k_tmps::Array{rateType, 1} + + # Constant values + Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n - 1) + n_curr::Int # Storage for the current extrapolation order + n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter + coefficients::extrapolation_coefficients + stage_number::Vector{Int} # stage_number[n] contains information for extrapolation order (n - 1) + sigma::Rational{Int} # Parameter for order selection + + du1::rateType + du2::rateType + J::JType + W::WType + tf::TFType + uf::UFType + linsolve_tmps::Array{rateType, 1} + linsolve::Array{F, 1} + jac_config::JCType + grad_config::GCType + # Values to check overflow in T1 computation + diff1::Array{uType, 1} + diff2::Array{uType, 1} + #Stepsizing caches + work::Array{QType, 1} + dt_new::Array{QType, 1} +end + +function alg_cache(alg::ImplicitEulerBarycentricExtrapolation, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + # Initialize cache's members + utilde = zero(u) + u_temp1 = zero(u) + u_temp2 = zero(u) + u_temp3 = Array{typeof(u), 1}(undef, Threads.nthreads()) + u_temp4 = Array{typeof(u), 1}(undef, Threads.nthreads()) + + for i in 1:Threads.nthreads() + u_temp3[i] = zero(u) + u_temp4[i] = zero(u) + end + tmp = zero(u) + T = Vector{typeof(u)}(undef, alg.max_order + 1) + for i in 1:(alg.max_order + 1) + T[i] = zero(u) + end + res = uEltypeNoUnits.(zero(u)) + fsalfirst = zero(rate_prototype) + k = zero(rate_prototype) + k_tmps = Array{typeof(k), 1}(undef, Threads.nthreads()) + for i in 1:Threads.nthreads() + k_tmps[i] = zero(rate_prototype) + end + + cc = alg_cache(alg, u, rate_prototype, uEltypeNoUnits, uBottomEltypeNoUnits, + tTypeNoUnits, uprev, uprev2, f, t, dt, reltol, p, calck, Val(false)) + + du1 = zero(rate_prototype) + du2 = zero(rate_prototype) + + if DiffEqBase.has_jac(f) && !DiffEqBase.has_Wfact(f) && f.jac_prototype !== nothing + W_el = WOperator(f, dt, true) + J = nothing # is J = W.J better? + else + J = false .* _vec(rate_prototype) .* _vec(rate_prototype)' # uEltype? + W_el = zero(J) + end + + W = Array{typeof(W_el), 1}(undef, Threads.nthreads()) + W[1] = W_el + for i in 2:Threads.nthreads() + if W_el isa WOperator + W[i] = WOperator(f, dt, true) + else + W[i] = zero(W_el) + end + end + + tf = TimeGradientWrapper(f, uprev, p) + uf = UJacobianWrapper(f, t, p) + linsolve_tmp = zero(rate_prototype) + linsolve_tmps = Array{typeof(linsolve_tmp), 1}(undef, Threads.nthreads()) + + for i in 1:Threads.nthreads() + linsolve_tmps[i] = zero(rate_prototype) + end + + linprob = LinearProblem(W[1], _vec(linsolve_tmps[1]); u0 = _vec(k_tmps[1])) + linsolve1 = init(linprob, alg.linsolve, alias_A = true, alias_b = true) + #Pl = LinearSolve.InvPreconditioner(Diagonal(_vec(weight))), + #Pr = Diagonal(_vec(weight))) + + linsolve = Array{typeof(linsolve1), 1}(undef, Threads.nthreads()) + linsolve[1] = linsolve1 + for i in 2:Threads.nthreads() + linprob = LinearProblem(W[i], _vec(linsolve_tmps[i]); u0 = _vec(k_tmps[i])) + linsolve[i] = init(linprob, alg.linsolve, alias_A = true, alias_b = true) + #Pl = LinearSolve.InvPreconditioner(Diagonal(_vec(weight))), + #Pr = Diagonal(_vec(weight))) + end + grad_config = build_grad_config(alg, f, tf, du1, t) + jac_config = build_jac_config(alg, f, uf, du1, uprev, u, du1, du2) + + diff1 = Array{typeof(u), 1}(undef, Threads.nthreads()) + diff2 = Array{typeof(u), 1}(undef, Threads.nthreads()) + for i in 1:Threads.nthreads() + diff1[i] = zero(u) + diff2[i] = zero(u) + end + + # Initialize the cache + ImplicitEulerBarycentricExtrapolationCache(utilde, u_temp1, u_temp2, u_temp3, u_temp4, + tmp, T, res, fsalfirst, k, k_tmps, + cc.Q, cc.n_curr, cc.n_old, cc.coefficients, + cc.stage_number, cc.sigma, du1, du2, J, W, + tf, uf, linsolve_tmps, + linsolve, jac_config, grad_config, diff1, + diff2, cc.work, cc.dt_new) +end diff --git a/src/caches/feagin_caches.jl b/src/caches/feagin_caches.jl new file mode 100644 index 0000000000..47defa81a2 --- /dev/null +++ b/src/caches/feagin_caches.jl @@ -0,0 +1,248 @@ +@cache struct Feagin10Cache{uType, uNoUnitsType, rateType, TabType} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + k2::rateType + k3::rateType + k4::rateType + k5::rateType + k6::rateType + k7::rateType + k8::rateType + k9::rateType + k10::rateType + k11::rateType + k12::rateType + k13::rateType + k14::rateType + k15::rateType + k16::rateType + k17::rateType + tmp::uType + atmp::uNoUnitsType + k::rateType + tab::TabType +end + +function alg_cache(alg::Feagin10, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tab = Feagin10ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + k1 = zero(rate_prototype) + k2 = zero(rate_prototype) + k3 = zero(rate_prototype) + k4 = zero(rate_prototype) + k5 = zero(rate_prototype) + k6 = zero(rate_prototype) + k7 = zero(rate_prototype) + k8 = zero(rate_prototype) + k9 = zero(rate_prototype) + k10 = zero(rate_prototype) + k11 = zero(rate_prototype) + k12 = zero(rate_prototype) + k13 = zero(rate_prototype) + k14 = zero(rate_prototype) + k15 = zero(rate_prototype) + k16 = zero(rate_prototype) + k17 = zero(rate_prototype) + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + k = zero(rate_prototype) + + Feagin10Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, + k15, k16, k17, tmp, atmp, k, tab) +end + +function alg_cache(alg::Feagin10, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + Feagin10ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct Feagin12Cache{uType, uNoUnitsType, rateType, TabType} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + k2::rateType + k3::rateType + k4::rateType + k5::rateType + k6::rateType + k7::rateType + k8::rateType + k9::rateType + k10::rateType + k11::rateType + k12::rateType + k13::rateType + k14::rateType + k15::rateType + k16::rateType + k17::rateType + k18::rateType + k19::rateType + k20::rateType + k21::rateType + k22::rateType + k23::rateType + k24::rateType + k25::rateType + tmp::uType + atmp::uNoUnitsType + k::rateType + tab::TabType +end + +function alg_cache(alg::Feagin12, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tab = Feagin12ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + k1 = zero(rate_prototype) + k2 = zero(rate_prototype) + k3 = zero(rate_prototype) + k4 = zero(rate_prototype) + k5 = zero(rate_prototype) + k6 = zero(rate_prototype) + k7 = zero(rate_prototype) + k8 = zero(rate_prototype) + k9 = zero(rate_prototype) + k10 = zero(rate_prototype) + k11 = zero(rate_prototype) + k12 = zero(rate_prototype) + k13 = zero(rate_prototype) + k14 = zero(rate_prototype) + k15 = zero(rate_prototype) + k16 = zero(rate_prototype) + k17 = zero(rate_prototype) + k18 = zero(rate_prototype) + k19 = zero(rate_prototype) + k20 = zero(rate_prototype) + k21 = zero(rate_prototype) + k22 = zero(rate_prototype) + k23 = zero(rate_prototype) + k24 = zero(rate_prototype) + k25 = zero(rate_prototype) + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + k = zero(rate_prototype) + + Feagin12Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, + k15, k16, k17, k18, k19, k20, k21, k22, k23, k24, k25, tmp, atmp, k, tab) +end + +function alg_cache(alg::Feagin12, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + Feagin12ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct Feagin14Cache{uType, uNoUnitsType, rateType, TabType} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + k2::rateType + k3::rateType + k4::rateType + k5::rateType + k6::rateType + k7::rateType + k8::rateType + k9::rateType + k10::rateType + k11::rateType + k12::rateType + k13::rateType + k14::rateType + k15::rateType + k16::rateType + k17::rateType + k18::rateType + k19::rateType + k20::rateType + k21::rateType + k22::rateType + k23::rateType + k24::rateType + k25::rateType + k26::rateType + k27::rateType + k28::rateType + k29::rateType + k30::rateType + k31::rateType + k32::rateType + k33::rateType + k34::rateType + k35::rateType + tmp::uType + atmp::uNoUnitsType + k::rateType + tab::TabType +end + +function alg_cache(alg::Feagin14, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tab = Feagin14ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + k1 = zero(rate_prototype) + k2 = zero(rate_prototype) + k3 = zero(rate_prototype) + k4 = zero(rate_prototype) + k5 = zero(rate_prototype) + k6 = zero(rate_prototype) + k7 = zero(rate_prototype) + k8 = zero(rate_prototype) + k9 = zero(rate_prototype) + k10 = zero(rate_prototype) + k11 = zero(rate_prototype) + k12 = zero(rate_prototype) + k13 = zero(rate_prototype) + k14 = zero(rate_prototype) + k15 = zero(rate_prototype) + k16 = zero(rate_prototype) + k17 = zero(rate_prototype) + k18 = zero(rate_prototype) + k19 = zero(rate_prototype) + k20 = zero(rate_prototype) + k21 = zero(rate_prototype) + k22 = zero(rate_prototype) + k23 = zero(rate_prototype) + k24 = zero(rate_prototype) + k25 = zero(rate_prototype) + k26 = zero(rate_prototype) + k27 = zero(rate_prototype) + k28 = zero(rate_prototype) + k29 = zero(rate_prototype) + k30 = zero(rate_prototype) + k31 = zero(rate_prototype) + k32 = zero(rate_prototype) + k33 = zero(rate_prototype) + k34 = zero(rate_prototype) + k35 = zero(rate_prototype) + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + k = zero(rate_prototype) + + Feagin14Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, + k15, k16, + k17, k18, k19, k20, k21, k22, k23, k24, k25, k26, k27, k28, k29, k30, + k31, k32, k33, k34, k35, tmp, atmp, k, tab) +end + +function alg_cache(alg::Feagin14, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + Feagin14ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end diff --git a/src/caches/firk_caches.jl b/src/caches/firk_caches.jl index fb1489270b..3f6bfee39f 100644 --- a/src/caches/firk_caches.jl +++ b/src/caches/firk_caches.jl @@ -274,7 +274,7 @@ function alg_cache(alg::RadauIIA5, u, rate_prototype, ::Type{uEltypeNoUnits}, Convergence, alg.step_limiter!) end -mutable struct RadauIIA7ConstantCache{F, Tab, Tol, Dt, U, JType} <: +mutable struct RadauIIA9ConstantCache{F, Tab, Tol, Dt, U, JType} <: OrdinaryDiffEqConstantCache uf::F tab::Tab @@ -291,22 +291,22 @@ mutable struct RadauIIA7ConstantCache{F, Tab, Tol, Dt, U, JType} <: J::JType end -function alg_cache(alg::RadauIIA7, u, rate_prototype, ::Type{uEltypeNoUnits}, +function alg_cache(alg::RadauIIA9, u, rate_prototype, ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} uf = UDerivativeWrapper(f, t, p) uToltype = constvalue(uBottomEltypeNoUnits) - tab = RadauIIA7Tableau(uToltype, constvalue(tTypeNoUnits)) + tab = RadauIIA9Tableau(uToltype, constvalue(tTypeNoUnits)) κ = alg.κ !== nothing ? convert(uToltype, alg.κ) : convert(uToltype, 1 // 100) J = false .* _vec(rate_prototype) .* _vec(rate_prototype)' - RadauIIA7ConstantCache(uf, tab, κ, one(uToltype), 10000, u, u, u, u, dt, dt, + RadauIIA9ConstantCache(uf, tab, κ, one(uToltype), 10000, u, u, u, u, dt, dt, Convergence, J) end -mutable struct RadauIIA7Cache{uType, cuType, uNoUnitsType, rateType, JType, W1Type, W2Type, +mutable struct RadauIIA9Cache{uType, cuType, uNoUnitsType, rateType, JType, W1Type, W2Type, UF, JC, F1, F2, Tab, Tol, Dt, rTol, aTol, StepLimiter} <: OrdinaryDiffEqMutableCache u::uType @@ -370,15 +370,15 @@ mutable struct RadauIIA7Cache{uType, cuType, uNoUnitsType, rateType, JType, W1Ty status::NLStatus step_limiter!::StepLimiter end -TruncatedStacktraces.@truncate_stacktrace RadauIIA7Cache 1 +TruncatedStacktraces.@truncate_stacktrace RadauIIA9Cache 1 -function alg_cache(alg::RadauIIA7, u, rate_prototype, ::Type{uEltypeNoUnits}, +function alg_cache(alg::RadauIIA9, u, rate_prototype, ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} uf = UJacobianWrapper(f, t, p) uToltype = constvalue(uBottomEltypeNoUnits) - tab = RadauIIA7Tableau(uToltype, constvalue(tTypeNoUnits)) + tab = RadauIIA9Tableau(uToltype, constvalue(tTypeNoUnits)) κ = alg.κ !== nothing ? convert(uToltype, alg.κ) : convert(uToltype, 1 // 100) @@ -459,7 +459,7 @@ function alg_cache(alg::RadauIIA7, u, rate_prototype, ::Type{uEltypeNoUnits}, rtol = reltol isa Number ? reltol : zero(reltol) atol = reltol isa Number ? reltol : zero(reltol) - RadauIIA7Cache(u, uprev, + RadauIIA9Cache(u, uprev, z1, z2, z3, z4, z5, w1, w2, w3, w4, w5, dw1, ubuff, dw23, dw45, cubuff1, cubuff2, cont1, cont2, cont3, cont4, du1, fsalfirst, k, k2, k3, k4, k5, fw1, fw2, fw3, fw4, fw5, diff --git a/src/caches/low_storage_rk_caches.jl b/src/caches/low_storage_rk_caches.jl new file mode 100644 index 0000000000..a903e155ad --- /dev/null +++ b/src/caches/low_storage_rk_caches.jl @@ -0,0 +1,3839 @@ + +# 2N low storage methods introduced by Williamson +@cache struct LowStorageRK2NCache{uType, rateType, TabType, StageLimiter, StepLimiter, + Thread} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + tmp::uType # tmp acts as second register and fsal both + tab::TabType + williamson_condition::Bool + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct LowStorageRK2NConstantCache{N, T, T2} <: OrdinaryDiffEqConstantCache + A2end::SVector{N, T} # A1 is always zero + B1::T + B2end::SVector{N, T} + c2end::SVector{N, T2} # c1 is always zero +end + +function ORK256ConstantCache(T, T2) + A2 = convert(T, -1.0) + A3 = convert(T, -1.55798) + A4 = convert(T, -1.0) + A5 = convert(T, -0.45031) + A2end = SVector(A2, A3, A4, A5) + + B1 = convert(T, 0.2) + B2 = convert(T, 0.83204) + B3 = convert(T, 0.6) + B4 = convert(T, 0.35394) + B5 = convert(T, 0.2) + B2end = SVector(B2, B3, B4, B5) + + c2 = convert(T2, 0.2) + c3 = convert(T2, 0.2) + c4 = convert(T2, 0.8) + c5 = convert(T2, 0.8) + c2end = SVector(c2, c3, c4, c5) + + LowStorageRK2NConstantCache{4, T, T2}(A2end, B1, B2end, c2end) +end + +function alg_cache(alg::ORK256, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tab = ORK256ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + tmp = zero(u) + williamson_condition = alg.williamson_condition + if calck + k = zero(rate_prototype) + williamson_condition = false + else + if williamson_condition + k = tmp + else + k = zero(rate_prototype) + end + end + LowStorageRK2NCache(u, uprev, k, tmp, tab, williamson_condition, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::ORK256, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + ORK256ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function CarpenterKennedy2N54ConstantCache(T, T2) + A2 = convert(T, -567301805773 // 1357537059087) + A3 = convert(T, -2404267990393 // 2016746695238) + A4 = convert(T, -3550918686646 // 2091501179385) + A5 = convert(T, -1275806237668 // 842570457699) + A2end = SVector(A2, A3, A4, A5) + + B1 = convert(T, 1432997174477 // 9575080441755) + B2 = convert(T, 5161836677717 // 13612068292357) + B3 = convert(T, 1720146321549 // 2090206949498) + B4 = convert(T, 3134564353537 // 4481467310338) + B5 = convert(T, 2277821191437 // 14882151754819) + B2end = SVector(B2, B3, B4, B5) + + c2 = convert(T2, 1432997174477 // 9575080441755) + c3 = convert(T2, 2526269341429 // 6820363962896) + c4 = convert(T2, 2006345519317 // 3224310063776) + c5 = convert(T2, 2802321613138 // 2924317926251) + c2end = SVector(c2, c3, c4, c5) + + LowStorageRK2NConstantCache{4, T, T2}(A2end, B1, B2end, c2end) +end + +function alg_cache(alg::CarpenterKennedy2N54, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tab = CarpenterKennedy2N54ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + tmp = zero(u) + williamson_condition = alg.williamson_condition + if calck + k = zero(rate_prototype) + williamson_condition = false + else + if williamson_condition + k = tmp + else + k = zero(rate_prototype) + end + end + LowStorageRK2NCache(u, uprev, k, tmp, tab, williamson_condition, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::CarpenterKennedy2N54, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + CarpenterKennedy2N54ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) +end + +function SHLDDRK64ConstantCache(T, T2) + #TODO: Solve the order conditions with more accuracy + A2 = convert(T, -0.4919575) + A3 = convert(T, -0.8946264) + A4 = convert(T, -1.5526678) + A5 = convert(T, -3.4077973) + A6 = convert(T, -1.0742640) + A2end = SVector(A2, A3, A4, A5, A6) + + B1 = convert(T, 0.1453095) + B2 = convert(T, 0.4653797) + B3 = convert(T, 0.4675397) + B4 = convert(T, 0.7795279) + B5 = convert(T, 0.3574327) + B6 = convert(T, 0.15) + B2end = SVector(B2, B3, B4, B5, B6) + + c2 = convert(T2, 0.1453095) + c3 = convert(T2, 0.3817422) + c4 = convert(T2, 0.6367813) + c5 = convert(T2, 0.7560744) + c6 = convert(T2, 0.9271047) + c2end = SVector(c2, c3, c4, c5, c6) + + LowStorageRK2NConstantCache{5, T, T2}(A2end, B1, B2end, c2end) +end + +function alg_cache(alg::SHLDDRK64, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tab = SHLDDRK64ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + tmp = zero(u) + williamson_condition = alg.williamson_condition + if calck + k = zero(rate_prototype) + williamson_condition = false + else + if williamson_condition + k = tmp + else + k = zero(rate_prototype) + end + end + LowStorageRK2NCache(u, uprev, k, tmp, tab, williamson_condition, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::SHLDDRK64, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SHLDDRK64ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function DGLDDRK73_CConstantCache(T, T2) + A2 = convert(T, -0.8083163874983830) + A3 = convert(T, -1.503407858773331) + A4 = convert(T, -1.053064525050744) + A5 = convert(T, -1.463149119280508) + A6 = convert(T, -0.6592881281087830) + A7 = convert(T, -1.667891931891068) + A2end = SVector(A2, A3, A4, A5, A6, A7) + + B1 = convert(T, 0.01197052673097840) + B2 = convert(T, 0.8886897793820711) + B3 = convert(T, 0.4578382089261419) + B4 = convert(T, 0.5790045253338471) + B5 = convert(T, 0.3160214638138484) + B6 = convert(T, 0.2483525368264122) + B7 = convert(T, 0.06771230959408840) + B2end = SVector(B2, B3, B4, B5, B6, B7) + + c2 = convert(T2, 0.01197052673097840) + c3 = convert(T2, 0.1823177940361990) + c4 = convert(T2, 0.5082168062551849) + c5 = convert(T2, 0.6532031220148590) + c6 = convert(T2, 0.8534401385678250) + c7 = convert(T2, 0.9980466084623790) + c2end = SVector(c2, c3, c4, c5, c6, c7) + + LowStorageRK2NConstantCache{6, T, T2}(A2end, B1, B2end, c2end) +end + +function alg_cache(alg::DGLDDRK73_C, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tab = DGLDDRK73_CConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + tmp = zero(u) + williamson_condition = alg.williamson_condition + if calck + k = zero(rate_prototype) + williamson_condition = false + else + if williamson_condition + k = tmp + else + k = zero(rate_prototype) + end + end + LowStorageRK2NCache(u, uprev, k, tmp, tab, williamson_condition, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::DGLDDRK73_C, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + DGLDDRK73_CConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function DGLDDRK84_CConstantCache(T, T2) + A2 = convert(T, -0.7212962482279240) + A3 = convert(T, -0.01077336571612980) + A4 = convert(T, -0.5162584698930970) + A5 = convert(T, -1.730100286632201) + A6 = convert(T, -5.200129304403076) + A7 = convert(T, 0.7837058945416420) + A8 = convert(T, -0.5445836094332190) + A2end = SVector(A2, A3, A4, A5, A6, A7, A8) + + B1 = convert(T, 0.2165936736758085) + B2 = convert(T, 0.1773950826411583) + B3 = convert(T, 0.01802538611623290) + B4 = convert(T, 0.08473476372541490) + B5 = convert(T, 0.8129106974622483) + B6 = convert(T, 1.903416030422760) + B7 = convert(T, 0.1314841743399048) + B8 = convert(T, 0.2082583170674149) + B2end = SVector(B2, B3, B4, B5, B6, B7, B8) + + c2 = convert(T2, 0.2165936736758085) + c3 = convert(T2, 0.2660343487538170) + c4 = convert(T2, 0.2840056122522720) + c5 = convert(T2, 0.3251266843788570) + c6 = convert(T2, 0.4555149599187530) + c7 = convert(T2, 0.7713219317101170) + c8 = convert(T2, 0.9199028964538660) + c2end = SVector(c2, c3, c4, c5, c6, c7, c8) + + LowStorageRK2NConstantCache{7, T, T2}(A2end, B1, B2end, c2end) +end + +function alg_cache(alg::DGLDDRK84_C, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tab = DGLDDRK84_CConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + tmp = zero(u) + williamson_condition = alg.williamson_condition + if calck + k = zero(rate_prototype) + williamson_condition = false + else + if williamson_condition + k = tmp + else + k = zero(rate_prototype) + end + end + LowStorageRK2NCache(u, uprev, k, tmp, tab, williamson_condition, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::DGLDDRK84_C, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + DGLDDRK84_CConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function DGLDDRK84_FConstantCache(T, T2) + A2 = convert(T, -0.5534431294501569) + A3 = convert(T, 0.01065987570203490) + A4 = convert(T, -0.5515812888932000) + A5 = convert(T, -1.885790377558741) + A6 = convert(T, -5.701295742793264) + A7 = convert(T, 2.113903965664793) + A8 = convert(T, -0.5339578826675280) + A2end = SVector(A2, A3, A4, A5, A6, A7, A8) + + B1 = convert(T, 0.08037936882736950) + B2 = convert(T, 0.5388497458569843) + B3 = convert(T, 0.01974974409031960) + B4 = convert(T, 0.09911841297339970) + B5 = convert(T, 0.7466920411064123) + B6 = convert(T, 1.679584245618894) + B7 = convert(T, 0.2433728067008188) + B8 = convert(T, 0.1422730459001373) + B2end = SVector(B2, B3, B4, B5, B6, B7, B8) + + c2 = convert(T2, 0.08037936882736950) + c3 = convert(T2, 0.3210064250338430) + c4 = convert(T2, 0.3408501826604660) + c5 = convert(T2, 0.3850364824285470) + c6 = convert(T2, 0.5040052477534100) + c7 = convert(T2, 0.6578977561168540) + c8 = convert(T2, 0.9484087623348481) + c2end = SVector(c2, c3, c4, c5, c6, c7, c8) + + LowStorageRK2NConstantCache{7, T, T2}(A2end, B1, B2end, c2end) +end + +function alg_cache(alg::DGLDDRK84_F, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tab = DGLDDRK84_FConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + tmp = zero(u) + williamson_condition = alg.williamson_condition + if calck + k = zero(rate_prototype) + williamson_condition = false + else + if williamson_condition + k = tmp + else + k = zero(rate_prototype) + end + end + LowStorageRK2NCache(u, uprev, k, tmp, tab, williamson_condition, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::DGLDDRK84_F, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + DGLDDRK84_FConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function NDBLSRK124ConstantCache(T, T2) + A2 = convert(T, -0.0923311242368072) + A3 = convert(T, -0.9441056581158819) + A4 = convert(T, -4.3271273247576394) + A5 = convert(T, -2.1557771329026072) + A6 = convert(T, -0.9770727190189062) + A7 = convert(T, -0.7581835342571139) + A8 = convert(T, -1.7977525470825499) + A9 = convert(T, -2.6915667972700770) + A10 = convert(T, -4.6466798960268143) + A11 = convert(T, -0.1539613783825189) + A12 = convert(T, -0.5943293901830616) + A2end = SVector(A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12) + + B1 = convert(T, 0.0650008435125904) + B2 = convert(T, 0.0161459902249842) + B3 = convert(T, 0.5758627178358159) + B4 = convert(T, 0.1649758848361671) + B5 = convert(T, 0.3934619494248182) + B6 = convert(T, 0.0443509641602719) + B7 = convert(T, 0.2074504268408778) + B8 = convert(T, 0.6914247433015102) + B9 = convert(T, 0.3766646883450449) + B10 = convert(T, 0.0757190350155483) + B11 = convert(T, 0.2027862031054088) + B12 = convert(T, 0.2167029365631842) + B2end = SVector(B2, B3, B4, B5, B6, B7, B8, B9, B10, B11, B12) + + c2 = convert(T2, 0.0650008435125904) + c3 = convert(T2, 0.0796560563081853) + c4 = convert(T2, 0.1620416710085376) + c5 = convert(T2, 0.2248877362907778) + c6 = convert(T2, 0.2952293985641261) + c7 = convert(T2, 0.3318332506149405) + c8 = convert(T2, 0.4094724050198658) + c9 = convert(T2, 0.6356954475753369) + c10 = convert(T2, 0.6806551557645497) + c11 = convert(T2, 0.7143773712418350) + c12 = convert(T2, 0.9032588871651854) + c2end = SVector(c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12) + + LowStorageRK2NConstantCache{11, T, T2}(A2end, B1, B2end, c2end) +end + +function alg_cache(alg::NDBLSRK124, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tab = NDBLSRK124ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + tmp = zero(u) + williamson_condition = alg.williamson_condition + if calck + k = zero(rate_prototype) + williamson_condition = false + else + if williamson_condition + k = tmp + else + k = zero(rate_prototype) + end + end + LowStorageRK2NCache(u, uprev, k, tmp, tab, williamson_condition, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::NDBLSRK124, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + NDBLSRK124ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function NDBLSRK134ConstantCache(T, T2) + A2 = convert(T, -0.6160178650170565) + A3 = convert(T, -0.4449487060774118) + A4 = convert(T, -1.0952033345276178) + A5 = convert(T, -1.2256030785959187) + A6 = convert(T, -0.2740182222332805) + A7 = convert(T, -0.0411952089052647) + A8 = convert(T, -0.1797084899153560) + A9 = convert(T, -1.1771530652064288) + A10 = convert(T, -0.4078831463120878) + A11 = convert(T, -0.8295636426191777) + A12 = convert(T, -4.7895970584252288) + A13 = convert(T, -0.6606671432964504) + A2end = SVector(A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12, A13) + + B1 = convert(T, 0.0271990297818803) + B2 = convert(T, 0.1772488819905108) + B3 = convert(T, 0.0378528418949694) + B4 = convert(T, 0.6086431830142991) + B5 = convert(T, 0.2154313974316100) + B6 = convert(T, 0.2066152563885843) + B7 = convert(T, 0.0415864076069797) + B8 = convert(T, 0.0219891884310925) + B9 = convert(T, 0.9893081222650993) + B10 = convert(T, 0.0063199019859826) + B11 = convert(T, 0.3749640721105318) + B12 = convert(T, 1.6080235151003195) + B13 = convert(T, 0.0961209123818189) + B2end = SVector(B2, B3, B4, B5, B6, B7, B8, B9, B10, B11, B12, B13) + + c2 = convert(T2, 0.0271990297818803) + c3 = convert(T2, 0.0952594339119365) + c4 = convert(T2, 0.1266450286591127) + c5 = convert(T2, 0.1825883045699772) + c6 = convert(T2, 0.3737511439063931) + c7 = convert(T2, 0.5301279418422206) + c8 = convert(T2, 0.5704177433952291) + c9 = convert(T2, 0.5885784947099155) + c10 = convert(T2, 0.6160769826246714) + c11 = convert(T2, 0.6223252334314046) + c12 = convert(T2, 0.6897593128753419) + c13 = convert(T2, 0.9126827615920843) + c2end = SVector(c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13) + + LowStorageRK2NConstantCache{12, T, T2}(A2end, B1, B2end, c2end) +end + +function alg_cache(alg::NDBLSRK134, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tab = NDBLSRK134ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + tmp = zero(u) + williamson_condition = alg.williamson_condition + if calck + k = zero(rate_prototype) + williamson_condition = false + else + if williamson_condition + k = tmp + else + k = zero(rate_prototype) + end + end + LowStorageRK2NCache(u, uprev, k, tmp, tab, williamson_condition, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::NDBLSRK134, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + NDBLSRK134ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function NDBLSRK144ConstantCache(T, T2) + A2 = convert(T, -0.7188012108672410) + A3 = convert(T, -0.7785331173421570) + A4 = convert(T, -0.0053282796654044) + A5 = convert(T, -0.8552979934029281) + A6 = convert(T, -3.9564138245774565) + A7 = convert(T, -1.5780575380587385) + A8 = convert(T, -2.0837094552574054) + A9 = convert(T, -0.7483334182761610) + A10 = convert(T, -0.7032861106563359) + A11 = convert(T, 0.0013917096117681) + A12 = convert(T, -0.0932075369637460) + A13 = convert(T, -0.9514200470875948) + A14 = convert(T, -7.1151571693922548) + A2end = SVector(A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12, A13, A14) + + B1 = convert(T, 0.0367762454319673) + B2 = convert(T, 0.3136296607553959) + B3 = convert(T, 0.1531848691869027) + B4 = convert(T, 0.0030097086818182) + B5 = convert(T, 0.3326293790646110) + B6 = convert(T, 0.2440251405350864) + B7 = convert(T, 0.3718879239592277) + B8 = convert(T, 0.6204126221582444) + B9 = convert(T, 0.1524043173028741) + B10 = convert(T, 0.0760894927419266) + B11 = convert(T, 0.0077604214040978) + B12 = convert(T, 0.0024647284755382) + B13 = convert(T, 0.0780348340049386) + B14 = convert(T, 5.5059777270269628) + B2end = SVector(B2, B3, B4, B5, B6, B7, B8, B9, B10, B11, B12, B13, B14) + + c2 = convert(T2, 0.0367762454319673) + c3 = convert(T2, 0.1249685262725025) + c4 = convert(T2, 0.2446177702277698) + c5 = convert(T2, 0.2476149531070420) + c6 = convert(T2, 0.2969311120382472) + c7 = convert(T2, 0.3978149645802642) + c8 = convert(T2, 0.5270854589440328) + c9 = convert(T2, 0.6981269994175695) + c10 = convert(T2, 0.8190890835352128) + c11 = convert(T2, 0.8527059887098624) + c12 = convert(T2, 0.8604711817462826) + c13 = convert(T2, 0.8627060376969976) + c14 = convert(T2, 0.8734213127600976) + c2end = SVector(c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14) + + LowStorageRK2NConstantCache{13, T, T2}(A2end, B1, B2end, c2end) +end + +function alg_cache(alg::NDBLSRK144, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tab = NDBLSRK144ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + tmp = zero(u) + williamson_condition = alg.williamson_condition + if calck + k = zero(rate_prototype) + williamson_condition = false + else + if williamson_condition + k = tmp + else + k = zero(rate_prototype) + end + end + LowStorageRK2NCache(u, uprev, k, tmp, tab, williamson_condition, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::NDBLSRK144, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + NDBLSRK144ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +# 2C low storage methods introduced by Calvo, Franco, Rández (2004) +@cache struct LowStorageRK2CCache{uType, rateType, TabType, StageLimiter, StepLimiter, + Thread} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + tmp::uType + fsalfirst::rateType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct LowStorageRK2CConstantCache{N, T, T2} <: OrdinaryDiffEqConstantCache + A2end::SVector{N, T} # A1 is always zero + B1::T + B2end::SVector{N, T} + c2end::SVector{N, T2} # c1 is always zero +end + +function CFRLDDRK64ConstantCache(T, T2) + A2 = convert(T, 0.17985400977138) + A3 = convert(T, 0.14081893152111) + A4 = convert(T, 0.08255631629428) + A5 = convert(T, 0.65804425034331) + A6 = convert(T, 0.31862993413251) + A2end = SVector(A2, A3, A4, A5, A6) + + B1 = convert(T, 0.10893125722541) + B2 = convert(T, 0.13201701492152) + B3 = convert(T, 0.38911623225517) + B4 = convert(T, -0.59203884581148) + B5 = convert(T, 0.47385028714844) + B6 = convert(T, 0.48812405426094) + B2end = SVector(B2, B3, B4, B5, B6) + + c2 = convert(T2, 0.28878526699679) + c3 = convert(T2, 0.38176720366804) + c4 = convert(T2, 0.71262082069639) + c5 = convert(T2, 0.69606990893393) + c6 = convert(T2, 0.83050587987157) + c2end = SVector(c2, c3, c4, c5, c6) + + LowStorageRK2CConstantCache{5, T, T2}(A2end, B1, B2end, c2end) +end + +function alg_cache(alg::CFRLDDRK64, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = CFRLDDRK64ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK2CCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::CFRLDDRK64, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + CFRLDDRK64ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function TSLDDRK74ConstantCache(T, T2) + A2 = convert(T, 0.241566650129646868) + A3 = convert(T, 0.0423866513027719953) + A4 = convert(T, 0.215602732678803776) + A5 = convert(T, 0.232328007537583987) + A6 = convert(T, 0.256223412574146438) + A7 = convert(T, 0.0978694102142697230) + A2end = SVector(A2, A3, A4, A5, A6, A7) + + B1 = convert(T, 0.0941840925477795334) + B2 = convert(T, 0.149683694803496998) + B3 = convert(T, 0.285204742060440058) + B4 = convert(T, -0.122201846148053668) + B5 = convert(T, 0.0605151571191401122) + B6 = convert(T, 0.345986987898399296) + B7 = convert(T, 0.186627171718797670) + B2end = SVector(B2, B3, B4, B5, B6, B7) + + c2 = convert(T2, 0.335750742677426401) + c3 = convert(T2, 0.286254438654048527) + c4 = convert(T2, 0.744675262090520366) + c5 = convert(T2, 0.639198690801246909) + c6 = convert(T2, 0.723609252956949472) + c7 = convert(T2, 0.91124223849547205) + c2end = SVector(c2, c3, c4, c5, c6, c7) + + LowStorageRK2CConstantCache{6, T, T2}(A2end, B1, B2end, c2end) +end + +function alg_cache(alg::TSLDDRK74, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = TSLDDRK74ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + LowStorageRK2CCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::TSLDDRK74, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + TSLDDRK74ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +# 3S low storage methods introduced by Ketcheson +@cache struct LowStorageRK3SCache{uType, rateType, TabType, StageLimiter, StepLimiter, + Thread} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + tmp::uType + fsalfirst::rateType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct LowStorageRK3SConstantCache{N, T, T2} <: OrdinaryDiffEqConstantCache + γ12end::SVector{N, T} # γ11 is always zero + γ22end::SVector{N, T} # γ21 is always one + γ32end::SVector{N, T} # γ31 is always zero + # TODO: γ302 == γ303 == 0 in all emthods implemented below -> possible optimisation? + δ2end::SVector{N, T} # δ1 is always one + β1::T + β2end::SVector{N, T} + c2end::SVector{N, T2} # c1 is always zero +end + +function ParsaniKetchesonDeconinck3S32ConstantCache(T, T2) + γ102 = convert(T, -1.2664395576322218e-1) + γ103 = convert(T, 1.1426980685848858e+0) + γ12end = SVector(γ102, γ103) + + γ202 = convert(T, 6.5427782599406470e-1) + γ203 = convert(T, -8.2869287683723744e-2) + γ22end = SVector(γ202, γ203) + + γ302 = convert(T, 0.0000000000000000e+0) + γ303 = convert(T, 0.0000000000000000e+0) + γ32end = SVector(γ302, γ303) + + δ02 = convert(T, 7.2196567116037724e-1) + δ03 = convert(T, 0.0000000000000000e+0) + δ2end = SVector(δ02, δ03) + + β1 = convert(T, 7.2366074728360086e-1) + β02 = convert(T, 3.4217876502651023e-1) + β03 = convert(T, 3.6640216242653251e-1) + β2end = SVector(β02, β03) + + c02 = convert(T2, 7.2366074728360086e-1) + c03 = convert(T2, 5.9236433182015646e-1) + c2end = SVector(c02, c03) + + LowStorageRK3SConstantCache{2, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end) +end + +function alg_cache(alg::ParsaniKetchesonDeconinck3S32, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = ParsaniKetchesonDeconinck3S32ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK3SCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::ParsaniKetchesonDeconinck3S32, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + ParsaniKetchesonDeconinck3S32ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) +end + +function ParsaniKetchesonDeconinck3S82ConstantCache(T, T2) + γ102 = convert(T, 4.2397552118208004e-1) + γ103 = convert(T, -2.3528852074619033e-1) + γ104 = convert(T, 7.9598685017877846e-1) + γ105 = convert(T, -1.3205224623823271e+0) + γ106 = convert(T, 2.1452956294251941e+0) + γ107 = convert(T, -9.5532770501880648e-1) + γ108 = convert(T, 2.5361391125131094e-1) + γ12end = SVector(γ102, γ103, γ104, γ105, γ106, γ107, γ108) + + γ202 = convert(T, 4.4390665802303775e-1) + γ203 = convert(T, 7.5333732286056154e-1) + γ204 = convert(T, 6.5885460813015481e-2) + γ205 = convert(T, 6.3976199384289623e-1) + γ206 = convert(T, -7.3823030755143193e-1) + γ207 = convert(T, 7.0177211879534529e-1) + γ208 = convert(T, 4.0185379950224559e-1) + γ22end = SVector(γ202, γ203, γ204, γ205, γ206, γ207, γ208) + + γ302 = convert(T, 0.0000000000000000e+0) + γ303 = convert(T, 0.0000000000000000e+0) + γ304 = convert(T, 5.8415358412023582e-2) + γ305 = convert(T, 6.4219008773865116e-1) + γ306 = convert(T, 6.8770305706885126e-1) + γ307 = convert(T, 6.3729822311671305e-2) + γ308 = convert(T, -3.3679429978131387e-1) + γ32end = SVector(γ302, γ303, γ304, γ305, γ306, γ307, γ308) + + δ02 = convert(T, 2.9762522910396538e-1) + δ03 = convert(T, 3.4212961014330662e-1) + δ04 = convert(T, 5.7010739154759105e-1) + δ05 = convert(T, 4.1350769551529132e-1) + δ06 = convert(T, -1.4040672669058066e-1) + δ07 = convert(T, 2.1249567092409008e-1) + δ08 = convert(T, 0.0000000000000000e+0) + δ2end = SVector(δ02, δ03, δ04, δ05, δ06, δ07, δ08) + + β1 = convert(T, 9.9292229393265474e-1) + β02 = convert(T, 5.2108385130005974e-1) + β03 = convert(T, 3.8505327083543915e-3) + β04 = convert(T, 7.9714199213087467e-1) + β05 = convert(T, -8.1822460276649120e-2) + β06 = convert(T, 8.4604310411858186e-1) + β07 = convert(T, -1.0191166090841246e-1) + β08 = convert(T, 6.3190236038107500e-2) + β2end = SVector(β02, β03, β04, β05, β06, β07, β08) + + c02 = convert(T2, 9.9292229393265474e-1) + c03 = convert(T2, 1.0732413280565014e+0) + c04 = convert(T2, 2.5057060509809409e-1) + c05 = convert(T2, 1.0496674928979783e+0) + c06 = convert(T2, -6.7488037049720317e-1) + c07 = convert(T2, -1.5868411612120166e+0) + c08 = convert(T2, 2.1138242369563969e+0) + c2end = SVector(c02, c03, c04, c05, c06, c07, c08) + + LowStorageRK3SConstantCache{7, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end) +end + +function alg_cache(alg::ParsaniKetchesonDeconinck3S82, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = ParsaniKetchesonDeconinck3S82ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK3SCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::ParsaniKetchesonDeconinck3S82, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + ParsaniKetchesonDeconinck3S82ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) +end + +function ParsaniKetchesonDeconinck3S53ConstantCache(T, T2) + γ102 = convert(T, 2.5876919610938998e-1) + γ103 = convert(T, -1.3243708384977859e-1) + γ104 = convert(T, 5.0556648948362981e-2) + γ105 = convert(T, 5.6705507883024708e-1) + γ12end = SVector(γ102, γ103, γ104, γ105) + + γ202 = convert(T, 5.5284013909611196e-1) + γ203 = convert(T, 6.7318513326032769e-1) + γ204 = convert(T, 2.8031054965521607e-1) + γ205 = convert(T, 5.5215115815918758e-1) + γ22end = SVector(γ202, γ203, γ204, γ205) + + γ302 = convert(T, 0.0000000000000000e+0) + γ303 = convert(T, 0.0000000000000000e+0) + γ304 = convert(T, 2.7525797946334213e-1) + γ305 = convert(T, -8.9505445022148511e-1) + γ32end = SVector(γ302, γ303, γ304, γ305) + + δ02 = convert(T, 3.4076878915216791e-1) + δ03 = convert(T, 3.4143871647890728e-1) + δ04 = convert(T, 7.2292984084963252e-1) + δ05 = convert(T, 0.0000000000000000e+0) + δ2end = SVector(δ02, δ03, δ04, δ05) + + β1 = convert(T, 2.3002859824852059e-1) + β02 = convert(T, 3.0214498165167158e-1) + β03 = convert(T, 8.0256010238856679e-1) + β04 = convert(T, 4.3621618871511753e-1) + β05 = convert(T, 1.1292705979513513e-1) + β2end = SVector(β02, β03, β04, β05) + + c02 = convert(T2, 2.3002859824852059e-1) + c03 = convert(T2, 4.0500453764839639e-1) + c04 = convert(T2, 8.9478204142351003e-1) + c05 = convert(T2, 7.2351146275625733e-1) + c2end = SVector(c02, c03, c04, c05) + + LowStorageRK3SConstantCache{4, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end) +end + +function alg_cache(alg::ParsaniKetchesonDeconinck3S53, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = ParsaniKetchesonDeconinck3S53ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK3SCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::ParsaniKetchesonDeconinck3S53, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + ParsaniKetchesonDeconinck3S53ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) +end + +function ParsaniKetchesonDeconinck3S173ConstantCache(T, T2) + γ102 = convert(T, 7.9377023961829174e-1) + γ103 = convert(T, -8.3475116244241754e-2) + γ104 = convert(T, -1.6706337980062214e-2) + γ105 = convert(T, 3.6410691500331427e-1) + γ106 = convert(T, 6.9178255181542780e-1) + γ107 = convert(T, 1.4887115004739182e+0) + γ108 = convert(T, 4.5336125560871188e-1) + γ109 = convert(T, -1.2705776046458739e-1) + γ110 = convert(T, 8.3749845457747696e-1) + γ111 = convert(T, 1.5709218393361746e-1) + γ112 = convert(T, -5.7768207086288348e-1) + γ113 = convert(T, -5.7340394122375393e-1) + γ114 = convert(T, -1.2050734846514470e+0) + γ115 = convert(T, -2.8100719513641002e+0) + γ116 = convert(T, 1.6142798657609492e-1) + γ117 = convert(T, -2.5801264756641613e+0) + γ12end = SVector( + γ102, γ103, γ104, γ105, γ106, γ107, γ108, γ109, γ110, γ111, γ112, γ113, + γ114, γ115, γ116, γ117) + + γ202 = convert(T, 3.2857861940811250e-1) + γ203 = convert(T, 1.1276843361180819e+0) + γ204 = convert(T, 1.3149447395238016e+0) + γ205 = convert(T, 5.2062891534209055e-1) + γ206 = convert(T, 8.8127462325164985e-1) + γ207 = convert(T, 4.2020606445856712e-1) + γ208 = convert(T, 7.6532635739246124e-2) + γ209 = convert(T, 4.4386734924685722e-1) + γ210 = convert(T, 6.6503093955199682e-2) + γ211 = convert(T, 1.5850209163184039e+0) + γ212 = convert(T, 1.1521721573462576e+0) + γ213 = convert(T, 1.1172750819374575e+0) + γ214 = convert(T, 7.7630223917584007e-1) + γ215 = convert(T, 1.0046657060652295e+0) + γ216 = convert(T, -1.9795868964959054e-1) + γ217 = convert(T, 1.3350583594705518e+0) + γ22end = SVector( + γ202, γ203, γ204, γ205, γ206, γ207, γ208, γ209, γ210, γ211, γ212, γ213, + γ214, γ215, γ216, γ217) + + γ302 = convert(T, 0.0000000000000000e+0) + γ303 = convert(T, 0.0000000000000000e+0) + γ304 = convert(T, 8.4034574578399479e-1) + γ305 = convert(T, 8.5047738439705145e-1) + γ306 = convert(T, 1.4082448501410852e-1) + γ307 = convert(T, -3.2678802469519369e-1) + γ308 = convert(T, 5.3716357620635535e-1) + γ309 = convert(T, 9.0228922115199051e-1) + γ310 = convert(T, 1.5960226946983552e-1) + γ311 = convert(T, 1.1038153140686748e+0) + γ312 = convert(T, 1.0843516423068365e-1) + γ313 = convert(T, 4.6212710442787724e-1) + γ314 = convert(T, -3.3448312125108398e-1) + γ315 = convert(T, 1.1153826567096696e+0) + γ316 = convert(T, 1.5503248734613539e+0) + γ317 = convert(T, -1.2200245424704212e+0) + γ32end = SVector( + γ302, γ303, γ304, γ305, γ306, γ307, γ308, γ309, γ310, γ311, γ312, γ313, + γ314, γ315, γ316, γ317) + + δ02 = convert(T, -3.7235794357769936e-1) + δ03 = convert(T, 3.3315440189685536e-1) + δ04 = convert(T, -8.2667630338402520e-1) + δ05 = convert(T, -5.4628377681035534e-1) + δ06 = convert(T, 6.0210777634642887e-1) + δ07 = convert(T, -5.7528717894031067e-1) + δ08 = convert(T, 5.0914861529202782e-1) + δ09 = convert(T, 3.8258114767897194e-1) + δ10 = convert(T, -4.6279063221185290e-1) + δ11 = convert(T, -2.0820434288562648e-1) + δ12 = convert(T, 1.4398056081552713e+0) + δ13 = convert(T, -2.8056600927348752e-1) + δ14 = convert(T, 2.2767189929551406e+0) + δ15 = convert(T, -5.8917530100546356e-1) + δ16 = convert(T, 9.1328651048418164e-1) + δ17 = convert(T, 0.0000000000000000e+0) + δ2end = SVector(δ02, δ03, δ04, δ05, δ06, δ07, δ08, δ09, δ10, δ11, δ12, δ13, δ14, δ15, + δ16, δ17) + + β1 = convert(T, 4.9565403010221741e-2) + β02 = convert(T, 9.7408718698159397e-2) + β03 = convert(T, -1.7620737976801870e-1) + β04 = convert(T, 1.4852069175460250e-1) + β05 = convert(T, -3.3127657103714951e-2) + β06 = convert(T, 4.8294609330498492e-2) + β07 = convert(T, 4.9622612199980112e-2) + β08 = convert(T, 8.7340766269850378e-1) + β09 = convert(T, -2.8692804399085370e-1) + β10 = convert(T, 1.2679897532256112e+0) + β11 = convert(T, -1.0217436118953449e-2) + β12 = convert(T, 8.4665570032598350e-2) + β13 = convert(T, 2.8253854742588246e-2) + β14 = convert(T, -9.2936733010804407e-2) + β15 = convert(T, -8.4798124766803512e-2) + β16 = convert(T, -1.6923145636158564e-2) + β17 = convert(T, -4.7305106233879957e-2) + β2end = SVector(β02, β03, β04, β05, β06, β07, β08, β09, β10, β11, β12, β13, β14, β15, + β16, β17) + + c02 = convert(T2, 4.9565403010221741e-2) + c03 = convert(T2, 1.3068799001687578e-1) + c04 = convert(T2, -1.5883063460310493e-1) + c05 = convert(T2, 3.5681144740196935e-1) + c06 = convert(T2, 7.6727123317642698e-2) + c07 = convert(T2, 1.0812579255374613e-1) + c08 = convert(T2, 1.8767228084815801e-1) + c09 = convert(T2, 9.6162976936182631e-1) + c10 = convert(T2, -2.2760719867560897e-1) + c11 = convert(T2, 1.1115681606027146e+0) + c12 = convert(T2, 6.1266845427676520e-1) + c13 = convert(T2, 1.0729473245077408e+0) + c14 = convert(T2, 3.7824186468104548e-1) + c15 = convert(T2, 7.9041891347646720e-1) + c16 = convert(T2, -1.0406955693161675e+0) + c17 = convert(T2, -2.4607146824557105e-1) + c2end = SVector(c02, c03, c04, c05, c06, c07, c08, c09, c10, c11, c12, c13, c14, c15, + c16, c17) + + LowStorageRK3SConstantCache{16, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end) +end + +function alg_cache(alg::ParsaniKetchesonDeconinck3S173, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = ParsaniKetchesonDeconinck3S173ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK3SCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::ParsaniKetchesonDeconinck3S173, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + ParsaniKetchesonDeconinck3S173ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) +end + +function ParsaniKetchesonDeconinck3S94ConstantCache(T, T2) + γ102 = convert(T, -4.6556413837561301e+0) + γ103 = convert(T, -7.7202649689034453e-1) + γ104 = convert(T, -4.0244202720632174e+0) + γ105 = convert(T, -2.1296873883702272e-2) + γ106 = convert(T, -2.4350219407769953e+0) + γ107 = convert(T, 1.9856336960249132e-2) + γ108 = convert(T, -2.8107894116913812e-1) + γ109 = convert(T, 1.6894354373677900e-1) + γ12end = SVector(γ102, γ103, γ104, γ105, γ106, γ107, γ108, γ109) + + γ202 = convert(T, 2.4992627683300688e+0) + γ203 = convert(T, 5.8668202764174726e-1) + γ204 = convert(T, 1.2051419816240785e+0) + γ205 = convert(T, 3.4747937498564541e-1) + γ206 = convert(T, 1.3213458736302766e+0) + γ207 = convert(T, 3.1196363453264964e-1) + γ208 = convert(T, 4.3514189245414447e-1) + γ209 = convert(T, 2.3596980658341213e-1) + γ22end = SVector(γ202, γ203, γ204, γ205, γ206, γ207, γ208, γ209) + + γ302 = convert(T, 0.0000000000000000e+0) + γ303 = convert(T, 0.0000000000000000e+0) + γ304 = convert(T, 7.6209857891449362e-1) + γ305 = convert(T, -1.9811817832965520e-1) + γ306 = convert(T, -6.2289587091629484e-1) + γ307 = convert(T, -3.7522475499063573e-1) + γ308 = convert(T, -3.3554373281046146e-1) + γ309 = convert(T, -4.5609629702116454e-2) + γ32end = SVector(γ302, γ303, γ304, γ305, γ306, γ307, γ308, γ309) + + δ02 = convert(T, 1.2629238731608268e+0) + δ03 = convert(T, 7.5749675232391733e-1) + δ04 = convert(T, 5.1635907196195419e-1) + δ05 = convert(T, -2.7463346616574083e-2) + δ06 = convert(T, -4.3826743572318672e-1) + δ07 = convert(T, 1.2735870231839268e+0) + δ08 = convert(T, -6.2947382217730230e-1) + δ09 = convert(T, 0.0000000000000000e+0) + δ2end = SVector(δ02, δ03, δ04, δ05, δ06, δ07, δ08, δ09) + + β1 = convert(T, 2.8363432481011769e-1) + β02 = convert(T, 9.7364980747486463e-1) + β03 = convert(T, 3.3823592364196498e-1) + β04 = convert(T, -3.5849518935750763e-1) + β05 = convert(T, -4.1139587569859462e-3) + β06 = convert(T, 1.4279689871485013e+0) + β07 = convert(T, 1.8084680519536503e-2) + β08 = convert(T, 1.6057708856060501e-1) + β09 = convert(T, 2.9522267863254809e-1) + β2end = SVector(β02, β03, β04, β05, β06, β07, β08, β09) + + c02 = convert(T2, 2.8363432481011769e-1) + c03 = convert(T2, 5.4840742446661772e-1) + c04 = convert(T2, 3.6872298094969475e-1) + c05 = convert(T2, -6.8061183026103156e-1) + c06 = convert(T2, 3.5185265855105619e-1) + c07 = convert(T2, 1.6659419385562171e+0) + c08 = convert(T2, 9.7152778807463247e-1) + c09 = convert(T2, 9.0515694340066954e-1) + c2end = SVector(c02, c03, c04, c05, c06, c07, c08, c09) + + LowStorageRK3SConstantCache{8, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end) +end + +function alg_cache(alg::ParsaniKetchesonDeconinck3S94, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = ParsaniKetchesonDeconinck3S94ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK3SCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::ParsaniKetchesonDeconinck3S94, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + ParsaniKetchesonDeconinck3S94ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) +end + +function ParsaniKetchesonDeconinck3S184ConstantCache(T, T2) + γ102 = convert(T, 1.1750819811951678e+0) + γ103 = convert(T, 3.0909017892654811e-1) + γ104 = convert(T, 1.4409117788115862e+0) + γ105 = convert(T, -4.3563049445694069e-1) + γ106 = convert(T, 2.0341503014683893e-1) + γ107 = convert(T, 4.9828356971917692e-1) + γ108 = convert(T, 3.5307737157745489e+0) + γ109 = convert(T, -7.9318790975894626e-1) + γ110 = convert(T, 8.9120513355345166e-1) + γ111 = convert(T, 5.7091009196320974e-1) + γ112 = convert(T, 1.6912188575015419e-2) + γ113 = convert(T, 1.0077912519329719e+0) + γ114 = convert(T, -6.8532953752099512e-1) + γ115 = convert(T, 1.0488165551884063e+0) + γ116 = convert(T, 8.3647761371829943e-1) + γ117 = convert(T, 1.3087909830445710e+0) + γ118 = convert(T, 9.0419681700177323e-1) + γ12end = SVector( + γ102, γ103, γ104, γ105, γ106, γ107, γ108, γ109, γ110, γ111, γ112, γ113, + γ114, γ115, γ116, γ117, γ118) + + γ202 = convert(T, -1.2891068509748144e-1) + γ203 = convert(T, 3.5609406666728954e-1) + γ204 = convert(T, -4.0648075226104241e-1) + γ205 = convert(T, 6.0714786995207426e-1) + γ206 = convert(T, 1.0253501186236846e+0) + γ207 = convert(T, 2.4411240760769423e-1) + γ208 = convert(T, -1.2813606970134104e+0) + γ209 = convert(T, 8.1625711892373898e-1) + γ210 = convert(T, 1.0171269354643386e-1) + γ211 = convert(T, 1.9379378662711269e-1) + γ212 = convert(T, 7.4408643544851782e-1) + γ213 = convert(T, -1.2591764563430008e-1) + γ214 = convert(T, 1.1996463179654226e+0) + γ215 = convert(T, 4.5772068865370406e-2) + γ216 = convert(T, 8.3622292077033844e-1) + γ217 = convert(T, -1.4179124272450148e+0) + γ218 = convert(T, 1.3661459065331649e-1) + γ22end = SVector( + γ202, γ203, γ204, γ205, γ206, γ207, γ208, γ209, γ210, γ211, γ212, γ213, + γ214, γ215, γ216, γ217, γ218) + + γ302 = convert(T, 0.0000000000000000e+0) + γ303 = convert(T, 0.0000000000000000e+0) + γ304 = convert(T, 2.5583378537249163e-1) + γ305 = convert(T, 5.2676794366988289e-1) + γ306 = convert(T, -2.5648375621792202e-1) + γ307 = convert(T, 3.1932438003236391e-1) + γ308 = convert(T, -3.1106815010852862e-1) + γ309 = convert(T, 4.7631196164025996e-1) + γ310 = convert(T, -9.8853727938895783e-2) + γ311 = convert(T, 1.9274726276883622e-1) + γ312 = convert(T, 3.2389860855971508e-2) + γ313 = convert(T, 7.5923980038397509e-2) + γ314 = convert(T, 2.0635456088664017e-1) + γ315 = convert(T, -8.9741032556032857e-2) + γ316 = convert(T, 2.6899932505676190e-2) + γ317 = convert(T, 4.1882069379552307e-2) + γ318 = convert(T, 6.2016148912381761e-2) + γ32end = SVector( + γ302, γ303, γ304, γ305, γ306, γ307, γ308, γ309, γ310, γ311, γ312, γ313, + γ314, γ315, γ316, γ317, γ318) + + δ02 = convert(T, 3.5816500441970289e-1) + δ03 = convert(T, 5.8208024465093577e-1) + δ04 = convert(T, -2.2615285894283538e-1) + δ05 = convert(T, -2.1715466578266213e-1) + δ06 = convert(T, -4.6990441450888265e-1) + δ07 = convert(T, -2.7986911594744995e-1) + δ08 = convert(T, 9.8513926355272197e-1) + δ09 = convert(T, -1.1899324232814899e-1) + δ10 = convert(T, 4.2821073124370562e-1) + δ11 = convert(T, -8.2196355299900403e-1) + δ12 = convert(T, 5.8113997057675074e-2) + δ13 = convert(T, -6.1283024325436919e-1) + δ14 = convert(T, 5.6800136190634054e-1) + δ15 = convert(T, -3.3874970570335106e-1) + δ16 = convert(T, -7.3071238125137772e-1) + δ17 = convert(T, 8.3936016960374532e-2) + δ18 = convert(T, 0.0000000000000000e+0) + δ2end = SVector(δ02, δ03, δ04, δ05, δ06, δ07, δ08, δ09, δ10, δ11, δ12, δ13, δ14, δ15, + δ16, δ17, δ18) + + β1 = convert(T, 1.2384169480626298e-1) + β02 = convert(T, 1.0176262534280349e+0) + β03 = convert(T, -6.9732026387527429e-2) + β04 = convert(T, 3.4239356067806476e-1) + β05 = convert(T, 1.8177707207807942e-2) + β06 = convert(T, -6.1188746289480445e-3) + β07 = convert(T, 7.8242308902580354e-2) + β08 = convert(T, -3.7642864750532951e-1) + β09 = convert(T, -4.5078383666690258e-2) + β10 = convert(T, -7.5734228201432585e-1) + β11 = convert(T, -2.7149222760935121e-1) + β12 = convert(T, 1.1833684341657344e-3) + β13 = convert(T, 2.8858319979308041e-2) + β14 = convert(T, 4.6005267586974657e-1) + β15 = convert(T, 1.8014887068775631e-2) + β16 = convert(T, -1.5508175395461857e-2) + β17 = convert(T, -4.0095737929274988e-1) + β18 = convert(T, 1.4949678367038011e-1) + β2end = SVector(β02, β03, β04, β05, β06, β07, β08, β09, β10, β11, β12, β13, β14, β15, + β16, β17, β18) + + c02 = convert(T2, 1.2384169480626298e-1) + c03 = convert(T2, 1.1574324659554065e+0) + c04 = convert(T2, 5.4372099141546926e-1) + c05 = convert(T2, 8.8394666834280744e-1) + c06 = convert(T2, -1.2212042176605774e-1) + c07 = convert(T2, 4.4125685133082082e-1) + c08 = convert(T2, 3.8039092095473748e-1) + c09 = convert(T2, 5.4591107347528367e-2) + c10 = convert(T2, 4.8731855535356028e-1) + c11 = convert(T2, -2.3007964303896034e-1) + c12 = convert(T2, -1.8907656662915873e-1) + c13 = convert(T2, 8.1059805668623763e-1) + c14 = convert(T2, 7.7080875997868803e-1) + c15 = convert(T2, 1.1712158507200179e+0) + c16 = convert(T2, 1.2755351018003545e+0) + c17 = convert(T2, 8.0422507946168564e-1) + c18 = convert(T2, 9.7508680250761848e-1) + c2end = SVector(c02, c03, c04, c05, c06, c07, c08, c09, c10, c11, c12, c13, c14, c15, + c16, c17, c18) + + LowStorageRK3SConstantCache{17, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end) +end + +function alg_cache(alg::ParsaniKetchesonDeconinck3S184, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = ParsaniKetchesonDeconinck3S184ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK3SCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::ParsaniKetchesonDeconinck3S184, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + ParsaniKetchesonDeconinck3S184ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) +end + +function ParsaniKetchesonDeconinck3S105ConstantCache(T, T2) + γ102 = convert(T, 4.0436600785287713e-1) + γ103 = convert(T, -8.5034274641295027e-1) + γ104 = convert(T, -6.9508941671218478e+0) + γ105 = convert(T, 9.2387652252320684e-1) + γ106 = convert(T, -2.5631780399589106e+0) + γ107 = convert(T, 2.5457448699988827e-1) + γ108 = convert(T, 3.1258317336761454e-1) + γ109 = convert(T, -7.0071148003175443e-1) + γ110 = convert(T, 4.8396209710057070e-1) + γ12end = SVector(γ102, γ103, γ104, γ105, γ106, γ107, γ108, γ109, γ110) + + γ202 = convert(T, 6.8714670697294733e-1) + γ203 = convert(T, 1.0930247604585732e+0) + γ204 = convert(T, 3.2259753823377983e+0) + γ205 = convert(T, 1.0411537008416110e+0) + γ206 = convert(T, 1.2928214888638039e+0) + γ207 = convert(T, 7.3914627692888835e-1) + γ208 = convert(T, 1.2391292570651462e-1) + γ209 = convert(T, 1.8427534793568445e-1) + γ210 = convert(T, 5.7127889427161162e-2) + γ22end = SVector(γ202, γ203, γ204, γ205, γ206, γ207, γ208, γ209, γ210) + + γ302 = convert(T, 0.0000000000000000e+0) + γ303 = convert(T, 0.0000000000000000e+0) + γ304 = convert(T, -2.3934051593398129e+0) + γ305 = convert(T, -1.9028544220991284e+0) + γ306 = convert(T, -2.8200422105835639e+0) + γ307 = convert(T, -1.8326984641282289e+0) + γ308 = convert(T, -2.1990945108072310e-1) + γ309 = convert(T, -4.0824306603783045e-1) + γ310 = convert(T, -1.3776697911236280e-1) + γ32end = SVector(γ302, γ303, γ304, γ305, γ306, γ307, γ308, γ309, γ310) + + δ02 = convert(T, -1.3317784091400336e-1) + δ03 = convert(T, 8.2604227852898304e-1) + δ04 = convert(T, 1.5137004305165804e+0) + δ05 = convert(T, -1.3058100631721905e+0) + δ06 = convert(T, 3.0366787893355149e+0) + δ07 = convert(T, -1.4494582670831953e+0) + δ08 = convert(T, 3.8343138733685103e+0) + δ09 = convert(T, 4.1222939718018692e+0) + δ10 = convert(T, 0.0000000000000000e+0) + δ2end = SVector(δ02, δ03, δ04, δ05, δ06, δ07, δ08, δ09, δ10) + + β1 = convert(T, 2.5978835757039448e-1) + β02 = convert(T, 1.7770088002098183e-2) + β03 = convert(T, 2.4816366373161344e-1) + β04 = convert(T, 7.9417368275785671e-1) + β05 = convert(T, 3.8853912968701337e-1) + β06 = convert(T, 1.4550516642704694e-1) + β07 = convert(T, 1.5875173794655811e-1) + β08 = convert(T, 1.6506056315937651e-1) + β09 = convert(T, 2.1180932999328042e-1) + β10 = convert(T, 1.5593923403495016e-1) + β2end = SVector(β02, β03, β04, β05, β06, β07, β08, β09, β10) + + c02 = convert(T2, 2.5978835757039448e-1) + c03 = convert(T2, 9.9045731158085557e-2) + c04 = convert(T2, 2.1555118823045644e-1) + c05 = convert(T2, 5.0079500784155040e-1) + c06 = convert(T2, 5.5922519148547800e-1) + c07 = convert(T2, 5.4499869734044426e-1) + c08 = convert(T2, 7.6152246625852738e-1) + c09 = convert(T2, 8.4270620830633836e-1) + c10 = convert(T2, 9.1522098071770008e-1) + c2end = SVector(c02, c03, c04, c05, c06, c07, c08, c09, c10) + + LowStorageRK3SConstantCache{9, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end) +end + +function alg_cache(alg::ParsaniKetchesonDeconinck3S105, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = ParsaniKetchesonDeconinck3S105ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK3SCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::ParsaniKetchesonDeconinck3S105, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + ParsaniKetchesonDeconinck3S105ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) +end + +function ParsaniKetchesonDeconinck3S205ConstantCache(T, T2) + γ102 = convert(T, -1.1682479703229380e+0) + γ103 = convert(T, -2.5112155037089772e+0) + γ104 = convert(T, -5.5259960154735988e-1) + γ105 = convert(T, 2.9243033509511740e-3) + γ106 = convert(T, -4.7948973385386493e+0) + γ107 = convert(T, -5.3095533497183016e+0) + γ108 = convert(T, -2.3624194456630736e+0) + γ109 = convert(T, 2.0068995756589547e-1) + γ110 = convert(T, -1.4985808661597710e+0) + γ111 = convert(T, 4.8941228502377687e-1) + γ112 = convert(T, -1.0387512755259576e-1) + γ113 = convert(T, -1.3287664273288191e-1) + γ114 = convert(T, 7.5858678822837511e-1) + γ115 = convert(T, -4.3321586294096939e+0) + γ116 = convert(T, 4.8199700138402146e-1) + γ117 = convert(T, -7.0924756614960671e-3) + γ118 = convert(T, -8.8422252029506054e-1) + γ119 = convert(T, -8.9129367099545231e-1) + γ120 = convert(T, 1.5297157134040762e+0) + γ12end = SVector( + γ102, γ103, γ104, γ105, γ106, γ107, γ108, γ109, γ110, γ111, γ112, γ113, + γ114, γ115, γ116, γ117, γ118, γ119, γ120) + + γ202 = convert(T, 8.8952052154583572e-1) + γ203 = convert(T, 8.8988129100385194e-1) + γ204 = convert(T, 3.5701564494677057e-1) + γ205 = convert(T, 2.4232462479216824e-1) + γ206 = convert(T, 1.2727083024258155e+0) + γ207 = convert(T, 1.1126977210342681e+0) + γ208 = convert(T, 5.1360709645409097e-1) + γ209 = convert(T, 1.1181089682044856e-1) + γ210 = convert(T, 2.7881272382085232e-1) + γ211 = convert(T, 4.9032886260666715e-2) + γ212 = convert(T, 4.1871051065897870e-2) + γ213 = convert(T, 4.4602463796686219e-2) + γ214 = convert(T, 1.4897271251154750e-2) + γ215 = convert(T, 2.6244269699436817e-1) + γ216 = convert(T, -4.7486056986590294e-3) + γ217 = convert(T, 2.3219312682036197e-2) + γ218 = convert(T, 6.2852588972458059e-2) + γ219 = convert(T, 5.4473719351268962e-2) + γ220 = convert(T, 2.4345446089014514e-2) + γ22end = SVector( + γ202, γ203, γ204, γ205, γ206, γ207, γ208, γ209, γ210, γ211, γ212, γ213, + γ214, γ215, γ216, γ217, γ218, γ219, γ220) + + γ302 = convert(T, 0.0000000000000000e+0) + γ303 = convert(T, 0.0000000000000000e+0) + γ304 = convert(T, 1.9595487007932735e-1) + γ305 = convert(T, -6.9871675039100595e-5) + γ306 = convert(T, 1.0592231169810050e-1) + γ307 = convert(T, 1.0730426871909635e+0) + γ308 = convert(T, 8.9257826744389124e-1) + γ309 = convert(T, -1.4078912484894415e-1) + γ310 = convert(T, -2.6869890558434262e-1) + γ311 = convert(T, -6.5175753568318007e-2) + γ312 = convert(T, 4.9177812903108553e-1) + γ313 = convert(T, 4.6017684776493678e-1) + γ314 = convert(T, -6.4689512947008251e-3) + γ315 = convert(T, 4.4034728024115377e-1) + γ316 = convert(T, 6.1086885767527943e-1) + γ317 = convert(T, 5.0546454457410162e-1) + γ318 = convert(T, 5.4668509293072887e-1) + γ319 = convert(T, 7.1414182420995431e-1) + γ320 = convert(T, -1.0558095282893749e+0) + γ32end = SVector( + γ302, γ303, γ304, γ305, γ306, γ307, γ308, γ309, γ310, γ311, γ312, γ313, + γ314, γ315, γ316, γ317, γ318, γ319, γ320) + + δ02 = convert(T, 1.4375468781258596e+0) + δ03 = convert(T, 1.5081653637261594e+0) + δ04 = convert(T, -1.4575347066062688e-1) + δ05 = convert(T, 3.1495761082838158e-1) + δ06 = convert(T, 3.5505919368536931e-1) + δ07 = convert(T, 2.3616389374566960e-1) + δ08 = convert(T, 1.0267488547302055e-1) + δ09 = convert(T, 3.5991243524519438e+0) + δ10 = convert(T, 1.5172890003890782e+0) + δ11 = convert(T, 1.8171662741779953e+0) + δ12 = convert(T, 2.8762263521436831e+0) + δ13 = convert(T, 4.6350154228218754e-1) + δ14 = convert(T, 1.5573122110727220e+0) + δ15 = convert(T, 2.0001066778080254e+0) + δ16 = convert(T, 9.1690694855534305e-1) + δ17 = convert(T, 2.0474618401365854e+0) + δ18 = convert(T, -3.2336329115436924e-1) + δ19 = convert(T, 3.2899060754742177e-1) + δ20 = convert(T, 0.0000000000000000e+0) + δ2end = SVector(δ02, δ03, δ04, δ05, δ06, δ07, δ08, δ09, δ10, δ11, δ12, δ13, δ14, δ15, + δ16, δ17, δ18, δ19, δ20) + + β1 = convert(T, 1.7342385375780556e-1) + β02 = convert(T, 2.8569004728564801e-1) + β03 = convert(T, 6.8727044379779589e-1) + β04 = convert(T, 1.2812121060977319e-1) + β05 = convert(T, 4.9137180740403122e-4) + β06 = convert(T, 4.7033584446956857e-2) + β07 = convert(T, 4.4539998128170821e-1) + β08 = convert(T, 1.2259824887343720e+0) + β09 = convert(T, 2.0616463985024421e-2) + β10 = convert(T, 1.5941162575324802e-1) + β11 = convert(T, 1.2953803678226099e+0) + β12 = convert(T, 1.7287352967302603e-3) + β13 = convert(T, 1.1660483420536467e-1) + β14 = convert(T, 7.7997036621815521e-2) + β15 = convert(T, 3.2563250234418012e-1) + β16 = convert(T, 1.0611520488333197e+0) + β17 = convert(T, 6.5891625628040993e-4) + β18 = convert(T, 8.3534647700054046e-2) + β19 = convert(T, 9.8972579458252483e-2) + β20 = convert(T, 4.3010116145097040e-2) + β2end = SVector(β02, β03, β04, β05, β06, β07, β08, β09, β10, β11, β12, β13, β14, β15, + β16, β17, β18, β19, β20) + + c02 = convert(T2, 1.7342385375780556e-1) + c03 = convert(T2, 3.0484982420032158e-1) + c04 = convert(T2, 5.5271395645729193e-1) + c05 = convert(T2, 4.7079204549750037e-2) + c06 = convert(T2, 1.5652540451324129e-1) + c07 = convert(T2, 1.8602224049074517e-1) + c08 = convert(T2, 2.8426620035751449e-1) + c09 = convert(T2, 9.5094727548792268e-1) + c10 = convert(T2, 6.8046501070096010e-1) + c11 = convert(T2, 5.9705366562360063e-1) + c12 = convert(T2, 1.8970821645077285e+0) + c13 = convert(T2, 2.9742664004529606e-1) + c14 = convert(T2, 6.0813463700134940e-1) + c15 = convert(T2, 7.3080004188477765e-1) + c16 = convert(T2, 9.1656999044951792e-1) + c17 = convert(T2, 1.4309687554614530e+0) + c18 = convert(T2, 4.1043824968249148e-1) + c19 = convert(T2, 8.4898255952298962e-1) + c20 = convert(T2, 3.3543896258348421e-1) + c2end = SVector(c02, c03, c04, c05, c06, c07, c08, c09, c10, c11, c12, c13, c14, c15, + c16, c17, c18, c19, c20) + + LowStorageRK3SConstantCache{19, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end) +end + +function alg_cache(alg::ParsaniKetchesonDeconinck3S205, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = ParsaniKetchesonDeconinck3S205ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK3SCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::ParsaniKetchesonDeconinck3S205, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + ParsaniKetchesonDeconinck3S205ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) +end + +# 3S+ low storage methods: 3S methods adding another memory location for the embedded method (non-FSAL version) +# ## References +# - Ranocha, Dalcin, Parsani, Ketcheson (2021) +# Optimized Runge-Kutta Methods with Automatic Step Size Control for +# Compressible Computational Fluid Dynamics +# [arXiv:2104.06836](https://arxiv.org/abs/2104.06836) +@cache struct LowStorageRK3SpCache{uType, rateType, uNoUnitsType, TabType, StageLimiter, + StepLimiter, Thread} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + k::rateType + utilde::uType + tmp::uType + atmp::uNoUnitsType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct LowStorageRK3SpConstantCache{N, T, T2} <: OrdinaryDiffEqConstantCache + γ12end::SVector{N, T} # γ11 is always zero + γ22end::SVector{N, T} # γ21 is always one + γ32end::SVector{N, T} # γ31 is always zero + # TODO: γ302 == γ303 == 0 in all emthods implemented below -> possible optimization? + δ2end::SVector{N, T} # δ1 is always one + β1::T + β2end::SVector{N, T} + c2end::SVector{N, T2} # c1 is always zero + bhat1::T + bhat2end::SVector{N, T} +end + +function RDPK3Sp35ConstantCache(T, T2) + γ12end = SVector(convert(T, big"2.587669070352079020144955303389306026e-01"), + convert(T, big"-1.324366873994502973977035353758550057e-01"), + convert(T, big"5.055601231460399101814291350373559483e-02"), + convert(T, big"5.670552807902877312521811889846000976e-01")) + + γ22end = SVector(convert(T, big"5.528418745102160639901976698795928733e-01"), + convert(T, big"6.731844400389673824374042790213570079e-01"), + convert(T, big"2.803103804507635075215805236096803381e-01"), + convert(T, big"5.521508873507393276457754945308880998e-01")) + + γ32end = SVector(convert(T, big"0.000000000000000000000000000000000000e+00"), + convert(T, big"0.000000000000000000000000000000000000e+00"), + convert(T, big"2.752585813446636957256614568573008811e-01"), + convert(T, big"-8.950548709279785077579454232514633376e-01")) + + δ2end = SVector(convert(T, big"3.407687209321455242558804921815861422e-01"), + convert(T, big"3.414399280584625023244387687873774697e-01"), + convert(T, big"7.229302732875589702087936723400941329e-01"), + convert(T, big"0.000000000000000000000000000000000000e+00")) + + β1 = convert(T, big"2.300285062878154351930669430512780706e-01") + β2end = SVector(convert(T, big"3.021457892454169700189445968126242994e-01"), + convert(T, big"8.025601039472704213300183888573974531e-01"), + convert(T, big"4.362158997637629844305216319994356355e-01"), + convert(T, big"1.129268494470295369172265188216779157e-01")) + + c2end = SVector(convert(T, big"2.300285062878154351930669430512780706e-01"), + convert(T, big"4.050049049262914975700372321130661410e-01"), + convert(T, big"8.947823877926760224705450466361360720e-01"), + convert(T, big"7.235108137218888081489570284485201518e-01")) + + # difference of the usual bhat coefficients and the main b coefficients + bhat1 = convert(T, + big"1.046363371354093758897668305991705199e-01" + - + big"1.147931563369900682037379182772608287e-01") + bhat2end = SVector( + convert(T, + big"9.520431574956758809511173383346476348e-02" + - + big"8.933559295232859013880114997436974196e-02"), + convert(T, + big"4.482446645568668405072421350300379357e-01" + - + big"4.355858717379231779899161991033964256e-01"), + convert(T, + big"2.449030295461310135957132640369862245e-01" + - + big"2.473585295257286267503182138232950881e-01"), + convert(T, + big"1.070116530120251819121660365003405564e-01" + - + big"1.129268494470295369172265188216779157e-01")) + + LowStorageRK3SpConstantCache{4, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end, + bhat1, bhat2end) +end + +function alg_cache(alg::RDPK3Sp35, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + k = zero(rate_prototype) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + utilde = zero(u) + tmp = zero(u) + if eltype(u) === uEltypeNoUnits + atmp = utilde # alias the vectors to save memory + else + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + end + tab = RDPK3Sp35ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + LowStorageRK3SpCache( + u, uprev, fsalfirst, k, utilde, tmp, atmp, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::RDPK3Sp35, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + RDPK3Sp35ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function RDPK3Sp49ConstantCache(T, T2) + γ12end = SVector(convert(T, big"-4.655641301259180308677051498071354582e+00"), + convert(T, big"-7.720264924836063859141482018013692338e-01"), + convert(T, big"-4.024423213419724605695005429153112050e+00"), + convert(T, big"-2.129685246739018613087466942802498152e-02"), + convert(T, big"-2.435022519234470128602335652131234586e+00"), + convert(T, big"1.985627480986167686791439120784668251e-02"), + convert(T, big"-2.810790112885283952929218377438668784e-01"), + convert(T, big"1.689434895835535695524003319503844110e-01")) + + γ22end = SVector(convert(T, big"2.499262752607825957145627300817258023e+00"), + convert(T, big"5.866820365436136799319929406678132638e-01"), + convert(T, big"1.205141365412670762568835277881144391e+00"), + convert(T, big"3.474793796700868848597960521248007941e-01"), + convert(T, big"1.321346140128723105871355808477092220e+00"), + convert(T, big"3.119636324379370564023292317172847140e-01"), + convert(T, big"4.351419055894087609560896967082486864e-01"), + convert(T, big"2.359698299440788299161958168555704234e-01")) + + γ32end = SVector(convert(T, big"0.000000000000000000000000000000000000e+00"), + convert(T, big"0.000000000000000000000000000000000000e+00"), + convert(T, big"7.621037111138170045618771082985664430e-01"), + convert(T, big"-1.981182159087218433914909510116664154e-01"), + convert(T, big"-6.228960706317566993192689455719570179e-01"), + convert(T, big"-3.752246993432626328289874575355102038e-01"), + convert(T, big"-3.355436539000946543242869676125143358e-01"), + convert(T, big"-4.560963110717484359015342341157302403e-02")) + + δ2end = SVector(convert(T, big"1.262923854387806460989545005598562667e+00"), + convert(T, big"7.574967177560872438940839460448329992e-01"), + convert(T, big"5.163591158111222863455531895152351544e-01"), + convert(T, big"-2.746333792042827389548936599648122146e-02"), + convert(T, big"-4.382674653941770848797864513655752318e-01"), + convert(T, big"1.273587103668392811985704533534301656e+00"), + convert(T, big"-6.294740045442794829622796613103492913e-01"), + convert(T, big"0.000000000000000000000000000000000000e+00")) + + β1 = convert(T, big"2.836343531977826022543660465926414772e-01") + β2end = SVector(convert(T, big"9.736497978646965372894268287659773644e-01"), + convert(T, big"3.382358566377620380505126936670933370e-01"), + convert(T, big"-3.584937820217850715182820651063453804e-01"), + convert(T, big"-4.113955814725134294322006403954822487e-03"), + convert(T, big"1.427968962196019024010757034274849198e+00"), + convert(T, big"1.808467712038743032991177525728915926e-02"), + convert(T, big"1.605771316794521018947553625079465692e-01"), + convert(T, big"2.952226811394310028003810072027839487e-01")) + + c2end = SVector(convert(T, big"2.836343531977826022543660465926414772e-01"), + convert(T, big"5.484073767552486705240014599676811834e-01"), + convert(T, big"3.687229456675706936558667052479014150e-01"), + convert(T, big"-6.806119916032093175251948474173648331e-01"), + convert(T, big"3.518526451892056368706593492732753284e-01"), + convert(T, big"1.665941920204672094647868254892387293e+00"), + convert(T, big"9.715276989307335935187466054546761665e-01"), + convert(T, big"9.051569554420045339601721625247585643e-01")) + + # difference of the usual bhat coefficients and the main b coefficients + bhat1 = convert(T, + big"4.550655927970944948340364817140593012e-02" + - + big"4.503731969165884304041981629148469971e-02") + bhat2end = SVector( + convert(T, + big"1.175968310492638562142460384341959193e-01" + - + big"1.859217322011968812563859888433403777e-01"), + convert(T, + big"3.658257330515213200375475084421083608e-02" + - + big"3.329727509207630932171676116314110008e-02"), + convert(T, + big"-5.311555834355629559010061596928357525e-03" + - + big"-4.784222621050198909820741390895649698e-03"), + convert(T, + big"5.178250012713127329531367677410650996e-03" + - + big"4.055848062637567925908043629915811671e-03"), + convert(T, + big"4.954639022118682638697706200022961443e-01" + - + big"4.185027999682794463309031355073933444e-01"), + convert(T, + big"-5.999303132737865921441409466809521699e-03" + - + big"-4.381894507474277848407591859322000026e-03"), + convert(T, + big"9.405093434568315929035250835218733824e-02" + - + big"2.712846097324442608251358061215836749e-02"), + convert(T, + big"2.169318087627035072893925375820310602e-01" + - + big"2.952226811394310028003810072027839487e-01")) + + LowStorageRK3SpConstantCache{8, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end, + bhat1, bhat2end) +end + +function alg_cache(alg::RDPK3Sp49, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + k = zero(rate_prototype) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + utilde = zero(u) + tmp = zero(u) + if eltype(u) === uEltypeNoUnits + atmp = utilde # alias the vectors to save memory + else + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + end + tab = RDPK3Sp49ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + LowStorageRK3SpCache( + u, uprev, fsalfirst, k, utilde, tmp, atmp, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::RDPK3Sp49, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + RDPK3Sp49ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function RDPK3Sp510ConstantCache(T, T2) + γ12end = SVector(convert(T, big"4.043660078504695837542588769963326988e-01"), + convert(T, big"-8.503427464263185087039788184485627962e-01"), + convert(T, big"-6.950894167072419998080989313353063399e+00"), + convert(T, big"9.238765225328278557805080247596562995e-01"), + convert(T, big"-2.563178039957404359875124580586147888e+00"), + convert(T, big"2.545744869966347362604059848503340890e-01"), + convert(T, big"3.125831733863168874151935287174374515e-01"), + convert(T, big"-7.007114800567584871263283872289072079e-01"), + convert(T, big"4.839620970980726631935174740648996010e-01")) + + γ22end = SVector(convert(T, big"6.871467069752345566001768382316915820e-01"), + convert(T, big"1.093024760468898686510433898645775908e+00"), + convert(T, big"3.225975382330161123625348062949430509e+00"), + convert(T, big"1.041153700841396427100436517666787823e+00"), + convert(T, big"1.292821488864702752767390075072674807e+00"), + convert(T, big"7.391462769297006312785029455392854586e-01"), + convert(T, big"1.239129257039300081860496157739352186e-01"), + convert(T, big"1.842753479366766790220633908793933781e-01"), + convert(T, big"5.712788942697077644959290025755003720e-02")) + + γ32end = SVector(convert(T, big"0.000000000000000000000000000000000000e+00"), + convert(T, big"0.000000000000000000000000000000000000e+00"), + convert(T, big"-2.393405159342139386425044844626597490e+00"), + convert(T, big"-1.902854422095986544338294743445530533e+00"), + convert(T, big"-2.820042210583207174321941694153843259e+00"), + convert(T, big"-1.832698464130564949123807896975136336e+00"), + convert(T, big"-2.199094510750697865007677774395365522e-01"), + convert(T, big"-4.082430660384876496971887725512427800e-01"), + convert(T, big"-1.377669791121207993339861855818881150e-01")) + + δ2end = SVector(convert(T, big"-1.331778409133849616712007380176762548e-01"), + convert(T, big"8.260422785246030254485064732649153253e-01"), + convert(T, big"1.513700430513332405798616943654007796e+00"), + convert(T, big"-1.305810063177048110528482211982726539e+00"), + convert(T, big"3.036678789342507704281817524408221954e+00"), + convert(T, big"-1.449458267074592489788800461540171106e+00"), + convert(T, big"3.834313873320957483471400258279635203e+00"), + convert(T, big"4.122293971923324492772059928094971199e+00"), + convert(T, big"0.000000000000000000000000000000000000e+00")) + + β1 = convert(T, big"2.597883575710995826783320802193635406e-01") + β2end = SVector(convert(T, big"1.777008800169541694837687556103565007e-02"), + convert(T, big"2.481636637328140606807905234325691851e-01"), + convert(T, big"7.941736827560429420202759490815682546e-01"), + convert(T, big"3.885391296871822541486945325814526190e-01"), + convert(T, big"1.455051664264339366757555740296587660e-01"), + convert(T, big"1.587517379462528932413419955691782412e-01"), + convert(T, big"1.650605631567659573994022720500446501e-01"), + convert(T, big"2.118093299943235065178000892467421832e-01"), + convert(T, big"1.559392340339606299335442956580114440e-01")) + + c2end = SVector(convert(T, big"2.597883575710995826783320802193635406e-01"), + convert(T, big"9.904573115730917688557891428202061598e-02"), + convert(T, big"2.155511882303785204133426661931565216e-01"), + convert(T, big"5.007950078421880417512789524851012021e-01"), + convert(T, big"5.592251914858131230054392022144328176e-01"), + convert(T, big"5.449986973408778242805929551952000165e-01"), + convert(T, big"7.615224662599497796472095353126697300e-01"), + convert(T, big"8.427062083059167761623893618875787414e-01"), + convert(T, big"9.152209807185253394871325258038753352e-01")) + + # difference of the usual bhat coefficients and the main b coefficients + bhat1 = convert(T, + big"5.734588484676193812418453938089759359e-02" + - + big"-2.280102305596364773323878383881954511e-03") + bhat2end = SVector( + convert(T, + big"1.971447518039733870541652912891291496e-02" + - + big"1.407393020823230537861040991952849386e-02"), + convert(T, + big"7.215296605683716720707226840456658773e-02" + - + big"2.332691794172822486743039657924919496e-01"), + convert(T, + big"1.739659489807939956977075317768151880e-01" + - + big"4.808266700465181307162297999657715930e-02"), + convert(T, + big"3.703693600445487815015171515640585668e-01" + - + big"4.119003221139622842134291677033040683e-01"), + convert(T, + big"-1.215599039055065009827765147821222534e-01" + - + big"-1.291461071364752805327361051196128312e-01"), + convert(T, + big"1.180372945491121604465067725859678821e-01" + - + big"1.220746011038579789984601943748468541e-01"), + convert(T, + big"4.155688823364870056536983972605056553e-02" + - + big"4.357858803113387764356338334851554715e-02"), + convert(T, + big"1.227886627910379901351569893551486490e-01" + - + big"1.025076875289905073925255867102192694e-01"), + convert(T, + big"1.456284232223684285998448928597043056e-01" + - + big"1.559392340339606299335442956580114440e-01")) + + LowStorageRK3SpConstantCache{9, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end, + bhat1, bhat2end) +end + +function alg_cache(alg::RDPK3Sp510, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + k = zero(rate_prototype) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + utilde = zero(u) + tmp = zero(u) + if eltype(u) === uEltypeNoUnits + atmp = utilde # alias the vectors to save memory + else + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + end + tab = RDPK3Sp510ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK3SpCache( + u, uprev, fsalfirst, k, utilde, tmp, atmp, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::RDPK3Sp510, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + RDPK3Sp510ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +# 3S+ FSAL low storage methods: 3S methods adding another memory location for the embedded method (FSAL version) +# ## References +# - Ranocha, Dalcin, Parsani, Ketcheson (2021) +# Optimized Runge-Kutta Methods with Automatic Step Size Control for +# Compressible Computational Fluid Dynamics +# [arXiv:2104.06836](https://arxiv.org/abs/2104.06836) +@cache struct LowStorageRK3SpFSALCache{ + uType, rateType, uNoUnitsType, TabType, StageLimiter, + StepLimiter, Thread} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + k::rateType + utilde::uType + tmp::uType + atmp::uNoUnitsType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct LowStorageRK3SpFSALConstantCache{N, T, T2} <: OrdinaryDiffEqConstantCache + γ12end::SVector{N, T} # γ11 is always zero + γ22end::SVector{N, T} # γ21 is always one + γ32end::SVector{N, T} # γ31 is always zero + # TODO: γ302 == γ303 == 0 in all emthods implemented below -> possible optimization? + δ2end::SVector{N, T} # δ1 is always one + β1::T + β2end::SVector{N, T} + c2end::SVector{N, T2} # c1 is always zero + bhat1::T + bhat2end::SVector{N, T} + bhatfsal::T +end + +function RDPK3SpFSAL35ConstantCache(T, T2) + γ12end = SVector(convert(T, big"2.587771979725733308135192812685323706e-01"), + convert(T, big"-1.324380360140723382965420909764953437e-01"), + convert(T, big"5.056033948190826045833606441415585735e-02"), + convert(T, big"5.670532000739313812633197158607642990e-01")) + + γ22end = SVector(convert(T, big"5.528354909301389892439698870483746541e-01"), + convert(T, big"6.731871608203061824849561782794643600e-01"), + convert(T, big"2.803103963297672407841316576323901761e-01"), + convert(T, big"5.521525447020610386070346724931300367e-01")) + + γ32end = SVector(convert(T, big"0.000000000000000000000000000000000000e+00"), + convert(T, big"0.000000000000000000000000000000000000e+00"), + convert(T, big"2.752563273304676380891217287572780582e-01"), + convert(T, big"-8.950526174674033822276061734289327568e-01")) + + δ2end = SVector(convert(T, big"3.407655879334525365094815965895763636e-01"), + convert(T, big"3.414382655003386206551709871126405331e-01"), + convert(T, big"7.229275366787987419692007421895451953e-01"), + convert(T, big"0.000000000000000000000000000000000000e+00")) + + β1 = convert(T, big"2.300298624518076223899418286314123354e-01") + β2end = SVector(convert(T, big"3.021434166948288809034402119555380003e-01"), + convert(T, big"8.025606185416310937583009085873554681e-01"), + convert(T, big"4.362158943603440930655148245148766471e-01"), + convert(T, big"1.129272530455059129782111662594436580e-01")) + + c2end = SVector(convert(T, big"2.300298624518076223899418286314123354e-01"), + convert(T, big"4.050046072094990912268498160116125481e-01"), + convert(T, big"8.947822893693433545220710894560512805e-01"), + convert(T, big"7.235136928826589010272834603680114769e-01")) + + # difference of the usual bhat coefficients and the main b coefficients + bhat1 = convert(T, + big"9.484166705035703392326247283838082847e-02" + - + big"1.147935971023541171733601324486904546e-01") + bhat2end = SVector( + convert(T, + big"1.726371339430353766966762629176676070e-01" + - + big"8.933442853113315592708384523126474636e-02"), + convert(T, + big"3.998243189084371024483169698618455770e-01" + - + big"4.355871025008616992483722693795608738e-01"), + convert(T, + big"1.718016807580178450618829007973835152e-01" + - + big"2.473576188201451146729725866810402672e-01"), + convert(T, + big"5.881914422155740300718268359027168467e-02" + - + big"1.129272530455059129782111662594436580e-01")) + bhatfsal = convert(T, big"1.020760551185952388626787099944507877e-01") + + LowStorageRK3SpFSALConstantCache{4, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, + c2end, bhat1, bhat2end, bhatfsal) +end + +function alg_cache(alg::RDPK3SpFSAL35, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + k = zero(rate_prototype) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + utilde = zero(u) + tmp = zero(u) + if eltype(u) === uEltypeNoUnits + atmp = utilde # alias the vectors to save memory + else + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + end + tab = RDPK3SpFSAL35ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK3SpFSALCache(u, uprev, fsalfirst, k, utilde, tmp, atmp, tab, + alg.stage_limiter!, alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::RDPK3SpFSAL35, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + RDPK3SpFSAL35ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function RDPK3SpFSAL49ConstantCache(T, T2) + γ12end = SVector(convert(T, big"-4.655641447335068552684422206224169103e+00"), + convert(T, big"-7.720265099645871829248487209517314217e-01"), + convert(T, big"-4.024436690519806086742256154738379161e+00"), + convert(T, big"-2.129676284018530966221583708648634733e-02"), + convert(T, big"-2.435022509790109546199372365866450709e+00"), + convert(T, big"1.985627297131987000579523283542615256e-02"), + convert(T, big"-2.810791146791038566946663374735713961e-01"), + convert(T, big"1.689434168754859644351230590422137972e-01")) + + γ22end = SVector(convert(T, big"2.499262792574495009336242992898153462e+00"), + convert(T, big"5.866820377718875577451517985847920081e-01"), + convert(T, big"1.205146086523094569925592464380295241e+00"), + convert(T, big"3.474793722186732780030762737753849272e-01"), + convert(T, big"1.321346060965113109321230804210670518e+00"), + convert(T, big"3.119636464694193615946633676950358444e-01"), + convert(T, big"4.351419539684379261368971206040518552e-01"), + convert(T, big"2.359698130028753572503744518147537768e-01")) + + γ32end = SVector(convert(T, big"0.000000000000000000000000000000000000e+00"), + convert(T, big"0.000000000000000000000000000000000000e+00"), + convert(T, big"7.621006678721315291614677352949377871e-01"), + convert(T, big"-1.981182504339400567765766904309673119e-01"), + convert(T, big"-6.228959218699007450469629366684127462e-01"), + convert(T, big"-3.752248380775956442989480369774937099e-01"), + convert(T, big"-3.355438309135169811915662336248989661e-01"), + convert(T, big"-4.560955005031121479972862973705108039e-02")) + + δ2end = SVector(convert(T, big"1.262923876648114432874834923838556100e+00"), + convert(T, big"7.574967189685911558308119415539596711e-01"), + convert(T, big"5.163589453140728104667573195005629833e-01"), + convert(T, big"-2.746327421802609557034437892013640319e-02"), + convert(T, big"-4.382673178127944142238606608356542890e-01"), + convert(T, big"1.273587294602656522645691372699677063e+00"), + convert(T, big"-6.294740283927400326554066998751383342e-01"), + convert(T, big"0.000000000000000000000000000000000000e+00")) + + β1 = convert(T, big"2.836343005184365275160654678626695428e-01") + β2end = SVector(convert(T, big"9.736500104654741223716056170419660217e-01"), + convert(T, big"3.382359225242515288768487569778320563e-01"), + convert(T, big"-3.584943611106183357043212309791897386e-01"), + convert(T, big"-4.113944068471528211627210454497620358e-03"), + convert(T, big"1.427968894048586363415504654313371031e+00"), + convert(T, big"1.808470948394314017665968411915568633e-02"), + convert(T, big"1.605770645946802213926893453819236685e-01"), + convert(T, big"2.952227015964591648775833803635147962e-01")) + + c2end = SVector(convert(T, big"2.836343005184365275160654678626695428e-01"), + convert(T, big"5.484076570002894365286665352032296535e-01"), + convert(T, big"3.687228761669438493478872632332010073e-01"), + convert(T, big"-6.806126440140844191258463830024463902e-01"), + convert(T, big"3.518526124230705801739919476290327750e-01"), + convert(T, big"1.665941994879593315477304663913129942e+00"), + convert(T, big"9.715279295934715835299192116436237065e-01"), + convert(T, big"9.051569840159589594903399929316959062e-01")) + + # difference of the usual bhat coefficients and the main b coefficients + bhat1 = convert(T, + big"2.483675912451591196775756814283216443e-02" + - + big"4.503732627263753698356970706617404465e-02") + bhat2end = SVector( + convert(T, + big"1.866327774562103796990092260942180726e-01" + - + big"1.859217303699847950262276860012454333e-01"), + convert(T, + big"5.671080795936984495604436622517631183e-02" + - + big"3.329729672569717599759560403851202805e-02"), + convert(T, + big"-3.447695439149287702616943808570747099e-03" + - + big"-4.784204180958975587114459316829942677e-03"), + convert(T, + big"3.602245056516636472203469198006404016e-03" + - + big"4.055835961031310727671557609188874328e-03"), + convert(T, + big"4.545570622145088936800484247980581766e-01" + - + big"4.185027772596074197662616795629003544e-01"), + convert(T, + big"-2.434665289427612407531544765622888855e-04" + - + big"-4.381901968919326084347037216500072323e-03 "), + convert(T, + big"6.642755361103549971517945063138312147e-02" + - + big"2.712843796446089829255188189179448399e-02"), + convert(T, + big"1.613697079523505006226025497715177578e-01" + - + big"2.952227015964591648775833803635147962e-01")) + bhatfsal = convert(T, big"4.955424859358438183052504342394102722e-02") + + LowStorageRK3SpFSALConstantCache{8, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, + c2end, bhat1, bhat2end, bhatfsal) +end + +function alg_cache(alg::RDPK3SpFSAL49, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + k = zero(rate_prototype) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + utilde = zero(u) + tmp = zero(u) + if eltype(u) === uEltypeNoUnits + atmp = utilde # alias the vectors to save memory + else + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + end + tab = RDPK3SpFSAL49ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK3SpFSALCache(u, uprev, fsalfirst, k, utilde, tmp, atmp, tab, + alg.stage_limiter!, alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::RDPK3SpFSAL49, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + RDPK3SpFSAL49ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function RDPK3SpFSAL510ConstantCache(T, T2) + γ12end = SVector(convert(T, big"4.043660121685749695640462197806189975e-01"), + convert(T, big"-8.503427289575839690883191973980814832e-01"), + convert(T, big"-6.950894175262117526410215315179482885e+00"), + convert(T, big"9.238765192731084931855438934978371889e-01"), + convert(T, big"-2.563178056509891340215942413817786020e+00"), + convert(T, big"2.545744879365226143946122067064118430e-01"), + convert(T, big"3.125831707411998258746812355492206137e-01"), + convert(T, big"-7.007114414440507927791249989236719346e-01"), + convert(T, big"4.839621016023833375810172323297465039e-01")) + + γ22end = SVector(convert(T, big"6.871467028161416909922221357014564412e-01"), + convert(T, big"1.093024748914750833700799552463885117e+00"), + convert(T, big"3.225975379607193001678365742708874597e+00"), + convert(T, big"1.041153702510101386914019859778740444e+00"), + convert(T, big"1.292821487912164945157744726076279306e+00"), + convert(T, big"7.391462755788122847651304143259254381e-01"), + convert(T, big"1.239129251371800313941948224441873274e-01"), + convert(T, big"1.842753472370123193132193302369345580e-01"), + convert(T, big"5.712788998796583446479387686662738843e-02")) + + γ32end = SVector(convert(T, big"0.000000000000000000000000000000000000e+00"), + convert(T, big"0.000000000000000000000000000000000000e+00"), + convert(T, big"-2.393405133244194727221124311276648940e+00"), + convert(T, big"-1.902854422421760920850597670305403139e+00"), + convert(T, big"-2.820042207399977261483046412236557428e+00"), + convert(T, big"-1.832698465277380999601896111079977378e+00"), + convert(T, big"-2.199094483084671192328083958346519535e-01"), + convert(T, big"-4.082430635847870963724591602173546218e-01"), + convert(T, big"-1.377669797880289713535665985132703979e-01")) + + δ2end = SVector(convert(T, big"-1.331778419508803397033287009506932673e-01"), + convert(T, big"8.260422814750207498262063505871077303e-01"), + convert(T, big"1.513700425755728332485300719652378197e+00"), + convert(T, big"-1.305810059935023735972298885749903694e+00"), + convert(T, big"3.036678802924163246003321318996156380e+00"), + convert(T, big"-1.449458274398895177922690618003584514e+00"), + convert(T, big"3.834313899176362315089976408899373409e+00"), + convert(T, big"4.122293760012985409330881631526514714e+00"), + convert(T, big"0.000000000000000000000000000000000000e+00")) + + β1 = convert(T, big"2.597883554788674084039539165398464630e-01") + β2end = SVector(convert(T, big"1.777008889438867858759149597539211023e-02"), + convert(T, big"2.481636629715501931294746189266601496e-01"), + convert(T, big"7.941736871152005775821844297293296135e-01"), + convert(T, big"3.885391285642019129575902994397298066e-01"), + convert(T, big"1.455051657916305055730603387469193768e-01"), + convert(T, big"1.587517385964749337690916959584348979e-01"), + convert(T, big"1.650605617880053419242434594242509601e-01"), + convert(T, big"2.118093284937153836908655490906875007e-01"), + convert(T, big"1.559392342362059886106995325687547506e-01")) + + c2end = SVector(convert(T, big"2.597883554788674084039539165398464630e-01"), + convert(T, big"9.904573247592460887087003212056568980e-02"), + convert(T, big"2.155511890524058691860390281856497503e-01"), + convert(T, big"5.007950088969676776844289399972611534e-01"), + convert(T, big"5.592251911688643533787800688765883636e-01"), + convert(T, big"5.449986978853637084972622392134732553e-01"), + convert(T, big"7.615224694532590139829150720490417596e-01"), + convert(T, big"8.427062083267360939805493320684741215e-01"), + convert(T, big"9.152209805057669959657927210873423883e-01")) + + # difference of the usual bhat coefficients and the main b coefficients + bhat1 = convert(T, + big"-2.019255440012066080909442770590267512e-02" + - + big"-2.280100321836980811830528665041532799e-03") + bhat2end = SVector( + convert(T, + big"2.737903480959184339932730854141598275e-02" + - + big"1.407393115790186300730580636032878435e-02"), + convert(T, + big"3.028818636145965534365173822296811090e-01" + - + big"2.332691775508456597719992034291118324e-01"), + convert(T, + big"-3.656843880622222190071445247906780540e-02" + - + big"4.808266741353862546318531020856621860e-02"), + convert(T, + big"3.982664774676767729863101188528827405e-01" + - + big"4.119003217706951892385733111000873172e-01"), + convert(T, + big"-5.715959421140685436681459970502471634e-02" + - + big"-1.291461067807736321056740833501596735e-01"), + convert(T, + big"9.849855103848558320961101178888983150e-02" + - + big"1.220746013848710098878384114422516148e-01"), + convert(T, + big"6.654601552456084978615342374581437947e-02" + - + big"4.357858583174420432201228508067333299e-02"), + convert(T, + big"9.073479542748112726465375642050504556e-02" + - + big"1.025076877568080726158907518254273554e-01"), + convert(T, + big"8.432289325330803924891866923939606351e-02" + - + big"1.559392342362059886106995325687547506e-01")) + bhatfsal = convert(T, big"4.529095628204896774513180907141004447e-02") + + LowStorageRK3SpFSALConstantCache{9, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, + c2end, bhat1, bhat2end, bhatfsal) +end + +function alg_cache(alg::RDPK3SpFSAL510, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + k = zero(rate_prototype) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + utilde = zero(u) + tmp = zero(u) + if eltype(u) === uEltypeNoUnits + atmp = utilde # alias the vectors to save memory + else + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + end + tab = RDPK3SpFSAL510ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK3SpFSALCache(u, uprev, fsalfirst, k, utilde, tmp, atmp, tab, + alg.stage_limiter!, alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::RDPK3SpFSAL510, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + RDPK3SpFSAL510ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +# 2R+ low storage methods introduced by van der Houwen +@cache struct LowStorageRK2RPCache{uType, rateType, uNoUnitsType, TabType, StageLimiter, + StepLimiter, Thread} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + gprev::uType + fsalfirst::rateType + tmp::uType + atmp::uNoUnitsType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct LowStorageRK2RPConstantCache{N, T, T2} <: OrdinaryDiffEqConstantCache + Aᵢ::SVector{N, T} + Bₗ::T + B̂ₗ::T + Bᵢ::SVector{N, T} + B̂ᵢ::SVector{N, T} + Cᵢ::SVector{N, T2} +end + +function CKLLSRK43_2ConstantCache(T, T2) + A1 = convert(T, Int128(11847461282814) // Int128(36547543011857)) + A2 = convert(T, Int128(3943225443063) // Int128(7078155732230)) + A3 = convert(T, Int128(-346793006927) // Int128(4029903576067)) + Aᵢ = SVector(A1, A2, A3) + + B1 = convert(T, Int128(1017324711453) // Int128(9774461848756)) + B2 = convert(T, Int128(8237718856693) // Int128(13685301971492)) + B3 = convert(T, Int128(57731312506979) // Int128(19404895981398)) + Bᵢ = SVector(B1, B2, B3) + + B̂1 = convert(T, Int128(15763415370699) // Int128(46270243929542)) + B̂2 = convert(T, Int128(514528521746) // Int128(5659431552419)) + B̂3 = convert(T, Int128(27030193851939) // Int128(9429696342944)) + B̂ᵢ = SVector(B̂1, B̂2, B̂3) + + Bₗ = convert(T, Int128(-101169746363290) // Int128(37734290219643)) + B̂ₗ = convert(T, Int128(-69544964788955) // Int128(30262026368149)) + + C1 = convert(T2, Int128(11847461282814) // Int128(36547543011857)) # A1 + C2 = convert(T2, Int128(2079258608735161403527719) // Int128(3144780143828896577027540)) # A2 + B1 + C3 = convert(T2, + Int128(41775191021672206476512620310545281003) // + Int128(67383242951014563804622635478530729598)) # A3 + B1 + B2 + Cᵢ = SVector(C1, C2, C3) + + LowStorageRK2RPConstantCache{3, T, T2}(Aᵢ, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) +end + +function alg_cache(alg::CKLLSRK43_2, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + k = zero(rate_prototype) + gprev = zero(u) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = CKLLSRK43_2ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK2RPCache(u, uprev, k, gprev, fsalfirst, tmp, atmp, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::CKLLSRK43_2, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + CKLLSRK43_2ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function CKLLSRK54_3CConstantCache(T, T2) + A1 = convert(T, BigInt(970286171893) // BigInt(4311952581923)) + A2 = convert(T, BigInt(6584761158862) // BigInt(12103376702013)) + A3 = convert(T, BigInt(2251764453980) // BigInt(15575788980749)) + A4 = convert(T, BigInt(26877169314380) // BigInt(34165994151039)) + Aᵢ = SVector(A1, A2, A3, A4) + + B1 = convert(T, BigInt(1153189308089) // BigInt(22510343858157)) + B2 = convert(T, BigInt(1772645290293) // BigInt(4653164025191)) + B3 = convert(T, BigInt(-1672844663538) // BigInt(4480602732383)) + B4 = convert(T, BigInt(2114624349019) // BigInt(3568978502595)) + Bᵢ = SVector(B1, B2, B3, B4) + + B̂1 = convert(T, BigInt(1016888040809) // BigInt(7410784769900)) + B̂2 = convert(T, BigInt(11231460423587) // BigInt(58533540763752)) + B̂3 = convert(T, BigInt(-1563879915014) // BigInt(6823010717585)) + B̂4 = convert(T, BigInt(606302364029) // BigInt(971179775848)) + B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4) + + Bₗ = convert(T, BigInt(5198255086312) // BigInt(14908931495163)) + B̂ₗ = convert(T, BigInt(1097981568119) // BigInt(3980877426909)) + + C1 = convert(T2, BigInt(970286171893) // BigInt(4311952581923)) # A1 + C2 = convert(T2, + BigInt(18020302501594987297224499) // BigInt(30272352378568762325374449)) # A2 + B1 + C3 = convert(T2, + BigInt(940957347754451928235896289983310398260) // + BigInt(1631475460071027605339136597003329167263)) # A3 + B1 + B2 + C4 = convert(T2, + BigInt(8054848232572758807908657851968985615984276476412066) // + BigInt(8139155613487734148190408375391604039319069461908135)) # A4 + B1 + B2 + B3 + Cᵢ = SVector(C1, C2, C3, C4) + + LowStorageRK2RPConstantCache{4, T, T2}(Aᵢ, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) +end + +function alg_cache(alg::CKLLSRK54_3C, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + k = zero(rate_prototype) + gprev = zero(u) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = CKLLSRK54_3CConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK2RPCache(u, uprev, k, gprev, fsalfirst, tmp, atmp, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::CKLLSRK54_3C, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + CKLLSRK54_3CConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function CKLLSRK95_4SConstantCache(T, T2) + A1 = convert(T, BigInt(1107026461565) // BigInt(5417078080134)) + A2 = convert(T, BigInt(38141181049399) // BigInt(41724347789894)) + A3 = convert(T, BigInt(493273079041) // BigInt(11940823631197)) + A4 = convert(T, BigInt(1851571280403) // BigInt(6147804934346)) + A5 = convert(T, BigInt(11782306865191) // BigInt(62590030070788)) + A6 = convert(T, BigInt(9452544825720) // BigInt(13648368537481)) + A7 = convert(T, BigInt(4435885630781) // BigInt(26285702406235)) + A8 = convert(T, BigInt(2357909744247) // BigInt(11371140753790)) + Aᵢ = SVector(A1, A2, A3, A4, A5, A6, A7, A8) + + B1 = convert(T, BigInt(2274579626619) // BigInt(23610510767302)) + B2 = convert(T, BigInt(693987741272) // BigInt(12394497460941)) + B3 = convert(T, BigInt(-347131529483) // BigInt(15096185902911)) + B4 = convert(T, BigInt(1144057200723) // BigInt(32081666971178)) + B5 = convert(T, BigInt(1562491064753) // BigInt(11797114684756)) + B6 = convert(T, BigInt(13113619727965) // BigInt(44346030145118)) + B7 = convert(T, BigInt(393957816125) // BigInt(7825732611452)) + B8 = convert(T, BigInt(720647959663) // BigInt(6565743875477)) + Bᵢ = SVector(B1, B2, B3, B4, B5, B6, B7, B8) + + B̂1 = convert(T, BigInt(266888888871) // BigInt(3040372307578)) + B̂2 = convert(T, BigInt(34125631160) // BigInt(2973680843661)) + B̂3 = convert(T, BigInt(-653811289250) // BigInt(9267220972999)) + B̂4 = convert(T, BigInt(323544662297) // BigInt(2461529853637)) + B̂5 = convert(T, BigInt(1105885670474) // BigInt(4964345317203)) + B̂6 = convert(T, BigInt(1408484642121) // BigInt(8758221613943)) + B̂7 = convert(T, BigInt(1454774750537) // BigInt(11112645198328)) + B̂8 = convert(T, BigInt(772137014323) // BigInt(4386814405182)) + B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4, B̂5, B̂6, B̂7, B̂8) + + Bₗ = convert(T, BigInt(3559252274877) // BigInt(14424734981077)) + B̂ₗ = convert(T, BigInt(277420604269) // BigInt(1857595682219)) + + C1 = convert(T2, BigInt(1107026461565) // BigInt(5417078080134)) # A1 + C2 = convert(T2, + BigInt(248859529315327119359384971) // BigInt(246283290687986423455311497)) # A2 + B1 + C3 = convert(T2, + BigInt(676645811244741430568548054467096184193) // + BigInt(3494367591912647069105975861901917224854)) # A3 + B1 + B2 + C4 = convert(T2, + BigInt(974370561662349106845723178377944301517533305964589) // + BigInt(2263290880944514209862892217007179742168288737673791)) # A4 + B1 + B2 + B3 + C5 = convert(T2, + BigInt(23738915426186839814576142955255044211724736499516359049188590711) // + BigInt(67203160149331519751012175988216621571869262839903428488408759604)) # A5 + B1 + B2 + B3 + B4 + C6 = convert(T2, + BigInt(1882683585832901544671586749377753597775777511029847145277760106172106584376955) // + BigInt(1901663903553486696887572033100456166564493852721284994300276200102719954709068)) # A6 + B1 + B2 + B3 + B4 + B5 + C7 = convert(T2, + BigInt(61872982955093233917984290421186995265732234396821660871734841970091372539489172106504162637) // + BigInt(81207728164913218881758751120099941603350662788460257311895072645631357391473675997419584220)) # A7 + B1 + B2 + B3 + B4 + B5 + B6 + C8 = convert(T2, + BigInt(197565042693102647130189450792520184956129841555961940530192020871289515369046683661585184411130637357) // + BigInt(232196202198018941876505157326935602816917261769279531369710269478309137067357703513986211472070374865)) # A8 + B1 + B2 + B3 + B4 + B5 + B6 + B7 + Cᵢ = SVector(C1, C2, C3, C4, C5, C6, C7, C8) + + LowStorageRK2RPConstantCache{8, T, T2}(Aᵢ, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) +end + +function alg_cache(alg::CKLLSRK95_4S, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + k = zero(rate_prototype) + gprev = zero(u) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = CKLLSRK95_4SConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK2RPCache(u, uprev, k, gprev, fsalfirst, tmp, atmp, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::CKLLSRK95_4S, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + CKLLSRK95_4SConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function CKLLSRK95_4CConstantCache(T, T2) + A1 = convert(T, BigInt(2756167973529) // BigInt(16886029417639)) + A2 = convert(T, BigInt(11436141375279) // BigInt(13592993952163)) + A3 = convert(T, BigInt(88551658327) // BigInt(2352971381260)) + A4 = convert(T, BigInt(1882111988787) // BigInt(5590444193957)) + A5 = convert(T, BigInt(846820081679) // BigInt(4754706910573)) + A6 = convert(T, BigInt(4475289710031) // BigInt(6420120086209)) + A7 = convert(T, BigInt(118394748311) // BigInt(9144450320350)) + A8 = convert(T, BigInt(3307377157135) // BigInt(13111544596386)) + Aᵢ = SVector(A1, A2, A3, A4, A5, A6, A7, A8) + + B1 = convert(T, BigInt(1051460336009) // BigInt(14326298067773)) + B2 = convert(T, BigInt(930517604889) // BigInt(7067438519321)) + B3 = convert(T, BigInt(-311910530565) // BigInt(11769786407153)) + B4 = convert(T, BigInt(-410144036239) // BigInt(7045999268647)) + B5 = convert(T, BigInt(16692278975653) // BigInt(83604524739127)) + B6 = convert(T, BigInt(3777666801280) // BigInt(13181243438959)) + B7 = convert(T, BigInt(286682614203) // BigInt(12966190094317)) + B8 = convert(T, BigInt(3296161604512) // BigInt(22629905347183)) + Bᵢ = SVector(B1, B2, B3, B4, B5, B6, B7, B8) + + B̂1 = convert(T, BigInt(3189770262221) // BigInt(35077884776239)) + B̂2 = convert(T, BigInt(780043871774) // BigInt(11919681558467)) + B̂3 = convert(T, BigInt(-483824475979) // BigInt(5387739450692)) + B̂4 = convert(T, BigInt(1306553327038) // BigInt(9528955984871)) + B̂5 = convert(T, BigInt(6521106697498) // BigInt(22565577506855)) + B̂6 = convert(T, BigInt(1400555694605) // BigInt(19784728594468)) + B̂7 = convert(T, BigInt(1183541508418) // BigInt(13436305181271)) + B̂8 = convert(T, BigInt(3036254792728) // BigInt(15493572606329)) + B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4, B̂5, B̂6, B̂7, B̂8) + + Bₗ = convert(T, BigInt(2993490409874) // BigInt(13266828321767)) + B̂ₗ = convert(T, BigInt(638483435745) // BigInt(4187244659458)) + + C1 = convert(T2, BigInt(2756167973529) // BigInt(16886029417639)) # A1 + C2 = convert(T2, + BigInt(178130064075748009421121134) // BigInt(194737282992122861693942999)) # A2 + B1 + C3 = convert(T2, + BigInt(57818276708998807530478158133449099851) // + BigInt(238238895426494403638887583424360627580)) # A3 + B1 + B2 + C4 = convert(T2, + BigInt(3432454166457135667348375590572529790194124848059104) // + BigInt(6662096512485931545803670383440459769502981926779993)) # A4 + B1 + B2 + B3 + C5 = convert(T2, + BigInt(11915126765643872062053118401193741919814944004335534493046474237) // + BigInt(39923715169802034300462756237193519081954994679332637422466438119)) # A5 + B1 + B2 + B3 + B4 + C6 = convert(T2, + BigInt(4583883621300589683158355859163890943947800555246686854224916208836514024614442) // + BigInt(4506922925096139856045533451931734406235454975594364558624038359246205017801029)) # A6 + B1 + B2 + B3 + B4 + B5 + C7 = convert(T2, + BigInt(52423219056629312880725209686636192777075511202228566787042655312097949192300218484424118619) // + BigInt(84615702680158836756876794083943762639542619835321175569533203672153042594634924742431352650)) # A7 + B1 + B2 + B3 + B4 + B5 + B6 + C8 = convert(T2, + BigInt(1385843715228499555828057735261132084759031703937678116167963792224108372724503731226480538087331079769069) // + BigInt(1573111845759510782008384284066606688388217112071821912231287750254246452350240904652428530379336814559998)) # A8 + B1 + B2 + B3 + B4 + B5 + B6 + B7 + Cᵢ = SVector(C1, C2, C3, C4, C5, C6, C7, C8) + + LowStorageRK2RPConstantCache{8, T, T2}(Aᵢ, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) +end + +function alg_cache(alg::CKLLSRK95_4C, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + k = zero(rate_prototype) + gprev = zero(u) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = CKLLSRK95_4CConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK2RPCache(u, uprev, k, gprev, fsalfirst, tmp, atmp, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::CKLLSRK95_4C, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + CKLLSRK95_4CConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function CKLLSRK95_4MConstantCache(T, T2) + A1 = convert(T, BigInt(5573095071601) // BigInt(11304125995793)) + A2 = convert(T, BigInt(315581365608) // BigInt(4729744040249)) + A3 = convert(T, BigInt(8734064225157) // BigInt(30508564569118)) + A4 = convert(T, BigInt(6457785058448) // BigInt(14982850401353)) + A5 = convert(T, BigInt(5771559441664) // BigInt(18187997215013)) + A6 = convert(T, BigInt(1906712129266) // BigInt(6681214991155)) + A7 = convert(T, BigInt(311585568784) // BigInt(2369973437185)) + A8 = convert(T, BigInt(-4840285693886) // BigInt(7758383361725)) + Aᵢ = SVector(A1, A2, A3, A4, A5, A6, A7, A8) + + B1 = convert(T, BigInt(549666665015) // BigInt(5899839355879)) + B2 = convert(T, BigInt(-548816778320) // BigInt(9402908589133)) + B3 = convert(T, BigInt(1672704946363) // BigInt(13015471661974)) + B4 = convert(T, BigInt(1025420337373) // BigInt(5970204766762)) + B5 = convert(T, BigInt(1524419752016) // BigInt(6755273790179)) + B6 = convert(T, BigInt(-10259399787359) // BigInt(43440802207630)) + B7 = convert(T, BigInt(4242280279850) // BigInt(10722460893763)) + B8 = convert(T, BigInt(1887552771913) // BigInt(6099058196803)) + Bᵢ = SVector(B1, B2, B3, B4, B5, B6, B7, B8) + + B̂1 = convert(T, BigInt(330911065672) // BigInt(9937126492277)) + B̂2 = convert(T, BigInt(-872991930418) // BigInt(11147305689291)) + B̂3 = convert(T, BigInt(2575378033706) // BigInt(14439313202205)) + B̂4 = convert(T, BigInt(3046892121673) // BigInt(11013392356255)) + B̂5 = convert(T, BigInt(1780184658016) // BigInt(8929499316295)) + B̂6 = convert(T, BigInt(10265149063) // BigInt(2098741126425)) + B̂7 = convert(T, BigInt(1643090076625) // BigInt(4891294770654)) + B̂8 = convert(T, BigInt(116106750067) // BigInt(3955800826265)) + B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4, B̂5, B̂6, B̂7, B̂8) + + Bₗ = convert(T, BigInt(-453873186647) // BigInt(15285235680030)) + B̂ₗ = convert(T, BigInt(866868642257) // BigInt(42331321870877)) + + C1 = convert(T2, BigInt(5573095071601) // BigInt(11304125995793)) + C2 = convert(T2, + BigInt(4461661993774357683398167) // BigInt(27904730031895199210773871)) + C3 = convert(T2, + BigInt(543425730194107827015264404954831354769) // + BigInt(1692482454734045499140692116457071506026)) + C4 = convert(T2, + BigInt(6429586327013850295560537918723231687699697140756067) // + BigInt(10818243561353065593628044468492745774799533452459554)) + C5 = convert(T2, + BigInt(555984804780268998022260997164198311752115182012221553157164786) // + BigInt(852213854337283773231630192518719827415190771786411558523853399)) + C6 = convert(T2, + BigInt(1789345671284476461332539715762783748132668223013904373945129499237446392572) // + BigInt(2114764997945705573761804541148983827155257005191540481884326639410208291635)) + C7 = convert(T2, + BigInt(2972211964132922642906704796208250552795647483819924111704054115070043529037601892705217) // + BigInt(6517454043294174770082798998332814729652497865130816822916618330047242844192616374937270)) + C8 = convert(T2, + BigInt(22038106775746116973750004935225594022265950105933360206617843987546593773108577078867914238620973639) // + BigInt(228770596964454885481304478061363897900267080665965044117230250287302271092811814450282133504194141850)) + Cᵢ = SVector(C1, C2, C3, C4, C5, C6, C7, C8) + + LowStorageRK2RPConstantCache{8, T, T2}(Aᵢ, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) +end + +function alg_cache(alg::CKLLSRK95_4M, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + k = zero(rate_prototype) + gprev = zero(u) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = CKLLSRK95_4MConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK2RPCache(u, uprev, k, gprev, fsalfirst, tmp, atmp, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::CKLLSRK95_4M, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + CKLLSRK95_4MConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +# 3R+ low storage methods introduced by van der Houwen +@cache struct LowStorageRK3RPCache{uType, rateType, uNoUnitsType, TabType, StageLimiter, + StepLimiter, Thread} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + uᵢ₋₁::uType + uᵢ₋₂::uType + fᵢ₋₂::rateType + gprev::uType + fsalfirst::rateType + tmp::uType + atmp::uNoUnitsType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct LowStorageRK3RPConstantCache{N, T, T2} <: OrdinaryDiffEqConstantCache + Aᵢ₁::SVector{N, T} + Aᵢ₂::SVector{N, T} + Bₗ::T + B̂ₗ::T + Bᵢ::SVector{N, T} + B̂ᵢ::SVector{N, T} + Cᵢ::SVector{N, T2} +end + +function CKLLSRK54_3C_3RConstantCache(T, T2) + A₁1 = convert(T, BigInt(2365592473904) // BigInt(8146167614645)) + A₁2 = convert(T, BigInt(4278267785271) // BigInt(6823155464066)) + A₁3 = convert(T, BigInt(2789585899612) // BigInt(8986505720531)) + A₁4 = convert(T, BigInt(15310836689591) // BigInt(24358012670437)) + Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4) + + A₂1 = convert(T, BigInt(0) // BigInt(1)) + A₂2 = convert(T, BigInt(-722262345248) // BigInt(10870640012513)) + A₂3 = convert(T, BigInt(1365858020701) // BigInt(8494387045469)) + A₂4 = convert(T, BigInt(3819021186) // BigInt(2763618202291)) + Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4) + + B1 = convert(T, BigInt(846876320697) // BigInt(6523801458457)) + B2 = convert(T, BigInt(3032295699695) // BigInt(12397907741132)) + B3 = convert(T, BigInt(612618101729) // BigInt(6534652265123)) + B4 = convert(T, BigInt(1155491934595) // BigInt(2954287928812)) + Bᵢ = SVector(B1, B2, B3, B4) + + B̂1 = convert(T, BigInt(1296459667021) // BigInt(9516889378644)) + B̂2 = convert(T, BigInt(2599004989233) // BigInt(11990680747819)) + B̂3 = convert(T, BigInt(1882083615375) // BigInt(8481715831096)) + B̂4 = convert(T, BigInt(1577862909606) // BigInt(5567358792761)) + B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4) + + Bₗ = convert(T, BigInt(707644755468) // BigInt(5028292464395)) + B̂ₗ = convert(T, BigInt(328334985361) // BigInt(2316973589007)) + + C1 = convert(T2, BigInt(2365592473904) // BigInt(8146167614645)) + C2 = convert(T2, + BigInt(41579400703344293287237655) // BigInt(74172066799272566561857858)) + C3 = convert(T2, + BigInt(299308060739053880467044545349561265546) // + BigInt(497993456493513966629488516767096447823)) + C4 = convert(T2, + BigInt(5468330126750791548369684419304733938034170906513585) // + BigInt(5444638279732761024893610553331663911104849888809108)) + Cᵢ = SVector(C1, C2, C3, C4) + + LowStorageRK3RPConstantCache{4, T, T2}(Aᵢ₁, Aᵢ₂, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) +end + +function alg_cache(alg::CKLLSRK54_3C_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + k = zero(rate_prototype) + uᵢ₋₁ = zero(u) + uᵢ₋₂ = zero(u) + fᵢ₋₂ = zero(rate_prototype) + gprev = zero(u) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = CKLLSRK54_3C_3RConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK3RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, fᵢ₋₂, gprev, fsalfirst, tmp, atmp, tab, + alg.stage_limiter!, alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::CKLLSRK54_3C_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + CKLLSRK54_3C_3RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function CKLLSRK54_3M_3RConstantCache(T, T2) + A₁1 = convert(T, BigInt(17396840518954) // BigInt(49788467287365)) + A₁2 = convert(T, BigInt(21253110367599) // BigInt(14558944785238)) + A₁3 = convert(T, BigInt(4293647616769) // BigInt(14519312872408)) + A₁4 = convert(T, BigInt(-8941886866937) // BigInt(7464816931160)) + Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4) + + A₂1 = convert(T, BigInt(0) // BigInt(1)) + A₂2 = convert(T, BigInt(-12587430488023) // BigInt(11977319897242)) + A₂3 = convert(T, BigInt(6191878339181) // BigInt(13848262311063)) + A₂4 = convert(T, BigInt(19121624165801) // BigInt(12321025968027)) + Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4) + + B1 = convert(T, BigInt(1977388745448) // BigInt(17714523675943)) + B2 = convert(T, BigInt(6528140725453) // BigInt(14879534818174)) + B3 = convert(T, BigInt(4395900531415) // BigInt(55649460397719)) + B4 = convert(T, BigInt(6567440254656) // BigInt(15757960182571)) + Bᵢ = SVector(B1, B2, B3, B4) + + B̂1 = convert(T, BigInt(390601394181) // BigInt(3503051559916)) + B̂2 = convert(T, BigInt(31150720071161) // BigInt(68604711794052)) + B̂3 = convert(T, BigInt(416927665232) // BigInt(6953044279741)) + B̂4 = convert(T, BigInt(3879867616328) // BigInt(8869216637007)) + B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4) + + Bₗ = convert(T, BigInt(-436008689643) // BigInt(9453681332953)) + B̂ₗ = convert(T, BigInt(-163749046041) // BigInt(2599987820560)) + + C1 = convert(T2, BigInt(17396840518954) // BigInt(49788467287365)) + C2 = convert(T2, BigInt(2546271293606266795002053) // BigInt(6227754966395669782804057)) + C3 = convert(T2, + BigInt(3043453778831534771251734214272440269577) // + BigInt(3561810617861654942925591050154818470872)) + C4 = convert(T2, + BigInt(10963106193663894855575270257133723083246622141340761) // + BigInt(12121458300971454511596914396147459030814063072954120)) + Cᵢ = SVector(C1, C2, C3, C4) + + LowStorageRK3RPConstantCache{4, T, T2}(Aᵢ₁, Aᵢ₂, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) +end + +function alg_cache(alg::CKLLSRK54_3M_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + k = zero(rate_prototype) + uᵢ₋₁ = zero(u) + uᵢ₋₂ = zero(u) + fᵢ₋₂ = zero(rate_prototype) + gprev = zero(u) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = CKLLSRK54_3M_3RConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK3RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, fᵢ₋₂, gprev, fsalfirst, tmp, atmp, tab, + alg.stage_limiter!, alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::CKLLSRK54_3M_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + CKLLSRK54_3M_3RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function CKLLSRK54_3N_3RConstantCache(T, T2) + A₁1 = convert(T, BigInt(4745337637855) // BigInt(22386579876409)) + A₁2 = convert(T, BigInt(6808157035527) // BigInt(13197844641179)) + A₁3 = convert(T, BigInt(4367509502613) // BigInt(10454198590847)) + A₁4 = convert(T, BigInt(1236962429870) // BigInt(3429868089329)) + Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4) + + A₂1 = convert(T, BigInt(0) // BigInt(1)) + A₂2 = convert(T, BigInt(546509042554) // BigInt(9152262712923)) + A₂3 = convert(T, BigInt(625707605167) // BigInt(5316659119056)) + A₂4 = convert(T, BigInt(582400652113) // BigInt(7078426004906)) + Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4) + + B1 = convert(T, BigInt(314199625218) // BigInt(7198350928319)) + B2 = convert(T, BigInt(6410344372641) // BigInt(17000082738695)) + B3 = convert(T, BigInt(292278564125) // BigInt(5593752632744)) + B4 = convert(T, BigInt(5010207514426) // BigInt(21876007855139)) + Bᵢ = SVector(B1, B2, B3, B4) + + B̂1 = convert(T, BigInt(1276689330531) // BigInt(10575835502045)) + B̂2 = convert(T, BigInt(267542835879) // BigInt(1241767155676)) + B̂3 = convert(T, BigInt(1564039648689) // BigInt(9024646069760)) + B̂4 = convert(T, BigInt(3243722451631) // BigInt(13364844673806)) + B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4) + + Bₗ = convert(T, BigInt(5597675544274) // BigInt(18784428342765)) + B̂ₗ = convert(T, BigInt(606464709716) // BigInt(2447238536635)) + + C1 = convert(T2, BigInt(4745337637855) // BigInt(22386579876409)) + C2 = convert(T2, + BigInt(6320253019873211389522417) // BigInt(10980921945492108365568747)) + C3 = convert(T2, + BigInt(231699760563456147635097088564862719039) // + BigInt(400094496217566390613617613962197753808)) + C4 = convert(T2, + BigInt(2565873674791335200443549967376635530873909687156071) // + BigInt(2970969302106648098855751120425897741072516011514170)) + Cᵢ = SVector(C1, C2, C3, C4) + + LowStorageRK3RPConstantCache{4, T, T2}(Aᵢ₁, Aᵢ₂, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) +end + +function alg_cache(alg::CKLLSRK54_3N_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + k = zero(rate_prototype) + uᵢ₋₁ = zero(u) + uᵢ₋₂ = zero(u) + fᵢ₋₂ = zero(rate_prototype) + gprev = zero(u) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = CKLLSRK54_3N_3RConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK3RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, fᵢ₋₂, gprev, fsalfirst, tmp, atmp, tab, + alg.stage_limiter!, alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::CKLLSRK54_3N_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + CKLLSRK54_3N_3RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function CKLLSRK85_4C_3RConstantCache(T, T2) + A₁1 = convert(T, BigInt(141236061735) // BigInt(3636543850841)) + A₁2 = convert(T, BigInt(7367658691349) // BigInt(25881828075080)) + A₁3 = convert(T, BigInt(6185269491390) // BigInt(13597512850793)) + A₁4 = convert(T, BigInt(2669739616339) // BigInt(18583622645114)) + A₁5 = convert(T, BigInt(42158992267337) // BigInt(9664249073111)) + A₁6 = convert(T, BigInt(970532350048) // BigInt(4459675494195)) + A₁7 = convert(T, BigInt(1415616989537) // BigInt(7108576874996)) + Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4, A₁5, A₁6, A₁7) + + A₂1 = convert(T, BigInt(0) // BigInt(1)) + A₂2 = convert(T, BigInt(-343061178215) // BigInt(2523150225462)) + A₂3 = convert(T, BigInt(-4057757969325) // BigInt(18246604264081)) + A₂4 = convert(T, BigInt(1415180642415) // BigInt(13311741862438)) + A₂5 = convert(T, BigInt(-93461894168145) // BigInt(25333855312294)) + A₂6 = convert(T, BigInt(7285104933991) // BigInt(14106269434317)) + A₂7 = convert(T, BigInt(-4825949463597) // BigInt(16828400578907)) + Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4, A₂5, A₂6, A₂7) + + B1 = convert(T, BigInt(514862045033) // BigInt(4637360145389)) + B2 = convert(T, BigInt(0) // BigInt(1)) + B3 = convert(T, BigInt(0) // BigInt(1)) + B4 = convert(T, BigInt(0) // BigInt(1)) + B5 = convert(T, BigInt(2561084526938) // BigInt(7959061818733)) + B6 = convert(T, BigInt(4857652849) // BigInt(7350455163355)) + B7 = convert(T, BigInt(1059943012790) // BigInt(2822036905401)) + Bᵢ = SVector(B1, B2, B3, B4, B5, B6, B7) + + B̂1 = convert(T, BigInt(1269299456316) // BigInt(16631323494719)) + B̂2 = convert(T, BigInt(0) // BigInt(1)) + B̂3 = convert(T, BigInt(2153976949307) // BigInt(22364028786708)) + B̂4 = convert(T, BigInt(2303038467735) // BigInt(18680122447354)) + B̂5 = convert(T, BigInt(7354111305649) // BigInt(15643939971922)) + B̂6 = convert(T, BigInt(768474111281) // BigInt(10081205039574)) + B̂7 = convert(T, BigInt(3439095334143) // BigInt(10786306938509)) + B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4, B̂5, B̂6, B̂7) + + Bₗ = convert(T, BigInt(2987336121747) // BigInt(15645656703944)) + B̂ₗ = convert(T, BigInt(-3808726110015) // BigInt(23644487528593)) + + C1 = convert(T2, BigInt(141236061735) // BigInt(3636543850841)) + C2 = convert(T2, + BigInt(4855329627204641469273019) // BigInt(32651870171503411731843480)) + C3 = convert(T2, + BigInt(395246570619540395679764439681768625174) // + BigInt(1150568172675067443707820382013045349637)) + C4 = convert(T2, + BigInt(103533040647279909858308372897770021461) // + BigInt(286797987459862321650077169609703051387)) + C5 = convert(T2, + BigInt(890342029406775514852349518244920625309) // + BigInt(1135377348321966192554675673174478190626)) + C6 = convert(T2, + BigInt(82180664649829640456237722943611531408) // + BigInt(97244490215364259564723087293866304345)) + C7 = convert(T2, + BigInt(1524044277359326675923410465291452002169116939509651) // + BigInt(4415279581486844959297591640758696961331751174567964)) + Cᵢ = SVector(C1, C2, C3, C4, C5, C6, C7) + + LowStorageRK3RPConstantCache{7, T, T2}(Aᵢ₁, Aᵢ₂, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) +end + +function alg_cache(alg::CKLLSRK85_4C_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + k = zero(rate_prototype) + uᵢ₋₁ = zero(u) + uᵢ₋₂ = zero(u) + fᵢ₋₂ = zero(rate_prototype) + gprev = zero(u) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = CKLLSRK85_4C_3RConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK3RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, fᵢ₋₂, gprev, fsalfirst, tmp, atmp, tab, + alg.stage_limiter!, alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::CKLLSRK85_4C_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + CKLLSRK85_4C_3RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function CKLLSRK85_4M_3RConstantCache(T, T2) + A₁1 = convert(T, BigInt(967290102210) // BigInt(6283494269639)) + A₁2 = convert(T, BigInt(852959821520) // BigInt(5603806251467)) + A₁3 = convert(T, BigInt(8043261511347) // BigInt(8583649637008)) + A₁4 = convert(T, BigInt(-115941139189) // BigInt(8015933834062)) + A₁5 = convert(T, BigInt(2151445634296) // BigInt(7749920058933)) + A₁6 = convert(T, BigInt(15619711431787) // BigInt(74684159414562)) + A₁7 = convert(T, BigInt(12444295717883) // BigInt(11188327299274)) + Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4, A₁5, A₁6, A₁7) + + A₂1 = convert(T, BigInt(0) // BigInt(1)) + A₂2 = convert(T, BigInt(475331134681) // BigInt(7396070923784)) + A₂3 = convert(T, BigInt(-8677837986029) // BigInt(16519245648862)) + A₂4 = convert(T, BigInt(2224500752467) // BigInt(10812521810777)) + A₂5 = convert(T, BigInt(1245361422071) // BigInt(3717287139065)) + A₂6 = convert(T, BigInt(1652079198131) // BigInt(3788458824028)) + A₂7 = convert(T, BigInt(-5225103653628) // BigInt(8584162722535)) + Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4, A₂5, A₂6, A₂7) + + B1 = convert(T, BigInt(83759458317) // BigInt(1018970565139)) + B2 = convert(T, BigInt(0) // BigInt(1)) + B3 = convert(T, BigInt(0) // BigInt(1)) + B4 = convert(T, BigInt(0) // BigInt(1)) + B5 = convert(T, BigInt(6968891091250) // BigInt(16855527649349)) + B6 = convert(T, BigInt(783521911849) // BigInt(8570887289572)) + B7 = convert(T, BigInt(3686104854613) // BigInt(11232032898210)) + Bᵢ = SVector(B1, B2, B3, B4, B5, B6, B7) + + B̂1 = convert(T, BigInt(-2632078767757) // BigInt(9365288548818)) + B̂2 = convert(T, BigInt(0) // BigInt(1)) + B̂3 = convert(T, BigInt(138832778584802) // BigInt(30360463697573)) + B̂4 = convert(T, BigInt(7424139574315) // BigInt(5603229049946)) + B̂5 = convert(T, BigInt(-32993229351515) // BigInt(6883415042289)) + B̂6 = convert(T, BigInt(-3927384735361) // BigInt(7982454543710)) + B̂7 = convert(T, BigInt(9224293159931) // BigInt(15708162311543)) + B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4, B̂5, B̂6, B̂7) + + Bₗ = convert(T, BigInt(517396786175) // BigInt(6104475356879)) + B̂ₗ = convert(T, BigInt(624338737541) // BigInt(7691046757191)) + + C1 = convert(T2, BigInt(967290102210) // BigInt(6283494269639)) + C2 = convert(T2, + BigInt(8972214919142352493858707) // BigInt(41446148478994088895191128)) + C3 = convert(T2, + BigInt(35682660731882055122214991891899678815) // + BigInt(72242678055272695781813348615158920272)) + C4 = convert(T2, + BigInt(24151963894889409757443700144610337197) // + BigInt(88316684951621554188239538678367088186)) + C5 = convert(T2, + BigInt(20396803294876689925555603189127802602) // + BigInt(29355195069529377650856010387665377655)) + C6 = convert(T2, + BigInt(104860372573190455963699691732496938387) // + BigInt(144152676952392296448858925279884773652)) + C7 = convert(T2, + BigInt(1648260218501227913212294426176971326433416596592133) // + BigInt(1649556119556299790473636959153132604082083356090490)) + Cᵢ = SVector(C1, C2, C3, C4, C5, C6, C7) + + LowStorageRK3RPConstantCache{7, T, T2}(Aᵢ₁, Aᵢ₂, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) +end + +function alg_cache(alg::CKLLSRK85_4M_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + k = zero(rate_prototype) + uᵢ₋₁ = zero(u) + uᵢ₋₂ = zero(u) + fᵢ₋₂ = zero(rate_prototype) + gprev = zero(u) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = CKLLSRK85_4M_3RConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK3RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, fᵢ₋₂, gprev, fsalfirst, tmp, atmp, tab, + alg.stage_limiter!, alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::CKLLSRK85_4M_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + CKLLSRK85_4M_3RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function CKLLSRK85_4P_3RConstantCache(T, T2) + A₁1 = convert(T, BigInt(1298271176151) // BigInt(60748409385661)) + A₁2 = convert(T, BigInt(14078610000243) // BigInt(41877490110127)) + A₁3 = convert(T, BigInt(553998884433) // BigInt(1150223130613)) + A₁4 = convert(T, BigInt(15658478150918) // BigInt(92423611770207)) + A₁5 = convert(T, BigInt(18843935397718) // BigInt(7227975568851)) + A₁6 = convert(T, BigInt(6206560082614) // BigInt(27846110321329)) + A₁7 = convert(T, BigInt(2841125392315) // BigInt(14844217636077)) + Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4, A₁5, A₁6, A₁7) + + A₂1 = convert(T, BigInt(0) // BigInt(1)) + A₂2 = convert(T, BigInt(-2491873887327) // BigInt(11519757507826)) + A₂3 = convert(T, BigInt(-3833614938189) // BigInt(14183712281236)) + A₂4 = convert(T, BigInt(628609886693) // BigInt(8177399110319)) + A₂5 = convert(T, BigInt(-4943723744483) // BigInt(2558074780976)) + A₂6 = convert(T, BigInt(1024000837540) // BigInt(1998038638351)) + A₂7 = convert(T, BigInt(-2492809296391) // BigInt(9064568868273)) + Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4, A₂5, A₂6, A₂7) + + B1 = convert(T, BigInt(346820227625) // BigInt(3124407780749)) + B2 = convert(T, BigInt(0) // BigInt(1)) + B3 = convert(T, BigInt(0) // BigInt(1)) + B4 = convert(T, BigInt(0) // BigInt(1)) + B5 = convert(T, BigInt(814249513470) // BigInt(2521483007009)) + B6 = convert(T, BigInt(195246859987) // BigInt(15831935944600)) + B7 = convert(T, BigInt(3570596951509) // BigInt(9788921605312)) + Bᵢ = SVector(B1, B2, B3, B4, B5, B6, B7) + + B̂1 = convert(T, BigInt(679447319381) // BigInt(8240332772531)) + B̂2 = convert(T, BigInt(0) // BigInt(1)) + B̂3 = convert(T, BigInt(798472430005) // BigInt(13882421602211)) + B̂4 = convert(T, BigInt(972791992243) // BigInt(13597677393897)) + B̂5 = convert(T, BigInt(2994516937385) // BigInt(6097853295694)) + B̂6 = convert(T, BigInt(1424705874463) // BigInt(19211220871144)) + B̂7 = convert(T, BigInt(11199564863291) // BigInt(35136367926059)) + B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4, B̂5, B̂6, B̂7) + + Bₗ = convert(T, BigInt(1886338382073) // BigInt(9981671730680)) + B̂ₗ = convert(T, BigInt(-1307718103703) // BigInt(13694144003901)) + + C1 = convert(T2, BigInt(1298271176151) // BigInt(60748409385661)) + C2 = convert(T2, + BigInt(57828749177833338114741189) // BigInt(482418531105044571804353902)) + C3 = convert(T2, + BigInt(16431909216114342992530887716659137419) // + BigInt(50972944352640941110022041298448213332)) + C4 = convert(T2, + BigInt(843711271601954807241466442429582743082) // + BigInt(2361379786784371499429045948205315798717)) + C5 = convert(T2, + BigInt(45377346645618697840609101263059649515) // + BigInt(57769368855607143441437855651622233424)) + C6 = convert(T2, + BigInt(147132600561369761792017800077859262701) // + BigInt(173834563932749284125206995856250290771)) + C7 = convert(T2, + BigInt(123785620236259768586332555932209432529705897037921) // + BigInt(353351523019265026737831367789312912172448045683187)) + Cᵢ = SVector(C1, C2, C3, C4, C5, C6, C7) + + LowStorageRK3RPConstantCache{7, T, T2}(Aᵢ₁, Aᵢ₂, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) +end + +function alg_cache(alg::CKLLSRK85_4P_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + k = zero(rate_prototype) + uᵢ₋₁ = zero(u) + uᵢ₋₂ = zero(u) + fᵢ₋₂ = zero(rate_prototype) + gprev = zero(u) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = CKLLSRK85_4P_3RConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK3RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, fᵢ₋₂, gprev, fsalfirst, tmp, atmp, tab, + alg.stage_limiter!, alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::CKLLSRK85_4P_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + CKLLSRK85_4P_3RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +# 4R+ low storage methods introduced by van der Houwen +@cache struct LowStorageRK4RPCache{uType, rateType, uNoUnitsType, TabType, StageLimiter, + StepLimiter, Thread} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + uᵢ₋₁::uType + uᵢ₋₂::uType + uᵢ₋₃::uType + fᵢ₋₂::rateType + fᵢ₋₃::rateType + gprev::uType + fsalfirst::rateType + tmp::uType + atmp::uNoUnitsType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct LowStorageRK4RPConstantCache{N, T, T2} <: OrdinaryDiffEqConstantCache + Aᵢ₁::SVector{N, T} + Aᵢ₂::SVector{N, T} + Aᵢ₃::SVector{N, T} + Bₗ::T + B̂ₗ::T + Bᵢ::SVector{N, T} + B̂ᵢ::SVector{N, T} + Cᵢ::SVector{N, T2} +end + +function CKLLSRK54_3N_4RConstantCache(T, T2) + A₁1 = convert(T, BigInt(9435338793489) // BigInt(32856462503258)) + A₁2 = convert(T, BigInt(6195609865473) // BigInt(14441396468602)) + A₁3 = convert(T, BigInt(7502925572378) // BigInt(28098850972003)) + A₁4 = convert(T, BigInt(4527781290407) // BigInt(9280887680514)) + Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4) + + A₂1 = convert(T, BigInt(0) // BigInt(1)) + A₂2 = convert(T, BigInt(2934593324920) // BigInt(16923654741811)) + A₂3 = convert(T, BigInt(16352725096886) // BigInt(101421723321009)) + A₂4 = convert(T, BigInt(3004243580591) // BigInt(16385320447374)) + Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4) + + A₃1 = convert(T, BigInt(0) // BigInt(1)) + A₃2 = convert(T, BigInt(0) // BigInt(1)) + A₃3 = convert(T, BigInt(390352446067) // BigInt(5989890148791)) + A₃4 = convert(T, BigInt(902830387041) // BigInt(8154716972155)) + Aᵢ₃ = SVector(A₃1, A₃2, A₃3, A₃4) + + B1 = convert(T, BigInt(929310922418) // BigInt(8329727308495)) + B2 = convert(T, BigInt(4343420149496) // BigInt(15735497610667)) + B3 = convert(T, BigInt(885252399220) // BigInt(9490460854667)) + B4 = convert(T, BigInt(3341719902227) // BigInt(13464012733180)) + Bᵢ = SVector(B1, B2, B3, B4) + + B̂1 = convert(T, BigInt(2929323122013) // BigInt(17725327880387)) + B̂2 = convert(T, BigInt(4379799101587) // BigInt(35838171763617)) + B̂3 = convert(T, BigInt(2267325134734) // BigInt(9725002913543)) + B̂4 = convert(T, BigInt(1519467056643) // BigInt(5852430786130)) + B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4) + + Bₗ = convert(T, BigInt(2131913067577) // BigInt(7868783702050)) + B̂ₗ = convert(T, BigInt(3636375423974) // BigInt(16547514622827)) + + C1 = convert(T2, BigInt(9435338793489) // BigInt(32856462503258)) + C2 = convert(T2, + BigInt(147231987957505837822553443) // BigInt(244401207824228867478118222)) + C3 = convert(T2, + BigInt(401086457089554669663078760253749450489) // + BigInt(812866282711293513804077001645679258017)) + C4 = convert(T2, + BigInt(153823244836258719400905156342054669945035476219421) // + BigInt(172160249040778711548900853819650745575758693592285)) + Cᵢ = SVector(C1, C2, C3, C4) + + LowStorageRK4RPConstantCache{4, T, T2}(Aᵢ₁, Aᵢ₂, Aᵢ₃, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) +end + +function alg_cache(alg::CKLLSRK54_3N_4R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + k = zero(rate_prototype) + uᵢ₋₁ = zero(u) + uᵢ₋₂ = zero(u) + uᵢ₋₃ = zero(u) + fᵢ₋₂ = zero(rate_prototype) + fᵢ₋₃ = zero(rate_prototype) + gprev = zero(u) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = CKLLSRK54_3N_4RConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK4RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, uᵢ₋₃, fᵢ₋₂, fᵢ₋₃, gprev, fsalfirst, tmp, + atmp, tab, alg.stage_limiter!, alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::CKLLSRK54_3N_4R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + CKLLSRK54_3N_4RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function CKLLSRK54_3M_4RConstantCache(T, T2) + A₁1 = convert(T, BigInt(7142524119) // BigInt(20567653057)) + A₁2 = convert(T, BigInt(20567653057) // BigInt(89550000000)) + A₁3 = convert(T, BigInt(7407775) // BigInt(2008982)) + A₁4 = convert(T, BigInt(-4577300) // BigInt(867302297)) + Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4) + + A₂1 = convert(T, BigInt(0) // BigInt(1)) + A₂2 = convert(T, BigInt(15198616943) // BigInt(89550000000)) + A₂3 = convert(T, BigInt(-226244183627) // BigInt(80359280000)) + A₂4 = convert(T, BigInt(33311687500) // BigInt(8703531091)) + Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4) + + A₃1 = convert(T, BigInt(0) // BigInt(1)) + A₃2 = convert(T, BigInt(0) // BigInt(1)) + A₃3 = convert(T, BigInt(9890667227) // BigInt(80359280000)) + A₃4 = convert(T, BigInt(-20567653057) // BigInt(6979191486)) + Aᵢ₃ = SVector(A₃1, A₃2, A₃3, A₃4) + + B1 = convert(T, BigInt(297809) // BigInt(2384418)) + B2 = convert(T, BigInt(0) // BigInt(1)) + B3 = convert(T, BigInt(156250000) // BigInt(270591503)) + B4 = convert(T, BigInt(5030000) // BigInt(888933)) + Bᵢ = SVector(B1, B2, B3, B4) + + B̂1 = convert(T, BigInt(121286694859) // BigInt(931793198518)) + B̂2 = convert(T, BigInt(0) // BigInt(1)) + B̂3 = convert(T, BigInt(9680751416357) // BigInt(17201392077364)) + B̂4 = convert(T, BigInt(6633076090000) // BigInt(1042143269349)) + B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4) + + Bₗ = convert(T, BigInt(-2927) // BigInt(546)) + B̂ₗ = convert(T, BigInt(-127961558623) // BigInt(21123456354)) + + C1 = convert(T2, BigInt(7142524119) // BigInt(20567653057)) + C2 = convert(T2, BigInt(1997) // BigInt(5000)) + C3 = convert(T2, BigInt(199) // BigInt(200)) + C4 = convert(T2, BigInt(1) // BigInt(1)) + Cᵢ = SVector(C1, C2, C3, C4) + + LowStorageRK4RPConstantCache{4, T, T2}(Aᵢ₁, Aᵢ₂, Aᵢ₃, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) +end + +function alg_cache(alg::CKLLSRK54_3M_4R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + k = zero(rate_prototype) + uᵢ₋₁ = zero(u) + uᵢ₋₂ = zero(u) + uᵢ₋₃ = zero(u) + fᵢ₋₂ = zero(rate_prototype) + fᵢ₋₃ = zero(rate_prototype) + gprev = zero(u) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = CKLLSRK54_3M_4RConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK4RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, uᵢ₋₃, fᵢ₋₂, fᵢ₋₃, gprev, fsalfirst, tmp, + atmp, tab, alg.stage_limiter!, alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::CKLLSRK54_3M_4R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + CKLLSRK54_3M_4RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function CKLLSRK65_4M_4RConstantCache(T, T2) + A₁1 = convert(T, BigInt(1811061732419) // BigInt(6538712036350)) + A₁2 = convert(T, BigInt(936386506953) // BigInt(6510757757683)) + A₁3 = convert(T, BigInt(8253430823511) // BigInt(9903985211908)) + A₁4 = convert(T, BigInt(4157325866175) // BigInt(11306150349782)) + A₁5 = convert(T, BigInt(3299942024581) // BigInt(13404534943033)) + Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4, A₁5) + + A₂1 = convert(T, BigInt(0) // BigInt(1)) + A₂2 = convert(T, BigInt(968127049827) // BigInt(6993254963231)) + A₂3 = convert(T, BigInt(-4242729801665) // BigInt(12001587034923)) + A₂4 = convert(T, BigInt(1960956671631) // BigInt(3017447659538)) + A₂5 = convert(T, BigInt(2088737530132) // BigInt(14638867961951)) + Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4, A₂5) + + A₃1 = convert(T, BigInt(0) // BigInt(1)) + A₃2 = convert(T, BigInt(0) // BigInt(1)) + A₃3 = convert(T, BigInt(332803037697) // BigInt(7529436905221)) + A₃4 = convert(T, BigInt(-19590089343957) // BigInt(51581831082203)) + A₃5 = convert(T, BigInt(3811366828049) // BigInt(10653298326636)) + Aᵢ₃ = SVector(A₃1, A₃2, A₃3, A₃4, A₃5) + + B1 = convert(T, BigInt(1437717300581) // BigInt(14622899446031)) + B2 = convert(T, BigInt(0) // BigInt(1)) + B3 = convert(T, BigInt(3070006287879) // BigInt(9321175678070)) + B4 = convert(T, BigInt(2276970273632) // BigInt(7940670647385)) + B5 = convert(T, BigInt(-1056149936631) // BigInt(7427907425983)) + Bᵢ = SVector(B1, B2, B3, B4, B5) + + B̂1 = convert(T, BigInt(399352205828) // BigInt(2843676810815)) + B̂2 = convert(T, BigInt(0) // BigInt(1)) + B̂3 = convert(T, BigInt(460449895996) // BigInt(4301836608005)) + B̂4 = convert(T, BigInt(15965746118666) // BigInt(21690343195681)) + B̂5 = convert(T, BigInt(-19281717001664) // BigInt(29911607353389)) + B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4, B̂5) + + Bₗ = convert(T, BigInt(2571845656138) // BigInt(6012342010435)) + B̂ₗ = convert(T, BigInt(5058427127221) // BigInt(7651806618075)) + + C1 = convert(T2, BigInt(1811061732419) // BigInt(6538712036350)) + C2 = convert(T2, + BigInt(12851630287335503073915984) // BigInt(45531389003311376172753773)) + C3 = convert(T2, + BigInt(468994575306978457607500930904657513641) // + BigInt(894975528626103930282351283769588361564)) + C4 = convert(T2, + BigInt(4735520442856752193881763097298943558246492547269018) // + BigInt(6433166018040288425494806218280078848936316641536447)) + C5 = convert(T2, + BigInt(25828983228256103590265182981008154883102570637999497) // + BigInt(30568689961801519095090666149791133914967119469889228)) + Cᵢ = SVector(C1, C2, C3, C4, C5) + + LowStorageRK4RPConstantCache{5, T, T2}(Aᵢ₁, Aᵢ₂, Aᵢ₃, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) +end + +function alg_cache(alg::CKLLSRK65_4M_4R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + k = zero(rate_prototype) + uᵢ₋₁ = zero(u) + uᵢ₋₂ = zero(u) + uᵢ₋₃ = zero(u) + fᵢ₋₂ = zero(rate_prototype) + fᵢ₋₃ = zero(rate_prototype) + gprev = zero(u) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = CKLLSRK65_4M_4RConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK4RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, uᵢ₋₃, fᵢ₋₂, fᵢ₋₃, gprev, fsalfirst, tmp, + atmp, tab, alg.stage_limiter!, alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::CKLLSRK65_4M_4R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + CKLLSRK65_4M_4RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function CKLLSRK85_4FM_4RConstantCache(T, T2) + A₁1 = convert(T, BigInt(319960152914) // BigInt(39034091721739)) + A₁2 = convert(T, BigInt(16440040368765) // BigInt(7252463661539)) + A₁3 = convert(T, BigInt(1381950791880) // BigInt(6599155371617)) + A₁4 = convert(T, BigInt(18466735994895) // BigInt(7394178462407)) + A₁5 = convert(T, BigInt(2786140924985) // BigInt(14262827431161)) + A₁6 = convert(T, BigInt(28327099865656) // BigInt(21470840267743)) + A₁7 = convert(T, BigInt(0) // BigInt(1)) + Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4, A₁5, A₁6, A₁7) + + A₂1 = convert(T, BigInt(0) // BigInt(1)) + A₂2 = convert(T, BigInt(-16195115415565) // BigInt(7808461210678)) + A₂3 = convert(T, BigInt(-1316066362688) // BigInt(10261382634081)) + A₂4 = convert(T, BigInt(-23893000145797) // BigInt(9614512377075)) + A₂5 = convert(T, BigInt(6556893593075) // BigInt(12530787773541)) + A₂6 = convert(T, BigInt(-5015572218207) // BigInt(5719938983072)) + A₂7 = convert(T, BigInt(0) // BigInt(1)) + Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4, A₂5, A₂6, A₂7) + + A₃1 = convert(T, BigInt(0) // BigInt(1)) + A₃2 = convert(T, BigInt(0) // BigInt(1)) + A₃3 = convert(T, BigInt(334167490531) // BigInt(1677017272502)) + A₃4 = convert(T, BigInt(4579492417936) // BigInt(7930641522963)) + A₃5 = convert(T, BigInt(-2255846922213) // BigInt(30066310003000)) + A₃6 = convert(T, BigInt(3212719728776) // BigInt(7037340048693)) + A₃7 = convert(T, BigInt(0) // BigInt(1)) + Aᵢ₃ = SVector(A₃1, A₃2, A₃3, A₃4, A₃5, A₃6, A₃7) + + B1 = convert(T, BigInt(1147876221211) // BigInt(13910763665259)) + B2 = convert(T, BigInt(0) // BigInt(1)) + B3 = convert(T, BigInt(182134362610) // BigInt(9852075053293)) + B4 = convert(T, BigInt(3396705055007) // BigInt(8495597747463)) + B5 = convert(T, BigInt(363006049056) // BigInt(22366003978609)) + B6 = convert(T, BigInt(6078825123673) // BigInt(15200143133108)) + B7 = convert(T, BigInt(583593328277) // BigInt(7028929464160)) + Bᵢ = SVector(B1, B2, B3, B4, B5, B6, B7) + + B̂1 = convert(T, BigInt(2023383632057) // BigInt(26525303340911)) + B̂2 = convert(T, BigInt(0) // BigInt(1)) + B̂3 = convert(T, BigInt(480990062147) // BigInt(12694528747923)) + B̂4 = convert(T, BigInt(14502014597821) // BigInt(36979005529861)) + B̂5 = convert(T, BigInt(-3883966523914) // BigInt(63014133260123)) + B̂6 = convert(T, BigInt(1643296191892) // BigInt(3432451463915)) + B̂7 = convert(T, BigInt(2576984903812) // BigInt(11692468803935)) + B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4, B̂5, B̂6, B̂7) + + Bₗ = convert(T, BigInt(0) // BigInt(1)) + B̂ₗ = convert(T, BigInt(-2393889703871) // BigInt(16641202878460)) + + C1 = convert(T2, BigInt(319960152914) // BigInt(39034091721739)) + C2 = convert(T2, + BigInt(10916931475666701983218135) // BigInt(56630581182979020764713442)) + C3 = convert(T2, + BigInt(31845189551971545944223680050155078355) // + BigInt(113561670251926090809438891701398790454)) + C4 = convert(T2, + BigInt(585892393366635581491792016142825500310911249371223) // + BigInt(871432942801472160798333604371480303171919616321325)) + C5 = convert(T2, + BigInt(6030664727234996630401450278844701818157369618311237) // + BigInt(8305630304762506786823923305099106403075216590053000)) + C6 = convert(T2, + BigInt(190737487565451971541550207118478711767748834018874068552898297) // + BigInt(190737487565451971541550204260359567420033302718711745345318816)) + C7 = convert(T2, + BigInt(194373043039840208108258122050794558876) // + BigInt(388106905684556737922360607016380520227)) + Cᵢ = SVector(C1, C2, C3, C4, C5, C6, C7) + + LowStorageRK4RPConstantCache{7, T, T2}(Aᵢ₁, Aᵢ₂, Aᵢ₃, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) +end + +function alg_cache(alg::CKLLSRK85_4FM_4R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + k = zero(rate_prototype) + uᵢ₋₁ = zero(u) + uᵢ₋₂ = zero(u) + uᵢ₋₃ = zero(u) + fᵢ₋₂ = zero(rate_prototype) + fᵢ₋₃ = zero(rate_prototype) + gprev = zero(u) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = CKLLSRK85_4FM_4RConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK4RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, uᵢ₋₃, fᵢ₋₂, fᵢ₋₃, gprev, fsalfirst, tmp, + atmp, tab, alg.stage_limiter!, alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::CKLLSRK85_4FM_4R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + CKLLSRK85_4FM_4RConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) +end + +# 5R+ low storage methods introduced by van der Houwen +@cache struct LowStorageRK5RPCache{uType, rateType, uNoUnitsType, TabType, StageLimiter, + StepLimiter, Thread} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + uᵢ₋₁::uType + uᵢ₋₂::uType + uᵢ₋₃::uType + uᵢ₋₄::uType + fᵢ₋₂::rateType + fᵢ₋₃::rateType + fᵢ₋₄::rateType + gprev::uType + fsalfirst::rateType + tmp::uType + atmp::uNoUnitsType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct LowStorageRK5RPConstantCache{N, T, T2} <: OrdinaryDiffEqConstantCache + Aᵢ₁::SVector{N, T} + Aᵢ₂::SVector{N, T} + Aᵢ₃::SVector{N, T} + Aᵢ₄::SVector{N, T} + Bₗ::T + B̂ₗ::T + Bᵢ::SVector{N, T} + B̂ᵢ::SVector{N, T} + Cᵢ::SVector{N, T2} +end + +function CKLLSRK75_4M_5RConstantCache(T, T2) + A₁1 = convert(T, BigInt(984894634849) // BigInt(6216792334776)) + A₁2 = convert(T, BigInt(984894634849) // BigInt(5526037630912)) + A₁3 = convert(T, BigInt(13256335809797) // BigInt(10977774807827)) + A₁4 = convert(T, BigInt(5386479425293) // BigInt(11045691190948)) + A₁5 = convert(T, BigInt(-1717767168952) // BigInt(11602237717369)) + A₁6 = convert(T, BigInt(-10054679524430) // BigInt(10306851287569)) + Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4, A₁5, A₁6) + + A₂1 = convert(T, BigInt(0) // BigInt(1)) + A₂2 = convert(T, BigInt(890852251480) // BigInt(14995156510369)) + A₂3 = convert(T, BigInt(-18544705752398) // BigInt(18426539884027)) + A₂4 = convert(T, BigInt(1115398761892) // BigInt(28058504699217)) + A₂5 = convert(T, BigInt(5538441135605) // BigInt(13014942352969)) + A₂6 = convert(T, BigInt(23855853001162) // BigInt(20968156556405)) + Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4, A₂5, A₂6) + + A₃1 = convert(T, BigInt(0) // BigInt(1)) + A₃2 = convert(T, BigInt(0) // BigInt(1)) + A₃3 = convert(T, BigInt(1722683259617) // BigInt(5669183367476)) + A₃4 = convert(T, BigInt(342961171087) // BigInt(6505721096888)) + A₃5 = convert(T, BigInt(-14472869285404) // BigInt(19736045536601)) + A₃6 = convert(T, BigInt(-8169744035288) // BigInt(5424738459363)) + Aᵢ₃ = SVector(A₃1, A₃2, A₃3, A₃4, A₃5, A₃6) + + A₄1 = convert(T, BigInt(0) // BigInt(1)) + A₄2 = convert(T, BigInt(0) // BigInt(1)) + A₄3 = convert(T, BigInt(0) // BigInt(1)) + A₄4 = convert(T, BigInt(762111618422) // BigInt(5198184381557)) + A₄5 = convert(T, BigInt(2896263505307) // BigInt(6364015805096)) + A₄6 = convert(T, BigInt(60049403517654) // BigInt(26787923986853)) + Aᵢ₄ = SVector(A₄1, A₄2, A₄3, A₄4, A₄5, A₄6) + + B1 = convert(T, BigInt(1008141064049) // BigInt(9867084721348)) + B2 = convert(T, BigInt(0) // BigInt(1)) + B3 = convert(T, BigInt(8222186491841) // BigInt(18352662300888)) + B4 = convert(T, BigInt(514621697208) // BigInt(8712119383831)) + B5 = convert(T, BigInt(1808964136873) // BigInt(4546032443428)) + B6 = convert(T, BigInt(-362754645297) // BigInt(3989911846061)) + Bᵢ = SVector(B1, B2, B3, B4, B5, B6) + + B̂1 = convert(T, BigInt(1633918545125) // BigInt(12016465907206)) + B̂2 = convert(T, BigInt(0) // BigInt(1)) + B̂3 = convert(T, BigInt(5614864639673) // BigInt(10804025076427)) + B̂4 = convert(T, BigInt(229286380958) // BigInt(6920724258831)) + B̂5 = convert(T, BigInt(5960415897193) // BigInt(14726168927560)) + B̂6 = convert(T, BigInt(-4042532386559) // BigInt(22820216867423)) + B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4, B̂5, B̂6) + + Bₗ = convert(T, BigInt(599706619333) // BigInt(7161178965783)) + B̂ₗ = convert(T, BigInt(930770261899) // BigInt(11134660916874)) + + C1 = convert(T2, BigInt(984894634849) // BigInt(6216792334776)) + C2 = convert(T2, + BigInt(19691532261044641782999041) // BigInt(82863799157714161922926528)) + C3 = convert(T2, + BigInt(579140763944732527715749105230082493541) // + BigInt(1146776047854201324825397010814855303604)) + C4 = convert(T2, + BigInt(1904235205010770769196995566618512437342488019008993) // + BigInt(2620260981179174237577004881164696841381017975634264)) + C5 = convert(T2, + BigInt(4745866356039511505795256436748010529615723318082554645080208661) // + BigInt(46784744516176933667763632070461960177241008032286254911869725672)) + C6 = convert(T2, + BigInt(309879595293732553069368807532997606922999693101104106883289601491) // + BigInt(309879595293732553069368804305686805880909932549908997963514738540)) + Cᵢ = SVector(C1, C2, C3, C4, C5, C6) + + LowStorageRK5RPConstantCache{6, T, T2}(Aᵢ₁, Aᵢ₂, Aᵢ₃, Aᵢ₄, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) +end + +function alg_cache(alg::CKLLSRK75_4M_5R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + k = zero(rate_prototype) + uᵢ₋₁ = zero(u) + uᵢ₋₂ = zero(u) + uᵢ₋₃ = zero(u) + uᵢ₋₄ = zero(u) + fᵢ₋₂ = zero(rate_prototype) + fᵢ₋₃ = zero(rate_prototype) + fᵢ₋₄ = zero(rate_prototype) + gprev = zero(u) + if calck + fsalfirst = zero(rate_prototype) + else + fsalfirst = k + end + tab = CKLLSRK75_4M_5RConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + LowStorageRK5RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, uᵢ₋₃, uᵢ₋₄, fᵢ₋₂, fᵢ₋₃, fᵢ₋₄, gprev, + fsalfirst, tmp, atmp, tab, alg.stage_limiter!, alg.step_limiter!, + alg.thread) +end + +function alg_cache(alg::CKLLSRK75_4M_5R, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + CKLLSRK75_4M_5RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end diff --git a/src/caches/rkc_caches.jl b/src/caches/rkc_caches.jl new file mode 100644 index 0000000000..2594804d1d --- /dev/null +++ b/src/caches/rkc_caches.jl @@ -0,0 +1,348 @@ +mutable struct ROCK2ConstantCache{T, T2, zType} <: OrdinaryDiffEqConstantCache + ms::SVector{46, Int} + fp1::SVector{46, T} + fp2::SVector{46, T} + recf::Vector{T2} + zprev::zType + mdeg::Int + deg_index::Int + start::Int + min_stage::Int + max_stage::Int +end +@cache struct ROCK2Cache{uType, rateType, uNoUnitsType, C <: ROCK2ConstantCache} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + uᵢ₋₁::uType + uᵢ₋₂::uType + tmp::uType + atmp::uNoUnitsType + fsalfirst::rateType + k::rateType + constantcache::C +end + +function alg_cache(alg::ROCK2, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + constantcache = ROCK2ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits), + u) + uᵢ₋₁ = zero(u) + uᵢ₋₂ = zero(u) + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + fsalfirst = zero(rate_prototype) + k = zero(rate_prototype) + ROCK2Cache(u, uprev, uᵢ₋₁, uᵢ₋₂, tmp, atmp, fsalfirst, k, constantcache) +end + +function alg_cache(alg::ROCK2, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + ROCK2ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits), u) +end + +mutable struct ROCK4ConstantCache{T, T2, T3, T4, zType} <: OrdinaryDiffEqConstantCache + ms::SVector{50, Int} + fpa::Vector{T} + fpb::Vector{T2} + fpbe::Vector{T3} + recf::Vector{T4} + zprev::zType + mdeg::Int + deg_index::Int + start::Int + min_stage::Int + max_stage::Int +end + +@cache struct ROCK4Cache{uType, rateType, uNoUnitsType, C <: ROCK4ConstantCache} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + uᵢ₋₁::uType + uᵢ₋₂::uType + uᵢ₋₃::uType + tmp::uType + atmp::uNoUnitsType + fsalfirst::rateType + k::rateType + constantcache::C +end + +function alg_cache(alg::ROCK4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + constantcache = ROCK4ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits), + u) + uᵢ₋₁ = zero(u) + uᵢ₋₂ = zero(u) + uᵢ₋₃ = zero(u) + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + fsalfirst = zero(rate_prototype) + k = zero(rate_prototype) + ROCK4Cache(u, uprev, uᵢ₋₁, uᵢ₋₂, uᵢ₋₃, tmp, atmp, fsalfirst, k, constantcache) +end + +function alg_cache(alg::ROCK4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + ROCK4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits), u) +end + +mutable struct RKCConstantCache{zType} <: OrdinaryDiffEqConstantCache + #to match the types to call maxeig! + zprev::zType +end +@cache struct RKCCache{uType, rateType, uNoUnitsType, C <: RKCConstantCache} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + gprev::uType + gprev2::uType + tmp::uType + atmp::uNoUnitsType + fsalfirst::rateType + k::rateType + constantcache::C +end + +function alg_cache(alg::RKC, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + constantcache = RKCConstantCache(u) + gprev = zero(u) + gprev2 = zero(u) + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + fsalfirst = zero(rate_prototype) + k = zero(rate_prototype) + RKCCache(u, uprev, gprev, gprev2, tmp, atmp, fsalfirst, k, constantcache) +end + +function alg_cache(alg::RKC, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + RKCConstantCache(u) +end + +@cache mutable struct IRKCConstantCache{uType, rateType, N} <: OrdinaryDiffEqConstantCache + minm::Int + zprev::uType + nlsolver::N + du₁::rateType + du₂::rateType +end + +@cache mutable struct IRKCCache{uType, rateType, uNoUnitsType, N, C <: IRKCConstantCache} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + gprev::uType + gprev2::uType + fsalfirst::rateType + f1ⱼ₋₁::rateType + f1ⱼ₋₂::rateType + f2ⱼ₋₁::rateType + atmp::uNoUnitsType + nlsolver::N + du₁::rateType + du₂::rateType + constantcache::C +end + +function alg_cache(alg::IRKC, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + γ, c = 1.0, 1.0 + nlsolver = build_nlsolver(alg, u, uprev, p, t, dt, f, rate_prototype, uEltypeNoUnits, + uBottomEltypeNoUnits, tTypeNoUnits, γ, c, Val(false)) + zprev = u + du₁ = rate_prototype + du₂ = rate_prototype + IRKCConstantCache(50, zprev, nlsolver, du₁, du₂) +end + +function alg_cache(alg::IRKC, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + γ, c = 1.0, 1.0 + nlsolver = build_nlsolver(alg, u, uprev, p, t, dt, f, rate_prototype, uEltypeNoUnits, + uBottomEltypeNoUnits, tTypeNoUnits, γ, c, Val(true)) + + gprev = zero(u) + gprev2 = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + fsalfirst = zero(rate_prototype) + zprev = zero(u) + f1ⱼ₋₁ = zero(rate_prototype) + f1ⱼ₋₂ = zero(rate_prototype) + f2ⱼ₋₁ = zero(rate_prototype) + du₁ = zero(rate_prototype) + du₂ = zero(rate_prototype) + constantcache = IRKCConstantCache(50, zprev, nlsolver, du₁, du₂) + IRKCCache(u, uprev, gprev, gprev2, fsalfirst, f1ⱼ₋₁, f1ⱼ₋₂, f2ⱼ₋₁, atmp, nlsolver, du₁, + du₂, constantcache) +end + +mutable struct ESERK4ConstantCache{T, zType} <: OrdinaryDiffEqConstantCache + ms::SVector{46, Int} + Cᵤ::SVector{4, Int} + Cₑ::SVector{4, Int} + zprev::zType + Bᵢ::Vector{T} + mdeg::Int + start::Int + internal_deg::Int +end + +@cache struct ESERK4Cache{uType, rateType, uNoUnitsType, C <: ESERK4ConstantCache} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + uᵢ::uType + uᵢ₋₁::uType + uᵢ₋₂::uType + Sᵢ::uType + tmp::uType + atmp::uNoUnitsType + fsalfirst::rateType + k::rateType + constantcache::C +end + +function alg_cache(alg::ESERK4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + constantcache = ESERK4ConstantCache(u) + uᵢ = zero(u) + uᵢ₋₁ = zero(u) + uᵢ₋₂ = zero(u) + Sᵢ = zero(u) + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + fsalfirst = zero(rate_prototype) + k = zero(rate_prototype) + ESERK4Cache(u, uprev, uᵢ, uᵢ₋₁, uᵢ₋₂, Sᵢ, tmp, atmp, fsalfirst, k, constantcache) +end + +function alg_cache(alg::ESERK4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + ESERK4ConstantCache(u) +end + +mutable struct ESERK5ConstantCache{T, zType} <: OrdinaryDiffEqConstantCache + ms::SVector{49, Int} + Cᵤ::SVector{5, Int} + Cₑ::SVector{5, Int} + zprev::zType + Bᵢ::Vector{T} + mdeg::Int + start::Int + internal_deg::Int +end + +@cache struct ESERK5Cache{uType, rateType, uNoUnitsType, C <: ESERK5ConstantCache} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + uᵢ::uType + uᵢ₋₁::uType + uᵢ₋₂::uType + Sᵢ::uType + tmp::uType + atmp::uNoUnitsType + fsalfirst::rateType + k::rateType + constantcache::C +end + +function alg_cache(alg::ESERK5, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + constantcache = ESERK5ConstantCache(u) + uᵢ = zero(u) + uᵢ₋₁ = zero(u) + uᵢ₋₂ = zero(u) + Sᵢ = zero(u) + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + fsalfirst = zero(rate_prototype) + k = zero(rate_prototype) + ESERK5Cache(u, uprev, uᵢ, uᵢ₋₁, uᵢ₋₂, Sᵢ, tmp, atmp, fsalfirst, k, constantcache) +end + +function alg_cache(alg::ESERK5, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + ESERK5ConstantCache(u) +end + +mutable struct SERK2ConstantCache{T, zType} <: OrdinaryDiffEqConstantCache + ms::SVector{11, Int} + zprev::zType + Bᵢ::Vector{T} + mdeg::Int + start::Int + internal_deg::Int +end + +@cache struct SERK2Cache{uType, rateType, uNoUnitsType, C <: SERK2ConstantCache} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + uᵢ₋₁::uType + uᵢ₋₂::uType + Sᵢ::uType + tmp::uType + atmp::uNoUnitsType + fsalfirst::rateType + k::rateType + constantcache::C +end + +function alg_cache(alg::SERK2, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + constantcache = SERK2ConstantCache(u) + uᵢ₋₁ = zero(u) + uᵢ₋₂ = zero(u) + Sᵢ = zero(u) + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + fsalfirst = zero(rate_prototype) + k = zero(rate_prototype) + SERK2Cache(u, uprev, uᵢ₋₁, uᵢ₋₂, Sᵢ, tmp, atmp, fsalfirst, k, constantcache) +end + +function alg_cache(alg::SERK2, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SERK2ConstantCache(u) +end diff --git a/src/caches/rkn_caches.jl b/src/caches/rkn_caches.jl new file mode 100644 index 0000000000..7582e1f498 --- /dev/null +++ b/src/caches/rkn_caches.jl @@ -0,0 +1,683 @@ +@cache struct Nystrom4Cache{uType, rateType, reducedRateType} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + k₂::reducedRateType + k₃::reducedRateType + k₄::reducedRateType + k::rateType + tmp::uType +end + +# struct Nystrom4ConstantCache <: OrdinaryDiffEqConstantCache end + +function alg_cache(alg::Nystrom4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + reduced_rate_prototype = rate_prototype.x[2] + k₁ = zero(rate_prototype) + k₂ = zero(reduced_rate_prototype) + k₃ = zero(reduced_rate_prototype) + k₄ = zero(reduced_rate_prototype) + k = zero(rate_prototype) + tmp = zero(u) + Nystrom4Cache(u, uprev, k₁, k₂, k₃, k₄, k, tmp) +end + +struct Nystrom4ConstantCache <: OrdinaryDiffEqConstantCache end + +function alg_cache(alg::Nystrom4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + Nystrom4ConstantCache() +end + +# alg_cache(alg::Nystrom4,u,rate_prototype,::Type{uEltypeNoUnits},::Type{uBottomEltypeNoUnits},::Type{tTypeNoUnits},uprev,uprev2,f,t,dt,reltol,p,calck,::Val{false}) where {uEltypeNoUnits,uBottomEltypeNoUnits,tTypeNoUnits} = Nystrom4ConstantCache(constvalue(uBottomEltypeNoUnits),constvalue(tTypeNoUnits)) + +@cache struct FineRKN4Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + k2::reducedRateType + k3::reducedRateType + k4::reducedRateType + k5::reducedRateType + k::rateType + utilde::uType + tmp::uType + atmp::uNoUnitsType + tab::TabType +end + +function alg_cache(alg::FineRKN4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + reduced_rate_prototype = rate_prototype.x[2] + tab = FineRKN4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + k1 = zero(rate_prototype) + k2 = zero(reduced_rate_prototype) + k3 = zero(reduced_rate_prototype) + k4 = zero(reduced_rate_prototype) + k5 = zero(reduced_rate_prototype) + k = zero(rate_prototype) + utilde = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + tmp = zero(u) + FineRKN4Cache(u, uprev, k1, k2, k3, k4, k5, k, utilde, tmp, atmp, tab) +end + +function alg_cache(alg::FineRKN4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + FineRKN4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct FineRKN5Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + k2::reducedRateType + k3::reducedRateType + k4::reducedRateType + k5::reducedRateType + k6::reducedRateType + k7::reducedRateType + k::rateType + utilde::uType + tmp::uType + atmp::uNoUnitsType + tab::TabType +end + +function alg_cache(alg::FineRKN5, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + reduced_rate_prototype = rate_prototype.x[2] + tab = FineRKN5ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + k1 = zero(rate_prototype) + k2 = zero(reduced_rate_prototype) + k3 = zero(reduced_rate_prototype) + k4 = zero(reduced_rate_prototype) + k5 = zero(reduced_rate_prototype) + k6 = zero(reduced_rate_prototype) + k7 = zero(reduced_rate_prototype) + k = zero(rate_prototype) + utilde = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + tmp = zero(u) + FineRKN5Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k, utilde, tmp, atmp, tab) +end + +function alg_cache(alg::FineRKN5, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + FineRKN5ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct Nystrom4VelocityIndependentCache{uType, rateType, reducedRateType} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + k₂::reducedRateType + k₃::reducedRateType + k::rateType + tmp::uType +end + +function alg_cache(alg::Nystrom4VelocityIndependent, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + reduced_rate_prototype = rate_prototype.x[2] + k₁ = zero(rate_prototype) + k₂ = zero(reduced_rate_prototype) + k₃ = zero(reduced_rate_prototype) + k = zero(rate_prototype) + tmp = zero(u) + Nystrom4VelocityIndependentCache(u, uprev, k₁, k₂, k₃, k, tmp) +end + +struct Nystrom4VelocityIndependentConstantCache <: OrdinaryDiffEqConstantCache end + +function alg_cache(alg::Nystrom4VelocityIndependent, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + Nystrom4VelocityIndependentConstantCache() +end + +@cache struct IRKN3Cache{uType, rateType, TabType} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + uprev2::uType + fsalfirst::rateType + k₂::rateType + k::rateType + tmp::uType + tmp2::rateType + onestep_cache::Nystrom4VelocityIndependentCache + tab::TabType +end + +function alg_cache(alg::IRKN3, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + k₁ = zero(rate_prototype) + k₂ = zero(rate_prototype) + k₃ = zero(rate_prototype) + k = zero(rate_prototype) + tmp = zero(u) + tab = IRKN3ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + IRKN3Cache(u, uprev, uprev2, k₁, k₂, k, tmp, k₃, + Nystrom4VelocityIndependentCache(u, uprev, k₁, k₂.x[2], k₃.x[2], k, tmp), + tab) +end + +function alg_cache(alg::IRKN3, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + IRKN3ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct IRKN4Cache{uType, rateType, TabType} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + uprev2::uType + fsalfirst::rateType + k₂::rateType + k₃::rateType + k::rateType + tmp::uType + tmp2::rateType + onestep_cache::Nystrom4VelocityIndependentCache + tab::TabType +end + +function alg_cache(alg::IRKN4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + k₁ = zero(rate_prototype) + k₂ = zero(rate_prototype) + k₃ = zero(rate_prototype) + k = zero(rate_prototype) + tmp = zero(u) + tmp2 = zero(rate_prototype) + tab = IRKN4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + IRKN4Cache(u, uprev, uprev2, k₁, k₂, k₃, k, tmp, tmp2, + Nystrom4VelocityIndependentCache(u, uprev, k₁, k₂.x[2], k₃.x[2], k, tmp), + tab) +end + +function alg_cache(alg::IRKN4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + IRKN4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct Nystrom5VelocityIndependentCache{uType, rateType, reducedRateType, TabType} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + k₂::reducedRateType + k₃::reducedRateType + k₄::reducedRateType + k::rateType + tmp::uType + tab::TabType +end + +function alg_cache(alg::Nystrom5VelocityIndependent, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + reduced_rate_prototype = rate_prototype.x[2] + k₁ = zero(rate_prototype) + k₂ = zero(reduced_rate_prototype) + k₃ = zero(reduced_rate_prototype) + k₄ = zero(reduced_rate_prototype) + k = zero(rate_prototype) + tmp = zero(u) + tab = Nystrom5VelocityIndependentConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + Nystrom5VelocityIndependentCache(u, uprev, k₁, k₂, k₃, k₄, k, tmp, tab) +end + +function alg_cache(alg::Nystrom5VelocityIndependent, u, rate_prototype, + ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + Nystrom5VelocityIndependentConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) +end + +struct DPRKN4Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + k2::reducedRateType + k3::reducedRateType + k4::reducedRateType + k::rateType + utilde::uType + tmp::uType + atmp::uNoUnitsType + tab::TabType +end + +function alg_cache(alg::DPRKN4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + reduced_rate_prototype = rate_prototype.x[2] + tab = DPRKN4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + k1 = zero(rate_prototype) + k2 = zero(reduced_rate_prototype) + k3 = zero(reduced_rate_prototype) + k4 = zero(reduced_rate_prototype) + k = zero(rate_prototype) + utilde = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + tmp = zero(u) + DPRKN4Cache(u, uprev, k1, k2, k3, k4, k, utilde, tmp, atmp, tab) +end + +function alg_cache(alg::DPRKN4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + DPRKN4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct DPRKN5Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + k2::reducedRateType + k3::reducedRateType + k4::reducedRateType + k5::reducedRateType + k6::reducedRateType + k::rateType + utilde::uType + tmp::uType + atmp::uNoUnitsType + tab::TabType +end + +function alg_cache(alg::DPRKN5, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + reduced_rate_prototype = rate_prototype.x[2] + tab = DPRKN5ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + k1 = zero(rate_prototype) + k2 = zero(reduced_rate_prototype) + k3 = zero(reduced_rate_prototype) + k4 = zero(reduced_rate_prototype) + k5 = zero(reduced_rate_prototype) + k6 = zero(reduced_rate_prototype) + k = zero(rate_prototype) + utilde = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + tmp = zero(u) + DPRKN5Cache(u, uprev, k1, k2, k3, k4, k5, k6, k, utilde, tmp, atmp, tab) +end + +function alg_cache(alg::DPRKN5, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + DPRKN5ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct DPRKN6Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + k2::reducedRateType + k3::reducedRateType + k4::reducedRateType + k5::reducedRateType + k6::reducedRateType + k::rateType + utilde::uType + tmp::uType + atmp::uNoUnitsType + tab::TabType +end + +function alg_cache(alg::DPRKN6, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + reduced_rate_prototype = rate_prototype.x[2] + tab = DPRKN6ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + k1 = zero(rate_prototype) + k2 = zero(reduced_rate_prototype) + k3 = zero(reduced_rate_prototype) + k4 = zero(reduced_rate_prototype) + k5 = zero(reduced_rate_prototype) + k6 = zero(reduced_rate_prototype) + k = zero(rate_prototype) + utilde = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + tmp = zero(u) + DPRKN6Cache(u, uprev, k1, k2, k3, k4, k5, k6, k, utilde, tmp, atmp, tab) +end + +function alg_cache(alg::DPRKN6, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + DPRKN6ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct DPRKN6FMCache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + k2::reducedRateType + k3::reducedRateType + k4::reducedRateType + k5::reducedRateType + k6::reducedRateType + k::rateType + utilde::uType + tmp::uType + atmp::uNoUnitsType + tab::TabType +end + +function alg_cache(alg::DPRKN6FM, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + reduced_rate_prototype = rate_prototype.x[2] + tab = DPRKN6FMConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + k1 = zero(rate_prototype) + k2 = zero(reduced_rate_prototype) + k3 = zero(reduced_rate_prototype) + k4 = zero(reduced_rate_prototype) + k5 = zero(reduced_rate_prototype) + k6 = zero(reduced_rate_prototype) + k = zero(rate_prototype) + utilde = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + tmp = zero(u) + DPRKN6FMCache(u, uprev, k1, k2, k3, k4, k5, k6, k, utilde, tmp, atmp, tab) +end + +function alg_cache(alg::DPRKN6FM, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + DPRKN6FMConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct DPRKN8Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + k2::reducedRateType + k3::reducedRateType + k4::reducedRateType + k5::reducedRateType + k6::reducedRateType + k7::reducedRateType + k8::reducedRateType + k9::reducedRateType + k::rateType + utilde::uType + tmp::uType + atmp::uNoUnitsType + tab::TabType +end + +function alg_cache(alg::DPRKN8, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + reduced_rate_prototype = rate_prototype.x[2] + tab = DPRKN8ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + k1 = zero(rate_prototype) + k2 = zero(reduced_rate_prototype) + k3 = zero(reduced_rate_prototype) + k4 = zero(reduced_rate_prototype) + k5 = zero(reduced_rate_prototype) + k6 = zero(reduced_rate_prototype) + k7 = zero(reduced_rate_prototype) + k8 = zero(reduced_rate_prototype) + k9 = zero(reduced_rate_prototype) + k = zero(rate_prototype) + utilde = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + tmp = zero(u) + DPRKN8Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8, k9, k, utilde, tmp, atmp, tab) +end + +function alg_cache(alg::DPRKN8, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + DPRKN8ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct DPRKN12Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + k2::reducedRateType + k3::reducedRateType + k4::reducedRateType + k5::reducedRateType + k6::reducedRateType + k7::reducedRateType + k8::reducedRateType + k9::reducedRateType + k10::reducedRateType + k11::reducedRateType + k12::reducedRateType + k13::reducedRateType + k14::reducedRateType + k15::reducedRateType + k16::reducedRateType + k17::reducedRateType + k::rateType + utilde::uType + tmp::uType + atmp::uNoUnitsType + tab::TabType +end + +function alg_cache(alg::DPRKN12, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + reduced_rate_prototype = rate_prototype.x[2] + tab = DPRKN12ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + k1 = zero(rate_prototype) + k2 = zero(reduced_rate_prototype) + k3 = zero(reduced_rate_prototype) + k4 = zero(reduced_rate_prototype) + k5 = zero(reduced_rate_prototype) + k6 = zero(reduced_rate_prototype) + k7 = zero(reduced_rate_prototype) + k8 = zero(reduced_rate_prototype) + k9 = zero(reduced_rate_prototype) + k10 = zero(reduced_rate_prototype) + k11 = zero(reduced_rate_prototype) + k12 = zero(reduced_rate_prototype) + k13 = zero(reduced_rate_prototype) + k14 = zero(reduced_rate_prototype) + k15 = zero(reduced_rate_prototype) + k16 = zero(reduced_rate_prototype) + k17 = zero(reduced_rate_prototype) + k = zero(rate_prototype) + utilde = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + tmp = zero(u) + DPRKN12Cache( + u, uprev, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, + k16, k17, k, utilde, tmp, atmp, tab) +end + +function alg_cache(alg::DPRKN12, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + DPRKN12ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct ERKN4Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + k2::reducedRateType + k3::reducedRateType + k4::reducedRateType + k::rateType + utilde::uType + tmp::uType + atmp::uNoUnitsType + tab::TabType +end + +function alg_cache(alg::ERKN4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + reduced_rate_prototype = rate_prototype.x[2] + tab = ERKN4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + k1 = zero(rate_prototype) + k2 = zero(reduced_rate_prototype) + k3 = zero(reduced_rate_prototype) + k4 = zero(reduced_rate_prototype) + k = zero(rate_prototype) + utilde = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + tmp = zero(u) + ERKN4Cache(u, uprev, k1, k2, k3, k4, k, utilde, tmp, atmp, tab) +end + +function alg_cache(alg::ERKN4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + ERKN4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct ERKN5Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + k2::reducedRateType + k3::reducedRateType + k4::reducedRateType + k::rateType + utilde::uType + tmp::uType + atmp::uNoUnitsType + tab::TabType +end + +function alg_cache(alg::ERKN5, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + reduced_rate_prototype = rate_prototype.x[2] + tab = ERKN5ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + k1 = zero(rate_prototype) + k2 = zero(reduced_rate_prototype) + k3 = zero(reduced_rate_prototype) + k4 = zero(reduced_rate_prototype) + k = zero(rate_prototype) + utilde = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + tmp = zero(u) + ERKN5Cache(u, uprev, k1, k2, k3, k4, k, utilde, tmp, atmp, tab) +end + +function alg_cache(alg::ERKN5, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + ERKN5ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct ERKN7Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + k2::reducedRateType + k3::reducedRateType + k4::reducedRateType + k5::reducedRateType + k6::reducedRateType + k7::reducedRateType + k::rateType + utilde::uType + tmp::uType + atmp::uNoUnitsType + tab::TabType +end + +function alg_cache(alg::ERKN7, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + reduced_rate_prototype = rate_prototype.x[2] + tab = ERKN7ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + k1 = zero(rate_prototype) + k2 = zero(reduced_rate_prototype) + k3 = zero(reduced_rate_prototype) + k4 = zero(reduced_rate_prototype) + k5 = zero(reduced_rate_prototype) + k6 = zero(reduced_rate_prototype) + k7 = zero(reduced_rate_prototype) + k = zero(rate_prototype) + utilde = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + tmp = zero(u) + ERKN7Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k, utilde, tmp, atmp, tab) +end + +function alg_cache(alg::ERKN7, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + ERKN7ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end diff --git a/src/caches/ssprk_caches.jl b/src/caches/ssprk_caches.jl new file mode 100644 index 0000000000..b2c8833c69 --- /dev/null +++ b/src/caches/ssprk_caches.jl @@ -0,0 +1,1265 @@ +@cache struct SSPRK22Cache{uType, rateType, StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + fsalfirst::rateType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct SSPRK22ConstantCache <: OrdinaryDiffEqConstantCache end + +function alg_cache(alg::SSPRK22, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + k = zero(rate_prototype) + if calck + fsalfirst = zero(k) + else + fsalfirst = k + end + SSPRK22Cache(u, uprev, k, fsalfirst, alg.stage_limiter!, alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::SSPRK22, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SSPRK22ConstantCache() +end + +@cache struct SSPRK33Cache{uType, rateType, StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + fsalfirst::rateType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct SSPRK33ConstantCache <: OrdinaryDiffEqConstantCache end + +function alg_cache(alg::SSPRK33, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + k = zero(rate_prototype) + if calck + fsalfirst = zero(k) + else + fsalfirst = k + end + SSPRK33Cache(u, uprev, k, fsalfirst, alg.stage_limiter!, alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::SSPRK33, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SSPRK33ConstantCache() +end + +@cache struct KYKSSPRK42Cache{ + uType, + rateType, + TabType, + StageLimiter, + StepLimiter, + Thread +} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + tmp::uType + fsalfirst::rateType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct KYKSSPRK42ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + α20::T + α21::T + α30::T + α32::T + α40::T + α43::T + β10::T + β21::T + β30::T + β32::T + β40::T + β43::T + c1::T2 + c2::T2 + c3::T2 +end + +function KYKSSPRK42ConstantCache(T, T2) + α20 = T(0.394806441339829) + α21 = T(0.605193558660171) + α30 = T(0.002797307087390) + α32 = T(0.997202692912610) + α40 = T(0.252860909354373) + α43 = T(0.747139090645627) + β10 = T(0.406584463657504) + β21 = T(0.246062298456822) + β30 = T(0.013637216641451) + β32 = T(0.405447122055692) + β40 = T(0.016453567333598) + β43 = T(0.303775146447707) + c1 = T2(0.406584463657504) + c2 = T2(0.4921245969136438) + c3 = T2(0.9098323119879613) + KYKSSPRK42ConstantCache(α20, α21, α30, α32, α40, α43, β10, β21, β30, β32, β40, β43, c1, + c2, c3) +end + +function alg_cache(alg::KYKSSPRK42, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + tab = KYKSSPRK42ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + KYKSSPRK42Cache( + u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, alg.step_limiter!, + alg.thread) +end + +function alg_cache(alg::KYKSSPRK42, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + KYKSSPRK42ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct SSPRK53Cache{uType, rateType, TabType, StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + fsalfirst::rateType + tmp::uType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct SSPRK53ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + α30::T + α32::T + α40::T + α43::T + α52::T + α54::T + β10::T + β21::T + β32::T + β43::T + β54::T + c1::T2 + c2::T2 + c3::T2 + c4::T2 + + function SSPRK53ConstantCache(T, T2) + α30 = T(0.355909775063327) + α32 = T(0.644090224936674) + α40 = T(0.367933791638137) + α43 = T(0.632066208361863) + α52 = T(0.237593836598569) + α54 = T(0.762406163401431) + β10 = T(0.377268915331368) + β21 = T(0.377268915331368) + β32 = T(0.242995220537396) + β43 = T(0.238458932846290) + β54 = T(0.287632146308408) + c1 = T2(0.377268915331368) + c2 = T2(0.754537830662736) + c3 = T2(0.728985661612188) + c4 = T2(0.699226135931670) + + new{T, T2}(α30, α32, α40, α43, α52, α54, β10, β21, β32, β43, β54, c1, c2, c3, c4) + end +end + +function alg_cache(alg::SSPRK53, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + if calck + fsalfirst = zero(k) + else + fsalfirst = k + end + tab = SSPRK53ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + SSPRK53Cache(u, uprev, k, fsalfirst, tmp, tab, alg.stage_limiter!, alg.step_limiter!, + alg.thread) +end + +function alg_cache(alg::SSPRK53, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SSPRK53ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct SHLDDRK52Cache{uType, rateType, TabType, StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + tmp::uType + fsalfirst::rateType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct SHLDDRK52ConstantCache{T1, T2} <: OrdinaryDiffEqConstantCache + α2::T1 + α3::T1 + α4::T1 + α5::T1 + β1::T1 + β2::T1 + β3::T1 + β4::T1 + β5::T1 + c2::T2 + c3::T2 + c4::T2 + c5::T2 +end + +function SHLDDRK52ConstantCache(T1, T2) + α2 = T1(-0.6913065) + α3 = T1(-2.655155) + α4 = T1(-0.8147688) + α5 = T1(-0.6686587) + β1 = T1(0.1) + β2 = T1(0.75) + β3 = T1(0.7) + β4 = T1(0.479313) + β5 = T1(0.310392) + c2 = T2(0.1) + c3 = T2(0.3315201) + c4 = T2(0.4577796) + c5 = T2(0.8666528) + SHLDDRK52ConstantCache(α2, α3, α4, α5, β1, β2, β3, β4, β5, c2, c3, c4, c5) +end + +function alg_cache(alg::SHLDDRK52, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SHLDDRK52ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function alg_cache(alg::SHLDDRK52, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + tab = SHLDDRK52ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + SHLDDRK52Cache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, alg.step_limiter!, + alg.thread) +end + +@cache mutable struct SHLDDRK_2NCache{uType, rateType, TabType, StageLimiter, StepLimiter, + Thread} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + tmp::uType + fsalfirst::rateType + tab::TabType + step::Int + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +mutable struct SHLDDRK_2NConstantCache{T1, T2} <: OrdinaryDiffEqConstantCache + α21::T1 + α31::T1 + α41::T1 + α51::T1 + β11::T1 + β21::T1 + β31::T1 + β41::T1 + β51::T1 + c21::T2 + c31::T2 + c41::T2 + c51::T2 + + α22::T1 + α32::T1 + α42::T1 + α52::T1 + α62::T1 + β12::T1 + β22::T1 + β32::T1 + β42::T1 + β52::T1 + β62::T1 + c22::T2 + c32::T2 + c42::T2 + c52::T2 + c62::T2 + + step::Int +end + +function SHLDDRK_2NConstantCache(T1, T2) + α21 = T1(-0.6051226) + α31 = T1(-2.0437564) + α41 = T1(-0.7406999) + α51 = T1(-4.4231765) + β11 = T1(0.2687454) + β21 = T1(0.8014706) + β31 = T1(0.5051570) + β41 = T1(0.5623568) + β51 = T1(0.0590065) + c21 = T2(0.2687454) + c31 = T2(0.5852280) + c41 = T2(0.6827066) + c51 = T2(1.1646854) + + α22 = T1(-0.4412737) + α32 = T1(-1.0739820) + α42 = T1(-1.7063570) + α52 = T1(-2.7979293) + α62 = T1(-4.0913537) + β12 = T1(0.1158488) + β22 = T1(0.3728769) + β32 = T1(0.7379536) + β42 = T1(0.5798110) + β52 = T1(1.0312849) + β62 = T1(0.15) + c22 = T2(0.1158485) + c32 = T2(0.3241850) + c42 = T2(0.6193208) + c52 = T2(0.8034472) + c62 = T2(0.9184166) + SHLDDRK_2NConstantCache( + α21, α31, α41, α51, β11, β21, β31, β41, β51, c21, c31, c41, c51, + α22, α32, α42, α52, α62, β12, β22, β32, β42, β52, β62, c22, c32, + c42, c52, c62, 1) +end + +function alg_cache(alg::SHLDDRK_2N, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SHLDDRK_2NConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function alg_cache(alg::SHLDDRK_2N, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + tab = SHLDDRK_2NConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + SHLDDRK_2NCache(u, uprev, k, tmp, fsalfirst, tab, 1, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +@cache struct SSPRK53_2N1Cache{ + uType, + rateType, + TabType, + StageLimiter, + StepLimiter, + Thread +} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + fsalfirst::rateType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct SSPRK53_2N1ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + α40::T + α43::T + β10::T + β21::T + β32::T + β43::T + β54::T + c1::T2 + c2::T2 + c3::T2 + c4::T2 + + function SSPRK53_2N1ConstantCache(T, T2) + α40 = T(0.571403511494104) + α43 = T(0.428596488505896) + β10 = T(0.443568244942995) + β21 = T(0.291111420073766) + β32 = T(0.270612601278217) + β43 = T(0.110577759392786) + β54 = T(0.458557505351052) + c1 = T2(0.443568244942995) + c2 = T2(0.734679665016762) + c3 = T2(1.005292266294979) + c4 = T2(0.541442494648948) + + new{T, T2}(α40, α43, β10, β21, β32, β43, β54, c1, c2, c3, c4) + end +end + +function alg_cache(alg::SSPRK53_2N1, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + k = zero(rate_prototype) + if calck + fsalfirst = zero(k) + else + fsalfirst = k + end + tab = SSPRK53_2N1ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + SSPRK53_2N1Cache(u, uprev, k, fsalfirst, tab, alg.stage_limiter!, alg.step_limiter!, + alg.thread) +end + +function alg_cache(alg::SSPRK53_2N1, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SSPRK53_2N1ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct SSPRK53_2N2Cache{ + uType, + rateType, + TabType, + StageLimiter, + StepLimiter, + Thread +} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + fsalfirst::rateType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct SSPRK53_2N2ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + α30::T + α32::T + α50::T + α54::T + β10::T + β21::T + β32::T + β43::T + β54::T + c1::T2 + c2::T2 + c3::T2 + c4::T2 + + function SSPRK53_2N2ConstantCache(T, T2) + α30 = T(0.682342861037239) + α32 = T(0.317657138962761) + α50 = T(0.045230974482400) + α54 = T(0.954769025517600) + β10 = T(0.465388589249323) + β21 = T(0.465388589249323) + β32 = T(0.124745797313998) + β43 = T(0.465388589249323) + β54 = T(0.154263303748666) + c1 = T2(0.465388589249323) + c2 = T2(0.930777178498646) + c3 = T2(0.420413812847710) + c4 = T2(0.885802402097033) + + new{T, T2}(α30, α32, α50, α54, β10, β21, β32, β43, β54, c1, c2, c3, c4) + end +end + +function alg_cache(alg::SSPRK53_2N2, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + k = zero(rate_prototype) + if calck + fsalfirst = zero(k) + else + fsalfirst = k + end + tab = SSPRK53_2N2ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + SSPRK53_2N2Cache(u, uprev, k, fsalfirst, tab, alg.stage_limiter!, alg.step_limiter!, + alg.thread) +end + +function alg_cache(alg::SSPRK53_2N2, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SSPRK53_2N2ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct SSPRK53_HCache{uType, rateType, TabType, StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + fsalfirst::rateType + tmp::uType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct SSPRK53_HConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + α30::T + α32::T + α40::T + α41::T + α43::T + β10::T + β21::T + β32::T + β43::T + β54::T + c1::T2 + c2::T2 + c3::T2 + c4::T2 + + function SSPRK53_HConstantCache(T, T2) + α30 = T(0.308684154602513) + α32 = T(0.691315845397487) + α40 = T(0.280514990468574) + α41 = T(0.270513101776498) + α43 = T(0.448971907754928) + β10 = T(0.377268915331368) + β21 = T(0.377268915331368) + β32 = T(0.260811979144498) + β43 = T(0.169383144652957) + β54 = T(0.377268915331368) + c1 = T2(0.377268915331368) + c2 = T2(0.754537830662737) + c3 = T2(0.782435937433493) + c4 = T2(0.622731084668631) + + new{T, T2}(α30, α32, α40, α41, α43, β10, β21, β32, β43, β54, c1, c2, c3, c4) + end +end + +function alg_cache(alg::SSPRK53_H, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + if calck + fsalfirst = zero(k) + else + fsalfirst = k + end + tab = SSPRK53_HConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + SSPRK53_HCache(u, uprev, k, fsalfirst, tmp, tab, alg.stage_limiter!, alg.step_limiter!, + alg.thread) +end + +function alg_cache(alg::SSPRK53_H, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SSPRK53_HConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct SSPRK63Cache{uType, rateType, TabType, StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + fsalfirst::rateType + tmp::uType + u₂::uType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct SSPRK63ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + α40::T + α41::T + α43::T + α62::T + α65::T + β10::T + β21::T + β32::T + β43::T + β54::T + β65::T + c1::T2 + c2::T2 + c3::T2 + c4::T2 + c5::T2 + + function SSPRK63ConstantCache(T, T2) + α40 = T(0.476769811285196) + α41 = T(0.098511733286064) + α43 = T(0.424718455428740) + α62 = T(0.155221702560091) + α65 = T(0.844778297439909) + β10 = T(0.284220721334261) + β21 = T(0.284220721334261) + β32 = T(0.284220721334261) + β43 = T(0.120713785765930) + β54 = T(0.284220721334261) + β65 = T(0.240103497065900) + c1 = T2(0.284220721334261) + c2 = T2(0.568441442668522) + c3 = T2(0.852662164002783) + c4 = T2(0.510854218958172) + c5 = T2(0.795074940292433) + + new{T, T2}(α40, α41, α43, α62, α65, β10, β21, β32, β43, β54, β65, c1, c2, c3, c4, + c5) + end +end + +function alg_cache(alg::SSPRK63, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + u₂ = zero(u) + k = zero(rate_prototype) + if calck + fsalfirst = zero(k) + else + fsalfirst = k + end + tab = SSPRK63ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + SSPRK63Cache(u, uprev, k, fsalfirst, tmp, u₂, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::SSPRK63, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SSPRK63ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct SSPRK73Cache{uType, rateType, TabType, StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + fsalfirst::rateType + tmp::uType + u₁::uType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct SSPRK73ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + α40::T + α43::T + α50::T + α51::T + α54::T + α73::T + α76::T + β10::T + β21::T + β32::T + β43::T + β54::T + β65::T + β76::T + c1::T2 + c2::T2 + c3::T2 + c4::T2 + c5::T2 + c6::T2 + + function SSPRK73ConstantCache(T, T2) + α40 = T(0.184962588071072) + α43 = T(0.815037411928928) + α50 = T(0.180718656570380) + α51 = T(0.314831034403793) + α54 = T(0.504450309025826) + α73 = T(0.120199000000000) + α76 = T(0.879801000000000) + β10 = T(0.233213863663009) + β21 = T(0.233213863663009) + β32 = T(0.233213863663009) + β43 = T(0.190078023865845) + β54 = T(0.117644805593912) + β65 = T(0.233213863663009) + β76 = T(0.205181790464579) + c1 = T2(0.233213863663009) + c2 = T2(0.466427727326018) + c3 = T2(0.699641590989027) + c4 = T2(0.760312095463379) + c5 = T2(0.574607439040817) + c6 = T2(0.807821302703826) + + new{T, T2}( + α40, α43, α50, α51, α54, α73, α76, β10, β21, β32, β43, β54, β65, β76, c1, + c2, c3, c4, c5, c6) + end +end + +function alg_cache(alg::SSPRK73, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + u₁ = zero(u) + k = zero(rate_prototype) + if calck + fsalfirst = zero(k) + else + fsalfirst = k + end + tab = SSPRK73ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + SSPRK73Cache(u, uprev, k, fsalfirst, tmp, u₁, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::SSPRK73, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SSPRK73ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct SSPRK83Cache{uType, rateType, TabType, StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + fsalfirst::rateType + tmp::uType + u₂::uType + u₃::uType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct SSPRK83ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + α50::T + α51::T + α54::T + α61::T + α65::T + α72::T + α73::T + α76::T + β10::T + β21::T + β32::T + β43::T + β54::T + β65::T + β76::T + β87::T + c1::T2 + c2::T2 + c3::T2 + c4::T2 + c5::T2 + c6::T2 + c7::T2 + + function SSPRK83ConstantCache(T, T2) + α50 = T(0.421366967085359) + α51 = T(0.005949401107575) + α54 = T(0.572683631807067) + α61 = T(0.004254010666365) + α65 = T(0.995745989333635) + α72 = T(0.104380143093325) + α73 = T(0.243265240906726) + α76 = T(0.652354615999950) + β10 = T(0.195804015330143) + β21 = T(0.195804015330143) + β32 = T(0.195804015330143) + β43 = T(0.195804015330143) + β54 = T(0.112133754621673) + β65 = T(0.194971062960412) + β76 = T(0.127733653231944) + β87 = T(0.195804015330143) + c1 = T2(0.195804015330143) + c2 = T2(0.391608030660286) + c3 = T2(0.587412045990429) + c4 = T2(0.783216061320572) + c5 = T2(0.561833689734037) + c6 = T2(0.755247658555329) + c7 = T2(0.804195984669857) + + new{T, T2}(α50, α51, α54, α61, α65, α72, α73, α76, β10, β21, β32, β43, β54, β65, + β76, β87, c1, c2, c3, c4, c5, c6, c7) + end +end + +function alg_cache(alg::SSPRK83, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + u₂ = zero(u) + u₃ = zero(u) + k = zero(rate_prototype) + if calck + fsalfirst = zero(k) + else + fsalfirst = k + end + tab = SSPRK83ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + SSPRK83Cache(u, uprev, k, fsalfirst, tmp, u₂, u₃, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::SSPRK83, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SSPRK83ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct SSPRK43Cache{uType, rateType, uNoUnitsType, TabType, StageLimiter, + StepLimiter, Thread} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + fsalfirst::rateType + utilde::uType + atmp::uNoUnitsType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct SSPRK43ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + one_third_u::T + two_thirds_u::T + half_u::T + half_t::T2 + + function SSPRK43ConstantCache(T, T2) + one_third_u = inv(T(3)) + two_thirds_u = 2 * one_third_u + half_u = T(0.5) + half_t = T2(0.5) + + new{T, T2}(one_third_u, two_thirds_u, half_u, half_t) + end +end + +function alg_cache(alg::SSPRK43, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + k = zero(rate_prototype) + if calck + fsalfirst = zero(k) + else + fsalfirst = k + end + utilde = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + tab = SSPRK43ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + SSPRK43Cache(u, uprev, k, fsalfirst, utilde, atmp, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::SSPRK43, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SSPRK43ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct SSPRK432Cache{ + uType, + rateType, + uNoUnitsType, + StageLimiter, + StepLimiter, + Thread +} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + fsalfirst::rateType + utilde::uType + atmp::uNoUnitsType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct SSPRK432ConstantCache <: OrdinaryDiffEqConstantCache end + +function alg_cache(alg::SSPRK432, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + k = zero(rate_prototype) + if calck + fsalfirst = zero(k) + else + fsalfirst = k + end + utilde = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + SSPRK432Cache(u, uprev, k, fsalfirst, utilde, atmp, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::SSPRK432, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SSPRK432ConstantCache() +end + +@cache mutable struct SSPRKMSVS32Cache{uType, rateType, dtArrayType, dtType, StageLimiter, + StepLimiter, Thread} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + u_2::uType + u_1::uType + k::rateType + tmp::uType + dts::dtArrayType + dtf::dtArrayType + μ::dtType + v_n::Float64 + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread + step::Int +end + +@cache mutable struct SSPRKMSVS32ConstantCache{uType, dtArrayType, dtType} <: + OrdinaryDiffEqConstantCache + u_2::uType + u_1::uType + dts::dtArrayType + dtf::dtArrayType + μ::dtType + v_n::Float64 + step::Int +end + +function alg_cache(alg::SSPRKMSVS32, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + fsalfirst = zero(rate_prototype) + dts = fill(zero(dt), 3) + dtf = fill(zero(dt), 2) + μ = zero(dt) + u_2 = zero(u) + u_1 = zero(u) + k = zero(rate_prototype) + tmp = zero(u) + SSPRKMSVS32Cache(u, uprev, fsalfirst, u_2, u_1, k, tmp, dts, dtf, μ, 0.5, + alg.stage_limiter!, alg.step_limiter!, alg.thread, 1) +end + +function alg_cache(alg::SSPRKMSVS32, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + dts = fill(zero(dt), 3) + dtf = fill(zero(dt), 2) + μ = zero(dt) + u_2 = u + u_1 = u + SSPRKMSVS32ConstantCache(u_2, u_1, dts, dtf, μ, 0.5, 1) +end + +@cache mutable struct SSPRKMSVS43Cache{ + uType, + rateType, + StageLimiter, + StepLimiter, + Thread +} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + fsalfirst::rateType + u_3::uType + u_2::uType + u_1::uType + k::rateType + k1::rateType + k2::rateType + k3::rateType + tmp::uType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread + step::Int +end + +@cache mutable struct SSPRKMSVS43ConstantCache{uType, rateType} <: + OrdinaryDiffEqConstantCache + u_3::uType + u_2::uType + u_1::uType + k1::rateType + k2::rateType + k3::rateType + step::Int +end + +function alg_cache(alg::SSPRKMSVS43, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + fsalfirst = zero(rate_prototype) + u_3 = zero(u) + u_2 = zero(u) + u_1 = zero(u) + k = zero(rate_prototype) + k1 = zero(rate_prototype) + k2 = zero(rate_prototype) + k3 = zero(rate_prototype) + tmp = zero(u) + SSPRKMSVS43Cache(u, uprev, fsalfirst, u_3, u_2, u_1, k, k1, k2, k3, tmp, + alg.stage_limiter!, alg.step_limiter!, alg.thread, 1) +end + +function alg_cache(alg::SSPRKMSVS43, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + u_3 = u + u_2 = u + u_1 = u + k1 = rate_prototype + k2 = rate_prototype + k3 = rate_prototype + SSPRKMSVS43ConstantCache(u_3, u_2, u_1, k1, k2, k3, 1) +end + +@cache struct SSPRK932Cache{ + uType, + rateType, + uNoUnitsType, + StageLimiter, + StepLimiter, + Thread +} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + fsalfirst::rateType + utilde::uType + atmp::uNoUnitsType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct SSPRK932ConstantCache <: OrdinaryDiffEqConstantCache end + +function alg_cache(alg::SSPRK932, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + k = zero(rate_prototype) + if calck + fsalfirst = zero(k) + else + fsalfirst = k + end + utilde = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + SSPRK932Cache(u, uprev, k, fsalfirst, utilde, atmp, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::SSPRK932, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SSPRK932ConstantCache() +end + +@cache struct SSPRK54Cache{uType, rateType, TabType, StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + fsalfirst::rateType + k₃::rateType + u₂::uType + u₃::uType + tmp::uType # should be u₄, but tmp is needed for callbacks + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct SSPRK54ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + β10::T + α20::T + α21::T + β21::T + α30::T + α32::T + β32::T + α40::T + α43::T + β43::T + α52::T + α53::T + β53::T + α54::T + β54::T + c1::T2 + c2::T2 + c3::T2 + c4::T2 + + function SSPRK54ConstantCache(T, T2) + β10 = T(0.391752226571890) + α20 = T(0.444370493651235) + α21 = T(0.555629506348765) + β21 = T(0.368410593050371) + α30 = T(0.620101851488403) + α32 = T(0.379898148511597) + β32 = T(0.251891774271694) + α40 = T(0.178079954393132) + α43 = T(0.821920045606868) + β43 = T(0.544974750228521) + α52 = T(0.517231671970585) + α53 = T(0.096059710526147) + β53 = T(0.063692468666290) + α54 = T(0.386708617503269) + β54 = T(0.226007483236906) + c1 = T2(0.391752226571890) + c2 = T2(0.586079689311540) + c3 = T2(0.474542363121400) + c4 = T2(0.935010630967653) + + new{T, T2}(β10, α20, α21, β21, α30, α32, β32, α40, α43, β43, α52, α53, β53, α54, + β54, c1, c2, c3, c4) + end +end + +function alg_cache(alg::SSPRK54, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + u₂ = zero(u) + u₃ = zero(u) + tmp = zero(u) + k = zero(rate_prototype) + if calck + fsalfirst = zero(k) + else + fsalfirst = k + end + k₃ = zero(rate_prototype) + tab = SSPRK54ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + SSPRK54Cache(u, uprev, k, fsalfirst, k₃, u₂, u₃, tmp, tab, alg.stage_limiter!, + alg.step_limiter!, alg.thread) +end + +function alg_cache(alg::SSPRK54, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SSPRK54ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct SSPRK104Cache{uType, rateType, StageLimiter, StepLimiter, Thread} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k::rateType + fsalfirst::rateType + k₄::rateType + tmp::uType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +struct SSPRK104ConstantCache <: OrdinaryDiffEqConstantCache end + +function alg_cache(alg::SSPRK104, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + if calck + fsalfirst = zero(k) + else + fsalfirst = k + end + k₄ = zero(rate_prototype) + SSPRK104Cache(u, uprev, k, fsalfirst, k₄, tmp, alg.stage_limiter!, alg.step_limiter!, + alg.thread) +end + +function alg_cache(alg::SSPRK104, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SSPRK104ConstantCache() +end diff --git a/src/caches/symplectic_caches.jl b/src/caches/symplectic_caches.jl new file mode 100644 index 0000000000..71c55340dc --- /dev/null +++ b/src/caches/symplectic_caches.jl @@ -0,0 +1,419 @@ +@cache struct SymplecticEulerCache{uType, rateType} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + tmp::uType + k::rateType + fsalfirst::rateType +end + +function alg_cache(alg::SymplecticEuler, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SymplecticEulerCache(u, uprev, zero(u), zero(rate_prototype), zero(rate_prototype)) +end + +struct SymplecticEulerConstantCache <: OrdinaryDiffEqConstantCache end + +function alg_cache(alg::SymplecticEuler, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SymplecticEulerConstantCache() +end + +@cache struct VelocityVerletCache{uType, rateType, uEltypeNoUnits} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + tmp::uType + k::rateType + fsalfirst::rateType + half::uEltypeNoUnits +end + +struct VelocityVerletConstantCache{uEltypeNoUnits} <: OrdinaryDiffEqConstantCache + half::uEltypeNoUnits +end + +function alg_cache(alg::VelocityVerlet, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(rate_prototype) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + half = uEltypeNoUnits(1 // 2) + VelocityVerletCache(u, uprev, k, tmp, fsalfirst, half) +end + +function alg_cache(alg::VelocityVerlet, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + VelocityVerletConstantCache(uEltypeNoUnits(1 // 2)) +end + +@cache struct Symplectic2Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + tmp::uType + k::rateType + fsalfirst::rateType + tab::tableauType +end + +function alg_cache(alg::VerletLeapfrog, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + tab = VerletLeapfrogConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + Symplectic2Cache(u, uprev, k, tmp, fsalfirst, tab) +end + +function alg_cache(alg::VerletLeapfrog, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + VerletLeapfrogConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function alg_cache(alg::PseudoVerletLeapfrog, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + tab = PseudoVerletLeapfrogConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + Symplectic2Cache(u, uprev, k, tmp, fsalfirst, tab) +end + +function alg_cache(alg::PseudoVerletLeapfrog, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + PseudoVerletLeapfrogConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) +end + +function alg_cache(alg::McAte2, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + tab = McAte2ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + Symplectic2Cache(u, uprev, k, tmp, fsalfirst, tab) +end + +function alg_cache(alg::McAte2, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + McAte2ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct Symplectic3Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + tmp::uType + k::rateType + fsalfirst::rateType + tab::tableauType +end + +function alg_cache(alg::Ruth3, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + tab = Ruth3ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + Symplectic3Cache(u, uprev, k, tmp, fsalfirst, tab) +end + +function alg_cache(alg::Ruth3, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + Ruth3ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function alg_cache(alg::McAte3, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + tab = McAte3ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + Symplectic3Cache(u, uprev, k, tmp, fsalfirst, tab) +end + +function alg_cache(alg::McAte3, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + McAte3ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct Symplectic4Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + tmp::uType + k::rateType + fsalfirst::rateType + tab::tableauType +end + +function alg_cache(alg::McAte4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + tab = McAte4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + Symplectic4Cache(u, uprev, k, tmp, fsalfirst, tab) +end + +function alg_cache(alg::McAte4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + McAte4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function alg_cache(alg::CandyRoz4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + tab = CandyRoz4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + Symplectic4Cache(u, uprev, k, tmp, fsalfirst, tab) +end + +function alg_cache(alg::CandyRoz4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + McAte4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct Symplectic45Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + tmp::uType + k::rateType + fsalfirst::rateType + tab::tableauType +end + +function alg_cache(alg::CalvoSanz4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + tab = CalvoSanz4ConstantCache(constvalue(uBottomEltypeNoUnits), + constvalue(tTypeNoUnits)) + Symplectic45Cache(u, uprev, k, tmp, fsalfirst, tab) +end + +function alg_cache(alg::CalvoSanz4, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + CalvoSanz4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +function alg_cache(alg::McAte42, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + tab = McAte42ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + Symplectic45Cache(u, uprev, k, tmp, fsalfirst, tab) +end + +function alg_cache(alg::McAte42, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + McAte42ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct Symplectic5Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + tmp::uType + k::rateType + fsalfirst::rateType + tab::tableauType +end + +function alg_cache(alg::McAte5, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + tab = McAte5ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + Symplectic5Cache(u, uprev, k, tmp, fsalfirst, tab) +end + +function alg_cache(alg::McAte5, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + McAte5ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct Symplectic6Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + tmp::uType + k::rateType + fsalfirst::rateType + tab::tableauType +end + +function alg_cache(alg::Yoshida6, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + tab = Yoshida6ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + Symplectic6Cache(u, uprev, k, tmp, fsalfirst, tab) +end + +function alg_cache(alg::Yoshida6, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + Yoshida6ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct Symplectic62Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + tmp::uType + k::rateType + fsalfirst::rateType + tab::tableauType +end + +function alg_cache(alg::KahanLi6, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + tab = KahanLi6ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + Symplectic62Cache(u, uprev, k, tmp, fsalfirst, tab) +end + +function alg_cache(alg::KahanLi6, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + KahanLi6ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct McAte8Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + tmp::uType + k::rateType + fsalfirst::rateType + tab::tableauType +end + +function alg_cache(alg::McAte8, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + tab = McAte8ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + McAte8Cache(u, uprev, k, tmp, fsalfirst, tab) +end + +function alg_cache(alg::McAte8, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + McAte8ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct KahanLi8Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + tmp::uType + k::rateType + fsalfirst::rateType + tab::tableauType +end + +function alg_cache(alg::KahanLi8, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + tab = KahanLi8ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + KahanLi8Cache(u, uprev, k, tmp, fsalfirst, tab) +end + +function alg_cache(alg::KahanLi8, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + KahanLi8ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end + +@cache struct SofSpa10Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache + u::uType + uprev::uType + tmp::uType + k::rateType + fsalfirst::rateType + tab::tableauType +end + +function alg_cache(alg::SofSpa10, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tmp = zero(u) + k = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + tab = SofSpa10ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + SofSpa10Cache(u, uprev, k, tmp, fsalfirst, tab) +end + +function alg_cache(alg::SofSpa10, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + SofSpa10ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) +end diff --git a/src/caches/verner_caches.jl b/src/caches/verner_caches.jl new file mode 100644 index 0000000000..08b1de0919 --- /dev/null +++ b/src/caches/verner_caches.jl @@ -0,0 +1,258 @@ +@cache struct Vern6Cache{uType, rateType, uNoUnitsType, TabType, StageLimiter, StepLimiter, + Thread} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k1::rateType + k2::rateType + k3::rateType + k4::rateType + k5::rateType + k6::rateType + k7::rateType + k8::rateType + k9::rateType + utilde::uType + tmp::uType + rtmp::rateType + atmp::uNoUnitsType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +TruncatedStacktraces.@truncate_stacktrace Vern6Cache 1 + +function alg_cache(alg::Vern6, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tab = Vern6Tableau(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + k1 = zero(rate_prototype) + k2 = zero(rate_prototype) + k3 = k2 + k4 = zero(rate_prototype) + k5 = zero(rate_prototype) + k6 = zero(rate_prototype) + k7 = zero(rate_prototype) + k8 = k3 + k9 = zero(rate_prototype) + utilde = zero(u) + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + rtmp = uEltypeNoUnits === eltype(u) ? utilde : zero(rate_prototype) + Vern6Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8, k9, utilde, tmp, rtmp, atmp, tab, + alg.stage_limiter!, alg.step_limiter!, alg.thread) +end + +struct Vern6ConstantCache{TabType} <: OrdinaryDiffEqConstantCache + tab::TabType +end + +function alg_cache(alg::Vern6, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tab = Vern6Tableau(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + Vern6ConstantCache(tab) +end + +@cache struct Vern7Cache{uType, rateType, uNoUnitsType, StageLimiter, StepLimiter, + Thread} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k1::rateType + k2::rateType + k3::rateType + k4::rateType + k5::rateType + k6::rateType + k7::rateType + k8::rateType + k9::rateType + k10::rateType + utilde::uType + tmp::uType + rtmp::rateType + atmp::uNoUnitsType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +TruncatedStacktraces.@truncate_stacktrace Vern7Cache 1 + +function alg_cache(alg::Vern7, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + k1 = zero(rate_prototype) + k2 = zero(rate_prototype) + k3 = k2 + k4 = zero(rate_prototype) + k5 = zero(rate_prototype) + k6 = zero(rate_prototype) + k7 = zero(rate_prototype) + k8 = zero(rate_prototype) + k9 = zero(rate_prototype) + k10 = k2 + utilde = zero(u) + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + rtmp = uEltypeNoUnits === eltype(u) ? utilde : zero(rate_prototype) + Vern7Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, utilde, tmp, rtmp, atmp, + alg.stage_limiter!, alg.step_limiter!, alg.thread) +end + +struct Vern7ConstantCache <: OrdinaryDiffEqConstantCache end + +function alg_cache(alg::Vern7, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + Vern7ConstantCache() +end + +@cache struct Vern8Cache{uType, rateType, uNoUnitsType, TabType, StageLimiter, StepLimiter, + Thread} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k1::rateType + k2::rateType + k3::rateType + k4::rateType + k5::rateType + k6::rateType + k7::rateType + k8::rateType + k9::rateType + k10::rateType + k11::rateType + k12::rateType + k13::rateType + utilde::uType + tmp::uType + rtmp::rateType + atmp::uNoUnitsType + tab::TabType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +TruncatedStacktraces.@truncate_stacktrace Vern8Cache 1 + +function alg_cache(alg::Vern8, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tab = Vern8Tableau(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + k1 = zero(rate_prototype) + k2 = zero(rate_prototype) + k3 = k2 + k4 = zero(rate_prototype) + k5 = k2 + k6 = zero(rate_prototype) + k7 = zero(rate_prototype) + k8 = zero(rate_prototype) + tmp = zero(u) + k9 = zero(rate_prototype) + k10 = zero(rate_prototype) + k11 = zero(rate_prototype) + k12 = zero(rate_prototype) + k13 = k4 + utilde = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + rtmp = uEltypeNoUnits === eltype(u) ? utilde : zero(rate_prototype) + Vern8Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, utilde, + tmp, rtmp, atmp, tab, alg.stage_limiter!, alg.step_limiter!, alg.thread) +end + +struct Vern8ConstantCache{TabType} <: OrdinaryDiffEqConstantCache + tab::TabType +end + +function alg_cache(alg::Vern8, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + tab = Vern8Tableau(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) + Vern8ConstantCache(tab) +end + +@cache struct Vern9Cache{uType, rateType, uNoUnitsType, StageLimiter, StepLimiter, + Thread} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + k1::rateType + k2::rateType + k3::rateType + k4::rateType + k5::rateType + k6::rateType + k7::rateType + k8::rateType + k9::rateType + k10::rateType + k11::rateType + k12::rateType + k13::rateType + k14::rateType + k15::rateType + k16::rateType + utilde::uType + tmp::uType + rtmp::rateType + atmp::uNoUnitsType + stage_limiter!::StageLimiter + step_limiter!::StepLimiter + thread::Thread +end + +TruncatedStacktraces.@truncate_stacktrace Vern9Cache 1 + +function alg_cache(alg::Vern9, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + k1 = zero(rate_prototype) + k2 = zero(rate_prototype) + k3 = k2 + k4 = zero(rate_prototype) + k5 = k3 + k6 = zero(rate_prototype) + k7 = k4 + k8 = k5 + k9 = zero(rate_prototype) + k10 = zero(rate_prototype) + k11 = zero(rate_prototype) + k12 = zero(rate_prototype) + k13 = zero(rate_prototype) + k14 = zero(rate_prototype) + k15 = zero(rate_prototype) + k16 = k6 + utilde = zero(u) + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) + rtmp = uEltypeNoUnits === eltype(u) ? utilde : zero(rate_prototype) + Vern9Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, + k16, utilde, tmp, rtmp, atmp, alg.stage_limiter!, alg.step_limiter!, + alg.thread) +end + +struct Vern9ConstantCache <: OrdinaryDiffEqConstantCache end + +function alg_cache(alg::Vern9, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, + dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + Vern9ConstantCache() +end diff --git a/src/dense/verner_addsteps.jl b/src/dense/verner_addsteps.jl new file mode 100644 index 0000000000..9395b42cda --- /dev/null +++ b/src/dense/verner_addsteps.jl @@ -0,0 +1,1323 @@ +@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern6Cache, + always_calc_begin = false, allow_calc_end = true, + force_calc_end = false) + if length(k) < 9 || always_calc_begin + @unpack c1, c2, c3, c4, c5, c6, a21, a31, a32, a41, a43, a51, a53, a54, a61, a63, a64, a65, a71, a73, a74, a75, a76, a81, a83, a84, a85, a86, a87, a91, a94, a95, a96, a97, a98 = cache.tab + @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, tmp = cache + @.. broadcast=false tmp=uprev + dt * (a21 * k1) + f(k2, tmp, p, t + c1 * dt) + @.. broadcast=false tmp=uprev + dt * (a31 * k1 + a32 * k2) + f(k3, tmp, p, t + c2 * dt) + @.. broadcast=false tmp=uprev + dt * (a41 * k1 + a43 * k3) + f(k4, tmp, p, t + c3 * dt) + @.. broadcast=false tmp=uprev + dt * (a51 * k1 + a53 * k3 + a54 * k4) + f(k5, tmp, p, t + c4 * dt) + @.. broadcast=false tmp=uprev + dt * (a61 * k1 + a63 * k3 + a64 * k4 + a65 * k5) + f(k6, tmp, p, t + c5 * dt) + @.. broadcast=false tmp=uprev + + dt * (a71 * k1 + a73 * k3 + a74 * k4 + a75 * k5 + a76 * k6) + f(k7, tmp, p, t + c6 * dt) + @.. broadcast=false tmp=uprev + + dt * + (a81 * k1 + a83 * k3 + a84 * k4 + a85 * k5 + a86 * k6 + + a87 * k7) + f(k8, tmp, p, t + dt) + @.. broadcast=false tmp=uprev + + dt * + (a91 * k1 + a94 * k4 + a95 * k5 + a96 * k6 + a97 * k7 + + a98 * k8) + f(k9, tmp, p, t + dt) + copyat_or_push!(k, 1, k1) + copyat_or_push!(k, 2, k2) + copyat_or_push!(k, 3, k3) + copyat_or_push!(k, 4, k4) + copyat_or_push!(k, 5, k5) + copyat_or_push!(k, 6, k6) + copyat_or_push!(k, 7, k7) + copyat_or_push!(k, 8, k8) + copyat_or_push!(k, 9, k9) + end + if (allow_calc_end && length(k) < 12) || force_calc_end # Have not added the extra stages yet + @unpack c10, a1001, a1004, a1005, a1006, a1007, a1008, a1009, c11, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, c12, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211 = cache.tab.extra + @unpack tmp = cache + rtmp = similar(cache.k1) + uidx = eachindex(uprev) + @.. broadcast=false tmp=uprev + + dt * + (a1001 * k[1] + a1004 * k[4] + a1005 * k[5] + a1006 * k[6] + + a1007 * k[7] + a1008 * k[8] + a1009 * k[9]) + f(rtmp, tmp, p, t + c10 * dt) + copyat_or_push!(k, 10, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a1101 * k[1] + a1104 * k[4] + a1105 * k[5] + a1106 * k[6] + + a1107 * k[7] + a1108 * k[8] + a1109 * k[9] + a1110 * k[10]) + f(rtmp, tmp, p, t + c11 * dt) + copyat_or_push!(k, 11, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a1201 * k[1] + a1204 * k[4] + a1205 * k[5] + a1206 * k[6] + + a1207 * k[7] + a1208 * k[8] + a1209 * k[9] + + a1210 * k[10] + a1211 * k[11]) + f(rtmp, tmp, p, t + c12 * dt) + copyat_or_push!(k, 12, rtmp) + end + nothing +end + +@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern7Cache, + always_calc_begin = false, allow_calc_end = true, + force_calc_end = false) + T = constvalue(recursive_unitless_bottom_eltype(u)) + T2 = constvalue(typeof(one(t))) + if length(k) < 10 || always_calc_begin + @OnDemandTableauExtract Vern7Tableau T T2 + @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, tmp = cache + f(k1, uprev, p, t) + @.. broadcast=false tmp=uprev + dt * (a021 * k1) + f(k2, tmp, p, t + c2 * dt) + @.. broadcast=false tmp=uprev + dt * (a031 * k1 + a032 * k2) + f(k3, tmp, p, t + c3 * dt) + @.. broadcast=false tmp=uprev + dt * (a041 * k1 + a043 * k3) + f(k4, tmp, p, t + c4 * dt) + @.. broadcast=false tmp=uprev + dt * (a051 * k1 + a053 * k3 + a054 * k4) + f(k5, tmp, p, t + c5 * dt) + @.. broadcast=false tmp=uprev + dt * (a061 * k1 + a063 * k3 + a064 * k4 + a065 * k5) + f(k6, tmp, p, t + c6 * dt) + @.. broadcast=false tmp=uprev + + dt * + (a071 * k1 + a073 * k3 + a074 * k4 + a075 * k5 + a076 * k6) + f(k7, tmp, p, t + c7 * dt) + @.. broadcast=false tmp=uprev + + dt * + (a081 * k1 + a083 * k3 + a084 * k4 + a085 * k5 + a086 * k6 + + a087 * k7) + f(k8, tmp, p, t + c8 * dt) + @.. broadcast=false tmp=uprev + + dt * + (a091 * k1 + a093 * k3 + a094 * k4 + a095 * k5 + a096 * k6 + + a097 * k7 + a098 * k8) + f(k9, tmp, p, t + dt) + @.. broadcast=false tmp=uprev + + dt * + (a101 * k1 + a103 * k3 + a104 * k4 + a105 * k5 + a106 * k6 + + a107 * k7) + f(k10, tmp, p, t + dt) + copyat_or_push!(k, 1, k1) + copyat_or_push!(k, 2, k2) + copyat_or_push!(k, 3, k3) + copyat_or_push!(k, 4, k4) + copyat_or_push!(k, 5, k5) + copyat_or_push!(k, 6, k6) + copyat_or_push!(k, 7, k7) + copyat_or_push!(k, 8, k8) + copyat_or_push!(k, 9, k9) + copyat_or_push!(k, 10, k10) + end + if (allow_calc_end && length(k) < 16) || force_calc_end # Have not added the extra stages yet + @unpack tmp = cache + rtmp = similar(cache.k1) + @OnDemandTableauExtract Vern7ExtraStages T T2 + @.. broadcast=false tmp=uprev + + dt * + (a1101 * k[1] + a1104 * k[4] + a1105 * k[5] + a1106 * k[6] + + a1107 * k[7] + a1108 * k[8] + a1109 * k[9]) + f(rtmp, tmp, p, t + c11 * dt) + copyat_or_push!(k, 11, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a1201 * k[1] + a1204 * k[4] + a1205 * k[5] + a1206 * k[6] + + a1207 * k[7] + a1208 * k[8] + a1209 * k[9] + a1211 * k[11]) + f(rtmp, tmp, p, t + c12 * dt) + copyat_or_push!(k, 12, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a1301 * k[1] + a1304 * k[4] + a1305 * k[5] + a1306 * k[6] + + a1307 * k[7] + a1308 * k[8] + a1309 * k[9] + + a1311 * k[11] + a1312 * k[12]) + f(rtmp, tmp, p, t + c13 * dt) + copyat_or_push!(k, 13, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a1401 * k[1] + a1404 * k[4] + a1405 * k[5] + a1406 * k[6] + + a1407 * k[7] + a1408 * k[8] + a1409 * k[9] + + a1411 * k[11] + a1412 * k[12] + a1413 * k[13]) + f(rtmp, tmp, p, t + c14 * dt) + copyat_or_push!(k, 14, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a1501 * k[1] + a1504 * k[4] + a1505 * k[5] + a1506 * k[6] + + a1507 * k[7] + a1508 * k[8] + a1509 * k[9] + + a1511 * k[11] + a1512 * k[12] + a1513 * k[13]) + f(rtmp, tmp, p, t + c15 * dt) + copyat_or_push!(k, 15, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a1601 * k[1] + a1604 * k[4] + a1605 * k[5] + a1606 * k[6] + + a1607 * k[7] + a1608 * k[8] + a1609 * k[9] + + a1611 * k[11] + a1612 * k[12] + a1613 * k[13]) + f(rtmp, tmp, p, t + c16 * dt) + copyat_or_push!(k, 16, rtmp) + end + nothing +end + +@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern7Cache{<:Array}, + always_calc_begin = false, allow_calc_end = true, + force_calc_end = false) + T = constvalue(recursive_unitless_bottom_eltype(u)) + T2 = constvalue(typeof(one(t))) + if length(k) < 10 || always_calc_begin + @OnDemandTableauExtract Vern7Tableau T T2 + + @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, tmp = cache + f(k1, uprev, p, t) + + @inbounds @simd ivdep for i in eachindex(u) + tmp[i] = uprev[i] + dt * (a021 * k1[i]) + end + f(k2, tmp, p, t + c2 * dt) + + @inbounds @simd ivdep for i in eachindex(u) + tmp[i] = uprev[i] + dt * (a031 * k1[i] + a032 * k2[i]) + end + f(k3, tmp, p, t + c3 * dt) + + @inbounds @simd ivdep for i in eachindex(u) + tmp[i] = uprev[i] + dt * (a041 * k1[i] + a043 * k3[i]) + end + f(k4, tmp, p, t + c4 * dt) + + @inbounds @simd ivdep for i in eachindex(u) + tmp[i] = uprev[i] + dt * (a051 * k1[i] + a053 * k3[i] + a054 * k4[i]) + end + f(k5, tmp, p, t + c5 * dt) + + @inbounds @simd ivdep for i in eachindex(u) + tmp[i] = uprev[i] + + dt * (a061 * k1[i] + a063 * k3[i] + a064 * k4[i] + a065 * k5[i]) + end + f(k6, tmp, p, t + c6 * dt) + + @inbounds @simd ivdep for i in eachindex(u) + tmp[i] = uprev[i] + + dt * (a071 * k1[i] + a073 * k3[i] + a074 * k4[i] + a075 * k5[i] + + a076 * k6[i]) + end + f(k7, tmp, p, t + c7 * dt) + + @inbounds @simd ivdep for i in eachindex(u) + tmp[i] = uprev[i] + + dt * (a081 * k1[i] + a083 * k3[i] + a084 * k4[i] + a085 * k5[i] + + a086 * k6[i] + a087 * k7[i]) + end + f(k8, tmp, p, t + c8 * dt) + + @inbounds @simd ivdep for i in eachindex(u) + tmp[i] = uprev[i] + + dt * (a091 * k1[i] + a093 * k3[i] + a094 * k4[i] + a095 * k5[i] + + a096 * k6[i] + a097 * k7[i] + a098 * k8[i]) + end + f(k9, tmp, p, t + dt) + + @inbounds @simd ivdep for i in eachindex(u) + tmp[i] = uprev[i] + + dt * (a101 * k1[i] + a103 * k3[i] + a104 * k4[i] + a105 * k5[i] + + a106 * k6[i] + a107 * k7[i]) + end + f(k10, tmp, p, t + dt) + + copyat_or_push!(k, 1, k1) + copyat_or_push!(k, 2, k2) + copyat_or_push!(k, 3, k3) + copyat_or_push!(k, 4, k4) + copyat_or_push!(k, 5, k5) + copyat_or_push!(k, 6, k6) + copyat_or_push!(k, 7, k7) + copyat_or_push!(k, 8, k8) + copyat_or_push!(k, 9, k9) + copyat_or_push!(k, 10, k10) + end + if (allow_calc_end && length(k) < 16) || force_calc_end # Have not added the extra stages yet + @unpack tmp = cache + rtmp = similar(cache.k1) + @OnDemandTableauExtract Vern7ExtraStages T T2 + + @inbounds @simd ivdep for i in eachindex(u) + tmp[i] = uprev[i] + + dt * (a1101 * k[1][i] + a1104 * k[4][i] + a1105 * k[5][i] + + a1106 * k[6][i] + a1107 * k[7][i] + a1108 * k[8][i] + a1109 * k[9][i]) + end + f(rtmp, tmp, p, t + c11 * dt) + copyat_or_push!(k, 11, rtmp) + + @inbounds @simd ivdep for i in eachindex(u) + tmp[i] = uprev[i] + + dt * (a1201 * k[1][i] + a1204 * k[4][i] + a1205 * k[5][i] + + a1206 * k[6][i] + a1207 * k[7][i] + a1208 * k[8][i] + + a1209 * k[9][i] + a1211 * k[11][i]) + end + f(rtmp, tmp, p, t + c12 * dt) + copyat_or_push!(k, 12, rtmp) + + @inbounds @simd ivdep for i in eachindex(u) + tmp[i] = uprev[i] + + dt * (a1301 * k[1][i] + a1304 * k[4][i] + a1305 * k[5][i] + + a1306 * k[6][i] + a1307 * k[7][i] + a1308 * k[8][i] + + a1309 * k[9][i] + a1311 * k[11][i] + a1312 * k[12][i]) + end + f(rtmp, tmp, p, t + c13 * dt) + copyat_or_push!(k, 13, rtmp) + + @inbounds @simd ivdep for i in eachindex(u) + tmp[i] = uprev[i] + + dt * (a1401 * k[1][i] + a1404 * k[4][i] + a1405 * k[5][i] + + a1406 * k[6][i] + a1407 * k[7][i] + a1408 * k[8][i] + + a1409 * k[9][i] + a1411 * k[11][i] + a1412 * k[12][i] + + a1413 * k[13][i]) + end + f(rtmp, tmp, p, t + c14 * dt) + copyat_or_push!(k, 14, rtmp) + + @inbounds @simd ivdep for i in eachindex(u) + tmp[i] = uprev[i] + + dt * (a1501 * k[1][i] + a1504 * k[4][i] + a1505 * k[5][i] + + a1506 * k[6][i] + a1507 * k[7][i] + a1508 * k[8][i] + + a1509 * k[9][i] + a1511 * k[11][i] + a1512 * k[12][i] + + a1513 * k[13][i]) + end + f(rtmp, tmp, p, t + c15 * dt) + copyat_or_push!(k, 15, rtmp) + + @inbounds @simd ivdep for i in eachindex(u) + tmp[i] = uprev[i] + + dt * (a1601 * k[1][i] + a1604 * k[4][i] + a1605 * k[5][i] + + a1606 * k[6][i] + a1607 * k[7][i] + a1608 * k[8][i] + + a1609 * k[9][i] + a1611 * k[11][i] + a1612 * k[12][i] + + a1613 * k[13][i]) + end + f(rtmp, tmp, p, t + c16 * dt) + copyat_or_push!(k, 16, rtmp) + end + nothing +end + +@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern8Cache, + always_calc_begin = false, allow_calc_end = true, + force_calc_end = false) + if length(k) < 13 || always_calc_begin + @unpack c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, a0201, a0301, a0302, a0401, a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, a0704, a0705, a0706, a0801, a0804, a0805, a0806, a0807, a0901, a0904, a0905, a0906, a0907, a0908, a1001, a1004, a1005, a1006, a1007, a1008, a1009, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211, a1301, a1304, a1305, a1306, a1307, a1308, a1309, a1310 = cache.tab + @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, tmp = cache + f(k1, uprev, p, t) + @.. broadcast=false tmp=uprev + dt * (a0201 * k1) + f(k2, tmp, p, t + c2 * dt) + @.. broadcast=false tmp=uprev + dt * (a0301 * k1 + a0302 * k2) + f(k3, tmp, p, t + c3 * dt) + @.. broadcast=false tmp=uprev + dt * (a0401 * k1 + a0403 * k3) + f(k4, tmp, p, t + c4 * dt) + @.. broadcast=false tmp=uprev + dt * (a0501 * k1 + a0503 * k3 + a0504 * k4) + f(k5, tmp, p, t + c5 * dt) + @.. broadcast=false tmp=uprev + dt * (a0601 * k1 + a0604 * k4 + a0605 * k5) + f(k6, tmp, p, t + c6 * dt) + @.. broadcast=false tmp=uprev + + dt * (a0701 * k1 + a0704 * k4 + a0705 * k5 + a0706 * k6) + f(k7, tmp, p, t + c7 * dt) + @.. broadcast=false tmp=uprev + + dt * (a0801 * k1 + a0804 * k4 + a0805 * k5 + a0806 * k6 + + a0807 * k7) + f(k8, tmp, p, t + c8 * dt) + @.. broadcast=false tmp=uprev + + dt * (a0901 * k1 + a0904 * k4 + a0905 * k5 + a0906 * k6 + + a0907 * k7 + a0908 * k8) + f(k9, tmp, p, t + c9 * dt) + @.. broadcast=false tmp=uprev + + dt * (a1001 * k1 + a1004 * k4 + a1005 * k5 + a1006 * k6 + + a1007 * k7 + a1008 * k8 + a1009 * k9) + f(k10, tmp, p, t + c10 * dt) + @.. broadcast=false tmp=uprev + + dt * (a1101 * k1 + a1104 * k4 + a1105 * k5 + a1106 * k6 + + a1107 * k7 + a1108 * k8 + a1109 * k9 + a1110 * k10) + f(k11, tmp, p, t + c11 * dt) + @.. broadcast=false tmp=uprev + + dt * (a1201 * k1 + a1204 * k4 + a1205 * k5 + a1206 * k6 + + a1207 * k7 + a1208 * k8 + a1209 * k9 + a1210 * k10 + + a1211 * k11) + f(k12, tmp, p, t + dt) + @.. broadcast=false tmp=uprev + + dt * (a1301 * k1 + a1304 * k4 + a1305 * k5 + a1306 * k6 + + a1307 * k7 + a1308 * k8 + a1309 * k9 + a1310 * k10) + f(k13, tmp, p, t + dt) + copyat_or_push!(k, 1, k1) + copyat_or_push!(k, 2, k2) + copyat_or_push!(k, 3, k3) + copyat_or_push!(k, 4, k4) + copyat_or_push!(k, 5, k5) + copyat_or_push!(k, 6, k6) + copyat_or_push!(k, 7, k7) + copyat_or_push!(k, 8, k8) + copyat_or_push!(k, 9, k9) + copyat_or_push!(k, 10, k10) + copyat_or_push!(k, 11, k11) + copyat_or_push!(k, 12, k12) + copyat_or_push!(k, 13, k13) + end + if (allow_calc_end && length(k) < 21) || force_calc_end # Have not added the extra stages yet + rtmp = similar(cache.k1) + @unpack c14, a1401, a1406, a1407, a1408, a1409, a1410, a1411, a1412, c15, a1501, a1506, a1507, a1508, a1509, a1510, a1511, a1512, a1514, c16, a1601, a1606, a1607, a1608, a1609, a1610, a1611, a1612, a1614, a1615, c17, a1701, a1706, a1707, a1708, a1709, a1710, a1711, a1712, a1714, a1715, a1716, c18, a1801, a1806, a1807, a1808, a1809, a1810, a1811, a1812, a1814, a1815, a1816, a1817, c19, a1901, a1906, a1907, a1908, a1909, a1910, a1911, a1912, a1914, a1915, a1916, a1917, c20, a2001, a2006, a2007, a2008, a2009, a2010, a2011, a2012, a2014, a2015, a2016, a2017, c21, a2101, a2106, a2107, a2108, a2109, a2110, a2111, a2112, a2114, a2115, a2116, a2117 = cache.tab.extra + @unpack tmp = cache + @.. broadcast=false tmp=uprev + + dt * + (a1401 * k[1] + a1406 * k[6] + a1407 * k[7] + a1408 * k[8] + + a1409 * k[9] + a1410 * k[10] + a1411 * k[11] + + a1412 * k[12]) + f(rtmp, tmp, p, t + c14 * dt) + copyat_or_push!(k, 14, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a1501 * k[1] + a1506 * k[6] + a1507 * k[7] + a1508 * k[8] + + a1509 * k[9] + a1510 * k[10] + a1511 * k[11] + + a1512 * k[12] + a1514 * k[14]) + f(rtmp, tmp, p, t + c15 * dt) + copyat_or_push!(k, 15, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a1601 * k[1] + a1606 * k[6] + a1607 * k[7] + a1608 * k[8] + + a1609 * k[9] + a1610 * k[10] + a1611 * k[11] + + a1612 * k[12] + a1614 * k[14] + a1615 * k[15]) + f(rtmp, tmp, p, t + c16 * dt) + copyat_or_push!(k, 16, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a1701 * k[1] + a1706 * k[6] + a1707 * k[7] + a1708 * k[8] + + a1709 * k[9] + a1710 * k[10] + a1711 * k[11] + + a1712 * k[12] + a1714 * k[14] + a1715 * k[15] + + a1716 * k[16]) + f(rtmp, tmp, p, t + c17 * dt) + copyat_or_push!(k, 17, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a1801 * k[1] + a1806 * k[6] + a1807 * k[7] + a1808 * k[8] + + a1809 * k[9] + a1810 * k[10] + a1811 * k[11] + + a1812 * k[12] + a1814 * k[14] + a1815 * k[15] + + a1816 * k[16] + a1817 * k[17]) + f(rtmp, tmp, p, t + c18 * dt) + copyat_or_push!(k, 18, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a1901 * k[1] + a1906 * k[6] + a1907 * k[7] + a1908 * k[8] + + a1909 * k[9] + a1910 * k[10] + a1911 * k[11] + + a1912 * k[12] + a1914 * k[14] + a1915 * k[15] + + a1916 * k[16] + a1917 * k[17]) + f(rtmp, tmp, p, t + c19 * dt) + copyat_or_push!(k, 19, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a2001 * k[1] + a2006 * k[6] + a2007 * k[7] + a2008 * k[8] + + a2009 * k[9] + a2010 * k[10] + a2011 * k[11] + + a2012 * k[12] + a2014 * k[14] + a2015 * k[15] + + a2016 * k[16] + a2017 * k[17]) + f(rtmp, tmp, p, t + c20 * dt) + copyat_or_push!(k, 20, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a2101 * k[1] + a2106 * k[6] + a2107 * k[7] + a2108 * k[8] + + a2109 * k[9] + a2110 * k[10] + a2111 * k[11] + + a2112 * k[12] + a2114 * k[14] + a2115 * k[15] + + a2116 * k[16] + a2117 * k[17]) + f(rtmp, tmp, p, t + c21 * dt) + copyat_or_push!(k, 21, rtmp) + end + nothing +end + +@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern9Cache, + always_calc_begin = false, allow_calc_end = true, + force_calc_end = false) + T = constvalue(recursive_unitless_bottom_eltype(u)) + T2 = constvalue(typeof(one(t))) + if length(k) < 10 || always_calc_begin + @OnDemandTableauExtract Vern9Tableau T T2 + @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, tmp = cache + uidx = eachindex(uprev) + f(k1, uprev, p, t) + @.. broadcast=false tmp=uprev + dt * (a0201 * k1) + f(k2, tmp, p, t + c1 * dt) + @.. broadcast=false tmp=uprev + dt * (a0301 * k1 + a0302 * k2) + f(k3, tmp, p, t + c2 * dt) + @.. broadcast=false tmp=uprev + dt * (a0401 * k1 + a0403 * k3) + f(k4, tmp, p, t + c3 * dt) + @.. broadcast=false tmp=uprev + dt * (a0501 * k1 + a0503 * k3 + a0504 * k4) + f(k5, tmp, p, t + c4 * dt) + @.. broadcast=false tmp=uprev + dt * (a0601 * k1 + a0604 * k4 + a0605 * k5) + f(k6, tmp, p, t + c5 * dt) + @.. broadcast=false tmp=uprev + + dt * (a0701 * k1 + a0704 * k4 + a0705 * k5 + a0706 * k6) + f(k7, tmp, p, t + c6 * dt) + @.. broadcast=false tmp=uprev + dt * (a0801 * k1 + a0806 * k6 + a0807 * k7) + f(k8, tmp, p, t + c7 * dt) + @.. broadcast=false tmp=uprev + + dt * (a0901 * k1 + a0906 * k6 + a0907 * k7 + a0908 * k8) + f(k9, tmp, p, t + c8 * dt) + @.. broadcast=false tmp=uprev + + dt * (a1001 * k1 + a1006 * k6 + a1007 * k7 + a1008 * k8 + + a1009 * k9) + f(k10, tmp, p, t + c9 * dt) + @.. broadcast=false tmp=uprev + + dt * (a1101 * k1 + a1106 * k6 + a1107 * k7 + a1108 * k8 + + a1109 * k9 + a1110 * k10) + f(k11, tmp, p, t + c10 * dt) + @.. broadcast=false tmp=uprev + + dt * (a1201 * k1 + a1206 * k6 + a1207 * k7 + a1208 * k8 + + a1209 * k9 + a1210 * k10 + a1211 * k11) + f(k12, tmp, p, t + c11 * dt) + @.. broadcast=false tmp=uprev + + dt * (a1301 * k1 + a1306 * k6 + a1307 * k7 + a1308 * k8 + + a1309 * k9 + a1310 * k10 + a1311 * k11 + a1312 * k12) + f(k13, tmp, p, t + c12 * dt) + @.. broadcast=false tmp=uprev + + dt * (a1401 * k1 + a1406 * k6 + a1407 * k7 + a1408 * k8 + + a1409 * k9 + a1410 * k10 + a1411 * k11 + a1412 * k12 + + a1413 * k13) + f(k14, tmp, p, t + c13 * dt) + @.. broadcast=false tmp=uprev + + dt * (a1501 * k1 + a1506 * k6 + a1507 * k7 + a1508 * k8 + + a1509 * k9 + a1510 * k10 + a1511 * k11 + a1512 * k12 + + a1513 * k13 + a1514 * k14) + f(k15, tmp, p, t + dt) + @.. broadcast=false tmp=uprev + + dt * (a1601 * k1 + a1606 * k6 + a1607 * k7 + a1608 * k8 + + a1609 * k9 + a1610 * k10 + a1611 * k11 + a1612 * k12 + + a1613 * k13) + f(k16, tmp, p, t + dt) + copyat_or_push!(k, 1, k1) + copyat_or_push!(k, 2, k8) + copyat_or_push!(k, 3, k9) + copyat_or_push!(k, 4, k10) + copyat_or_push!(k, 5, k11) + copyat_or_push!(k, 6, k12) + copyat_or_push!(k, 7, k13) + copyat_or_push!(k, 8, k14) + copyat_or_push!(k, 9, k15) + copyat_or_push!(k, 10, k16) + end + if (allow_calc_end && length(k) < 20) || force_calc_end # Have not added the extra stages yet + rtmp = similar(cache.k1) + uidx = eachindex(uprev) + @unpack tmp = cache + @OnDemandTableauExtract Vern9ExtraStages T T2 + @.. broadcast=false tmp=uprev + + dt * + (a1701 * k[1] + a1708 * k[2] + a1709 * k[3] + a1710 * k[4] + + a1711 * k[5] + a1712 * k[6] + a1713 * k[7] + a1714 * k[8] + + a1715 * k[9]) + f(rtmp, tmp, p, t + c17 * dt) + copyat_or_push!(k, 11, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a1801 * k[1] + a1808 * k[2] + a1809 * k[3] + a1810 * k[4] + + a1811 * k[5] + a1812 * k[6] + a1813 * k[7] + a1814 * k[8] + + a1815 * k[9] + a1817 * k[11]) + f(rtmp, tmp, p, t + c18 * dt) + copyat_or_push!(k, 12, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a1901 * k[1] + a1908 * k[2] + a1909 * k[3] + a1910 * k[4] + + a1911 * k[5] + a1912 * k[6] + a1913 * k[7] + a1914 * k[8] + + a1915 * k[9] + a1917 * k[11] + a1918 * k[12]) + f(rtmp, tmp, p, t + c19 * dt) + copyat_or_push!(k, 13, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a2001 * k[1] + a2008 * k[2] + a2009 * k[3] + a2010 * k[4] + + a2011 * k[5] + a2012 * k[6] + a2013 * k[7] + a2014 * k[8] + + a2015 * k[9] + a2017 * k[11] + a2018 * k[12] + + a2019 * k[13]) + f(rtmp, tmp, p, t + c20 * dt) + copyat_or_push!(k, 14, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a2101 * k[1] + a2108 * k[2] + a2109 * k[3] + a2110 * k[4] + + a2111 * k[5] + a2112 * k[6] + a2113 * k[7] + a2114 * k[8] + + a2115 * k[9] + a2117 * k[11] + a2118 * k[12] + + a2119 * k[13] + a2120 * k[14]) + f(rtmp, tmp, p, t + c21 * dt) + copyat_or_push!(k, 15, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a2201 * k[1] + a2208 * k[2] + a2209 * k[3] + a2210 * k[4] + + a2211 * k[5] + a2212 * k[6] + a2213 * k[7] + a2214 * k[8] + + a2215 * k[9] + a2217 * k[11] + a2218 * k[12] + + a2219 * k[13] + a2220 * k[14] + a2221 * k[15]) + f(rtmp, tmp, p, t + c22 * dt) + copyat_or_push!(k, 16, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a2301 * k[1] + a2308 * k[2] + a2309 * k[3] + a2310 * k[4] + + a2311 * k[5] + a2312 * k[6] + a2313 * k[7] + a2314 * k[8] + + a2315 * k[9] + a2317 * k[11] + a2318 * k[12] + + a2319 * k[13] + a2320 * k[14] + a2321 * k[15]) + f(rtmp, tmp, p, t + c23 * dt) + copyat_or_push!(k, 17, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a2401 * k[1] + a2408 * k[2] + a2409 * k[3] + a2410 * k[4] + + a2411 * k[5] + a2412 * k[6] + a2413 * k[7] + a2414 * k[8] + + a2415 * k[9] + a2417 * k[11] + a2418 * k[12] + + a2419 * k[13] + a2420 * k[14] + a2421 * k[15]) + f(rtmp, tmp, p, t + c24 * dt) + copyat_or_push!(k, 18, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a2501 * k[1] + a2508 * k[2] + a2509 * k[3] + a2510 * k[4] + + a2511 * k[5] + a2512 * k[6] + a2513 * k[7] + a2514 * k[8] + + a2515 * k[9] + a2517 * k[11] + a2518 * k[12] + + a2519 * k[13] + a2520 * k[14] + a2521 * k[15]) + f(rtmp, tmp, p, t + c25 * dt) + copyat_or_push!(k, 19, rtmp) + @.. broadcast=false tmp=uprev + + dt * + (a2601 * k[1] + a2608 * k[2] + a2609 * k[3] + a2610 * k[4] + + a2611 * k[5] + a2612 * k[6] + a2613 * k[7] + a2614 * k[8] + + a2615 * k[9] + a2617 * k[11] + a2618 * k[12] + + a2619 * k[13] + a2620 * k[14] + a2621 * k[15]) + f(rtmp, tmp, p, t + c26 * dt) + copyat_or_push!(k, 20, rtmp) + end + nothing +end +@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern9Cache{<:Array}, + always_calc_begin = false, allow_calc_end = true, + force_calc_end = false) + T = constvalue(recursive_unitless_bottom_eltype(u)) + T2 = constvalue(typeof(one(t))) + if length(k) < 10 || always_calc_begin + @OnDemandTableauExtract Vern9Tableau T T2 + @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, tmp = cache + uidx = eachindex(uprev) + f(k1, uprev, p, t) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + dt * (a0201 * k1[i]) + end + f(k2, tmp, p, t + c1 * dt) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + dt * (a0301 * k1[i] + a0302 * k2[i]) + end + f(k3, tmp, p, t + c2 * dt) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + dt * (a0401 * k1[i] + a0403 * k3[i]) + end + f(k4, tmp, p, t + c3 * dt) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + dt * (a0501 * k1[i] + a0503 * k3[i] + a0504 * k4[i]) + end + f(k5, tmp, p, t + c4 * dt) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + dt * (a0601 * k1[i] + a0604 * k4[i] + a0605 * k5[i]) + end + f(k6, tmp, p, t + c5 * dt) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + + dt * (a0701 * k1[i] + a0704 * k4[i] + a0705 * k5[i] + a0706 * k6[i]) + end + f(k7, tmp, p, t + c6 * dt) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + dt * (a0801 * k1[i] + a0806 * k6[i] + a0807 * k7[i]) + end + f(k8, tmp, p, t + c7 * dt) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + + dt * (a0901 * k1[i] + a0906 * k6[i] + a0907 * k7[i] + a0908 * k8[i]) + end + f(k9, tmp, p, t + c8 * dt) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + + dt * (a1001 * k1[i] + a1006 * k6[i] + a1007 * k7[i] + a1008 * k8[i] + + a1009 * k9[i]) + end + f(k10, tmp, p, t + c9 * dt) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + + dt * (a1101 * k1[i] + a1106 * k6[i] + a1107 * k7[i] + a1108 * k8[i] + + a1109 * k9[i] + a1110 * k10[i]) + end + f(k11, tmp, p, t + c10 * dt) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + + dt * (a1201 * k1[i] + a1206 * k6[i] + a1207 * k7[i] + a1208 * k8[i] + + a1209 * k9[i] + a1210 * k10[i] + a1211 * k11[i]) + end + f(k12, tmp, p, t + c11 * dt) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + + dt * (a1301 * k1[i] + a1306 * k6[i] + a1307 * k7[i] + a1308 * k8[i] + + a1309 * k9[i] + a1310 * k10[i] + a1311 * k11[i] + a1312 * k12[i]) + end + f(k13, tmp, p, t + c12 * dt) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + + dt * (a1401 * k1[i] + a1406 * k6[i] + a1407 * k7[i] + a1408 * k8[i] + + a1409 * k9[i] + a1410 * k10[i] + a1411 * k11[i] + a1412 * k12[i] + + a1413 * k13[i]) + end + f(k14, tmp, p, t + c13 * dt) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + + dt * (a1501 * k1[i] + a1506 * k6[i] + a1507 * k7[i] + a1508 * k8[i] + + a1509 * k9[i] + a1510 * k10[i] + a1511 * k11[i] + a1512 * k12[i] + + a1513 * k13[i] + a1514 * k14[i]) + end + f(k15, tmp, p, t + dt) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + + dt * (a1601 * k1[i] + a1606 * k6[i] + a1607 * k7[i] + a1608 * k8[i] + + a1609 * k9[i] + a1610 * k10[i] + a1611 * k11[i] + a1612 * k12[i] + + a1613 * k13[i]) + end + f(k16, tmp, p, t + dt) + copyat_or_push!(k, 1, k1) + copyat_or_push!(k, 2, k8) + copyat_or_push!(k, 3, k9) + copyat_or_push!(k, 4, k10) + copyat_or_push!(k, 5, k11) + copyat_or_push!(k, 6, k12) + copyat_or_push!(k, 7, k13) + copyat_or_push!(k, 8, k14) + copyat_or_push!(k, 9, k15) + copyat_or_push!(k, 10, k16) + end + if (allow_calc_end && length(k) < 20) || force_calc_end # Have not added the extra stages yet + rtmp = similar(cache.k1) + uidx = eachindex(uprev) + @unpack tmp = cache + @OnDemandTableauExtract Vern9ExtraStages T T2 + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + + dt * (a1701 * k[1][i] + a1708 * k[2][i] + a1709 * k[3][i] + + a1710 * k[4][i] + a1711 * k[5][i] + a1712 * k[6][i] + + a1713 * k[7][i] + a1714 * k[8][i] + a1715 * k[9][i]) + end + f(rtmp, tmp, p, t + c17 * dt) + copyat_or_push!(k, 11, rtmp) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + + dt * (a1801 * k[1][i] + a1808 * k[2][i] + a1809 * k[3][i] + + a1810 * k[4][i] + a1811 * k[5][i] + a1812 * k[6][i] + + a1813 * k[7][i] + a1814 * k[8][i] + a1815 * k[9][i] + + a1817 * k[11][i]) + end + f(rtmp, tmp, p, t + c18 * dt) + copyat_or_push!(k, 12, rtmp) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + + dt * (a1901 * k[1][i] + a1908 * k[2][i] + a1909 * k[3][i] + + a1910 * k[4][i] + a1911 * k[5][i] + a1912 * k[6][i] + + a1913 * k[7][i] + a1914 * k[8][i] + a1915 * k[9][i] + + a1917 * k[11][i] + a1918 * k[12][i]) + end + f(rtmp, tmp, p, t + c19 * dt) + copyat_or_push!(k, 13, rtmp) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + + dt * (a2001 * k[1][i] + a2008 * k[2][i] + a2009 * k[3][i] + + a2010 * k[4][i] + a2011 * k[5][i] + a2012 * k[6][i] + + a2013 * k[7][i] + a2014 * k[8][i] + a2015 * k[9][i] + + a2017 * k[11][i] + a2018 * k[12][i] + a2019 * k[13][i]) + end + f(rtmp, tmp, p, t + c20 * dt) + copyat_or_push!(k, 14, rtmp) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + + dt * (a2101 * k[1][i] + a2108 * k[2][i] + a2109 * k[3][i] + + a2110 * k[4][i] + a2111 * k[5][i] + a2112 * k[6][i] + + a2113 * k[7][i] + a2114 * k[8][i] + a2115 * k[9][i] + + a2117 * k[11][i] + a2118 * k[12][i] + a2119 * k[13][i] + + a2120 * k[14][i]) + end + f(rtmp, tmp, p, t + c21 * dt) + copyat_or_push!(k, 15, rtmp) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + + dt * (a2201 * k[1][i] + a2208 * k[2][i] + a2209 * k[3][i] + + a2210 * k[4][i] + a2211 * k[5][i] + a2212 * k[6][i] + + a2213 * k[7][i] + a2214 * k[8][i] + a2215 * k[9][i] + + a2217 * k[11][i] + a2218 * k[12][i] + a2219 * k[13][i] + + a2220 * k[14][i] + a2221 * k[15][i]) + end + f(rtmp, tmp, p, t + c22 * dt) + copyat_or_push!(k, 16, rtmp) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + + dt * (a2301 * k[1][i] + a2308 * k[2][i] + a2309 * k[3][i] + + a2310 * k[4][i] + a2311 * k[5][i] + a2312 * k[6][i] + + a2313 * k[7][i] + a2314 * k[8][i] + a2315 * k[9][i] + + a2317 * k[11][i] + a2318 * k[12][i] + a2319 * k[13][i] + + a2320 * k[14][i] + a2321 * k[15][i]) + end + f(rtmp, tmp, p, t + c23 * dt) + copyat_or_push!(k, 17, rtmp) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + + dt * (a2401 * k[1][i] + a2408 * k[2][i] + a2409 * k[3][i] + + a2410 * k[4][i] + a2411 * k[5][i] + a2412 * k[6][i] + + a2413 * k[7][i] + a2414 * k[8][i] + a2415 * k[9][i] + + a2417 * k[11][i] + a2418 * k[12][i] + a2419 * k[13][i] + + a2420 * k[14][i] + a2421 * k[15][i]) + end + f(rtmp, tmp, p, t + c24 * dt) + copyat_or_push!(k, 18, rtmp) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + + dt * (a2501 * k[1][i] + a2508 * k[2][i] + a2509 * k[3][i] + + a2510 * k[4][i] + a2511 * k[5][i] + a2512 * k[6][i] + + a2513 * k[7][i] + a2514 * k[8][i] + a2515 * k[9][i] + + a2517 * k[11][i] + a2518 * k[12][i] + a2519 * k[13][i] + + a2520 * k[14][i] + a2521 * k[15][i]) + end + f(rtmp, tmp, p, t + c25 * dt) + copyat_or_push!(k, 19, rtmp) + + @inbounds @simd ivdep for i in uidx + tmp[i] = uprev[i] + + dt * (a2601 * k[1][i] + a2608 * k[2][i] + a2609 * k[3][i] + + a2610 * k[4][i] + a2611 * k[5][i] + a2612 * k[6][i] + + a2613 * k[7][i] + a2614 * k[8][i] + a2615 * k[9][i] + + a2617 * k[11][i] + a2618 * k[12][i] + a2619 * k[13][i] + + a2620 * k[14][i] + a2621 * k[15][i]) + end + f(rtmp, tmp, p, t + c26 * dt) + copyat_or_push!(k, 20, rtmp) + end + nothing +end + +@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern6ConstantCache, + always_calc_begin = false, allow_calc_end = true, + force_calc_end = false) + if length(k) < 9 || always_calc_begin + @unpack c1, c2, c3, c4, c5, c6, a21, a31, a32, a41, a43, a51, a53, a54, a61, a63, a64, a65, a71, a73, a74, a75, a76, a81, a83, a84, a85, a86, a87, a91, a94, a95, a96, a97, a98 = cache.tab + copyat_or_push!(k, 1, f(uprev, p, t)) + copyat_or_push!(k, 2, f(uprev + dt * (a21 * k[1]), p, t + c1 * dt)) + copyat_or_push!(k, 3, f(uprev + dt * (a31 * k[1] + a32 * k[2]), p, t + c2 * dt)) + copyat_or_push!(k, 4, f(uprev + dt * (a41 * k[1] + a43 * k[3]), p, t + c3 * dt)) + copyat_or_push!(k, 5, + f(uprev + dt * (a51 * k[1] + a53 * k[3] + a54 * k[4]), p, + t + c4 * dt)) + copyat_or_push!(k, 6, + f(uprev + dt * (a61 * k[1] + a63 * k[3] + a64 * k[4] + a65 * k[5]), + p, t + c5 * dt)) + copyat_or_push!(k, 7, + f( + uprev + + dt * + (a71 * k[1] + a73 * k[3] + a74 * k[4] + a75 * k[5] + a76 * k[6]), + p, t + c6 * dt)) + copyat_or_push!(k, 8, + f( + uprev + + dt * + (a81 * k[1] + a83 * k[3] + a84 * k[4] + a85 * k[5] + a86 * k[6] + + a87 * k[7]), + p, + t + dt)) + copyat_or_push!(k, 9, + f( + uprev + + dt * + (a91 * k[1] + a94 * k[4] + a95 * k[5] + a96 * k[6] + a97 * k[7] + + a98 * k[8]), + p, + t + dt)) + end + if (allow_calc_end && length(k) < 12) || force_calc_end # Have not added the extra stages yet + @unpack c10, a1001, a1004, a1005, a1006, a1007, a1008, a1009, c11, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, c12, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211 = cache.tab.extra + copyat_or_push!(k, 10, + f( + uprev + + dt * + (a1001 * k[1] + a1004 * k[4] + a1005 * k[5] + a1006 * k[6] + + a1007 * k[7] + a1008 * k[8] + a1009 * k[9]), + p, + t + c10 * dt)) + copyat_or_push!(k, 11, + f( + uprev + + dt * + (a1101 * k[1] + a1104 * k[4] + a1105 * k[5] + a1106 * k[6] + + a1107 * k[7] + a1108 * k[8] + a1109 * k[9] + a1110 * k[10]), + p, + t + c11 * dt)) + copyat_or_push!(k, 12, + f( + uprev + + dt * + (a1201 * k[1] + a1204 * k[4] + a1205 * k[5] + a1206 * k[6] + + a1207 * k[7] + a1208 * k[8] + a1209 * k[9] + a1210 * k[10] + + a1211 * k[11]), + p, + t + c12 * dt)) + end + nothing +end + +@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern7ConstantCache, + always_calc_begin = false, allow_calc_end = true, + force_calc_end = false) + T = constvalue(recursive_unitless_bottom_eltype(u)) + T2 = constvalue(typeof(one(t))) + if length(k) < 10 || always_calc_begin + @OnDemandTableauExtract Vern7Tableau T T2 + copyat_or_push!(k, 1, f(uprev, p, t)) + copyat_or_push!(k, 2, f(uprev + dt * (a021 * k[1]), p, t + c2 * dt)) + copyat_or_push!(k, 3, f(uprev + dt * (a031 * k[1] + a032 * k[2]), p, t + c3 * dt)) + copyat_or_push!(k, 4, f(uprev + dt * (a041 * k[1] + a043 * k[3]), p, t + c4 * dt)) + copyat_or_push!(k, 5, + f(uprev + dt * (a051 * k[1] + a053 * k[3] + a054 * k[4]), p, + t + c5 * dt)) + copyat_or_push!(k, 6, + f(uprev + + dt * (a061 * k[1] + a063 * k[3] + a064 * k[4] + a065 * k[5]), p, + t + c6 * dt)) + copyat_or_push!(k, 7, + f( + uprev + + dt * (a071 * k[1] + a073 * k[3] + a074 * k[4] + a075 * k[5] + + a076 * k[6]), + p, + t + c7 * dt)) + copyat_or_push!(k, 8, + f( + uprev + + dt * (a081 * k[1] + a083 * k[3] + a084 * k[4] + a085 * k[5] + + a086 * k[6] + a087 * k[7]), + p, + t + c8 * dt)) + copyat_or_push!(k, 9, + f( + uprev + + dt * (a091 * k[1] + a093 * k[3] + a094 * k[4] + a095 * k[5] + + a096 * k[6] + a097 * k[7] + a098 * k[8]), + p, + t + dt)) + copyat_or_push!(k, 10, + f( + uprev + + dt * (a101 * k[1] + a103 * k[3] + a104 * k[4] + a105 * k[5] + + a106 * k[6] + a107 * k[7]), + p, + t + dt)) + end + if (allow_calc_end && length(k) < 16) || force_calc_end # Have not added the extra stages yet + @OnDemandTableauExtract Vern7ExtraStages T T2 + copyat_or_push!(k, 11, + f( + uprev + + dt * + (a1101 * k[1] + a1104 * k[4] + a1105 * k[5] + a1106 * k[6] + + a1107 * k[7] + a1108 * k[8] + a1109 * k[9]), + p, + t + c11 * dt)) + copyat_or_push!(k, 12, + f( + uprev + + dt * + (a1201 * k[1] + a1204 * k[4] + a1205 * k[5] + a1206 * k[6] + + a1207 * k[7] + a1208 * k[8] + a1209 * k[9] + a1211 * k[11]), + p, + t + c12 * dt)) + copyat_or_push!(k, 13, + f( + uprev + + dt * + (a1301 * k[1] + a1304 * k[4] + a1305 * k[5] + a1306 * k[6] + + a1307 * k[7] + a1308 * k[8] + a1309 * k[9] + a1311 * k[11] + + a1312 * k[12]), + p, + t + c13 * dt)) + copyat_or_push!(k, 14, + f( + uprev + + dt * + (a1401 * k[1] + a1404 * k[4] + a1405 * k[5] + a1406 * k[6] + + a1407 * k[7] + a1408 * k[8] + a1409 * k[9] + a1411 * k[11] + + a1412 * k[12] + a1413 * k[13]), + p, + t + c14 * dt)) + copyat_or_push!(k, 15, + f( + uprev + + dt * + (a1501 * k[1] + a1504 * k[4] + a1505 * k[5] + a1506 * k[6] + + a1507 * k[7] + a1508 * k[8] + a1509 * k[9] + a1511 * k[11] + + a1512 * k[12] + a1513 * k[13]), + p, + t + c15 * dt)) + copyat_or_push!(k, 16, + f( + uprev + + dt * + (a1601 * k[1] + a1604 * k[4] + a1605 * k[5] + a1606 * k[6] + + a1607 * k[7] + a1608 * k[8] + a1609 * k[9] + a1611 * k[11] + + a1612 * k[12] + a1613 * k[13]), + p, + t + c16 * dt)) + end + nothing +end + +@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern8ConstantCache, + always_calc_begin = false, allow_calc_end = true, + force_calc_end = false) + if length(k) < 13 || always_calc_begin + @unpack c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, a0201, a0301, a0302, a0401, a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, a0704, a0705, a0706, a0801, a0804, a0805, a0806, a0807, a0901, a0904, a0905, a0906, a0907, a0908, a1001, a1004, a1005, a1006, a1007, a1008, a1009, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211, a1301, a1304, a1305, a1306, a1307, a1308, a1309, a1310 = cache.tab + copyat_or_push!(k, 1, f(uprev, p, t)) + copyat_or_push!(k, 2, f(uprev + dt * (a0201 * k[1]), p, t + c2 * dt)) + copyat_or_push!(k, 3, f(uprev + dt * (a0301 * k[1] + a0302 * k[2]), p, t + c3 * dt)) + copyat_or_push!(k, 4, f(uprev + dt * (a0401 * k[1] + a0403 * k[3]), p, t + c4 * dt)) + copyat_or_push!(k, 5, + f(uprev + dt * (a0501 * k[1] + a0503 * k[3] + a0504 * k[4]), p, + t + c5 * dt)) + copyat_or_push!(k, 6, + f(uprev + dt * (a0601 * k[1] + a0604 * k[4] + a0605 * k[5]), p, + t + c6 * dt)) + copyat_or_push!(k, 7, + f(uprev + + dt * (a0701 * k[1] + a0704 * k[4] + a0705 * k[5] + a0706 * k[6]), + p, t + c7 * dt)) + copyat_or_push!(k, 8, + f( + uprev + + dt * + (a0801 * k[1] + a0804 * k[4] + a0805 * k[5] + a0806 * k[6] + + a0807 * k[7]), + p, + t + c8 * dt)) + copyat_or_push!(k, 9, + f( + uprev + + dt * + (a0901 * k[1] + a0904 * k[4] + a0905 * k[5] + a0906 * k[6] + + a0907 * k[7] + a0908 * k[8]), + p, + t + c9 * dt)) + copyat_or_push!(k, 10, + f( + uprev + + dt * + (a1001 * k[1] + a1004 * k[4] + a1005 * k[5] + a1006 * k[6] + + a1007 * k[7] + a1008 * k[8] + a1009 * k[9]), + p, + t + c10 * dt)) + copyat_or_push!(k, 11, + f( + uprev + + dt * + (a1101 * k[1] + a1104 * k[4] + a1105 * k[5] + a1106 * k[6] + + a1107 * k[7] + a1108 * k[8] + a1109 * k[9] + a1110 * k[10]), + p, + t + c11 * dt)) + copyat_or_push!(k, 12, + f( + uprev + + dt * + (a1201 * k[1] + a1204 * k[4] + a1205 * k[5] + a1206 * k[6] + + a1207 * k[7] + a1208 * k[8] + a1209 * k[9] + a1210 * k[10] + + a1211 * k[11]), + p, + t + dt)) + copyat_or_push!(k, 13, + f( + uprev + + dt * + (a1301 * k[1] + a1304 * k[4] + a1305 * k[5] + a1306 * k[6] + + a1307 * k[7] + a1308 * k[8] + a1309 * k[9] + a1310 * k[10]), + p, + t + dt)) + end + if (allow_calc_end && length(k) < 21) || force_calc_end # Have not added the extra stages yet + @unpack c14, a1401, a1406, a1407, a1408, a1409, a1410, a1411, a1412, c15, a1501, a1506, a1507, a1508, a1509, a1510, a1511, a1512, a1514, c16, a1601, a1606, a1607, a1608, a1609, a1610, a1611, a1612, a1614, a1615, c17, a1701, a1706, a1707, a1708, a1709, a1710, a1711, a1712, a1714, a1715, a1716, c18, a1801, a1806, a1807, a1808, a1809, a1810, a1811, a1812, a1814, a1815, a1816, a1817, c19, a1901, a1906, a1907, a1908, a1909, a1910, a1911, a1912, a1914, a1915, a1916, a1917, c20, a2001, a2006, a2007, a2008, a2009, a2010, a2011, a2012, a2014, a2015, a2016, a2017, c21, a2101, a2106, a2107, a2108, a2109, a2110, a2111, a2112, a2114, a2115, a2116, a2117 = cache.tab.extra + copyat_or_push!(k, 14, + f( + uprev + + dt * + (a1401 * k[1] + a1406 * k[6] + a1407 * k[7] + a1408 * k[8] + + a1409 * k[9] + a1410 * k[10] + a1411 * k[11] + a1412 * k[12]), + p, + t + c14 * dt)) + copyat_or_push!(k, 15, + f( + uprev + + dt * + (a1501 * k[1] + a1506 * k[6] + a1507 * k[7] + a1508 * k[8] + + a1509 * k[9] + a1510 * k[10] + a1511 * k[11] + a1512 * k[12] + + a1514 * k[14]), + p, + t + c15 * dt)) + copyat_or_push!(k, 16, + f( + uprev + + dt * + (a1601 * k[1] + a1606 * k[6] + a1607 * k[7] + a1608 * k[8] + + a1609 * k[9] + a1610 * k[10] + a1611 * k[11] + a1612 * k[12] + + a1614 * k[14] + a1615 * k[15]), + p, + t + c16 * dt)) + copyat_or_push!(k, 17, + f( + uprev + + dt * + (a1701 * k[1] + a1706 * k[6] + a1707 * k[7] + a1708 * k[8] + + a1709 * k[9] + a1710 * k[10] + a1711 * k[11] + a1712 * k[12] + + a1714 * k[14] + a1715 * k[15] + a1716 * k[16]), + p, + t + c17 * dt)) + copyat_or_push!(k, 18, + f( + uprev + + dt * + (a1801 * k[1] + a1806 * k[6] + a1807 * k[7] + a1808 * k[8] + + a1809 * k[9] + a1810 * k[10] + a1811 * k[11] + a1812 * k[12] + + a1814 * k[14] + a1815 * k[15] + a1816 * k[16] + a1817 * k[17]), + p, t + c18 * dt)) + copyat_or_push!(k, 19, + f( + uprev + + dt * + (a1901 * k[1] + a1906 * k[6] + a1907 * k[7] + a1908 * k[8] + + a1909 * k[9] + a1910 * k[10] + a1911 * k[11] + a1912 * k[12] + + a1914 * k[14] + a1915 * k[15] + a1916 * k[16] + a1917 * k[17]), + p, t + c19 * dt)) + copyat_or_push!(k, 20, + f( + uprev + + dt * + (a2001 * k[1] + a2006 * k[6] + a2007 * k[7] + a2008 * k[8] + + a2009 * k[9] + a2010 * k[10] + a2011 * k[11] + a2012 * k[12] + + a2014 * k[14] + a2015 * k[15] + a2016 * k[16] + a2017 * k[17]), + p, t + c20 * dt)) + copyat_or_push!(k, 21, + f( + uprev + + dt * + (a2101 * k[1] + a2106 * k[6] + a2107 * k[7] + a2108 * k[8] + + a2109 * k[9] + a2110 * k[10] + a2111 * k[11] + a2112 * k[12] + + a2114 * k[14] + a2115 * k[15] + a2116 * k[16] + a2117 * k[17]), + p, t + c21 * dt)) + end + nothing +end + +@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern9ConstantCache, + always_calc_begin = false, allow_calc_end = true, + force_calc_end = false) + T = constvalue(recursive_unitless_bottom_eltype(u)) + T2 = constvalue(typeof(one(t))) + if length(k) < 10 || always_calc_begin + @OnDemandTableauExtract Vern9Tableau T T2 + copyat_or_push!(k, 1, f(uprev, p, t)) + copyat_or_push!(k, 2, f(uprev + dt * (a0201 * k[1]), p, t + c1 * dt)) + copyat_or_push!(k, 3, f(uprev + dt * (a0301 * k[1] + a0302 * k[2]), p, t + c2 * dt)) + copyat_or_push!(k, 4, f(uprev + dt * (a0401 * k[1] + a0403 * k[3]), p, t + c3 * dt)) + copyat_or_push!(k, 5, + f(uprev + dt * (a0501 * k[1] + a0503 * k[3] + a0504 * k[4]), p, + t + c4 * dt)) + copyat_or_push!(k, 6, + f(uprev + dt * (a0601 * k[1] + a0604 * k[4] + a0605 * k[5]), p, + t + c5 * dt)) + copyat_or_push!(k, 7, + f(uprev + + dt * (a0701 * k[1] + a0704 * k[4] + a0705 * k[5] + a0706 * k[6]), + p, t + c6 * dt)) + copyat_or_push!(k, 2, + f(uprev + dt * (a0801 * k[1] + a0806 * k[6] + a0807 * k[7]), p, + t + c7 * dt)) + copyat_or_push!(k, 3, + f(uprev + + dt * (a0901 * k[1] + a0906 * k[6] + a0907 * k[7] + a0908 * k[2]), + p, t + c8 * dt)) + copyat_or_push!(k, 4, + f( + uprev + + dt * + (a1001 * k[1] + a1006 * k[6] + a1007 * k[7] + a1008 * k[2] + + a1009 * k[3]), + p, + t + c9 * dt)) + copyat_or_push!(k, 5, + f( + uprev + + dt * + (a1101 * k[1] + a1106 * k[6] + a1107 * k[7] + a1108 * k[2] + + a1109 * k[3] + a1110 * k[4]), + p, + t + c10 * dt)) + temp6 = recursivecopy(k[6]) + temp7 = recursivecopy(k[7]) + copyat_or_push!(k, 6, + f( + uprev + + dt * + (a1201 * k[1] + a1206 * temp6 + a1207 * temp7 + a1208 * k[2] + + a1209 * k[3] + a1210 * k[4] + a1211 * k[5]), + p, + t + c11 * dt)) + copyat_or_push!(k, 7, + f( + uprev + + dt * + (a1301 * k[1] + a1306 * temp6 + a1307 * temp7 + a1308 * k[2] + + a1309 * k[3] + a1310 * k[4] + a1311 * k[5] + a1312 * k[6]), + p, + t + c12 * dt)) + copyat_or_push!(k, 8, + f( + uprev + + dt * + (a1401 * k[1] + a1406 * temp6 + a1407 * temp7 + a1408 * k[2] + + a1409 * k[3] + a1410 * k[4] + a1411 * k[5] + a1412 * k[6] + + a1413 * k[7]), + p, + t + c13 * dt)) + copyat_or_push!(k, 9, + f( + uprev + + dt * + (a1501 * k[1] + a1506 * temp6 + a1507 * temp7 + a1508 * k[2] + + a1509 * k[3] + a1510 * k[4] + a1511 * k[5] + a1512 * k[6] + + a1513 * k[7] + a1514 * k[8]), + p, + t + dt)) + copyat_or_push!(k, 10, + f( + uprev + + dt * + (a1601 * k[1] + a1606 * temp6 + a1607 * temp7 + a1608 * k[2] + + a1609 * k[3] + a1610 * k[4] + a1611 * k[5] + a1612 * k[6] + + a1613 * k[7]), + p, + t + dt)) + end + if (allow_calc_end && length(k) < 20) || force_calc_end # Have not added the extra stages yet + @OnDemandTableauExtract Vern9ExtraStages T T2 + copyat_or_push!(k, 11, + f( + uprev + + dt * + (a1701 * k[1] + a1708 * k[2] + a1709 * k[3] + a1710 * k[4] + + a1711 * k[5] + a1712 * k[6] + a1713 * k[7] + a1714 * k[8] + + a1715 * k[9]), + p, + t + c17 * dt)) + copyat_or_push!(k, 12, + f( + uprev + + dt * + (a1801 * k[1] + a1808 * k[2] + a1809 * k[3] + a1810 * k[4] + + a1811 * k[5] + a1812 * k[6] + a1813 * k[7] + a1814 * k[8] + + a1815 * k[9] + a1817 * k[11]), + p, + t + c18 * dt)) + copyat_or_push!(k, 13, + f( + uprev + + dt * + (a1901 * k[1] + a1908 * k[2] + a1909 * k[3] + a1910 * k[4] + + a1911 * k[5] + a1912 * k[6] + a1913 * k[7] + a1914 * k[8] + + a1915 * k[9] + a1917 * k[11] + a1918 * k[12]), + p, + t + c19 * dt)) + copyat_or_push!(k, 14, + f( + uprev + + dt * + (a2001 * k[1] + a2008 * k[2] + a2009 * k[3] + a2010 * k[4] + + a2011 * k[5] + a2012 * k[6] + a2013 * k[7] + a2014 * k[8] + + a2015 * k[9] + a2017 * k[11] + a2018 * k[12] + a2019 * k[13]), + p, + t + c20 * dt)) + copyat_or_push!(k, 15, + f( + uprev + + dt * + (a2101 * k[1] + a2108 * k[2] + a2109 * k[3] + a2110 * k[4] + + a2111 * k[5] + a2112 * k[6] + a2113 * k[7] + a2114 * k[8] + + a2115 * k[9] + a2117 * k[11] + a2118 * k[12] + a2119 * k[13] + + a2120 * k[14]), + p, + t + c21 * dt)) + copyat_or_push!(k, 16, + f( + uprev + + dt * + (a2201 * k[1] + a2208 * k[2] + a2209 * k[3] + a2210 * k[4] + + a2211 * k[5] + a2212 * k[6] + a2213 * k[7] + a2214 * k[8] + + a2215 * k[9] + a2217 * k[11] + a2218 * k[12] + a2219 * k[13] + + a2220 * k[14] + a2221 * k[15]), + p, + t + c22 * dt)) + copyat_or_push!(k, 17, + f( + uprev + + dt * + (a2301 * k[1] + a2308 * k[2] + a2309 * k[3] + a2310 * k[4] + + a2311 * k[5] + a2312 * k[6] + a2313 * k[7] + a2314 * k[8] + + a2315 * k[9] + a2317 * k[11] + a2318 * k[12] + a2319 * k[13] + + a2320 * k[14] + a2321 * k[15]), + p, + t + c23 * dt)) + copyat_or_push!(k, 18, + f( + uprev + + dt * + (a2401 * k[1] + a2408 * k[2] + a2409 * k[3] + a2410 * k[4] + + a2411 * k[5] + a2412 * k[6] + a2413 * k[7] + a2414 * k[8] + + a2415 * k[9] + a2417 * k[11] + a2418 * k[12] + a2419 * k[13] + + a2420 * k[14] + a2421 * k[15]), + p, + t + c24 * dt)) + copyat_or_push!(k, 19, + f( + uprev + + dt * + (a2501 * k[1] + a2508 * k[2] + a2509 * k[3] + a2510 * k[4] + + a2511 * k[5] + a2512 * k[6] + a2513 * k[7] + a2514 * k[8] + + a2515 * k[9] + a2517 * k[11] + a2518 * k[12] + a2519 * k[13] + + a2520 * k[14] + a2521 * k[15]), + p, + t + c25 * dt)) + copyat_or_push!(k, 20, + f( + uprev + + dt * + (a2601 * k[1] + a2608 * k[2] + a2609 * k[3] + a2610 * k[4] + + a2611 * k[5] + a2612 * k[6] + a2613 * k[7] + a2614 * k[8] + + a2615 * k[9] + a2617 * k[11] + a2618 * k[12] + a2619 * k[13] + + a2620 * k[14] + a2621 * k[15]), + p, + t + c26 * dt)) + end + nothing +end diff --git a/src/integrators/controllers.jl b/src/integrators/controllers.jl index 903064e6e2..5db779bb62 100644 --- a/src/integrators/controllers.jl +++ b/src/integrators/controllers.jl @@ -403,7 +403,7 @@ end if fac_default_gamma(alg) fac = gamma else - if alg isa Union{RadauIIA3, RadauIIA5, RadauIIA7} + if alg isa Union{RadauIIA3, RadauIIA5, RadauIIA9} @unpack iter = integrator.cache @unpack maxiters = alg else diff --git a/src/integrators/integrator_interface.jl b/src/integrators/integrator_interface.jl index 58624905ac..d53859da46 100644 --- a/src/integrators/integrator_interface.jl +++ b/src/integrators/integrator_interface.jl @@ -113,7 +113,7 @@ end end # avoid method ambiguity -# for typ in (Union{RadauIIA3, RadauIIA5, RadauIIA7}) +# for typ in (Union{RadauIIA3, RadauIIA5, RadauIIA9}) # @eval @inline function DiffEqBase.get_tmp_cache(integrator, alg::$typ, # cache::OrdinaryDiffEqConstantCache) # nothing @@ -126,7 +126,7 @@ end (cache.tmp,) end @inline function DiffEqBase.get_tmp_cache( - integrator, alg::Union{RadauIIA3, RadauIIA5, RadauIIA7}, + integrator, alg::Union{RadauIIA3, RadauIIA5, RadauIIA9}, cache::OrdinaryDiffEqMutableCache) (cache.tmp, cache.atmp) end diff --git a/src/perform_step/extrapolation_perform_step.jl b/src/perform_step/extrapolation_perform_step.jl new file mode 100644 index 0000000000..48fec8c66d --- /dev/null +++ b/src/perform_step/extrapolation_perform_step.jl @@ -0,0 +1,3639 @@ +function initialize!(integrator, cache::AitkenNevilleCache) + integrator.kshortsize = 2 + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # For the interpolation, needs k at the updated point + integrator.stats.nf += 1 + + cache.step_no = 1 + alg = unwrap_alg(integrator, false) + cache.cur_order = max(alg.init_order, alg.min_order) +end + +function perform_step!(integrator, cache::AitkenNevilleCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + alg = unwrap_alg(integrator, false) + @unpack k, fsalfirst, T, utilde, atmp, dtpropose, cur_order, A = cache + @unpack u_tmps, k_tmps = cache + + max_order = min(size(T, 1), cur_order + 1) + + if !isthreaded(alg.threading) + for i in 1:max_order + dt_temp = dt / (2^(i - 1)) + # Solve using Euler method + @muladd @.. broadcast=false u=uprev + dt_temp * fsalfirst + f(k, u, p, t + dt_temp) + integrator.stats.nf += 1 + for j in 2:(2^(i - 1)) + @muladd @.. broadcast=false u=u + dt_temp * k + f(k, u, p, t + j * dt_temp) + integrator.stats.nf += 1 + end + @.. broadcast=false T[i, 1]=u + end + else + let max_order = max_order, uprev = uprev, dt = dt, fsalfirst = fsalfirst, p = p, + t = t, + u_tmps = u_tmps, k_tmps = k_tmps, T = T + # Balance workload of threads by computing T[1,1] with T[max_order,1] on + # same thread, T[2,1] with T[max_order-1,1] on same thread. Similarly fill + # first column of T matrix + @threaded alg.threading for i in 1:2 + startIndex = (i == 1) ? 1 : max_order + endIndex = (i == 1) ? max_order - 1 : max_order + for index in startIndex:endIndex + dt_temp = dt / (2^(index - 1)) + # Solve using Euler method + @muladd @.. broadcast=false u_tmps[Threads.threadid()]=uprev + + dt_temp * + fsalfirst + f(k_tmps[Threads.threadid()], u_tmps[Threads.threadid()], p, + t + dt_temp) + for j in 2:(2^(index - 1)) + @muladd @.. broadcast=false u_tmps[Threads.threadid()]=u_tmps[Threads.threadid()] + + dt_temp * + k_tmps[Threads.threadid()] + f(k_tmps[Threads.threadid()], u_tmps[Threads.threadid()], p, + t + j * dt_temp) + end + @.. broadcast=false T[index, 1]=u_tmps[Threads.threadid()] + end + end + end + integrator.stats.nf += 2^max_order - 1 + end + + # Richardson extrapolation + tmp = 1 + for j in 2:max_order + tmp *= 2 + for i in j:max_order + @.. broadcast=false T[i, j]=(tmp * T[i, j - 1] - T[i - 1, j - 1]) / (tmp - 1) + end + end + + if integrator.opts.adaptive + minimum_work = Inf + if isone(cache.step_no) + range_start = 2 + else + range_start = max(2, cur_order - 1) + end + + for i in range_start:max_order + A = 2^(i - 1) + @.. broadcast=false utilde=T[i, i] - T[i, i - 1] + atmp = calculate_residuals(utilde, uprev, T[i, i], integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, + t) + EEst = integrator.opts.internalnorm(atmp, t) + + beta1 = integrator.opts.controller.beta1 + e = integrator.EEst + qold = integrator.qold + + integrator.opts.controller.beta1 = 1 / (i + 1) + integrator.EEst = EEst + dtpropose = step_accept_controller!(integrator, alg, + stepsize_controller!(integrator, alg)) + integrator.EEst = e + integrator.opts.controller.beta1 = beta1 + integrator.qold = qold + + work = A / dtpropose + + if work < minimum_work + integrator.opts.controller.beta1 = 1 / (i + 1) + cache.dtpropose = dtpropose + cache.cur_order = i + minimum_work = work + integrator.EEst = EEst + end + end + end + + # using extrapolated value of u + @.. broadcast=false u=T[cache.cur_order, cache.cur_order] + cache.step_no = cache.step_no + 1 + f(k, u, p, t + dt) + integrator.stats.nf += 1 +end + +function initialize!(integrator, cache::AitkenNevilleConstantCache) + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + cache.step_no = 1 + alg = unwrap_alg(integrator, false) + cache.cur_order = max(alg.init_order, alg.min_order) +end + +function perform_step!(integrator, cache::AitkenNevilleConstantCache, repeat_step = false) + @unpack t, dt, uprev, f, p = integrator + alg = unwrap_alg(integrator, false) + @unpack dtpropose, T, cur_order, work, A = cache + + max_order = min(size(T, 1), cur_order + 1) + + if !isthreaded(alg.threading) + for i in 1:max_order + dt_temp = dt / (2^(i - 1)) # Romberg sequence + + # Solve using Euler method with dt_temp = dt/n_{i} + @muladd u = @.. broadcast=false uprev+dt_temp * integrator.fsalfirst + k = f(u, p, t + dt_temp) + integrator.stats.nf += 1 + + for j in 2:(2^(i - 1)) + @muladd u = @.. broadcast=false u+dt_temp * k + k = f(u, p, t + j * dt_temp) + integrator.stats.nf += 1 + end + T[i, 1] = u + end + else + let max_order = max_order, dt = dt, uprev = uprev, integrator = integrator, p = p, + t = t, T = T + # Balance workload of threads by computing T[1,1] with T[max_order,1] on + # same thread, T[2,1] with T[max_order-1,1] on same thread. Similarly fill + # first column of T matrix + @threaded alg.threading for i in 1:2 + startIndex = (i == 1) ? 1 : max_order + endIndex = (i == 1) ? max_order - 1 : max_order + + for index in startIndex:endIndex + dt_temp = dt / 2^(index - 1) + @muladd u = @.. broadcast=false uprev+dt_temp * integrator.fsalfirst + k_temp = f(u, p, t + dt_temp) + for j in 2:(2^(index - 1)) + @muladd u = @.. broadcast=false u+dt_temp * k_temp + k_temp = f(u, p, t + j * dt_temp) + end + T[index, 1] = u + end + end + end + + integrator.stats.nf += 2^max_order - 1 + end + + # Richardson extrapolation + tmp = 1 + for j in 2:max_order + tmp *= 2 + for i in j:max_order + T[i, j] = (tmp * T[i, j - 1] - T[i - 1, j - 1]) / (tmp - 1) + end + end + + if integrator.opts.adaptive + minimum_work = Inf + if isone(cache.step_no) + range_start = 2 + else + range_start = max(2, cur_order - 1) + end + + for i in range_start:max_order + A = 2^(i - 1) + utilde = T[i, i] - T[i, i - 1] + atmp = calculate_residuals(utilde, uprev, T[i, i], integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, + t) + EEst = integrator.opts.internalnorm(atmp, t) + + beta1 = integrator.opts.controller.beta1 + e = integrator.EEst + qold = integrator.qold + + integrator.opts.controller.beta1 = 1 / (i + 1) + integrator.EEst = EEst + dtpropose = step_accept_controller!(integrator, alg, + stepsize_controller!(integrator, alg)) + integrator.EEst = e + integrator.opts.controller.beta1 = beta1 + integrator.qold = qold + + work = A / dtpropose + + if work < minimum_work + integrator.opts.controller.beta1 = 1 / (i + 1) + cache.dtpropose = dtpropose + cache.cur_order = i + minimum_work = work + integrator.EEst = EEst + end + end + end + + cache.step_no = cache.step_no + 1 + + # Use extrapolated value of u + integrator.u = T[cache.cur_order, cache.cur_order] + + k = f(integrator.u, p, t + dt) + integrator.stats.nf += 1 + integrator.fsallast = k + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +function initialize!(integrator, cache::ImplicitEulerExtrapolationCache) + integrator.kshortsize = 2 + + integrator.fsalfirst = zero(first(cache.k_tmps)) + integrator.f(integrator.fsalfirst, integrator.u, integrator.p, integrator.t) + integrator.fsallast = zero(integrator.fsalfirst) + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.stats.nf += 1 + + cache.step_no = 1 + #alg = unwrap_alg(integrator, true) + #cache.cur_order = max(alg.init_order, alg.min_order) +end + +function perform_step!(integrator, cache::ImplicitEulerExtrapolationCache, + repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + alg = unwrap_alg(integrator, true) + @unpack T, utilde, atmp, dtpropose, n_curr, A, stage_number, diff1, diff2 = cache + @unpack J, W, uf, tf, jac_config = cache + @unpack u_tmps, k_tmps, linsolve_tmps, u_tmps2 = cache + + @unpack sequence = cache + + if integrator.opts.adaptive + # Set up the order window + # alg.min_order + 1 ≦ n_curr ≦ alg.max_order - 1 is enforced by step_*_controller! + if !(alg.min_order + 1 <= n_curr <= alg.max_order - 1) + error("Something went wrong while setting up the order window: $n_curr ∉ [$(alg.min_order+1),$(alg.max_order-1)]. + Please report this error ") + end + win_min = n_curr - 1 + win_max = n_curr + 1 + + # Set up the current extrapolation order + cache.n_old = n_curr # Save the suggested order for step_*_controller! + n_curr = win_min # Start with smallest order in the order window + end + + if !isthreaded(alg.threading) + calc_J!(J, integrator, cache) # Store the calculated jac as it won't change in internal discretisation + for index in 1:(n_curr + 1) + dt_temp = dt / sequence[index] + jacobian2W!(W[1], integrator.f.mass_matrix, dt_temp, J, false) + integrator.stats.nw += 1 + @.. broadcast=false k_tmps[1]=integrator.fsalfirst + @.. broadcast=false u_tmps[1]=uprev + + for j in 1:sequence[index] + @.. broadcast=false linsolve_tmps[1]=dt_temp * k_tmps[1] + + linsolve = cache.linsolve[1] + + if !repeat_step && j == 1 + linres = dolinsolve(integrator, linsolve; A = W[1], + b = _vec(linsolve_tmps[1]), linu = _vec(k_tmps[1])) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[1]), linu = _vec(k_tmps[1])) + end + + cache.linsolve[1] = linres.cache + + integrator.stats.nsolve += 1 + @.. broadcast=false k_tmps[1]=-k_tmps[1] + @.. broadcast=false u_tmps2[1]=u_tmps[1] + @.. broadcast=false u_tmps[1]=u_tmps[1] + k_tmps[1] + if index <= 2 && j >= 2 + # Deuflhard Stability check for initial two sequences + @.. broadcast=false diff2[1]=u_tmps[1] - u_tmps2[1] + @.. broadcast=false diff2[1]=0.5 * (diff2[1] - diff1[1]) + if integrator.opts.internalnorm(diff1[1], t) < + integrator.opts.internalnorm(diff2[1], t) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + @.. broadcast=false diff1[1]=u_tmps[1] - u_tmps2[1] + + f(k_tmps[1], u_tmps[1], p, t + j * dt_temp) + integrator.stats.nf += 1 + end + + @.. broadcast=false T[index, 1]=u_tmps[1] + end + else + calc_J!(J, integrator, cache) # Store the calculated jac as it won't change in internal discretisation + let n_curr = n_curr, uprev = uprev, dt = dt, p = p, t = t, T = T, W = W, + integrator = integrator, cache = cache, repeat_step = repeat_step, + k_tmps = k_tmps, u_tmps = u_tmps, u_tmps2 = u_tmps2, diff1 = diff1, + diff2 = diff2 + + @threaded alg.threading for i in 1:2 + startIndex = (i == 1) ? 1 : n_curr + 1 + endIndex = (i == 1) ? n_curr : n_curr + 1 + for index in startIndex:endIndex + dt_temp = dt / sequence[index] + jacobian2W!( + W[Threads.threadid()], integrator.f.mass_matrix, dt_temp, J, + false) + @.. broadcast=false k_tmps[Threads.threadid()]=integrator.fsalfirst + @.. broadcast=false u_tmps[Threads.threadid()]=uprev + for j in 1:sequence[index] + @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_temp * + k_tmps[Threads.threadid()] + + linsolve = cache.linsolve[Threads.threadid()] + + if !repeat_step && j == 1 + linres = dolinsolve(integrator, linsolve; + A = W[Threads.threadid()], + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + end + + cache.linsolve[Threads.threadid()] = linres.cache + + @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] + @.. broadcast=false u_tmps2[Threads.threadid()]=u_tmps[Threads.threadid()] + @.. broadcast=false u_tmps[Threads.threadid()]=u_tmps[Threads.threadid()] + + k_tmps[Threads.threadid()] + if index <= 2 && j >= 2 + # Deuflhard Stability check for initial two sequences + @.. broadcast=false diff2[Threads.threadid()]=u_tmps[Threads.threadid()] - + u_tmps2[Threads.threadid()] + @.. broadcast=false diff2[Threads.threadid()]=0.5 * + (diff2[Threads.threadid()] - + diff1[Threads.threadid()]) + if integrator.opts.internalnorm(diff1[Threads.threadid()], t) < + integrator.opts.internalnorm(diff2[Threads.threadid()], t) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + @.. broadcast=false diff1[Threads.threadid()]=u_tmps[Threads.threadid()] - + u_tmps2[Threads.threadid()] + f(k_tmps[Threads.threadid()], u_tmps[Threads.threadid()], p, + t + j * dt_temp) + end + + @.. broadcast=false T[index, 1]=u_tmps[Threads.threadid()] + end + integrator.force_stepfail ? break : continue + end + end + + nevals = sum(sequence[1:(n_curr + 1)]) - 1 + integrator.stats.nw += n_curr + 1 + integrator.stats.nf += nevals + integrator.stats.nsolve += nevals + end + + if integrator.force_stepfail + return + end + + # Polynomial extrapolation + for j in 2:(n_curr + 1) + for i in j:(n_curr + 1) + @.. broadcast=false T[i, j]=((sequence[i] / sequence[i - j + 1]) * T[i, j - 1] - + T[i - 1, j - 1]) / + ((sequence[i] / sequence[i - j + 1]) - 1) + end + end + + if integrator.opts.adaptive + # Compute all information relating to an extrapolation order ≦ win_min + for i in (win_min - 1):win_min + @.. broadcast=false integrator.u=T[i + 1, i + 1] + @.. broadcast=false cache.utilde=T[i + 1, i] + + calculate_residuals!(cache.res, integrator.u, cache.utilde, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(cache.res, t) + cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! + stepsize_controller_internal!(integrator, alg) # Update cache.Q + end + + # Check if an approximation of some order in the order window can be accepted + # Make sure a stepsize scaling factor of order (alg.min_order + 1) is provided for the step_*_controller! + while n_curr <= win_max + if accept_step_controller(integrator, integrator.opts.controller) + # Accept current approximation u of order n_curr + break + elseif (n_curr < alg.min_order + 1) || + integrator.EEst <= + typeof(integrator.EEst)(prod(sequence[(n_curr + 2):(win_max + 1)] .// + sequence[1]^2)) + # Reject current approximation order but pass convergence monitor + # Compute approximation of order (n_curr + 1) + n_curr = n_curr + 1 + cache.n_curr = n_curr + + dt_temp = dt / sequence[n_curr + 1] + jacobian2W!(W[1], integrator.f.mass_matrix, dt_temp, J, false) + integrator.stats.nw += 1 + @.. broadcast=false k_tmps[1]=integrator.fsalfirst + @.. broadcast=false u_tmps[1]=uprev + + for j in 1:sequence[n_curr + 1] + @.. broadcast=false linsolve_tmps[1]=dt_temp * k_tmps[1] + + linsolve = cache.linsolve[1] + + if !repeat_step && j == 1 + linres = dolinsolve(integrator, linsolve; A = W[1], + b = _vec(linsolve_tmps[1]), + linu = _vec(k_tmps[1])) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[1]), + linu = _vec(k_tmps[1])) + end + + cache.linsolve[1] = linres.cache + + integrator.stats.nsolve += 1 + @.. broadcast=false k_tmps[1]=-k_tmps[1] + @.. broadcast=false u_tmps[1]=u_tmps[1] + k_tmps[1] + f(k_tmps[1], u_tmps[1], p, t + j * dt_temp) + integrator.stats.nf += 1 + end + + @.. broadcast=false T[n_curr + 1, 1]=u_tmps[1] + + for j in 2:(n_curr + 1) + for i in j:(n_curr + 1) + @.. broadcast=false T[i, j]=((sequence[i] / sequence[i - j + 1]) * + T[i, j - 1] - T[i - 1, j - 1]) / + ((sequence[i] / sequence[i - j + 1]) - + 1) + end + end + + @.. broadcast=false integrator.u=T[n_curr + 1, n_curr + 1] + @.. broadcast=false cache.utilde=T[n_curr + 1, n_curr] + + calculate_residuals!(cache.res, integrator.u, cache.utilde, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(cache.res, t) + stepsize_controller_internal!(integrator, alg) # Update cache.Q + else + # Reject the current approximation and not pass convergence monitor + break + end + end + else + @.. broadcast=false integrator.u=T[n_curr + 1, n_curr + 1] + end + + cache.step_no = cache.step_no + 1 + f(integrator.fsallast, integrator.u, p, t + dt) + integrator.stats.nf += 1 +end + +function initialize!(integrator, cache::ImplicitEulerExtrapolationConstantCache) + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +function perform_step!(integrator, cache::ImplicitEulerExtrapolationConstantCache, + repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + alg = unwrap_alg(integrator, true) + @unpack dtpropose, T, n_curr, work, A, tf, uf = cache + @unpack sequence, stage_number = cache + + if integrator.opts.adaptive + # Set up the order window + # alg.min_order + 1 ≦ n_curr ≦ alg.max_order - 1 is enforced by step_*_controller! + if !(alg.min_order + 1 <= n_curr <= alg.max_order - 1) + error("Something went wrong while setting up the order window: $n_curr ∉ [$(alg.min_order+1),$(alg.max_order-1)]. + Please report this error ") + end + win_min = n_curr - 1 + win_max = n_curr + 1 + + # Set up the current extrapolation order + cache.n_old = n_curr # Save the suggested order for step_*_controller! + n_curr = win_min # Start with smallest order in the order window + end + + J = calc_J(integrator, cache) # Store the calculated jac as it won't change in internal discretisation + if !isthreaded(alg.threading) + for index in 1:(n_curr + 1) + dt_temp = dt / sequence[index] + W = dt_temp * J - integrator.f.mass_matrix + integrator.stats.nw += 1 + k_copy = integrator.fsalfirst + u_tmp = uprev + diff1 = zero(u_tmp) + for j in 1:sequence[index] + k = _reshape(W \ -_vec(dt_temp * k_copy), axes(uprev)) + integrator.stats.nsolve += 1 + u_tmp2 = u_tmp + u_tmp = u_tmp + k + if index <= 2 && j >= 2 + # Deuflhard Stability check for initial two sequences + diff2 = u_tmp - u_tmp2 + diff2 = 0.5 * (diff2 - diff1) + if integrator.opts.internalnorm(diff1, t) < + integrator.opts.internalnorm(diff2, t) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + diff1 = u_tmp - u_tmp2 + k_copy = f(u_tmp, p, t + j * dt_temp) + integrator.stats.nf += 1 + end + + T[index, 1] = u_tmp + end + else + J = calc_J(integrator, cache) # Store the calculated jac as it won't change in internal discretisation + let n_curr = n_curr, dt = dt, integrator = integrator, cache = cache, + repeat_step = repeat_step, + uprev = uprev, T = T + + @threaded alg.threading for i in 1:2 + startIndex = (i == 1) ? 1 : n_curr + 1 + endIndex = (i == 1) ? n_curr : n_curr + 1 + for index in startIndex:endIndex + dt_temp = dt / sequence[index] + W = dt_temp * J - integrator.f.mass_matrix + k_copy = integrator.fsalfirst + u_tmp = uprev + diff1 = zero(u_tmp) + for j in 1:sequence[index] + k = _reshape(W \ -_vec(dt_temp * k_copy), axes(uprev)) + u_tmp2 = u_tmp + u_tmp = u_tmp + k + if index <= 2 && j >= 2 + # Deuflhard Stability check for initial two sequences + diff2 = u_tmp - u_tmp2 + diff2 = 0.5 * (diff2 - diff1) + if integrator.opts.internalnorm(diff1, t) < + integrator.opts.internalnorm(diff2, t) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + diff1 = u_tmp - u_tmp2 + k_copy = f(u_tmp, p, t + j * dt_temp) + end + T[index, 1] = u_tmp + end + integrator.force_stepfail ? break : continue + end + end + + if integrator.force_stepfail + return + end + + nevals = sum(sequence[1:(n_curr + 1)]) - 1 + integrator.stats.nw += n_curr + 1 + integrator.stats.nf += nevals + integrator.stats.nsolve += nevals + end + + # Richardson extrapolation + tmp = 1 + for j in 2:(n_curr + 1) + tmp *= 2 + for i in j:(n_curr + 1) + T[i, j] = ((sequence[i] / sequence[i - j + 1]) * T[i, j - 1] - + T[i - 1, j - 1]) / + ((sequence[i] / sequence[i - j + 1]) - 1) + end + end + + integrator.dt = dt + + if integrator.opts.adaptive + # Compute all information relating to an extrapolation order ≦ win_min + for i in (win_min - 1):win_min + u = T[i + 1, i + 1] + utilde = T[i + 1, i] + res = calculate_residuals(u, utilde, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, + t) + integrator.EEst = integrator.opts.internalnorm(res, t) + cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! + stepsize_controller_internal!(integrator, alg) # Update cache.Q + end + + # Check if an approximation of some order in the order window can be accepted + # Make sure a stepsize scaling factor of order (alg.min_order + 1) is provided for the step_*_controller! + while n_curr <= win_max + if accept_step_controller(integrator, integrator.opts.controller) + # Accept current approximation u of order n_curr + break + elseif (n_curr < alg.min_order + 1) || + integrator.EEst <= + typeof(integrator.EEst)(prod(sequence[(n_curr + 2):(win_max + 1)] .// + sequence[1]^2)) + # Reject current approximation order but pass convergence monitor + # Always compute approximation of order (n_curr + 1) + n_curr = n_curr + 1 + cache.n_curr = n_curr + + # Update T + dt_temp = dt / sequence[n_curr + 1] + W = dt_temp * J - integrator.f.mass_matrix + integrator.stats.nw += 1 + k_copy = integrator.fsalfirst + u_tmp = uprev + + for j in 1:sequence[n_curr + 1] + k = _reshape(W \ -_vec(dt_temp * k_copy), axes(uprev)) + integrator.stats.nsolve += 1 + u_tmp = u_tmp + k + k_copy = f(u_tmp, p, t + j * dt_temp) + integrator.stats.nf += 1 + end + + T[n_curr + 1, 1] = u_tmp + + #Extrapolate to new order + for j in 2:(n_curr + 1) + for i in j:(n_curr + 1) + T[i, j] = ((sequence[i] / sequence[i - j + 1]) * T[i, j - 1] - + T[i - 1, j - 1]) / + ((sequence[i] / sequence[i - j + 1]) - 1) + end + end + # Update u, integrator.EEst and cache.Q + u = T[n_curr + 1, n_curr + 1] + utilde = T[n_curr + 1, n_curr] + res = calculate_residuals(u, utilde, integrator.opts.abstol, + integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(res, t) + stepsize_controller_internal!(integrator, alg) # Update cache.Q + else + # Reject the current approximation and not pass convergence monitor + break + end + end + else + integrator.u = T[n_curr + 1, n_curr + 1] + end + + # Use extrapolated value of u + integrator.u = T[n_curr + 1, n_curr + 1] + k_temp = f(integrator.u, p, t + dt) + integrator.stats.nf += 1 + integrator.fsallast = k_temp + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +function initialize!(integrator, cache::ExtrapolationMidpointDeuflhardCache) + # cf. initialize! of MidpointCache + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation +end + +function perform_step!(integrator, cache::ExtrapolationMidpointDeuflhardCache, + repeat_step = false) + # Unpack all information needed + @unpack t, uprev, dt, f, p = integrator + alg = unwrap_alg(integrator, false) + @unpack n_curr, u_temp1, u_temp2, utilde, res, T, fsalfirst, k = cache + @unpack u_temp3, u_temp4, k_tmps = cache + + # Coefficients for obtaining u + @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients + # Coefficients for obtaining utilde + @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients + # Additional constant information + @unpack subdividing_sequence = cache.coefficients + @unpack stage_number = cache + @unpack sequence_factor = alg + + fill!(cache.Q, zero(eltype(cache.Q))) + tol = integrator.opts.internalnorm(integrator.opts.reltol, t) # Used by the convergence monitor + + if integrator.opts.adaptive + # Set up the order window + win_min = max(alg.min_order, n_curr - 1) + win_max = min(alg.max_order, n_curr + 1) + + # Set up the current extrapolation order + cache.n_old = n_curr # Save the suggested order for step_*_controller! + n_curr = win_min # Start with smallest order in the order window + end + + #Compute the internal discretisations + if !isthreaded(alg.threading) + for i in 0:n_curr + j_int = sequence_factor * subdividing_sequence[i + 1] + dt_int = dt / j_int # Stepsize of the ith internal discretisation + @.. broadcast=false u_temp2=uprev + @.. broadcast=false u_temp1=u_temp2 + dt_int * fsalfirst # Euler starting step + for j in 2:j_int + f(k, cache.u_temp1, p, t + (j - 1) * dt_int) + integrator.stats.nf += 1 + @.. broadcast=false T[i + 1]=u_temp2 + 2 * dt_int * k # Explicit Midpoint rule + @.. broadcast=false u_temp2=u_temp1 + @.. broadcast=false u_temp1=T[i + 1] + end + end + else + if alg.sequence == :romberg + # Compute solution by using maximum two threads for romberg sequence + # One thread will fill T matrix till second last element and another thread will + # fill last element of T matrix. + # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) + # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, + dt = dt, u_temp3 = u_temp3, + u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T + + @threaded alg.threading for i in 1:2 + startIndex = (i == 1) ? 0 : n_curr + endIndex = (i == 1) ? n_curr - 1 : n_curr + for index in startIndex:endIndex + j_int_temp = sequence_factor * subdividing_sequence[index + 1] + dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation + @.. broadcast=false u_temp4[Threads.threadid()]=uprev + @.. broadcast=false u_temp3[Threads.threadid()]=u_temp4[Threads.threadid()] + + dt_int_temp * + fsalfirst # Euler starting step + for j in 2:j_int_temp + f(k_tmps[Threads.threadid()], + cache.u_temp3[Threads.threadid()], + p, t + (j - 1) * dt_int_temp) + @.. broadcast=false T[index + 1]=u_temp4[Threads.threadid()] + + 2 * dt_int_temp * + k_tmps[Threads.threadid()] # Explicit Midpoint rule + @.. broadcast=false u_temp4[Threads.threadid()]=u_temp3[Threads.threadid()] + @.. broadcast=false u_temp3[Threads.threadid()]=T[index + 1] + end + end + end + end + else + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, + dt = dt, u_temp3 = u_temp3, + u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T + + @threaded alg.threading for i in 0:(n_curr ÷ 2) + indices = (i, n_curr - i) + for index in indices + j_int_temp = sequence_factor * subdividing_sequence[index + 1] + dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation + @.. broadcast=false u_temp4[Threads.threadid()]=uprev + @.. broadcast=false u_temp3[Threads.threadid()]=u_temp4[Threads.threadid()] + + dt_int_temp * + fsalfirst # Euler starting step + for j in 2:j_int_temp + f(k_tmps[Threads.threadid()], u_temp3[Threads.threadid()], p, + t + (j - 1) * dt_int_temp) + @.. broadcast=false T[index + 1]=u_temp4[Threads.threadid()] + + 2 * dt_int_temp * + k_tmps[Threads.threadid()] # Explicit Midpoint rule + @.. broadcast=false u_temp4[Threads.threadid()]=u_temp3[Threads.threadid()] + @.. broadcast=false u_temp3[Threads.threadid()]=T[index + 1] + end + if indices[2] <= indices[1] + break + end + end + end + end + end + nevals = cache.stage_number[n_curr - alg.min_order + 1] - 1 + integrator.stats.nf += nevals + end + + if integrator.opts.adaptive + # Compute all information relating to an extrapolation order ≦ win_min + for i in (alg.min_order):n_curr + + #integrator.u .= extrapolation_scalars[i+1] * sum( broadcast(*, cache.T[1:(i+1)], extrapolation_weights[1:(i+1), (i+1)]) ) # Approximation of extrapolation order i + #cache.utilde .= extrapolation_scalars_2[i] * sum( broadcast(*, cache.T[2:(i+1)], extrapolation_weights_2[1:i, i]) ) # and its internal counterpart + + u_temp1 .= false + u_temp2 .= false + for j in 1:(i + 1) + @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (i + 1)] + end + for j in 2:(i + 1) + @.. broadcast=false u_temp2+=cache.T[j] * extrapolation_weights_2[j - 1, i] + end + @.. broadcast=false integrator.u=extrapolation_scalars[i + 1] * u_temp1 + @.. broadcast=false cache.utilde=extrapolation_scalars_2[i] * u_temp2 + + calculate_residuals!(cache.res, integrator.u, cache.utilde, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(cache.res, t) + cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! + stepsize_controller_internal!(integrator, alg) # Update cache.Q + end + + # Check if an approximation of some order in the order window can be accepted + while n_curr <= win_max + if accept_step_controller(integrator, integrator.opts.controller) + # Accept current approximation u of order n_curr + break + elseif integrator.EEst <= + tol^(stage_number[n_curr - alg.min_order + 1] / + stage_number[win_max - alg.min_order + 1] - 1) + # Reject current approximation order but pass convergence monitor + # Compute approximation of order (n_curr + 1) + n_curr = n_curr + 1 + cache.n_curr = n_curr + + # Update cache.T + j_int = sequence_factor * subdividing_sequence[n_curr + 1] + dt_int = dt / j_int # Stepsize of the new internal discretisation + @.. broadcast=false u_temp2=uprev + @.. broadcast=false u_temp1=u_temp2 + dt_int * fsalfirst # Euler starting step + for j in 2:j_int + f(k, cache.u_temp1, p, t + (j - 1) * dt_int) + integrator.stats.nf += 1 + @.. broadcast=false T[n_curr + 1]=u_temp2 + 2 * dt_int * k + @.. broadcast=false u_temp2=u_temp1 + @.. broadcast=false u_temp1=T[n_curr + 1] + end + + # Update u, integrator.EEst and cache.Q + #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr + #cache.utilde .= extrapolation_scalars_2[n_curr] * sum( broadcast(*, cache.T[2:(n_curr+1)], extrapolation_weights_2[1:n_curr, n_curr]) ) # and its internal counterpart + + u_temp1 .= false + u_temp2 .= false + for j in 1:(n_curr + 1) + @.. broadcast=false u_temp1+=cache.T[j] * + extrapolation_weights[j, (n_curr + 1)] + end + for j in 2:(n_curr + 1) + @.. broadcast=false u_temp2+=cache.T[j] * + extrapolation_weights_2[j - 1, n_curr] + end + @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 + @.. broadcast=false cache.utilde=extrapolation_scalars_2[n_curr] * u_temp2 + + calculate_residuals!(cache.res, integrator.u, cache.utilde, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(cache.res, t) + stepsize_controller_internal!(integrator, alg) # Update cache.Q + else + # Reject the current approximation and not pass convergence monitor + break + end + end + else + + #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr + u_temp1 .= false + for j in 1:(n_curr + 1) + @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (n_curr + 1)] + end + @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 + end + + f(cache.k, integrator.u, p, t + dt) # Update FSAL + integrator.stats.nf += 1 +end + +function initialize!(integrator, cache::ExtrapolationMidpointDeuflhardConstantCache) + # cf. initialize! of MidpointConstantCache + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +function perform_step!(integrator, cache::ExtrapolationMidpointDeuflhardConstantCache, + repeat_step = false) + # Unpack all information needed + @unpack t, uprev, dt, f, p = integrator + alg = unwrap_alg(integrator, false) + @unpack n_curr = cache + # Coefficients for obtaining u + @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients + # Coefficients for obtaining utilde + @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients + # Additional constant information + @unpack subdividing_sequence = cache.coefficients + @unpack stage_number = cache + @unpack sequence_factor = alg + + # Create auxiliary variables + u_temp1, u_temp2 = copy(uprev), copy(uprev) # Auxiliary variables for computing the internal discretisations + u, utilde = copy(uprev), copy(uprev) # Storage for the latest approximation and its internal counterpart + tol = integrator.opts.internalnorm(integrator.opts.reltol, t) # Used by the convergence monitor + T = fill(zero(uprev), alg.max_order + 1) # Storage for the internal discretisations obtained by the explicit midpoint rule + fill!(cache.Q, zero(eltype(cache.Q))) + + # Start computation + if integrator.opts.adaptive + # Set up the order window + win_min = max(alg.min_order, n_curr - 1) + win_max = min(alg.max_order, n_curr + 1) + + # Set up the current extrapolation order + cache.n_old = n_curr # Save the suggested order for step_*_controller! + n_curr = win_min # Start with smallest order in the order window + end + + # Compute the internal discretisations + if !isthreaded(alg.threading) + for i in 0:n_curr + j_int = sequence_factor * subdividing_sequence[i + 1] + dt_int = dt / j_int # Stepsize of the ith internal discretisation + u_temp2 = uprev + u_temp1 = u_temp2 + dt_int * integrator.fsalfirst # Euler starting step + for j in 2:j_int + T[i + 1] = u_temp2 + 2 * dt_int * f(u_temp1, p, t + (j - 1) * dt_int) # Explicit Midpoint rule + integrator.stats.nf += 1 + u_temp2 = u_temp1 + u_temp1 = T[i + 1] + end + end + else + if alg.sequence == :romberg + # Compute solution by using maximum two threads for romberg sequence + # One thread will fill T matrix till second last element and another thread will + # fill last element of T matrix. + # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) + # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, + dt = dt, + integrator = integrator, p = p, t = t, T = T + + @threaded alg.threading for i in 1:2 + startIndex = (i == 1) ? 0 : n_curr + endIndex = (i == 1) ? n_curr - 1 : n_curr + for index in startIndex:endIndex + j_int_temp = sequence_factor * subdividing_sequence[index + 1] + dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation + u_temp4 = uprev + u_temp3 = u_temp4 + dt_int_temp * integrator.fsalfirst # Euler starting step + for j in 2:j_int_temp + T[index + 1] = u_temp4 + + 2 * dt_int_temp * + f(u_temp3, p, t + (j - 1) * dt_int_temp) # Explicit Midpoint rule + u_temp4 = u_temp3 + u_temp3 = T[index + 1] + end + end + end + end + else + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, dt = dt, + uprev = uprev, + p = p, t = t, T = T + + @threaded alg.threading for i in 0:(n_curr ÷ 2) + indices = (i, n_curr - i) + for index in indices + j_int_temp = sequence_factor * subdividing_sequence[index + 1] + dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation + u_temp4 = uprev + u_temp3 = u_temp4 + dt_int_temp * integrator.fsalfirst # Euler starting step + for j in 2:j_int_temp + T[index + 1] = u_temp4 + + 2 * dt_int_temp * + f(u_temp3, p, t + (j - 1) * dt_int_temp) # Explicit Midpoint rule + u_temp4 = u_temp3 + u_temp3 = T[index + 1] + end + if indices[2] <= indices[1] + break + end + end + end + end + end + nevals = cache.stage_number[n_curr - alg.min_order + 1] - 1 + integrator.stats.nf += nevals + end + + if integrator.opts.adaptive + # Compute all information relating to an extrapolation order ≦ win_min + for i in (alg.min_order):n_curr + u = eltype(uprev).(extrapolation_scalars[i + 1]) * + sum(broadcast(*, T[1:(i + 1)], + eltype(uprev).(extrapolation_weights[1:(i + 1), (i + 1)]))) # Approximation of extrapolation order i + utilde = eltype(uprev).(extrapolation_scalars_2[i]) * + sum(broadcast(*, T[2:(i + 1)], + eltype(uprev).(extrapolation_weights_2[1:i, i]))) # and its internal counterpart + res = calculate_residuals(u, utilde, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, + t) + integrator.EEst = integrator.opts.internalnorm(res, t) + cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! + stepsize_controller_internal!(integrator, alg) # Update cache.Q + end + + # Check if an approximation of some order in the order window can be accepted + while n_curr <= win_max + if accept_step_controller(integrator, integrator.opts.controller) + # Accept current approximation u of order n_curr + break + elseif integrator.EEst <= + tol^(stage_number[n_curr - alg.min_order + 1] / + stage_number[win_max - alg.min_order + 1] - 1) + # Reject current approximation order but pass convergence monitor + # Compute approximation of order (n_curr + 1) + n_curr = n_curr + 1 + cache.n_curr = n_curr + + # Update T + j_int = sequence_factor * subdividing_sequence[n_curr + 1] + dt_int = dt / j_int # Stepsize of the new internal discretisation + u_temp2 = uprev + u_temp1 = u_temp2 + dt_int * integrator.fsalfirst # Euler starting step + for j in 2:j_int + T[n_curr + 1] = u_temp2 + + 2 * dt_int * f(u_temp1, p, t + (j - 1) * dt_int) + integrator.stats.nf += 1 + u_temp2 = u_temp1 + u_temp1 = T[n_curr + 1] + end + + # Update u, integrator.EEst and cache.Q + u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * + sum(broadcast(*, T[1:(n_curr + 1)], + eltype(uprev).(extrapolation_weights[1:(n_curr + 1), + (n_curr + 1)]))) # Approximation of extrapolation order n_curr + utilde = eltype(uprev).(extrapolation_scalars_2[n_curr]) * + sum(broadcast(*, T[2:(n_curr + 1)], + eltype(uprev).(extrapolation_weights_2[1:n_curr, + n_curr]))) # and its internal counterpart + res = calculate_residuals(u, utilde, integrator.opts.abstol, + integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(res, t) + stepsize_controller_internal!(integrator, alg) # Update cache.Q + else + # Reject the current approximation and not pass convergence monitor + break + end + end + else + u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * + sum(broadcast(*, T[1:(n_curr + 1)], + eltype(uprev).(extrapolation_weights[1:(n_curr + 1), + (n_curr + 1)]))) # Approximation of extrapolation order n_curr + end + + # Save the latest approximation and update FSAL + integrator.u = u + integrator.fsallast = f(u, p, t + dt) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +function initialize!(integrator, cache::ImplicitDeuflhardExtrapolationCache) + # cf. initialize! of MidpointCache + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation +end + +function perform_step!(integrator, cache::ImplicitDeuflhardExtrapolationCache, + repeat_step = false) + # Unpack all information needed + @unpack t, uprev, dt, f, p = integrator + alg = unwrap_alg(integrator, true) + @unpack n_curr, u_temp1, u_temp2, utilde, res, T, fsalfirst, k, diff1, diff2 = cache + @unpack u_temp3, u_temp4, k_tmps = cache + + # Coefficients for obtaining u + @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients + # Coefficients for obtaining utilde + @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients + # Additional constant information + @unpack subdividing_sequence = cache.coefficients + @unpack stage_number = cache + + @unpack J, W, uf, tf, linsolve_tmps, jac_config = cache + + fill!(cache.Q, zero(eltype(cache.Q))) + + if integrator.opts.adaptive + # Set up the order window + win_min = max(alg.min_order, n_curr - 1) + win_max = min(alg.max_order, n_curr + 1) + + # Set up the current extrapolation order + cache.n_old = n_curr # Save the suggested order for step_*_controller! + n_curr = win_min # Start with smallest order in the order window + end + + #Compute the internal discretisations + calc_J!(J, integrator, cache) # Store the calculated jac as it won't change in internal discretisation + if !isthreaded(alg.threading) + for i in 0:n_curr + j_int = 4 * subdividing_sequence[i + 1] + dt_int = dt / j_int # Stepsize of the ith internal discretisation + jacobian2W!(W[1], integrator.f.mass_matrix, dt_int, J, false) + integrator.stats.nw += 1 + @.. broadcast=false u_temp2=uprev + @.. broadcast=false linsolve_tmps[1]=dt_int * fsalfirst + + linsolve = cache.linsolve[1] + + if !repeat_step + linres = dolinsolve(integrator, linsolve; A = W[1], + b = _vec(linsolve_tmps[1]), linu = _vec(k)) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[1]), linu = _vec(k)) + end + + cache.linsolve[1] = linres.cache + + integrator.stats.nsolve += 1 + @.. broadcast=false k=-k + @.. broadcast=false u_temp1=u_temp2 + k # Euler starting step + @.. broadcast=false diff1[1]=u_temp1 - u_temp2 + for j in 2:j_int + f(k, cache.u_temp1, p, t + (j - 1) * dt_int) + integrator.stats.nf += 1 + @.. broadcast=false linsolve_tmps[1]=dt_int * k - (u_temp1 - u_temp2) + + linsolve = cache.linsolve[1] + + if !repeat_step && j == 1 + linres = dolinsolve(integrator, linsolve; A = W[1], + b = _vec(linsolve_tmps[1]), linu = _vec(k)) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[1]), linu = _vec(k)) + end + cache.linsolve[1] = linres.cache + + integrator.stats.nsolve += 1 + @.. broadcast=false k=-k + @.. broadcast=false T[i + 1]=2 * u_temp1 - u_temp2 + 2 * k # Explicit Midpoint rule + @.. broadcast=false u_temp2=u_temp1 + @.. broadcast=false u_temp1=T[i + 1] + if (i <= 1) + # Deuflhard Stability check for initial two sequences + @.. broadcast=false diff2[1]=u_temp1 - u_temp2 + if (integrator.opts.internalnorm(diff1[1], t) < + integrator.opts.internalnorm(0.5 * (diff2[1] - diff1[1]), t)) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + end + end + else + if alg.sequence == :romberg + # Compute solution by using maximum two threads for romberg sequence + # One thread will fill T matrix till second last element and another thread will + # fill last element of T matrix. + # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) + # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, + dt = dt, u_temp3 = u_temp3, + u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T + + @threaded alg.threading for i in 1:2 + startIndex = (i == 1) ? 0 : n_curr + endIndex = (i == 1) ? n_curr - 1 : n_curr + + for index in startIndex:endIndex + j_int_temp = 4 * subdividing_sequence[index + 1] + dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation + jacobian2W!(W[Threads.threadid()], integrator.f.mass_matrix, + dt_int_temp, J, false) + @.. broadcast=false u_temp4[Threads.threadid()]=uprev + @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * + fsalfirst + + linsolve = cache.linsolve[Threads.threadid()] + + if !repeat_step + linres = dolinsolve(integrator, linsolve; + A = W[Threads.threadid()], + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + end + cache.linsolve[Threads.threadid()] = linres.cache + + @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] + @.. broadcast=false u_temp3[Threads.threadid()]=u_temp4[Threads.threadid()] + + k_tmps[Threads.threadid()] # Euler starting step + @.. broadcast=false diff1[Threads.threadid()]=u_temp3[Threads.threadid()] - + u_temp4[Threads.threadid()] + for j in 2:j_int_temp + f(k_tmps[Threads.threadid()], + cache.u_temp3[Threads.threadid()], + p, t + (j - 1) * dt_int_temp) + @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * + k_tmps[Threads.threadid()] - + (u_temp3[Threads.threadid()] - + u_temp4[Threads.threadid()]) + + linsolve = cache.linsolve[Threads.threadid()] + + if !repeat_step && j == 1 + linres = dolinsolve(integrator, linsolve; + A = W[Threads.threadid()], + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + end + cache.linsolve[Threads.threadid()] = linres.cache + + @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] + @.. broadcast=false T[index + 1]=2 * + u_temp3[Threads.threadid()] - + u_temp4[Threads.threadid()] + + 2 * k_tmps[Threads.threadid()] # Explicit Midpoint rule + @.. broadcast=false u_temp4[Threads.threadid()]=u_temp3[Threads.threadid()] + @.. broadcast=false u_temp3[Threads.threadid()]=T[index + 1] + if (index <= 1) + # Deuflhard Stability check for initial two sequences + @.. broadcast=false diff2[Threads.threadid()]=u_temp3[Threads.threadid()] - + u_temp4[Threads.threadid()] + @.. broadcast=false diff2[Threads.threadid()]=0.5 * + (diff2[Threads.threadid()] - + diff1[Threads.threadid()]) + if (integrator.opts.internalnorm(diff1[Threads.threadid()], + t) < + integrator.opts.internalnorm(diff2[Threads.threadid()], + t)) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + end + end + integrator.force_stepfail ? break : continue + end + end + else + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, + dt = dt, u_temp3 = u_temp3, + u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T + + @threaded alg.threading for i in 0:(n_curr ÷ 2) + indices = i != n_curr - i ? (i, n_curr - i) : (-1, n_curr - i) #Use flag to avoid union + for index in indices + index == -1 && continue + j_int_temp = 4 * subdividing_sequence[index + 1] + dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation + jacobian2W!(W[Threads.threadid()], integrator.f.mass_matrix, + dt_int_temp, J, false) + @.. broadcast=false u_temp4[Threads.threadid()]=uprev + @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * + fsalfirst + + linsolve = cache.linsolve[Threads.threadid()] + + if !repeat_step + linres = dolinsolve(integrator, linsolve; + A = W[Threads.threadid()], + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + end + cache.linsolve[Threads.threadid()] = linres.cache + + @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] + @.. broadcast=false u_temp3[Threads.threadid()]=u_temp4[Threads.threadid()] + + k_tmps[Threads.threadid()] # Euler starting step + @.. broadcast=false diff1[Threads.threadid()]=u_temp3[Threads.threadid()] - + u_temp4[Threads.threadid()] + for j in 2:j_int_temp + f(k_tmps[Threads.threadid()], + cache.u_temp3[Threads.threadid()], + p, t + (j - 1) * dt_int_temp) + @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * + k_tmps[Threads.threadid()] - + (u_temp3[Threads.threadid()] - + u_temp4[Threads.threadid()]) + + linsolve = cache.linsolve[Threads.threadid()] + + if !repeat_step && j == 1 + linres = dolinsolve(integrator, linsolve; + A = W[Threads.threadid()], + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + end + cache.linsolve[Threads.threadid()] = linres.cache + + @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] + @.. broadcast=false T[index + 1]=2 * + u_temp3[Threads.threadid()] - + u_temp4[Threads.threadid()] + + 2 * k_tmps[Threads.threadid()] # Explicit Midpoint rule + @.. broadcast=false u_temp4[Threads.threadid()]=u_temp3[Threads.threadid()] + @.. broadcast=false u_temp3[Threads.threadid()]=T[index + 1] + if (index <= 1) + # Deuflhard Stability check for initial two sequences + @.. broadcast=false diff2[Threads.threadid()]=u_temp3[Threads.threadid()] - + u_temp4[Threads.threadid()] + @.. broadcast=false diff2[Threads.threadid()]=0.5 * + (diff2[Threads.threadid()] - + diff1[Threads.threadid()]) + if (integrator.opts.internalnorm(diff1[Threads.threadid()], + t) < + integrator.opts.internalnorm(diff2[Threads.threadid()], + t)) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + end + end + integrator.force_stepfail ? break : continue + end + end + end + end + + if integrator.force_stepfail + return + end + + if integrator.opts.adaptive + # Compute all information relating to an extrapolation order ≦ win_min + for i in (alg.min_order):n_curr + + #integrator.u .= extrapolation_scalars[i+1] * sum( broadcast(*, cache.T[1:(i+1)], extrapolation_weights[1:(i+1), (i+1)]) ) # Approximation of extrapolation order i + #cache.utilde .= extrapolation_scalars_2[i] * sum( broadcast(*, cache.T[2:(i+1)], extrapolation_weights_2[1:i, i]) ) # and its internal counterpart + + u_temp1 .= false + u_temp2 .= false + for j in 1:(i + 1) + @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (i + 1)] + end + for j in 2:(i + 1) + @.. broadcast=false u_temp2+=cache.T[j] * extrapolation_weights_2[j - 1, i] + end + @.. broadcast=false integrator.u=extrapolation_scalars[i + 1] * u_temp1 + @.. broadcast=false cache.utilde=extrapolation_scalars_2[i] * u_temp2 + + calculate_residuals!(cache.res, integrator.u, cache.utilde, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(cache.res, t) + cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! + stepsize_controller_internal!(integrator, alg) # Update cache.Q + end + + # Check if an approximation of some order in the order window can be accepted + while n_curr <= win_max + tol = integrator.opts.internalnorm(cache.utilde - integrator.u, t) / + integrator.EEst # Used by the convergence monitor + if accept_step_controller(integrator, integrator.opts.controller) + # Accept current approximation u of order n_curr + break + elseif integrator.EEst <= + tol^(stage_number[n_curr - alg.min_order + 1] / + stage_number[win_max - alg.min_order + 1] - 1) + # Reject current approximation order but pass convergence monitor + # Compute approximation of order (n_curr + 1) + n_curr = n_curr + 1 + cache.n_curr = n_curr + + # Update cache.T + j_int = 4 * subdividing_sequence[n_curr + 1] + dt_int = dt / j_int # Stepsize of the new internal discretisation + jacobian2W!(W[1], integrator.f.mass_matrix, dt_int, J, false) + integrator.stats.nw += 1 + @.. broadcast=false u_temp2=uprev + @.. broadcast=false linsolve_tmps[1]=dt_int * fsalfirst + + linsolve = cache.linsolve[1] + linres = dolinsolve(integrator, linsolve; b = _vec(linsolve_tmps[1]), + linu = _vec(k)) + cache.linsolve[1] = linres.cache + + integrator.stats.nsolve += 1 + @.. broadcast=false k=-k + @.. broadcast=false u_temp1=u_temp2 + k # Euler starting step + for j in 2:j_int + f(k, cache.u_temp1, p, t + (j - 1) * dt_int) + integrator.stats.nf += 1 + @.. broadcast=false linsolve_tmps[1]=dt_int * k - (u_temp1 - u_temp2) + + linsolve = cache.linsolve[1] + linres = dolinsolve(integrator, linsolve; b = _vec(linsolve_tmps[1]), + linu = _vec(k)) + cache.linsolve[1] = linres.cache + + integrator.stats.nsolve += 1 + @.. broadcast=false k=-k + @.. broadcast=false T[n_curr + 1]=2 * u_temp1 - u_temp2 + 2 * k # Explicit Midpoint rule + @.. broadcast=false u_temp2=u_temp1 + @.. broadcast=false u_temp1=T[n_curr + 1] + end + + # Update u, integrator.EEst and cache.Q + #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr + #cache.utilde .= extrapolation_scalars_2[n_curr] * sum( broadcast(*, cache.T[2:(n_curr+1)], extrapolation_weights_2[1:n_curr, n_curr]) ) # and its internal counterpart + + u_temp1 .= false + u_temp2 .= false + for j in 1:(n_curr + 1) + @.. broadcast=false u_temp1+=cache.T[j] * + extrapolation_weights[j, (n_curr + 1)] + end + for j in 2:(n_curr + 1) + @.. broadcast=false u_temp2+=cache.T[j] * + extrapolation_weights_2[j - 1, n_curr] + end + @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 + @.. broadcast=false cache.utilde=extrapolation_scalars_2[n_curr] * u_temp2 + + calculate_residuals!(cache.res, integrator.u, cache.utilde, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(cache.res, t) + stepsize_controller_internal!(integrator, alg) # Update cache.Q + else + # Reject the current approximation and not pass convergence monitor + break + end + end + else + + #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr + u_temp1 .= false + for j in 1:(n_curr + 1) + @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (n_curr + 1)] + end + @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 + end + + f(cache.k, integrator.u, p, t + dt) # Update FSAL + integrator.stats.nf += 1 +end + +function initialize!(integrator, cache::ImplicitDeuflhardExtrapolationConstantCache) + # cf. initialize! of MidpointConstantCache + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +function perform_step!(integrator, cache::ImplicitDeuflhardExtrapolationConstantCache, + repeat_step = false) + # Unpack all information needed + @unpack t, uprev, dt, f, p = integrator + alg = unwrap_alg(integrator, true) + @unpack n_curr = cache + # Coefficients for obtaining u + @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients + # Coefficients for obtaining utilde + @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients + # Additional constant information + @unpack subdividing_sequence = cache.coefficients + @unpack stage_number = cache + + # Create auxiliary variables + u_temp1, u_temp2 = copy(uprev), copy(uprev) # Auxiliary variables for computing the internal discretisations + u, utilde = copy(uprev), copy(uprev) # Storage for the latest approximation and its internal counterpart + T = fill(zero(uprev), alg.max_order + 1) # Storage for the internal discretisations obtained by the explicit midpoint rule + fill!(cache.Q, zero(eltype(cache.Q))) + + # Start computation + if integrator.opts.adaptive + # Set up the order window + win_min = max(alg.min_order, n_curr - 1) + win_max = min(alg.max_order, n_curr + 1) + + # Set up the current extrapolation order + cache.n_old = n_curr # Save the suggested order for step_*_controller! + n_curr = win_min # Start with smallest order in the order window + end + + # Compute the internal discretisations + J = calc_J(integrator, cache) # Store the calculated jac as it won't change in internal discretisation + if !isthreaded(alg.threading) + for i in 0:n_curr + j_int = 4 * subdividing_sequence[i + 1] + dt_int = dt / j_int # Stepsize of the ith internal discretisation + W = dt_int * J - integrator.f.mass_matrix + integrator.stats.nw += 1 + u_temp2 = uprev + u_temp1 = u_temp2 + + _reshape(W \ -_vec(dt_int * integrator.fsalfirst), axes(uprev)) # Euler starting step + diff1 = u_temp1 - u_temp2 + for j in 2:j_int + T[i + 1] = 2 * u_temp1 - u_temp2 + + 2 * _reshape( + W \ + -_vec(dt_int * f(u_temp1, p, t + (j - 1) * dt_int) - + (u_temp1 - u_temp2)), + axes(uprev)) + integrator.stats.nf += 1 + u_temp2 = u_temp1 + u_temp1 = T[i + 1] + if (i <= 1) + # Deuflhard Stability check for initial two sequences + diff2 = u_temp1 - u_temp2 + if (integrator.opts.internalnorm(diff1, t) < + integrator.opts.internalnorm(0.5 * (diff2 - diff1), t)) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + end + end + else + if alg.sequence == :romberg + # Compute solution by using maximum two threads for romberg sequence + # One thread will fill T matrix till second last element and another thread will + # fill last element of T matrix. + # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) + # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, + dt = dt, u_temp2 = u_temp2, + u_temp2 = u_temp2, p = p, t = t, T = T + + @threaded alg.threading for i in 1:2 + startIndex = (i == 1) ? 0 : n_curr + endIndex = (i == 1) ? n_curr - 1 : n_curr + + for index in startIndex:endIndex + j_int = 4 * subdividing_sequence[index + 1] + dt_int = dt / j_int # Stepsize of the ith internal discretisation + W = dt_int * J - integrator.f.mass_matrix + integrator.stats.nw += 1 + u_temp4 = uprev + u_temp3 = u_temp4 + + _reshape(W \ -_vec(dt_int * integrator.fsalfirst), + axes(uprev)) # Euler starting step + diff1 = u_temp3 - u_temp4 + for j in 2:j_int + T[index + 1] = 2 * u_temp3 - u_temp4 + + 2 * _reshape( + W \ + -_vec(dt_int * f(u_temp3, p, + t + (j - 1) * dt_int) - + (u_temp3 - u_temp4)), + axes(uprev)) + integrator.stats.nf += 1 + u_temp4 = u_temp3 + u_temp3 = T[index + 1] + if (index <= 1) + # Deuflhard Stability check for initial two sequences + diff2 = u_temp3 - u_temp4 + if (integrator.opts.internalnorm(diff1[1], t) < + integrator.opts.internalnorm( + 0.5 * + (diff2[1] - diff1[1]), t)) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + end + end + integrator.force_stepfail ? break : continue + end + end + else + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, + dt = dt, + integrator = integrator, p = p, t = t, T = T + + @threaded alg.threading for i in 0:(n_curr ÷ 2) + indices = i != n_curr - i ? (i, n_curr - i) : (-1, n_curr - i) + for index in indices + index == -1 && continue + j_int = 4 * subdividing_sequence[index + 1] + dt_int = dt / j_int # Stepsize of the ith internal discretisation + W = dt_int * J - integrator.f.mass_matrix + integrator.stats.nw += 1 + u_temp4 = uprev + u_temp3 = u_temp4 + + _reshape(W \ -_vec(dt_int * integrator.fsalfirst), + axes(uprev)) # Euler starting step + diff1 = u_temp3 - u_temp4 + for j in 2:j_int + T[index + 1] = 2 * u_temp3 - u_temp4 + + 2 * _reshape( + W \ + -_vec(dt_int * f(u_temp3, p, + t + (j - 1) * dt_int) - + (u_temp3 - u_temp4)), + axes(uprev)) + integrator.stats.nf += 1 + u_temp4 = u_temp3 + u_temp3 = T[index + 1] + if (index <= 1) + # Deuflhard Stability check for initial two sequences + diff2 = u_temp3 - u_temp4 + if (integrator.opts.internalnorm(diff1, t) < + integrator.opts.internalnorm(0.5 * (diff2 - diff1), t)) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + end + end + integrator.force_stepfail ? break : continue + end + end + end + end + + if integrator.force_stepfail + return + end + + if integrator.opts.adaptive + # Compute all information relating to an extrapolation order ≦ win_min + for i in (alg.min_order):n_curr + u = eltype(uprev).(extrapolation_scalars[i + 1]) * + sum(broadcast(*, T[1:(i + 1)], + eltype(uprev).(extrapolation_weights[1:(i + 1), (i + 1)]))) # Approximation of extrapolation order i + utilde = eltype(uprev).(extrapolation_scalars_2[i]) * + sum(broadcast(*, T[2:(i + 1)], + eltype(uprev).(extrapolation_weights_2[1:i, i]))) # and its internal counterpart + res = calculate_residuals(u, utilde, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, + t) + integrator.EEst = integrator.opts.internalnorm(res, t) + cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! + stepsize_controller_internal!(integrator, alg) # Update cache.Q + end + + # Check if an approximation of some order in the order window can be accepted + while n_curr <= win_max + tol = integrator.opts.internalnorm(utilde - u, t) / integrator.EEst # Used by the convergence monitor + if accept_step_controller(integrator, integrator.opts.controller) + # Accept current approximation u of order n_curr + break + elseif integrator.EEst <= + tol^(stage_number[n_curr - alg.min_order + 1] / + stage_number[win_max - alg.min_order + 1] - 1) + # Reject current approximation order but pass convergence monitor + # Compute approximation of order (n_curr + 1) + n_curr = n_curr + 1 + cache.n_curr = n_curr + + # Update T + j_int = 4 * subdividing_sequence[n_curr + 1] + dt_int = dt / j_int # Stepsize of the new internal discretisation + W = dt_int * J - integrator.f.mass_matrix + integrator.stats.nw += 1 + u_temp2 = uprev + u_temp1 = u_temp2 + + _reshape(W \ -_vec(dt_int * integrator.fsalfirst), axes(uprev)) # Euler starting step + for j in 2:j_int + T[n_curr + 1] = 2 * u_temp1 - u_temp2 + + 2 * _reshape( + W \ + -_vec(dt_int * + f(u_temp1, p, t + (j - 1) * dt_int) - + (u_temp1 - u_temp2)), + axes(uprev)) + integrator.stats.nf += 1 + u_temp2 = u_temp1 + u_temp1 = T[n_curr + 1] + end + + # Update u, integrator.EEst and cache.Q + u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * + sum(broadcast(*, T[1:(n_curr + 1)], + eltype(uprev).(extrapolation_weights[1:(n_curr + 1), + (n_curr + 1)]))) # Approximation of extrapolation order n_curr + utilde = eltype(uprev).(extrapolation_scalars_2[n_curr]) * + sum(broadcast(*, T[2:(n_curr + 1)], + eltype(uprev).(extrapolation_weights_2[1:n_curr, + n_curr]))) # and its internal counterpart + res = calculate_residuals(u, utilde, integrator.opts.abstol, + integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(res, t) + stepsize_controller_internal!(integrator, alg) # Update cache.Q + else + # Reject the current approximation and not pass convergence monitor + break + end + end + else + u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * + sum(broadcast(*, T[1:(n_curr + 1)], + eltype(uprev).(extrapolation_weights[1:(n_curr + 1), + (n_curr + 1)]))) # Approximation of extrapolation order n_curr + end + + # Save the latest approximation and update FSAL + integrator.u = u + integrator.fsallast = f(u, p, t + dt) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.stats.nf += 1 +end + +function initialize!(integrator, cache::ExtrapolationMidpointHairerWannerCache) + # cf. initialize! of MidpointCache + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation +end + +function perform_step!(integrator, cache::ExtrapolationMidpointHairerWannerCache, + repeat_step = false) + # Unpack all information needed + @unpack t, uprev, dt, f, p = integrator + alg = unwrap_alg(integrator, false) + @unpack n_curr, u_temp1, u_temp2, utilde, res, T, fsalfirst, k = cache + @unpack u_temp3, u_temp4, k_tmps = cache + # Coefficients for obtaining u + @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients + # Coefficients for obtaining utilde + @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients + # Additional constant information + @unpack subdividing_sequence = cache.coefficients + @unpack sequence_factor = alg + + fill!(cache.Q, zero(eltype(cache.Q))) + + if integrator.opts.adaptive + # Set up the order window + # alg.min_order + 1 ≦ n_curr ≦ alg.max_order - 1 is enforced by step_*_controller! + if !(alg.min_order + 1 <= n_curr <= alg.max_order - 1) + error("Something went wrong while setting up the order window: $n_curr ∉ [$(alg.min_order+1),$(alg.max_order-1)]. + Please report this error ") + end + win_min = n_curr - 1 + win_max = n_curr + 1 + + # Set up the current extrapolation order + cache.n_old = n_curr # Save the suggested order for step_*_controller! + n_curr = win_min # Start with smallest order in the order window + end + + #Compute the internal discretisations + if !isthreaded(alg.threading) + for i in 0:n_curr + j_int = sequence_factor * subdividing_sequence[i + 1] + dt_int = dt / j_int # Stepsize of the ith internal discretisation + @.. broadcast=false u_temp2=uprev + @.. broadcast=false u_temp1=u_temp2 + dt_int * fsalfirst # Euler starting step + for j in 2:j_int + f(k, cache.u_temp1, p, t + (j - 1) * dt_int) + integrator.stats.nf += 1 + @.. broadcast=false T[i + 1]=u_temp2 + 2 * dt_int * k # Explicit Midpoint rule + @.. broadcast=false u_temp2=u_temp1 + @.. broadcast=false u_temp1=T[i + 1] + end + end + else + if alg.sequence == :romberg + # Compute solution by using maximum two threads for romberg sequence + # One thread will fill T matrix till second last element and another thread will + # fill last element of T matrix. + # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) + # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, + dt = dt, u_temp3 = u_temp3, + u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T + + @threaded alg.threading for i in 1:2 + startIndex = (i == 1) ? 0 : n_curr + endIndex = (i == 1) ? n_curr - 1 : n_curr + + for index in startIndex:endIndex + j_int_temp = sequence_factor * subdividing_sequence[index + 1] + dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation + @.. broadcast=false u_temp4[Threads.threadid()]=uprev + @.. broadcast=false u_temp3[Threads.threadid()]=u_temp4[Threads.threadid()] + + dt_int_temp * + fsalfirst # Euler starting step + for j in 2:j_int_temp + f(k_tmps[Threads.threadid()], + cache.u_temp3[Threads.threadid()], + p, t + (j - 1) * dt_int_temp) + @.. broadcast=false T[index + 1]=u_temp4[Threads.threadid()] + + 2 * dt_int_temp * + k_tmps[Threads.threadid()] # Explicit Midpoint rule + @.. broadcast=false u_temp4[Threads.threadid()]=u_temp3[Threads.threadid()] + @.. broadcast=false u_temp3[Threads.threadid()]=T[index + 1] + end + end + end + end + else + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, + dt = dt, u_temp3 = u_temp3, + u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T + + @threaded alg.threading for i in 0:(n_curr ÷ 2) + indices = i != n_curr - i ? (i, n_curr - i) : (-1, n_curr - i) + for index in indices + index == -1 && continue + j_int_temp = sequence_factor * subdividing_sequence[index + 1] + dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation + @.. broadcast=false u_temp4[Threads.threadid()]=uprev + @.. broadcast=false u_temp3[Threads.threadid()]=u_temp4[Threads.threadid()] + + dt_int_temp * + fsalfirst # Euler starting step + for j in 2:j_int_temp + f(k_tmps[Threads.threadid()], + cache.u_temp3[Threads.threadid()], + p, t + (j - 1) * dt_int_temp) + @.. broadcast=false T[index + 1]=u_temp4[Threads.threadid()] + + 2 * dt_int_temp * + k_tmps[Threads.threadid()] # Explicit Midpoint rule + @.. broadcast=false u_temp4[Threads.threadid()]=u_temp3[Threads.threadid()] + @.. broadcast=false u_temp3[Threads.threadid()]=T[index + 1] + end + end + end + end + end + nevals = cache.stage_number[n_curr + 1] - 1 + integrator.stats.nf += nevals + end + + if integrator.opts.adaptive + # Compute all information relating to an extrapolation order ≦ win_min + for i in (win_min - 1):win_min + + #integrator.u .= extrapolation_scalars[i+1] * sum( broadcast(*, cache.T[1:(i+1)], extrapolation_weights[1:(i+1), (i+1)]) ) # Approximation of extrapolation order i + #cache.utilde .= extrapolation_scalars_2[i] * sum( broadcast(*, cache.T[2:(i+1)], extrapolation_weights_2[1:i, i]) ) # and its internal counterpart + + u_temp1 .= false + u_temp2 .= false + for j in 1:(i + 1) + @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (i + 1)] + end + for j in 2:(i + 1) + @.. broadcast=false u_temp2+=cache.T[j] * extrapolation_weights_2[j - 1, i] + end + @.. broadcast=false integrator.u=extrapolation_scalars[i + 1] * u_temp1 + @.. broadcast=false cache.utilde=extrapolation_scalars_2[i] * u_temp2 + + calculate_residuals!(cache.res, integrator.u, cache.utilde, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(cache.res, t) + cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! + stepsize_controller_internal!(integrator, alg) # Update cache.Q + end + + # Check if an approximation of some order in the order window can be accepted + # Make sure a stepsize scaling factor of order (alg.min_order + 1) is provided for the step_*_controller! + while n_curr <= win_max + if accept_step_controller(integrator, integrator.opts.controller) + # Accept current approximation u of order n_curr + break + elseif (n_curr < alg.min_order + 1) || + integrator.EEst <= + typeof(integrator.EEst)(prod(subdividing_sequence[(n_curr + 2):(win_max + 1)] .// + subdividing_sequence[1]^2)) + # Reject current approximation order but pass convergence monitor + # Compute approximation of order (n_curr + 1) + n_curr = n_curr + 1 + cache.n_curr = n_curr + + # Update cache.T + j_int = sequence_factor * subdividing_sequence[n_curr + 1] + dt_int = dt / j_int # Stepsize of the new internal discretisation + @.. broadcast=false u_temp2=uprev + @.. broadcast=false u_temp1=u_temp2 + dt_int * fsalfirst # Euler starting step + for j in 2:j_int + f(k, cache.u_temp1, p, t + (j - 1) * dt_int) + integrator.stats.nf += 1 + @.. broadcast=false T[n_curr + 1]=u_temp2 + 2 * dt_int * k + @.. broadcast=false u_temp2=u_temp1 + @.. broadcast=false u_temp1=T[n_curr + 1] + end + + # Update u, integrator.EEst and cache.Q + #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr + #cache.utilde .= extrapolation_scalars_2[n_curr] * sum( broadcast(*, cache.T[2:(n_curr+1)], extrapolation_weights_2[1:n_curr, n_curr]) ) # and its internal counterpart + + u_temp1 .= false + u_temp2 .= false + for j in 1:(n_curr + 1) + @.. broadcast=false u_temp1+=cache.T[j] * + extrapolation_weights[j, (n_curr + 1)] + end + for j in 2:(n_curr + 1) + @.. broadcast=false u_temp2+=cache.T[j] * + extrapolation_weights_2[j - 1, n_curr] + end + @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 + @.. broadcast=false cache.utilde=extrapolation_scalars_2[n_curr] * u_temp2 + + calculate_residuals!(cache.res, integrator.u, cache.utilde, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(cache.res, t) + stepsize_controller_internal!(integrator, alg) # Update cache.Q + else + # Reject the current approximation and not pass convergence monitor + break + end + end + else + + #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr + u_temp1 .= false + for j in 1:(n_curr + 1) + @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (n_curr + 1)] + end + @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 + end + + f(cache.k, integrator.u, p, t + dt) # Update FSAL + integrator.stats.nf += 1 +end + +function initialize!(integrator, cache::ExtrapolationMidpointHairerWannerConstantCache) + # cf. initialize! of MidpointConstantCache + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +function perform_step!(integrator, cache::ExtrapolationMidpointHairerWannerConstantCache, + repeat_step = false) + # Unpack all information needed + @unpack t, uprev, dt, f, p = integrator + alg = unwrap_alg(integrator, false) + @unpack n_curr = cache + # Coefficients for obtaining u + @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients + # Coefficients for obtaining utilde + @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients + # Additional constant information + @unpack subdividing_sequence = cache.coefficients + @unpack sequence_factor = alg + + # Create auxiliary variables + u_temp1, u_temp2 = copy(uprev), copy(uprev) # Auxiliary variables for computing the internal discretisations + u, utilde = copy(uprev), copy(uprev) # Storage for the latest approximation and its internal counterpart + T = fill(zero(uprev), alg.max_order + 1) # Storage for the internal discretisations obtained by the explicit midpoint rule + fill!(cache.Q, zero(eltype(cache.Q))) + + if integrator.opts.adaptive + # Set up the order window + # alg.min_order + 1 ≦ n_curr ≦ alg.max_order - 1 is enforced by step_*_controller! + if !(alg.min_order + 1 <= n_curr <= alg.max_order - 1) + error("Something went wrong while setting up the order window: $n_curr ∉ [$(alg.min_order+1),$(alg.max_order-1)]. + Please report this error ") + end + win_min = n_curr - 1 + win_max = n_curr + 1 + + # Set up the current extrapolation order + cache.n_old = n_curr # Save the suggested order for step_*_controller! + n_curr = win_min # Start with smallest order in the order window + end + + #Compute the internal discretisations + if !isthreaded(alg.threading) + for i in 0:n_curr + j_int = sequence_factor * subdividing_sequence[i + 1] + dt_int = dt / j_int # Stepsize of the ith internal discretisation + u_temp2 = uprev + u_temp1 = u_temp2 + dt_int * integrator.fsalfirst # Euler starting step + for j in 2:j_int + T[i + 1] = u_temp2 + 2 * dt_int * f(u_temp1, p, t + (j - 1) * dt_int) # Explicit Midpoint rule + integrator.stats.nf += 1 + u_temp2 = u_temp1 + u_temp1 = T[i + 1] + end + end + else + if alg.sequence == :romberg + # Compute solution by using maximum two threads for romberg sequence + # One thread will fill T matrix till second last element and another thread will + # fill last element of T matrix. + # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) + # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, dt = dt, + uprev = uprev, + integrator = integrator, T = T, p = p, t = t + + @threaded alg.threading for i in 1:2 + startIndex = (i == 1) ? 0 : n_curr + endIndex = (i == 1) ? n_curr - 1 : n_curr + for index in startIndex:endIndex + j_int_temp = sequence_factor * subdividing_sequence[index + 1] + dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation + u_temp4 = uprev + u_temp3 = u_temp4 + dt_int_temp * integrator.fsalfirst # Euler starting step + for j in 2:j_int_temp + T[index + 1] = u_temp4 + + 2 * dt_int_temp * + f(u_temp3, p, t + (j - 1) * dt_int_temp) # Explicit Midpoint rule + u_temp4 = u_temp3 + u_temp3 = T[index + 1] + end + end + end + end + else + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, dt = dt, + uprev = uprev, + integrator = integrator, T = T, p = p, t = t + + @threaded alg.threading for i in 0:(n_curr ÷ 2) + indices = i != n_curr - i ? (i, n_curr - i) : (-1, n_curr - i) + for index in indices + index == -1 && continue + j_int_temp = sequence_factor * subdividing_sequence[index + 1] + dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation + u_temp4 = uprev + u_temp3 = u_temp4 + dt_int_temp * integrator.fsalfirst # Euler starting step + for j in 2:j_int_temp + T[index + 1] = u_temp4 + + 2 * dt_int_temp * + f(u_temp3, p, t + (j - 1) * dt_int_temp) # Explicit Midpoint rule + u_temp4 = u_temp3 + u_temp3 = T[index + 1] + end + end + end + end + end + nevals = cache.stage_number[n_curr + 1] - 1 + integrator.stats.nf += nevals + end + if integrator.opts.adaptive + # Compute all information relating to an extrapolation order ≦ win_min + for i in (win_min - 1):win_min + u = eltype(uprev).(extrapolation_scalars[i + 1]) * + sum(broadcast(*, T[1:(i + 1)], + eltype(uprev).(extrapolation_weights[1:(i + 1), (i + 1)]))) # Approximation of extrapolation order i + utilde = eltype(uprev).(extrapolation_scalars_2[i]) * + sum(broadcast(*, T[2:(i + 1)], + eltype(uprev).(extrapolation_weights_2[1:i, i]))) # and its internal counterpart + res = calculate_residuals(u, utilde, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, + t) + integrator.EEst = integrator.opts.internalnorm(res, t) + cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! + stepsize_controller_internal!(integrator, alg) # Update cache.Q + end + + # Check if an approximation of some order in the order window can be accepted + # Make sure a stepsize scaling factor of order (alg.min_order + 1) is provided for the step_*_controller! + while n_curr <= win_max + if accept_step_controller(integrator, integrator.opts.controller) + # Accept current approximation u of order n_curr + break + elseif (n_curr < alg.min_order + 1) || + integrator.EEst <= + typeof(integrator.EEst)(prod(subdividing_sequence[(n_curr + 2):(win_max + 1)] .// + subdividing_sequence[1]^2)) + # Reject current approximation order but pass convergence monitor + # Always compute approximation of order (n_curr + 1) + n_curr = n_curr + 1 + cache.n_curr = n_curr + + # Update T + j_int = sequence_factor * subdividing_sequence[n_curr + 1] + dt_int = dt / j_int # Stepsize of the new internal discretisation + u_temp2 = uprev + u_temp1 = u_temp2 + dt_int * integrator.fsalfirst # Euler starting step + for j in 2:j_int + T[n_curr + 1] = u_temp2 + + 2 * dt_int * f(u_temp1, p, t + (j - 1) * dt_int) + integrator.stats.nf += 1 + u_temp2 = u_temp1 + u_temp1 = T[n_curr + 1] + end + + # Update u, integrator.EEst and cache.Q + u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * + sum(broadcast(*, T[1:(n_curr + 1)], + eltype(uprev).(extrapolation_weights[1:(n_curr + 1), + (n_curr + 1)]))) # Approximation of extrapolation order n_curr + utilde = eltype(uprev).(extrapolation_scalars_2[n_curr]) * + sum(broadcast(*, T[2:(n_curr + 1)], + eltype(uprev).(extrapolation_weights_2[1:n_curr, + n_curr]))) # and its internal counterpart + res = calculate_residuals(u, utilde, integrator.opts.abstol, + integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(res, t) + stepsize_controller_internal!(integrator, alg) # Update cache.Q + else + # Reject the current approximation and not pass convergence monitor + break + end + end + else + u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * + sum(broadcast(*, T[1:(n_curr + 1)], + eltype(uprev).(extrapolation_weights[1:(n_curr + 1), + (n_curr + 1)]))) # Approximation of extrapolation order n_curr + end + + # Save the latest approximation and update FSAL + integrator.u = u + integrator.fsallast = f(u, p, t + dt) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.stats.nf += 1 +end + +function initialize!(integrator, cache::ImplicitHairerWannerExtrapolationConstantCache) + # cf. initialize! of MidpointConstantCache + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +function perform_step!(integrator, cache::ImplicitHairerWannerExtrapolationConstantCache, + repeat_step = false) + # Unpack all information needed + @unpack t, uprev, dt, f, p = integrator + alg = unwrap_alg(integrator, true) + @unpack n_curr = cache + # Coefficients for obtaining u + @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients + # Coefficients for obtaining utilde + @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients + # Additional constant information + @unpack subdividing_sequence = cache.coefficients + + # Create auxiliary variables + u_temp1, u_temp2 = copy(uprev), copy(uprev) # Auxiliary variables for computing the internal discretisations + u, utilde = copy(uprev), copy(uprev) # Storage for the latest approximation and its internal counterpart + T = fill(zero(uprev), alg.max_order + 1) # Storage for the internal discretisations obtained by the explicit midpoint rule + fill!(cache.Q, zero(eltype(cache.Q))) + + if integrator.opts.adaptive + # Set up the order window + # alg.min_order + 1 ≦ n_curr ≦ alg.max_order - 1 is enforced by step_*_controller! + if !(alg.min_order + 1 <= n_curr <= alg.max_order - 1) + error("Something went wrong while setting up the order window: $n_curr ∉ [$(alg.min_order+1),$(alg.max_order-1)]. + Please report this error ") + end + win_min = n_curr - 1 + win_max = n_curr + 1 + + # Set up the current extrapolation order + cache.n_old = n_curr # Save the suggested order for step_*_controller! + n_curr = win_min # Start with smallest order in the order window + end + + #Compute the internal discretisations + J = calc_J(integrator, cache) # Store the calculated jac as it won't change in internal discretisation + if !isthreaded(alg.threading) + for i in 0:n_curr + j_int = 4 * subdividing_sequence[i + 1] + dt_int = dt / j_int # Stepsize of the ith internal discretisation + W = dt_int * J - integrator.f.mass_matrix + integrator.stats.nw += 1 + u_temp2 = uprev + u_temp1 = u_temp2 + + _reshape(W \ -_vec(dt_int * integrator.fsalfirst), axes(uprev)) # Euler starting step + diff1 = u_temp1 - u_temp2 + for j in 2:(j_int + 1) + T[i + 1] = 2 * u_temp1 - u_temp2 + + 2 * _reshape( + W \ + -_vec(dt_int * f(u_temp1, p, t + (j - 1) * dt_int) - + (u_temp1 - u_temp2)), + axes(uprev)) + integrator.stats.nf += 1 + if (j == j_int + 1) + T[i + 1] = 0.5(T[i + 1] + u_temp2) + end + u_temp2 = u_temp1 + u_temp1 = T[i + 1] + if (i <= 1) + # Deuflhard Stability check for initial two sequences + diff2 = u_temp1 - u_temp2 + if (integrator.opts.internalnorm(diff1, t) < + integrator.opts.internalnorm(0.5 * (diff2 - diff1), t)) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + diff1 = u_temp1 - u_temp2 + end + end + else + if alg.sequence == :romberg + # Compute solution by using maximum two threads for romberg sequence + # One thread will fill T matrix till second last element and another thread will + # fill last element of T matrix. + # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) + # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, + dt = dt, u_temp2 = u_temp2, + u_temp2 = u_temp2, p = p, t = t, T = T + + @threaded alg.threading for i in 1:2 + startIndex = (i == 1) ? 0 : n_curr + endIndex = (i == 1) ? n_curr - 1 : n_curr + + for index in startIndex:endIndex + j_int = 4 * subdividing_sequence[index + 1] + dt_int = dt / j_int # Stepsize of the ith internal discretisation + W = dt_int * J - integrator.f.mass_matrix + integrator.stats.nw += 1 + u_temp4 = uprev + u_temp3 = u_temp4 + + _reshape(W \ -_vec(dt_int * integrator.fsalfirst), + axes(uprev)) # Euler starting step + diff1 = u_temp3 - u_temp4 + for j in 2:(j_int + 1) + T[index + 1] = 2 * u_temp3 - u_temp4 + + 2 * _reshape( + W \ + -_vec(dt_int * f(u_temp3, p, + t + (j - 1) * dt_int) - + (u_temp3 - u_temp4)), + axes(uprev)) + integrator.stats.nf += 1 + if (j == j_int + 1) + T[index + 1] = 0.5(T[index + 1] + u_temp4) + end + u_temp4 = u_temp3 + u_temp3 = T[index + 1] + if (index <= 1) + # Deuflhard Stability check for initial two sequences + diff2 = u_temp3 - u_temp4 + if (integrator.opts.internalnorm(diff1, t) < + integrator.opts.internalnorm(0.5 * (diff2 - diff1), t)) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + diff1 = u_temp3 - u_temp4 + end + end + integrator.force_stepfail ? break : continue + end + end + else + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, + dt = dt, + integrator = integrator, p = p, t = t, T = T + + @threaded alg.threading for i in 0:(n_curr ÷ 2) + indices = i != n_curr - i ? (i, n_curr - i) : (-1, n_curr - i) + for index in indices + index == -1 && continue + j_int = 4 * subdividing_sequence[index + 1] + dt_int = dt / j_int # Stepsize of the ith internal discretisation + W = dt_int * J - integrator.f.mass_matrix + integrator.stats.nw += 1 + u_temp4 = uprev + u_temp3 = u_temp4 + + _reshape(W \ -_vec(dt_int * integrator.fsalfirst), + axes(uprev)) # Euler starting step + diff1 = u_temp3 - u_temp4 + for j in 2:(j_int + 1) + T[index + 1] = 2 * u_temp3 - u_temp4 + + 2 * _reshape( + W \ + -_vec(dt_int * f(u_temp3, p, + t + (j - 1) * dt_int) - + (u_temp3 - u_temp4)), + axes(uprev)) + integrator.stats.nf += 1 + if (j == j_int + 1) + T[index + 1] = 0.5(T[index + 1] + u_temp4) + end + u_temp4 = u_temp3 + u_temp3 = T[index + 1] + if (index <= 1) + # Deuflhard Stability check for initial two sequences + diff2 = u_temp3 - u_temp4 + if (integrator.opts.internalnorm(diff1, t) < + integrator.opts.internalnorm(0.5 * (diff2 - diff1), t)) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + diff1 = u_temp3 - u_temp4 + end + end + integrator.force_stepfail ? break : continue + end + end + end + end + + if integrator.force_stepfail + return + end + + if integrator.opts.adaptive + # Compute all information relating to an extrapolation order ≦ win_min + for i in (win_min - 1):win_min + u = eltype(uprev).(extrapolation_scalars[i + 1]) * + sum(broadcast(*, T[1:(i + 1)], + eltype(uprev).(extrapolation_weights[1:(i + 1), (i + 1)]))) # Approximation of extrapolation order i + utilde = eltype(uprev).(extrapolation_scalars_2[i]) * + sum(broadcast(*, T[2:(i + 1)], + eltype(uprev).(extrapolation_weights_2[1:i, i]))) # and its internal counterpart + res = calculate_residuals(u, utilde, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, + t) + integrator.EEst = integrator.opts.internalnorm(res, t) + cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! + stepsize_controller_internal!(integrator, alg) # Update cache.Q + end + + # Check if an approximation of some order in the order window can be accepted + # Make sure a stepsize scaling factor of order (alg.min_order + 1) is provided for the step_*_controller! + while n_curr <= win_max + if accept_step_controller(integrator, integrator.opts.controller) + # Accept current approximation u of order n_curr + break + elseif (n_curr < alg.min_order + 1) || + integrator.EEst <= + typeof(integrator.EEst)(prod(subdividing_sequence[(n_curr + 2):(win_max + 1)] .// + subdividing_sequence[1]^2)) + # Reject current approximation order but pass convergence monitor + # Always compute approximation of order (n_curr + 1) + n_curr = n_curr + 1 + cache.n_curr = n_curr + + # Update T + j_int = 4 * subdividing_sequence[n_curr + 1] + dt_int = dt / j_int # Stepsize of the new internal discretisation + W = dt_int * J - integrator.f.mass_matrix + integrator.stats.nw += 1 + u_temp2 = uprev + u_temp1 = u_temp2 + + _reshape(W \ -_vec(dt_int * integrator.fsalfirst), axes(uprev)) # Euler starting step + for j in 2:(j_int + 1) + T[n_curr + 1] = 2 * u_temp1 - u_temp2 + + 2 * _reshape( + W \ + -_vec(dt_int * + f(u_temp1, p, t + (j - 1) * dt_int) - + (u_temp1 - u_temp2)), + axes(uprev)) + integrator.stats.nf += 1 + if (j == j_int + 1) + T[n_curr + 1] = 0.5(T[n_curr + 1] + u_temp2) + end + u_temp2 = u_temp1 + u_temp1 = T[n_curr + 1] + end + + # Update u, integrator.EEst and cache.Q + u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * + sum(broadcast(*, T[1:(n_curr + 1)], + eltype(uprev).(extrapolation_weights[1:(n_curr + 1), + (n_curr + 1)]))) # Approximation of extrapolation order n_curr + utilde = eltype(uprev).(extrapolation_scalars_2[n_curr]) * + sum(broadcast(*, T[2:(n_curr + 1)], + eltype(uprev).(extrapolation_weights_2[1:n_curr, + n_curr]))) # and its internal counterpart + res = calculate_residuals(u, utilde, integrator.opts.abstol, + integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(res, t) + stepsize_controller_internal!(integrator, alg) # Update cache.Q + else + # Reject the current approximation and not pass convergence monitor + break + end + end + else + u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * + sum(broadcast(*, T[1:(n_curr + 1)], + eltype(uprev).(extrapolation_weights[1:(n_curr + 1), + (n_curr + 1)]))) # Approximation of extrapolation order n_curr + end + + # Save the latest approximation and update FSAL + integrator.u = u + integrator.fsallast = f(u, p, t + dt) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +function initialize!(integrator, cache::ImplicitHairerWannerExtrapolationCache) + # cf. initialize! of MidpointCache + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation +end + +function perform_step!(integrator, cache::ImplicitHairerWannerExtrapolationCache, + repeat_step = false) + # Unpack all information needed + @unpack t, uprev, dt, f, p = integrator + alg = unwrap_alg(integrator, true) + @unpack n_curr, u_temp1, u_temp2, utilde, res, T, fsalfirst, k, diff1, diff2 = cache + @unpack u_temp3, u_temp4, k_tmps = cache + # Coefficients for obtaining u + @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients + # Coefficients for obtaining utilde + @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients + # Additional constant information + @unpack subdividing_sequence = cache.coefficients + + @unpack J, W, uf, tf, linsolve_tmps, jac_config = cache + + fill!(cache.Q, zero(eltype(cache.Q))) + + if integrator.opts.adaptive + # Set up the order window + # alg.min_order + 1 ≦ n_curr ≦ alg.max_order - 1 is enforced by step_*_controller! + if !(alg.min_order + 1 <= n_curr <= alg.max_order - 1) + error("Something went wrong while setting up the order window: $n_curr ∉ [$(alg.min_order+1),$(alg.max_order-1)]. + Please report this error ") + end + win_min = n_curr - 1 + win_max = n_curr + 1 + + # Set up the current extrapolation order + cache.n_old = n_curr # Save the suggested order for step_*_controller! + n_curr = win_min # Start with smallest order in the order window + end + + #Compute the internal discretisations + calc_J!(J, integrator, cache) # Store the calculated jac as it won't change in internal discretisation + if !isthreaded(alg.threading) + for i in 0:n_curr + j_int = 4 * subdividing_sequence[i + 1] + dt_int = dt / j_int # Stepsize of the ith internal discretisation + jacobian2W!(W[1], integrator.f.mass_matrix, dt_int, J, false) + integrator.stats.nw += 1 + @.. broadcast=false u_temp2=uprev + @.. broadcast=false linsolve_tmps[1]=dt_int * fsalfirst + + linsolve = cache.linsolve[1] + if !repeat_step + linres = dolinsolve(integrator, linsolve; A = W[1], + b = _vec(linsolve_tmps[1]), linu = _vec(k)) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[1]), linu = _vec(k)) + end + cache.linsolve[1] = linres.cache + + integrator.stats.nsolve += 1 + @.. broadcast=false k=-k + @.. broadcast=false u_temp1=u_temp2 + k # Euler starting step + @.. broadcast=false diff1[1]=u_temp1 - u_temp2 + for j in 2:(j_int + 1) + f(k, cache.u_temp1, p, t + (j - 1) * dt_int) + integrator.stats.nf += 1 + @.. broadcast=false linsolve_tmps[1]=dt_int * k - (u_temp1 - u_temp2) + + linsolve = cache.linsolve[1] + + if !repeat_step && j == 1 + linres = dolinsolve(integrator, linsolve; A = W[1], + b = _vec(linsolve_tmps[1]), linu = _vec(k)) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[1]), linu = _vec(k)) + end + cache.linsolve[1] = linres.cache + + integrator.stats.nsolve += 1 + @.. broadcast=false k=-k + @.. broadcast=false T[i + 1]=2 * u_temp1 - u_temp2 + 2 * k # Explicit Midpoint rule + if (j == j_int + 1) + @.. broadcast=false T[i + 1]=0.5(T[i + 1] + u_temp2) + end + @.. broadcast=false u_temp2=u_temp1 + @.. broadcast=false u_temp1=T[i + 1] + if (i <= 1) + # Deuflhard Stability check for initial two sequences + @.. broadcast=false diff2[1]=u_temp1 - u_temp2 + @.. broadcast=false diff2[1]=0.5 * (diff2[1] - diff1[1]) + if (integrator.opts.internalnorm(diff1[1], t) < + integrator.opts.internalnorm(diff2[1], t)) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + @.. broadcast=false diff1[1]=u_temp1 - u_temp2 + end + end + else + if alg.sequence == :romberg + # Compute solution by using maximum two threads for romberg sequence + # One thread will fill T matrix till second last element and another thread will + # fill last element of T matrix. + # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) + # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, + dt = dt, u_temp3 = u_temp3, + u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T + + @threaded alg.threading for i in 1:2 + startIndex = (i == 1) ? 0 : n_curr + endIndex = (i == 1) ? n_curr - 1 : n_curr + + for index in startIndex:endIndex + j_int_temp = 4 * subdividing_sequence[index + 1] + dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation + jacobian2W!(W[Threads.threadid()], integrator.f.mass_matrix, + dt_int_temp, J, false) + @.. broadcast=false u_temp4[Threads.threadid()]=uprev + @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * + fsalfirst + + linsolve = cache.linsolve[Threads.threadid()] + + if !repeat_step + linres = dolinsolve(integrator, linsolve; + A = W[Threads.threadid()], + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + end + cache.linsolve[Threads.threadid()] = linres.cache + + @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] + @.. broadcast=false u_temp3[Threads.threadid()]=u_temp4[Threads.threadid()] + + k_tmps[Threads.threadid()] # Euler starting step + @.. broadcast=false diff1[Threads.threadid()]=u_temp3[Threads.threadid()] - + u_temp4[Threads.threadid()] + for j in 2:(j_int_temp + 1) + f(k_tmps[Threads.threadid()], + cache.u_temp3[Threads.threadid()], + p, t + (j - 1) * dt_int_temp) + @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * + k_tmps[Threads.threadid()] - + (u_temp3[Threads.threadid()] - + u_temp4[Threads.threadid()]) + + linsolve = cache.linsolve[Threads.threadid()] + if !repeat_step && j == 1 + linres = dolinsolve(integrator, linsolve; + A = W[Threads.threadid()], + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + end + cache.linsolve[Threads.threadid()] = linres.cache + + @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] + @.. broadcast=false T[index + 1]=2 * + u_temp3[Threads.threadid()] - + u_temp4[Threads.threadid()] + + 2 * k_tmps[Threads.threadid()] # Explicit Midpoint rule + if (j == j_int_temp + 1) + @.. broadcast=false T[index + 1]=0.5(T[index + 1] + + u_temp4[Threads.threadid()]) + end + @.. broadcast=false u_temp4[Threads.threadid()]=u_temp3[Threads.threadid()] + @.. broadcast=false u_temp3[Threads.threadid()]=T[index + 1] + if (index <= 1) + # Deuflhard Stability check for initial two sequences + @.. broadcast=false diff2[Threads.threadid()]=u_temp3[Threads.threadid()] - + u_temp4[Threads.threadid()] + @.. broadcast=false diff2[Threads.threadid()]=0.5 * + (diff2[Threads.threadid()] - + diff1[Threads.threadid()]) + if (integrator.opts.internalnorm(diff1[Threads.threadid()], + t) < + integrator.opts.internalnorm(diff2[Threads.threadid()], + t)) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + @.. broadcast=false diff1[Threads.threadid()]=u_temp3[Threads.threadid()] - + u_temp4[Threads.threadid()] + end + end + integrator.force_stepfail ? break : continue + end + end + else + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, + dt = dt, u_temp3 = u_temp3, + u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T + + @threaded alg.threading for i in 0:(n_curr ÷ 2) + tid = Threads.threadid() + linsolvetmp = linsolve_tmps[tid] + ktmp = k_tmps[tid] + indices = i != n_curr - i ? (i, n_curr - i) : (-1, n_curr - i) #Use flag to avoid type union/branch + for index in indices + index == -1 && continue + j_int_temp = 4 * subdividing_sequence[index + 1] + dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation + jacobian2W!(W[tid], integrator.f.mass_matrix, dt_int_temp, J, false) + @.. broadcast=false u_temp4[tid]=uprev + @.. broadcast=false linsolvetmp=dt_int_temp * fsalfirst + + linsolve = cache.linsolve[tid] + if !repeat_step + linres = dolinsolve(integrator, linsolve; A = W[tid], + b = _vec(linsolvetmp), linu = _vec(ktmp)) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolvetmp), linu = _vec(ktmp)) + end + cache.linsolve[tid] = linres.cache + + @.. broadcast=false ktmp=-ktmp + @.. broadcast=false u_temp3[tid]=u_temp4[tid] + ktmp # Euler starting step + @.. broadcast=false diff1[tid]=u_temp3[tid] - u_temp4[tid] + for j in 2:(j_int_temp + 1) + f(ktmp, cache.u_temp3[tid], p, t + (j - 1) * dt_int_temp) + @.. broadcast=false linsolvetmp=dt_int_temp * ktmp - + (u_temp3[tid] - u_temp4[tid]) + + linsolve = cache.linsolve[tid] + + if (!repeat_step && j == 1) + linres = dolinsolve(integrator, linsolve; A = W[tid], + b = _vec(linsolvetmp), + linu = _vec(ktmp)) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolvetmp), + linu = _vec(ktmp)) + end + cache.linsolve[tid] = linres.cache + + @.. broadcast=false ktmp=-ktmp + @.. broadcast=false T[index + 1]=2 * u_temp3[tid] - + u_temp4[tid] + 2 * ktmp # Explicit Midpoint rule + if (j == j_int_temp + 1) + @.. broadcast=false T[index + 1]=0.5(T[index + 1] + + u_temp4[tid]) + end + @.. broadcast=false u_temp4[tid]=u_temp3[tid] + @.. broadcast=false u_temp3[tid]=T[index + 1] + if (index <= 1) + # Deuflhard Stability check for initial two sequences + @.. broadcast=false diff2[tid]=u_temp3[tid] - u_temp4[tid] + @.. broadcast=false diff2[tid]=0.5 * + (diff2[tid] - diff1[tid]) + if (integrator.opts.internalnorm(diff1[tid], t) < + integrator.opts.internalnorm(diff2[tid], t)) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + @.. broadcast=false diff1[tid]=u_temp3[tid] - u_temp4[tid] + end + end + integrator.force_stepfail ? break : continue + end + end + end + end + + if integrator.force_stepfail + return + end + + if integrator.opts.adaptive + # Compute all information relating to an extrapolation order ≦ win_min + for i in (win_min - 1):win_min + + #integrator.u .= extrapolation_scalars[i+1] * sum( broadcast(*, cache.T[1:(i+1)], extrapolation_weights[1:(i+1), (i+1)]) ) # Approximation of extrapolation order i + #cache.utilde .= extrapolation_scalars_2[i] * sum( broadcast(*, cache.T[2:(i+1)], extrapolation_weights_2[1:i, i]) ) # and its internal counterpart + + u_temp1 .= false + u_temp2 .= false + for j in 1:(i + 1) + @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (i + 1)] + end + for j in 2:(i + 1) + @.. broadcast=false u_temp2+=cache.T[j] * extrapolation_weights_2[j - 1, i] + end + @.. broadcast=false integrator.u=extrapolation_scalars[i + 1] * u_temp1 + @.. broadcast=false cache.utilde=extrapolation_scalars_2[i] * u_temp2 + + calculate_residuals!(cache.res, integrator.u, cache.utilde, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(cache.res, t) + cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! + stepsize_controller_internal!(integrator, alg) # Update cache.Q + end + + # Check if an approximation of some order in the order window can be accepted + # Make sure a stepsize scaling factor of order (alg.min_order + 1) is provided for the step_*_controller! + while n_curr <= win_max + EEst1 = one(integrator.EEst) + for i in (n_curr + 2):(win_max + 1) + EEst1 *= subdividing_sequence[i] / subdividing_sequence[1] + end + EEst1 *= EEst1 + if accept_step_controller(integrator, integrator.opts.controller) + # Accept current approximation u of order n_curr + break + elseif (n_curr < alg.min_order + 1) || integrator.EEst <= EEst1 + # Reject current approximation order but pass convergence monitor + # Compute approximation of order (n_curr + 1) + n_curr = n_curr + 1 + cache.n_curr = n_curr + + # Update cache.T + j_int = 4 * subdividing_sequence[n_curr + 1] + dt_int = dt / j_int # Stepsize of the new internal discretisation + jacobian2W!(W[1], integrator.f.mass_matrix, dt_int, J, false) + integrator.stats.nw += 1 + @.. broadcast=false u_temp2=uprev + @.. broadcast=false linsolve_tmps[1]=dt_int * fsalfirst + + linsolve = cache.linsolve[1] + + if !repeat_step + linres = dolinsolve(integrator, linsolve; A = W[1], + b = _vec(linsolve_tmps[1]), linu = _vec(k)) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[1]), linu = _vec(k)) + end + cache.linsolve[1] = linres.cache + + integrator.stats.nsolve += 1 + @.. broadcast=false k=-k + @.. broadcast=false u_temp1=u_temp2 + k # Euler starting step + for j in 2:(j_int + 1) + f(k, cache.u_temp1, p, t + (j - 1) * dt_int) + integrator.stats.nf += 1 + @.. broadcast=false linsolve_tmps[1]=dt_int * k - (u_temp1 - u_temp2) + + linsolve = cache.linsolve[1] + + if !repeat_step && j == 1 + linres = dolinsolve(integrator, linsolve; A = W[1], + b = _vec(linsolve_tmps[1]), linu = _vec(k)) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[1]), linu = _vec(k)) + end + cache.linsolve[1] = linres.cache + + integrator.stats.nsolve += 1 + @.. broadcast=false k=-k + @.. broadcast=false T[n_curr + 1]=2 * u_temp1 - u_temp2 + 2 * k # Explicit Midpoint rule + if (j == j_int + 1) + @.. broadcast=false T[n_curr + 1]=0.5(T[n_curr + 1] + u_temp2) + end + @.. broadcast=false u_temp2=u_temp1 + @.. broadcast=false u_temp1=T[n_curr + 1] + end + + # Update u, integrator.EEst and cache.Q + #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr + #cache.utilde .= extrapolation_scalars_2[n_curr] * sum( broadcast(*, cache.T[2:(n_curr+1)], extrapolation_weights_2[1:n_curr, n_curr]) ) # and its internal counterpart + + u_temp1 .= false + u_temp2 .= false + for j in 1:(n_curr + 1) + @.. broadcast=false u_temp1+=cache.T[j] * + extrapolation_weights[j, (n_curr + 1)] + end + for j in 2:(n_curr + 1) + @.. broadcast=false u_temp2+=cache.T[j] * + extrapolation_weights_2[j - 1, n_curr] + end + @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 + @.. broadcast=false cache.utilde=extrapolation_scalars_2[n_curr] * u_temp2 + + calculate_residuals!(cache.res, integrator.u, cache.utilde, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(cache.res, t) + stepsize_controller_internal!(integrator, alg) # Update cache.Q + else + # Reject the current approximation and not pass convergence monitor + break + end + end + else + + #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr + u_temp1 .= false + for j in 1:(n_curr + 1) + @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (n_curr + 1)] + end + @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 + end + + f(cache.k, integrator.u, p, t + dt) # Update FSAL + integrator.stats.nf += 1 +end + +function initialize!(integrator, cache::ImplicitEulerBarycentricExtrapolationConstantCache) + # cf. initialize! of MidpointConstantCache + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +function perform_step!(integrator, + cache::ImplicitEulerBarycentricExtrapolationConstantCache, + repeat_step = false) + # Unpack all information needed + @unpack t, uprev, dt, f, p = integrator + alg = unwrap_alg(integrator, true) + @unpack n_curr = cache + # Coefficients for obtaining u + @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients + # Coefficients for obtaining utilde + @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients + # Additional constant information + @unpack subdividing_sequence = cache.coefficients + @unpack sequence_factor = alg + + # Create auxiliary variables + u_temp1, u_temp2 = copy(uprev), copy(uprev) # Auxiliary variables for computing the internal discretisations + u, utilde = copy(uprev), copy(uprev) # Storage for the latest approximation and its internal counterpart + T = fill(zero(uprev), alg.max_order + 1) # Storage for the internal discretisations obtained by the explicit midpoint rule + fill!(cache.Q, zero(eltype(cache.Q))) + + if integrator.opts.adaptive + # Set up the order window + # alg.min_order + 1 ≦ n_curr ≦ alg.max_order - 1 is enforced by step_*_controller! + if !(alg.min_order + 1 <= n_curr <= alg.max_order - 1) + error("Something went wrong while setting up the order window: $n_curr ∉ [$(alg.min_order+1),$(alg.max_order-1)]. + Please report this error ") + end + win_min = n_curr - 1 + win_max = n_curr + 1 + + # Set up the current extrapolation order + cache.n_old = n_curr # Save the suggested order for step_*_controller! + n_curr = win_min # Start with smallest order in the order window + end + + #Compute the internal discretisations + J = calc_J(integrator, cache) # Store the calculated jac as it won't change in internal discretisation + if !isthreaded(alg.threading) + for i in 0:n_curr + j_int = sequence_factor * subdividing_sequence[i + 1] + dt_int = dt / j_int # Stepsize of the ith internal discretisation + W = dt_int * J - integrator.f.mass_matrix + integrator.stats.nw += 1 + u_temp2 = uprev + u_temp1 = u_temp2 + + _reshape(W \ -_vec(dt_int * integrator.fsalfirst), axes(uprev)) # Euler starting step + diff1 = u_temp1 - u_temp2 + for j in 2:(j_int + 1) + T[i + 1] = u_temp1 + + _reshape( + W \ -_vec(dt_int * f(u_temp1, p, t + (j - 1) * dt_int)), + axes(uprev)) + integrator.stats.nf += 1 + if (j == j_int + 1) + T[i + 1] = 0.25(T[i + 1] + 2 * u_temp1 + u_temp2) + end + u_temp2 = u_temp1 + u_temp1 = T[i + 1] + if (i <= 1) + # Deuflhard Stability check for initial two sequences + diff2 = u_temp1 - u_temp2 + if (integrator.opts.internalnorm(diff1, t) < + integrator.opts.internalnorm(0.5 * (diff2 - diff1), t)) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + diff1 = u_temp1 - u_temp2 + end + end + else + if alg.sequence == :romberg + # Compute solution by using maximum two threads for romberg sequence + # One thread will fill T matrix till second last element and another thread will + # fill last element of T matrix. + # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) + # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, + dt = dt, u_temp2 = u_temp2, + u_temp2 = u_temp2, p = p, t = t, T = T + + @threaded alg.threading for i in 1:2 + startIndex = (i == 1) ? 0 : n_curr + endIndex = (i == 1) ? n_curr - 1 : n_curr + + for index in startIndex:endIndex + j_int = sequence_factor * subdividing_sequence[index + 1] + dt_int = dt / j_int # Stepsize of the ith internal discretisation + W = dt_int * J - integrator.f.mass_matrix + integrator.stats.nw += 1 + u_temp4 = uprev + u_temp3 = u_temp4 + + _reshape(W \ -_vec(dt_int * integrator.fsalfirst), + axes(uprev)) # Euler starting step + diff1 = u_temp3 - u_temp4 + for j in 2:(j_int + 1) + T[index + 1] = u_temp3 + _reshape( + W \ + -_vec(dt_int * f(u_temp3, p, + t + (j - 1) * dt_int)), + axes(uprev)) + integrator.stats.nf += 1 + if (j == j_int + 1) + T[index + 1] = 0.25(T[index + 1] + 2 * u_temp3 + u_temp4) + end + u_temp4 = u_temp3 + u_temp3 = T[index + 1] + if (index <= 1) + # Deuflhard Stability check for initial two sequences + diff2 = u_temp3 - u_temp4 + if (integrator.opts.internalnorm(diff1, t) < + integrator.opts.internalnorm(0.5 * (diff2 - diff1), t)) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + diff1 = u_temp3 - u_temp4 + end + end + integrator.force_stepfail ? break : continue + end + end + else + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, + dt = dt, + integrator = integrator, p = p, t = t, T = T + + @threaded alg.threading for i in 0:(n_curr ÷ 2) + indices = i != n_curr - i ? (i, n_curr - i) : (-1, n_curr - i) + for index in indices + index == -1 && continue + j_int = sequence_factor * subdividing_sequence[index + 1] + dt_int = dt / j_int # Stepsize of the ith internal discretisation + W = dt_int * J - integrator.f.mass_matrix + integrator.stats.nw += 1 + u_temp4 = uprev + u_temp3 = u_temp4 + + _reshape(W \ -_vec(dt_int * integrator.fsalfirst), + axes(uprev)) # Euler starting step + diff1 = u_temp3 - u_temp4 + for j in 2:(j_int + 1) + T[index + 1] = u_temp3 + _reshape( + W \ + -_vec(dt_int * f(u_temp3, p, + t + (j - 1) * dt_int)), + axes(uprev)) + integrator.stats.nf += 1 + if (j == j_int + 1) + T[index + 1] = 0.25(T[index + 1] + 2 * u_temp3 + u_temp4) + end + u_temp4 = u_temp3 + u_temp3 = T[index + 1] + if (index <= 1) + # Deuflhard Stability check for initial two sequences + diff2 = u_temp3 - u_temp4 + if (integrator.opts.internalnorm(diff1, t) < + integrator.opts.internalnorm(0.5 * (diff2 - diff1), t)) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + diff1 = u_temp3 - u_temp4 + end + end + integrator.force_stepfail ? break : continue + end + end + end + end + + if integrator.force_stepfail + return + end + + if integrator.opts.adaptive + # Compute all information relating to an extrapolation order ≦ win_min + for i in (win_min - 1):win_min + u = eltype(uprev).(extrapolation_scalars[i + 1]) * + sum(broadcast(*, T[1:(i + 1)], + eltype(uprev).(extrapolation_weights[1:(i + 1), (i + 1)]))) # Approximation of extrapolation order i + utilde = eltype(uprev).(extrapolation_scalars_2[i]) * + sum(broadcast(*, T[2:(i + 1)], + eltype(uprev).(extrapolation_weights_2[1:i, i]))) # and its internal counterpart + res = calculate_residuals(u, utilde, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, + t) + integrator.EEst = integrator.opts.internalnorm(res, t) + cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! + stepsize_controller_internal!(integrator, alg) # Update cache.Q + end + + # Check if an approximation of some order in the order window can be accepted + # Make sure a stepsize scaling factor of order (alg.min_order + 1) is provided for the step_*_controller! + while n_curr <= win_max + if accept_step_controller(integrator, integrator.opts.controller) + # Accept current approximation u of order n_curr + break + elseif (n_curr < alg.min_order + 1) || + integrator.EEst <= + typeof(integrator.EEst)(prod(subdividing_sequence[(n_curr + 2):(win_max + 1)] .// + subdividing_sequence[1]^2)) + # Reject current approximation order but pass convergence monitor + # Always compute approximation of order (n_curr + 1) + n_curr = n_curr + 1 + cache.n_curr = n_curr + + # Update T + j_int = sequence_factor * subdividing_sequence[n_curr + 1] + dt_int = dt / j_int # Stepsize of the new internal discretisation + W = dt_int * J - integrator.f.mass_matrix + integrator.stats.nw += 1 + u_temp2 = uprev + u_temp1 = u_temp2 + + _reshape(W \ -_vec(dt_int * integrator.fsalfirst), axes(uprev)) # Euler starting step + for j in 2:(j_int + 1) + T[n_curr + 1] = u_temp1 + _reshape( + W \ + -_vec(dt_int * + f(u_temp1, p, t + (j - 1) * dt_int)), + axes(uprev)) + integrator.stats.nf += 1 + if (j == j_int + 1) + T[n_curr + 1] = 0.25(T[n_curr + 1] + 2 * u_temp1 + u_temp2) + end + u_temp2 = u_temp1 + u_temp1 = T[n_curr + 1] + end + + # Update u, integrator.EEst and cache.Q + u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * + sum(broadcast(*, T[1:(n_curr + 1)], + eltype(uprev).(extrapolation_weights[1:(n_curr + 1), + (n_curr + 1)]))) # Approximation of extrapolation order n_curr + utilde = eltype(uprev).(extrapolation_scalars_2[n_curr]) * + sum(broadcast(*, T[2:(n_curr + 1)], + eltype(uprev).(extrapolation_weights_2[1:n_curr, + n_curr]))) # and its internal counterpart + res = calculate_residuals(u, utilde, integrator.opts.abstol, + integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(res, t) + stepsize_controller_internal!(integrator, alg) # Update cache.Q + else + # Reject the current approximation and not pass convergence monitor + break + end + end + else + u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * + sum(broadcast(*, T[1:(n_curr + 1)], + eltype(uprev).(extrapolation_weights[1:(n_curr + 1), + (n_curr + 1)]))) # Approximation of extrapolation order n_curr + end + + # Save the latest approximation and update FSAL + integrator.u = u + integrator.fsallast = f(u, p, t + dt) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +function initialize!(integrator, cache::ImplicitEulerBarycentricExtrapolationCache) + # cf. initialize! of MidpointCache + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation +end + +function perform_step!(integrator, cache::ImplicitEulerBarycentricExtrapolationCache, + repeat_step = false) + # Unpack all information needed + @unpack t, uprev, dt, f, p = integrator + alg = unwrap_alg(integrator, true) + @unpack n_curr, u_temp1, u_temp2, utilde, res, T, fsalfirst, k, diff1, diff2 = cache + @unpack u_temp3, u_temp4, k_tmps = cache + # Coefficients for obtaining u + @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients + # Coefficients for obtaining utilde + @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients + # Additional constant information + @unpack subdividing_sequence = cache.coefficients + @unpack sequence_factor = alg + + @unpack J, W, uf, tf, linsolve_tmps, jac_config = cache + + fill!(cache.Q, zero(eltype(cache.Q))) + + if integrator.opts.adaptive + # Set up the order window + # alg.min_order + 1 ≦ n_curr ≦ alg.max_order - 1 is enforced by step_*_controller! + if !(alg.min_order + 1 <= n_curr <= alg.max_order - 1) + error("Something went wrong while setting up the order window: $n_curr ∉ [$(alg.min_order+1),$(alg.max_order-1)]. + Please report this error ") + end + win_min = n_curr - 1 + win_max = n_curr + 1 + + # Set up the current extrapolation order + cache.n_old = n_curr # Save the suggested order for step_*_controller! + n_curr = win_min # Start with smallest order in the order window + end + + #Compute the internal discretisations + calc_J!(J, integrator, cache) # Store the calculated jac as it won't change in internal discretisation + if !isthreaded(alg.threading) + for i in 0:n_curr + j_int = sequence_factor * subdividing_sequence[i + 1] + dt_int = dt / j_int # Stepsize of the ith internal discretisation + jacobian2W!(W[1], integrator.f.mass_matrix, dt_int, J, false) + integrator.stats.nw += 1 + @.. broadcast=false u_temp2=uprev + @.. broadcast=false linsolve_tmps[1]=dt_int * fsalfirst + + linsolve = cache.linsolve[1] + + if !repeat_step + linres = dolinsolve(integrator, linsolve; A = W[1], + b = _vec(linsolve_tmps[1]), linu = _vec(k)) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[1]), linu = _vec(k)) + end + cache.linsolve[1] = linres.cache + + integrator.stats.nsolve += 1 + @.. broadcast=false k=-k + @.. broadcast=false u_temp1=u_temp2 + k # Euler starting step + @.. broadcast=false diff1[1]=u_temp1 - u_temp2 + for j in 2:(j_int + 1) + f(k, cache.u_temp1, p, t + (j - 1) * dt_int) + integrator.stats.nf += 1 + @.. broadcast=false linsolve_tmps[1]=dt_int * k + + linsolve = cache.linsolve[1] + if !repeat_step && j == 1 + linres = dolinsolve(integrator, linsolve; A = W[1], + b = _vec(linsolve_tmps[1]), linu = _vec(k)) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[1]), linu = _vec(k)) + end + cache.linsolve[1] = linres.cache + + integrator.stats.nsolve += 1 + @.. broadcast=false k=-k + @.. broadcast=false T[i + 1]=u_temp1 + k + if (j == j_int + 1) + @.. broadcast=false T[i + 1]=0.25(T[i + 1] + 2 * u_temp1 + u_temp2) + end + @.. broadcast=false u_temp2=u_temp1 + @.. broadcast=false u_temp1=T[i + 1] + if (i <= 1) + # Deuflhard Stability check for initial two sequences + @.. broadcast=false diff2[1]=u_temp1 - u_temp2 + @.. broadcast=false diff2[1]=0.5 * (diff2[1] - diff1[1]) + if (integrator.opts.internalnorm(diff1[1], t) < + integrator.opts.internalnorm(diff2[1], t)) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + @.. broadcast=false diff1[1]=u_temp1 - u_temp2 + end + end + else + if alg.sequence == :romberg + # Compute solution by using maximum two threads for romberg sequence + # One thread will fill T matrix till second last element and another thread will + # fill last element of T matrix. + # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) + # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, + dt = dt, u_temp3 = u_temp3, + u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T + + @threaded alg.threading for i in 1:2 + startIndex = (i == 1) ? 0 : n_curr + endIndex = (i == 1) ? n_curr - 1 : n_curr + + for index in startIndex:endIndex + j_int_temp = sequence_factor * subdividing_sequence[index + 1] + dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation + jacobian2W!(W[Threads.threadid()], integrator.f.mass_matrix, + dt_int_temp, J, false) + @.. broadcast=false u_temp4[Threads.threadid()]=uprev + @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * + fsalfirst + + linsolve = cache.linsolve[Threads.threadid()] + + if !repeat_step + linres = dolinsolve(integrator, linsolve; + A = W[Threads.threadid()], + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + end + cache.linsolve[Threads.threadid()] = linres.cache + + @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] + @.. broadcast=false u_temp3[Threads.threadid()]=u_temp4[Threads.threadid()] + + k_tmps[Threads.threadid()] # Euler starting step + @.. broadcast=false diff1[Threads.threadid()]=u_temp3[Threads.threadid()] - + u_temp4[Threads.threadid()] + for j in 2:(j_int_temp + 1) + f(k_tmps[Threads.threadid()], + cache.u_temp3[Threads.threadid()], + p, t + (j - 1) * dt_int_temp) + @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * + k_tmps[Threads.threadid()] + + linsolve = cache.linsolve[Threads.threadid()] + + if !repeat_step && j == 1 + linres = dolinsolve(integrator, linsolve; + A = W[Threads.threadid()], + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + end + cache.linsolve[Threads.threadid()] = linres.cache + + @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] + @.. broadcast=false T[index + 1]=u_temp3[Threads.threadid()] + + k_tmps[Threads.threadid()] # Explicit Midpoint rule + if (j == j_int_temp + 1) + @.. broadcast=false T[index + 1]=0.25(T[index + 1] + + 2 * + u_temp3[Threads.threadid()] + + u_temp4[Threads.threadid()]) + end + @.. broadcast=false u_temp4[Threads.threadid()]=u_temp3[Threads.threadid()] + @.. broadcast=false u_temp3[Threads.threadid()]=T[index + 1] + if (index <= 1) + # Deuflhard Stability check for initial two sequences + @.. broadcast=false diff2[Threads.threadid()]=u_temp3[Threads.threadid()] - + u_temp4[Threads.threadid()] + @.. broadcast=false diff2[Threads.threadid()]=0.5 * + (diff2[Threads.threadid()] - + diff1[Threads.threadid()]) + if (integrator.opts.internalnorm(diff1[Threads.threadid()], + t) < + integrator.opts.internalnorm(diff2[Threads.threadid()], + t)) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + @.. broadcast=false diff1[Threads.threadid()]=u_temp3[Threads.threadid()] - + u_temp4[Threads.threadid()] + end + end + integrator.force_stepfail ? break : continue + end + end + else + let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, + dt = dt, u_temp3 = u_temp3, + u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T + + @threaded alg.threading for i in 0:(n_curr ÷ 2) + indices = i != n_curr - i ? (i, n_curr - i) : (-1, n_curr - i) + for index in indices + index == -1 && continue + j_int_temp = sequence_factor * subdividing_sequence[index + 1] + dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation + jacobian2W!(W[Threads.threadid()], integrator.f.mass_matrix, + dt_int_temp, J, false) + @.. broadcast=false u_temp4[Threads.threadid()]=uprev + @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * + fsalfirst + + linsolve = cache.linsolve[Threads.threadid()] + + if !repeat_step + linres = dolinsolve(integrator, linsolve; + A = W[Threads.threadid()], + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + end + cache.linsolve[Threads.threadid()] = linres.cache + + @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] + @.. broadcast=false u_temp3[Threads.threadid()]=u_temp4[Threads.threadid()] + + k_tmps[Threads.threadid()] # Euler starting step + @.. broadcast=false diff1[Threads.threadid()]=u_temp3[Threads.threadid()] - + u_temp4[Threads.threadid()] + for j in 2:(j_int_temp + 1) + f(k_tmps[Threads.threadid()], + cache.u_temp3[Threads.threadid()], + p, t + (j - 1) * dt_int_temp) + @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * + k_tmps[Threads.threadid()] + + linsolve = cache.linsolve[Threads.threadid()] + + if (!repeat_step && j == 1) + linres = dolinsolve(integrator, linsolve; + A = W[Threads.threadid()], + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[Threads.threadid()]), + linu = _vec(k_tmps[Threads.threadid()])) + end + cache.linsolve[Threads.threadid()] = linres.cache + + @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] + @.. broadcast=false T[index + 1]=u_temp3[Threads.threadid()] + + k_tmps[Threads.threadid()] # Explicit Midpoint rule + if (j == j_int_temp + 1) + @.. broadcast=false T[index + 1]=0.25(T[index + 1] + + 2 * + u_temp3[Threads.threadid()] + + u_temp4[Threads.threadid()]) + end + @.. broadcast=false u_temp4[Threads.threadid()]=u_temp3[Threads.threadid()] + @.. broadcast=false u_temp3[Threads.threadid()]=T[index + 1] + if (index <= 1) + # Deuflhard Stability check for initial two sequences + @.. broadcast=false diff2[Threads.threadid()]=u_temp3[Threads.threadid()] - + u_temp4[Threads.threadid()] + @.. broadcast=false diff2[Threads.threadid()]=0.5 * + (diff2[Threads.threadid()] - + diff1[Threads.threadid()]) + if (integrator.opts.internalnorm(diff1[Threads.threadid()], + t) < + integrator.opts.internalnorm(diff2[Threads.threadid()], + t)) + # Divergence of iteration, overflow is possible. Force fail and start with smaller step + integrator.force_stepfail = true + return + end + end + @.. broadcast=false diff1[Threads.threadid()]=u_temp3[Threads.threadid()] - + u_temp4[Threads.threadid()] + end + end + integrator.force_stepfail ? break : continue + end + end + end + end + + if integrator.force_stepfail + return + end + + if integrator.opts.adaptive + # Compute all information relating to an extrapolation order ≦ win_min + for i in (win_min - 1):win_min + + #integrator.u .= extrapolation_scalars[i+1] * sum( broadcast(*, cache.T[1:(i+1)], extrapolation_weights[1:(i+1), (i+1)]) ) # Approximation of extrapolation order i + #cache.utilde .= extrapolation_scalars_2[i] * sum( broadcast(*, cache.T[2:(i+1)], extrapolation_weights_2[1:i, i]) ) # and its internal counterpart + + u_temp1 .= false + u_temp2 .= false + for j in 1:(i + 1) + @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (i + 1)] + end + for j in 2:(i + 1) + @.. broadcast=false u_temp2+=cache.T[j] * extrapolation_weights_2[j - 1, i] + end + @.. broadcast=false integrator.u=extrapolation_scalars[i + 1] * u_temp1 + @.. broadcast=false cache.utilde=extrapolation_scalars_2[i] * u_temp2 + + calculate_residuals!(cache.res, integrator.u, cache.utilde, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(cache.res, t) + cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! + stepsize_controller_internal!(integrator, alg) # Update cache.Q + end + + # Check if an approximation of some order in the order window can be accepted + # Make sure a stepsize scaling factor of order (alg.min_order + 1) is provided for the step_*_controller! + while n_curr <= win_max + EEst1 = one(integrator.EEst) + for i in (n_curr + 2):(win_max + 1) + EEst1 *= subdividing_sequence[i] / subdividing_sequence[1] + end + EEst1 *= EEst1 + + #@show integrator.opts.internalnorm(integrator.u - cache.utilde,t) + if accept_step_controller(integrator, integrator.opts.controller) + # Accept current approximation u of order n_curr + break + elseif (n_curr < alg.min_order + 1) || integrator.EEst <= EEst1 + # Reject current approximation order but pass convergence monitor + # Compute approximation of order (n_curr + 1) + n_curr = n_curr + 1 + cache.n_curr = n_curr + + # Update cache.T + j_int = sequence_factor * subdividing_sequence[n_curr + 1] + dt_int = dt / j_int # Stepsize of the new internal discretisation + jacobian2W!(W[1], integrator.f.mass_matrix, dt_int, J, false) + integrator.stats.nw += 1 + @.. broadcast=false u_temp2=uprev + @.. broadcast=false linsolve_tmps[1]=dt_int * fsalfirst + + linsolve = cache.linsolve[1] + + if !repeat_step + linres = dolinsolve(integrator, linsolve; A = W[1], + b = _vec(linsolve_tmps[1]), linu = _vec(k)) + else + linres = dolinsolve(integrator, linsolve; A = nothing, + b = _vec(linsolve_tmps[1]), linu = _vec(k)) + end + cache.linsolve[1] = linres.cache + + integrator.stats.nsolve += 1 + @.. broadcast=false k=-k + @.. broadcast=false u_temp1=u_temp2 + k # Euler starting step + for j in 2:(j_int + 1) + f(k, cache.u_temp1, p, t + (j - 1) * dt_int) + integrator.stats.nf += 1 + @.. broadcast=false linsolve_tmps[1]=dt_int * k + + linsolve = cache.linsolve[1] + linres = dolinsolve(integrator, linsolve; b = _vec(linsolve_tmps[1]), + linu = _vec(k)) + cache.linsolve[1] = linres.cache + + integrator.stats.nsolve += 1 + @.. broadcast=false k=-k + @.. broadcast=false T[n_curr + 1]=u_temp1 + k # Explicit Midpoint rule + if (j == j_int + 1) + @.. broadcast=false T[n_curr + 1]=0.25(T[n_curr + 1] + 2 * u_temp1 + + u_temp2) + end + @.. broadcast=false u_temp2=u_temp1 + @.. broadcast=false u_temp1=T[n_curr + 1] + end + + # Update u, integrator.EEst and cache.Q + #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr + #cache.utilde .= extrapolation_scalars_2[n_curr] * sum( broadcast(*, cache.T[2:(n_curr+1)], extrapolation_weights_2[1:n_curr, n_curr]) ) # and its internal counterpart + + u_temp1 .= false + u_temp2 .= false + for j in 1:(n_curr + 1) + @.. broadcast=false u_temp1+=cache.T[j] * + extrapolation_weights[j, (n_curr + 1)] + end + for j in 2:(n_curr + 1) + @.. broadcast=false u_temp2+=cache.T[j] * + extrapolation_weights_2[j - 1, n_curr] + end + @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 + @.. broadcast=false cache.utilde=extrapolation_scalars_2[n_curr] * u_temp2 + + calculate_residuals!(cache.res, integrator.u, cache.utilde, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(cache.res, t) + stepsize_controller_internal!(integrator, alg) # Update cache.Q + else + # Reject the current approximation and not pass convergence monitor + break + end + end + else + + #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr + u_temp1 .= false + for j in 1:(n_curr + 1) + @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (n_curr + 1)] + end + @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 + end + + f(cache.k, integrator.u, p, t + dt) # Update FSAL + integrator.stats.nf += 1 +end diff --git a/src/perform_step/feagin_rk_perform_step.jl b/src/perform_step/feagin_rk_perform_step.jl new file mode 100644 index 0000000000..a0ded6fa0b --- /dev/null +++ b/src/perform_step/feagin_rk_perform_step.jl @@ -0,0 +1,1288 @@ +function initialize!(integrator, cache::Feagin10ConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +@muladd function perform_step!(integrator, cache::Feagin10ConstantCache, + repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1203, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211, a1300, a1302, a1303, a1305, a1306, a1307, a1308, a1309, a1310, a1311, a1312, a1400, a1401, a1404, a1406, a1412, a1413, a1500, a1502, a1514, a1600, a1601, a1602, a1604, a1605, a1606, a1607, a1608, a1609, a1610, a1611, a1612, a1613, a1614, a1615, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16 = cache + k1 = integrator.fsalfirst + a = dt * a0100 + k2 = f(uprev + a * k1, p, t + c1 * dt) + k3 = f(uprev + dt * (a0200 * k1 + a0201 * k2), p, t + c2 * dt) + k4 = f(uprev + dt * (a0300 * k1 + a0302 * k3), p, t + c3 * dt) + k5 = f(uprev + dt * (a0400 * k1 + a0402 * k3 + a0403 * k4), p, t + c4 * dt) + k6 = f(uprev + dt * (a0500 * k1 + a0503 * k4 + a0504 * k5), p, t + c5 * dt) + k7 = f(uprev + dt * (a0600 * k1 + a0603 * k4 + a0604 * k5 + a0605 * k6), p, t + c6 * dt) + k8 = f(uprev + dt * (a0700 * k1 + a0704 * k5 + a0705 * k6 + a0706 * k7), p, t + c7 * dt) + k9 = f(uprev + dt * (a0800 * k1 + a0805 * k6 + a0806 * k7 + a0807 * k8), p, t + c8 * dt) + k10 = f(uprev + dt * (a0900 * k1 + a0905 * k6 + a0906 * k7 + a0907 * k8 + a0908 * k9), + p, t + c9 * dt) + k11 = f( + uprev + + dt * + (a1000 * k1 + a1005 * k6 + a1006 * k7 + a1007 * k8 + a1008 * k9 + a1009 * k10), + p, t + c10 * dt) + k12 = f( + uprev + + dt * + (a1100 * k1 + a1105 * k6 + a1106 * k7 + a1107 * k8 + a1108 * k9 + a1109 * k10 + + a1110 * k11), + p, + t + c11 * dt) + k13 = f( + uprev + + dt * + (a1200 * k1 + a1203 * k4 + a1204 * k5 + a1205 * k6 + a1206 * k7 + a1207 * k8 + + a1208 * k9 + a1209 * k10 + a1210 * k11 + a1211 * k12), + p, + t + c12 * dt) + k14 = f( + uprev + + dt * + (a1300 * k1 + a1302 * k3 + a1303 * k4 + a1305 * k6 + a1306 * k7 + a1307 * k8 + + a1308 * k9 + a1309 * k10 + a1310 * k11 + a1311 * k12 + a1312 * k13), + p, + t + c13 * dt) + k15 = f( + uprev + + dt * + (a1400 * k1 + a1401 * k2 + a1404 * k5 + a1406 * k7 + a1412 * k13 + a1413 * k14), + p, t + c14 * dt) + k16 = f(uprev + dt * (a1500 * k1 + a1502 * k3 + a1514 * k15), p, t + c15 * dt) + k17 = f( + uprev + + dt * + (a1600 * k1 + a1601 * k2 + a1602 * k3 + a1604 * k5 + a1605 * k6 + a1606 * k7 + + a1607 * k8 + a1608 * k9 + a1609 * k10 + a1610 * k11 + a1611 * k12 + + a1612 * k13 + a1613 * k14 + a1614 * k15 + a1615 * k16), + p, + t + c16 * dt) + integrator.stats.nf += 16 + u = uprev + + dt * + (b1 * k1 + b2 * k2 + b3 * k3 + b5 * k5 + b7 * k7 + b9 * k9 + b10 * k10 + b11 * k11 + + b12 * k12 + b13 * k13 + b14 * k14 + b15 * k15 + b16 * k16 + b17 * k17) + if integrator.opts.adaptive + utilde = @.. broadcast=false dt*(k2-k16)*adaptiveConst + atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + k = f(u, p, t + dt) # For the interpolation, needs k at the updated point + integrator.stats.nf += 1 + integrator.fsallast = k + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.u = u +end + +function initialize!(integrator, cache::Feagin10Cache) + integrator.fsalfirst = cache.fsalfirst + integrator.fsallast = cache.k + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 +end + +#= +@muladd function perform_step!(integrator, cache::Feagin10Cache, repeat_step=false) + @unpack t,dt,uprev,u,f,p = integrator + @unpack adaptiveConst,a0100,a0200,a0201,a0300,a0302,a0400,a0402,a0403,a0500,a0503,a0504,a0600,a0603,a0604,a0605,a0700,a0704,a0705,a0706,a0800,a0805,a0806,a0807,a0900,a0905,a0906,a0907,a0908,a1000,a1005,a1006,a1007,a1008,a1009,a1100,a1105,a1106,a1107,a1108,a1109,a1110,a1200,a1203,a1204,a1205,a1206,a1207,a1208,a1209,a1210,a1211,a1300,a1302,a1303,a1305,a1306,a1307,a1308,a1309,a1310,a1311,a1312,a1400,a1401,a1404,a1406,a1412,a1413,a1500,a1502,a1514,a1600,a1601,a1602,a1604,a1605,a1606,a1607,a1608,a1609,a1610,a1611,a1612,a1613,a1614,a1615,b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,c11,c12,c13,c14,c15,c16 = cache.tab + @unpack k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12,k13,k14,k15,k16,k17,tmp,atmp,uprev,k = cache + k1 = cache.fsalfirst + a = dt*a0100 + @.. broadcast=false tmp = uprev + a*k1 + f(k2, tmp, p, t + c1*dt) + @.. broadcast=false tmp = uprev + dt*(a0200*k1 + a0201*k2) + f(k3, tmp, p, t + c2*dt ) + @.. broadcast=false tmp = uprev + dt*(a0300*k1 + a0302*k3) + f(k4, tmp, p, t + c3*dt) + @.. broadcast=false tmp = uprev + dt*(a0400*k1 + a0402*k3 + a0403*k4) + f(k5, tmp, p, t + c4*dt) + @.. broadcast=false tmp = uprev + dt*(a0500*k1 + a0503*k4 + a0504*k5) + f(k6, tmp, p, t + c5*dt) + @.. broadcast=false tmp = uprev + dt*(a0600*k1 + a0603*k4 + a0604*k5 + a0605*k6) + f(k7, tmp, p, t + c6*dt) + @.. broadcast=false tmp = uprev + dt*(a0700*k1 + a0704*k5 + a0705*k6 + a0706*k7) + f(k8, tmp, p, t + c7*dt) + @.. broadcast=false tmp = uprev + dt*(a0800*k1 + a0805*k6 + a0806*k7 + a0807*k8) + f(k9, tmp, p, t + c8*dt) + @.. broadcast=false tmp = uprev + dt*(a0900*k1 + a0905*k6 + a0906*k7 + a0907*k8 + a0908*k9) + f(k10, tmp, p, t + c9*dt) + @.. broadcast=false tmp = uprev + dt*(a1000*k1 + a1005*k6 + a1006*k7 + a1007*k8 + a1008*k9 + a1009*k10) + f(k11, tmp, p, t + c10*dt) + @.. broadcast=false tmp = uprev + dt*(a1100*k1 + a1105*k6 + a1106*k7 + a1107*k8 + a1108*k9 + a1109*k10 + a1110*k11) + f(k12, tmp, p, t + c11*dt) + @.. broadcast=false tmp = uprev + dt*(a1200*k1 + a1203*k4 + a1204*k5 + a1205*k6 + a1206*k7 + a1207*k8 + a1208*k9 + a1209*k10 + a1210*k11 + a1211*k12) + f(k13, tmp, p, t + c12*dt) + @.. broadcast=false tmp = uprev + dt*(a1300*k1 + a1302*k3 + a1303*k4 + a1305*k6 + a1306*k7 + a1307*k8 + a1308*k9 + a1309*k10 + a1310*k11 + a1311*k12 + a1312*k13) + f(k14, tmp, p, t + c13*dt) + @.. broadcast=false tmp = uprev + dt*(a1400*k1 + a1401*k2 + a1404*k5 + a1406*k7 + a1412*k13 + a1413*k14) + f(k15, tmp, p, t + c14*dt) + @.. broadcast=false tmp = uprev + dt*(a1500*k1 + a1502*k3 + a1514*k15) + f(k16, tmp, p, t + c15*dt) + @.. broadcast=false tmp = uprev + dt*(a1600*k1 + a1601*k2 + a1602*k3 + a1604*k5 + a1605*k6 + a1606*k7 + a1607*k8 + a1608*k9 + a1609*k10 + a1610*k11 + a1611*k12 + a1612*k13 + a1613*k14 + a1614*k15 + a1615*k16) + f(k17, tmp, p, t + c16*dt) + @.. broadcast=false u = uprev + dt*(b1*k1 + b2*k2 + b3*k3 + b5*k5 + b7*k7 + b9*k9 + b10*k10 + b11*k11 + b12*k12 + b13*k13 + b14*k14 + b15*k15 + b16*k16 + b17*k17) + if integrator.opts.adaptive + @.. broadcast=false tmp = dt*(k2 - k16) * adaptiveConst + calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, integrator.opts.reltol,integrator.opts.internalnorm,t) + integrator.EEst = integrator.opts.internalnorm(atmp,t) + end + f(integrator.fsallast,u,p,t+dt) # For the interpolation, needs k at the updated point +end +=# + +@muladd function perform_step!(integrator, cache::Feagin10Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + uidx = eachindex(integrator.uprev) + @unpack adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1203, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211, a1300, a1302, a1303, a1305, a1306, a1307, a1308, a1309, a1310, a1311, a1312, a1400, a1401, a1404, a1406, a1412, a1413, a1500, a1502, a1514, a1600, a1601, a1602, a1604, a1605, a1606, a1607, a1608, a1609, a1610, a1611, a1612, a1613, a1614, a1615, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16 = cache.tab + @unpack k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, k17, tmp, atmp, uprev, k = cache + k1 = cache.fsalfirst + a = dt * a0100 + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + a * k1[i] + end + f(k2, tmp, p, t + c1 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + dt * (a0200 * k1[i] + a0201 * k2[i]) + end + f(k3, tmp, p, t + c2 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + dt * (a0300 * k1[i] + a0302 * k3[i]) + end + f(k4, tmp, p, t + c3 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + dt * (a0400 * k1[i] + a0402 * k3[i] + a0403 * k4[i]) + end + f(k5, tmp, p, t + c4 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + dt * (a0500 * k1[i] + a0503 * k4[i] + a0504 * k5[i]) + end + f(k6, tmp, p, t + c5 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a0600 * k1[i] + a0603 * k4[i] + a0604 * k5[i] + a0605 * k6[i]) + end + f(k7, tmp, p, t + c6 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a0700 * k1[i] + a0704 * k5[i] + a0705 * k6[i] + a0706 * k7[i]) + end + f(k8, tmp, p, t + c7 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a0800 * k1[i] + a0805 * k6[i] + a0806 * k7[i] + a0807 * k8[i]) + end + f(k9, tmp, p, t + c8 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a0900 * k1[i] + a0905 * k6[i] + a0906 * k7[i] + a0907 * k8[i] + + a0908 * k9[i]) + end + f(k10, tmp, p, t + c9 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a1000 * k1[i] + a1005 * k6[i] + a1006 * k7[i] + a1007 * k8[i] + + a1008 * k9[i] + a1009 * k10[i]) + end + f(k11, tmp, p, t + c10 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a1100 * k1[i] + a1105 * k6[i] + a1106 * k7[i] + a1107 * k8[i] + + a1108 * k9[i] + a1109 * k10[i] + a1110 * k11[i]) + end + f(k12, tmp, p, t + c11 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a1200 * k1[i] + a1203 * k4[i] + a1204 * k5[i] + a1205 * k6[i] + + a1206 * k7[i] + a1207 * k8[i] + a1208 * k9[i] + a1209 * k10[i] + + a1210 * k11[i] + a1211 * k12[i]) + end + f(k13, tmp, p, t + c12 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a1300 * k1[i] + a1302 * k3[i] + a1303 * k4[i] + a1305 * k6[i] + + a1306 * k7[i] + a1307 * k8[i] + a1308 * k9[i] + a1309 * k10[i] + + a1310 * k11[i] + a1311 * k12[i] + a1312 * k13[i]) + end + f(k14, tmp, p, t + c13 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a1400 * k1[i] + a1401 * k2[i] + a1404 * k5[i] + a1406 * k7[i] + + a1412 * k13[i] + a1413 * k14[i]) + end + f(k15, tmp, p, t + c14 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + dt * (a1500 * k1[i] + a1502 * k3[i] + a1514 * k15[i]) + end + f(k16, tmp, p, t + c15 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a1600 * k1[i] + a1601 * k2[i] + a1602 * k3[i] + a1604 * k5[i] + + a1605 * k6[i] + a1606 * k7[i] + a1607 * k8[i] + a1608 * k9[i] + + a1609 * k10[i] + a1610 * k11[i] + a1611 * k12[i] + + a1612 * k13[i] + a1613 * k14[i] + a1614 * k15[i] + + a1615 * k16[i]) + end + f(k17, tmp, p, t + c16 * dt) + @tight_loop_macros for i in uidx + @inbounds u[i] = uprev[i] + + dt * + (b1 * k1[i] + b2 * k2[i] + b3 * k3[i] + b5 * k5[i] + b7 * k7[i] + + b9 * k9[i] + b10 * k10[i] + b11 * k11[i] + b12 * k12[i] + + b13 * k13[i] + b14 * k14[i] + b15 * k15[i] + b16 * k16[i] + + b17 * k17[i]) + end + integrator.stats.nf += 16 + if integrator.opts.adaptive + @tight_loop_macros for i in uidx + @inbounds tmp[i] = dt * (k2[i] - k16[i]) * adaptiveConst + end + calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + f(integrator.fsallast, u, p, t + dt) # For the interpolation, needs k at the updated point + integrator.stats.nf += 1 +end + +function initialize!(integrator, cache::Feagin12ConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +@muladd function perform_step!(integrator, cache::Feagin12ConstantCache, + repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1208, a1209, a1210, a1211, a1300, a1308, a1309, a1310, a1311, a1312, a1400, a1408, a1409, a1410, a1411, a1412, a1413, a1500, a1508, a1509, a1510, a1511, a1512, a1513, a1514, a1600, a1608, a1609, a1610, a1611, a1612, a1613, a1614, a1615, a1700, a1705, a1706, a1707, a1708, a1709, a1710, a1711, a1712, a1713, a1714, a1715, a1716, a1800, a1805, a1806, a1807, a1808, a1809, a1810, a1811, a1812, a1813, a1814, a1815, a1816, a1817, a1900, a1904, a1905, a1906, a1908, a1909, a1910, a1911, a1912, a1913, a1914, a1915, a1916, a1917, a1918, a2000, a2003, a2004, a2005, a2007, a2009, a2010, a2017, a2018, a2019, a2100, a2102, a2103, a2106, a2107, a2109, a2110, a2117, a2118, a2119, a2120, a2200, a2201, a2204, a2206, a2220, a2221, a2300, a2302, a2322, a2400, a2401, a2402, a2404, a2406, a2407, a2408, a2409, a2410, a2411, a2412, a2413, a2414, a2415, a2416, a2417, a2418, a2419, a2420, a2421, a2422, a2423, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, b19, b20, b21, b22, b23, b24, b25 = cache + k1 = integrator.fsalfirst + a = dt * a0100 + k2 = f(uprev + a * k1, p, t + c1 * dt) + k3 = f(uprev + dt * (a0200 * k1 + a0201 * k2), p, t + c2 * dt) + k4 = f(uprev + dt * (a0300 * k1 + a0302 * k3), p, t + c3 * dt) + k5 = f(uprev + dt * (a0400 * k1 + a0402 * k3 + a0403 * k4), p, t + c4 * dt) + k6 = f(uprev + dt * (a0500 * k1 + a0503 * k4 + a0504 * k5), p, t + c5 * dt) + k7 = f(uprev + dt * (a0600 * k1 + a0603 * k4 + a0604 * k5 + a0605 * k6), p, t + c6 * dt) + k8 = f(uprev + dt * (a0700 * k1 + a0704 * k5 + a0705 * k6 + a0706 * k7), p, t + c7 * dt) + k9 = f(uprev + dt * (a0800 * k1 + a0805 * k6 + a0806 * k7 + a0807 * k8), p, t + c8 * dt) + k10 = f(uprev + dt * (a0900 * k1 + a0905 * k6 + a0906 * k7 + a0907 * k8 + a0908 * k9), + p, t + c9 * dt) + k11 = f( + uprev + + dt * + (a1000 * k1 + a1005 * k6 + a1006 * k7 + a1007 * k8 + a1008 * k9 + a1009 * k10), + p, t + c10 * dt) + k12 = f( + uprev + + dt * + (a1100 * k1 + a1105 * k6 + a1106 * k7 + a1107 * k8 + a1108 * k9 + a1109 * k10 + + a1110 * k11), + p, + t + c11 * dt) + k13 = f( + uprev + + dt * (a1200 * k1 + a1208 * k9 + a1209 * k10 + a1210 * k11 + a1211 * k12), p, + t + c12 * dt) + k14 = f( + uprev + + dt * (a1300 * k1 + a1308 * k9 + a1309 * k10 + a1310 * k11 + a1311 * k12 + + a1312 * k13), + p, + t + c13 * dt) + k15 = f( + uprev + + dt * (a1400 * k1 + a1408 * k9 + a1409 * k10 + a1410 * k11 + a1411 * k12 + + a1412 * k13 + a1413 * k14), + p, + t + c14 * dt) + k16 = f( + uprev + + dt * (a1500 * k1 + a1508 * k9 + a1509 * k10 + a1510 * k11 + a1511 * k12 + + a1512 * k13 + a1513 * k14 + a1514 * k15), + p, + t + c15 * dt) + k17 = f( + uprev + + dt * ((a1600 * k1 + a1608 * k9 + a1609 * k10) + + (a1610 * k11 + a1611 * k12 + a1612 * k13 + a1613 * k14) + + (a1614 * k15 + a1615 * k16)), + p, + t + c16 * dt) + k18 = f( + uprev + + dt * ((a1700 * k1 + a1705 * k6 + a1706 * k7) + + (a1707 * k8 + a1708 * k9 + a1709 * k10 + a1710 * k11) + + (a1711 * k12 + a1712 * k13 + a1713 * k14 + a1714 * k15) + + (a1715 * k16 + a1716 * k17)), + p, + t + c17 * dt) + k19 = f( + uprev + + dt * ((a1800 * k1 + a1805 * k6 + a1806 * k7) + + (a1807 * k8 + a1808 * k9 + a1809 * k10 + a1810 * k11) + + (a1811 * k12 + a1812 * k13 + a1813 * k14 + a1814 * k15) + + (a1815 * k16 + a1816 * k17 + a1817 * k18)), + p, + t + c18 * dt) + k20 = f( + uprev + + dt * ((a1900 * k1 + a1904 * k5 + a1905 * k6) + + (a1906 * k7 + a1908 * k9 + a1909 * k10 + a1910 * k11) + + (a1911 * k12 + a1912 * k13 + a1913 * k14 + a1914 * k15) + + (a1915 * k16 + a1916 * k17 + a1917 * k18 + a1918 * k19)), + p, + t + c19 * dt) + k21 = f( + uprev + + dt * ((a2000 * k1 + a2003 * k4 + a2004 * k5) + + (a2005 * k6 + a2007 * k8 + a2009 * k10 + a2010 * k11) + + (a2017 * k18 + a2018 * k19 + a2019 * k20)), + p, + t + c20 * dt) + k22 = f( + uprev + + dt * ((a2100 * k1 + a2102 * k3 + a2103 * k4) + + (a2106 * k7 + a2107 * k8 + a2109 * k10 + a2110 * k11) + + (a2117 * k18 + a2118 * k19 + a2119 * k20 + a2120 * k21)), + p, + t + c21 * dt) + k23 = f( + uprev + + dt * ((a2200 * k1 + a2201 * k2 + a2204 * k5) + + (a2206 * k7 + a2220 * k21 + a2221 * k22)), + p, + t + c22 * dt) + k24 = f(uprev + dt * (a2300 * k1 + a2302 * k3 + a2322 * k23), p, t + c23 * dt) + k25 = f( + uprev + + dt * ((a2400 * k1 + a2401 * k2 + a2402 * k3) + + (a2404 * k5 + a2406 * k7 + a2407 * k8 + a2408 * k9) + + (a2409 * k10 + a2410 * k11 + a2411 * k12 + a2412 * k13) + + (a2413 * k14 + a2414 * k15 + a2415 * k16 + a2416 * k17) + + (a2417 * k18 + a2418 * k19 + a2419 * k20 + a2420 * k21) + + (a2421 * k22 + a2422 * k23 + a2423 * k24)), + p, + t + c24 * dt) + integrator.stats.nf += 24 + u = uprev + + dt * ((b1 * k1 + b2 * k2 + b3 * k3 + b5 * k5) + + (b7 * k7 + b8 * k8 + b10 * k10 + b11 * k11) + + (b13 * k13 + b14 * k14 + b15 * k15 + b16 * k16) + + (b17 * k17 + b18 * k18 + b19 * k19 + b20 * k20) + + (b21 * k21 + b22 * k22 + b23 * k23) + (b24 * k24 + b25 * k25)) + k = f(u, p, t + dt) + integrator.stats.nf += 1 + integrator.fsallast = k + if integrator.opts.adaptive + utilde = @.. broadcast=false dt*(k2-k24)*adaptiveConst + atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.u = u +end + +function initialize!(integrator, cache::Feagin12Cache) + integrator.fsalfirst = cache.fsalfirst + integrator.fsallast = cache.k + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 +end + +#= +@muladd function perform_step!(integrator, cache::Feagin12Cache, repeat_step=false) + @unpack t,dt,uprev,u,f,p = integrator + @unpack adaptiveConst,a0100,a0200,a0201,a0300,a0302,a0400,a0402,a0403,a0500,a0503,a0504,a0600,a0603,a0604,a0605,a0700,a0704,a0705,a0706,a0800,a0805,a0806,a0807,a0900,a0905,a0906,a0907,a0908,a1000,a1005,a1006,a1007,a1008,a1009,a1100,a1105,a1106,a1107,a1108,a1109,a1110,a1200,a1208,a1209,a1210,a1211,a1300,a1308,a1309,a1310,a1311,a1312,a1400,a1408,a1409,a1410,a1411,a1412,a1413,a1500,a1508,a1509,a1510,a1511,a1512,a1513,a1514,a1600,a1608,a1609,a1610,a1611,a1612,a1613,a1614,a1615,a1700,a1705,a1706,a1707,a1708,a1709,a1710,a1711,a1712,a1713,a1714,a1715,a1716,a1800,a1805,a1806,a1807,a1808,a1809,a1810,a1811,a1812,a1813,a1814,a1815,a1816,a1817,a1900,a1904,a1905,a1906,a1908,a1909,a1910,a1911,a1912,a1913,a1914,a1915,a1916,a1917,a1918,a2000,a2003,a2004,a2005,a2007,a2009,a2010,a2017,a2018,a2019,a2100,a2102,a2103,a2106,a2107,a2109,a2110,a2117,a2118,a2119,a2120,a2200,a2201,a2204,a2206,a2220,a2221,a2300,a2302,a2322,a2400,a2401,a2402,a2404,a2406,a2407,a2408,a2409,a2410,a2411,a2412,a2413,a2414,a2415,a2416,a2417,a2418,a2419,a2420,a2421,a2422,a2423,c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,c11,c12,c13,c14,c15,c16,c17,c18,c19,c20,c21,c22,c23,c24,b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19,b20,b21,b22,b23,b24,b25 = cache.tab + @unpack k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12,k13,k14,k15,k16,k17,k18,k19,k20,k21,k22,k23,k24,k25,tmp,atmp,uprev,k = cache + k1 = cache.fsalfirst + a = dt*a0100 + @.. broadcast=false tmp = uprev + a*k1 + f(k2, tmp, p, t + c1*dt) + @.. broadcast=false tmp = uprev + dt*(a0200*k1 + a0201*k2) + f(k3, tmp, p, t + c2*dt ) + @.. broadcast=false tmp = uprev + dt*(a0300*k1 + a0302*k3) + f(k4, tmp, p, t + c3*dt) + @.. broadcast=false tmp = uprev + dt*(a0400*k1 + a0402*k3 + a0403*k4) + f(k5, tmp, p, t + c4*dt) + @.. broadcast=false tmp = uprev + dt*(a0500*k1 + a0503*k4 + a0504*k5) + f(k6, tmp, p, t + c5*dt) + @.. broadcast=false tmp = uprev + dt*(a0600*k1 + a0603*k4 + a0604*k5 + a0605*k6) + f(k7, tmp, p, t + c6*dt) + @.. broadcast=false tmp = uprev + dt*(a0700*k1 + a0704*k5 + a0705*k6 + a0706*k7) + f(k8, tmp, p, t + c7*dt) + @.. broadcast=false tmp = uprev + dt*(a0800*k1 + a0805*k6 + a0806*k7 + a0807*k8) + f(k9, tmp, p, t + c8*dt) + @.. broadcast=false tmp = uprev + dt*(a0900*k1 + a0905*k6 + a0906*k7 + a0907*k8 + a0908*k9) + f(k10, tmp, p, t + c9*dt) + @.. broadcast=false tmp = uprev + dt*(a1000*k1 + a1005*k6 + a1006*k7 + a1007*k8 + a1008*k9 + a1009*k10) + f(k11, tmp, p, t + c10*dt) + @.. broadcast=false tmp = uprev + dt*(a1100*k1 + a1105*k6 + a1106*k7 + a1107*k8 + a1108*k9 + a1109*k10 + a1110*k11) + f(k12, tmp, p, t + c11*dt) + @.. broadcast=false tmp = uprev + dt*(a1200*k1 + a1208*k9 + a1209*k10 + a1210*k11 + a1211*k12) + f(k13, tmp, p, t + c12*dt) + @.. broadcast=false tmp = uprev + dt*(a1300*k1 + a1308*k9 + a1309*k10 + a1310*k11 + a1311*k12 + a1312*k13) + f(k14, tmp, p, t + c13*dt) + @.. broadcast=false tmp = uprev + dt*(a1400*k1 + a1408*k9 + a1409*k10 + a1410*k11 + a1411*k12 + a1412*k13 + a1413*k14) + f(k15, tmp, p, t + c14*dt) + @.. broadcast=false tmp = uprev + dt*(a1500*k1 + a1508*k9 + a1509*k10 + a1510*k11 + a1511*k12 + a1512*k13 + a1513*k14 + a1514*k15) + f(k16, tmp, p, t + c15*dt) + @.. broadcast=false tmp = uprev + dt*((a1600*k1 + a1608*k9 + a1609*k10) + (a1610*k11 + a1611*k12 + a1612*k13 + a1613*k14) + (a1614*k15 + a1615*k16)) + f(k17, tmp, p, t + c16*dt) + @.. broadcast=false tmp = uprev + dt*((a1700*k1 + a1705*k6 + a1706*k7) + (a1707*k8 + a1708*k9 + a1709*k10 + a1710*k11) + (a1711*k12 + a1712*k13 + a1713*k14 + a1714*k15) + (a1715*k16 + a1716*k17)) + f(k18, tmp, p, t + c17*dt) + @.. broadcast=false tmp = uprev + dt*((a1800*k1 + a1805*k6 + a1806*k7) + (a1807*k8 + a1808*k9 + a1809*k10 + a1810*k11) + (a1811*k12 + a1812*k13 + a1813*k14 + a1814*k15) + (a1815*k16 + a1816*k17 + a1817*k18)) + f(k19, tmp, p, t + c18*dt) + @.. broadcast=false tmp = uprev + dt*((a1900*k1 + a1904*k5 + a1905*k6) + (a1906*k7 + a1908*k9 + a1909*k10 + a1910*k11) + (a1911*k12 + a1912*k13 + a1913*k14 + a1914*k15) + (a1915*k16 + a1916*k17 + a1917*k18 + a1918*k19)) + f(k20, tmp, p, t + c19*dt) + @.. broadcast=false tmp = uprev + dt*((a2000*k1 + a2003*k4 + a2004*k5) + (a2005*k6 + a2007*k8 + a2009*k10 + a2010*k11) + (a2017*k18 + a2018*k19 + a2019*k20)) + f(k21, tmp, p, t + c20*dt) + @.. broadcast=false tmp = uprev + dt*((a2100*k1 + a2102*k3 + a2103*k4) + (a2106*k7 + a2107*k8 + a2109*k10 + a2110*k11) + (a2117*k18 + a2118*k19 + a2119*k20 + a2120*k21)) + f(k22, tmp, p, t + c21*dt) + @.. broadcast=false tmp = uprev + dt*((a2200*k1 + a2201*k2 + a2204*k5) + (a2206*k7 + a2220*k21 + a2221*k22)) + f(k23, tmp, p, t + c22*dt) + @.. broadcast=false tmp = uprev + dt*(a2300*k1 + a2302*k3 + a2322*k23) + f(k24, tmp, p, t + c23*dt) + @.. broadcast=false tmp = uprev + dt*((a2400*k1 + a2401*k2 + a2402*k3) + (a2404*k5 + a2406*k7 + a2407*k8 + a2408*k9) + (a2409*k10 + a2410*k11 + a2411*k12 + a2412*k13) + (a2413*k14 + a2414*k15 + a2415*k16 + a2416*k17) + (a2417*k18 + a2418*k19 + a2419*k20 + a2420*k21) + (a2421*k22 + a2422*k23 + a2423*k24)) + f(k25, tmp, p, t + c24*dt) + @.. broadcast=false u = uprev + dt*((b1*k1 + b2*k2 + b3*k3 + b5*k5) + (b7*k7 + b8*k8 + b10*k10 + b11*k11) + (b13*k13 + b14*k14 + b15*k15 + b16*k16) + (b17*k17 + b18*k18 + b19*k19 + b20*k20) + (b21*k21 + b22*k22 + b23*k23) + (b24*k24 + b25*k25)) + if integrator.opts.adaptive + @.. broadcast=false tmp = dt*(k2 - k24) * adaptiveConst + calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, integrator.opts.reltol,integrator.opts.internalnorm,t) + integrator.EEst = integrator.opts.internalnorm(atmp,t) + end + f(k, u, p, t+dt) +end +=# + +@muladd function perform_step!(integrator, cache::Feagin12Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + uidx = eachindex(integrator.uprev) + @unpack adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1208, a1209, a1210, a1211, a1300, a1308, a1309, a1310, a1311, a1312, a1400, a1408, a1409, a1410, a1411, a1412, a1413, a1500, a1508, a1509, a1510, a1511, a1512, a1513, a1514, a1600, a1608, a1609, a1610, a1611, a1612, a1613, a1614, a1615, a1700, a1705, a1706, a1707, a1708, a1709, a1710, a1711, a1712, a1713, a1714, a1715, a1716, a1800, a1805, a1806, a1807, a1808, a1809, a1810, a1811, a1812, a1813, a1814, a1815, a1816, a1817, a1900, a1904, a1905, a1906, a1908, a1909, a1910, a1911, a1912, a1913, a1914, a1915, a1916, a1917, a1918, a2000, a2003, a2004, a2005, a2007, a2009, a2010, a2017, a2018, a2019, a2100, a2102, a2103, a2106, a2107, a2109, a2110, a2117, a2118, a2119, a2120, a2200, a2201, a2204, a2206, a2220, a2221, a2300, a2302, a2322, a2400, a2401, a2402, a2404, a2406, a2407, a2408, a2409, a2410, a2411, a2412, a2413, a2414, a2415, a2416, a2417, a2418, a2419, a2420, a2421, a2422, a2423, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, b19, b20, b21, b22, b23, b24, b25 = cache.tab + @unpack k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, k17, k18, k19, k20, k21, k22, k23, k24, k25, tmp, atmp, uprev, k = cache + k1 = cache.fsalfirst + a = dt * a0100 + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + a * k1[i] + end + f(k2, tmp, p, t + c1 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + dt * (a0200 * k1[i] + a0201 * k2[i]) + end + f(k3, tmp, p, t + c2 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + dt * (a0300 * k1[i] + a0302 * k3[i]) + end + f(k4, tmp, p, t + c3 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + dt * (a0400 * k1[i] + a0402 * k3[i] + a0403 * k4[i]) + end + f(k5, tmp, p, t + c4 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + dt * (a0500 * k1[i] + a0503 * k4[i] + a0504 * k5[i]) + end + f(k6, tmp, p, t + c5 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a0600 * k1[i] + a0603 * k4[i] + a0604 * k5[i] + a0605 * k6[i]) + end + f(k7, tmp, p, t + c6 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a0700 * k1[i] + a0704 * k5[i] + a0705 * k6[i] + a0706 * k7[i]) + end + f(k8, tmp, p, t + c7 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a0800 * k1[i] + a0805 * k6[i] + a0806 * k7[i] + a0807 * k8[i]) + end + f(k9, tmp, p, t + c8 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a0900 * k1[i] + a0905 * k6[i] + a0906 * k7[i] + a0907 * k8[i] + + a0908 * k9[i]) + end + f(k10, tmp, p, t + c9 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a1000 * k1[i] + a1005 * k6[i] + a1006 * k7[i] + a1007 * k8[i] + + a1008 * k9[i] + a1009 * k10[i]) + end + f(k11, tmp, p, t + c10 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a1100 * k1[i] + a1105 * k6[i] + a1106 * k7[i] + a1107 * k8[i] + + a1108 * k9[i] + a1109 * k10[i] + a1110 * k11[i]) + end + f(k12, tmp, p, t + c11 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * (a1200 * k1[i] + a1208 * k9[i] + a1209 * k10[i] + + a1210 * k11[i] + a1211 * k12[i]) + end + f(k13, tmp, p, t + c12 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * (a1300 * k1[i] + a1308 * k9[i] + a1309 * k10[i] + + a1310 * k11[i] + a1311 * k12[i] + a1312 * k13[i]) + end + f(k14, tmp, p, t + c13 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * (a1400 * k1[i] + a1408 * k9[i] + a1409 * k10[i] + + a1410 * k11[i] + a1411 * k12[i] + a1412 * k13[i] + + a1413 * k14[i]) + end + f(k15, tmp, p, t + c14 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * (a1500 * k1[i] + a1508 * k9[i] + a1509 * k10[i] + + a1510 * k11[i] + a1511 * k12[i] + a1512 * k13[i] + + a1513 * k14[i] + a1514 * k15[i]) + end + f(k16, tmp, p, t + c15 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * ((a1600 * k1[i] + a1608 * k9[i] + a1609 * k10[i]) + + (a1610 * k11[i] + a1611 * k12[i] + a1612 * k13[i] + + a1613 * k14[i]) + (a1614 * k15[i] + a1615 * k16[i])) + end + f(k17, tmp, p, t + c16 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * ((a1700 * k1[i] + a1705 * k6[i] + a1706 * k7[i]) + + (a1707 * k8[i] + a1708 * k9[i] + a1709 * k10[i] + + a1710 * k11[i]) + + (a1711 * k12[i] + a1712 * k13[i] + a1713 * k14[i] + + a1714 * k15[i]) + (a1715 * k16[i] + a1716 * k17[i])) + end + f(k18, tmp, p, t + c17 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * ((a1800 * k1[i] + a1805 * k6[i] + a1806 * k7[i]) + + (a1807 * k8[i] + a1808 * k9[i] + a1809 * k10[i] + + a1810 * k11[i]) + + (a1811 * k12[i] + a1812 * k13[i] + a1813 * k14[i] + + a1814 * k15[i]) + + (a1815 * k16[i] + a1816 * k17[i] + a1817 * k18[i])) + end + f(k19, tmp, p, t + c18 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * ((a1900 * k1[i] + a1904 * k5[i] + a1905 * k6[i]) + + (a1906 * k7[i] + a1908 * k9[i] + a1909 * k10[i] + + a1910 * k11[i]) + + (a1911 * k12[i] + a1912 * k13[i] + a1913 * k14[i] + + a1914 * k15[i]) + + (a1915 * k16[i] + a1916 * k17[i] + a1917 * k18[i] + + a1918 * k19[i])) + end + f(k20, tmp, p, t + c19 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * ((a2000 * k1[i] + a2003 * k4[i] + a2004 * k5[i]) + + (a2005 * k6[i] + a2007 * k8[i] + a2009 * k10[i] + + a2010 * k11[i]) + + (a2017 * k18[i] + a2018 * k19[i] + a2019 * k20[i])) + end + f(k21, tmp, p, t + c20 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * ((a2100 * k1[i] + a2102 * k3[i] + a2103 * k4[i]) + + (a2106 * k7[i] + a2107 * k8[i] + a2109 * k10[i] + + a2110 * k11[i]) + + (a2117 * k18[i] + a2118 * k19[i] + a2119 * k20[i] + + a2120 * k21[i])) + end + f(k22, tmp, p, t + c21 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * ((a2200 * k1[i] + a2201 * k2[i] + a2204 * k5[i]) + + (a2206 * k7[i] + a2220 * k21[i] + a2221 * k22[i])) + end + f(k23, tmp, p, t + c22 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + dt * (a2300 * k1[i] + a2302 * k3[i] + a2322 * k23[i]) + end + f(k24, tmp, p, t + c23 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * ((a2400 * k1[i] + a2401 * k2[i] + a2402 * k3[i]) + + (a2404 * k5[i] + a2406 * k7[i] + a2407 * k8[i] + + a2408 * k9[i]) + + (a2409 * k10[i] + a2410 * k11[i] + a2411 * k12[i] + + a2412 * k13[i]) + + (a2413 * k14[i] + a2414 * k15[i] + a2415 * k16[i] + + a2416 * k17[i]) + + (a2417 * k18[i] + a2418 * k19[i] + a2419 * k20[i] + + a2420 * k21[i]) + + (a2421 * k22[i] + a2422 * k23[i] + a2423 * k24[i])) + end + f(k25, tmp, p, t + c24 * dt) + @tight_loop_macros for i in uidx + @inbounds u[i] = uprev[i] + + dt * ((b1 * k1[i] + b2 * k2[i] + b3 * k3[i] + b5 * k5[i]) + + (b7 * k7[i] + b8 * k8[i] + b10 * k10[i] + b11 * k11[i]) + + (b13 * k13[i] + b14 * k14[i] + b15 * k15[i] + b16 * k16[i]) + + (b17 * k17[i] + b18 * k18[i] + b19 * k19[i] + b20 * k20[i]) + + (b21 * k21[i] + b22 * k22[i] + b23 * k23[i]) + + (b24 * k24[i] + b25 * k25[i])) + end + integrator.stats.nf += 24 + if integrator.opts.adaptive + @tight_loop_macros for i in uidx + @inbounds tmp[i] = dt * (k2[i] - k24[i]) * adaptiveConst + end + calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + f(k, u, p, t + dt) + integrator.stats.nf += 1 +end + +function initialize!(integrator, cache::Feagin14ConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +@muladd function perform_step!(integrator, cache::Feagin14ConstantCache, + repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1208, a1209, a1210, a1211, a1300, a1308, a1309, a1310, a1311, a1312, a1400, a1408, a1409, a1410, a1411, a1412, a1413, a1500, a1508, a1509, a1510, a1511, a1512, a1513, a1514, a1600, a1608, a1609, a1610, a1611, a1612, a1613, a1614, a1615, a1700, a1712, a1713, a1714, a1715, a1716, a1800, a1812, a1813, a1814, a1815, a1816, a1817, a1900, a1912, a1913, a1914, a1915, a1916, a1917, a1918, a2000, a2012, a2013, a2014, a2015, a2016, a2017, a2018, a2019, a2100, a2112, a2113, a2114, a2115, a2116, a2117, a2118, a2119, a2120, a2200, a2212, a2213, a2214, a2215, a2216, a2217, a2218, a2219, a2220, a2221, a2300, a2308, a2309, a2310, a2311, a2312, a2313, a2314, a2315, a2316, a2317, a2318, a2319, a2320, a2321, a2322, a2400, a2408, a2409, a2410, a2411, a2412, a2413, a2414, a2415, a2416, a2417, a2418, a2419, a2420, a2421, a2422, a2423, a2500, a2508, a2509, a2510, a2511, a2512, a2513, a2514, a2515, a2516, a2517, a2518, a2519, a2520, a2521, a2522, a2523, a2524, a2600, a2605, a2606, a2607, a2608, a2609, a2610, a2612, a2613, a2614, a2615, a2616, a2617, a2618, a2619, a2620, a2621, a2622, a2623, a2624, a2625, a2700, a2705, a2706, a2707, a2708, a2709, a2711, a2712, a2713, a2714, a2715, a2716, a2717, a2718, a2719, a2720, a2721, a2722, a2723, a2724, a2725, a2726, a2800, a2805, a2806, a2807, a2808, a2810, a2811, a2813, a2814, a2815, a2823, a2824, a2825, a2826, a2827, a2900, a2904, a2905, a2906, a2909, a2910, a2911, a2913, a2914, a2915, a2923, a2924, a2925, a2926, a2927, a2928, a3000, a3003, a3004, a3005, a3007, a3009, a3010, a3013, a3014, a3015, a3023, a3024, a3025, a3027, a3028, a3029, a3100, a3102, a3103, a3106, a3107, a3109, a3110, a3113, a3114, a3115, a3123, a3124, a3125, a3127, a3128, a3129, a3130, a3200, a3201, a3204, a3206, a3230, a3231, a3300, a3302, a3332, a3400, a3401, a3402, a3404, a3406, a3407, a3409, a3410, a3411, a3412, a3413, a3414, a3415, a3416, a3417, a3418, a3419, a3420, a3421, a3422, a3423, a3424, a3425, a3426, a3427, a3428, a3429, a3430, a3431, a3432, a3433, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31, b32, b33, b34, b35 = cache + k1 = integrator.fsalfirst + a = dt * a0100 + k2 = f(uprev + a * k1, p, t + c1 * dt) + k3 = f(uprev + dt * (a0200 * k1 + a0201 * k2), p, t + c2 * dt) + k4 = f(uprev + dt * (a0300 * k1 + a0302 * k3), p, t + c3 * dt) + k5 = f(uprev + dt * (a0400 * k1 + a0402 * k3 + a0403 * k4), p, t + c4 * dt) + k6 = f(uprev + dt * (a0500 * k1 + a0503 * k4 + a0504 * k5), p, t + c5 * dt) + k7 = f(uprev + dt * (a0600 * k1 + a0603 * k4 + a0604 * k5 + a0605 * k6), p, t + c6 * dt) + k8 = f(uprev + dt * (a0700 * k1 + a0704 * k5 + a0705 * k6 + a0706 * k7), p, t + c7 * dt) + k9 = f(uprev + dt * (a0800 * k1 + a0805 * k6 + a0806 * k7 + a0807 * k8), p, t + c8 * dt) + k10 = f(uprev + dt * (a0900 * k1 + a0905 * k6 + a0906 * k7 + a0907 * k8 + a0908 * k9), + p, t + c9 * dt) + k11 = f( + uprev + + dt * + (a1000 * k1 + a1005 * k6 + a1006 * k7 + a1007 * k8 + a1008 * k9 + a1009 * k10), + p, t + c10 * dt) + k12 = f( + uprev + + dt * + (a1100 * k1 + a1105 * k6 + a1106 * k7 + a1107 * k8 + a1108 * k9 + a1109 * k10 + + a1110 * k11), + p, + t + c11 * dt) + k13 = f( + uprev + + dt * (a1200 * k1 + a1208 * k9 + a1209 * k10 + a1210 * k11 + a1211 * k12), p, + t + c12 * dt) + k14 = f( + uprev + + dt * (a1300 * k1 + a1308 * k9 + a1309 * k10 + a1310 * k11 + a1311 * k12 + + a1312 * k13), + p, + t + c13 * dt) + k15 = f( + uprev + + dt * (a1400 * k1 + a1408 * k9 + a1409 * k10 + a1410 * k11 + a1411 * k12 + + a1412 * k13 + a1413 * k14), + p, + t + c14 * dt) + k16 = f( + uprev + + dt * (a1500 * k1 + a1508 * k9 + a1509 * k10 + a1510 * k11 + a1511 * k12 + + a1512 * k13 + a1513 * k14 + a1514 * k15), + p, + t + c15 * dt) + k17 = f( + uprev + + dt * (a1600 * k1 + a1608 * k9 + a1609 * k10 + a1610 * k11 + a1611 * k12 + + a1612 * k13 + a1613 * k14 + a1614 * k15 + a1615 * k16), + p, + t + c16 * dt) + k18 = f( + uprev + + dt * (a1700 * k1 + a1712 * k13 + a1713 * k14 + a1714 * k15 + a1715 * k16 + + a1716 * k17), + p, + t + c17 * dt) + k19 = f( + uprev + + dt * (a1800 * k1 + a1812 * k13 + a1813 * k14 + a1814 * k15 + a1815 * k16 + + a1816 * k17 + a1817 * k18), + p, + t + c18 * dt) + k20 = f( + uprev + + dt * (a1900 * k1 + a1912 * k13 + a1913 * k14 + a1914 * k15 + a1915 * k16 + + a1916 * k17 + a1917 * k18 + a1918 * k19), + p, + t + c19 * dt) + k21 = f( + uprev + + dt * (a2000 * k1 + a2012 * k13 + a2013 * k14 + a2014 * k15 + a2015 * k16 + + a2016 * k17 + a2017 * k18 + a2018 * k19 + a2019 * k20), + p, + t + c20 * dt) + k22 = f( + uprev + + dt * (a2100 * k1 + a2112 * k13 + a2113 * k14 + a2114 * k15 + a2115 * k16 + + a2116 * k17 + a2117 * k18 + a2118 * k19 + a2119 * k20 + a2120 * k21), + p, + t + c21 * dt) + k23 = f( + uprev + + dt * (a2200 * k1 + a2212 * k13 + a2213 * k14 + a2214 * k15 + a2215 * k16 + + a2216 * k17 + a2217 * k18 + a2218 * k19 + a2219 * k20 + a2220 * k21 + + a2221 * k22), + p, + t + c22 * dt) + k24 = f( + uprev + + dt * (a2300 * k1 + a2308 * k9 + a2309 * k10 + a2310 * k11 + a2311 * k12 + + a2312 * k13 + a2313 * k14 + a2314 * k15 + a2315 * k16 + a2316 * k17 + + a2317 * k18 + a2318 * k19 + a2319 * k20 + a2320 * k21 + a2321 * k22 + + a2322 * k23), + p, + t + c23 * dt) + k25 = f( + uprev + + dt * (a2400 * k1 + a2408 * k9 + a2409 * k10 + a2410 * k11 + a2411 * k12 + + a2412 * k13 + a2413 * k14 + a2414 * k15 + a2415 * k16 + a2416 * k17 + + a2417 * k18 + a2418 * k19 + a2419 * k20 + a2420 * k21 + a2421 * k22 + + a2422 * k23 + a2423 * k24), + p, + t + c24 * dt) + k26 = f( + uprev + + dt * (a2500 * k1 + a2508 * k9 + a2509 * k10 + a2510 * k11 + a2511 * k12 + + a2512 * k13 + a2513 * k14 + a2514 * k15 + a2515 * k16 + a2516 * k17 + + a2517 * k18 + a2518 * k19 + a2519 * k20 + a2520 * k21 + a2521 * k22 + + a2522 * k23 + a2523 * k24 + a2524 * k25), + p, + t + c25 * dt) + k27 = f( + uprev + + dt * + (a2600 * k1 + a2605 * k6 + a2606 * k7 + a2607 * k8 + a2608 * k9 + a2609 * k10 + + a2610 * k11 + a2612 * k13 + a2613 * k14 + a2614 * k15 + a2615 * k16 + + a2616 * k17 + a2617 * k18 + a2618 * k19 + a2619 * k20 + a2620 * k21 + + a2621 * k22 + a2622 * k23 + a2623 * k24 + a2624 * k25 + a2625 * k26), + p, + t + c26 * dt) + k28 = f( + uprev + + dt * + (a2700 * k1 + a2705 * k6 + a2706 * k7 + a2707 * k8 + a2708 * k9 + a2709 * k10 + + a2711 * k12 + a2712 * k13 + a2713 * k14 + a2714 * k15 + a2715 * k16 + + a2716 * k17 + a2717 * k18 + a2718 * k19 + a2719 * k20 + a2720 * k21 + + a2721 * k22 + a2722 * k23 + a2723 * k24 + a2724 * k25 + a2725 * k26 + + a2726 * k27), + p, + t + c27 * dt) + k29 = f( + uprev + + dt * + (a2800 * k1 + a2805 * k6 + a2806 * k7 + a2807 * k8 + a2808 * k9 + a2810 * k11 + + a2811 * k12 + a2813 * k14 + a2814 * k15 + a2815 * k16 + a2823 * k24 + + a2824 * k25 + a2825 * k26 + a2826 * k27 + a2827 * k28), + p, + t + c28 * dt) + k30 = f( + uprev + + dt * + (a2900 * k1 + a2904 * k5 + a2905 * k6 + a2906 * k7 + a2909 * k10 + a2910 * k11 + + a2911 * k12 + a2913 * k14 + a2914 * k15 + a2915 * k16 + a2923 * k24 + + a2924 * k25 + a2925 * k26 + a2926 * k27 + a2927 * k28 + a2928 * k29), + p, + t + c29 * dt) + k31 = f( + uprev + + dt * + (a3000 * k1 + a3003 * k4 + a3004 * k5 + a3005 * k6 + a3007 * k8 + a3009 * k10 + + a3010 * k11 + a3013 * k14 + a3014 * k15 + a3015 * k16 + a3023 * k24 + + a3024 * k25 + a3025 * k26 + a3027 * k28 + a3028 * k29 + a3029 * k30), + p, + t + c30 * dt) + k32 = f( + uprev + + dt * + (a3100 * k1 + a3102 * k3 + a3103 * k4 + a3106 * k7 + a3107 * k8 + a3109 * k10 + + a3110 * k11 + a3113 * k14 + a3114 * k15 + a3115 * k16 + a3123 * k24 + + a3124 * k25 + a3125 * k26 + a3127 * k28 + a3128 * k29 + a3129 * k30 + + a3130 * k31), + p, + t + c31 * dt) + k33 = f( + uprev + + dt * + (a3200 * k1 + a3201 * k2 + a3204 * k5 + a3206 * k7 + a3230 * k31 + a3231 * k32), + p, t + c32 * dt) + k34 = f(uprev + dt * (a3300 * k1 + a3302 * k3 + a3332 * k33), p, t + c33 * dt) + k35 = f( + uprev + + dt * + (a3400 * k1 + a3401 * k2 + a3402 * k3 + a3404 * k5 + a3406 * k7 + a3407 * k8 + + a3409 * k10 + a3410 * k11 + a3411 * k12 + a3412 * k13 + a3413 * k14 + + a3414 * k15 + a3415 * k16 + a3416 * k17 + a3417 * k18 + a3418 * k19 + + a3419 * k20 + a3420 * k21 + a3421 * k22 + a3422 * k23 + a3423 * k24 + + a3424 * k25 + a3425 * k26 + a3426 * k27 + a3427 * k28 + a3428 * k29 + + a3429 * k30 + a3430 * k31 + a3431 * k32 + a3432 * k33 + a3433 * k34), + p, + t + c34 * dt) + integrator.stats.nf += 34 + u = uprev + + dt * + (b1 * k1 + b2 * k2 + b3 * k3 + b5 * k5 + b7 * k7 + b8 * k8 + b10 * k10 + b11 * k11 + + b12 * k12 + b14 * k14 + b15 * k15 + b16 * k16 + b18 * k18 + b19 * k19 + b20 * k20 + + b21 * k21 + b22 * k22 + b23 * k23 + b24 * k24 + b25 * k25 + b26 * k26 + b27 * k27 + + b28 * k28 + b29 * k29 + b30 * k30 + b31 * k31 + b32 * k32 + b33 * k33 + b34 * k34 + + b35 * k35) + if integrator.opts.adaptive + utilde = @.. broadcast=false dt*(k2-k34)*adaptiveConst + atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + k = f(u, p, t + dt) # For the interpolation, needs k at the updated point + integrator.stats.nf += 1 + integrator.fsallast = k + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.u = u +end + +function initialize!(integrator, cache::Feagin14Cache) + integrator.fsalfirst = cache.fsalfirst + integrator.fsallast = cache.k + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 +end + +#= +@muladd function perform_step!(integrator, cache::Feagin14Cache, repeat_step=false) + @unpack t,dt,uprev,u,f,p = integrator + @unpack adaptiveConst,a0100,a0200,a0201,a0300,a0302,a0400,a0402,a0403,a0500,a0503,a0504,a0600,a0603,a0604,a0605,a0700,a0704,a0705,a0706,a0800,a0805,a0806,a0807,a0900,a0905,a0906,a0907,a0908,a1000,a1005,a1006,a1007,a1008,a1009,a1100,a1105,a1106,a1107,a1108,a1109,a1110,a1200,a1208,a1209,a1210,a1211,a1300,a1308,a1309,a1310,a1311,a1312,a1400,a1408,a1409,a1410,a1411,a1412,a1413,a1500,a1508,a1509,a1510,a1511,a1512,a1513,a1514,a1600,a1608,a1609,a1610,a1611,a1612,a1613,a1614,a1615,a1700,a1712,a1713,a1714,a1715,a1716,a1800,a1812,a1813,a1814,a1815,a1816,a1817,a1900,a1912,a1913,a1914,a1915,a1916,a1917,a1918,a2000,a2012,a2013,a2014,a2015,a2016,a2017,a2018,a2019,a2100,a2112,a2113,a2114,a2115,a2116,a2117,a2118,a2119,a2120,a2200,a2212,a2213,a2214,a2215,a2216,a2217,a2218,a2219,a2220,a2221,a2300,a2308,a2309,a2310,a2311,a2312,a2313,a2314,a2315,a2316,a2317,a2318,a2319,a2320,a2321,a2322,a2400,a2408,a2409,a2410,a2411,a2412,a2413,a2414,a2415,a2416,a2417,a2418,a2419,a2420,a2421,a2422,a2423,a2500,a2508,a2509,a2510,a2511,a2512,a2513,a2514,a2515,a2516,a2517,a2518,a2519,a2520,a2521,a2522,a2523,a2524,a2600,a2605,a2606,a2607,a2608,a2609,a2610,a2612,a2613,a2614,a2615,a2616,a2617,a2618,a2619,a2620,a2621,a2622,a2623,a2624,a2625,a2700,a2705,a2706,a2707,a2708,a2709,a2711,a2712,a2713,a2714,a2715,a2716,a2717,a2718,a2719,a2720,a2721,a2722,a2723,a2724,a2725,a2726,a2800,a2805,a2806,a2807,a2808,a2810,a2811,a2813,a2814,a2815,a2823,a2824,a2825,a2826,a2827,a2900,a2904,a2905,a2906,a2909,a2910,a2911,a2913,a2914,a2915,a2923,a2924,a2925,a2926,a2927,a2928,a3000,a3003,a3004,a3005,a3007,a3009,a3010,a3013,a3014,a3015,a3023,a3024,a3025,a3027,a3028,a3029,a3100,a3102,a3103,a3106,a3107,a3109,a3110,a3113,a3114,a3115,a3123,a3124,a3125,a3127,a3128,a3129,a3130,a3200,a3201,a3204,a3206,a3230,a3231,a3300,a3302,a3332,a3400,a3401,a3402,a3404,a3406,a3407,a3409,a3410,a3411,a3412,a3413,a3414,a3415,a3416,a3417,a3418,a3419,a3420,a3421,a3422,a3423,a3424,a3425,a3426,a3427,a3428,a3429,a3430,a3431,a3432,a3433,c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,c11,c12,c13,c14,c15,c16,c17,c18,c19,c20,c21,c22,c23,c24,c25,c26,c27,c28,c29,c30,c31,c32,c33,c34,b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35 = cache.tab + @unpack k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12,k13,k14,k15,k16,k17,k18,k19,k20,k21,k22,k23,k24,k25,k26,k27,k28,k29,k30,k31,k32,k33,k34,k35,tmp,atmp,uprev,k = cache + k1 = cache.fsalfirst + f(k1, uprev, p, t) + a = dt*a0100 + @.. broadcast=false tmp = uprev + a*k1 + f(k2, tmp, p, t + c1*dt) + @.. broadcast=false tmp = uprev + dt*(a0200*k1 + a0201*k2) + f(k3, tmp, p, t + c2*dt ) + @.. broadcast=false tmp = uprev + dt*(a0300*k1 + a0302*k3) + f(k4, tmp, p, t + c3*dt) + @.. broadcast=false tmp = uprev + dt*(a0400*k1 + a0402*k3 + a0403*k4) + f(k5, tmp, p, t + c4*dt) + @.. broadcast=false tmp = uprev + dt*(a0500*k1 + a0503*k4 + a0504*k5) + f(k6, tmp, p, t + c5*dt) + @.. broadcast=false tmp = uprev + dt*(a0600*k1 + a0603*k4 + a0604*k5 + a0605*k6) + f(k7, tmp, p, t + c6*dt) + @.. broadcast=false tmp = uprev + dt*(a0700*k1 + a0704*k5 + a0705*k6 + a0706*k7) + f(k8, tmp, p, t + c7*dt) + @.. broadcast=false tmp = uprev + dt*(a0800*k1 + a0805*k6 + a0806*k7 + a0807*k8) + f(k9, tmp, p, t + c8*dt) + @.. broadcast=false tmp = uprev + dt*(a0900*k1 + a0905*k6 + a0906*k7 + a0907*k8 + a0908*k9) + f(k10, tmp, p, t + c9*dt) + @.. broadcast=false tmp = uprev + dt*(a1000*k1 + a1005*k6 + a1006*k7 + a1007*k8 + a1008*k9 + a1009*k10) + f(k11, tmp, p, t + c10*dt) + @.. broadcast=false tmp = uprev + dt*(a1100*k1 + a1105*k6 + a1106*k7 + a1107*k8 + a1108*k9 + a1109*k10 + a1110*k11) + f(k12, tmp, p, t + c11*dt) + @.. broadcast=false tmp = uprev + dt*(a1200*k1 + a1208*k9 + a1209*k10 + a1210*k11 + a1211*k12) + f(k13, tmp, p, t + c12*dt) + @.. broadcast=false tmp = uprev + dt*(a1300*k1 + a1308*k9 + a1309*k10 + a1310*k11 + a1311*k12 + a1312*k13) + f(k14, tmp, p, t + c13*dt) + @.. broadcast=false tmp = uprev + dt*(a1400*k1 + a1408*k9 + a1409*k10 + a1410*k11 + a1411*k12 + a1412*k13 + a1413*k14) + f(k15, tmp, p, t + c14*dt) + @.. broadcast=false tmp = uprev + dt*(a1500*k1 + a1508*k9 + a1509*k10 + a1510*k11 + a1511*k12 + a1512*k13 + a1513*k14 + a1514*k15) + f(k16, tmp, p, t + c15*dt) + @.. broadcast=false tmp = uprev + dt*(a1600*k1 + a1608*k9 + a1609*k10 + a1610*k11 + a1611*k12 + a1612*k13 + a1613*k14 + a1614*k15 + a1615*k16) + f(k17, tmp, p, t + c16*dt) + @.. broadcast=false tmp = uprev + dt*(a1700*k1 + a1712*k13 + a1713*k14 + a1714*k15 + a1715*k16 + a1716*k17) + f(k18, tmp, p, t + c17*dt) + @.. broadcast=false tmp = uprev + dt*(a1800*k1 + a1812*k13 + a1813*k14 + a1814*k15 + a1815*k16 + a1816*k17 + a1817*k18) + f(k19, tmp, p, t + c18*dt) + @.. broadcast=false tmp = uprev + dt*(a1900*k1 + a1912*k13 + a1913*k14 + a1914*k15 + a1915*k16 + a1916*k17 + a1917*k18 + a1918*k19) + f(k20, tmp, p, t + c19*dt) + @.. broadcast=false tmp = uprev + dt*(a2000*k1 + a2012*k13 + a2013*k14 + a2014*k15 + a2015*k16 + a2016*k17 + a2017*k18 + a2018*k19 + a2019*k20) + f(k21, tmp, p, t + c20*dt) + @.. broadcast=false tmp = uprev + dt*(a2100*k1 + a2112*k13 + a2113*k14 + a2114*k15 + a2115*k16 + a2116*k17 + a2117*k18 + a2118*k19 + a2119*k20 + a2120*k21) + f(k22, tmp, p, t + c21*dt) + @.. broadcast=false tmp = uprev + dt*(a2200*k1 + a2212*k13 + a2213*k14 + a2214*k15 + a2215*k16 + a2216*k17 + a2217*k18 + a2218*k19 + a2219*k20 + a2220*k21 + a2221*k22) + f(k23, tmp, p, t + c22*dt) + @.. broadcast=false tmp = uprev + dt*(a2300*k1 + a2308*k9 + a2309*k10 + a2310*k11 + a2311*k12 + a2312*k13 + a2313*k14 + a2314*k15 + a2315*k16 + a2316*k17 + a2317*k18 + a2318*k19 + a2319*k20 + a2320*k21 + a2321*k22 + a2322*k23) + f(k24, tmp, p, t + c23*dt) + @.. broadcast=false tmp = uprev + dt*(a2400*k1 + a2408*k9 + a2409*k10 + a2410*k11 + a2411*k12 + a2412*k13 + a2413*k14 + a2414*k15 + a2415*k16 + a2416*k17 + a2417*k18 + a2418*k19 + a2419*k20 + a2420*k21 + a2421*k22 + a2422*k23 + a2423*k24) + f(k25, tmp, p, t + c24*dt) + @.. broadcast=false tmp = uprev + dt*(a2500*k1 + a2508*k9 + a2509*k10 + a2510*k11 + a2511*k12 + a2512*k13 + a2513*k14 + a2514*k15 + a2515*k16 + a2516*k17 + a2517*k18 + a2518*k19 + a2519*k20 + a2520*k21 + a2521*k22 + a2522*k23 + a2523*k24 + a2524*k25) + f(k26, tmp, p, t + c25*dt) + @.. broadcast=false tmp = uprev + dt*(a2600*k1 + a2605*k6 + a2606*k7 + a2607*k8 + a2608*k9 + a2609*k10 + a2610*k11 + a2612*k13 + a2613*k14 + a2614*k15 + a2615*k16 + a2616*k17 + a2617*k18 + a2618*k19 + a2619*k20 + a2620*k21 + a2621*k22 + a2622*k23 + a2623*k24 + a2624*k25 + a2625*k26) + f(k27, tmp, p, t + c26*dt) + @.. broadcast=false tmp = uprev + dt*(a2700*k1 + a2705*k6 + a2706*k7 + a2707*k8 + a2708*k9 + a2709*k10 + a2711*k12 + a2712*k13 + a2713*k14 + a2714*k15 + a2715*k16 + a2716*k17 + a2717*k18 + a2718*k19 + a2719*k20 + a2720*k21 + a2721*k22 + a2722*k23 + a2723*k24 + a2724*k25 + a2725*k26 + a2726*k27) + f(k28, tmp, p, t + c27*dt) + @.. broadcast=false tmp = uprev + dt*(a2800*k1 + a2805*k6 + a2806*k7 + a2807*k8 + a2808*k9 + a2810*k11 + a2811*k12 + a2813*k14 + a2814*k15 + a2815*k16 + a2823*k24 + a2824*k25 + a2825*k26 + a2826*k27 + a2827*k28) + f(k29, tmp, p, t + c28*dt) + @.. broadcast=false tmp = uprev + dt*(a2900*k1 + a2904*k5 + a2905*k6 + a2906*k7 + a2909*k10 + a2910*k11 + a2911*k12 + a2913*k14 + a2914*k15 + a2915*k16 + a2923*k24 + a2924*k25 + a2925*k26 + a2926*k27 + a2927*k28 + a2928*k29) + f(k30, tmp, p, t + c29*dt) + @.. broadcast=false tmp = uprev + dt*(a3000*k1 + a3003*k4 + a3004*k5 + a3005*k6 + a3007*k8 + a3009*k10 + a3010*k11 + a3013*k14 + a3014*k15 + a3015*k16 + a3023*k24 + a3024*k25 + a3025*k26 + a3027*k28 + a3028*k29 + a3029*k30) + f(k31, tmp, p, t + c30*dt) + @.. broadcast=false tmp = uprev + dt*(a3100*k1 + a3102*k3 + a3103*k4 + a3106*k7 + a3107*k8 + a3109*k10 + a3110*k11 + a3113*k14 + a3114*k15 + a3115*k16 + a3123*k24 + a3124*k25 + a3125*k26 + a3127*k28 + a3128*k29 + a3129*k30 + a3130*k31) + f(k32, tmp, p, t + c31*dt) + @.. broadcast=false tmp = uprev + dt*(a3200*k1 + a3201*k2 + a3204*k5 + a3206*k7 + a3230*k31 + a3231*k32) + f(k33, tmp, p, t + c32*dt) + @.. broadcast=false tmp = uprev + dt*(a3300*k1 + a3302*k3 + a3332*k33) + f(k34, tmp, p, t + c33*dt) + @.. broadcast=false tmp = uprev + dt*(a3400*k1 + a3401*k2 + a3402*k3 + a3404*k5 + a3406*k7 + a3407*k8 + a3409*k10 + a3410*k11 + a3411*k12 + a3412*k13 + a3413*k14 + a3414*k15 + a3415*k16 + a3416*k17 + a3417*k18 + a3418*k19 + a3419*k20 + a3420*k21 + a3421*k22 + a3422*k23 + a3423*k24 + a3424*k25 + a3425*k26 + a3426*k27 + a3427*k28 + a3428*k29 + a3429*k30 + a3430*k31 + a3431*k32 + a3432*k33 + a3433*k34) + f(k35, tmp, p, t + c34*dt) + @.. broadcast=false u = uprev + dt*(b1*k1 + b2*k2 + b3*k3 + b5*k5 + b7*k7 + b8*k8 + b10*k10 + b11*k11 + b12*k12 + b14*k14 + b15*k15 + b16*k16 + b18*k18 + b19*k19 + b20*k20 + b21*k21 + b22*k22 + b23*k23 + b24*k24 + b25*k25 + b26*k26 + b27*k27 + b28*k28 + b29*k29 + b30*k30 + b31*k31 + b32*k32 + b33*k33 + b34*k34 + b35*k35) + if integrator.opts.adaptive + @.. broadcast=false tmp = dt*(k2 - k34) * adaptiveConst + calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, integrator.opts.reltol,integrator.opts.internalnorm,t) + integrator.EEst = integrator.opts.internalnorm(atmp,t) + end + f(integrator.fsallast,u,p,t+dt) # For the interpolation, needs k at the updated point +end +=# + +@muladd function perform_step!(integrator, cache::Feagin14Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + uidx = eachindex(integrator.uprev) + @unpack adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1208, a1209, a1210, a1211, a1300, a1308, a1309, a1310, a1311, a1312, a1400, a1408, a1409, a1410, a1411, a1412, a1413, a1500, a1508, a1509, a1510, a1511, a1512, a1513, a1514, a1600, a1608, a1609, a1610, a1611, a1612, a1613, a1614, a1615, a1700, a1712, a1713, a1714, a1715, a1716, a1800, a1812, a1813, a1814, a1815, a1816, a1817, a1900, a1912, a1913, a1914, a1915, a1916, a1917, a1918, a2000, a2012, a2013, a2014, a2015, a2016, a2017, a2018, a2019, a2100, a2112, a2113, a2114, a2115, a2116, a2117, a2118, a2119, a2120, a2200, a2212, a2213, a2214, a2215, a2216, a2217, a2218, a2219, a2220, a2221, a2300, a2308, a2309, a2310, a2311, a2312, a2313, a2314, a2315, a2316, a2317, a2318, a2319, a2320, a2321, a2322, a2400, a2408, a2409, a2410, a2411, a2412, a2413, a2414, a2415, a2416, a2417, a2418, a2419, a2420, a2421, a2422, a2423, a2500, a2508, a2509, a2510, a2511, a2512, a2513, a2514, a2515, a2516, a2517, a2518, a2519, a2520, a2521, a2522, a2523, a2524, a2600, a2605, a2606, a2607, a2608, a2609, a2610, a2612, a2613, a2614, a2615, a2616, a2617, a2618, a2619, a2620, a2621, a2622, a2623, a2624, a2625, a2700, a2705, a2706, a2707, a2708, a2709, a2711, a2712, a2713, a2714, a2715, a2716, a2717, a2718, a2719, a2720, a2721, a2722, a2723, a2724, a2725, a2726, a2800, a2805, a2806, a2807, a2808, a2810, a2811, a2813, a2814, a2815, a2823, a2824, a2825, a2826, a2827, a2900, a2904, a2905, a2906, a2909, a2910, a2911, a2913, a2914, a2915, a2923, a2924, a2925, a2926, a2927, a2928, a3000, a3003, a3004, a3005, a3007, a3009, a3010, a3013, a3014, a3015, a3023, a3024, a3025, a3027, a3028, a3029, a3100, a3102, a3103, a3106, a3107, a3109, a3110, a3113, a3114, a3115, a3123, a3124, a3125, a3127, a3128, a3129, a3130, a3200, a3201, a3204, a3206, a3230, a3231, a3300, a3302, a3332, a3400, a3401, a3402, a3404, a3406, a3407, a3409, a3410, a3411, a3412, a3413, a3414, a3415, a3416, a3417, a3418, a3419, a3420, a3421, a3422, a3423, a3424, a3425, a3426, a3427, a3428, a3429, a3430, a3431, a3432, a3433, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31, b32, b33, b34, b35 = cache.tab + @unpack k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, k17, k18, k19, k20, k21, k22, k23, k24, k25, k26, k27, k28, k29, k30, k31, k32, k33, k34, k35, tmp, atmp, uprev, k = cache + k1 = cache.fsalfirst + a = dt * a0100 + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + a * k1[i] + end + f(k2, tmp, p, t + c1 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + dt * (a0200 * k1[i] + a0201 * k2[i]) + end + f(k3, tmp, p, t + c2 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + dt * (a0300 * k1[i] + a0302 * k3[i]) + end + f(k4, tmp, p, t + c3 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + dt * (a0400 * k1[i] + a0402 * k3[i] + a0403 * k4[i]) + end + f(k5, tmp, p, t + c4 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + dt * (a0500 * k1[i] + a0503 * k4[i] + a0504 * k5[i]) + end + f(k6, tmp, p, t + c5 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a0600 * k1[i] + a0603 * k4[i] + a0604 * k5[i] + a0605 * k6[i]) + end + f(k7, tmp, p, t + c6 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a0700 * k1[i] + a0704 * k5[i] + a0705 * k6[i] + a0706 * k7[i]) + end + f(k8, tmp, p, t + c7 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a0800 * k1[i] + a0805 * k6[i] + a0806 * k7[i] + a0807 * k8[i]) + end + f(k9, tmp, p, t + c8 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a0900 * k1[i] + a0905 * k6[i] + a0906 * k7[i] + a0907 * k8[i] + + a0908 * k9[i]) + end + f(k10, tmp, p, t + c9 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a1000 * k1[i] + a1005 * k6[i] + a1006 * k7[i] + a1007 * k8[i] + + a1008 * k9[i] + a1009 * k10[i]) + end + f(k11, tmp, p, t + c10 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a1100 * k1[i] + a1105 * k6[i] + a1106 * k7[i] + a1107 * k8[i] + + a1108 * k9[i] + a1109 * k10[i] + a1110 * k11[i]) + end + f(k12, tmp, p, t + c11 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * (a1200 * k1[i] + a1208 * k9[i] + a1209 * k10[i] + + a1210 * k11[i] + a1211 * k12[i]) + end + f(k13, tmp, p, t + c12 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * (a1300 * k1[i] + a1308 * k9[i] + a1309 * k10[i] + + a1310 * k11[i] + a1311 * k12[i] + a1312 * k13[i]) + end + f(k14, tmp, p, t + c13 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * (a1400 * k1[i] + a1408 * k9[i] + a1409 * k10[i] + + a1410 * k11[i] + a1411 * k12[i] + a1412 * k13[i] + + a1413 * k14[i]) + end + f(k15, tmp, p, t + c14 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * (a1500 * k1[i] + a1508 * k9[i] + a1509 * k10[i] + + a1510 * k11[i] + a1511 * k12[i] + a1512 * k13[i] + + a1513 * k14[i] + a1514 * k15[i]) + end + f(k16, tmp, p, t + c15 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * (a1600 * k1[i] + a1608 * k9[i] + a1609 * k10[i] + + a1610 * k11[i] + a1611 * k12[i] + a1612 * k13[i] + + a1613 * k14[i] + a1614 * k15[i] + a1615 * k16[i]) + end + f(k17, tmp, p, t + c16 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * (a1700 * k1[i] + a1712 * k13[i] + a1713 * k14[i] + + a1714 * k15[i] + a1715 * k16[i] + a1716 * k17[i]) + end + f(k18, tmp, p, t + c17 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * (a1800 * k1[i] + a1812 * k13[i] + a1813 * k14[i] + + a1814 * k15[i] + a1815 * k16[i] + a1816 * k17[i] + + a1817 * k18[i]) + end + f(k19, tmp, p, t + c18 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * (a1900 * k1[i] + a1912 * k13[i] + a1913 * k14[i] + + a1914 * k15[i] + a1915 * k16[i] + a1916 * k17[i] + + a1917 * k18[i] + a1918 * k19[i]) + end + f(k20, tmp, p, t + c19 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * (a2000 * k1[i] + a2012 * k13[i] + a2013 * k14[i] + + a2014 * k15[i] + a2015 * k16[i] + a2016 * k17[i] + + a2017 * k18[i] + a2018 * k19[i] + a2019 * k20[i]) + end + f(k21, tmp, p, t + c20 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * (a2100 * k1[i] + a2112 * k13[i] + a2113 * k14[i] + + a2114 * k15[i] + a2115 * k16[i] + a2116 * k17[i] + + a2117 * k18[i] + a2118 * k19[i] + a2119 * k20[i] + + a2120 * k21[i]) + end + f(k22, tmp, p, t + c21 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * (a2200 * k1[i] + a2212 * k13[i] + a2213 * k14[i] + + a2214 * k15[i] + a2215 * k16[i] + a2216 * k17[i] + + a2217 * k18[i] + a2218 * k19[i] + a2219 * k20[i] + + a2220 * k21[i] + a2221 * k22[i]) + end + f(k23, tmp, p, t + c22 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * (a2300 * k1[i] + a2308 * k9[i] + a2309 * k10[i] + + a2310 * k11[i] + a2311 * k12[i] + a2312 * k13[i] + + a2313 * k14[i] + a2314 * k15[i] + a2315 * k16[i] + + a2316 * k17[i] + a2317 * k18[i] + a2318 * k19[i] + + a2319 * k20[i] + a2320 * k21[i] + a2321 * k22[i] + + a2322 * k23[i]) + end + f(k24, tmp, p, t + c23 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * (a2400 * k1[i] + a2408 * k9[i] + a2409 * k10[i] + + a2410 * k11[i] + a2411 * k12[i] + a2412 * k13[i] + + a2413 * k14[i] + a2414 * k15[i] + a2415 * k16[i] + + a2416 * k17[i] + a2417 * k18[i] + a2418 * k19[i] + + a2419 * k20[i] + a2420 * k21[i] + a2421 * k22[i] + + a2422 * k23[i] + a2423 * k24[i]) + end + f(k25, tmp, p, t + c24 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * (a2500 * k1[i] + a2508 * k9[i] + a2509 * k10[i] + + a2510 * k11[i] + a2511 * k12[i] + a2512 * k13[i] + + a2513 * k14[i] + a2514 * k15[i] + a2515 * k16[i] + + a2516 * k17[i] + a2517 * k18[i] + a2518 * k19[i] + + a2519 * k20[i] + a2520 * k21[i] + a2521 * k22[i] + + a2522 * k23[i] + a2523 * k24[i] + a2524 * k25[i]) + end + f(k26, tmp, p, t + c25 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a2600 * k1[i] + a2605 * k6[i] + a2606 * k7[i] + a2607 * k8[i] + + a2608 * k9[i] + a2609 * k10[i] + a2610 * k11[i] + + a2612 * k13[i] + a2613 * k14[i] + a2614 * k15[i] + + a2615 * k16[i] + a2616 * k17[i] + a2617 * k18[i] + + a2618 * k19[i] + a2619 * k20[i] + a2620 * k21[i] + + a2621 * k22[i] + a2622 * k23[i] + a2623 * k24[i] + + a2624 * k25[i] + a2625 * k26[i]) + end + f(k27, tmp, p, t + c26 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a2700 * k1[i] + a2705 * k6[i] + a2706 * k7[i] + a2707 * k8[i] + + a2708 * k9[i] + a2709 * k10[i] + a2711 * k12[i] + + a2712 * k13[i] + a2713 * k14[i] + a2714 * k15[i] + + a2715 * k16[i] + a2716 * k17[i] + a2717 * k18[i] + + a2718 * k19[i] + a2719 * k20[i] + a2720 * k21[i] + + a2721 * k22[i] + a2722 * k23[i] + a2723 * k24[i] + + a2724 * k25[i] + a2725 * k26[i] + a2726 * k27[i]) + end + f(k28, tmp, p, t + c27 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a2800 * k1[i] + a2805 * k6[i] + a2806 * k7[i] + a2807 * k8[i] + + a2808 * k9[i] + a2810 * k11[i] + a2811 * k12[i] + + a2813 * k14[i] + a2814 * k15[i] + a2815 * k16[i] + + a2823 * k24[i] + a2824 * k25[i] + a2825 * k26[i] + + a2826 * k27[i] + a2827 * k28[i]) + end + f(k29, tmp, p, t + c28 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a2900 * k1[i] + a2904 * k5[i] + a2905 * k6[i] + a2906 * k7[i] + + a2909 * k10[i] + a2910 * k11[i] + a2911 * k12[i] + + a2913 * k14[i] + a2914 * k15[i] + a2915 * k16[i] + + a2923 * k24[i] + a2924 * k25[i] + a2925 * k26[i] + + a2926 * k27[i] + a2927 * k28[i] + a2928 * k29[i]) + end + f(k30, tmp, p, t + c29 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a3000 * k1[i] + a3003 * k4[i] + a3004 * k5[i] + a3005 * k6[i] + + a3007 * k8[i] + a3009 * k10[i] + a3010 * k11[i] + + a3013 * k14[i] + a3014 * k15[i] + a3015 * k16[i] + + a3023 * k24[i] + a3024 * k25[i] + a3025 * k26[i] + + a3027 * k28[i] + a3028 * k29[i] + a3029 * k30[i]) + end + f(k31, tmp, p, t + c30 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a3100 * k1[i] + a3102 * k3[i] + a3103 * k4[i] + a3106 * k7[i] + + a3107 * k8[i] + a3109 * k10[i] + a3110 * k11[i] + + a3113 * k14[i] + a3114 * k15[i] + a3115 * k16[i] + + a3123 * k24[i] + a3124 * k25[i] + a3125 * k26[i] + + a3127 * k28[i] + a3128 * k29[i] + a3129 * k30[i] + + a3130 * k31[i]) + end + f(k32, tmp, p, t + c31 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a3200 * k1[i] + a3201 * k2[i] + a3204 * k5[i] + a3206 * k7[i] + + a3230 * k31[i] + a3231 * k32[i]) + end + f(k33, tmp, p, t + c32 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + dt * (a3300 * k1[i] + a3302 * k3[i] + a3332 * k33[i]) + end + f(k34, tmp, p, t + c33 * dt) + @tight_loop_macros for i in uidx + @inbounds tmp[i] = uprev[i] + + dt * + (a3400 * k1[i] + a3401 * k2[i] + a3402 * k3[i] + a3404 * k5[i] + + a3406 * k7[i] + a3407 * k8[i] + a3409 * k10[i] + + a3410 * k11[i] + a3411 * k12[i] + a3412 * k13[i] + + a3413 * k14[i] + a3414 * k15[i] + a3415 * k16[i] + + a3416 * k17[i] + a3417 * k18[i] + a3418 * k19[i] + + a3419 * k20[i] + a3420 * k21[i] + a3421 * k22[i] + + a3422 * k23[i] + a3423 * k24[i] + a3424 * k25[i] + + a3425 * k26[i] + a3426 * k27[i] + a3427 * k28[i] + + a3428 * k29[i] + a3429 * k30[i] + a3430 * k31[i] + + a3431 * k32[i] + a3432 * k33[i] + a3433 * k34[i]) + end + f(k35, tmp, p, t + c34 * dt) + @tight_loop_macros for i in uidx + @inbounds u[i] = uprev[i] + + dt * + (b1 * k1[i] + b2 * k2[i] + b3 * k3[i] + b5 * k5[i] + b7 * k7[i] + + b8 * k8[i] + b10 * k10[i] + b11 * k11[i] + b12 * k12[i] + + b14 * k14[i] + b15 * k15[i] + b16 * k16[i] + b18 * k18[i] + + b19 * k19[i] + b20 * k20[i] + b21 * k21[i] + b22 * k22[i] + + b23 * k23[i] + b24 * k24[i] + b25 * k25[i] + b26 * k26[i] + + b27 * k27[i] + b28 * k28[i] + b29 * k29[i] + b30 * k30[i] + + b31 * k31[i] + b32 * k32[i] + b33 * k33[i] + b34 * k34[i] + + b35 * k35[i]) + end + integrator.stats.nf += 35 + if integrator.opts.adaptive + @tight_loop_macros for i in uidx + @inbounds tmp[i] = dt * (k2[i] - k34[i]) * adaptiveConst + end + calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + f(integrator.fsallast, u, p, t + dt) # For the interpolation, needs k at the updated point + integrator.stats.nf += 1 +end diff --git a/src/perform_step/firk_perform_step.jl b/src/perform_step/firk_perform_step.jl index ba2db6da42..b60e9b0e38 100644 --- a/src/perform_step/firk_perform_step.jl +++ b/src/perform_step/firk_perform_step.jl @@ -51,7 +51,7 @@ function initialize!(integrator, cache::RadauIIA5ConstantCache) nothing end -function initialize!(integrator, cache::RadauIIA7ConstantCache) +function initialize!(integrator, cache::RadauIIA9ConstantCache) integrator.kshortsize = 2 integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal @@ -98,7 +98,7 @@ function initialize!(integrator, cache::RadauIIA5Cache) nothing end -function initialize!(integrator, cache::RadauIIA7Cache) +function initialize!(integrator, cache::RadauIIA9Cache) integrator.kshortsize = 2 integrator.fsalfirst = cache.fsalfirst integrator.fsallast = cache.k @@ -784,7 +784,7 @@ end return end -@muladd function perform_step!(integrator, cache::RadauIIA7ConstantCache, +@muladd function perform_step!(integrator, cache::RadauIIA9ConstantCache, repeat_step = false) @unpack t, dt, uprev, u, f, p = integrator @unpack T11, T12, T13, T14, T15, T21, T22, T23, T24, T25, T31, T32, T33, T34, T35, T41, T42, T43, T44, T45, T51 = cache.tab #= T52 = 1, T53 = 0, T54 = 1, T55 = 0=# @@ -1014,7 +1014,7 @@ end return end -@muladd function perform_step!(integrator, cache::RadauIIA7Cache, repeat_step = false) +@muladd function perform_step!(integrator, cache::RadauIIA9Cache, repeat_step = false) @unpack t, dt, uprev, u, f, p, fsallast, fsalfirst = integrator @unpack T11, T12, T13, T14, T15, T21, T22, T23, T24, T25, T31, T32, T33, T34, T35, T41, T42, T43, T44, T45, T51 = cache.tab #= T52 = 1, T53 = 0, T54 = 1, T55 = 0=# @unpack TI11, TI12, TI13, TI14, TI15, TI21, TI22, TI23, TI24, TI25, TI31, TI32, TI33, TI34, TI35, TI41, TI42, TI43, TI44, TI45, TI51, TI52, TI53, TI54, TI55 = cache.tab diff --git a/src/perform_step/low_storage_rk_perform_step.jl b/src/perform_step/low_storage_rk_perform_step.jl new file mode 100644 index 0000000000..4ee07826a7 --- /dev/null +++ b/src/perform_step/low_storage_rk_perform_step.jl @@ -0,0 +1,842 @@ + +# 2N low storage methods +function initialize!(integrator, cache::LowStorageRK2NConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::LowStorageRK2NConstantCache, + repeat_step = false) + @unpack t, dt, u, f, p = integrator + @unpack A2end, B1, B2end, c2end = cache + + # u1 + tmp = dt * integrator.fsalfirst + u = u + B1 * tmp + + # other stages + for i in eachindex(A2end) + k = f(u, p, t + c2end[i] * dt) + integrator.stats.nf += 1 + tmp = A2end[i] * tmp + dt * k + u = u + B2end[i] * tmp + end + + integrator.stats.nf += 1 + integrator.k[1] = integrator.fsalfirst + integrator.fsalfirst = f(u, p, t + dt) # For interpolation, then FSAL'd + integrator.u = u +end + +function initialize!(integrator, cache::LowStorageRK2NCache) + @unpack k, tmp, williamson_condition = cache + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = k + integrator.fsalfirst = k # used for get_du + integrator.fsallast = k + integrator.f(k, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation + integrator.stats.nf += 1 +end + +@muladd function perform_step!(integrator, cache::LowStorageRK2NCache, repeat_step = false) + @unpack t, dt, u, f, p = integrator + @unpack k, tmp, williamson_condition, stage_limiter!, step_limiter!, thread = cache + @unpack A2end, B1, B2end, c2end = cache.tab + + # u1 + f(k, u, p, t) + integrator.stats.nf += 1 + @.. broadcast=false thread=thread tmp=dt * k + @.. broadcast=false thread=thread u=u + B1 * tmp + # other stages + for i in eachindex(A2end) + if williamson_condition + f(ArrayFuse(tmp, u, (A2end[i], dt, B2end[i])), u, p, t + c2end[i] * dt) + else + @.. broadcast=false thread=thread tmp=A2end[i] * tmp + stage_limiter!(u, integrator, p, t + c2end[i] * dt) + f(k, u, p, t + c2end[i] * dt) + @.. broadcast=false thread=thread tmp=tmp + dt * k + @.. broadcast=false thread=thread u=u + B2end[i] * tmp + end + integrator.stats.nf += 1 + end + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) +end + +# 2C low storage methods +function initialize!(integrator, cache::LowStorageRK2CConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::LowStorageRK2CConstantCache, + repeat_step = false) + @unpack t, dt, u, f, p = integrator + @unpack A2end, B1, B2end, c2end = cache + + # u1 + k = integrator.fsalfirst = f(u, p, t) + integrator.k[1] = integrator.fsalfirst + integrator.stats.nf += 1 + u = u + B1 * dt * k + + # other stages + for i in eachindex(A2end) + tmp = u + A2end[i] * dt * k + k = f(tmp, p, t + c2end[i] * dt) + integrator.stats.nf += 1 + u = u + B2end[i] * dt * k + end + + integrator.u = u +end + +function initialize!(integrator, cache::LowStorageRK2CCache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation + integrator.stats.nf += 1 +end + +@muladd function perform_step!(integrator, cache::LowStorageRK2CCache, repeat_step = false) + @unpack t, dt, u, f, p = integrator + @unpack k, fsalfirst, tmp, stage_limiter!, step_limiter!, thread = cache + @unpack A2end, B1, B2end, c2end = cache.tab + + # u1 + @.. broadcast=false thread=thread k=integrator.fsalfirst + @.. broadcast=false thread=thread u=u + B1 * dt * k + + # other stages + for i in eachindex(A2end) + @.. broadcast=false thread=thread tmp=u + A2end[i] * dt * k + f(k, tmp, p, t + c2end[i] * dt) + integrator.stats.nf += 1 + @.. broadcast=false thread=thread u=u + B2end[i] * dt * k + end + + f(k, u, p, t + dt) + integrator.stats.nf += 1 +end + +# 3S low storage methods +function initialize!(integrator, cache::LowStorageRK3SConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::LowStorageRK3SConstantCache, + repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end = cache + + # u1 + tmp = u + u = tmp + β1 * dt * integrator.fsalfirst + + # other stages + for i in eachindex(γ12end) + k = f(u, p, t + c2end[i] * dt) + integrator.stats.nf += 1 + tmp = tmp + δ2end[i] * u + u = γ12end[i] * u + γ22end[i] * tmp + γ32end[i] * uprev + β2end[i] * dt * k + end + + integrator.fsallast = f(u, p, t + dt) # For interpolation, then FSAL'd + integrator.stats.nf += 1 + integrator.k[1] = integrator.fsalfirst + integrator.u = u +end + +function initialize!(integrator, cache::LowStorageRK3SCache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation + integrator.stats.nf += 1 +end + +@muladd function perform_step!(integrator, cache::LowStorageRK3SCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, fsalfirst, tmp, stage_limiter!, step_limiter!, thread = cache + @unpack γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end = cache.tab + + # u1 + @.. broadcast=false thread=thread tmp=u + @.. broadcast=false thread=thread u=tmp + β1 * dt * integrator.fsalfirst + + # other stages + for i in eachindex(γ12end) + f(k, u, p, t + c2end[i] * dt) + integrator.stats.nf += 1 + @.. broadcast=false thread=thread tmp=tmp + δ2end[i] * u + @.. broadcast=false thread=thread u=γ12end[i] * u + γ22end[i] * tmp + + γ32end[i] * uprev + + β2end[i] * dt * k + end + + f(k, u, p, t + dt) + integrator.stats.nf += 1 +end + +# 3S+ low storage methods: 3S methods adding another memory location for the embedded method (non-FSAL version) +function initialize!(integrator, cache::LowStorageRK3SpConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::LowStorageRK3SpConstantCache, + repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end, bhat1, bhat2end = cache + + # u1 + integrator.fsalfirst = f(uprev, p, t) + integrator.stats.nf += 1 + integrator.k[1] = integrator.fsalfirst + tmp = uprev + u = tmp + β1 * dt * integrator.fsalfirst + if integrator.opts.adaptive + utilde = bhat1 * dt * integrator.fsalfirst + end + + # other stages + for i in eachindex(γ12end) + k = f(u, p, t + c2end[i] * dt) + integrator.stats.nf += 1 + tmp = tmp + δ2end[i] * u + u = γ12end[i] * u + γ22end[i] * tmp + γ32end[i] * uprev + β2end[i] * dt * k + if integrator.opts.adaptive + utilde = utilde + bhat2end[i] * dt * k + end + end + + if integrator.opts.adaptive + atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + + integrator.u = u +end + +function initialize!(integrator, cache::LowStorageRK3SpCache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::LowStorageRK3SpCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, tmp, utilde, atmp, stage_limiter!, step_limiter!, thread = cache + @unpack γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end, bhat1, bhat2end = cache.tab + + # u1 + f(integrator.fsalfirst, uprev, p, t) + integrator.stats.nf += 1 + @.. broadcast=false thread=thread tmp=uprev + @.. broadcast=false thread=thread u=tmp + β1 * dt * integrator.fsalfirst + if integrator.opts.adaptive + @.. broadcast=false thread=thread utilde=bhat1 * dt * integrator.fsalfirst + end + + # other stages + for i in eachindex(γ12end) + stage_limiter!(u, integrator, p, t + c2end[i] * dt) + f(k, u, p, t + c2end[i] * dt) + integrator.stats.nf += 1 + @.. broadcast=false thread=thread tmp=tmp + δ2end[i] * u + @.. broadcast=false thread=thread u=γ12end[i] * u + γ22end[i] * tmp + + γ32end[i] * uprev + β2end[i] * dt * k + if integrator.opts.adaptive + @.. broadcast=false thread=thread utilde=utilde + bhat2end[i] * dt * k + end + end + + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + + if integrator.opts.adaptive + calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t, + thread) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +# 3S+ FSAL low storage methods: 3S methods adding another memory location for the embedded method (FSAL version) +function initialize!(integrator, cache::LowStorageRK3SpFSALConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +@muladd function perform_step!(integrator, cache::LowStorageRK3SpFSALConstantCache, + repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end, bhat1, bhat2end, bhatfsal = cache + + # u1 + tmp = uprev + u = tmp + β1 * dt * integrator.fsalfirst + if integrator.opts.adaptive + utilde = bhat1 * dt * integrator.fsalfirst + end + + # other stages + for i in eachindex(γ12end) + k = f(u, p, t + c2end[i] * dt) + integrator.stats.nf += 1 + tmp = tmp + δ2end[i] * u + u = γ12end[i] * u + γ22end[i] * tmp + γ32end[i] * uprev + β2end[i] * dt * k + if integrator.opts.adaptive + utilde = utilde + bhat2end[i] * dt * k + end + end + + # FSAL + integrator.fsallast = f(u, p, t + dt) + integrator.stats.nf += 1 + + if integrator.opts.adaptive + utilde = utilde + bhatfsal * dt * integrator.fsallast + atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.u = u +end + +function initialize!(integrator, cache::LowStorageRK3SpFSALCache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation + integrator.stats.nf += 1 +end + +@muladd function perform_step!(integrator, cache::LowStorageRK3SpFSALCache, + repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, tmp, utilde, atmp, stage_limiter!, step_limiter!, thread = cache + @unpack γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end, bhat1, bhat2end, bhatfsal = cache.tab + + # u1 + @.. broadcast=false thread=thread tmp=uprev + @.. broadcast=false thread=thread u=tmp + β1 * dt * integrator.fsalfirst + if integrator.opts.adaptive + @.. broadcast=false thread=thread utilde=bhat1 * dt * integrator.fsalfirst + end + + # other stages + for i in eachindex(γ12end) + stage_limiter!(u, integrator, p, t + c2end[i] * dt) + f(k, u, p, t + c2end[i] * dt) + integrator.stats.nf += 1 + @.. broadcast=false thread=thread tmp=tmp + δ2end[i] * u + @.. broadcast=false thread=thread u=γ12end[i] * u + γ22end[i] * tmp + + γ32end[i] * uprev + β2end[i] * dt * k + if integrator.opts.adaptive + @.. broadcast=false thread=thread utilde=utilde + bhat2end[i] * dt * k + end + end + + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + + # FSAL + f(k, u, p, t + dt) + integrator.stats.nf += 1 + + if integrator.opts.adaptive + @.. broadcast=false thread=thread utilde=utilde + bhatfsal * dt * k + calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t, + thread) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +# 2R+ low storage methods +function initialize!(integrator, cache::LowStorageRK2RPConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::LowStorageRK2RPConstantCache, + repeat_step = false) + @unpack t, dt, u, uprev, f, fsalfirst, p = integrator + @unpack Aᵢ, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ = cache + + k = fsalfirst + integrator.opts.adaptive && (tmp = zero(uprev)) + + #stages 1 to s-1 + for i in eachindex(Aᵢ) + integrator.opts.adaptive && (tmp = tmp + (Bᵢ[i] - B̂ᵢ[i]) * dt * k) + gprev = u + Aᵢ[i] * dt * k + u = u + Bᵢ[i] * dt * k + k = f(gprev, p, t + Cᵢ[i] * dt) + integrator.stats.nf += 1 + end + + #last stage + integrator.opts.adaptive && (tmp = tmp + (Bₗ - B̂ₗ) * dt * k) + u = u + Bₗ * dt * k + + #Error estimate + if integrator.opts.adaptive + atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + + integrator.k[1] = integrator.fsalfirst + integrator.fsallast = f(u, p, t + dt) # For interpolation, then FSAL'd + integrator.stats.nf += 1 + integrator.u = u +end + +function initialize!(integrator, cache::LowStorageRK2RPCache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) + integrator.stats.nf += 1 +end + +@muladd function perform_step!(integrator, cache::LowStorageRK2RPCache, repeat_step = false) + @unpack t, dt, u, uprev, f, fsalfirst, p = integrator + @unpack k, gprev, tmp, atmp, stage_limiter!, step_limiter!, thread = cache + @unpack Aᵢ, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ = cache.tab + + @.. broadcast=false thread=thread k=fsalfirst + integrator.opts.adaptive && (@.. broadcast=false tmp=zero(uprev)) + + #stages 1 to s-1 + for i in eachindex(Aᵢ) + integrator.opts.adaptive && + (@.. broadcast=false thread=thread tmp=tmp + (Bᵢ[i] - B̂ᵢ[i]) * dt * k) + @.. broadcast=false thread=thread gprev=u + Aᵢ[i] * dt * k + @.. broadcast=false thread=thread u=u + Bᵢ[i] * dt * k + f(k, gprev, p, t + Cᵢ[i] * dt) + integrator.stats.nf += 1 + end + + #last stage + integrator.opts.adaptive && + (@.. broadcast=false thread=thread tmp=tmp + (Bₗ - B̂ₗ) * dt * k) + @.. broadcast=false thread=thread u=u + Bₗ * dt * k + + #Error estimate + if integrator.opts.adaptive + calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t, + thread) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + + f(k, u, p, t + dt) + integrator.stats.nf += 1 +end + +# 3R+ low storage methods +function initialize!(integrator, cache::LowStorageRK3RPConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::LowStorageRK3RPConstantCache, + repeat_step = false) + @unpack t, dt, u, uprev, f, fsalfirst, p = integrator + @unpack Aᵢ₁, Aᵢ₂, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ = cache + + fᵢ₋₂ = zero(fsalfirst) + k = fsalfirst + uᵢ₋₁ = uprev + uᵢ₋₂ = uprev + integrator.opts.adaptive && (tmp = zero(uprev)) + + #stages 1 to s-1 + for i in eachindex(Aᵢ₁) + integrator.opts.adaptive && (tmp = tmp + (Bᵢ[i] - B̂ᵢ[i]) * dt * k) + gprev = uᵢ₋₂ + (Aᵢ₁[i] * k + Aᵢ₂[i] * fᵢ₋₂) * dt + u = u + Bᵢ[i] * dt * k + fᵢ₋₂ = k + uᵢ₋₂ = uᵢ₋₁ + uᵢ₋₁ = u + k = f(gprev, p, t + Cᵢ[i] * dt) + integrator.stats.nf += 1 + end + + #last stage + integrator.opts.adaptive && (tmp = tmp + (Bₗ - B̂ₗ) * dt * k) + u = u + Bₗ * dt * k + + #Error estimate + if integrator.opts.adaptive + atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + + integrator.k[1] = integrator.fsalfirst + integrator.fsallast = f(u, p, t + dt) # For interpolation, then FSAL'd + integrator.stats.nf += 1 + integrator.u = u +end + +function initialize!(integrator, cache::LowStorageRK3RPCache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) + integrator.stats.nf += 1 +end + +@muladd function perform_step!(integrator, cache::LowStorageRK3RPCache, repeat_step = false) + @unpack t, dt, u, uprev, f, fsalfirst, p = integrator + @unpack k, uᵢ₋₁, uᵢ₋₂, gprev, fᵢ₋₂, tmp, atmp, stage_limiter!, step_limiter!, thread = cache + @unpack Aᵢ₁, Aᵢ₂, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ = cache.tab + + @.. broadcast=false thread=thread fᵢ₋₂=zero(fsalfirst) + @.. broadcast=false thread=thread k=fsalfirst + integrator.opts.adaptive && (@.. broadcast=false thread=thread tmp=zero(uprev)) + @.. broadcast=false thread=thread uᵢ₋₁=uprev + @.. broadcast=false thread=thread uᵢ₋₂=uprev + + #stages 1 to s-1 + for i in eachindex(Aᵢ₁) + integrator.opts.adaptive && + (@.. broadcast=false thread=thread tmp=tmp + (Bᵢ[i] - B̂ᵢ[i]) * dt * k) + @.. broadcast=false thread=thread gprev=uᵢ₋₂ + (Aᵢ₁[i] * k + Aᵢ₂[i] * fᵢ₋₂) * dt + @.. broadcast=false thread=thread u=u + Bᵢ[i] * dt * k + @.. broadcast=false thread=thread fᵢ₋₂=k + @.. broadcast=false thread=thread uᵢ₋₂=uᵢ₋₁ + @.. broadcast=false thread=thread uᵢ₋₁=u + f(k, gprev, p, t + Cᵢ[i] * dt) + integrator.stats.nf += 1 + end + + #last stage + integrator.opts.adaptive && + (@.. broadcast=false thread=thread tmp=tmp + (Bₗ - B̂ₗ) * dt * k) + @.. broadcast=false thread=thread u=u + Bₗ * dt * k + + #Error estimate + if integrator.opts.adaptive + calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t, + thread) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + + f(k, u, p, t + dt) + integrator.stats.nf += 1 +end + +# 4R+ low storage methods +function initialize!(integrator, cache::LowStorageRK4RPConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::LowStorageRK4RPConstantCache, + repeat_step = false) + @unpack t, dt, u, uprev, f, fsalfirst, p = integrator + @unpack Aᵢ₁, Aᵢ₂, Aᵢ₃, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ = cache + + fᵢ₋₂ = zero(fsalfirst) + fᵢ₋₃ = zero(fsalfirst) + k = fsalfirst + uᵢ₋₁ = uprev + uᵢ₋₂ = uprev + uᵢ₋₃ = uprev + integrator.opts.adaptive && (tmp = zero(uprev)) + + #stages 1 to s-1 + for i in eachindex(Aᵢ₁) + integrator.opts.adaptive && (tmp = tmp + (Bᵢ[i] - B̂ᵢ[i]) * dt * k) + gprev = uᵢ₋₃ + (Aᵢ₁[i] * k + Aᵢ₂[i] * fᵢ₋₂ + Aᵢ₃[i] * fᵢ₋₃) * dt + u = u + Bᵢ[i] * dt * k + fᵢ₋₃ = fᵢ₋₂ + fᵢ₋₂ = k + uᵢ₋₃ = uᵢ₋₂ + uᵢ₋₂ = uᵢ₋₁ + uᵢ₋₁ = u + k = f(gprev, p, t + Cᵢ[i] * dt) + integrator.stats.nf += 1 + end + + #last stage + integrator.opts.adaptive && (tmp = tmp + (Bₗ - B̂ₗ) * dt * k) + u = u + Bₗ * dt * k + + #Error estimate + if integrator.opts.adaptive + atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + + integrator.k[1] = integrator.fsalfirst + integrator.fsallast = f(u, p, t + dt) # For interpolation, then FSAL'd + integrator.stats.nf += 1 + integrator.u = u +end + +function initialize!(integrator, cache::LowStorageRK4RPCache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) + integrator.stats.nf += 1 +end + +@muladd function perform_step!(integrator, cache::LowStorageRK4RPCache, repeat_step = false) + @unpack t, dt, u, uprev, f, fsalfirst, p = integrator + @unpack k, uᵢ₋₁, uᵢ₋₂, uᵢ₋₃, gprev, fᵢ₋₂, fᵢ₋₃, tmp, atmp, stage_limiter!, step_limiter!, thread = cache + @unpack Aᵢ₁, Aᵢ₂, Aᵢ₃, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ = cache.tab + + @.. broadcast=false thread=thread fᵢ₋₂=zero(fsalfirst) + @.. broadcast=false thread=thread fᵢ₋₃=zero(fsalfirst) + @.. broadcast=false thread=thread k=fsalfirst + integrator.opts.adaptive && (@.. broadcast=false thread=thread tmp=zero(uprev)) + @.. broadcast=false thread=thread uᵢ₋₁=uprev + @.. broadcast=false thread=thread uᵢ₋₂=uprev + @.. broadcast=false thread=thread uᵢ₋₃=uprev + + #stages 1 to s-1 + for i in eachindex(Aᵢ₁) + integrator.opts.adaptive && + (@.. broadcast=false thread=thread tmp=tmp + (Bᵢ[i] - B̂ᵢ[i]) * dt * k) + @.. broadcast=false thread=thread gprev=uᵢ₋₃ + + (Aᵢ₁[i] * k + Aᵢ₂[i] * fᵢ₋₂ + + Aᵢ₃[i] * fᵢ₋₃) * + dt + @.. broadcast=false thread=thread u=u + Bᵢ[i] * dt * k + @.. broadcast=false thread=thread fᵢ₋₃=fᵢ₋₂ + @.. broadcast=false thread=thread fᵢ₋₂=k + @.. broadcast=false thread=thread uᵢ₋₃=uᵢ₋₂ + @.. broadcast=false thread=thread uᵢ₋₂=uᵢ₋₁ + @.. broadcast=false thread=thread uᵢ₋₁=u + f(k, gprev, p, t + Cᵢ[i] * dt) + integrator.stats.nf += 1 + end + + #last stage + integrator.opts.adaptive && + (@.. broadcast=false thread=thread tmp=tmp + (Bₗ - B̂ₗ) * dt * k) + @.. broadcast=false thread=thread u=u + Bₗ * dt * k + + #Error estimate + if integrator.opts.adaptive + calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t, + thread) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + + f(k, u, p, t + dt) + integrator.stats.nf += 1 +end + +# 5R+ low storage methods +function initialize!(integrator, cache::LowStorageRK5RPConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::LowStorageRK5RPConstantCache, + repeat_step = false) + @unpack t, dt, u, uprev, f, fsalfirst, p = integrator + @unpack Aᵢ₁, Aᵢ₂, Aᵢ₃, Aᵢ₄, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ = cache + + fᵢ₋₂ = zero(fsalfirst) + fᵢ₋₃ = zero(fsalfirst) + fᵢ₋₄ = zero(fsalfirst) + k = fsalfirst + uᵢ₋₁ = uprev + uᵢ₋₂ = uprev + uᵢ₋₃ = uprev + uᵢ₋₄ = uprev + integrator.opts.adaptive && (tmp = zero(uprev)) + + #stages 1 to s-1 + for i in eachindex(Aᵢ₁) + integrator.opts.adaptive && (tmp = tmp + (Bᵢ[i] - B̂ᵢ[i]) * dt * k) + gprev = uᵢ₋₄ + (Aᵢ₁[i] * k + Aᵢ₂[i] * fᵢ₋₂ + Aᵢ₃[i] * fᵢ₋₃ + Aᵢ₄[i] * fᵢ₋₄) * dt + u = u + Bᵢ[i] * dt * k + fᵢ₋₄ = fᵢ₋₃ + fᵢ₋₃ = fᵢ₋₂ + fᵢ₋₂ = k + uᵢ₋₄ = uᵢ₋₃ + uᵢ₋₃ = uᵢ₋₂ + uᵢ₋₂ = uᵢ₋₁ + uᵢ₋₁ = u + k = f(gprev, p, t + Cᵢ[i] * dt) + integrator.stats.nf += 1 + end + + #last stage + integrator.opts.adaptive && (tmp = tmp + (Bₗ - B̂ₗ) * dt * k) + u = u + Bₗ * dt * k + + #Error estimate + if integrator.opts.adaptive + atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + + integrator.k[1] = integrator.fsalfirst + integrator.fsallast = f(u, p, t + dt) # For interpolation, then FSAL'd + integrator.stats.nf += 1 + integrator.u = u +end + +function initialize!(integrator, cache::LowStorageRK5RPCache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) + integrator.stats.nf += 1 +end + +@muladd function perform_step!(integrator, cache::LowStorageRK5RPCache, repeat_step = false) + @unpack t, dt, u, uprev, f, fsalfirst, p = integrator + @unpack k, uᵢ₋₁, uᵢ₋₂, uᵢ₋₃, uᵢ₋₄, gprev, fᵢ₋₂, fᵢ₋₃, fᵢ₋₄, tmp, atmp, stage_limiter!, step_limiter!, thread = cache + @unpack Aᵢ₁, Aᵢ₂, Aᵢ₃, Aᵢ₄, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ = cache.tab + + @.. broadcast=false thread=thread fᵢ₋₂=zero(fsalfirst) + @.. broadcast=false thread=thread fᵢ₋₃=zero(fsalfirst) + @.. broadcast=false thread=thread fᵢ₋₄=zero(fsalfirst) + @.. broadcast=false thread=thread k=fsalfirst + integrator.opts.adaptive && (@.. broadcast=false thread=thread tmp=zero(uprev)) + @.. broadcast=false thread=thread uᵢ₋₁=uprev + @.. broadcast=false thread=thread uᵢ₋₂=uprev + @.. broadcast=false thread=thread uᵢ₋₃=uprev + @.. broadcast=false thread=thread uᵢ₋₄=uprev + + #stages 1 to s-1 + for i in eachindex(Aᵢ₁) + integrator.opts.adaptive && + (@.. broadcast=false thread=thread tmp=tmp + (Bᵢ[i] - B̂ᵢ[i]) * dt * k) + @.. broadcast=false thread=thread gprev=uᵢ₋₄ + + (Aᵢ₁[i] * k + Aᵢ₂[i] * fᵢ₋₂ + + Aᵢ₃[i] * fᵢ₋₃ + + Aᵢ₄[i] * fᵢ₋₄) * dt + @.. broadcast=false thread=thread u=u + Bᵢ[i] * dt * k + @.. broadcast=false thread=thread fᵢ₋₄=fᵢ₋₃ + @.. broadcast=false thread=thread fᵢ₋₃=fᵢ₋₂ + @.. broadcast=false thread=thread fᵢ₋₂=k + @.. broadcast=false thread=thread uᵢ₋₄=uᵢ₋₃ + @.. broadcast=false thread=thread uᵢ₋₃=uᵢ₋₂ + @.. broadcast=false thread=thread uᵢ₋₂=uᵢ₋₁ + @.. broadcast=false thread=thread uᵢ₋₁=u + f(k, gprev, p, t + Cᵢ[i] * dt) + integrator.stats.nf += 1 + end + + #last stage + integrator.opts.adaptive && + (@.. broadcast=false thread=thread tmp=tmp + (Bₗ - B̂ₗ) * dt * k) + @.. broadcast=false thread=thread u=u + Bₗ * dt * k + + #Error estimate + if integrator.opts.adaptive + calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t, + thread) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + + f(k, u, p, t + dt) + integrator.stats.nf += 1 +end diff --git a/src/perform_step/rkc_perform_step.jl b/src/perform_step/rkc_perform_step.jl new file mode 100644 index 0000000000..d96ce34b59 --- /dev/null +++ b/src/perform_step/rkc_perform_step.jl @@ -0,0 +1,1296 @@ +function initialize!(integrator, cache::ROCK2ConstantCache) + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + alg = unwrap_alg(integrator, true) + cache.max_stage = (alg.max_stages < 1 || alg.max_stages > 200) ? 200 : alg.max_stages + cache.min_stage = (alg.min_stages > cache.max_stage) ? cache.max_stage : alg.min_stages + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +@muladd function perform_step!(integrator, cache::ROCK2ConstantCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p, fsalfirst = integrator + @unpack ms, fp1, fp2, recf = cache + alg = unwrap_alg(integrator, true) + alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) + # The the number of degree for Chebyshev polynomial + mdeg = Int(floor(sqrt((1.5 + abs(dt) * integrator.eigen_est) / 0.811) + 1)) + mdeg = min(max(mdeg, cache.min_stage), cache.max_stage) + cache.mdeg = max(mdeg, 3) - 2 + choosedeg!(cache) + # recurrence + # for the first stage + tᵢ₋₁ = t + dt * recf[cache.start] + tᵢ₋₂ = t + dt * recf[cache.start] + tᵢ₋₃ = t + uᵢ₋₂ = copy(uprev) + uᵢ₋₁ = uprev + (dt * recf[cache.start]) * fsalfirst + cache.mdeg < 2 && (u = uᵢ₋₁) + # for the second to the ms[cache.mdeg] th stages + for i in 2:(cache.mdeg) + μ, κ = recf[cache.start + (i - 2) * 2 + 1], recf[cache.start + (i - 2) * 2 + 2] + ν = -1 - κ + u = f(uᵢ₋₁, p, tᵢ₋₁) + tᵢ₋₁ = dt * μ - ν * tᵢ₋₂ - κ * tᵢ₋₃ + u = (dt * μ) * u - ν * uᵢ₋₁ - κ * uᵢ₋₂ + i < cache.mdeg && (uᵢ₋₂ = uᵢ₋₁; + uᵢ₋₁ = u) + tᵢ₋₃ = tᵢ₋₂ + tᵢ₋₂ = tᵢ₋₁ + end # end if + # two-stage finishing procedure. + δt₁ = dt * fp1[cache.deg_index] + δt₂ = dt * fp2[cache.deg_index] + uᵢ₋₂ = f(u, p, tᵢ₋₁) + integrator.stats.nf += 1 + uᵢ₋₁ = u + δt₁ * uᵢ₋₂ + tᵢ₋₁ += δt₁ + u = f(uᵢ₋₁, p, tᵢ₋₁) + integrator.stats.nf += 1 + + if integrator.opts.adaptive + tmp = δt₂ * (u - uᵢ₋₂) + u = uᵢ₋₁ + δt₁ * u + tmp + else + u = uᵢ₋₁ + δt₁ * u + δt₂ * (u - uᵢ₋₂) + end + # error estimate + if integrator.opts.adaptive + atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast = f(u, p, t + dt) + integrator.stats.nf += 1 + integrator.u = u +end + +function initialize!(integrator, cache::ROCK2Cache) + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.fsalfirst = cache.fsalfirst # done by pointers, no copying + integrator.fsallast = cache.k + alg = unwrap_alg(integrator, true) + cache.constantcache.max_stage = (alg.max_stages < 1 || alg.max_stages > 200) ? 200 : + alg.max_stages + cache.constantcache.min_stage = (alg.min_stages > cache.constantcache.max_stage) ? + cache.constantcache.max_stage : alg.min_stages + + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 +end + +@muladd function perform_step!(integrator, cache::ROCK2Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p, fsalfirst = integrator + @unpack k, tmp, uᵢ₋₂, uᵢ₋₁, atmp = cache + @unpack ms, fp1, fp2, recf = cache.constantcache + ccache = cache.constantcache + alg = unwrap_alg(integrator, true) + alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) + # The the number of degree for Chebyshev polynomial + mdeg = Int(floor(sqrt((1.5 + abs(dt) * integrator.eigen_est) / 0.811) + 1)) + mdeg = min(max(mdeg, ccache.min_stage), ccache.max_stage) + ccache.mdeg = max(mdeg, 3) - 2 + choosedeg!(cache) + # recurrence + # for the first stage + tᵢ₋₁ = t + dt * recf[ccache.start] + tᵢ₋₂ = t + dt * recf[ccache.start] + tᵢ₋₃ = t + @.. broadcast=false uᵢ₋₂=uprev + @.. broadcast=false uᵢ₋₁=uprev + (dt * recf[ccache.start]) * fsalfirst + ccache.mdeg < 2 && (@.. broadcast=false u=uᵢ₋₁) + # for the second to the ms[ccache.mdeg] th stages + for i in 2:(ccache.mdeg) + μ, κ = recf[ccache.start + (i - 2) * 2 + 1], recf[ccache.start + (i - 2) * 2 + 2] + ν = -1 - κ + f(k, uᵢ₋₁, p, tᵢ₋₁) + tᵢ₋₁ = dt * μ - ν * tᵢ₋₂ - κ * tᵢ₋₃ + @.. broadcast=false u=(dt * μ) * k - ν * uᵢ₋₁ - κ * uᵢ₋₂ + if i < ccache.mdeg + @.. broadcast=false uᵢ₋₂=uᵢ₋₁ + @.. broadcast=false uᵢ₋₁=u + end + tᵢ₋₃ = tᵢ₋₂ + tᵢ₋₂ = tᵢ₋₁ + end # end if + # two-stage finishing procedure. + δt₁ = dt * fp1[ccache.deg_index] + δt₂ = dt * fp2[ccache.deg_index] + f(k, u, p, tᵢ₋₁) + integrator.stats.nf += 1 + @.. broadcast=false uᵢ₋₁=u + δt₁ * k + if integrator.opts.adaptive + @.. broadcast=false tmp=-δt₂ * k + else + @.. broadcast=false u=-δt₂ * k + end + c = DiffEqBase.value(sign(δt₁)) * integrator.opts.internalnorm(δt₁, t) + tᵢ₋₁ += c + f(k, uᵢ₋₁, p, tᵢ₋₁) + integrator.stats.nf += 1 + + if integrator.opts.adaptive + @.. broadcast=false tmp+=δt₂ * k + @.. broadcast=false u=uᵢ₋₁ + δt₁ * k + tmp + else + @.. broadcast=false u+=uᵢ₋₁ + (δt₁ + δt₂) * k + end + + # error estimate + if integrator.opts.adaptive + calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.k[1] = integrator.fsalfirst + f(integrator.fsallast, u, p, t + dt) + integrator.stats.nf += 1 + integrator.k[2] = integrator.fsallast + integrator.u = u +end + +function initialize!(integrator, cache::ROCK4ConstantCache) + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + alg = unwrap_alg(integrator, true) + cache.max_stage = (alg.max_stages < 1 || alg.max_stages > 152) ? 152 : alg.max_stages + cache.min_stage = (alg.min_stages > cache.max_stage) ? cache.max_stage : alg.min_stages + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +@muladd function perform_step!(integrator, cache::ROCK4ConstantCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p, fsalfirst = integrator + @unpack ms, fpa, fpb, fpbe, recf = cache + alg = unwrap_alg(integrator, true) + alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) + # The the number of degree for Chebyshev polynomial + mdeg = Int(floor(sqrt((3 + abs(dt) * integrator.eigen_est) / 0.353) + 1)) + mdeg = min(max(mdeg, cache.min_stage), cache.max_stage) + cache.mdeg = max(mdeg, 5) - 4 + choosedeg!(cache) + # recurrence + # for the first stage + tᵢ₋₁ = t + dt * recf[cache.start] + tᵢ₋₂ = t + dt * recf[cache.start] + tᵢ₋₃ = t + uᵢ₋₂ = copy(uprev) + uᵢ₋₁ = uprev + (dt * recf[cache.start]) * fsalfirst + cache.mdeg < 2 && (u = uᵢ₋₁) + # for the second to the cache.mdeg th stages + for i in 2:(cache.mdeg) + μ, κ = recf[cache.start + (i - 2) * 2 + 1], recf[cache.start + (i - 2) * 2 + 2] + ν = -1 - κ + u = f(uᵢ₋₁, p, tᵢ₋₁) + tᵢ₋₁ = dt * μ - ν * tᵢ₋₂ - κ * tᵢ₋₃ + u = (dt * μ) * u - ν * uᵢ₋₁ - κ * uᵢ₋₂ + i < cache.mdeg && (uᵢ₋₂ = uᵢ₋₁; + uᵢ₋₁ = u) + tᵢ₋₃ = tᵢ₋₂ + tᵢ₋₂ = tᵢ₋₁ + end + + # These constants correspond to the Buther Tableau coefficients of explicit RK methods + a₂₁ = dt * fpa[cache.deg_index][1] + a₃₁ = dt * fpa[cache.deg_index][2] + a₃₂ = dt * fpa[cache.deg_index][3] + a₄₁ = dt * fpa[cache.deg_index][4] + a₄₂ = dt * fpa[cache.deg_index][5] + a₄₃ = dt * fpa[cache.deg_index][6] + B₁ = dt * fpb[cache.deg_index][1] + B₂ = dt * fpb[cache.deg_index][2] + B₃ = dt * fpb[cache.deg_index][3] + B₄ = dt * fpb[cache.deg_index][4] + # coefficients of embedded method for error estimation + B̂₁ = dt * (fpbe[cache.deg_index][1] - fpb[cache.deg_index][1]) + B̂₂ = dt * (fpbe[cache.deg_index][2] - fpb[cache.deg_index][2]) + B̂₃ = dt * (fpbe[cache.deg_index][3] - fpb[cache.deg_index][3]) + B̂₄ = dt * (fpbe[cache.deg_index][4] - fpb[cache.deg_index][4]) + B̂₅ = dt * fpbe[cache.deg_index][5] + + # 4-stage finishing procedure. + # Stage-1 + uᵢ₋₁ = f(u, p, tᵢ₋₁) + integrator.stats.nf += 1 + uᵢ₋₂ = u + a₃₁ * uᵢ₋₁ + uᵢ₋₃ = u + a₄₁ * uᵢ₋₁ + u += B₁ * uᵢ₋₁ + integrator.opts.adaptive && (tmp = B̂₁ * uᵢ₋₁) + uᵢ₋₁ = u + (a₂₁ - B₁) * uᵢ₋₁ + + # Stage-2 + c₂ = a₂₁ + _c₂ = DiffEqBase.value(sign(c₂)) * integrator.opts.internalnorm(c₂, t) + tᵢ₋₂ = tᵢ₋₁ + _c₂ + uᵢ₋₁ = f(uᵢ₋₁, p, tᵢ₋₂) + integrator.stats.nf += 1 + uᵢ₋₂ += a₃₂ * uᵢ₋₁ + uᵢ₋₃ += a₄₂ * uᵢ₋₁ + u += B₂ * uᵢ₋₁ + integrator.opts.adaptive && (tmp += B̂₂ * uᵢ₋₁) + + # Stage-3 + c₃ = a₃₁ + a₃₂ + _c₃ = DiffEqBase.value(sign(c₃)) * integrator.opts.internalnorm(c₃, t) + tᵢ₋₂ = tᵢ₋₁ + _c₃ + uᵢ₋₂ = f(uᵢ₋₂, p, tᵢ₋₂) + integrator.stats.nf += 1 + uᵢ₋₃ += a₄₃ * uᵢ₋₂ + u += B₃ * uᵢ₋₂ + integrator.opts.adaptive && (tmp += B̂₃ * uᵢ₋₂) + + #Stage-4 + c₄ = a₄₁ + a₄₂ + a₄₃ + _c₄ = DiffEqBase.value(sign(c₄)) * integrator.opts.internalnorm(c₄, t) + tᵢ₋₂ = tᵢ₋₁ + _c₄ + uᵢ₋₃ = f(uᵢ₋₃, p, tᵢ₋₂) + integrator.stats.nf += 1 + u += B₄ * uᵢ₋₃ + integrator.opts.adaptive && (tmp += B̂₄ * uᵢ₋₃) + + uᵢ₋₁ = f(u, p, t + dt) + integrator.stats.nf += 1 + + #Error estimate (embedded method of order 3) + if integrator.opts.adaptive + tmp += B̂₅ * uᵢ₋₁ + atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast = uᵢ₋₁ + integrator.u = u +end + +function initialize!(integrator, cache::ROCK4Cache) + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.fsalfirst = cache.fsalfirst + integrator.fsallast = cache.k + alg = unwrap_alg(integrator, true) + cache.constantcache.max_stage = (alg.max_stages < 1 || alg.max_stages > 152) ? 152 : + alg.max_stages + cache.constantcache.min_stage = (alg.min_stages > cache.constantcache.max_stage) ? + cache.constantcache.max_stage : alg.min_stages + + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) + integrator.stats.nf += 1 +end + +@muladd function perform_step!(integrator, cache::ROCK4Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p, fsalfirst = integrator + @unpack uᵢ₋₁, uᵢ₋₂, uᵢ₋₃, tmp, atmp, k = cache + @unpack ms, fpa, fpb, fpbe, recf = cache.constantcache + ccache = cache.constantcache + alg = unwrap_alg(integrator, true) + alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) + # The the number of degree for Chebyshev polynomial + mdeg = Int(floor(sqrt((3 + abs(dt) * integrator.eigen_est) / 0.353) + 1)) + mdeg = min(max(mdeg, ccache.min_stage), ccache.max_stage) + ccache.mdeg = max(mdeg, 5) - 4 + choosedeg!(cache) + # recurrence + # for the first stage + tᵢ₋₁ = t + dt * recf[ccache.start] + tᵢ₋₂ = t + dt * recf[ccache.start] + tᵢ₋₃ = t + @.. broadcast=false uᵢ₋₂=uprev + @.. broadcast=false uᵢ₋₁=uprev + (dt * recf[ccache.start]) * fsalfirst + ccache.mdeg < 2 && (@.. broadcast=false u=uᵢ₋₁) + # for the second to the ccache.mdeg th stages + for i in 2:(ccache.mdeg) + μ, κ = recf[ccache.start + (i - 2) * 2 + 1], recf[ccache.start + (i - 2) * 2 + 2] + ν = -1 - κ + f(k, uᵢ₋₁, p, tᵢ₋₁) + tᵢ₋₁ = (dt * μ) - ν * tᵢ₋₂ - κ * tᵢ₋₃ + @.. broadcast=false u=(dt * μ) * k - ν * uᵢ₋₁ - κ * uᵢ₋₂ + if i < ccache.mdeg + @.. broadcast=false uᵢ₋₂=uᵢ₋₁ + @.. broadcast=false uᵢ₋₁=u + end + tᵢ₋₃ = tᵢ₋₂ + tᵢ₋₂ = tᵢ₋₁ + end + + # These constants correspond to the Buther Tableau coefficients of explicit RK methods + a₂₁ = dt * fpa[ccache.deg_index][1] + a₃₁ = dt * fpa[ccache.deg_index][2] + a₃₂ = dt * fpa[ccache.deg_index][3] + a₄₁ = dt * fpa[ccache.deg_index][4] + a₄₂ = dt * fpa[ccache.deg_index][5] + a₄₃ = dt * fpa[ccache.deg_index][6] + B₁ = dt * fpb[ccache.deg_index][1] + B₂ = dt * fpb[ccache.deg_index][2] + B₃ = dt * fpb[ccache.deg_index][3] + B₄ = dt * fpb[ccache.deg_index][4] + # coefficients of embedded method for error estimation + B̂₁ = dt * (fpbe[ccache.deg_index][1] - fpb[ccache.deg_index][1]) + B̂₂ = dt * (fpbe[ccache.deg_index][2] - fpb[ccache.deg_index][2]) + B̂₃ = dt * (fpbe[ccache.deg_index][3] - fpb[ccache.deg_index][3]) + B̂₄ = dt * (fpbe[ccache.deg_index][4] - fpb[ccache.deg_index][4]) + B̂₅ = dt * fpbe[ccache.deg_index][5] + + # 4-stage finishing procedure. + # Stage-1 + + f(k, u, p, tᵢ₋₁) + integrator.stats.nf += 1 + @.. broadcast=false uᵢ₋₂=u + a₃₁ * k + @.. broadcast=false uᵢ₋₃=u + a₄₁ * k + @.. broadcast=false uᵢ₋₁=u + a₂₁ * k + @.. broadcast=false u+=B₁ * k + integrator.opts.adaptive && (@.. broadcast=false tmp=B̂₁ * k) + + # Stage-2 + c₂ = a₂₁ + _c₂ = DiffEqBase.value(sign(c₂)) * integrator.opts.internalnorm(c₂, t) + tᵢ₋₂ = tᵢ₋₁ + _c₂ + f(k, uᵢ₋₁, p, tᵢ₋₂) + integrator.stats.nf += 1 + @.. broadcast=false uᵢ₋₂+=a₃₂ * k + @.. broadcast=false uᵢ₋₃+=a₄₂ * k + @.. broadcast=false u+=B₂ * k + integrator.opts.adaptive && (@.. broadcast=false tmp+=B̂₂ * k) + + # Stage-3 + c₃ = a₃₁ + a₃₂ + _c₃ = DiffEqBase.value(sign(c₃)) * integrator.opts.internalnorm(c₃, t) + tᵢ₋₂ = tᵢ₋₁ + _c₃ + f(k, uᵢ₋₂, p, tᵢ₋₂) + integrator.stats.nf += 1 + @.. broadcast=false uᵢ₋₃+=a₄₃ * k + @.. broadcast=false u+=B₃ * k + integrator.opts.adaptive && (@.. broadcast=false tmp+=B̂₃ * k) + + #Stage-4 + c₄ = a₄₁ + a₄₂ + a₄₃ + _c₄ = DiffEqBase.value(sign(c₄)) * integrator.opts.internalnorm(c₄, t) + tᵢ₋₂ = tᵢ₋₁ + _c₄ + f(k, uᵢ₋₃, p, tᵢ₋₂) + integrator.stats.nf += 1 + @.. broadcast=false u+=B₄ * k + integrator.opts.adaptive && (tmp += B̂₄ * k) + + f(k, u, p, t + dt) + integrator.stats.nf += 1 + + #Error estimate (embedded method of order 3) + if integrator.opts.adaptive + tmp += B̂₅ * k + calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + @.. broadcast=false integrator.fsallast=k + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.u = u +end + +function initialize!(integrator, cache::RKCConstantCache) + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +@muladd function perform_step!(integrator, cache::RKCConstantCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p, fsalfirst = integrator + alg = unwrap_alg(integrator, true) + alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) + # The the number of degree for Chebyshev polynomial + #maxm = max(2,Int(floor(sqrt(integrator.opts.internalnorm(integrator.opts.reltol,t)/(10*eps(integrator.opts.internalnorm(uprev,t))))))) + maxm = 50 + mdeg = 1 + Int(floor(sqrt(1.54 * abs(dt) * integrator.eigen_est + 1))) + mdeg = (mdeg > maxm) ? maxm : mdeg + + w0 = 1 + 2 / (13 * (mdeg^2)) + temp1 = w0^2 - 1 + temp2 = sqrt(temp1) + arg = mdeg * log(w0 + temp2) + w1 = (sinh(arg) * temp1) / (cosh(arg) * mdeg * temp2 - w0 * sinh(arg)) + b1 = 1 / ((2 * w0)^2) + b2 = b1 + + # stage-1 + gprev2 = copy(uprev) + μs = w1 * b1 + gprev = uprev + dt * μs * fsalfirst + th2 = zero(eltype(u)) + th1 = μs + z1 = w0 + z2 = one(eltype(u)) + dz1 = one(eltype(u)) + dz2 = zero(eltype(u)) + d2z1 = zero(eltype(u)) + d2z2 = zero(eltype(u)) + + # stage 2 - mdeg + for iter in 2:mdeg + z = 2 * w0 * z1 - z2 + dz = 2 * w0 * dz1 - dz2 + 2 * z1 + d2z = 2 * w0 * d2z1 - d2z2 + 4 * dz1 + b = d2z / (dz^2) + νs = 1 - z1 * b1 + μ = (2 * w0 * b) / b1 + ν = -b / b2 + μs = μ * w1 / w0 + #using u as temporary storage + u = f(gprev, p, t + dt * th1) + integrator.stats.nf += 1 + u = μ * gprev + ν * gprev2 + (1 - μ - ν) * uprev + dt * μs * (u - νs * fsalfirst) + th = μ * th1 + ν * th2 + μs * (1 - νs) + if (iter < mdeg) + gprev2 = gprev + gprev = u + th2 = th1 + th1 = th + b2 = b1 + b1 = b + z2 = z1 + z1 = z + dz2 = dz1 + dz1 = dz + d2z2 = d2z1 + d2z1 = d2z + end + end + # error estimate + if integrator.opts.adaptive + tmp = 0.8 * (uprev - u) + 0.4 * dt * (fsalfirst + gprev) + atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast = f(u, p, t + dt) + integrator.stats.nf += 1 + integrator.u = u +end + +function initialize!(integrator, cache::RKCCache) + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.fsalfirst = cache.fsalfirst # done by pointers, no copying + integrator.fsallast = cache.k + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 +end + +@muladd function perform_step!(integrator, cache::RKCCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p, fsalfirst = integrator + @unpack k, tmp, gprev2, gprev, atmp = cache + alg = unwrap_alg(integrator, true) + alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) + # The the number of degree for Chebyshev polynomial + #maxm = max(2,Int(floor(sqrt(integrator.opts.internalnorm(integrator.opts.reltol,t)/10eps(t))))) + maxm = 50 + mdeg = 1 + Int(floor(sqrt(1.54 * abs(dt) * integrator.eigen_est + 1))) + mdeg = (mdeg > maxm) ? maxm : mdeg + + w0 = 1 + 2 / (13 * (mdeg^2)) + temp1 = w0^2 - 1 + temp2 = sqrt(temp1) + arg = mdeg * log(w0 + temp2) + w1 = (sinh(arg) * temp1) / (cosh(arg) * mdeg * temp2 - w0 * sinh(arg)) + b1 = 1 / ((2 * w0)^2) + b2 = b1 + + # stage-1 + @.. broadcast=false gprev2=uprev + μs = w1 * b1 + @.. broadcast=false gprev=uprev + dt * μs * fsalfirst + th2 = zero(eltype(u)) + th1 = μs + z1 = w0 + z2 = one(eltype(u)) + dz1 = one(eltype(u)) + dz2 = zero(eltype(u)) + d2z1 = zero(eltype(u)) + d2z2 = zero(eltype(u)) + + # stage 2 - mdeg + for iter in 2:mdeg + z = 2 * w0 * z1 - z2 + dz = 2 * w0 * dz1 - dz2 + 2 * z1 + d2z = 2 * w0 * d2z1 - d2z2 + 4 * dz1 + b = d2z / (dz^2) + νs = 1 - z1 * b1 + μ = (2 * w0 * b) / b1 + ν = -b / b2 + μs = μ * w1 / w0 + f(k, gprev, p, t + dt * th1) + integrator.stats.nf += 1 + @.. broadcast=false u=μ * gprev + ν * gprev2 + (1 - μ - ν) * uprev + + dt * μs * (k - νs * fsalfirst) + th = μ * th1 + ν * th2 + μs * (1 - νs) + if (iter < mdeg) + gprev2 = gprev + gprev = u + th2 = th1 + th1 = th + b2 = b1 + b1 = b + z2 = z1 + z1 = z + dz2 = dz1 + dz1 = dz + d2z2 = d2z1 + d2z1 = d2z + end + end + # error estimate + if integrator.opts.adaptive + @.. broadcast=false tmp=0.8 * (uprev - u) + 0.4 * dt * (fsalfirst + gprev) + calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.k[1] = integrator.fsalfirst + f(integrator.fsallast, u, p, t + dt) + integrator.stats.nf += 1 + integrator.k[2] = integrator.fsallast + integrator.u = u +end + +function initialize!(integrator, cache::IRKCConstantCache) + @unpack uprev, p, t = integrator + @unpack f1, f2 = integrator.f + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + cache.du₁ = f1(uprev, p, t) + cache.du₂ = f2(uprev, p, t) + integrator.stats.nf += 1 + integrator.stats.nf2 += 1 + integrator.fsalfirst = cache.du₁ + cache.du₂ + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +function perform_step!(integrator, cache::IRKCConstantCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p, fsalfirst = integrator + @unpack minm, du₁, du₂, nlsolver = cache + @unpack f1, f2 = integrator.f + alg = unwrap_alg(integrator, true) + alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) + + # The the number of degree for Chebyshev polynomial + #maxm = max(2,Int(floor(sqrt(integrator.opts.internalnorm(integrator.opts.reltol,t)/(10 *eps(integrator.opts.internalnorm(uprev,t))))))) + maxm = 50 + mdeg = 1 + floor(Int, sqrt(1.54 * abs(dt) * integrator.eigen_est + 1)) + mdeg = min(maxm, max(minm, mdeg)) + + ω₀ = 1 + 2 / (13 * (mdeg^2)) + temp₁ = ω₀^2 - 1 + temp₂ = sqrt(temp₁) + θ = mdeg * log(ω₀ + temp₂) + ω₁ = (sinh(θ) * temp₁) / (cosh(θ) * mdeg * temp₂ - ω₀ * sinh(θ)) + Bⱼ₋₂ = 1 / (4 * ω₀^2) + Bⱼ₋₁ = 1 / ω₀ + + #stage-1 + f1ⱼ₋₂ = du₁ + gprev2 = copy(uprev) + μs = ω₁ * Bⱼ₋₁ + μs₁ = μs + + # initial guess for implicit part + # if alg.extrapolant == :linear + # nlsolver.z = dt*du₁ + # else # :constant + # nlsolver.z = zero(u) + # end + + nlsolver.z = dt * du₁ + + nlsolver.tmp = uprev + dt * μs₁ * du₂ + nlsolver.γ = μs₁ + nlsolver.c = μs + markfirststage!(nlsolver) + z = nlsolve!(nlsolver, integrator, cache, false) + # nlsolvefail(nlsolver) && return + gprev = nlsolver.tmp + μs₁ * z + + Cⱼ₋₂ = zero(eltype(u)) + Cⱼ₋₁ = μs + Tⱼ₋₁ = ω₀ + Tⱼ₋₂ = one(eltype(u)) + Tⱼ₋₁′ = one(eltype(u)) + Tⱼ₋₂′ = zero(eltype(u)) + Tⱼ₋₁″ = zero(eltype(u)) + Tⱼ₋₂″ = zero(eltype(u)) + + #stage- 2...mdeg + for iter in 2:mdeg + Tⱼ = 2 * ω₀ * Tⱼ₋₁ - Tⱼ₋₂ + Tⱼ′ = 2 * ω₀ * Tⱼ₋₁′ + 2 * Tⱼ₋₁ - Tⱼ₋₂′ + Tⱼ″ = 2 * ω₀ * Tⱼ₋₁″ + 4 * Tⱼ₋₁′ - Tⱼ₋₂″ + Bⱼ = Tⱼ″ / (Tⱼ′^2) + μ = (2 * ω₀ * Bⱼ) / Bⱼ₋₁ + ν = -Bⱼ / Bⱼ₋₂ + μs = (μ * ω₁) / ω₀ + νs = -(1 - Tⱼ₋₁ * Bⱼ₋₁) * μs + Cⱼ = μ * Cⱼ₋₁ + ν * Cⱼ₋₂ + μs + νs + + f1ⱼ₋₁ = f1(gprev, p, t + Cⱼ₋₁ * dt) + f2ⱼ₋₁ = f2(gprev, p, t + Cⱼ₋₁ * dt) + integrator.stats.nf += 1 + integrator.stats.nf2 += 1 + nlsolver.tmp = (1 - μ - ν) * uprev + μ * gprev + ν * gprev2 + dt * μs * f2ⱼ₋₁ + + dt * νs * du₂ + (νs - (1 - μ - ν) * μs₁) * dt * du₁ - + ν * μs₁ * dt * f1ⱼ₋₂ + nlsolver.z = dt * f1ⱼ₋₁ + nlsolver.c = Cⱼ + z = nlsolve!(nlsolver, integrator, cache, false) + # ignoring newton method's convergence failure + # nlsolvefail(nlsolver) && return + u = nlsolver.tmp + μs₁ * z + if (iter < mdeg) + f1ⱼ₋₂ = f1ⱼ₋₁ + gprev2 = gprev + gprev = u + Cⱼ₋₂ = Cⱼ₋₁ + Cⱼ₋₁ = Cⱼ + Bⱼ₋₂ = Bⱼ₋₁ + Bⱼ₋₁ = Bⱼ + Tⱼ₋₂ = Tⱼ₋₁ + Tⱼ₋₁ = Tⱼ + Tⱼ₋₂′ = Tⱼ₋₁′ + Tⱼ₋₁′ = Tⱼ′ + Tⱼ₋₂″ = Tⱼ₋₁″ + Tⱼ₋₁″ = Tⱼ″ + end + end + + cache.du₁ = f1(u, p, t + dt) + cache.du₂ = f2(u, p, t + dt) + integrator.stats.nf += 1 + integrator.stats.nf2 += 1 + # error estimate + if isnewton(nlsolver) && integrator.opts.adaptive + update_W!(integrator, cache, dt, false) + tmp = dt * (0.5 * (cache.du₂ - du₂) + (0.5 - μs₁) * (cache.du₁ - du₁)) + tmp = _reshape(get_W(nlsolver) \ _vec(tmp), axes(tmp)) + atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + + integrator.fsallast = cache.du₁ + cache.du₂ + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.u = u +end + +function initialize!(integrator, cache::IRKCCache) + @unpack uprev, p, t = integrator + @unpack f1, f2 = integrator.f + integrator.kshortsize = 2 + integrator.fsalfirst = cache.fsalfirst + integrator.fsallast = du_alias_or_new(cache.nlsolver, integrator.fsalfirst) + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + f1(cache.du₁, uprev, p, t) + f2(cache.du₂, uprev, p, t) + integrator.stats.nf += 1 + integrator.stats.nf2 += 1 + @.. broadcast=false integrator.fsalfirst=cache.du₁ + cache.du₂ +end + +function perform_step!(integrator, cache::IRKCCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack gprev, gprev2, f1ⱼ₋₁, f1ⱼ₋₂, f2ⱼ₋₁, du₁, du₂, atmp, nlsolver = cache + @unpack tmp, z = nlsolver + @unpack minm = cache.constantcache + @unpack f1, f2 = integrator.f + + alg = unwrap_alg(integrator, true) + alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) + # The the number of degree for Chebyshev polynomial + #maxm = max(2,int(floor(sqrt(integrator.opts.internalnorm(integrator.opts.reltol,t)/(10 *eps(integrator.opts.internalnorm(uprev,t))))))) + maxm = 50 + mdeg = 1 + Int(floor(sqrt(1.54 * abs(dt) * integrator.eigen_est + 1))) + mdeg = (mdeg < minm) ? minm : mdeg + mdeg = (mdeg >= maxm) ? maxm : mdeg + + ω₀ = 1 + 2 / (13 * (mdeg^2)) + temp₁ = ω₀^2 - 1 + temp₂ = sqrt(temp₁) + θ = mdeg * log(ω₀ + temp₂) + ω₁ = (sinh(θ) * temp₁) / (cosh(θ) * mdeg * temp₂ - ω₀ * sinh(θ)) + Bⱼ₋₂ = 1 / (4 * ω₀^2) + Bⱼ₋₁ = 1 / ω₀ + + #stage-1 + f1ⱼ₋₂ = du₁ + @.. broadcast=false gprev2=uprev + μs = ω₁ * Bⱼ₋₁ + μs₁ = μs + + # initial guess + # if alg.extrapolant == :linear + # @.. broadcast=false z = dt*du₁ + # else # :constant + # @.. broadcast=false z = zero(eltype(u)) + # end + @.. broadcast=false nlsolver.z=dt * du₁ + + @.. broadcast=false nlsolver.tmp=uprev + dt * μs₁ * du₂ + nlsolver.γ = μs₁ + nlsolver.c = μs + markfirststage!(nlsolver) + z = nlsolve!(nlsolver, integrator, cache, false) + # ignoring newton method's convergence failure + # nlsolvefail(nlsolver) && return + @.. broadcast=false gprev=nlsolver.tmp + μs₁ * nlsolver.z + + Cⱼ₋₂ = zero(eltype(u)) + Cⱼ₋₁ = μs + Tⱼ₋₁ = ω₀ + Tⱼ₋₂ = one(eltype(u)) + Tⱼ₋₁′ = one(eltype(u)) + Tⱼ₋₂′ = zero(eltype(u)) + Tⱼ₋₁″ = zero(eltype(u)) + Tⱼ₋₂″ = zero(eltype(u)) + + #stage- 2...mdeg + for iter in 2:mdeg + Tⱼ = 2 * ω₀ * Tⱼ₋₁ - Tⱼ₋₂ + Tⱼ′ = 2 * ω₀ * Tⱼ₋₁′ + 2 * Tⱼ₋₁ - Tⱼ₋₂′ + Tⱼ″ = 2 * ω₀ * Tⱼ₋₁″ + 4 * Tⱼ₋₁′ - Tⱼ₋₂″ + Bⱼ = Tⱼ″ / (Tⱼ′^2) + μ = (2 * ω₀ * Bⱼ) / Bⱼ₋₁ + ν = -Bⱼ / Bⱼ₋₂ + μs = (μ * ω₁) / ω₀ + νs = -(1 - Tⱼ₋₁ * Bⱼ₋₁) * μs + Cⱼ = μ * Cⱼ₋₁ + ν * Cⱼ₋₂ + μs + νs + + f1(f1ⱼ₋₁, gprev, p, t + Cⱼ₋₁ * dt) + f2(f2ⱼ₋₁, gprev, p, t + Cⱼ₋₁ * dt) + integrator.stats.nf += 1 + integrator.stats.nf2 += 1 + @.. broadcast=false nlsolver.tmp=(1 - μ - ν) * uprev + μ * gprev + ν * gprev2 + + dt * μs * f2ⱼ₋₁ + dt * νs * du₂ + + (νs - (1 - μ - ν) * μs₁) * dt * du₁ - + ν * μs₁ * dt * f1ⱼ₋₂ + @.. broadcast=false nlsolver.z=dt * f1ⱼ₋₁ + nlsolver.c = Cⱼ + + z = nlsolve!(nlsolver, integrator, cache, false) + # nlsolvefail(nlsolver) && return + @.. broadcast=false u=nlsolver.tmp + μs₁ * nlsolver.z + if (iter < mdeg) + @.. broadcast=false f1ⱼ₋₂=f1ⱼ₋₁ + @.. broadcast=false gprev2=gprev + @.. broadcast=false gprev=u + Cⱼ₋₂ = Cⱼ₋₁ + Cⱼ₋₁ = Cⱼ + Bⱼ₋₂ = Bⱼ₋₁ + Bⱼ₋₁ = Bⱼ + Tⱼ₋₂ = Tⱼ₋₁ + Tⱼ₋₁ = Tⱼ + Tⱼ₋₂′ = Tⱼ₋₁′ + Tⱼ₋₁′ = Tⱼ′ + Tⱼ₋₂″ = Tⱼ₋₁″ + Tⱼ₋₁″ = Tⱼ″ + end + end + + @.. broadcast=false f1ⱼ₋₁=du₁ + @.. broadcast=false f2ⱼ₋₁=du₂ + f1(du₁, u, p, t + dt) + f2(du₂, u, p, t + dt) + integrator.stats.nf += 1 + integrator.stats.nf2 += 1 + # error estimate + if isnewton(nlsolver) && integrator.opts.adaptive + update_W!(integrator, cache, dt, false) + @.. broadcast=false gprev=dt * 0.5 * (du₂ - f2ⱼ₋₁) + + dt * (0.5 - μs₁) * (du₁ - f1ⱼ₋₁) + + linsolve = nlsolver.cache.linsolve + linres = dolinsolve(integrator, linsolve; b = _vec(gprev), linu = _vec(tmp)) + + calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + + @.. broadcast=false integrator.fsallast=du₁ + du₂ + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.u = u +end + +function initialize!(integrator, cache::ESERK4ConstantCache) + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +@muladd function perform_step!(integrator, cache::ESERK4ConstantCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p, fsalfirst = integrator + @unpack ms, Cᵤ, Cₑ = cache + alg = unwrap_alg(integrator, true) + alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) + + mdeg = Int(floor(sqrt(abs(dt) * integrator.eigen_est)) + 1) + mdeg = (mdeg > 4000) ? 4000 : mdeg + cache.mdeg = mdeg + choosedeg_SERK!(integrator, cache) + mdeg = cache.mdeg + start = cache.start + internal_deg = cache.internal_deg + α = 2.0 / (mdeg^2) + + u = zero(uprev) + tmp = zero(uprev) + + for i in 1:4 + hᵢ = dt / i + tᵢ = t + Sᵢ = zero(u) + uᵢ₋₁ = uprev + uᵢ₋₂ = zero(u) + for j in 1:i + r = tᵢ + Sᵢ = (cache.Bᵢ[start]) * uᵢ₋₁ + for st in 1:mdeg + k = f(uᵢ₋₁, p, r) + integrator.stats.nf += 1 + + if st % internal_deg == 1 + uᵢ = uᵢ₋₁ + α * hᵢ * k + else + uᵢ = 2 * uᵢ₋₁ - uᵢ₋₂ + 2 * α * hᵢ * k + end + q = convert(Int, floor(st / internal_deg)) + r = tᵢ + α * (st^2 + q * internal_deg^2) * hᵢ + Sᵢ = Sᵢ + (cache.Bᵢ[start + st]) * uᵢ + if st < mdeg + uᵢ₋₂ = uᵢ₋₁ + uᵢ₋₁ = uᵢ + end + end + + if j < i + tᵢ = tᵢ + hᵢ + uᵢ₋₁ = Sᵢ + end + end + + u = u + Cᵤ[i] * Sᵢ + integrator.opts.adaptive && (tmp = tmp + Cₑ[i] * Sᵢ) + end + + u = u / 6 + if integrator.opts.adaptive + tmp = tmp / 6 + atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast = f(u, p, t + dt) + integrator.stats.nf += 1 + integrator.u = u +end + +function initialize!(integrator, cache::ESERK4Cache) + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.fsalfirst = cache.fsalfirst + integrator.fsallast = cache.k + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) + integrator.stats.nf += 1 +end + +@muladd function perform_step!(integrator, cache::ESERK4Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p, fsalfirst = integrator + @unpack uᵢ, uᵢ₋₁, uᵢ₋₂, Sᵢ, tmp, atmp, k = cache + @unpack ms, Cᵤ, Cₑ = cache.constantcache + ccache = cache.constantcache + alg = unwrap_alg(integrator, true) + alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) + + mdeg = Int(floor(sqrt(abs(dt) * integrator.eigen_est)) + 1) + mdeg = (mdeg > 4000) ? 4000 : mdeg + ccache.mdeg = mdeg + choosedeg_SERK!(integrator, cache) + mdeg = ccache.mdeg + start = ccache.start + internal_deg = ccache.internal_deg + α = 2.0 / (mdeg^2) + + @.. broadcast=false u=zero(uprev) + @.. broadcast=false tmp=zero(uprev) + for i in 1:4 + hᵢ = dt / i + tᵢ = t + @.. broadcast=false Sᵢ=zero(u) + @.. broadcast=false uᵢ₋₁=uprev + @.. broadcast=false uᵢ₋₂=zero(u) + for j in 1:i + r = tᵢ + @.. broadcast=false Sᵢ=(cache.constantcache.Bᵢ[start]) * uᵢ₋₁ + for st in 1:mdeg + f(k, uᵢ₋₁, p, r) + integrator.stats.nf += 1 + + if st % internal_deg == 1 + @.. broadcast=false uᵢ=uᵢ₋₁ + α * hᵢ * k + else + @.. broadcast=false uᵢ=2 * uᵢ₋₁ - uᵢ₋₂ + 2 * α * hᵢ * k + end + q = convert(Int, floor(st / internal_deg)) + r = tᵢ + α * (st^2 + q * internal_deg^2) * hᵢ + @.. broadcast=false Sᵢ=Sᵢ + (cache.constantcache.Bᵢ[start + st]) * uᵢ + if st < mdeg + @.. broadcast=false uᵢ₋₂=uᵢ₋₁ + @.. broadcast=false uᵢ₋₁=uᵢ + end + end + + if j < i + tᵢ = tᵢ + hᵢ + @.. broadcast=false uᵢ₋₁=Sᵢ + end + end + + @.. broadcast=false u=u + Cᵤ[i] * Sᵢ + integrator.opts.adaptive && (@.. broadcast=false tmp=tmp + Cₑ[i] * Sᵢ) + end + + @.. broadcast=false u=u / 6 + + if integrator.opts.adaptive + @.. broadcast=false tmp=tmp / 6 + calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.k[1] = integrator.fsalfirst + f(integrator.fsallast, u, p, t + dt) + integrator.stats.nf += 1 + integrator.k[2] = integrator.fsallast + integrator.u = u +end + +function initialize!(integrator, cache::ESERK5ConstantCache) + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +@muladd function perform_step!(integrator, cache::ESERK5ConstantCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p, fsalfirst = integrator + @unpack ms, Cᵤ, Cₑ, Bᵢ = cache + alg = unwrap_alg(integrator, true) + alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) + + mdeg = Int(floor(sqrt(abs(dt) * integrator.eigen_est / 0.98)) + 1) + mdeg = (mdeg > 2000) ? 2000 : mdeg + cache.mdeg = mdeg + choosedeg_SERK!(integrator, cache) + mdeg = cache.mdeg + start = cache.start + internal_deg = cache.internal_deg + α = 100.0 / (49.0 * mdeg^2) + + u = zero(uprev) + tmp = zero(uprev) + for i in 1:5 + hᵢ = dt / i + tᵢ = t + Sᵢ = zero(u) + uᵢ₋₁ = uprev + uᵢ₋₂ = zero(u) + for j in 1:i + r = tᵢ + Sᵢ = (Bᵢ[start]) * uᵢ₋₁ + for st in 1:mdeg + k = f(uᵢ₋₁, p, r) + integrator.stats.nf += 1 + + if st % internal_deg == 1 + uᵢ = uᵢ₋₁ + α * hᵢ * k + else + uᵢ = 2 * uᵢ₋₁ - uᵢ₋₂ + 2 * α * hᵢ * k + end + q = convert(Int, floor(st / internal_deg)) + r = tᵢ + α * (st^2 + q * internal_deg^2) * hᵢ + Sᵢ = Sᵢ + (Bᵢ[start + st]) * uᵢ + if st < mdeg + uᵢ₋₂ = uᵢ₋₁ + uᵢ₋₁ = uᵢ + end + end + + if j < i + tᵢ = tᵢ + hᵢ + uᵢ₋₁ = Sᵢ + end + end + + u = u + Cᵤ[i] * Sᵢ + integrator.opts.adaptive && (tmp = tmp + Cₑ[i] * Sᵢ) + end + + u = u / 24 + if integrator.opts.adaptive + tmp = tmp / 24 + atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast = f(u, p, t + dt) + integrator.stats.nf += 1 + integrator.u = u +end + +function initialize!(integrator, cache::ESERK5Cache) + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.fsalfirst = cache.fsalfirst + integrator.fsallast = cache.k + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) + integrator.stats.nf += 1 +end + +@muladd function perform_step!(integrator, cache::ESERK5Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p, fsalfirst = integrator + @unpack uᵢ, uᵢ₋₁, uᵢ₋₂, Sᵢ, tmp, atmp, k = cache + @unpack ms, Cᵤ, Cₑ, Bᵢ = cache.constantcache + ccache = cache.constantcache + alg = unwrap_alg(integrator, true) + alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) + + mdeg = Int(floor(sqrt(abs(dt) * integrator.eigen_est / 0.98)) + 1) + mdeg = (mdeg > 2000) ? 2000 : mdeg + ccache.mdeg = mdeg + choosedeg_SERK!(integrator, cache) + mdeg = ccache.mdeg + start = ccache.start + internal_deg = ccache.internal_deg + α = 100.0 / (49.0 * mdeg^2) + + @.. broadcast=false u=zero(uprev) + @.. broadcast=false tmp=zero(uprev) + for i in 1:5 + hᵢ = dt / i + tᵢ = t + @.. broadcast=false Sᵢ=zero(u) + @.. broadcast=false uᵢ₋₁=uprev + @.. broadcast=false uᵢ₋₂=zero(u) + for j in 1:i + r = tᵢ + @.. broadcast=false Sᵢ=(Bᵢ[start]) * uᵢ₋₁ + for st in 1:mdeg + f(k, uᵢ₋₁, p, r) + integrator.stats.nf += 1 + + if st % internal_deg == 1 + @.. broadcast=false uᵢ=uᵢ₋₁ + α * hᵢ * k + else + @.. broadcast=false uᵢ=2 * uᵢ₋₁ - uᵢ₋₂ + 2 * α * hᵢ * k + end + q = convert(Int, floor(st / internal_deg)) + r = tᵢ + α * (st^2 + q * internal_deg^2) * hᵢ + @.. broadcast=false Sᵢ=Sᵢ + (Bᵢ[start + st]) * uᵢ + if st < mdeg + @.. broadcast=false uᵢ₋₂=uᵢ₋₁ + @.. broadcast=false uᵢ₋₁=uᵢ + end + end + + if j < i + tᵢ = tᵢ + hᵢ + @.. broadcast=false uᵢ₋₁=Sᵢ + end + end + + @.. broadcast=false u=u + Cᵤ[i] * Sᵢ + integrator.opts.adaptive && (@.. broadcast=false tmp=tmp + Cₑ[i] * Sᵢ) + end + + @.. broadcast=false u=u / 24 + + if integrator.opts.adaptive + @.. broadcast=false tmp=tmp / 24 + calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.k[1] = integrator.fsalfirst + f(integrator.fsallast, u, p, t + dt) + integrator.stats.nf += 1 + integrator.k[2] = integrator.fsallast + integrator.u = u +end + +function initialize!(integrator, cache::SERK2ConstantCache) + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +@muladd function perform_step!(integrator, cache::SERK2ConstantCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p, fsalfirst = integrator + @unpack ms, Bᵢ = cache + alg = unwrap_alg(integrator, true) + alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) + + mdeg = Int(floor(sqrt(abs(dt) * integrator.eigen_est / 0.8)) + 1) + mdeg = (mdeg > 250) ? 250 : mdeg + cache.mdeg = mdeg + choosedeg_SERK!(integrator, cache) + mdeg = cache.mdeg + start = cache.start + internal_deg = cache.internal_deg + α = 1.0 / (0.4 * mdeg^2) + + uᵢ₋₁ = uprev + uᵢ₋₂ = uprev + Sᵢ = Bᵢ[start] * uprev + for i in 1:10 + k = f(uᵢ₋₁, p, t + (1 + (i - 1) * internal_deg^2) * α * dt) + integrator.stats.nf += 1 + u = uᵢ₋₁ + α * dt * k + Sᵢ = Sᵢ + Bᵢ[start + (i - 1) * internal_deg + 1] * u + uᵢ₋₂ = uᵢ₋₁ + uᵢ₋₁ = u + for j in 2:internal_deg + k = f(uᵢ₋₁, p, t + (j^2 + (i - 1) * internal_deg^2) * α * dt) + integrator.stats.nf += 1 + u = 2 * uᵢ₋₁ - uᵢ₋₂ + 2 * α * dt * k + Sᵢ = Sᵢ + Bᵢ[start + j + (i - 1) * internal_deg] * u + if j * i < mdeg + uᵢ₋₂ = uᵢ₋₁ + uᵢ₋₁ = u + end + end + end + u = Sᵢ + k = f(u, p, t + dt) + integrator.stats.nf += 1 + + if integrator.opts.adaptive + tmp = u - uprev - dt * k + atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast = k + integrator.u = u +end + +function initialize!(integrator, cache::SERK2Cache) + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.fsalfirst = cache.fsalfirst + integrator.fsallast = cache.k + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) + integrator.stats.nf += 1 +end + +@muladd function perform_step!(integrator, cache::SERK2Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p, fsalfirst = integrator + @unpack uᵢ₋₁, uᵢ₋₂, Sᵢ, tmp, atmp, k = cache + @unpack ms, Bᵢ = cache.constantcache + ccache = cache.constantcache + alg = unwrap_alg(integrator, true) + alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) + + mdeg = Int(floor(sqrt(abs(dt) * integrator.eigen_est / 0.8)) + 1) + mdeg = (mdeg > 250) ? 250 : mdeg + ccache.mdeg = mdeg + choosedeg_SERK!(integrator, cache) + mdeg = ccache.mdeg + start = ccache.start + internal_deg = ccache.internal_deg + α = 1.0 / (0.4 * mdeg^2) + + @.. broadcast=false uᵢ₋₁=uprev + @.. broadcast=false uᵢ₋₂=uprev + @.. broadcast=false Sᵢ=Bᵢ[start] * uprev + for i in 1:10 + f(k, uᵢ₋₁, p, t + (1 + (i - 1) * internal_deg^2) * α * dt) + integrator.stats.nf += 1 + @.. broadcast=false u=uᵢ₋₁ + α * dt * k + @.. broadcast=false Sᵢ=Sᵢ + Bᵢ[start + (i - 1) * internal_deg + 1] * u + @.. broadcast=false uᵢ₋₂=uᵢ₋₁ + @.. broadcast=false uᵢ₋₁=u + for j in 2:internal_deg + f(k, uᵢ₋₂, p, t + (j^2 + (i - 1) * internal_deg^2) * α * dt) + integrator.stats.nf += 1 + @.. broadcast=false u=2 * uᵢ₋₁ - uᵢ₋₂ + 2 * α * dt * k + @.. broadcast=false Sᵢ=Sᵢ + Bᵢ[start + j + (i - 1) * internal_deg] * u + if j < mdeg + @.. broadcast=false uᵢ₋₂=uᵢ₋₁ + @.. broadcast=false uᵢ₋₁=u + end + end + end + @.. broadcast=false u=Sᵢ + f(k, u, p, t + dt) + integrator.stats.nf += 1 + + if integrator.opts.adaptive + @.. broadcast=false tmp=u - uprev - dt * k + calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast = k + integrator.u = u +end diff --git a/src/perform_step/rkn_perform_step.jl b/src/perform_step/rkn_perform_step.jl new file mode 100644 index 0000000000..1c29dc53e4 --- /dev/null +++ b/src/perform_step/rkn_perform_step.jl @@ -0,0 +1,1821 @@ +## y'' = f(t, y, y') +## y(t₀) = y₀; y'(t₀) = y'₀ +## kᵢ' = f(t₀+cᵢh, y₀+cᵢhy'₀+h²∑āᵢⱼk'ⱼ, y'₀+h∑aᵢⱼk'ⱼ) +## y₁ = y₀ + hy'₀ + h²∑b̄ᵢk'ᵢ +## y'₁ = y'₀ + h∑bᵢk'ᵢ + +const NystromCCDefaultInitialization = Union{Nystrom4ConstantCache, FineRKN4ConstantCache, + FineRKN5ConstantCache, + Nystrom4VelocityIndependentConstantCache, + Nystrom5VelocityIndependentConstantCache, + IRKN3ConstantCache, IRKN4ConstantCache, + DPRKN4ConstantCache, DPRKN5ConstantCache, + DPRKN6FMConstantCache, DPRKN8ConstantCache, + DPRKN12ConstantCache, ERKN4ConstantCache, + ERKN5ConstantCache, ERKN7ConstantCache} + +function initialize!(integrator, cache::NystromCCDefaultInitialization) + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + duprev, uprev = integrator.uprev.x + kdu = integrator.f.f1(duprev, uprev, integrator.p, integrator.t) + ku = integrator.f.f2(duprev, uprev, integrator.p, integrator.t) + integrator.stats.nf += 1 + integrator.stats.nf2 += 1 + integrator.fsalfirst = ArrayPartition((kdu, ku)) +end + +const NystromDefaultInitialization = Union{Nystrom4Cache, FineRKN4Cache, FineRKN5Cache, + Nystrom4VelocityIndependentCache, + Nystrom5VelocityIndependentCache, + IRKN3Cache, IRKN4Cache, + DPRKN4Cache, DPRKN5Cache, + DPRKN6FMCache, DPRKN8Cache, + DPRKN12Cache, ERKN4Cache, + ERKN5Cache, ERKN7Cache} + +function initialize!(integrator, cache::NystromDefaultInitialization) + @unpack fsalfirst, k = cache + duprev, uprev = integrator.uprev.x + + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f.f1(integrator.k[1].x[1], duprev, uprev, integrator.p, integrator.t) + integrator.f.f2(integrator.k[1].x[2], duprev, uprev, integrator.p, integrator.t) + integrator.stats.nf += 1 + integrator.stats.nf2 += 1 +end + +@muladd function perform_step!(integrator, cache::Nystrom4ConstantCache, + repeat_step = false) + @unpack t, dt, f, p = integrator + duprev, uprev = integrator.uprev.x + k₁ = integrator.fsalfirst.x[1] + halfdt = dt / 2 + dtsq = dt^2 + eighth_dtsq = dtsq / 8 + half_dtsq = dtsq / 2 + ttmp = t + halfdt + + ## y₁ = y₀ + hy'₀ + h²∑b̄ᵢk'ᵢ + ku = uprev + halfdt * duprev + eighth_dtsq * k₁ + ## y'₁ = y'₀ + h∑bᵢk'ᵢ + kdu = duprev + halfdt * k₁ + + k₂ = f.f1(kdu, ku, p, ttmp) + ku = uprev + halfdt * duprev + eighth_dtsq * k₁ + kdu = duprev + halfdt * k₂ + + k₃ = f.f1(kdu, ku, p, ttmp) + ku = uprev + dt * duprev + half_dtsq * k₃ + kdu = duprev + dt * k₃ + + k₄ = f.f1(kdu, ku, p, t + dt) + u = uprev + (dtsq / 6) * (k₁ + k₂ + k₃) + dt * duprev + du = duprev + (dt / 6) * (k₁ + k₄ + 2 * (k₂ + k₃)) + + integrator.u = ArrayPartition((du, u)) + integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) + integrator.stats.nf += 4 + integrator.stats.nf2 += 1 + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +@muladd function perform_step!(integrator, cache::Nystrom4Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + du, u = integrator.u.x + duprev, uprev = integrator.uprev.x + @unpack tmp, fsalfirst, k₂, k₃, k₄, k = cache + kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] + k₁ = integrator.fsalfirst.x[1] + halfdt = dt / 2 + dtsq = dt^2 + eighth_dtsq = dtsq / 8 + half_dtsq = dtsq / 2 + ttmp = t + halfdt + + ## y₁ = y₀ + hy'₀ + h²∑b̄ᵢk'ᵢ + @.. broadcast=false ku=uprev + halfdt * duprev + eighth_dtsq * k₁ + ## y'₁ = y'₀ + h∑bᵢk'ᵢ + @.. broadcast=false kdu=duprev + halfdt * k₁ + + f.f1(k₂, kdu, ku, p, ttmp) + @.. broadcast=false ku=uprev + halfdt * duprev + eighth_dtsq * k₁ + @.. broadcast=false kdu=duprev + halfdt * k₂ + + f.f1(k₃, kdu, ku, p, ttmp) + @.. broadcast=false ku=uprev + dt * duprev + half_dtsq * k₃ + @.. broadcast=false kdu=duprev + dt * k₃ + + f.f1(k₄, kdu, ku, p, t + dt) + @.. broadcast=false u=uprev + (dtsq / 6) * (k₁ + k₂ + k₃) + dt * duprev + @.. broadcast=false du=duprev + (dt / 6) * (k₁ + k₄ + 2 * (k₂ + k₃)) + + f.f1(k.x[1], du, u, p, t + dt) + f.f2(k.x[2], du, u, p, t + dt) + integrator.stats.nf += 4 + integrator.stats.nf2 += 1 +end + +@muladd function perform_step!(integrator, cache::FineRKN4ConstantCache, + repeat_step = false) + @unpack t, dt, f, p = integrator + duprev, uprev = integrator.uprev.x + @unpack c2, c3, c4, c5, a21, a31, a32, a41, a43, a51, + a52, a53, a54, abar21, abar31, abar32, abar41, abar42, abar43, abar51, + abar52, abar53, abar54, b1, b3, b4, b5, bbar1, bbar3, bbar4, bbar5, btilde1, btilde3, btilde4, btilde5, bptilde1, + bptilde3, bptilde4, bptilde5 = cache + k1 = integrator.fsalfirst.x[1] + + ku = uprev + dt * (c2 * duprev + dt * (a21 * k1)) + kdu = duprev + dt * (abar21 * k1) + + k2 = f.f1(kdu, ku, p, t + dt * c2) + ku = uprev + dt * (c3 * duprev + dt * (a31 * k1 + a32 * k2)) + kdu = duprev + dt * (abar31 * k1 + abar32 * k2) + + k3 = f.f1(kdu, ku, p, t + dt * c3) + ku = uprev + dt * (c4 * duprev + dt * (a41 * k1 + a43 * k3)) # a42 = 0 + kdu = duprev + dt * (abar41 * k1 + abar42 * k2 + abar43 * k3) + + k4 = f.f1(kdu, ku, p, t + dt * c4) + ku = uprev + dt * (c5 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) + kdu = duprev + dt * (abar51 * k1 + abar52 * k2 + abar53 * k3 + abar54 * k4) + + k5 = f.f1(kdu, ku, p, t + dt * c5) + + u = uprev + dt * (duprev + dt * (b1 * k1 + b3 * k3 + b4 * k4 + b5 * k5)) # b2 = 0 + du = duprev + dt * (bbar1 * k1 + bbar3 * k3 + bbar4 * k4 + bbar5 * k5) # bbar2 = 0 + + integrator.u = ArrayPartition((du, u)) + integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) + integrator.stats.nf += 5 + integrator.stats.nf2 += 1 + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + + if integrator.opts.adaptive + dtsq = dt^2 + uhat = dtsq * (btilde1 * k1 + btilde3 * k3 + btilde4 * k4 + btilde5 * k5) # btilde2 = 0 + duhat = dt * (bptilde1 * k1 + bptilde3 * k3 + bptilde4 * k4 + bptilde5 * k5) # bptilde2 = 0 + utilde = ArrayPartition((duhat, uhat)) + atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +@muladd function perform_step!(integrator, cache::FineRKN4Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + du, u = integrator.u.x + duprev, uprev = integrator.uprev.x + @unpack tmp, atmp, fsalfirst, k2, k3, k4, k5, k, utilde = cache + @unpack c2, c3, c4, c5, a21, a31, a32, a41, a43, a51, + a52, a53, a54, abar21, abar31, abar32, abar41, abar42, abar43, abar51, + abar52, abar53, abar54, b1, b3, b4, b5, bbar1, bbar3, bbar4, bbar5, btilde1, btilde3, btilde4, btilde5, bptilde1, + bptilde3, bptilde4, bptilde5 = cache.tab + kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] + uidx = eachindex(integrator.uprev.x[2]) + k1 = integrator.fsalfirst.x[1] + + @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a21 * k1)) + @.. broadcast=false kdu=duprev + dt * (abar21 * k1) + + f.f1(k2, kdu, ku, p, t + dt * c2) + @.. broadcast=false ku=uprev + dt * (c3 * duprev + dt * (a31 * k1 + a32 * k2)) + @.. broadcast=false kdu=duprev + dt * (abar31 * k1 + abar32 * k2) + + f.f1(k3, kdu, ku, p, t + dt * c3) + @.. broadcast=false ku=uprev + + dt * (c4 * duprev + dt * (a41 * k1 + a43 * k3)) # a42 = 0 + @.. broadcast=false kdu=duprev + dt * (abar41 * k1 + abar42 * k2 + abar43 * k3) + + f.f1(k4, kdu, ku, p, t + dt * c4) + @.. broadcast=false ku=uprev + + dt * + (c5 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) + @.. broadcast=false kdu=duprev + + dt * (abar51 * k1 + abar52 * k2 + abar53 * k3 + abar54 * k4) + + f.f1(k5, kdu, ku, p, t + dt * c5) + @.. broadcast=false u=uprev + + dt * (duprev + dt * (b1 * k1 + b3 * k3 + b4 * k4 + b5 * k5)) # b2 = 0 + @.. broadcast=false du=duprev + + dt * + (bbar1 * k1 + bbar3 * k3 + bbar4 * k4 + bbar5 * k5) # bbar2 = 0 + + f.f1(k.x[1], du, u, p, t + dt) + f.f2(k.x[2], du, u, p, t + dt) + integrator.stats.nf += 5 + integrator.stats.nf2 += 1 + if integrator.opts.adaptive + duhat, uhat = utilde.x + dtsq = dt^2 + @.. broadcast=false uhat=dtsq * + (btilde1 * k1 + btilde3 * k3 + btilde4 * k4 + + btilde5 * k5) # btilde2 = 0 + @.. broadcast=false duhat=dt * + (bptilde1 * k1 + bptilde3 * k3 + bptilde4 * k4 + + bptilde5 * k5) # bptilde2 = 0 + + calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +@muladd function perform_step!(integrator, cache::FineRKN5ConstantCache, + repeat_step = false) + @unpack t, dt, f, p = integrator + duprev, uprev = integrator.uprev.x + @unpack c2, c3, c4, c5, c6, c7, a21, a31, a32, a41, a43, a51, a52, a53, a54, a61, a62, a63, a64, a71, a73, a74, a75, abar21, abar31, abar32, abar41, abar42, abar43, abar51, abar52, abar53, abar54, abar61, abar62, abar63, abar64, abar65, abar71, abar73, abar74, abar75, abar76, b1, b3, b4, b5, bbar1, bbar3, bbar4, bbar5, bbar6, btilde1, btilde3, btilde4, btilde5, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6, bptilde7 = cache + k1 = integrator.fsalfirst.x[1] + + ku = uprev + dt * (c2 * duprev + dt * (a21 * k1)) + kdu = duprev + dt * (abar21 * k1) + + k2 = f.f1(kdu, ku, p, t + dt * c2) + ku = uprev + dt * (c3 * duprev + dt * (a31 * k1 + a32 * k2)) + kdu = duprev + dt * (abar31 * k1 + abar32 * k2) + + k3 = f.f1(kdu, ku, p, t + dt * c3) + ku = uprev + dt * (c4 * duprev + dt * (a41 * k1 + a43 * k3)) # a42 = 0 + kdu = duprev + dt * (abar41 * k1 + abar42 * k2 + abar43 * k3) + + k4 = f.f1(kdu, ku, p, t + dt * c4) + ku = uprev + dt * (c5 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) + kdu = duprev + dt * (abar51 * k1 + abar52 * k2 + abar53 * k3 + abar54 * k4) + + k5 = f.f1(kdu, ku, p, t + dt * c5) + ku = uprev + + dt * (c6 * duprev + dt * (a61 * k1 + a62 * k2 + a63 * k3 + a64 * k4)) # a65 = 0 + kdu = duprev + + dt * (abar61 * k1 + abar62 * k2 + abar63 * k3 + abar64 * k4 + abar65 * k5) + + k6 = f.f1(kdu, ku, p, t + dt * c6) + ku = uprev + + dt * (c7 * duprev + + dt * (a71 * k1 + a73 * k3 + a74 * k4 + a75 * k5)) # a72 = a76 = 0 + kdu = duprev + + dt * (abar71 * k1 + abar73 * k3 + abar74 * k4 + abar75 * k5 + + abar76 * k6) # abar72 = 0 + + k7 = f.f1(kdu, ku, p, t + dt * c7) + u = uprev + dt * (duprev + dt * (b1 * k1 + b3 * k3 + b4 * k4 + b5 * k5)) # no b6, b7 + du = duprev + dt * (bbar1 * k1 + bbar3 * k3 + bbar4 * k4 + bbar5 * k5 + bbar6 * k6) # no b2, b7 + + integrator.u = ArrayPartition((du, u)) + integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) + integrator.stats.nf += 7 + integrator.stats.nf2 += 1 + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + + if integrator.opts.adaptive + dtsq = dt^2 + uhat = dtsq * (btilde1 * k1 + btilde3 * k3 + btilde4 * k4 + btilde5 * k5) + duhat = dt * (bptilde1 * k1 + bptilde3 * k3 + bptilde4 * k4 + bptilde5 * k5 + + bptilde6 * k6 + bptilde7 * k7) + utilde = ArrayPartition((duhat, uhat)) + atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +@muladd function perform_step!(integrator, cache::FineRKN5Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + du, u = integrator.u.x + duprev, uprev = integrator.uprev.x + @unpack tmp, atmp, fsalfirst, k2, k3, k4, k5, k6, k7, k, utilde = cache + @unpack c1, c2, c3, c4, c5, c6, c7, a21, a31, a32, a41, a43, a51, a52, a53, a54, a61, a62, a63, a64, a71, a73, a74, a75, abar21, abar31, abar32, abar41, abar42, abar43, abar51, abar52, abar53, abar54, abar61, abar62, abar63, abar64, abar65, abar71, abar73, abar74, abar75, abar76, b1, b3, b4, b5, bbar1, bbar3, bbar4, bbar5, bbar6, btilde1, btilde3, btilde4, btilde5, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6, bptilde7 = cache.tab + kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] + uidx = eachindex(integrator.uprev.x[2]) + k1 = integrator.fsalfirst.x[1] + + @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a21 * k1)) + @.. broadcast=false kdu=duprev + dt * (abar21 * k1) + + f.f1(k2, kdu, ku, p, t + dt * c2) + @.. broadcast=false ku=uprev + dt * (c3 * duprev + dt * (a31 * k1 + a32 * k2)) + @.. broadcast=false kdu=duprev + dt * (abar31 * k1 + abar32 * k2) + + f.f1(k3, kdu, ku, p, t + dt * c3) + @.. broadcast=false ku=uprev + + dt * (c4 * duprev + dt * (a41 * k1 + a43 * k3)) # a42 = 0 + @.. broadcast=false kdu=duprev + dt * (abar41 * k1 + abar42 * k2 + abar43 * k3) + + f.f1(k4, kdu, ku, p, t + dt * c4) + @.. broadcast=false ku=uprev + + dt * + (c5 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) + @.. broadcast=false kdu=duprev + + dt * (abar51 * k1 + abar52 * k2 + abar53 * k3 + abar54 * k4) + + f.f1(k5, kdu, ku, p, t + dt * c5) + @.. broadcast=false ku=uprev + + dt * (c6 * duprev + + dt * (a61 * k1 + a62 * k2 + a63 * k3 + a64 * k4)) # a65 = 0 + @.. broadcast=false kdu=duprev + + dt * (abar61 * k1 + abar62 * k2 + abar63 * k3 + abar64 * k4 + + abar65 * k5) + + f.f1(k6, kdu, ku, p, t + dt * c6) + @.. broadcast=false ku=uprev + + dt * (c7 * duprev + + dt * (a71 * k1 + a73 * k3 + a74 * k4 + a75 * k5)) # a72 = a76 = 0 + @.. broadcast=false kdu=duprev + + dt * (abar71 * k1 + abar73 * k3 + abar74 * k4 + + abar75 * k5 + abar76 * k6) # abar72 = 0 + + f.f1(k7, kdu, ku, p, t + dt * c7) + @.. broadcast=false u=uprev + + dt * (duprev + dt * (b1 * k1 + b3 * k3 + b4 * k4 + b5 * k5)) + @.. broadcast=false du=duprev + + dt * + (bbar1 * k1 + bbar3 * k3 + bbar4 * k4 + bbar5 * k5 + bbar6 * k6) + + f.f1(k.x[1], du, u, p, t + dt) + f.f2(k.x[2], du, u, p, t + dt) + integrator.stats.nf += 7 + integrator.stats.nf2 += 1 + if integrator.opts.adaptive + duhat, uhat = utilde.x + dtsq = dt^2 + @.. broadcast=false uhat=dtsq * + (btilde1 * k1 + btilde3 * k3 + btilde4 * k4 + + btilde5 * k5) + @.. broadcast=false duhat=dt * + (bptilde1 * k1 + bptilde3 * k3 + bptilde4 * k4 + + bptilde5 * k5 + bptilde6 * k6 + bptilde7 * k7) + + calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +@muladd function perform_step!(integrator, cache::Nystrom4VelocityIndependentConstantCache, + repeat_step = false) + @unpack t, dt, f, p = integrator + duprev, uprev = integrator.uprev.x + k₁ = integrator.fsalfirst.x[1] + halfdt = dt / 2 + dtsq = dt^2 + eighth_dtsq = dtsq / 8 + half_dtsq = dtsq / 2 + ttmp = t + halfdt + + ## y₁ = y₀ + hy'₀ + h²∑b̄ᵢk'ᵢ + ku = uprev + halfdt * duprev + eighth_dtsq * k₁ + + k₂ = f.f1(duprev, ku, p, ttmp) + ku = uprev + dt * duprev + half_dtsq * k₂ + + k₃ = f.f1(duprev, ku, p, t + dt) + u = uprev + (dtsq / 6) * (k₁ + 2 * k₂) + dt * duprev + du = duprev + (dt / 6) * (k₁ + k₃ + 4 * k₂) + + integrator.u = ArrayPartition((du, u)) + integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) + integrator.stats.nf += 3 + integrator.stats.nf2 += 1 + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +@muladd function perform_step!(integrator, cache::Nystrom4VelocityIndependentCache, + repeat_step = false) + @unpack t, dt, f, p = integrator + du, u = integrator.u.x + duprev, uprev = integrator.uprev.x + @unpack tmp, fsalfirst, k₂, k₃, k = cache + kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] + k₁ = integrator.fsalfirst.x[1] + halfdt = dt / 2 + dtsq = dt^2 + eighth_dtsq = dtsq / 8 + half_dtsq = dtsq / 2 + ttmp = t + halfdt + + ## y₁ = y₀ + hy'₀ + h²∑b̄ᵢk'ᵢ + @.. broadcast=false ku=uprev + halfdt * duprev + eighth_dtsq * k₁ + + f.f1(k₂, duprev, ku, p, ttmp) + @.. broadcast=false ku=uprev + dt * duprev + half_dtsq * k₂ + + f.f1(k₃, duprev, ku, p, t + dt) + @.. broadcast=false u=uprev + (dtsq / 6) * (k₁ + 2 * k₂) + dt * duprev + @.. broadcast=false du=duprev + (dt / 6) * (k₁ + k₃ + 4 * k₂) + + f.f1(k.x[1], du, u, p, t + dt) + f.f2(k.x[2], du, u, p, t + dt) + integrator.stats.nf += 3 + integrator.stats.nf2 += 1 +end + +@muladd function perform_step!(integrator, cache::IRKN3ConstantCache, repeat_step = false) + @unpack t, dt, k, tprev, f, p = integrator + duprev, uprev = integrator.uprev.x + duprev2, uprev2 = integrator.uprev2.x + @unpack bconst1, bconst2, c1, a21, b1, b2, bbar1, bbar2 = cache + k₁ = integrator.fsalfirst + # if there's a discontinuity or the solver is in the first step + if integrator.iter < 2 && !integrator.u_modified + perform_step!(integrator, Nystrom4VelocityIndependentConstantCache()) + k = integrator.fsallast + k1cache = ArrayPartition((k.x[1], f.f1(duprev, uprev, p, t + c1 * dt))) + kdu = uprev + dt * (c1 * duprev + dt * a21 * k1cache.x[1]) + k₂.x[1] = f.f1(duprev, kdu, p, t + c1 * dt) + integrator.stats.nf += 2 + else + kdu = uprev2 + dt * (c1 * duprev2 + dt * a21 * k1cache.x[1]) + ku = uprev + dt * (c1 * duprev + dt * a21 * k1cache.x[2]) + + k₂x1 = f.f1(duprev, ku, p, t + c1 * dt) + du = duprev + + dt * (b1 * k1cache.x[1] + bbar1 * k1cache.x[1] + b2 * (k₂x1 - k₂.x[1])) + u = uprev + bconst1 * dt * duprev + + dt * (bconst2 * duprev2 + dt * bbar2 * (k₂x1 - k₂.x[1])) + + integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), + f.f2(du, u, p, t + dt))) + integrator.stats.nf += 3 + integrator.stats.nf2 += 1 + copyto!(k₂.x[1], k₂.x[2]) + k1cache = ArrayPartition((k1cache.x[1], k.x[2])) + end # end if +end + +@muladd function perform_step!(integrator, cache::IRKN3Cache, repeat_step = false) + @unpack t, dt, k, tprev, f, p = integrator + du, u = integrator.u.x + duprev, uprev = integrator.uprev.x + duprev2, uprev2 = integrator.uprev2.x + uidx = eachindex(integrator.uprev.x[1]) + @unpack tmp, fsalfirst, k₂, k = cache + @unpack bconst1, bconst2, c1, a21, b1, b2, bbar1, bbar2 = cache.tab + kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] + k1cache = cache.tmp2 + k₁ = fsalfirst + # if there's a discontinuity or the solver is in the first step + if integrator.iter < 2 && !integrator.u_modified + perform_step!(integrator, integrator.cache.onestep_cache) + copyto!(k1cache.x[1], k.x[1]) + f.f1(k1cache.x[2], duprev, uprev, p, t + c1 * dt) + @.. broadcast=false kdu=uprev + dt * (c1 * duprev + dt * a21 * k1cache.x[2]) + f.f1(k₂.x[1], duprev, kdu, p, t + c1 * dt) + integrator.stats.nf += 2 + else + @.. broadcast=false kdu=uprev2 + dt * (c1 * duprev2 + dt * a21 * k1cache.x[1]) + @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1cache.x[2]) + + f.f1(k₂.x[2], duprev, ku, p, t + c1 * dt) + @tight_loop_macros for i in uidx + @inbounds u[i] = uprev[i] + bconst1 * dt * duprev[i] + + dt * + (bconst2 * duprev2[i] + dt * bbar2 * (k₂.x[2][i] - k₂.x[1][i])) + @inbounds du[i] = duprev[i] + + dt * (b1 * k1cache.x[1][i] + bbar1 * k1cache.x[2][i] + + b2 * (k₂.x[2][i] - k₂.x[1][i])) + end + f.f1(k.x[1], du, u, p, t + dt) + f.f2(k.x[2], du, u, p, t + dt) + integrator.stats.nf += 3 + integrator.stats.nf2 += 1 + copyto!(k₂.x[1], k₂.x[2]) + copyto!(k1cache.x[2], k1cache.x[1]) + copyto!(k1cache.x[1], k.x[1]) + end # end if +end + +@muladd function perform_step!(integrator, cache::IRKN4Cache, repeat_step = false) + @unpack t, dt, k, tprev, f, p = integrator + du, u = integrator.u.x + duprev, uprev = integrator.uprev.x + duprev2, uprev2 = integrator.uprev2.x + uidx = eachindex(integrator.uprev.x[1]) + @unpack tmp, tmp2, fsalfirst, k₂, k₃, k = cache + @unpack bconst1, bconst2, c1, c2, a21, a32, b1, b2, b3, bbar1, bbar2, bbar3 = cache.tab + kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] + k1cache = integrator.cache.tmp2 + k₁ = fsalfirst + # if there's a discontinuity or the solver is in the first step + if integrator.iter < 2 && !integrator.u_modified + perform_step!(integrator, integrator.cache.onestep_cache) + copyto!(k1cache.x[1], k.x[1]) + f.f1(k1cache.x[2], duprev, uprev, p, t + c1 * dt) + @.. broadcast=false kdu=uprev + dt * (c1 * duprev + dt * a21 * k1cache.x[1]) + f.f1(k₂.x[1], duprev, kdu, p, t + c1 * dt) + @.. broadcast=false kdu=uprev + dt * (c2 * duprev + dt * a32 * k1cache.x[2]) + f.f1(k₃.x[1], duprev, kdu, p, t + c1 * dt) + integrator.stats.nf += 3 + else + @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1cache.x[1]) + @.. broadcast=false kdu=uprev2 + dt * (c1 * duprev2 + dt * a21 * k1cache.x[2]) + + f.f1(k₂.x[2], duprev, ku, p, t + c1 * dt) + @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * a32 * k₂.x[2]) + @.. broadcast=false kdu=uprev2 + dt * (c2 * duprev2 + dt * a32 * k₂.x[1]) + + f.f1(k₃.x[2], duprev, ku, p, t + c2 * dt) + @tight_loop_macros for i in uidx + @inbounds u[i] = uprev[i] + dt * bconst1 * duprev[i] + + dt * (bconst2 * duprev2[i] + + dt * (bbar2 * (k₂.x[2][i] - k₂.x[1][i]) + + bbar3 * (k₃.x[2][i] - k₃.x[1][i]))) + @inbounds du[i] = duprev[i] + + dt * (b1 * k1cache.x[1][i] + bbar1 * k1cache.x[2][i] + + b2 * (k₂.x[2][i] - k₂.x[1][i]) + + b3 * (k₃.x[2][i] - k₃.x[1][i])) + end + f.f1(k.x[1], du, u, p, t + dt) + f.f2(k.x[2], du, u, p, t + dt) + integrator.stats.nf += 4 + integrator.stats.nf2 += 1 + copyto!(k₂.x[1], k₂.x[2]) + copyto!(k₃.x[1], k₃.x[2]) + copyto!(k1cache.x[2], k1cache.x[1]) + copyto!(k1cache.x[1], k.x[1]) + end # end if +end + +@muladd function perform_step!(integrator, cache::Nystrom5VelocityIndependentConstantCache, + repeat_step = false) + @unpack t, dt, f, p = integrator + duprev, uprev = integrator.uprev.x + @unpack c1, c2, a21, a31, a32, a41, a42, a43, bbar1, bbar2, bbar3, b1, b2, b3, b4 = cache + k₁ = integrator.fsalfirst.x[1] + + ku = uprev + dt * (c1 * duprev + dt * a21 * k₁) + + k₂ = f.f1(duprev, ku, p, t + c1 * dt) + ku = uprev + dt * (c2 * duprev + dt * (a31 * k₁ + a32 * k₂)) + + k₃ = f.f1(duprev, ku, p, t + c2 * dt) + ku = uprev + dt * (duprev + dt * (a41 * k₁ + a42 * k₂ + a43 * k₃)) + + k₄ = f.f1(duprev, ku, p, t + dt) + u = uprev + dt * (duprev + dt * (bbar1 * k₁ + bbar2 * k₂ + bbar3 * k₃)) + du = duprev + dt * (b1 * k₁ + b2 * k₂ + b3 * k₃ + b4 * k₄) + + integrator.u = ArrayPartition((du, u)) + integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) + integrator.stats.nf += 4 + integrator.stats.nf2 += 1 + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +@muladd function perform_step!(integrator, cache::Nystrom5VelocityIndependentCache, + repeat_step = false) + @unpack t, dt, f, p = integrator + du, u = integrator.u.x + duprev, uprev = integrator.uprev.x + uidx = eachindex(integrator.uprev.x[1]) + @unpack tmp, fsalfirst, k₂, k₃, k₄, k = cache + @unpack c1, c2, a21, a31, a32, a41, a42, a43, bbar1, bbar2, bbar3, b1, b2, b3, b4 = cache.tab + kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] + k₁ = integrator.fsalfirst.x[1] + + @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k₁) + + f.f1(k₂, du, ku, p, t + c1 * dt) + @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k₁ + a32 * k₂)) + + f.f1(k₃, du, ku, p, t + c2 * dt) + #@tight_loop_macros for i in uidx + # @inbounds ku[i] = uprev[i] + dt*(duprev[i] + dt*(a41*k₁[i] + a42*k₂[i] + a43*k₃[i])) + #end + @.. broadcast=false ku=uprev + dt * (duprev + dt * (a41 * k₁ + a42 * k₂ + a43 * k₃)) + + f.f1(k₄, duprev, ku, p, t + dt) + #@tight_loop_macros for i in uidx + # @inbounds u[i] = uprev[i] + dt*(duprev[i] + dt*(bbar1*k₁[i] + bbar2*k₂[i] + bbar3*k₃[i])) + # @inbounds du[i] = duprev[i] + dt*(b1*k₁[i] + b2*k₂[i] + b3*k₃[i] + b4*k₄[i]) + #end + @.. broadcast=false u=uprev + + dt * (duprev + dt * (bbar1 * k₁ + bbar2 * k₂ + bbar3 * k₃)) + @.. broadcast=false du=duprev + dt * (b1 * k₁ + b2 * k₂ + b3 * k₃ + b4 * k₄) + f.f1(k.x[1], du, u, p, t + dt) + f.f2(k.x[2], du, u, p, t + dt) + integrator.stats.nf += 4 + integrator.stats.nf2 += 1 + return nothing +end + +@muladd function perform_step!(integrator, cache::DPRKN4ConstantCache, repeat_step = false) + @unpack t, dt, f, p = integrator + duprev, uprev = integrator.uprev.x + @unpack c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, bp1, bp2, bp3, bp4, btilde1, btilde2, btilde3, btilde4, bptilde1, bptilde2, bptilde3, bptilde4 = cache + k1 = integrator.fsalfirst.x[1] + + ku = uprev + dt * (c1 * duprev + dt * a21 * k1) + + k2 = f.f1(duprev, ku, p, t + dt * c1) + ku = uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) + + k3 = f.f1(duprev, ku, p, t + dt * c2) + ku = uprev + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) + + k4 = f.f1(duprev, ku, p, t + dt * c3) + + u = uprev + dt * (duprev + dt * (b1 * k1 + b2 * k2 + b3 * k3)) + du = duprev + dt * (bp1 * k1 + bp2 * k2 + bp3 * k3 + bp4 * k4) + + integrator.u = ArrayPartition((du, u)) + integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) + integrator.stats.nf += 4 + integrator.stats.nf2 += 1 + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + + if integrator.opts.adaptive + dtsq = dt^2 + uhat = dtsq * (btilde1 * k1 + btilde2 * k2 + btilde3 * k3 + btilde4 * k4) + duhat = dt * (bptilde1 * k1 + bptilde2 * k2 + bptilde3 * k3 + bptilde4 * k4) + utilde = ArrayPartition((duhat, uhat)) + atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +@muladd function perform_step!(integrator, cache::DPRKN4Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + du, u = integrator.u.x + duprev, uprev = integrator.uprev.x + @unpack tmp, atmp, fsalfirst, k2, k3, k4, k, utilde = cache + @unpack c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, bp1, bp2, bp3, bp4, btilde1, btilde2, btilde3, btilde4, bptilde1, bptilde2, bptilde3, bptilde4 = cache.tab + kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] + uidx = eachindex(integrator.uprev.x[2]) + k1 = integrator.fsalfirst.x[1] + + @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1) + + f.f1(k2, duprev, ku, p, t + dt * c1) + @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) + + f.f1(k3, duprev, ku, p, t + dt * c2) + @.. broadcast=false ku=uprev + + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) + + f.f1(k4, duprev, ku, p, t + dt * c3) + @tight_loop_macros for i in uidx + @inbounds u[i] = uprev[i] + + dt * (duprev[i] + + dt * (b1 * k1[i] + b2 * k2[i] + b3 * k3[i])) + @inbounds du[i] = duprev[i] + + dt * (bp1 * k1[i] + bp2 * k2[i] + bp3 * k3[i] + bp4 * k4[i]) + end + + f.f1(k.x[1], du, u, p, t + dt) + f.f2(k.x[2], du, u, p, t + dt) + integrator.stats.nf += 4 + integrator.stats.nf2 += 1 + if integrator.opts.adaptive + duhat, uhat = utilde.x + dtsq = dt^2 + @tight_loop_macros for i in uidx + @inbounds uhat[i] = dtsq * + (btilde1 * k1[i] + btilde2 * k2[i] + btilde3 * k3[i] + + btilde4 * k4[i]) + @inbounds duhat[i] = dt * + (bptilde1 * k1[i] + bptilde2 * k2[i] + bptilde3 * k3[i] + + bptilde4 * k4[i]) + end + calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +@muladd function perform_step!(integrator, cache::DPRKN5ConstantCache, repeat_step = false) + @unpack t, dt, f, p = integrator + duprev, uprev = integrator.uprev.x + @unpack c1, c2, c3, c4, c5, a21, a31, a32, a41, a43, a51, a53, a54, a61, a63, a64, a65, b1, b3, b4, b5, bp1, bp3, bp4, bp5, bp6, btilde1, btilde3, btilde4, btilde5, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6 = cache + k1 = integrator.fsalfirst.x[1] + + ku = uprev + dt * (c1 * duprev + dt * a21 * k1) + + k2 = f.f1(duprev, ku, p, t + dt * c1) + ku = uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) + + k3 = f.f1(duprev, ku, p, t + dt * c2) + ku = uprev + dt * (c3 * duprev + dt * (a41 * k1 + a43 * k3)) + + k4 = f.f1(duprev, ku, p, t + dt * c3) + ku = uprev + dt * (c4 * duprev + dt * (a51 * k1 + a53 * k3 + a54 * k4)) + + k5 = f.f1(duprev, ku, p, t + dt * c4) + ku = uprev + + dt * (c5 * duprev + dt * (a61 * k1 + a63 * k3 + a64 * k4 + a65 * k5)) + + k6 = f.f1(duprev, ku, p, t + dt * c5) + u = uprev + + dt * (duprev + dt * (b1 * k1 + b3 * k3 + b4 * k4 + b5 * k5)) + du = duprev + + dt * (bp1 * k1 + bp3 * k3 + bp4 * k4 + bp5 * k5 + bp6 * k6) + + integrator.u = ArrayPartition((du, u)) + integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) + integrator.stats.nf += 6 + integrator.stats.nf2 += 1 + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + + if integrator.opts.adaptive + dtsq = dt^2 + uhat = dtsq * (btilde1 * k1 + btilde3 * k3 + btilde4 * k4 + btilde5 * k5) + duhat = dt * (bptilde1 * k1 + bptilde3 * k3 + bptilde4 * k4 + bptilde5 * k5 + + bptilde6 * k6) + utilde = ArrayPartition((duhat, uhat)) + atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +@muladd function perform_step!(integrator, cache::DPRKN5Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + du, u = integrator.u.x + duprev, uprev = integrator.uprev.x + @unpack tmp, atmp, fsalfirst, k2, k3, k4, k5, k6, k, utilde = cache + @unpack c1, c2, c3, c4, c5, a21, a31, a32, a41, a43, a51, a53, a54, a61, a63, a64, a65, b1, b3, b4, b5, bp1, bp3, bp4, bp5, bp6, btilde1, btilde3, btilde4, btilde5, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6 = cache.tab + kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] + uidx = eachindex(integrator.uprev.x[2]) + k1 = integrator.fsalfirst.x[1] + + @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1) + + f.f1(k2, duprev, ku, p, t + dt * c1) + @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) + + f.f1(k3, duprev, ku, p, t + dt * c2) + @.. broadcast=false ku=uprev + + dt * (c3 * duprev + dt * (a41 * k1 + a43 * k3)) + + f.f1(k4, duprev, ku, p, t + dt * c3) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c4 * duprev[i] + + dt * (a51 * k1[i] + a53 * k3[i] + a54 * k4[i])) + end + + f.f1(k5, duprev, ku, p, t + dt * c4) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c5 * duprev[i] + + dt * (a61 * k1[i] + a63 * k3[i] + a64 * k4[i] + a65 * k5[i])) + end + + f.f1(k6, duprev, ku, p, t + dt * c5) + @tight_loop_macros for i in uidx + @inbounds u[i] = uprev[i] + + dt * (duprev[i] + + dt * (b1 * k1[i] + b3 * k3[i] + b4 * k4[i] + b5 * k5[i])) + @inbounds du[i] = duprev[i] + + dt * (bp1 * k1[i] + bp3 * k3[i] + bp4 * k4[i] + bp5 * k5[i] + + bp6 * k6[i]) + end + + f.f1(k.x[1], du, u, p, t + dt) + f.f2(k.x[2], du, u, p, t + dt) + integrator.stats.nf += 6 + integrator.stats.nf2 += 1 + if integrator.opts.adaptive + duhat, uhat = utilde.x + dtsq = dt^2 + @tight_loop_macros for i in uidx + @inbounds uhat[i] = dtsq * + (btilde1 * k1[i] + btilde3 * k3[i] + btilde4 * k4[i] + + btilde5 * k5[i]) + @inbounds duhat[i] = dt * + (bptilde1 * k1[i] + bptilde3 * k3[i] + bptilde4 * k4[i] + + bptilde5 * k5[i] + bptilde6 * k6[i]) + end + calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +function initialize!(integrator, cache::DPRKN6ConstantCache) + duprev, uprev = integrator.uprev.x + integrator.kshortsize = 3 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + kdu = integrator.f.f1(duprev, uprev, integrator.p, integrator.t) + ku = integrator.f.f2(duprev, uprev, integrator.p, integrator.t) + integrator.stats.nf += 1 + integrator.stats.nf2 += 1 + integrator.fsalfirst = ArrayPartition((kdu, ku)) + integrator.fsallast = zero(integrator.fsalfirst) + + integrator.k[1] = integrator.fsalfirst + @inbounds for i in 2:(integrator.kshortsize - 1) + integrator.k[i] = zero(integrator.fsalfirst) + end + integrator.k[integrator.kshortsize] = integrator.fsallast +end + +@muladd function perform_step!(integrator, cache::DPRKN6ConstantCache, repeat_step = false) + @unpack t, dt, f, p = integrator + duprev, uprev = integrator.uprev.x + @unpack c1, c2, c3, c4, c5, a21, a31, a32, a41, a42, a43, a51, a52, a53, a54, a61, a63, a64, a65, b1, b3, b4, b5, bp1, bp3, bp4, bp5, bp6, btilde1, btilde2, btilde3, btilde4, btilde5, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6 = cache + k1 = integrator.fsalfirst.x[1] + + ku = uprev + dt * (c1 * duprev + dt * a21 * k1) + + k2 = f.f1(duprev, ku, p, t + dt * c1) + ku = uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) + + k3 = f.f1(duprev, ku, p, t + dt * c2) + ku = uprev + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) + + k4 = f.f1(duprev, ku, p, t + dt * c3) + ku = uprev + dt * (c4 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) + + k5 = f.f1(duprev, ku, p, t + dt * c4) + ku = uprev + dt * (c5 * duprev + dt * (a61 * k1 + a63 * k3 + a64 * k4 + a65 * k5)) # no a62 + + k6 = f.f1(duprev, ku, p, t + dt * c5) + u = uprev + dt * (duprev + dt * (b1 * k1 + b3 * k3 + b4 * k4 + b5 * k5)) # b1 -- b5, no b2 + du = duprev + dt * (bp1 * k1 + bp3 * k3 + bp4 * k4 + bp5 * k5 + bp6 * k6) # bp1 -- bp6, no bp2 + + #= + @tight_loop_macros for i in uidx + @inbounds u[i] = uprev[i] + dt*(duprev[i] + dt*(bhat1*k1.x[2][i] + bhat2*k2.x[2][i] + bhat3*k3.x[2][i])) + @inbounds du[i] = duprev[i]+ dt*(bphat1*k1.x[2][i] + bphat3*k3.x[2][i] + bphat4*k4.x[2][i] + bphat5*k5.x[2][i] + bphat6*k6.x[2][i]) + end + =# + + integrator.u = ArrayPartition((du, u)) + integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) + integrator.k[1] = ArrayPartition(integrator.fsalfirst.x[1], k2) + integrator.k[2] = ArrayPartition(k3, k4) + integrator.k[3] = ArrayPartition(k5, k6) + integrator.stats.nf += 6 + integrator.stats.nf2 += 1 + + if integrator.opts.adaptive + dtsq = dt^2 + uhat = dtsq * + (btilde1 * k1 + btilde2 * k2 + btilde3 * k3 + btilde4 * k4 + btilde5 * k5) + duhat = dt * (bptilde1 * k1 + bptilde3 * k3 + bptilde4 * k4 + bptilde5 * k5 + + bptilde6 * k6) + utilde = ArrayPartition((duhat, uhat)) + atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +function initialize!(integrator, cache::DPRKN6Cache) + @unpack fsalfirst, k = cache + duprev, uprev = integrator.uprev.x + + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 3 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = ArrayPartition(cache.fsalfirst.x[1], cache.k2) + integrator.k[2] = ArrayPartition(cache.k3, cache.k4) + integrator.k[3] = ArrayPartition(cache.k5, cache.k6) + integrator.f.f1(integrator.fsallast.x[1], duprev, uprev, integrator.p, integrator.t) + integrator.f.f2(integrator.fsallast.x[2], duprev, uprev, integrator.p, integrator.t) + integrator.stats.nf += 1 + integrator.stats.nf2 += 1 +end + +@muladd function perform_step!(integrator, cache::DPRKN6Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + du, u = integrator.u.x + duprev, uprev = integrator.uprev.x + @unpack tmp, atmp, fsalfirst, k2, k3, k4, k5, k6, k, utilde = cache + @unpack c1, c2, c3, c4, c5, a21, a31, a32, a41, a42, a43, a51, a52, a53, a54, a61, a63, a64, a65, b1, b3, b4, b5, bp1, bp3, bp4, bp5, bp6, btilde1, btilde2, btilde3, btilde4, btilde5, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6 = cache.tab + kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] + uidx = eachindex(integrator.uprev.x[2]) + k1 = integrator.fsalfirst.x[1] + + @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1) + + f.f1(k2, du, ku, p, t + dt * c1) + @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) + + f.f1(k3, du, ku, p, t + dt * c2) + @.. broadcast=false ku=uprev + + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) + + f.f1(k4, du, ku, p, t + dt * c3) + @.. broadcast=false ku=uprev + + dt * + (c4 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) + + f.f1(k5, du, ku, p, t + dt * c4) + @.. broadcast=false ku=uprev + + dt * + (c5 * duprev + dt * (a61 * k1 + a63 * k3 + a64 * k4 + a65 * k5)) # no a62 + + f.f1(k6, du, ku, p, t + dt * c5) + + @.. broadcast=false u=uprev + + dt * (duprev + dt * (b1 * k1 + b3 * k3 + b4 * k4 + b5 * k5)) # b1 -- b5, no b2 + @.. broadcast=false du=duprev + + dt * (bp1 * k1 + bp3 * k3 + bp4 * k4 + bp5 * k5 + bp6 * k6) # bp1 -- bp6, no bp2 + + #= + @tight_loop_macros for i in uidx + @inbounds u[i] = uprev[i] + dt*(duprev[i] + dt*(bhat1*k1.x[2][i] + bhat2*k2.x[2][i] + bhat3*k3.x[2][i])) + @inbounds du[i] = duprev[i]+ dt*(bphat1*k1.x[2][i] + bphat3*k3.x[2][i] + bphat4*k4.x[2][i] + bphat5*k5.x[2][i] + bphat6*k6.x[2][i]) + end + =# + + f.f1(k.x[1], du, u, p, t + dt) + f.f2(k.x[2], du, u, p, t + dt) + integrator.stats.nf += 6 + integrator.stats.nf2 += 1 + if integrator.opts.adaptive + duhat, uhat = utilde.x + dtsq = dt^2 + @.. broadcast=false uhat=dtsq * (btilde1 * k1 + btilde2 * k2 + btilde3 * k3 + + btilde4 * k4 + btilde5 * k5) + @.. broadcast=false duhat=dt * (bptilde1 * k1 + bptilde3 * k3 + bptilde4 * k4 + + bptilde5 * k5 + bptilde6 * k6) + calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +@muladd function perform_step!(integrator, cache::DPRKN6FMConstantCache, + repeat_step = false) + @unpack t, dt, f, p = integrator + duprev, uprev = integrator.uprev.x + @unpack c1, c2, c3, c4, c5, a21, a31, a32, a41, a42, a43, a51, a52, a53, a54, a61, a62, a63, a64, a65, b1, b2, b3, b4, b5, bp1, bp2, bp3, bp4, bp5, bp6, btilde1, btilde2, btilde3, btilde4, btilde5, bptilde1, bptilde2, bptilde3, bptilde4, bptilde5 = cache + k1 = integrator.fsalfirst.x[1] + + ku = uprev + dt * (c1 * duprev + dt * a21 * k1) + + k2 = f.f1(duprev, ku, p, t + dt * c1) + ku = uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) + + k3 = f.f1(duprev, ku, p, t + dt * c2) + ku = uprev + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) + + k4 = f.f1(duprev, ku, p, t + dt * c3) + ku = uprev + dt * (c4 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) + + k5 = f.f1(duprev, ku, p, t + dt * c4) + ku = uprev + + dt * (c5 * duprev + dt * (a61 * k1 + a62 * k2 + a63 * k3 + a64 * k4 + a65 * k5)) + + k6 = f.f1(duprev, ku, p, t + dt * c5) + u = uprev + + dt * (duprev + dt * (b1 * k1 + b2 * k2 + b3 * k3 + b4 * k4 + b5 * k5)) + du = duprev + + dt * (bp1 * k1 + bp2 * k2 + bp3 * k3 + bp4 * k4 + bp5 * k5 + bp6 * k6) + + integrator.u = ArrayPartition((du, u)) + integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) + integrator.stats.nf += 6 + integrator.stats.nf2 += 1 + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + + if integrator.opts.adaptive + dtsq = dt^2 + uhat = dtsq * + (btilde1 * k1 + btilde2 * k2 + btilde3 * k3 + btilde4 * k4 + btilde5 * k5) + duhat = dt * (bptilde1 * k1 + bptilde2 * k2 + bptilde3 * k3 + bptilde4 * k4 + + bptilde5 * k5) + utilde = ArrayPartition((duhat, uhat)) + atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +@muladd function perform_step!(integrator, cache::DPRKN6FMCache, repeat_step = false) + @unpack t, dt, f, p = integrator + du, u = integrator.u.x + duprev, uprev = integrator.uprev.x + @unpack tmp, atmp, fsalfirst, k2, k3, k4, k5, k6, k, utilde = cache + @unpack c1, c2, c3, c4, c5, a21, a31, a32, a41, a42, a43, a51, a52, a53, a54, a61, a62, a63, a64, a65, b1, b2, b3, b4, b5, bp1, bp2, bp3, bp4, bp5, bp6, btilde1, btilde2, btilde3, btilde4, btilde5, bptilde1, bptilde2, bptilde3, bptilde4, bptilde5 = cache.tab + kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] + uidx = eachindex(integrator.uprev.x[2]) + k1 = integrator.fsalfirst.x[1] + + @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1) + + f.f1(k2, duprev, ku, p, t + dt * c1) + @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) + + f.f1(k3, duprev, ku, p, t + dt * c2) + @.. broadcast=false ku=uprev + + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) + + f.f1(k4, duprev, ku, p, t + dt * c3) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c4 * duprev[i] + + dt * (a51 * k1[i] + a52 * k2[i] + a53 * k3[i] + a54 * k4[i])) + end + + f.f1(k5, duprev, ku, p, t + dt * c4) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c5 * duprev[i] + + dt * (a61 * k1[i] + a62 * k2[i] + a63 * k3[i] + a64 * k4[i] + + a65 * k5[i])) + end + + f.f1(k6, duprev, ku, p, t + dt * c5) + @tight_loop_macros for i in uidx + @inbounds u[i] = uprev[i] + + dt * (duprev[i] + + dt * + (b1 * k1[i] + b2 * k2[i] + b3 * k3[i] + b4 * k4[i] + b5 * k5[i])) + @inbounds du[i] = duprev[i] + + dt * (bp1 * k1[i] + bp2 * k2[i] + bp3 * k3[i] + bp4 * k4[i] + + bp5 * k5[i] + bp6 * k6[i]) + end + + f.f1(k.x[1], du, u, p, t + dt) + f.f2(k.x[2], du, u, p, t + dt) + integrator.stats.nf += 6 + integrator.stats.nf2 += 1 + if integrator.opts.adaptive + duhat, uhat = utilde.x + dtsq = dt^2 + @tight_loop_macros for i in uidx + @inbounds uhat[i] = dtsq * + (btilde1 * k1[i] + btilde2 * k2[i] + btilde3 * k3[i] + + btilde4 * k4[i] + btilde5 * k5[i]) + @inbounds duhat[i] = dt * + (bptilde1 * k1[i] + bptilde2 * k2[i] + bptilde3 * k3[i] + + bptilde4 * k4[i] + bptilde5 * k5[i]) + end + calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +@muladd function perform_step!(integrator, cache::DPRKN8ConstantCache, repeat_step = false) + @unpack t, dt, f, p = integrator + duprev, uprev = integrator.uprev.x + @unpack c1, c2, c3, c4, c5, c6, c7, c8, a21, a31, a32, a41, a42, a43, a51, a52, a53, a54, a61, a62, a63, a64, a65, a71, a72, a73, a74, a75, a76, a81, a82, a83, a84, a85, a86, a87, a91, a93, a94, a95, a96, a97, b1, b3, b4, b5, b6, b7, bp1, bp3, bp4, bp5, bp6, bp7, bp8, btilde1, btilde3, btilde4, btilde5, btilde6, btilde7, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6, bptilde7, bptilde8, bptilde9 = cache + k1 = integrator.fsalfirst.x[1] + + ku = uprev + dt * (c1 * duprev + dt * a21 * k1) + + k2 = f.f1(duprev, ku, p, t + dt * c1) + ku = uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) + + k3 = f.f1(duprev, ku, p, t + dt * c2) + ku = uprev + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) + + k4 = f.f1(duprev, ku, p, t + dt * c3) + ku = uprev + dt * (c4 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) + + k5 = f.f1(duprev, ku, p, t + dt * c4) + ku = uprev + + dt * (c5 * duprev + dt * (a61 * k1 + a62 * k2 + a63 * k3 + a64 * k4 + a65 * k5)) + + k6 = f.f1(duprev, ku, p, t + dt * c5) + ku = uprev + + dt * (c6 * duprev + + dt * (a71 * k1 + a72 * k2 + a73 * k3 + a74 * k4 + a75 * k5 + a76 * k6)) + + k7 = f.f1(duprev, ku, p, t + dt * c6) + ku = uprev + + dt * (c7 * duprev + + dt * (a81 * k1 + a82 * k2 + a83 * k3 + a84 * k4 + a85 * k5 + a86 * k6 + a87 * k7)) + + k8 = f.f1(duprev, ku, p, t + dt * c7) + ku = uprev + + dt * (c8 * duprev + + dt * (a91 * k1 + a93 * k3 + a94 * k4 + a95 * k5 + a96 * k6 + a97 * k7)) # no a92 & a98 + + k9 = f.f1(duprev, ku, p, t + dt * c8) + u = uprev + + dt * (duprev + dt * (b1 * k1 + b3 * k3 + b4 * k4 + b5 * k5 + b6 * k6 + b7 * k7)) # b1 -- b7, no b2 + du = duprev + + dt * (bp1 * k1 + bp3 * k3 + bp4 * k4 + bp5 * k5 + bp6 * k6 + bp7 * k7 + bp8 * k8) # bp1 -- bp8, no bp2 + + integrator.u = ArrayPartition((du, u)) + integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) + integrator.stats.nf += 9 + integrator.stats.nf2 += 1 + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + + if integrator.opts.adaptive + dtsq = dt^2 + uhat = dtsq * + (btilde1 * k1 + btilde3 * k3 + btilde4 * k4 + btilde5 * k5 + btilde6 * k6 + + btilde7 * k7) + duhat = dt * (bptilde1 * k1 + bptilde3 * k3 + bptilde4 * k4 + bptilde5 * k5 + + bptilde6 * k6 + bptilde7 * k7 + bptilde8 * k8 + bptilde9 * k9) + utilde = ArrayPartition((duhat, uhat)) + atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +@muladd function perform_step!(integrator, cache::DPRKN8Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + du, u = integrator.u.x + duprev, uprev = integrator.uprev.x + @unpack tmp, atmp, fsalfirst, k2, k3, k4, k5, k6, k7, k8, k9, k, utilde = cache + @unpack c1, c2, c3, c4, c5, c6, c7, c8, a21, a31, a32, a41, a42, a43, a51, a52, a53, a54, a61, a62, a63, a64, a65, a71, a72, a73, a74, a75, a76, a81, a82, a83, a84, a85, a86, a87, a91, a93, a94, a95, a96, a97, b1, b3, b4, b5, b6, b7, bp1, bp3, bp4, bp5, bp6, bp7, bp8, btilde1, btilde3, btilde4, btilde5, btilde6, btilde7, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6, bptilde7, bptilde8, bptilde9 = cache.tab + kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] + uidx = eachindex(integrator.uprev.x[2]) + k1 = integrator.fsalfirst.x[1] + + @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1) + + f.f1(k2, duprev, ku, p, t + dt * c1) + @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) + + f.f1(k3, duprev, ku, p, t + dt * c2) + @.. broadcast=false ku=uprev + + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) + + f.f1(k4, duprev, ku, p, t + dt * c3) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c4 * duprev[i] + + dt * (a51 * k1[i] + a52 * k2[i] + a53 * k3[i] + a54 * k4[i])) + end + + f.f1(k5, duprev, ku, p, t + dt * c4) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c5 * duprev[i] + + dt * (a61 * k1[i] + a62 * k2[i] + a63 * k3[i] + a64 * k4[i] + + a65 * k5[i])) + end + + f.f1(k6, duprev, ku, p, t + dt * c5) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c6 * duprev[i] + + dt * (a71 * k1[i] + a72 * k2[i] + a73 * k3[i] + a74 * k4[i] + + a75 * k5[i] + a76 * k6[i])) + end + + f.f1(k7, duprev, ku, p, t + dt * c6) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c7 * duprev[i] + + dt * (a81 * k1[i] + a82 * k2[i] + a83 * k3[i] + a84 * k4[i] + + a85 * k5[i] + a86 * k6[i] + a87 * k7[i])) + end + + f.f1(k8, duprev, ku, p, t + dt * c7) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c8 * duprev[i] + + dt * (a91 * k1[i] + a93 * k3[i] + a94 * k4[i] + a95 * k5[i] + + a96 * k6[i] + a97 * k7[i])) # no a92 & a98 + end + + f.f1(k9, duprev, ku, p, t + dt * c8) + @tight_loop_macros for i in uidx + @inbounds u[i] = uprev[i] + + dt * (duprev[i] + + dt * + (b1 * k1[i] + b3 * k3[i] + b4 * k4[i] + b5 * k5[i] + b6 * k6[i] + + b7 * k7[i])) # b1 -- b7, no b2 + @inbounds du[i] = duprev[i] + + dt * (bp1 * k1[i] + bp3 * k3[i] + bp4 * k4[i] + bp5 * k5[i] + + bp6 * k6[i] + bp7 * k7[i] + bp8 * k8[i]) # bp1 -- bp8, no bp2 + end + + f.f1(k.x[1], du, u, p, t + dt) + f.f2(k.x[2], du, u, p, t + dt) + integrator.stats.nf += 9 + integrator.stats.nf2 += 1 + if integrator.opts.adaptive + duhat, uhat = utilde.x + dtsq = dt^2 + @tight_loop_macros for i in uidx + @inbounds uhat[i] = dtsq * + (btilde1 * k1[i] + btilde3 * k3[i] + btilde4 * k4[i] + + btilde5 * k5[i] + btilde6 * k6[i] + btilde7 * k7[i]) + @inbounds duhat[i] = dt * + (bptilde1 * k1[i] + bptilde3 * k3[i] + bptilde4 * k4[i] + + bptilde5 * k5[i] + bptilde6 * k6[i] + bptilde7 * k7[i] + + bptilde8 * k8[i] + bptilde9 * k9[i]) + end + calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +@muladd function perform_step!(integrator, cache::DPRKN12ConstantCache, repeat_step = false) + @unpack t, dt, f, p = integrator + duprev, uprev = integrator.uprev.x + @unpack c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, a21, a31, a32, a41, a42, a43, a51, a53, a54, a61, a63, a64, a65, a71, a73, a74, a75, a76, a81, a84, a85, a86, a87, a91, a93, a94, a95, a96, a97, a98, a101, a103, a104, a105, a106, a107, a108, a109, a111, a113, a114, a115, a116, a117, a118, a119, a1110, a121, a123, a124, a125, a126, a127, a128, a129, a1210, a1211, a131, a133, a134, a135, a136, a137, a138, a139, a1310, a1311, a1312, a141, a143, a144, a145, a146, a147, a148, a149, a1410, a1411, a1412, a1413, a151, a153, a154, a155, a156, a157, a158, a159, a1510, a1511, a1512, a1513, a1514, a161, a163, a164, a165, a166, a167, a168, a169, a1610, a1611, a1612, a1613, a1614, a1615, a171, a173, a174, a175, a176, a177, a178, a179, a1710, a1711, a1712, a1713, a1714, a1715, b1, b7, b8, b9, b10, b11, b12, b13, b14, b15, bp1, bp7, bp8, bp9, bp10, bp11, bp12, bp13, bp14, bp15, bp16, bp17, btilde1, btilde7, btilde8, btilde9, btilde10, btilde11, btilde12, btilde13, btilde14, btilde15, bptilde1, bptilde7, bptilde8, bptilde9, bptilde10, bptilde11, bptilde12, bptilde13, bptilde14, bptilde15, bptilde16, bptilde17 = cache + k1 = integrator.fsalfirst.x[1] + + ku = uprev + dt * (c1 * duprev + dt * a21 * k1) + + k2 = f.f1(duprev, ku, p, t + dt * c1) + ku = uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) + + k3 = f.f1(duprev, ku, p, t + dt * c2) + ku = uprev + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) + + k4 = f.f1(duprev, ku, p, t + dt * c3) + ku = uprev + dt * (c4 * duprev + dt * (a51 * k1 + a53 * k3 + a54 * k4)) # no a52 + + k5 = f.f1(duprev, ku, p, t + dt * c4) + ku = uprev + dt * (c5 * duprev + dt * (a61 * k1 + a63 * k3 + a64 * k4 + a65 * k5)) # no a62 + + k6 = f.f1(duprev, ku, p, t + dt * c5) + ku = uprev + + dt * (c6 * duprev + dt * (a71 * k1 + a73 * k3 + a74 * k4 + a75 * k5 + a76 * k6)) # no a72 + + k7 = f.f1(duprev, ku, p, t + dt * c6) + ku = uprev + + dt * (c7 * duprev + dt * (a81 * k1 + a84 * k4 + a85 * k5 + a86 * k6 + a87 * k7)) # no a82, a83 + + k8 = f.f1(duprev, ku, p, t + dt * c7) + ku = uprev + + dt * (c8 * duprev + + dt * (a91 * k1 + a93 * k3 + a94 * k4 + a95 * k5 + a96 * k6 + a97 * k7 + a98 * k8)) # no a92 + + k9 = f.f1(duprev, ku, p, t + dt * c8) + ku = uprev + + dt * (c9 * duprev + + dt * (a101 * k1 + a103 * k3 + a104 * k4 + a105 * k5 + a106 * k6 + a107 * k7 + + a108 * k8 + a109 * k9)) # no a102 + + k10 = f.f1(duprev, ku, p, t + dt * c9) + ku = uprev + + dt * (c10 * duprev + + dt * (a111 * k1 + a113 * k3 + a114 * k4 + a115 * k5 + a116 * k6 + a117 * k7 + + a118 * k8 + a119 * k9 + a1110 * k10)) # no a112 + + k11 = f.f1(duprev, ku, p, t + dt * c10) + ku = uprev + + dt * (c11 * duprev + + dt * (a121 * k1 + a123 * k3 + a124 * k4 + a125 * k5 + a126 * k6 + a127 * k7 + + a128 * k8 + a129 * k9 + a1210 * k10 + a1211 * k11)) # no a122 + + k12 = f.f1(duprev, ku, p, t + dt * c11) + ku = uprev + + dt * (c12 * duprev + + dt * (a131 * k1 + a133 * k3 + a134 * k4 + a135 * k5 + a136 * k6 + a137 * k7 + + a138 * k8 + a139 * k9 + a1310 * k10 + a1311 * k11 + a1312 * k12)) # no a132 + + k13 = f.f1(duprev, ku, p, t + dt * c12) + ku = uprev + + dt * (c13 * duprev + + dt * (a141 * k1 + a143 * k3 + a144 * k4 + a145 * k5 + a146 * k6 + a147 * k7 + + a148 * k8 + a149 * k9 + a1410 * k10 + a1411 * k11 + a1412 * k12 + a1413 * k13)) # no a142 + + k14 = f.f1(duprev, ku, p, t + dt * c13) + ku = uprev + + dt * (c14 * duprev + + dt * (a151 * k1 + a153 * k3 + a154 * k4 + a155 * k5 + a156 * k6 + a157 * k7 + + a158 * k8 + a159 * k9 + a1510 * k10 + a1511 * k11 + a1512 * k12 + a1513 * k13 + + a1514 * k14)) # no a152 + + k15 = f.f1(duprev, ku, p, t + dt * c14) + ku = uprev + + dt * (c15 * duprev + + dt * (a161 * k1 + a163 * k3 + a164 * k4 + a165 * k5 + a166 * k6 + a167 * k7 + + a168 * k8 + a169 * k9 + a1610 * k10 + a1611 * k11 + a1612 * k12 + a1613 * k13 + + a1614 * k14 + a1615 * k15)) # no a162 + + k16 = f.f1(duprev, ku, p, t + dt * c15) + ku = uprev + + dt * (c16 * duprev + + dt * (a171 * k1 + a173 * k3 + a174 * k4 + a175 * k5 + a176 * k6 + a177 * k7 + + a178 * k8 + a179 * k9 + a1710 * k10 + a1711 * k11 + a1712 * k12 + a1713 * k13 + + a1714 * k14 + a1715 * k15)) # no a172, a1716 + + k17 = f.f1(duprev, ku, p, t + dt * c16) + u = uprev + + dt * (duprev + + dt * (b1 * k1 + b7 * k7 + b8 * k8 + b9 * k9 + b10 * k10 + b11 * k11 + b12 * k12 + + b13 * k13 + b14 * k14 + b15 * k15)) # b1 & b7 -- b15 + du = duprev + + dt * + (bp1 * k1 + bp7 * k7 + bp8 * k8 + bp9 * k9 + bp10 * k10 + bp11 * k11 + bp12 * k12 + + bp13 * k13 + bp14 * k14 + bp15 * k15 + bp16 * k16 + bp17 * k17) # bp1 & bp7 -- bp17 + + integrator.u = ArrayPartition((du, u)) + integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) + integrator.stats.nf += 17 + integrator.stats.nf2 += 1 + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + if integrator.opts.adaptive + dtsq = dt^2 + uhat = dtsq * + (btilde1 * k1 + btilde7 * k7 + btilde8 * k8 + btilde9 * k9 + btilde10 * k10 + + btilde11 * k11 + btilde12 * k12 + btilde13 * k13 + btilde14 * k14 + + btilde15 * k15) # btilde1 & btilde7 -- btilde15 + duhat = dt * (bptilde1 * k1 + bptilde7 * k7 + bptilde8 * k8 + bptilde9 * k9 + + bptilde10 * k10 + bptilde11 * k11 + bptilde12 * k12 + bptilde13 * k13 + + bptilde14 * k14 + bptilde15 * k15 + bptilde16 * k16 + bptilde17 * k17) # bptilde1 & bptilde7 -- bptilde17 + utilde = ArrayPartition((duhat, uhat)) + atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +@muladd function perform_step!(integrator, cache::DPRKN12Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + du, u = integrator.u.x + duprev, uprev = integrator.uprev.x + @unpack tmp, atmp, fsalfirst, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, k17, k, utilde = cache + @unpack c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, a21, a31, a32, a41, a42, a43, a51, a53, a54, a61, a63, a64, a65, a71, a73, a74, a75, a76, a81, a84, a85, a86, a87, a91, a93, a94, a95, a96, a97, a98, a101, a103, a104, a105, a106, a107, a108, a109, a111, a113, a114, a115, a116, a117, a118, a119, a1110, a121, a123, a124, a125, a126, a127, a128, a129, a1210, a1211, a131, a133, a134, a135, a136, a137, a138, a139, a1310, a1311, a1312, a141, a143, a144, a145, a146, a147, a148, a149, a1410, a1411, a1412, a1413, a151, a153, a154, a155, a156, a157, a158, a159, a1510, a1511, a1512, a1513, a1514, a161, a163, a164, a165, a166, a167, a168, a169, a1610, a1611, a1612, a1613, a1614, a1615, a171, a173, a174, a175, a176, a177, a178, a179, a1710, a1711, a1712, a1713, a1714, a1715, b1, b7, b8, b9, b10, b11, b12, b13, b14, b15, bp1, bp7, bp8, bp9, bp10, bp11, bp12, bp13, bp14, bp15, bp16, bp17, btilde1, btilde7, btilde8, btilde9, btilde10, btilde11, btilde12, btilde13, btilde14, btilde15, bptilde1, bptilde7, bptilde8, bptilde9, bptilde10, bptilde11, bptilde12, bptilde13, bptilde14, bptilde15, bptilde16, bptilde17 = cache.tab + kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] + uidx = eachindex(integrator.uprev.x[2]) + k1 = integrator.fsalfirst.x[1] + + @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1) + + f.f1(k2, duprev, ku, p, t + dt * c1) + @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) + + f.f1(k3, duprev, ku, p, t + dt * c2) + @.. broadcast=false ku=uprev + + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) + + f.f1(k4, duprev, ku, p, t + dt * c3) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * + (c4 * duprev[i] + dt * (a51 * k1[i] + a53 * k3[i] + a54 * k4[i])) # no a52 + end + + f.f1(k5, duprev, ku, p, t + dt * c4) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c5 * duprev[i] + + dt * (a61 * k1[i] + a63 * k3[i] + a64 * k4[i] + a65 * k5[i])) # no a62 + end + + f.f1(k6, duprev, ku, p, t + dt * c5) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c6 * duprev[i] + + dt * (a71 * k1[i] + a73 * k3[i] + a74 * k4[i] + a75 * k5[i] + + a76 * k6[i])) # no a72 + end + + f.f1(k7, duprev, ku, p, t + dt * c6) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c7 * duprev[i] + + dt * (a81 * k1[i] + a84 * k4[i] + a85 * k5[i] + a86 * k6[i] + + a87 * k7[i])) # no a82, a83 + end + + f.f1(k8, duprev, ku, p, t + dt * c7) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c8 * duprev[i] + + dt * (a91 * k1[i] + a93 * k3[i] + a94 * k4[i] + a95 * k5[i] + + a96 * k6[i] + a97 * k7[i] + a98 * k8[i])) # no a92 + end + + f.f1(k9, duprev, ku, p, t + dt * c8) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c9 * duprev[i] + + dt * + (a101 * k1[i] + a103 * k3[i] + a104 * k4[i] + a105 * k5[i] + + a106 * k6[i] + a107 * k7[i] + a108 * k8[i] + a109 * k9[i])) # no a102 + end + + f.f1(k10, duprev, ku, p, t + dt * c9) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c10 * duprev[i] + + dt * + (a111 * k1[i] + a113 * k3[i] + a114 * k4[i] + a115 * k5[i] + + a116 * k6[i] + a117 * k7[i] + a118 * k8[i] + a119 * k9[i] + + a1110 * k10[i])) # no a112 + end + + f.f1(k11, duprev, ku, p, t + dt * c10) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c11 * duprev[i] + + dt * + (a121 * k1[i] + a123 * k3[i] + a124 * k4[i] + a125 * k5[i] + + a126 * k6[i] + a127 * k7[i] + a128 * k8[i] + a129 * k9[i] + + a1210 * k10[i] + a1211 * k11[i])) # no a122 + end + + f.f1(k12, duprev, ku, p, t + dt * c11) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c12 * duprev[i] + + dt * + (a131 * k1[i] + a133 * k3[i] + a134 * k4[i] + a135 * k5[i] + + a136 * k6[i] + a137 * k7[i] + a138 * k8[i] + a139 * k9[i] + + a1310 * k10[i] + a1311 * k11[i] + a1312 * k12[i])) # no a132 + end + + f.f1(k13, duprev, ku, p, t + dt * c12) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c13 * duprev[i] + + dt * + (a141 * k1[i] + a143 * k3[i] + a144 * k4[i] + a145 * k5[i] + + a146 * k6[i] + a147 * k7[i] + a148 * k8[i] + a149 * k9[i] + + a1410 * k10[i] + a1411 * k11[i] + a1412 * k12[i] + + a1413 * k13[i])) # no a142 + end + + f.f1(k14, duprev, ku, p, t + dt * c13) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c14 * duprev[i] + + dt * + (a151 * k1[i] + a153 * k3[i] + a154 * k4[i] + a155 * k5[i] + + a156 * k6[i] + a157 * k7[i] + a158 * k8[i] + a159 * k9[i] + + a1510 * k10[i] + a1511 * k11[i] + a1512 * k12[i] + + a1513 * k13[i] + a1514 * k14[i])) # no a152 + end + + f.f1(k15, duprev, ku, p, t + dt * c14) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c15 * duprev[i] + + dt * + (a161 * k1[i] + a163 * k3[i] + a164 * k4[i] + a165 * k5[i] + + a166 * k6[i] + a167 * k7[i] + a168 * k8[i] + a169 * k9[i] + + a1610 * k10[i] + a1611 * k11[i] + a1612 * k12[i] + + a1613 * k13[i] + a1614 * k14[i] + a1615 * k15[i])) # no a162 + end + + f.f1(k16, duprev, ku, p, t + dt * c15) + @tight_loop_macros for i in uidx + @inbounds ku[i] = uprev[i] + + dt * (c16 * duprev[i] + + dt * + (a171 * k1[i] + a173 * k3[i] + a174 * k4[i] + a175 * k5[i] + + a176 * k6[i] + a177 * k7[i] + a178 * k8[i] + a179 * k9[i] + + a1710 * k10[i] + a1711 * k11[i] + a1712 * k12[i] + + a1713 * k13[i] + a1714 * k14[i] + a1715 * k15[i])) # no a172, a1716 + end + + f.f1(k17, duprev, ku, p, t + dt * c16) + @tight_loop_macros for i in uidx + @inbounds u[i] = uprev[i] + + dt * (duprev[i] + + dt * (b1 * k1[i] + b7 * k7[i] + b8 * k8[i] + b9 * k9[i] + + b10 * k10[i] + b11 * k11[i] + b12 * k12[i] + b13 * k13[i] + + b14 * k14[i] + b15 * k15[i])) # b1 & b7 -- b15 + @inbounds du[i] = duprev[i] + + dt * (bp1 * k1[i] + bp7 * k7[i] + bp8 * k8[i] + bp9 * k9[i] + + bp10 * k10[i] + bp11 * k11[i] + bp12 * k12[i] + bp13 * k13[i] + + bp14 * k14[i] + bp15 * k15[i] + bp16 * k16[i] + bp17 * k17[i]) # bp1 & bp7 -- bp17 + end + + f.f1(k.x[1], du, u, p, t + dt) + f.f2(k.x[2], du, u, p, t + dt) + integrator.stats.nf += 17 + integrator.stats.nf2 += 1 + if integrator.opts.adaptive + duhat, uhat = utilde.x + dtsq = dt^2 + @tight_loop_macros for i in uidx + @inbounds uhat[i] = dtsq * + (btilde1 * k1[i] + btilde7 * k7[i] + btilde8 * k8[i] + + btilde9 * k9[i] + btilde10 * k10[i] + btilde11 * k11[i] + + btilde12 * k12[i] + btilde13 * k13[i] + btilde14 * k14[i] + + btilde15 * k15[i]) # btilde1 & btilde7 -- btilde15 + @inbounds duhat[i] = dt * + (bptilde1 * k1[i] + bptilde7 * k7[i] + bptilde8 * k8[i] + + bptilde9 * k9[i] + bptilde10 * k10[i] + + bptilde11 * k11[i] + bptilde12 * k12[i] + + bptilde13 * k13[i] + bptilde14 * k14[i] + + bptilde15 * k15[i] + bptilde16 * k16[i] + + bptilde17 * k17[i]) # bptilde1 & bptilde7 -- bptilde17 + end + calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +@muladd function perform_step!(integrator, cache::ERKN4ConstantCache, repeat_step = false) + @unpack t, dt, f, p = integrator + duprev, uprev = integrator.uprev.x + @unpack c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, b4, bp1, bp2, bp3, bp4, btilde1, btilde2, btilde3, btilde4, bptilde1, bptilde2, bptilde3, bptilde4 = cache + k1 = integrator.fsalfirst.x[1] + + ku = uprev + dt * (c1 * duprev + dt * a21 * k1) + + k2 = f.f1(duprev, ku, p, t + dt * c1) + ku = uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) + + k3 = f.f1(duprev, ku, p, t + dt * c2) + ku = uprev + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) + + k4 = f.f1(duprev, ku, p, t + dt * c3) + u = uprev + dt * (duprev + dt * (b1 * k1 + b2 * k2 + b3 * k3 + b4 * k4)) + du = duprev + dt * (bp1 * k1 + bp2 * k2 + bp3 * k3 + bp4 * k4) + + integrator.u = ArrayPartition((du, u)) + integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) + integrator.stats.nf += 4 + integrator.stats.nf2 += 1 + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + + if integrator.opts.adaptive + dtsq = dt^2 + uhat = dtsq * (btilde1 * k1 + btilde2 * k2 + btilde3 * k3 + btilde4 * k4) + duhat = dt * (bptilde1 * k1 + bptilde2 * k2 + bptilde3 * k3 + bptilde4 * k4) + utilde = ArrayPartition((duhat, uhat)) + atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +@muladd function perform_step!(integrator, cache::ERKN4Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + du, u = integrator.u.x + duprev, uprev = integrator.uprev.x + @unpack tmp, atmp, fsalfirst, k2, k3, k4, k, utilde = cache + @unpack c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, b4, bp1, bp2, bp3, bp4, btilde1, btilde2, btilde3, btilde4, bptilde1, bptilde2, bptilde3, bptilde4 = cache.tab + kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] + uidx = eachindex(integrator.uprev.x[2]) + k1 = integrator.fsalfirst.x[1] + + @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1) + + f.f1(k2, duprev, ku, p, t + dt * c1) + @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) + + f.f1(k3, duprev, ku, p, t + dt * c2) + @.. broadcast=false ku=uprev + + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) + + f.f1(k4, duprev, ku, p, t + dt * c3) + @tight_loop_macros for i in uidx + @inbounds u[i] = uprev[i] + + dt * (duprev[i] + + dt * (b1 * k1[i] + b2 * k2[i] + b3 * k3[i] + b4 * k4[i])) + @inbounds du[i] = duprev[i] + + dt * (bp1 * k1[i] + bp2 * k2[i] + bp3 * k3[i] + bp4 * k4[i]) + end + + f.f1(k.x[1], du, u, p, t + dt) + f.f2(k.x[2], du, u, p, t + dt) + integrator.stats.nf += 4 + integrator.stats.nf2 += 1 + if integrator.opts.adaptive + duhat, uhat = utilde.x + dtsq = dt^2 + @tight_loop_macros for i in uidx + @inbounds uhat[i] = dtsq * + (btilde1 * k1[i] + btilde2 * k2[i] + btilde3 * k3[i] + + btilde4 * k4[i]) + @inbounds duhat[i] = dt * + (bptilde1 * k1[i] + bptilde2 * k2[i] + bptilde3 * k3[i] + + bptilde4 * k4[i]) + end + calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +@muladd function perform_step!(integrator, cache::ERKN5ConstantCache, repeat_step = false) + @unpack t, dt, f, p = integrator + duprev, uprev = integrator.uprev.x + @unpack c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, b4, bp1, bp2, bp3, bp4, btilde1, btilde2, btilde3, btilde4 = cache + k1 = integrator.fsalfirst.x[1] + + ku = uprev + dt * (c1 * duprev + dt * a21 * k1) + + k2 = f.f1(duprev, ku, p, t + dt * c1) + ku = uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) + + k3 = f.f1(duprev, ku, p, t + dt * c2) + ku = uprev + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) + + k4 = f.f1(duprev, ku, p, t + dt * c3) + u = uprev + dt * (duprev + dt * (b1 * k1 + b2 * k2 + b3 * k3 + b4 * k4)) + du = duprev + dt * (bp1 * k1 + bp2 * k2 + bp3 * k3 + bp4 * k4) + + integrator.u = ArrayPartition((du, u)) + integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) + integrator.stats.nf += 4 + integrator.stats.nf2 += 1 + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + if integrator.opts.adaptive + dtsq = dt^2 + uhat = dtsq * (btilde1 * k1 + btilde2 * k2 + btilde3 * k3 + btilde4 * k4) + atmp = calculate_residuals(uhat, integrator.uprev.x[2], integrator.u.x[2], + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +@muladd function perform_step!(integrator, cache::ERKN5Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + du, u = integrator.u.x + duprev, uprev = integrator.uprev.x + @unpack tmp, atmp, fsalfirst, k2, k3, k4, k, utilde = cache + @unpack c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, b4, bp1, bp2, bp3, bp4, btilde1, btilde2, btilde3, btilde4 = cache.tab + kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] + uidx = eachindex(integrator.uprev.x[2]) + k1 = integrator.fsalfirst.x[1] + + @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1) + + f.f1(k2, duprev, ku, p, t + dt * c1) + @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) + + f.f1(k3, duprev, ku, p, t + dt * c2) + @.. broadcast=false ku=uprev + + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) + + f.f1(k4, duprev, ku, p, t + dt * c3) + @tight_loop_macros for i in uidx + @inbounds u[i] = uprev[i] + + dt * (duprev[i] + + dt * (b1 * k1[i] + b2 * k2[i] + b3 * k3[i] + b4 * k4[i])) + @inbounds du[i] = duprev[i] + + dt * (bp1 * k1[i] + bp2 * k2[i] + bp3 * k3[i] + bp4 * k4[i]) + end + + f.f1(k.x[1], du, u, p, t + dt) + f.f2(k.x[2], du, u, p, t + dt) + integrator.stats.nf += 4 + integrator.stats.nf2 += 1 + if integrator.opts.adaptive + duhat, uhat = utilde.x + dtsq = dt^2 + @tight_loop_macros for i in uidx + @inbounds uhat[i] = dtsq * + (btilde1 * k1[i] + btilde2 * k2[i] + btilde3 * k3[i] + + btilde4 * k4[i]) + end + calculate_residuals!(atmp.x[2], uhat, integrator.uprev.x[2], integrator.u.x[2], + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp.x[2], t) + end +end + +@muladd function perform_step!(integrator, cache::ERKN7ConstantCache, repeat_step = false) + @unpack t, dt, f, p = integrator + duprev, uprev = integrator.uprev.x + @unpack c1, c2, c3, c4, c5, c6, a21, a31, a32, a41, a42, a43, a51, a52, a53, a54, a61, a62, a63, a64, a65, a71, a73, a74, a75, a76, b1, b3, b4, b5, b6, bp1, bp3, bp4, bp5, bp6, bp7, btilde1, btilde3, btilde4, btilde5, btilde6, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6, bptilde7 = cache + k1 = integrator.fsalfirst.x[1] + + ku = uprev + dt * (c1 * duprev + dt * a21 * k1) + + k2 = f.f1(duprev, ku, p, t + dt * c1) + ku = uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) + + k3 = f.f1(duprev, ku, p, t + dt * c2) + ku = uprev + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) + + k4 = f.f1(duprev, ku, p, t + dt * c3) + ku = uprev + dt * (c4 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) + + k5 = f.f1(duprev, ku, p, t + dt * c4) + ku = uprev + + dt * (c5 * duprev + dt * (a61 * k1 + a62 * k2 + a63 * k3 + a64 * k4 + a65 * k5)) + + k6 = f.f1(duprev, ku, p, t + dt * c5) + ku = uprev + + dt * (c6 * duprev + dt * (a71 * k1 + a73 * k3 + a74 * k4 + a75 * k5 + a76 * k6)) + + k7 = f.f1(duprev, ku, p, t + dt * c6) + u = uprev + dt * (duprev + dt * (b1 * k1 + b3 * k3 + b4 * k4 + b5 * k5 + b6 * k6)) + du = duprev + dt * (bp1 * k1 + bp3 * k3 + bp4 * k4 + bp5 * k5 + bp6 * k6 + bp7 * k7) + + integrator.u = ArrayPartition((du, u)) + integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) + integrator.stats.nf += 4 + integrator.stats.nf2 += 1 + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + + if integrator.opts.adaptive + dtsq = dt^2 + uhat = dtsq * + (btilde1 * k1 + btilde3 * k3 + btilde4 * k4 + btilde5 * k5 + btilde6 * k6) + duhat = dt * (bptilde1 * k1 + bptilde3 * k3 + bptilde4 * k4 + bptilde5 * k5 + + bptilde6 * k6 + bptilde7 * k7) + utilde = ArrayPartition((duhat, uhat)) + atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +@muladd function perform_step!(integrator, cache::ERKN7Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + du, u = integrator.u.x + duprev, uprev = integrator.uprev.x + @unpack tmp, atmp, fsalfirst, k2, k3, k4, k5, k6, k7, k, utilde = cache + @unpack c1, c2, c3, c4, c5, c6, a21, a31, a32, a41, a42, a43, a51, a52, a53, a54, a61, a62, a63, a64, a65, a71, a73, a74, a75, a76, b1, b3, b4, b5, b6, bp1, bp3, bp4, bp5, bp6, bp7, btilde1, btilde3, btilde4, btilde5, btilde6, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6, bptilde7 = cache.tab + kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] + uidx = eachindex(integrator.uprev.x[2]) + k1 = integrator.fsalfirst.x[1] + + @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1) + + f.f1(k2, duprev, ku, p, t + dt * c1) + @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) + + f.f1(k3, duprev, ku, p, t + dt * c2) + @.. broadcast=false ku=uprev + + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) + + f.f1(k4, duprev, ku, p, t + dt * c3) + @.. broadcast=false ku=uprev + + dt * + (c4 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) + + f.f1(k5, duprev, ku, p, t + dt * c4) + @.. broadcast=false ku=uprev + + dt * (c5 * duprev + + dt * (a61 * k1 + a62 * k2 + a63 * k3 + a64 * k4 + a65 * k5)) + + f.f1(k6, duprev, ku, p, t + dt * c5) + @.. broadcast=false ku=uprev + + dt * (c6 * duprev + + dt * (a71 * k1 + a73 * k3 + a74 * k4 + a75 * k5 + a76 * k6)) + + f.f1(k7, duprev, ku, p, t + dt * c6) + @tight_loop_macros for i in uidx + @inbounds u[i] = uprev[i] + + dt * (duprev[i] + + dt * + (b1 * k1[i] + b3 * k3[i] + b4 * k4[i] + b5 * k5[i] + b6 * k6[i])) + @inbounds du[i] = duprev[i] + + dt * (bp1 * k1[i] + bp3 * k3[i] + bp4 * k4[i] + bp5 * k5[i] + + bp6 * k6[i] + bp7 * k7[i]) + end + + f.f1(k.x[1], du, u, p, t + dt) + f.f2(k.x[2], du, u, p, t + dt) + integrator.stats.nf += 4 + integrator.stats.nf2 += 1 + if integrator.opts.adaptive + duhat, uhat = utilde.x + dtsq = dt^2 + @tight_loop_macros for i in uidx + @inbounds uhat[i] = dtsq * + (btilde1 * k1[i] + btilde3 * k3[i] + btilde4 * k4[i] + + btilde5 * k5[i] + btilde6 * k6[i]) + @inbounds duhat[i] = dt * + (bptilde1 * k1[i] + bptilde3 * k3[i] + bptilde4 * k4[i] + + bptilde5 * k5[i] + bptilde6 * k6[i] + bptilde7 * k7[i]) + end + calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, + integrator.opts.abstol, integrator.opts.reltol, + integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end diff --git a/src/perform_step/ssprk_perform_step.jl b/src/perform_step/ssprk_perform_step.jl new file mode 100644 index 0000000000..4f39c2e83c --- /dev/null +++ b/src/perform_step/ssprk_perform_step.jl @@ -0,0 +1,1707 @@ +function initialize!(integrator, cache::SSPRK22ConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK22ConstantCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + + # u1 -> stored as u + integrator.fsalfirst = f(uprev, p, t) + integrator.k[1] = integrator.fsalfirst + u = uprev + dt * integrator.fsalfirst + k = f(u, p, t + dt) + # u + u = (uprev + u + dt * k) / 2 + + integrator.stats.nf += 2 + integrator.u = u +end + +function initialize!(integrator, cache::SSPRK22Cache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK22Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, fsalfirst, stage_limiter!, step_limiter!, thread = cache + + # u1 -> stored as u + f(fsalfirst, uprev, p, t) + @.. broadcast=false thread=thread u=uprev + dt * fsalfirst + stage_limiter!(u, integrator, p, t + dt) + f(k, u, p, t + dt) + # u + @.. broadcast=false thread=thread u=(uprev + u + dt * k) / 2 + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + integrator.stats.nf += 2 +end + +function initialize!(integrator, cache::KYKSSPRK42Cache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation +end + +@muladd function perform_step!(integrator, cache::KYKSSPRK42Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, tmp, fsalfirst, stage_limiter!, step_limiter!, thread = cache + @unpack α20, α21, α30, α32, α40, α43, β10, β21, β30, β32, β40, β43, c1, c2, c3 = cache.tab + + δ = fsalfirst + # u1 -> stored as u + @.. broadcast=false thread=thread u=uprev + dt * β10 * δ + stage_limiter!(u, integrator, p, t + c1 * dt) + f(k, u, p, t + c1 * dt) + # u2 + @.. broadcast=false thread=thread tmp=α20 * uprev + α21 * u + dt * β21 * k + stage_limiter!(tmp, integrator, p, t + c2 * dt) + f(k, tmp, p, t + c2 * dt) + # u3 + @.. broadcast=false thread=thread tmp=α30 * uprev + α32 * tmp + dt * β30 * δ + + dt * β32 * k + stage_limiter!(tmp, integrator, p, t + c3 * dt) + f(k, tmp, p, t + c3 * dt) + # u + @.. broadcast=false thread=thread u=α40 * uprev + α43 * tmp + dt * β40 * δ + + dt * β43 * k + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + f(k, u, p, t + dt) +end + +function initialize!(integrator, cache::KYKSSPRK42ConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::KYKSSPRK42ConstantCache) + @unpack t, dt, uprev, u, f, p = integrator + @unpack α20, α21, α30, α32, α40, α43, β10, β21, β30, β32, β40, β43, c1, c2, c3 = cache + + #u1 + δ = integrator.fsalfirst + u = uprev + dt * β10 * δ + k = f(u, p, t + c1 * dt) + #u2 + tmp = α20 * uprev + α21 * u + dt * β21 * k + k = f(tmp, p, t + c2 * dt) + #u3 + tmp = α30 * uprev + α32 * tmp + dt * β30 * δ + dt * β32 * k + k = f(tmp, p, t + c3 * dt) + #u + u = α40 * uprev + α43 * tmp + dt * β40 * δ + dt * β43 * k + + integrator.fsallast = f(u, p, t + dt) # For interpolation, then FSAL'd + integrator.k[1] = integrator.fsalfirst + integrator.u = u +end + +function initialize!(integrator, cache::SHLDDRK52ConstantCache) + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +@muladd function perform_step!(integrator, cache::SHLDDRK52ConstantCache, + repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack α2, α3, α4, α5, β1, β2, β3, β4, β5, c2, c3, c4, c5 = cache + + # u1 + tmp = dt * integrator.fsalfirst + u = uprev + β1 * tmp + # u2 + tmp = α2 * tmp + dt * f(u, p, t + c2 * dt) + u = u + β2 * tmp + # u3 + tmp = α3 * tmp + dt * f(u, p, t + c3 * dt) + u = u + β3 * tmp + # u4 + tmp = α4 * tmp + dt * f(u, p, t + c4 * dt) + u = u + β4 * tmp + # u5 = u + tmp = α5 * tmp + dt * f(u, p, t + c5 * dt) + u = u + β5 * tmp + + integrator.fsallast = f(u, p, t + dt) # For interpolation, then FSAL'd + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.u = u +end + +function initialize!(integrator, cache::SHLDDRK52Cache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation +end + +@muladd function perform_step!(integrator, cache::SHLDDRK52Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, fsalfirst, tmp, stage_limiter!, step_limiter!, thread = cache + @unpack α2, α3, α4, α5, β1, β2, β3, β4, β5, c2, c3, c4, c5 = cache.tab + + # u1 + @.. thread=thread tmp=dt * fsalfirst + @.. thread=thread u=uprev + β1 * tmp + stage_limiter!(u, integrator, p, t + c2 * dt) + # u2 + f(k, u, p, t + c2 * dt) + @.. thread=thread tmp=α2 * tmp + dt * k + @.. thread=thread u=u + β2 * tmp + stage_limiter!(u, integrator, p, t + c3 * dt) + # u3 + f(k, u, p, t + c3 * dt) + @.. thread=thread tmp=α3 * tmp + dt * k + @.. thread=thread u=u + β3 * tmp + stage_limiter!(u, integrator, p, t + c4 * dt) + # u4 + f(k, u, p, t + c4 * dt) + @.. thread=thread tmp=α4 * tmp + dt * k + @.. thread=thread u=u + β4 * tmp + stage_limiter!(u, integrator, p, t + c5 * dt) + # u5 = u + f(k, u, p, t + c5 * dt) + @.. thread=thread tmp=α5 * tmp + dt * k + @.. thread=thread u=u + β5 * tmp + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + + f(k, u, p, t + dt) +end + +function initialize!(integrator, cache::SHLDDRK_2NConstantCache) + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +@muladd function perform_step!(integrator, cache::SHLDDRK_2NConstantCache, + repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack α21, α31, α41, α51, β11, β21, β31, β41, β51, c21, c31, c41, c51, α22, α32, α42, α52, α62, β12, β22, β32, β42, β52, β62, c22, c32, c42, c52, c62 = cache + + if integrator.u_modified + cache.step = 1 + end + # cnt = cache.step + + if cache.step % 2 == 1 + cache.step += 1 + # u1 + tmp = dt * integrator.fsalfirst + u = uprev + β11 * tmp + # u2 + tmp = α21 * tmp + dt * f(u, p, t + c21 * dt) + u = u + β21 * tmp + # u3 + tmp = α31 * tmp + dt * f(u, p, t + c31 * dt) + u = u + β31 * tmp + # u4 + tmp = α41 * tmp + dt * f(u, p, t + c41 * dt) + u = u + β41 * tmp + # u5 = u + tmp = α51 * tmp + dt * f(u, p, t + c51 * dt) + u = u + β51 * tmp + + else + cache.step += 1 + # u1 + tmp = dt * integrator.fsalfirst + u = uprev + β12 * tmp + # u2 + tmp = α22 * tmp + dt * f(u, p, t + c22 * dt) + u = u + β22 * tmp + # u3 + tmp = α32 * tmp + dt * f(u, p, t + c32 * dt) + u = u + β32 * tmp + # u4 + tmp = α42 * tmp + dt * f(u, p, t + c42 * dt) + u = u + β42 * tmp + # u5 = u + tmp = α52 * tmp + dt * f(u, p, t + c52 * dt) + u = u + β52 * tmp + tmp = α62 * tmp + dt * f(u, p, t + c62 * dt) + u = u + β62 * tmp + end + + integrator.fsallast = f(u, p, t + dt) # For interpolation, then FSAL'd + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.u = u +end + +function initialize!(integrator, cache::SHLDDRK_2NCache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation +end + +@muladd function perform_step!(integrator, cache::SHLDDRK_2NCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, fsalfirst, tmp, stage_limiter!, step_limiter!, thread = cache + @unpack α21, α31, α41, α51, β11, β21, β31, β41, β51, c21, c31, c41, c51, α22, α32, α42, α52, α62, β12, β22, β32, β42, β52, β62, c22, c32, c42, c52, c62 = cache.tab + + if integrator.u_modified + cache.step = 1 + end + + if cache.step % 2 == 1 + # u1 + @.. thread=thread tmp=dt * fsalfirst + @.. thread=thread u=uprev + β11 * tmp + stage_limiter!(u, integrator, p, t + c21 * dt) + # u2 + f(k, u, p, t + c21 * dt) + @.. thread=thread tmp=α21 * tmp + dt * k + @.. thread=thread u=u + β21 * tmp + stage_limiter!(u, integrator, p, t + c31 * dt) + # u3 + f(k, u, p, t + c31 * dt) + @.. thread=thread tmp=α31 * tmp + dt * k + @.. thread=thread u=u + β31 * tmp + stage_limiter!(u, integrator, p, t + c41 * dt) + # u4 + f(k, u, p, t + c41 * dt) + @.. thread=thread tmp=α41 * tmp + dt * k + @.. thread=thread u=u + β41 * tmp + stage_limiter!(u, integrator, p, t + c51 * dt) + # u5 = u + f(k, u, p, t + c51 * dt) + @.. thread=thread tmp=α51 * tmp + dt * k + @.. thread=thread u=u + β51 * tmp + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + + f(k, u, p, t + dt) + else + # u1 + @.. thread=thread tmp=dt * fsalfirst + @.. thread=thread u=uprev + β12 * tmp + stage_limiter!(u, integrator, p, t + c22 * dt) + # u2 + f(k, u, p, t + c22 * dt) + @.. thread=thread tmp=α22 * tmp + dt * k + @.. thread=thread u=u + β22 * tmp + stage_limiter!(u, integrator, p, t + c32 * dt) + # u3 + f(k, u, p, t + c32 * dt) + @.. thread=thread tmp=α32 * tmp + dt * k + @.. thread=thread u=u + β32 * tmp + stage_limiter!(u, integrator, p, t + c42 * dt) + # u4 + f(k, u, p, t + c42 * dt) + @.. thread=thread tmp=α42 * tmp + dt * k + @.. thread=thread u=u + β42 * tmp + stage_limiter!(u, integrator, p, t + c52 * dt) + # u5 = u + f(k, u, p, t + c52 * dt) + @.. thread=thread tmp=α52 * tmp + dt * k + @.. thread=thread u=u + β52 * tmp + stage_limiter!(u, integrator, p, t + c62 * dt) + # u6 = u + f(k, u, p, t + c62 * dt) + @.. thread=thread tmp=α62 * tmp + dt * k + @.. thread=thread u=u + β62 * tmp + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + + f(k, u, p, t + dt) + end +end + +function initialize!(integrator, cache::SSPRK33ConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK33ConstantCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + + # u1 + integrator.fsalfirst = f(uprev, p, t) + integrator.k[1] = integrator.fsalfirst + u = uprev + dt * integrator.fsalfirst + k = f(u, p, t + dt) + # u2 + u = (3 * uprev + u + dt * k) / 4 + k = f(u, p, t + dt / 2) + # u + u = (uprev + 2 * u + 2 * dt * k) / 3 + + integrator.stats.nf += 3 + integrator.u = u +end + +function initialize!(integrator, cache::SSPRK33Cache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK33Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, fsalfirst, stage_limiter!, step_limiter!, thread = cache + + # u1 + f(fsalfirst, uprev, p, t) + @.. broadcast=false thread=thread u=uprev + dt * fsalfirst + stage_limiter!(u, integrator, p, t + dt) + f(k, u, p, t + dt) + # u2 + @.. broadcast=false thread=thread u=(3 * uprev + u + dt * k) / 4 + stage_limiter!(u, integrator, p, t + dt / 2) + f(k, u, p, t + dt / 2) + # u + @.. broadcast=false thread=thread u=(uprev + 2 * u + 2 * dt * k) / 3 + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + integrator.stats.nf += 3 +end + +function initialize!(integrator, cache::SSPRK53ConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK53ConstantCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack α30, α32, α40, α43, α52, α54, β10, β21, β32, β43, β54, c1, c2, c3, c4 = cache + + # u1 + integrator.fsalfirst = f(uprev, p, t) + integrator.k[1] = integrator.fsalfirst + tmp = uprev + β10 * dt * integrator.fsalfirst + k = f(tmp, p, t + c1 * dt) + # u2 -> stored as u + u = tmp + β21 * dt * k + k = f(u, p, t + c2 * dt) + # u3 + tmp = α30 * uprev + α32 * u + β32 * dt * k + k = f(tmp, p, t + c3 * dt) + # u4 + tmp = α40 * uprev + α43 * tmp + β43 * dt * k + k = f(tmp, p, t + c4 * dt) + # u + u = α52 * u + α54 * tmp + β54 * dt * k + + integrator.stats.nf += 5 + integrator.u = u +end + +function initialize!(integrator, cache::SSPRK53Cache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK53Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, fsalfirst, tmp, stage_limiter!, step_limiter!, thread = cache + @unpack α30, α32, α40, α43, α52, α54, β10, β21, β32, β43, β54, c1, c2, c3, c4 = cache.tab + + # u1 + f(fsalfirst, uprev, p, t) + @.. broadcast=false thread=thread tmp=uprev + β10 * dt * fsalfirst + stage_limiter!(tmp, integrator, p, t + c1 * dt) + f(k, tmp, p, t + c1 * dt) + # u2 -> stored as u + @.. broadcast=false thread=thread u=tmp + β21 * dt * k + stage_limiter!(u, integrator, p, t + c2 * dt) + f(k, u, p, t + c2 * dt) + # u3 + @.. broadcast=false thread=thread tmp=α30 * uprev + α32 * u + β32 * dt * k + stage_limiter!(tmp, integrator, p, t + c3 * dt) + f(k, tmp, p, t + c3 * dt) + # u4 + @.. broadcast=false thread=thread tmp=α40 * uprev + α43 * tmp + β43 * dt * k + stage_limiter!(tmp, integrator, p, t + c4 * dt) + f(k, tmp, p, t + c4 * dt) + # u + @.. broadcast=false thread=thread u=α52 * u + α54 * tmp + β54 * dt * k + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + integrator.stats.nf += 5 +end + +function initialize!(integrator, cache::SSPRK53_2N1ConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK53_2N1ConstantCache, + repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack α40, α43, β10, β21, β32, β43, β54, c1, c2, c3, c4 = cache + #stores in u for all intermediate stages + # u1 + integrator.fsalfirst = f(uprev, p, t) + integrator.k[1] = integrator.fsalfirst + u = uprev + β10 * dt * integrator.fsalfirst + k = f(u, p, t + c1 * dt) + # u2 + u = u + β21 * dt * k + k = f(u, p, t + c2 * dt) + # u3 + u = u + β32 * dt * k + k = f(u, p, t + c3 * dt) + # u4 + u = α40 * uprev + α43 * u + β43 * dt * k + k = f(u, p, t + c4 * dt) + # u + u = u + β54 * dt * k + + integrator.stats.nf += 1 + integrator.u = u +end + +function initialize!(integrator, cache::SSPRK53_2N1Cache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK53_2N1Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, fsalfirst, stage_limiter!, step_limiter!, thread = cache + @unpack α40, α43, β10, β21, β32, β43, β54, c1, c2, c3, c4 = cache.tab + + #stores in u for all intermediate stages + # u1 + f(fsalfirst, uprev, p, t) + @.. broadcast=false thread=thread u=uprev + β10 * dt * fsalfirst + stage_limiter!(u, integrator, p, t + c1 * dt) + f(k, u, p, t + c1 * dt) + # u2 + @.. broadcast=false thread=thread u=u + β21 * dt * k + stage_limiter!(u, integrator, p, t + c2 * dt) + f(k, u, p, t + c2 * dt) + # u3 + @.. broadcast=false thread=thread u=u + β32 * dt * k + stage_limiter!(u, integrator, p, t + c3 * dt) + f(k, u, p, t + c3 * dt) + # u4 + @.. broadcast=false thread=thread u=α40 * uprev + α43 * u + β43 * dt * k + stage_limiter!(u, integrator, p, t + c4 * dt) + f(k, u, p, t + c4 * dt) + # u + @.. broadcast=false thread=thread u=u + β54 * dt * k + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + integrator.stats.nf += 5 +end + +function initialize!(integrator, cache::SSPRK53_2N2ConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK53_2N2ConstantCache, + repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack α30, α32, α50, α54, β10, β21, β32, β43, β54, c1, c2, c3, c4 = cache + #stores in u for all intermediate stages + # u1 + integrator.fsalfirst = f(uprev, p, t) + integrator.k[1] = integrator.fsalfirst + u = uprev + β10 * dt * integrator.fsalfirst + k = f(u, p, t + c1 * dt) + # u2 -> stored as u + u = u + β21 * dt * k + k = f(u, p, t + c2 * dt) + # u3 + u = α30 * uprev + α32 * u + β32 * dt * k + k = f(u, p, t + c3 * dt) + # u4 + u = u + β43 * dt * k + k = f(u, p, t + c4 * dt) + # u + u = α50 * uprev + α54 * u + β54 * dt * k + + integrator.stats.nf += 5 + integrator.u = u +end + +function initialize!(integrator, cache::SSPRK53_2N2Cache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK53_2N2Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, fsalfirst, stage_limiter!, step_limiter!, thread = cache + @unpack α30, α32, α50, α54, β10, β21, β32, β43, β54, c1, c2, c3, c4 = cache.tab + + # u1 + f(fsalfirst, uprev, p, t) + @.. broadcast=false thread=thread u=uprev + β10 * dt * fsalfirst + stage_limiter!(u, integrator, p, t + c1 * dt) + f(k, u, p, t + c1 * dt) + # u2 -> stored as u + @.. broadcast=false thread=thread u=u + β21 * dt * k + stage_limiter!(u, integrator, p, t + c2 * dt) + f(k, u, p, t + c2 * dt) + # u3 + @.. broadcast=false thread=thread u=α30 * uprev + α32 * u + β32 * dt * k + stage_limiter!(u, integrator, p, t + c3 * dt) + f(k, u, p, t + c3 * dt) + # u4 + @.. broadcast=false thread=thread u=u + β43 * dt * k + stage_limiter!(u, integrator, p, t + c4 * dt) + f(k, u, p, t + c4 * dt) + # u + @.. broadcast=false thread=thread u=α50 * uprev + α54 * u + β54 * dt * k + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + integrator.stats.nf += 5 +end + +function initialize!(integrator, cache::SSPRK53_HConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK53_HConstantCache, + repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack α30, α32, α40, α41, α43, β10, β21, β32, β43, β54, c1, c2, c3, c4 = cache + #stores in u for all intermediate stages + # u1 + integrator.fsalfirst = f(uprev, p, t) + integrator.k[1] = integrator.fsalfirst + tmp = uprev + β10 * dt * integrator.fsalfirst + k = f(tmp, p, t + c1 * dt) + # u2 + u = tmp + β21 * dt * k + k = f(u, p, t + c2 * dt) + # u3 + u = α30 * uprev + α32 * u + β32 * dt * k + k = f(u, p, t + c3 * dt) + # u4 + u = α40 * uprev + α41 * tmp + α43 * u + β43 * dt * k + k = f(u, p, t + c4 * dt) + # u + u = u + β54 * dt * k + + integrator.stats.nf += 5 + integrator.u = u +end + +function initialize!(integrator, cache::SSPRK53_HCache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK53_HCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, fsalfirst, tmp, stage_limiter!, step_limiter!, thread = cache + @unpack α30, α32, α40, α41, α43, β10, β21, β32, β43, β54, c1, c2, c3, c4 = cache.tab + #stores in u for all intermediate stages + # u1 + f(fsalfirst, uprev, p, t) + @.. broadcast=false thread=thread tmp=uprev + β10 * dt * fsalfirst + stage_limiter!(tmp, integrator, p, t + c1 * dt) + f(k, tmp, p, t + c1 * dt) + # u2 + @.. broadcast=false thread=thread u=tmp + β21 * dt * k + stage_limiter!(u, integrator, p, t + c2 * dt) + f(k, u, p, t + c2 * dt) + # u3 + @.. broadcast=false thread=thread u=α30 * uprev + α32 * u + β32 * dt * k + stage_limiter!(u, integrator, p, t + c3 * dt) + f(k, u, p, t + c3 * dt) + # u4 + @.. broadcast=false thread=thread u=α40 * uprev + α41 * tmp + α43 * u + β43 * dt * k + stage_limiter!(u, integrator, p, t + c4 * dt) + f(k, u, p, t + c4 * dt) + # u + @.. broadcast=false thread=thread u=u + β54 * dt * k + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + integrator.stats.nf += 5 +end + +function initialize!(integrator, cache::SSPRK63ConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK63ConstantCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack α40, α41, α43, α62, α65, β10, β21, β32, β43, β54, β65, c1, c2, c3, c4, c5 = cache + + # u1 -> stored as u + integrator.fsalfirst = f(uprev, p, t) + integrator.k[1] = integrator.fsalfirst + u = uprev + β10 * dt * integrator.fsalfirst + k = f(u, p, t + c1 * dt) + # u2 + u₂ = u + β21 * dt * k + k = f(u₂, p, t + c2 * dt) + # u3 + tmp = u₂ + β32 * dt * k + k = f(tmp, p, t + c3 * dt) + # u4 + tmp = α40 * uprev + α41 * u + α43 * tmp + β43 * dt * k + k = f(tmp, p, t + c4 * dt) + # u5 + tmp = tmp + β54 * dt * k + k = f(tmp, p, t + c5 * dt) + # u + u = α62 * u₂ + α65 * tmp + β65 * dt * k + + integrator.stats.nf += 6 + integrator.u = u +end + +function initialize!(integrator, cache::SSPRK63Cache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK63Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, fsalfirst, tmp, u₂, stage_limiter!, step_limiter!, thread = cache + @unpack α40, α41, α43, α62, α65, β10, β21, β32, β43, β54, β65, c1, c2, c3, c4, c5 = cache.tab + + # u1 -> stored as u + f(fsalfirst, uprev, p, t) + @.. broadcast=false thread=thread u=uprev + β10 * dt * fsalfirst + stage_limiter!(u, integrator, p, t + c1 * dt) + f(k, u, p, t + c1 * dt) + # u2 + @.. broadcast=false thread=thread u₂=u + β21 * dt * k + stage_limiter!(u₂, integrator, p, t + c2 * dt) + f(k, u₂, p, t + c2 * dt) + # u3 + @.. broadcast=false thread=thread tmp=u₂ + β32 * dt * k + stage_limiter!(tmp, integrator, p, t + c3 * dt) + f(k, tmp, p, t + c3 * dt) + # u4 + @.. broadcast=false thread=thread tmp=α40 * uprev + α41 * u + α43 * tmp + β43 * dt * k + stage_limiter!(tmp, integrator, p, t + c4 * dt) + f(k, tmp, p, t + c4 * dt) + # u5 + @.. broadcast=false thread=thread tmp=tmp + β54 * dt * k + stage_limiter!(tmp, integrator, p, t + c5 * dt) + f(k, tmp, p, t + c5 * dt) + # u + @.. broadcast=false thread=thread u=α62 * u₂ + α65 * tmp + β65 * dt * k + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + integrator.stats.nf += 6 +end + +function initialize!(integrator, cache::SSPRK73ConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK73ConstantCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack α40, α43, α50, α51, α54, α73, α76, β10, β21, β32, β43, β54, β65, β76, c1, c2, c3, c4, c5, c6 = cache + + # u1 + integrator.fsalfirst = f(uprev, p, t) + integrator.k[1] = integrator.fsalfirst + u₁ = uprev + β10 * dt * integrator.fsalfirst + k = f(u₁, p, t + c1 * dt) + # u2 + tmp = u₁ + β21 * dt * k + k = f(tmp, p, t + c2 * dt) + # u3 -> stored as u + u = tmp + β32 * dt * k + k = f(u, p, t + c3 * dt) + # u4 + tmp = α40 * uprev + α43 * u + β43 * dt * k + k = f(tmp, p, t + c4 * dt) + # u5 + tmp = α50 * uprev + α51 * u₁ + α54 * tmp + β54 * dt * k + k = f(tmp, p, t + c5 * dt) + # u6 + tmp = tmp + β65 * dt * k + k = f(tmp, p, t + c6 * dt) + # u + u = α73 * u + α76 * tmp + β76 * dt * k + + integrator.stats.nf += 7 + integrator.u = u +end + +function initialize!(integrator, cache::SSPRK73Cache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK73Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, fsalfirst, tmp, u₁, stage_limiter!, step_limiter!, thread = cache + @unpack α40, α43, α50, α51, α54, α73, α76, β10, β21, β32, β43, β54, β65, β76, c1, c2, c3, c4, c5, c6 = cache.tab + + # u1 + f(fsalfirst, uprev, p, t) + @.. broadcast=false thread=thread u₁=uprev + β10 * dt * fsalfirst + stage_limiter!(u₁, integrator, p, t + c1 * dt) + f(k, u₁, p, t + c1 * dt) + # u2 + @.. broadcast=false thread=thread tmp=u₁ + β21 * dt * k + stage_limiter!(tmp, integrator, p, t + c2 * dt) + f(k, tmp, p, t + c2 * dt) + # u3 -> stored as u + @.. broadcast=false thread=thread u=tmp + β32 * dt * k + stage_limiter!(u, integrator, p, t + c3 * dt) + f(k, u, p, t + c3 * dt) + # u4 + @.. broadcast=false thread=thread tmp=α40 * uprev + α43 * u + β43 * dt * k + stage_limiter!(tmp, integrator, p, t + c4 * dt) + f(k, tmp, p, t + c4 * dt) + # u5 + @.. broadcast=false thread=thread tmp=α50 * uprev + α51 * u₁ + α54 * tmp + β54 * dt * k + stage_limiter!(tmp, integrator, p, t + c5 * dt) + f(k, tmp, p, t + c5 * dt) + # u6 + @.. broadcast=false thread=thread tmp=tmp + β65 * dt * k + stage_limiter!(tmp, integrator, p, t + c6 * dt) + f(k, tmp, p, t + c6 * dt) + # u + @.. broadcast=false thread=thread u=α73 * u + α76 * tmp + β76 * dt * k + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + integrator.stats.nf += 7 +end + +function initialize!(integrator, cache::SSPRK83ConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK83ConstantCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack α50, α51, α54, α61, α65, α72, α73, α76, β10, β21, β32, β43, β54, β65, β76, β87, c1, c2, c3, c4, c5, c6, c7 = cache + + # u1 -> save as u + integrator.fsalfirst = f(uprev, p, t) + integrator.k[1] = integrator.fsalfirst + u = uprev + β10 * dt * integrator.fsalfirst + k = f(u, p, t + c1 * dt) + # u2 + u₂ = u + β21 * dt * k + k = f(u₂, p, t + c2 * dt) + # u3 + u₃ = u₂ + β32 * dt * k + k = f(u₃, p, t + c3 * dt) + # u4 + tmp = u₃ + β43 * dt * k + k = f(tmp, p, t + c4 * dt) + # u5 + tmp = α50 * uprev + α51 * u + α54 * tmp + β54 * dt * k + k = f(tmp, p, t + c5 * dt) + # u6 + tmp = α61 * u + α65 * tmp + β65 * dt * k + k = f(tmp, p, t + c6 * dt) + # u7 + tmp = α72 * u₂ + α73 * u₃ + α76 * tmp + β76 * dt * k + k = f(tmp, p, t + c7 * dt) + # u + u = tmp + β87 * dt * k + + integrator.stats.nf += 8 + integrator.u = u +end + +function initialize!(integrator, cache::SSPRK83Cache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK83Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, fsalfirst, tmp, u₂, u₃, stage_limiter!, step_limiter!, thread = cache + @unpack α50, α51, α54, α61, α65, α72, α73, α76, β10, β21, β32, β43, β54, β65, β76, β87, c1, c2, c3, c4, c5, c6, c7 = cache.tab + + # u1 -> save as u + f(fsalfirst, uprev, p, t) + @.. broadcast=false thread=thread u=uprev + β10 * dt * fsalfirst + stage_limiter!(u, integrator, p, t + c1 * dt) + f(k, u, p, t + c1 * dt) + # u2 + @.. broadcast=false thread=thread u₂=u + β21 * dt * k + stage_limiter!(u₂, integrator, p, t + c2 * dt) + f(k, u₂, p, t + c2 * dt) + # u3 + @.. broadcast=false thread=thread u₃=u₂ + β32 * dt * k + stage_limiter!(u₃, integrator, p, t + c3 * dt) + f(k, u₃, p, t + c3 * dt) + # u4 + @.. broadcast=false thread=thread tmp=u₃ + β43 * dt * k + stage_limiter!(tmp, integrator, p, t + c4 * dt) + f(k, tmp, p, t + c4 * dt) + # u5 + @.. broadcast=false thread=thread tmp=α50 * uprev + α51 * u + α54 * tmp + β54 * dt * k + stage_limiter!(tmp, integrator, p, t + c5 * dt) + f(k, tmp, p, t + c5 * dt) + # u6 + @.. broadcast=false thread=thread tmp=α61 * u + α65 * tmp + β65 * dt * k + stage_limiter!(tmp, integrator, p, t + c6 * dt) + f(k, tmp, p, t + c6 * dt) + # u7 + @.. broadcast=false thread=thread tmp=α72 * u₂ + α73 * u₃ + α76 * tmp + β76 * dt * k + stage_limiter!(tmp, integrator, p, t + c7 * dt) + f(k, tmp, p, t + c7 * dt) + # u + @.. broadcast=false thread=thread u=tmp + β87 * dt * k + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + integrator.stats.nf += 8 +end + +function initialize!(integrator, cache::SSPRK43ConstantCache) + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK43ConstantCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack one_third_u, two_thirds_u, half_u, half_t = cache + dt_2 = half_t * dt + + # u1 + integrator.fsalfirst = f(uprev, p, t) + integrator.k[1] = integrator.fsalfirst + u = uprev + dt_2 * integrator.fsalfirst + k = f(u, p, t + dt_2) + # u2 + u = u + dt_2 * k + k = f(u, p, t + dt) + u = u + dt_2 * k + if integrator.opts.adaptive + utilde = one_third_u * uprev + two_thirds_u * u # corresponds to bhat = (1/3, 1/3, 1/3, 0) + end + # u3 + u = two_thirds_u * uprev + one_third_u * u + k = f(u, p, t + dt_2) + # u + u = u + dt_2 * k # corresponds to b = (1/6, 1/6, 1/6, 1/2) + + integrator.stats.nf += 4 + if integrator.opts.adaptive + utilde = half_u * (utilde - u) # corresponds to bhat = (1/4, 1/4, 1/4, 1/4) + atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.u = u +end + +function initialize!(integrator, cache::SSPRK43Cache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK43Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, fsalfirst, utilde, atmp, stage_limiter!, step_limiter!, thread = cache + @unpack one_third_u, two_thirds_u, half_u, half_t = cache.tab + dt_2 = half_t * dt + + # u1 + f(fsalfirst, uprev, p, t) + @.. broadcast=false thread=thread u=uprev + dt_2 * fsalfirst + stage_limiter!(u, integrator, p, t + dt_2) + f(k, u, p, t + dt_2) + # u2 + @.. broadcast=false thread=thread u=u + dt_2 * k + stage_limiter!(u, integrator, p, t + dt) + f(k, u, p, t + dt) + # + @.. broadcast=false thread=thread u=u + dt_2 * k + stage_limiter!(u, integrator, p, t + dt + dt_2) + if integrator.opts.adaptive + @.. broadcast=false utilde=one_third_u * uprev + two_thirds_u * u # corresponds to bhat = (1/3, 1/3, 1/3, 0) + end + # u3 + @.. broadcast=false thread=thread u=two_thirds_u * uprev + one_third_u * u + f(k, u, p, t + dt_2) + # + @.. broadcast=false thread=thread u=u + dt_2 * k # corresponds to b = (1/6, 1/6, 1/6, 1/2) + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + + if integrator.opts.adaptive + @.. broadcast=false thread=thread utilde=half_u * (utilde - u) # corresponds to bhat = (1/4, 1/4, 1/4, 1/4) + calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t, + thread) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.stats.nf += 4 +end + +function initialize!(integrator, cache::SSPRK432ConstantCache) + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK432ConstantCache, + repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + dt_2 = dt / 2 + + # u1 + integrator.fsalfirst = f(uprev, p, t) + integrator.k[1] = integrator.fsalfirst + u = uprev + dt_2 * integrator.fsalfirst + k = f(u, p, t + dt_2) + # u2 + u = u + dt_2 * k + k = f(u, p, t + dt) + u = u + dt_2 * k + if integrator.opts.adaptive + utilde = (uprev + 2 * u) / 3 + end + # u3 + u = (2 * uprev + u) / 3 + k = f(u, p, t + dt_2) + # u + u = u + dt_2 * k + + integrator.stats.nf += 4 + if integrator.opts.adaptive + utilde = utilde - u + atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.u = u +end + +function initialize!(integrator, cache::SSPRK432Cache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK432Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, fsalfirst, utilde, atmp, stage_limiter!, step_limiter!, thread = cache + dt_2 = dt / 2 + + # u1 + f(fsalfirst, uprev, p, t) + @.. broadcast=false thread=thread u=uprev + dt_2 * fsalfirst + stage_limiter!(u, integrator, p, t + dt_2) + f(k, u, p, t + dt_2) + # u2 + @.. broadcast=false thread=thread u=u + dt_2 * k + stage_limiter!(u, integrator, p, t + dt) + f(k, u, p, t + dt) + # + @.. broadcast=false thread=thread u=u + dt_2 * k + stage_limiter!(u, integrator, p, t + dt + dt_2) + if integrator.opts.adaptive + @.. broadcast=false utilde=(uprev + 2 * u) / 3 + end + # u3 + @.. broadcast=false thread=thread u=(2 * uprev + u) / 3 + f(k, u, p, t + dt_2) + # + @.. broadcast=false thread=thread u=u + dt_2 * k + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + + if integrator.opts.adaptive + @.. broadcast=false thread=thread utilde=utilde - u + calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t, + thread) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.stats.nf += 4 +end + +function initialize!(integrator, cache::SSPRKMSVS32ConstantCache) + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRKMSVS32ConstantCache, + repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack u_1, u_2, dts, dtf, μ, v_n = cache + + if integrator.iter == 1 + cache.dts[1] = dt + cache.dts[2] = dt + cache.dtf[1] = dt + end + accpt = true + dt = dts[1] + + if cache.step < 3 #starting Procedure + k = f(u, p, t + dt) + u = uprev + dt * k + k = f(u, p, t + dt) + integrator.stats.nf += 2 + u = (uprev + u + dt * k) / 2 + if cache.step == 1 + u_2 = uprev + else + u_1 = uprev + end + if integrator.opts.adaptive + v_n = dt / dts[2] * 0.5 + cache.dtf[2] = dtf[1] + cache.dtf[1] = dt / v_n * 0.5 + if v_n > 0.5 + cache.step -= 1 + accpt = false + end + cache.dts[3] = dts[2] + cache.dts[2] = dt + dt = 0.9 * dtf[1] + μ = min(dtf[1], dtf[2]) + end + else + if integrator.opts.adaptive + Ω = (dts[2] + dts[3]) / dt + else + Ω = 2 + end + u = (Ω * Ω - 1) / (Ω * Ω) * (uprev + Ω / (Ω - 1) * dt * integrator.fsalfirst) + + 1 / (Ω * Ω) * u_2 + u_2 = u_1 + u_1 = uprev + if integrator.opts.adaptive + v_n = (dts[2] + dts[3] - dt) / (dts[2] + dts[3]) * 0.5 + dt = (dts[2] + dts[3]) / (dts[2] + dts[3] + μ) * μ + cache.dtf[2] = dtf[1] + dtf[1] = dt / v_n * 0.5 + cache.dts[3] = dts[2] + cache.dts[2] = dt + μ = min(dtf[1], dtf[2]) + end + end + if accpt == true + integrator.fsallast = f(u, p, t + dt) + integrator.stats.nf += 1 + integrator.k[1] = integrator.fsalfirst + integrator.u = u + else + integrator.fsallast = f(uprev, p, t + dt) + integrator.stats.nf += 1 + integrator.k[1] = integrator.fsalfirst + integrator.u = uprev + end + cache.dts[1] = dt + cache.step += 1 + cache.u_1 = u_1 + cache.u_2 = u_2 + cache.μ = μ +end + +function initialize!(integrator, cache::SSPRKMSVS32Cache) + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.fsalfirst = cache.fsalfirst # done by pointers, no copying + integrator.fsallast = cache.k + integrator.k[1] = integrator.fsalfirst + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) + integrator.stats.nf += 1 +end + +@muladd function perform_step!(integrator, cache::SSPRKMSVS32Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, fsalfirst, u_1, u_2, stage_limiter!, step_limiter!, thread = cache + + if cache.step < 3 + @.. broadcast=false thread=thread u=uprev + dt * fsalfirst + stage_limiter!(u, integrator, p, t + dt) + f(k, u, p, t + dt) + integrator.stats.nf += 1 + @.. broadcast=false thread=thread u=(uprev + u + dt * k) / 2 + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + + if cache.step == 1 + cache.u_2 .= uprev + else + cache.u_1 .= uprev + end + else + Ω = 2 + @.. broadcast=false thread=thread u=((Ω * Ω - 1) / (Ω * Ω)) * + (uprev + (Ω / (Ω - 1)) * dt * fsalfirst) + + (1 / (Ω * Ω)) * cache.u_2 + cache.u_2 .= u_1 + cache.u_1 .= uprev + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + end + cache.step += 1 + integrator.stats.nf += 1 + f(k, u, p, t + dt) +end + +function initialize!(integrator, cache::SSPRKMSVS43ConstantCache) + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRKMSVS43ConstantCache, + repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack u_1, u_2, u_3, k1, k2, k3 = cache + + if cache.step < 4 + u = uprev + dt * integrator.fsalfirst + k = f(u, p, t + dt) + u = (uprev + u + dt * k) / 2 + if cache.step == 1 + u_3 = uprev + cache.k3 = f(u_3, p, t + dt) + integrator.stats.nf += 1 + end + if cache.step == 2 + u_2 = uprev + cache.k2 = f(u_2, p, t + dt) + integrator.stats.nf += 1 + end + if cache.step == 3 + u_1 = uprev + cache.k1 = f(u_1, p, t + dt) + integrator.stats.nf += 1 + end + # u + else + u = (16 / 27) * (uprev + 3 * dt * integrator.fsalfirst) + + (11 / 27) * (u_3 + (12 / 11) * dt * k3) + cache.k3 = k2 + cache.k2 = k1 + cache.k1 = integrator.fsalfirst + u_3 = u_2 + u_2 = u_1 + u_1 = uprev + end + integrator.fsallast = f(u, p, t + dt) # For interpolation, then FSAL'd + integrator.stats.nf += 1 + integrator.k[1] = integrator.fsalfirst + integrator.u = u + cache.step += 1 + cache.u_1 = u_1 + cache.u_2 = u_2 + cache.u_3 = u_3 +end + +function initialize!(integrator, cache::SSPRKMSVS43Cache) + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.fsalfirst = cache.fsalfirst # done by pointers, no copying + integrator.fsallast = cache.k + integrator.k[1] = integrator.fsalfirst + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 +end + +@muladd function perform_step!(integrator, cache::SSPRKMSVS43Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, fsalfirst, u_1, u_2, u_3, stage_limiter!, step_limiter!, thread, k1, k2, k3 = cache + + if cache.step < 4 + @.. broadcast=false thread=thread u=uprev + dt * fsalfirst + stage_limiter!(u, integrator, p, t + dt) + f(k, u, p, t + dt) + integrator.stats.nf += 1 + @.. broadcast=false thread=thread u=(uprev + u + dt * k) / 2 + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + if cache.step == 1 + cache.u_3 .= uprev + f(k3, u_3, p, t + dt) + integrator.stats.nf += 1 + end + if cache.step == 2 + cache.u_2 .= uprev + f(k2, u_2, p, t + dt) + integrator.stats.nf += 1 + end + if cache.step == 3 + cache.u_1 .= uprev + f(k1, u_1, p, t + dt) + integrator.stats.nf += 1 + end + # u + else + @.. broadcast=false thread=thread u=(16 / 27) * (uprev + 3 * dt * fsalfirst) + + (11 / 27) * (u_3 + (12 / 11) * dt * k3) + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + cache.k3 .= k2 + cache.k2 .= k1 + cache.k1 .= fsalfirst + cache.u_3 .= u_2 + cache.u_2 .= u_1 + cache.u_1 .= uprev + end + cache.step += 1 + integrator.stats.nf += 1 + f(k, u, p, t + dt) +end + +function initialize!(integrator, cache::SSPRK932ConstantCache) + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK932ConstantCache, + repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + dt_6 = dt / 6 + dt_3 = dt / 3 + dt_2 = dt / 2 + + # u1 + integrator.fsalfirst = f(uprev, p, t) + integrator.k[1] = integrator.fsalfirst + u = uprev + dt_6 * integrator.fsalfirst + k = f(u, p, t + dt_6) + # u2 + u = u + dt_6 * k + k = f(u, p, t + dt_3) + # u3 + u = u + dt_6 * k + k = f(u, p, t + dt_2) + # u4 + u = u + dt_6 * k + k = f(u, p, t + 2 * dt_3) + # u5 + u = u + dt_6 * k + k = f(u, p, t + 5 * dt_6) + integrator.stats.nf += 6 + # u6 + u = u + dt_6 * k + if integrator.opts.adaptive + k = f(u, p, t + dt) + integrator.stats.nf += 1 + utilde = (uprev + 6 * u + 6 * dt * k) / 7 + end + # u6* + u = (3 * uprev + dt_2 * integrator.fsalfirst + 2 * u) / 5 + k = f(u, p, t + dt_2) + # u7* + u = u + dt_6 * k + k = f(u, p, t + 2 * dt_3) + # u8* + u = u + dt_6 * k + k = f(u, p, t + 5 * dt_6) + # u + u = u + dt_6 * k + + integrator.stats.nf += 3 + if integrator.opts.adaptive + utilde = utilde - u + atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.u = u +end + +function initialize!(integrator, cache::SSPRK932Cache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK932Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, fsalfirst, utilde, atmp, stage_limiter!, step_limiter!, thread = cache + dt_6 = dt / 6 + dt_3 = dt / 3 + dt_2 = dt / 2 + + # u1 + f(fsalfirst, uprev, p, t) + @.. broadcast=false thread=thread u=uprev + dt_6 * fsalfirst + stage_limiter!(u, integrator, p, t + dt_6) + f(k, u, p, t + dt_6) + # u2 + @.. broadcast=false thread=thread u=u + dt_6 * k + stage_limiter!(u, integrator, p, t + dt_3) + f(k, u, p, t + dt_3) + # u3 + @.. broadcast=false thread=thread u=u + dt_6 * k + stage_limiter!(u, integrator, p, t + dt_2) + f(k, u, p, t + dt_2) + # u4 + @.. broadcast=false thread=thread u=u + dt_6 * k + stage_limiter!(u, integrator, p, t + 2 * dt_3) + f(k, u, p, t + 2 * dt_3) + # u5 + @.. broadcast=false thread=thread u=u + dt_6 * k + stage_limiter!(u, integrator, p, t + 5 * dt_6) + f(k, u, p, t + 5 * dt_6) + integrator.stats.nf += 6 + # u6 + @.. broadcast=false thread=thread u=u + dt_6 * k + if integrator.opts.adaptive + stage_limiter!(u, integrator, p, t + dt) + f(k, u, p, t + dt) + integrator.stats.nf += 1 + @.. broadcast=false thread=thread utilde=(uprev + 6 * u + 6 * dt * k) / 7 + end + # u6* + @.. broadcast=false thread=thread u=(3 * uprev + dt_2 * integrator.fsalfirst + 2 * u) / + 5 + stage_limiter!(u, integrator, p, t + dt_6) + f(k, u, p, t + dt_2) + # u7* + @.. broadcast=false thread=thread u=u + dt_6 * k + stage_limiter!(u, integrator, p, t + 2 * dt_3) + f(k, u, p, t + 2 * dt_3) + # u8* + @.. broadcast=false thread=thread u=u + dt_6 * k + stage_limiter!(u, integrator, p, t + 5 * dt_6) + f(k, u, p, t + 5 * dt_6) + # u9* + @.. broadcast=false thread=thread u=u + dt_6 * k + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + integrator.stats.nf += 3 + + if integrator.opts.adaptive + @.. broadcast=false thread=thread utilde=utilde - u + calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t, + thread) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end +end + +function initialize!(integrator, cache::SSPRK54ConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK54ConstantCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack β10, α20, α21, β21, α30, α32, β32, α40, α43, β43, α52, α53, β53, α54, β54, c1, c2, c3, c4 = cache + + # u₁ + integrator.fsalfirst = f(uprev, p, t) + integrator.k[1] = integrator.fsalfirst + u₂ = uprev + β10 * dt * integrator.fsalfirst + k = f(u₂, p, t + c1 * dt) + # u₂ + u₂ = α20 * uprev + α21 * u₂ + β21 * dt * k + k = f(u₂, p, t + c2 * dt) + # u₃ + u₃ = α30 * uprev + α32 * u₂ + β32 * dt * k + k₃ = f(u₃, p, t + c3 * dt) + # u₄ -> stored as tmp + tmp = α40 * uprev + α43 * u₃ + β43 * dt * k₃ + k = f(tmp, p, t + c4 * dt) + # u + u = α52 * u₂ + α53 * u₃ + β53 * dt * k₃ + α54 * tmp + β54 * dt * k + + integrator.stats.nf += 5 + integrator.u = u +end + +function initialize!(integrator, cache::SSPRK54Cache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK54Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, fsalfirst, k₃, u₂, u₃, tmp, stage_limiter!, step_limiter!, thread = cache + @unpack β10, α20, α21, β21, α30, α32, β32, α40, α43, β43, α52, α53, β53, α54, β54, c1, c2, c3, c4 = cache.tab + + # u₁ + f(fsalfirst, uprev, p, t) + @.. broadcast=false thread=thread u₂=uprev + β10 * dt * fsalfirst + stage_limiter!(u₂, integrator, p, t + c1 * dt) + f(k, u₂, p, t + c1 * dt) + # u₂ + @.. broadcast=false thread=thread u₂=α20 * uprev + α21 * u₂ + β21 * dt * k + stage_limiter!(u₂, integrator, p, t + c2 * dt) + f(k, u₂, p, t + c2 * dt) + # u₃ + @.. broadcast=false thread=thread u₃=α30 * uprev + α32 * u₂ + β32 * dt * k + stage_limiter!(u₃, integrator, p, t + c3 * dt) + f(k₃, u₃, p, t + c3 * dt) + # u₄ -> stored as tmp + @.. broadcast=false thread=thread tmp=α40 * uprev + α43 * u₃ + β43 * dt * k₃ + stage_limiter!(tmp, integrator, p, t + c4 * dt) + f(k, tmp, p, t + c4 * dt) + # u + @.. broadcast=false thread=thread u=α52 * u₂ + α53 * u₃ + β53 * dt * k₃ + α54 * tmp + + β54 * dt * k + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + integrator.stats.nf += 5 +end + +function initialize!(integrator, cache::SSPRK104ConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + integrator.kshortsize = 1 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK104ConstantCache, + repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + dt_6 = dt / 6 + dt_3 = dt / 3 + dt_2 = dt / 2 + + integrator.fsalfirst = f(uprev, p, t) + integrator.k[1] = integrator.fsalfirst + tmp = uprev + dt_6 * integrator.fsalfirst # u₁ + k = f(tmp, p, t + dt_6) + tmp = tmp + dt_6 * k # u₂ + k = f(tmp, p, t + dt_3) + tmp = tmp + dt_6 * k # u₃ + k = f(tmp, p, t + dt_2) + u = tmp + dt_6 * k # u₄ + k₄ = f(u, p, t + 2 * dt_3) + tmp = (3 * uprev + 2 * u + 2 * dt_6 * k₄) / 5 # u₅ + k = f(tmp, p, t + dt_3) + tmp = tmp + dt_6 * k # u₆ + k = f(tmp, p, t + dt_2) + tmp = tmp + dt_6 * k # u₇ + k = f(tmp, p, t + 2 * dt_3) + tmp = tmp + dt_6 * k # u₈ + k = f(tmp, p, t + 5 * dt_6) + tmp = tmp + dt_6 * k # u₉ + k = f(tmp, p, t + dt) + u = (uprev + 9 * (u + dt_6 * k₄) + 15 * (tmp + dt_6 * k)) / 25 + + integrator.stats.nf += 10 + integrator.u = u +end + +function initialize!(integrator, cache::SSPRK104Cache) + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + integrator.kshortsize = 1 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst +end + +@muladd function perform_step!(integrator, cache::SSPRK104Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack k, fsalfirst, k₄, tmp, stage_limiter!, step_limiter!, thread = cache + dt_6 = dt / 6 + dt_3 = dt / 3 + dt_2 = dt / 2 + + f(fsalfirst, uprev, p, t) + @.. broadcast=false thread=thread tmp=uprev + dt_6 * fsalfirst + stage_limiter!(tmp, integrator, p, t + dt_6) + f(k, tmp, p, t + dt_6) + @.. broadcast=false tmp=tmp + dt_6 * k + stage_limiter!(tmp, integrator, p, t + dt_3) + f(k, tmp, p, t + dt_3) + @.. broadcast=false thread=thread tmp=tmp + dt_6 * k + stage_limiter!(tmp, integrator, p, t + dt_2) + f(k, tmp, p, t + dt_2) + @.. broadcast=false thread=thread u=tmp + dt_6 * k + stage_limiter!(u, integrator, p, t + 2 * dt_3) + f(k₄, u, p, t + 2 * dt_3) + @.. broadcast=false thread=thread tmp=(3 * uprev + 2 * u + 2 * dt_6 * k₄) / 5 + stage_limiter!(tmp, integrator, p, t + dt_3) + f(k, tmp, p, t + dt_3) + @.. broadcast=false thread=thread tmp=tmp + dt_6 * k + stage_limiter!(tmp, integrator, p, t + dt_2) + f(k, tmp, p, t + dt_2) + @.. broadcast=false thread=thread tmp=tmp + dt_6 * k + stage_limiter!(tmp, integrator, p, t + 2 * dt_3) + f(k, tmp, p, t + 2 * dt_3) + @.. broadcast=false thread=thread tmp=tmp + dt_6 * k + stage_limiter!(tmp, integrator, p, t + 5 * dt_6) + f(k, tmp, p, t + 5 * dt_6) + @.. broadcast=false thread=thread tmp=tmp + dt_6 * k + stage_limiter!(tmp, integrator, p, t + dt) + f(k, tmp, p, t + dt) + @.. broadcast=false thread=thread u=(uprev + 9 * (u + dt_6 * k₄) + + 15 * (tmp + dt_6 * k)) / 25 + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + integrator.stats.nf += 10 +end diff --git a/src/perform_step/symplectic_perform_step.jl b/src/perform_step/symplectic_perform_step.jl new file mode 100644 index 0000000000..413f1882a2 --- /dev/null +++ b/src/perform_step/symplectic_perform_step.jl @@ -0,0 +1,2025 @@ +# http://www.chimica.unipd.it/antonino.polimeno/pubblica/downloads/JChemPhys_101_4062.pdf + +function initialize!(integrator, cache::SymplecticEulerConstantCache) + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + # Do the calculation pre + # So that way FSAL interpolation + duprev, uprev = integrator.uprev.x + du, u = integrator.u.x + kdu = integrator.f.f1(duprev, uprev, integrator.p, integrator.t) + kuprev = integrator.f.f2(duprev, uprev, integrator.p, integrator.t) + @muladd du = duprev + integrator.dt * kdu + ku = integrator.f.f2(du, uprev, integrator.p, integrator.t) + integrator.stats.nf2 += 1 + integrator.stats.nf += 2 + integrator.fsalfirst = ArrayPartition((kdu, kuprev)) + integrator.fsallast = ArrayPartition((zero(kdu), ku)) +end + +@muladd function perform_step!(integrator, cache::SymplecticEulerConstantCache, + repeat_step = false) + @unpack t, dt, f, p = integrator + duprev, uprev = integrator.uprev.x + kuprev = integrator.fsalfirst.x[2] + u = uprev + dt * kuprev + # Now actually compute the step + # Do it at the end for interpolations! + kdu = f.f1(duprev, u, p, t) + du = duprev + dt * kdu + + ku = f.f2(du, u, p, t) + integrator.stats.nf2 += 1 + integrator.stats.nf += 1 + + integrator.u = ArrayPartition((du, u)) + integrator.fsallast = ArrayPartition((kdu, ku)) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +function initialize!(integrator, cache::SymplecticEulerCache) + integrator.kshortsize = 2 + @unpack k, fsalfirst = cache + integrator.fsalfirst = fsalfirst + integrator.fsallast = k + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + # Do the calculation pre + # So that way FSAL interpolation + duprev, uprev = integrator.uprev.x + du, u = integrator.u.x + kuprev = integrator.fsalfirst.x[2] + kdu, ku = integrator.fsallast.x + integrator.f.f1(kdu, duprev, uprev, integrator.p, integrator.t) + integrator.f.f2(kuprev, duprev, uprev, integrator.p, integrator.t) + @muladd @.. broadcast=false du=duprev + integrator.dt * kdu + integrator.f.f2(ku, du, uprev, integrator.p, integrator.t) + integrator.stats.nf += 1 + integrator.stats.nf2 += 2 +end + +@muladd function perform_step!(integrator, cache::SymplecticEulerCache, repeat_step = false) + @unpack t, dt, f, p = integrator + duprev, uprev = integrator.uprev.x + du, u = integrator.u.x + kuprev = integrator.fsalfirst.x[2] + kdu, ku = integrator.fsallast.x + @.. broadcast=false u=uprev + dt * kuprev + # Now actually compute the step + # Do it at the end for interpolations! + integrator.stats.nf2 += 1 + integrator.stats.nf += 1 + f.f1(kdu, duprev, u, p, t) + @.. broadcast=false du=duprev + dt * kdu + f.f2(ku, du, u, p, t) +end + +const MutableCachesHamilton = Union{Symplectic2Cache, Symplectic3Cache, + Symplectic4Cache, Symplectic45Cache, Symplectic5Cache, + Symplectic6Cache, Symplectic62Cache, + McAte8Cache, KahanLi8Cache, SofSpa10Cache} +const MutableCachesNewton = Union{VelocityVerletCache} + +const ConstantCachesHamilton = Union{Symplectic2ConstantCache, Symplectic3ConstantCache, + Symplectic4ConstantCache, Symplectic45ConstantCache, + Symplectic5ConstantCache, + Symplectic6ConstantCache, Symplectic62ConstantCache, + McAte8ConstantCache, KahanLi8ConstantCache, + SofSpa10ConstantCache} +const ConstantCachesNewton = Union{VelocityVerletConstantCache} + +# some of the algorithms are designed only for the case +# f.f2(p, q, pa, t) = p which is the Newton/Lagrange equations +# If called with different functions (which are possible in the Hamiltonian case) +# an exception is thrown to avoid silently calculate wrong results. +verify_f2(f, p, q, pa, t, ::Any, ::C) where {C <: ConstantCachesHamilton} = f(p, q, pa, t) +function verify_f2(f, res, p, q, pa, t, ::Any, ::C) where {C <: MutableCachesHamilton} + f(res, p, q, pa, t) +end + +function verify_f2(f, p, q, pa, t, integrator, ::C) where {C <: ConstantCachesNewton} + res = f(p, q, pa, t) + res == p ? p : throwex(integrator) +end +function verify_f2(f, res, p, q, pa, t, integrator, ::C) where {C <: MutableCachesNewton} + f(res, p, q, pa, t) + res == p ? res : throwex(integrator) +end +function throwex(integrator) + algn = typeof(integrator.alg) + throw(ArgumentError("Algorithm $algn is not applicable if f2(p, q, t) != p")) +end + +# provide the mutable uninitialized objects to keep state and derivative in case of mutable caches +# no such objects are required for constant caches +function alloc_symp_state(integrator) + (integrator.u.x..., integrator.cache.tmp.x...) +end + +# load state and derivatives at begin of symplectic iteration steps +function load_symp_state(integrator) + (integrator.uprev.x..., integrator.fsallast.x...) +end + +# store state and derivatives at the end of symplectic iteration steps +function store_symp_state!(integrator, ::OrdinaryDiffEqConstantCache, du, u, kdu, ku) + integrator.u = ArrayPartition((du, u)) + integrator.fsallast = ArrayPartition((kdu, ku)) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + nothing +end + +function store_symp_state!(integrator, ::OrdinaryDiffEqMutableCache, kdu, ku) + copyto!(integrator.k[1].x[1], integrator.k[2].x[1]) + copyto!(integrator.k[1].x[2], integrator.k[2].x[2]) + copyto!(integrator.k[2].x[2], ku) + copyto!(integrator.k[2].x[1], kdu) + nothing +end + +function initialize!(integrator, + cache::C) where {C <: + Union{MutableCachesHamilton, MutableCachesNewton}} + integrator.fsalfirst = cache.fsalfirst + integrator.fsallast = cache.k + + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + + duprev, uprev = integrator.uprev.x + integrator.f.f1(integrator.k[2].x[1], duprev, uprev, integrator.p, integrator.t) + verify_f2(integrator.f.f2, integrator.k[2].x[2], duprev, uprev, integrator.p, + integrator.t, integrator, cache) + integrator.stats.nf += 1 + integrator.stats.nf2 += 1 +end + +function initialize!(integrator, + cache::C) where { + C <: + Union{ConstantCachesHamilton, ConstantCachesNewton}} + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + duprev, uprev = integrator.uprev.x + kdu = integrator.f.f1(duprev, uprev, integrator.p, integrator.t) + ku = verify_f2(integrator.f.f2, duprev, uprev, integrator.p, integrator.t, integrator, + cache) + integrator.stats.nf += 1 + integrator.stats.nf2 += 1 + integrator.fsallast = ArrayPartition((kdu, ku)) + integrator.k[2] = integrator.fsallast + integrator.fsalfirst = integrator.fsallast +end + +@muladd function perform_step!(integrator, cache::VelocityVerletConstantCache, + repeat_step = false) + @unpack t, dt, f, p = integrator + duprev, uprev = load_symp_state(integrator) + + # x(t+Δt) = x(t) + v(t)*Δt + 1/2*a(t)*Δt^2 + ku = integrator.fsallast.x[1] + dtsq = dt^2 + half = cache.half + u = uprev + dt * duprev + dtsq * (half * ku) + kdu = f.f1(duprev, u, p, t + dt) + # v(t+Δt) = v(t) + 1/2*(a(t)+a(t+Δt))*Δt + du = duprev + dt * (half * ku + half * kdu) + + integrator.stats.nf += 2 + store_symp_state!(integrator, cache, du, u, kdu, du) +end + +@muladd function perform_step!(integrator, cache::VelocityVerletCache, repeat_step = false) + @unpack t, dt, f, p = integrator + duprev, uprev = load_symp_state(integrator) + du, u, kdu, ku = alloc_symp_state(integrator) + + # x(t+Δt) = x(t) + v(t)*Δt + 1/2*a(t)*Δt^2 + ku = integrator.fsallast.x[1] + dtsq = dt^2 + half = cache.half + @.. broadcast=false u=uprev + dt * duprev + dtsq * (half * ku) + f.f1(kdu, duprev, u, p, t + dt) + integrator.stats.nf += 2 + # v(t+Δt) = v(t) + 1/2*(a(t)+a(t+Δt))*Δt + @.. broadcast=false du=duprev + dt * (half * ku + half * kdu) + + store_symp_state!(integrator, cache, kdu, du) +end + +@muladd function perform_step!(integrator, cache::Symplectic2ConstantCache, + repeat_step = false) + @unpack t, dt, f, p = integrator + @unpack a1, a2, b1, b2 = cache + duprev, uprev, _, kuprev = load_symp_state(integrator) + + # update position + u = uprev + dt * b1 * kuprev + # update velocity + kdu = f.f1(duprev, u, p, t) + du = duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b2 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a2 * kdu + kdu = f.f1(du, u, p, tnew) + ku = f.f2(du, u, p, tnew) + + integrator.stats.nf += 3 + integrator.stats.nf2 += 2 + store_symp_state!(integrator, cache, du, u, kdu, ku) +end + +@muladd function perform_step!(integrator, cache::Symplectic2Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + @unpack a1, a2, b1, b2 = cache.tab + duprev, uprev, _, kuprev = load_symp_state(integrator) + du, u, kdu, ku = alloc_symp_state(integrator) + + # update position + @.. broadcast=false u=uprev + dt * b1 * kuprev + # update velocity + f.f1(kdu, duprev, u, p, t) + @.. broadcast=false du=duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b2 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a2 * kdu + f.f1(kdu, du, u, p, tnew) + f.f2(ku, du, u, p, tnew) + + integrator.stats.nf += 3 + integrator.stats.nf2 += 2 + store_symp_state!(integrator, cache, kdu, ku) +end + +@muladd function perform_step!(integrator, cache::Symplectic3ConstantCache, + repeat_step = false) + @unpack t, dt, f, p = integrator + @unpack a1, a2, a3, b1, b2, b3 = cache + duprev, uprev, _, kuprev = load_symp_state(integrator) + + # update position + u = uprev + dt * b1 * kuprev + # update velocity + kdu = f.f1(duprev, u, p, integrator.t) + du = duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b2 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a2 * kdu + + # update position & velocity + tnew = tnew + a2 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b3 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a3 * kdu + kdu = f.f1(du, u, p, tnew) + ku = f.f2(du, u, p, tnew) + + integrator.stats.nf += 4 + integrator.stats.nf2 += 3 + store_symp_state!(integrator, cache, du, u, kdu, ku) +end + +@muladd function perform_step!(integrator, cache::Symplectic3Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + @unpack a1, a2, a3, b1, b2, b3 = cache.tab + duprev, uprev, _, kuprev = load_symp_state(integrator) + du, u, kdu, ku = alloc_symp_state(integrator) + + # update position + @.. broadcast=false u=uprev + dt * b1 * kuprev + # update velocity + f.f1(kdu, duprev, u, p, integrator.t) + @.. broadcast=false du=duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b2 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a2 * kdu + + # update position & velocity + tnew = tnew + a2 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b3 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a3 * kdu + f.f1(kdu, du, u, p, tnew) + f.f2(ku, du, u, p, tnew) + + integrator.stats.nf += 4 + integrator.stats.nf2 += 3 + store_symp_state!(integrator, cache, kdu, ku) +end + +@muladd function perform_step!(integrator, cache::Symplectic4ConstantCache, + repeat_step = false) + @unpack t, dt, f, p = integrator + @unpack a1, a2, a3, a4, b1, b2, b3, b4 = cache + duprev, uprev, _, kuprev = load_symp_state(integrator) + + # update position + u = uprev + dt * b1 * kuprev + # update velocity + kdu = f.f1(duprev, u, p, t) + du = duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b2 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a2 * kdu + + # update position & velocity + tnew = tnew + a2 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b3 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a3 * kdu + + # update position & velocity + tnew = tnew + a3 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b4 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a4 * kdu + kdu = f.f1(du, u, p, tnew) + ku = f.f2(du, u, p, tnew) + + integrator.stats.nf += 5 + integrator.stats.nf2 += 4 + store_symp_state!(integrator, cache, du, u, kdu, ku) +end + +@muladd function perform_step!(integrator, cache::Symplectic4Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + @unpack a1, a2, a3, a4, b1, b2, b3, b4 = cache.tab + duprev, uprev, _, kuprev = load_symp_state(integrator) + du, u, kdu, ku = alloc_symp_state(integrator) + + # update position + @.. broadcast=false u=uprev + dt * b1 * kuprev + # update velocity + f.f1(kdu, duprev, u, p, t) + @.. broadcast=false du=duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b2 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a2 * kdu + + # update position & velocity + tnew = tnew + a2 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b3 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a3 * kdu + + # update position & velocity + tnew = tnew + a3 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b4 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a4 * kdu + f.f1(kdu, du, u, p, tnew) + f.f2(ku, du, u, p, tnew) + + integrator.stats.nf += 5 + integrator.stats.nf2 += 4 + store_symp_state!(integrator, cache, kdu, ku) +end + +@muladd function perform_step!(integrator, cache::Symplectic45ConstantCache, + repeat_step = false) + @unpack t, dt, f, p = integrator + alg = unwrap_alg(integrator, false) + @unpack a1, a2, a3, a4, a5, b1, b2, b3, b4, b5 = cache + duprev, uprev, _, kuprev = load_symp_state(integrator) + + # update position + u = uprev + dt * b1 * kuprev + # update velocity + kdu = f.f1(duprev, u, p, t) + du = duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b2 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a2 * kdu + + # update position & velocity + tnew = tnew + a2 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b3 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a3 * kdu + + # update position & velocity + tnew = tnew + a3 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b4 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a4 * kdu + + # update position & velocity + tnew = tnew + a4 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b5 * ku + + kdu = f.f1(du, u, p, tnew) + if alg isa McAte42 + du = du + dt * a5 * kdu + kdu = f.f1(du, u, p, tnew) + integrator.stats.nf += 1 + end + ku = f.f2(du, u, p, tnew) + + integrator.stats.nf += 5 + integrator.stats.nf2 += 5 + store_symp_state!(integrator, cache, du, u, kdu, ku) +end + +@muladd function perform_step!(integrator, cache::Symplectic45Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + alg = unwrap_alg(integrator, false) + @unpack a1, a2, a3, a4, a5, b1, b2, b3, b4, b5 = cache.tab + duprev, uprev, _, kuprev = load_symp_state(integrator) + du, u, kdu, ku = alloc_symp_state(integrator) + + # update position + @.. broadcast=false u=uprev + dt * b1 * kuprev + # update velocity + f.f1(kdu, duprev, u, p, t) + @.. broadcast=false du=duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b2 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a2 * kdu + + # update position & velocity + tnew = tnew + a2 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b3 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a3 * kdu + + # update position & velocity + tnew = tnew + a3 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b4 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a4 * kdu + + # update position & velocity + tnew = tnew + a4 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b5 * ku + + f.f1(kdu, du, u, p, tnew) + if alg isa McAte42 + @.. broadcast=false du=du + dt * a5 * kdu + f.f1(kdu, du, u, p, tnew) + integrator.stats.nf += 1 + end + f.f2(ku, du, u, p, tnew) + + integrator.stats.nf += 5 + integrator.stats.nf2 += 5 + store_symp_state!(integrator, cache, kdu, ku) +end + +@muladd function perform_step!(integrator, cache::Symplectic5ConstantCache, + repeat_step = false) + @unpack t, dt, f, p = integrator + @unpack a1, a2, a3, a4, a5, a6, b1, b2, b3, b4, b5, b6 = cache + duprev, uprev, _, kuprev = load_symp_state(integrator) + + # update position + u = uprev + dt * b1 * kuprev + # update velocity + kdu = f.f1(duprev, u, p, integrator.t) + du = duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b2 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a2 * kdu + + # update position & velocity + tnew = tnew + a2 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b3 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a3 * kdu + + # update position & velocity + tnew = tnew + a3 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b4 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a4 * kdu + + # update position & velocity + tnew = tnew + a4 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b5 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a5 * kdu + + tnew = tnew + a5 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b6 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a6 * kdu + kdu = f.f1(du, u, p, tnew) + ku = f.f2(du, u, p, tnew) + + integrator.stats.nf += 7 + integrator.stats.nf2 += 6 + store_symp_state!(integrator, cache, du, u, kdu, ku) +end + +@muladd function perform_step!(integrator, cache::Symplectic5Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + @unpack a1, a2, a3, a4, a5, a6, b1, b2, b3, b4, b5, b6 = cache.tab + duprev, uprev, _, kuprev = load_symp_state(integrator) + du, u, kdu, ku = alloc_symp_state(integrator) + + # update position + @.. broadcast=false u=uprev + dt * b1 * kuprev + # update velocity + f.f1(kdu, duprev, u, p, integrator.t) + @.. broadcast=false du=duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b2 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a2 * kdu + + # update position & velocity + tnew = tnew + a2 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b3 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a3 * kdu + + # update position & velocity + tnew = tnew + a3 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b4 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a4 * kdu + + # update position & velocity + tnew = tnew + a4 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b5 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a5 * kdu + + tnew = tnew + a5 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b6 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a6 * kdu + f.f1(kdu, du, u, p, tnew) + f.f2(ku, du, u, p, tnew) + + integrator.stats.nf += 7 + integrator.stats.nf2 += 6 + store_symp_state!(integrator, cache, kdu, ku) +end + +@muladd function perform_step!(integrator, cache::Symplectic6ConstantCache, + repeat_step = false) + @unpack t, dt, f, p = integrator + @unpack a1, a2, a3, a4, a5, a6, a7, a8, b1, b2, b3, b4, b5, b6, b7, b8 = cache + duprev, uprev, _, kuprev = load_symp_state(integrator) + + # update position + u = uprev + dt * b1 * kuprev + # update velocity + kdu = f.f1(duprev, u, p, integrator.t) + du = duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b2 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a2 * kdu + + # update position & velocity + tnew = tnew + a2 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b3 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a3 * kdu + + # update position & velocity + tnew = tnew + a3 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b4 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a4 * kdu + + # update position & velocity + tnew = tnew + a4 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b5 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a5 * kdu + + tnew = tnew + a5 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b6 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a6 * kdu + + tnew = tnew + a6 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b7 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a7 * kdu + + tnew = tnew + a7 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b8 * ku + + kdu = f.f1(du, u, p, tnew) + # @.. broadcast=false du = du + dt*a8*kdu + ku = f.f2(du, u, p, tnew) + + integrator.stats.nf += 8 + integrator.stats.nf2 += 8 + store_symp_state!(integrator, cache, du, u, kdu, ku) +end + +@muladd function perform_step!(integrator, cache::Symplectic6Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + @unpack a1, a2, a3, a4, a5, a6, a7, a8, b1, b2, b3, b4, b5, b6, b7, b8 = cache.tab + duprev, uprev, _, kuprev = load_symp_state(integrator) + du, u, kdu, ku = alloc_symp_state(integrator) + + # update position + @.. broadcast=false u=uprev + dt * b1 * kuprev + # update velocity + f.f1(kdu, duprev, u, p, integrator.t) + @.. broadcast=false du=duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b2 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a2 * kdu + + # update position & velocity + tnew = tnew + a2 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b3 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a3 * kdu + + # update position & velocity + tnew = tnew + a3 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b4 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a4 * kdu + + # update position & velocity + tnew = tnew + a4 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b5 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a5 * kdu + + tnew = tnew + a5 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b6 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a6 * kdu + + tnew = tnew + a6 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b7 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a7 * kdu + + tnew = tnew + a7 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b8 * ku + + f.f1(kdu, du, u, p, tnew) + # @.. broadcast=false du = du + dt*a8*kdu + f.f2(ku, du, u, p, tnew) + + integrator.stats.nf += 8 + integrator.stats.nf2 += 8 + store_symp_state!(integrator, cache, kdu, ku) +end + +@muladd function perform_step!(integrator, cache::Symplectic62ConstantCache, + repeat_step = false) + @unpack t, dt, f, p = integrator + @unpack a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10 = cache + duprev, uprev, _, kuprev = load_symp_state(integrator) + + # update position + u = uprev + dt * b1 * kuprev + # update velocity + kdu = f.f1(duprev, u, p, integrator.t) + du = duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b2 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a2 * kdu + + # update position & velocity + tnew = tnew + a2 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b3 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a3 * kdu + + # update position & velocity + tnew = tnew + a3 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b4 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a4 * kdu + + # update position & velocity + tnew = tnew + a4 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b5 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a5 * kdu + + tnew = tnew + a5 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b6 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a6 * kdu + + tnew = tnew + a6 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b7 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a7 * kdu + + tnew = tnew + a7 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b8 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a8 * kdu + + tnew = tnew + a8 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b9 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a9 * kdu + + tnew = tnew + a9 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b10 * ku + + kdu = f.f1(du, u, p, tnew) + # @.. broadcast=false du = du + dt*a10*kdu + ku = f.f2(du, u, p, tnew) + + integrator.stats.nf += 10 + integrator.stats.nf2 += 10 + store_symp_state!(integrator, cache, du, u, kdu, ku) +end + +@muladd function perform_step!(integrator, cache::Symplectic62Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + @unpack a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10 = cache.tab + duprev, uprev, _, kuprev = load_symp_state(integrator) + du, u, kdu, ku = alloc_symp_state(integrator) + + # update position + @.. broadcast=false u=uprev + dt * b1 * kuprev + # update velocity + f.f1(kdu, duprev, u, p, integrator.t) + @.. broadcast=false du=duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b2 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a2 * kdu + + # update position & velocity + tnew = tnew + a2 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b3 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a3 * kdu + + # update position & velocity + tnew = tnew + a3 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b4 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a4 * kdu + + # update position & velocity + tnew = tnew + a4 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b5 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a5 * kdu + + tnew = tnew + a5 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b6 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a6 * kdu + + tnew = tnew + a6 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b7 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a7 * kdu + + tnew = tnew + a7 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b8 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a8 * kdu + + tnew = tnew + a8 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b9 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a9 * kdu + + tnew = tnew + a9 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b10 * ku + + f.f1(kdu, du, u, p, tnew) + # @.. broadcast=false du = du + dt*a10*kdu + f.f2(ku, du, u, p, tnew) + + integrator.stats.nf += 10 + integrator.stats.nf2 += 10 + store_symp_state!(integrator, cache, kdu, ku) +end + +@muladd function perform_step!(integrator, cache::McAte8ConstantCache, repeat_step = false) + @unpack t, dt, f, p = integrator + @unpack a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, + b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16 = cache + duprev, uprev, _, kuprev = load_symp_state(integrator) + + # update position + u = uprev + dt * b1 * kuprev + # update velocity + kdu = f.f1(duprev, u, p, integrator.t) + du = duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b2 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a2 * kdu + + # update position & velocity + tnew = tnew + a2 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b3 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a3 * kdu + + # update position & velocity + tnew = tnew + a3 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b4 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a4 * kdu + + # update position & velocity + tnew = tnew + a4 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b5 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a5 * kdu + + tnew = tnew + a5 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b6 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a6 * kdu + + tnew = tnew + a6 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b7 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a7 * kdu + + tnew = tnew + a7 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b8 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a8 * kdu + + tnew = tnew + a8 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b9 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a9 * kdu + + tnew = tnew + a9 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b10 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a10 * kdu + + tnew = tnew + a10 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b11 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a11 * kdu + + tnew = tnew + a11 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b12 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a12 * kdu + + tnew = tnew + a12 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b13 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a13 * kdu + + tnew = tnew + a13 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b14 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a14 * kdu + + tnew = tnew + a14 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b15 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a15 * kdu + + tnew = tnew + a15 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b16 * ku + + kdu = f.f1(du, u, p, tnew) + # @.. broadcast=false du = du + dt*a16*kdu + ku = f.f2(du, u, p, tnew) + + integrator.stats.nf += 16 + integrator.stats.nf2 += 16 + store_symp_state!(integrator, cache, du, u, kdu, ku) +end + +@muladd function perform_step!(integrator, cache::McAte8Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + @unpack a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, + b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16 = cache.tab + duprev, uprev, _, kuprev = load_symp_state(integrator) + du, u, kdu, ku = alloc_symp_state(integrator) + + # update position + @.. broadcast=false u=uprev + dt * b1 * kuprev + # update velocity + f.f1(kdu, duprev, u, p, integrator.t) + @.. broadcast=false du=duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b2 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a2 * kdu + + # update position & velocity + tnew = tnew + a2 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b3 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a3 * kdu + + # update position & velocity + tnew = tnew + a3 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b4 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a4 * kdu + + # update position & velocity + tnew = tnew + a4 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b5 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a5 * kdu + + tnew = tnew + a5 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b6 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a6 * kdu + + tnew = tnew + a6 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b7 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a7 * kdu + + tnew = tnew + a7 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b8 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a8 * kdu + + tnew = tnew + a8 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b9 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a9 * kdu + + tnew = tnew + a9 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b10 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a10 * kdu + + tnew = tnew + a10 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b11 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a11 * kdu + + tnew = tnew + a11 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b12 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a12 * kdu + + tnew = tnew + a12 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b13 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a13 * kdu + + tnew = tnew + a13 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b14 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a14 * kdu + + tnew = tnew + a14 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b15 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a15 * kdu + + tnew = tnew + a15 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b16 * ku + + f.f1(kdu, du, u, p, tnew) + # @.. broadcast=false du = du + dt*a16*kdu + f.f2(ku, du, u, p, tnew) + + integrator.stats.nf += 16 + integrator.stats.nf2 += 16 + store_symp_state!(integrator, cache, kdu, ku) +end + +@muladd function perform_step!(integrator, cache::KahanLi8ConstantCache, + repeat_step = false) + @unpack t, dt, f, p = integrator + @unpack a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18, + b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18 = cache + duprev, uprev, _, kuprev = load_symp_state(integrator) + + # update position + u = uprev + dt * b1 * kuprev + # update velocity + kdu = f.f1(duprev, u, p, integrator.t) + du = duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b2 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a2 * kdu + + # update position & velocity + tnew = tnew + a2 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b3 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a3 * kdu + + # update position & velocity + tnew = tnew + a3 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b4 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a4 * kdu + + # update position & velocity + tnew = tnew + a4 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b5 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a5 * kdu + + tnew = tnew + a5 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b6 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a6 * kdu + + tnew = tnew + a6 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b7 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a7 * kdu + + tnew = tnew + a7 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b8 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a8 * kdu + + tnew = tnew + a8 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b9 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a9 * kdu + + tnew = tnew + a9 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b10 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a10 * kdu + + tnew = tnew + a10 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b11 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a11 * kdu + + tnew = tnew + a11 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b12 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a12 * kdu + + tnew = tnew + a12 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b13 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a13 * kdu + + tnew = tnew + a13 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b14 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a14 * kdu + + tnew = tnew + a14 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b15 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a15 * kdu + + tnew = tnew + a15 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b16 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a16 * kdu + + tnew = tnew + a16 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b17 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a17 * kdu + + tnew = tnew + a17 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b18 * ku + + kdu = f.f1(du, u, p, tnew) + # @.. broadcast=false du = du + dt*a18*kdu + ku = f.f2(du, u, p, tnew) + + integrator.stats.nf += 18 + integrator.stats.nf2 += 18 + store_symp_state!(integrator, cache, du, u, kdu, ku) +end + +@muladd function perform_step!(integrator, cache::KahanLi8Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + @unpack a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18, + b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18 = cache.tab + duprev, uprev, _, kuprev = load_symp_state(integrator) + du, u, kdu, ku = alloc_symp_state(integrator) + + # update position + @.. broadcast=false u=uprev + dt * b1 * kuprev + # update velocity + f.f1(kdu, duprev, u, p, integrator.t) + @.. broadcast=false du=duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b2 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a2 * kdu + + # update position & velocity + tnew = tnew + a2 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b3 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a3 * kdu + + # update position & velocity + tnew = tnew + a3 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b4 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a4 * kdu + + # update position & velocity + tnew = tnew + a4 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b5 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a5 * kdu + + tnew = tnew + a5 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b6 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a6 * kdu + + tnew = tnew + a6 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b7 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a7 * kdu + + tnew = tnew + a7 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b8 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a8 * kdu + + tnew = tnew + a8 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b9 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a9 * kdu + + tnew = tnew + a9 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b10 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a10 * kdu + + tnew = tnew + a10 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b11 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a11 * kdu + + tnew = tnew + a11 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b12 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a12 * kdu + + tnew = tnew + a12 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b13 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a13 * kdu + + tnew = tnew + a13 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b14 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a14 * kdu + + tnew = tnew + a14 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b15 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a15 * kdu + + tnew = tnew + a15 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b16 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a16 * kdu + + tnew = tnew + a16 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b17 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a17 * kdu + + tnew = tnew + a17 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b18 * ku + + f.f1(kdu, du, u, p, tnew) + # @.. broadcast=false du = du + dt*a18*kdu + f.f2(ku, du, u, p, tnew) + + integrator.stats.nf += 18 + integrator.stats.nf2 += 18 + store_symp_state!(integrator, cache, kdu, ku) +end + +@muladd function perform_step!(integrator, cache::SofSpa10ConstantCache, + repeat_step = false) + @unpack t, dt, f, p = integrator + @unpack a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18, + a19, a20, a21, a22, a23, a24, a25, a26, a27, a28, a29, a30, a31, a32, a33, a34, + a35, a36, + b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, + b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31, b32, b33, b34, + b35, b36 = cache + duprev, uprev, _, kuprev = load_symp_state(integrator) + + # update position + u = uprev + dt * b1 * kuprev + # update velocity + kdu = f.f1(duprev, u, p, integrator.t) + du = duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b2 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a2 * kdu + + # update position & velocity + tnew = tnew + a2 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b3 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a3 * kdu + + # update position & velocity + tnew = tnew + a3 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b4 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a4 * kdu + + # update position & velocity + tnew = tnew + a4 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b5 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a5 * kdu + + tnew = tnew + a5 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b6 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a6 * kdu + + tnew = tnew + a6 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b7 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a7 * kdu + + tnew = tnew + a7 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b8 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a8 * kdu + + tnew = tnew + a8 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b9 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a9 * kdu + + tnew = tnew + a9 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b10 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a10 * kdu + + tnew = tnew + a10 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b11 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a11 * kdu + + tnew = tnew + a11 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b12 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a12 * kdu + + tnew = tnew + a12 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b13 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a13 * kdu + + tnew = tnew + a13 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b14 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a14 * kdu + + tnew = tnew + a14 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b15 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a15 * kdu + + tnew = tnew + a15 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b16 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a16 * kdu + + tnew = tnew + a16 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b17 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a17 * kdu + + tnew = tnew + a17 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b18 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a18 * kdu + + tnew = tnew + a18 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b19 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a19 * kdu + + tnew = tnew + a19 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b20 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a20 * kdu + + tnew = tnew + a20 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b21 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a21 * kdu + + tnew = tnew + a21 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b22 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a22 * kdu + + tnew = tnew + a22 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b23 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a23 * kdu + + tnew = tnew + a23 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b24 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a24 * kdu + + tnew = tnew + a24 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b25 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a25 * kdu + + tnew = tnew + a25 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b26 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a26 * kdu + + tnew = tnew + a26 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b27 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a27 * kdu + + tnew = tnew + a27 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b28 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a28 * kdu + + tnew = tnew + a28 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b29 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a29 * kdu + + tnew = tnew + a29 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b30 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a30 * kdu + + tnew = tnew + a30 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b31 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a31 * kdu + + tnew = tnew + a31 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b32 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a32 * kdu + + tnew = tnew + a32 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b33 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a33 * kdu + + tnew = tnew + a33 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b34 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a34 * kdu + + tnew = tnew + a34 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b35 * ku + + kdu = f.f1(du, u, p, tnew) + du = du + dt * a35 * kdu + + tnew = tnew + a35 * dt + ku = f.f2(du, u, p, tnew) + u = u + dt * b36 * ku + + kdu = f.f1(du, u, p, tnew) + # @.. broadcast=false du = du + dt*a30*kdu + ku = f.f2(du, u, p, tnew) + + integrator.stats.nf += 36 + integrator.stats.nf2 += 36 + store_symp_state!(integrator, cache, du, u, kdu, ku) +end + +@muladd function perform_step!(integrator, cache::SofSpa10Cache, repeat_step = false) + @unpack t, dt, f, p = integrator + @unpack a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18, + a19, a20, a21, a22, a23, a24, a25, a26, a27, a28, a29, a30, a31, a32, a33, a34, + a35, a36, + b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, + b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31, b32, b33, b34, + b35, b36 = cache.tab + duprev, uprev, _, kuprev = load_symp_state(integrator) + du, u, kdu, ku = alloc_symp_state(integrator) + + # update position + @.. broadcast=false u=uprev + dt * b1 * kuprev + # update velocity + f.f1(kdu, duprev, u, p, integrator.t) + @.. broadcast=false du=duprev + dt * a1 * kdu + # update position & velocity + tnew = t + a1 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b2 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a2 * kdu + + # update position & velocity + tnew = tnew + a2 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b3 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a3 * kdu + + # update position & velocity + tnew = tnew + a3 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b4 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a4 * kdu + + # update position & velocity + tnew = tnew + a4 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b5 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a5 * kdu + + tnew = tnew + a5 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b6 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a6 * kdu + + tnew = tnew + a6 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b7 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a7 * kdu + + tnew = tnew + a7 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b8 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a8 * kdu + + tnew = tnew + a8 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b9 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a9 * kdu + + tnew = tnew + a9 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b10 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a10 * kdu + + tnew = tnew + a10 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b11 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a11 * kdu + + tnew = tnew + a11 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b12 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a12 * kdu + + tnew = tnew + a12 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b13 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a13 * kdu + + tnew = tnew + a13 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b14 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a14 * kdu + + tnew = tnew + a14 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b15 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a15 * kdu + + tnew = tnew + a15 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b16 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a16 * kdu + + tnew = tnew + a16 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b17 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a17 * kdu + + tnew = tnew + a17 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b18 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a18 * kdu + + tnew = tnew + a18 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b19 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a19 * kdu + + tnew = tnew + a19 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b20 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a20 * kdu + + tnew = tnew + a20 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b21 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a21 * kdu + + tnew = tnew + a21 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b22 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a22 * kdu + + tnew = tnew + a22 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b23 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a23 * kdu + + tnew = tnew + a23 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b24 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a24 * kdu + + tnew = tnew + a24 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b25 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a25 * kdu + + tnew = tnew + a25 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b26 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a26 * kdu + + tnew = tnew + a26 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b27 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a27 * kdu + + tnew = tnew + a27 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b28 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a28 * kdu + + tnew = tnew + a28 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b29 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a29 * kdu + + tnew = tnew + a29 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b30 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a30 * kdu + + tnew = tnew + a30 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b31 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a31 * kdu + + tnew = tnew + a31 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b32 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a32 * kdu + + tnew = tnew + a32 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b33 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a33 * kdu + + tnew = tnew + a33 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b34 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a34 * kdu + + tnew = tnew + a34 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b35 * ku + + f.f1(kdu, du, u, p, tnew) + @.. broadcast=false du=du + dt * a35 * kdu + + tnew = tnew + a35 * dt + f.f2(ku, du, u, p, tnew) + @.. broadcast=false u=u + dt * b36 * ku + + f.f1(kdu, du, u, p, tnew) + # @.. broadcast=false du = du + dt*a30*kdu + f.f2(ku, du, u, p, tnew) + + integrator.stats.nf += 36 + integrator.stats.nf2 += 36 + store_symp_state!(integrator, cache, kdu, ku) +end diff --git a/src/perform_step/verner_rk_perform_step.jl b/src/perform_step/verner_rk_perform_step.jl new file mode 100644 index 0000000000..0a44e217da --- /dev/null +++ b/src/perform_step/verner_rk_perform_step.jl @@ -0,0 +1,1284 @@ +function initialize!(integrator, cache::Vern6ConstantCache) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 + alg = unwrap_alg(integrator, false) + alg.lazy ? (integrator.kshortsize = 9) : (integrator.kshortsize = 12) + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + @inbounds for i in 2:8 + integrator.k[i] = zero(integrator.fsalfirst) + end + integrator.k[integrator.kshortsize] = integrator.fsallast + + if !alg.lazy + @inbounds for i in 10:12 + integrator.k[i] = zero(integrator.fsalfirst) + end + end +end + +@muladd function perform_step!(integrator, cache::Vern6ConstantCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack c1, c2, c3, c4, c5, c6, a21, a31, a32, a41, a43, a51, a53, a54, a61, a63, a64, a65, a71, a73, a74, a75, a76, a81, a83, a84, a85, a86, a87, a91, a94, a95, a96, a97, a98, btilde1, btilde4, btilde5, btilde6, btilde7, btilde8, btilde9 = cache.tab + k1 = integrator.fsalfirst + a = dt * a21 + k2 = f(uprev + a * k1, p, t + c1 * dt) + k3 = f(uprev + dt * (a31 * k1 + a32 * k2), p, t + c2 * dt) + k4 = f(uprev + dt * (a41 * k1 + a43 * k3), p, t + c3 * dt) + k5 = f(uprev + dt * (a51 * k1 + a53 * k3 + a54 * k4), p, t + c4 * dt) + k6 = f(uprev + dt * (a61 * k1 + a63 * k3 + a64 * k4 + a65 * k5), p, t + c5 * dt) + k7 = f(uprev + dt * (a71 * k1 + a73 * k3 + a74 * k4 + a75 * k5 + a76 * k6), p, + t + c6 * dt) + g8 = uprev + dt * (a81 * k1 + a83 * k3 + a84 * k4 + a85 * k5 + a86 * k6 + a87 * k7) + k8 = f(g8, p, t + dt) + u = uprev + dt * (a91 * k1 + a94 * k4 + a95 * k5 + a96 * k6 + a97 * k7 + a98 * k8) + integrator.fsallast = f(u, p, t + dt) + k9 = integrator.fsallast + integrator.stats.nf += 8 + if integrator.alg isa CompositeAlgorithm + g9 = u + ϱu = integrator.opts.internalnorm(k9 - k8, t) + ϱd = integrator.opts.internalnorm(g9 - g8, t) + integrator.eigen_est = ϱu / ϱd + end + if integrator.opts.adaptive + utilde = dt * + (btilde1 * k1 + btilde4 * k4 + btilde5 * k5 + btilde6 * k6 + btilde7 * k7 + + btilde8 * k8 + btilde9 * k9) + atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.k[1] = k1 + integrator.k[2] = k2 + integrator.k[3] = k3 + integrator.k[4] = k4 + integrator.k[5] = k5 + integrator.k[6] = k6 + integrator.k[7] = k7 + integrator.k[8] = k8 + integrator.k[9] = k9 + + alg = unwrap_alg(integrator, false) + if !alg.lazy && (integrator.opts.adaptive == false || + accept_step_controller(integrator, integrator.opts.controller)) + k = integrator.k + @unpack c10, a1001, a1004, a1005, a1006, a1007, a1008, a1009, c11, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, c12, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211 = cache.tab.extra + k[10] = f( + uprev + + dt * (a1001 * k[1] + a1004 * k[4] + a1005 * k[5] + a1006 * k[6] + + a1007 * k[7] + a1008 * k[8] + a1009 * k[9]), + p, + t + c10 * dt) + k[11] = f( + uprev + + dt * (a1101 * k[1] + a1104 * k[4] + a1105 * k[5] + a1106 * k[6] + + a1107 * k[7] + a1108 * k[8] + a1109 * k[9] + a1110 * k[10]), + p, + t + c11 * dt) + k[12] = f( + uprev + + dt * (a1201 * k[1] + a1204 * k[4] + a1205 * k[5] + a1206 * k[6] + + a1207 * k[7] + a1208 * k[8] + a1209 * k[9] + a1210 * k[10] + + a1211 * k[11]), + p, + t + c12 * dt) + integrator.stats.nf += 3 + end + + integrator.u = u +end + +function initialize!(integrator, cache::Vern6Cache) + alg = unwrap_alg(integrator, false) + alg.lazy ? (integrator.kshortsize = 9) : (integrator.kshortsize = 12) + integrator.fsalfirst = cache.k1 + integrator.fsallast = cache.k9 + @unpack k = integrator + resize!(k, integrator.kshortsize) + k[1] = cache.k1 + k[2] = cache.k2 + k[3] = cache.k3 + k[4] = cache.k4 + k[5] = cache.k5 + k[6] = cache.k6 + k[7] = cache.k7 + k[8] = cache.k8 + k[9] = cache.k9 # Set the pointers + + if !alg.lazy + k[10] = similar(cache.k1) + k[11] = similar(cache.k1) + k[12] = similar(cache.k1) + end + + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + integrator.stats.nf += 1 +end + +@muladd function perform_step!(integrator, cache::Vern6Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + uidx = eachindex(integrator.uprev) + @unpack c1, c2, c3, c4, c5, c6, a21, a31, a32, a41, a43, a51, a53, a54, a61, a63, a64, a65, a71, a73, a74, a75, a76, a81, a83, a84, a85, a86, a87, a91, a94, a95, a96, a97, a98, btilde1, btilde4, btilde5, btilde6, btilde7, btilde8, btilde9 = cache.tab + @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, utilde, tmp, rtmp, atmp, stage_limiter!, step_limiter!, thread = cache + a = dt * a21 + @.. broadcast=false thread=thread tmp=uprev + a * k1 + stage_limiter!(tmp, integrator, p, t + c1 * dt) + f(k2, tmp, p, t + c1 * dt) + @.. broadcast=false thread=thread tmp=uprev + dt * (a31 * k1 + a32 * k2) + stage_limiter!(tmp, integrator, p, t + c2 * dt) + f(k3, tmp, p, t + c2 * dt) + @.. broadcast=false thread=thread tmp=uprev + dt * (a41 * k1 + a43 * k3) + stage_limiter!(tmp, integrator, p, t + c3 * dt) + f(k4, tmp, p, t + c3 * dt) + @.. broadcast=false thread=thread tmp=uprev + dt * (a51 * k1 + a53 * k3 + a54 * k4) + stage_limiter!(tmp, integrator, p, t + c4 * dt) + f(k5, tmp, p, t + c4 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a61 * k1 + a63 * k3 + a64 * k4 + a65 * k5) + stage_limiter!(tmp, integrator, p, t + c5 * dt) + f(k6, tmp, p, t + c5 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a71 * k1 + a73 * k3 + a74 * k4 + a75 * k5 + + a76 * k6) + stage_limiter!(tmp, integrator, p, t + c6 * dt) + f(k7, tmp, p, t + c6 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a81 * k1 + a83 * k3 + a84 * k4 + a85 * k5 + + a86 * k6 + + a87 * k7) + stage_limiter!(tmp, integrator, p, t + dt) + f(k8, tmp, p, t + dt) + @.. broadcast=false thread=thread u=uprev + + dt * + (a91 * k1 + a94 * k4 + a95 * k5 + a96 * k6 + + a97 * k7 + a98 * k8) + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + f(k9, u, p, t + dt) + integrator.stats.nf += 8 + if integrator.alg isa CompositeAlgorithm + g9 = u + g8 = tmp + @.. broadcast=false thread=thread rtmp=k9 - k8 + ϱu = integrator.opts.internalnorm(rtmp, t) + @.. broadcast=false thread=thread utilde=g9 - g8 + ϱd = integrator.opts.internalnorm(utilde, t) + integrator.eigen_est = ϱu / ϱd + end + if integrator.opts.adaptive + @.. broadcast=false thread=thread utilde=dt * (btilde1 * k1 + btilde4 * k4 + + btilde5 * k5 + + btilde6 * k6 + btilde7 * k7 + + btilde8 * k8 + + btilde9 * k9) + calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t, + thread) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + + alg = unwrap_alg(integrator, false) + if !alg.lazy && (integrator.opts.adaptive == false || + accept_step_controller(integrator, integrator.opts.controller)) + k = integrator.k + @unpack c10, a1001, a1004, a1005, a1006, a1007, a1008, a1009, c11, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, c12, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211 = cache.tab.extra + @unpack tmp = cache + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a1001 * k[1] + a1004 * k[4] + a1005 * k[5] + + a1006 * k[6] + + a1007 * k[7] + a1008 * k[8] + a1009 * k[9]) + f(k[10], tmp, p, t + c10 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a1101 * k[1] + a1104 * k[4] + a1105 * k[5] + + a1106 * k[6] + + a1107 * k[7] + a1108 * k[8] + a1109 * k[9] + + a1110 * k[10]) + f(k[11], tmp, p, t + c11 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a1201 * k[1] + a1204 * k[4] + a1205 * k[5] + + a1206 * k[6] + + a1207 * k[7] + a1208 * k[8] + a1209 * k[9] + + a1210 * k[10] + a1211 * k[11]) + integrator.stats.nf += 3 + f(k[12], tmp, p, t + c12 * dt) + end + return nothing +end + +function initialize!(integrator, cache::Vern7ConstantCache) + alg = unwrap_alg(integrator, false) + alg.lazy ? (integrator.kshortsize = 10) : (integrator.kshortsize = 16) + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + @inbounds for i in eachindex(integrator.k) + integrator.k[i] = zero(integrator.uprev) ./ oneunit(integrator.t) + end +end + +@muladd function perform_step!(integrator, cache::Vern7ConstantCache, repeat_step = false) + @unpack t, dt, uprev, u, k, f, p = integrator + T = constvalue(recursive_unitless_bottom_eltype(u)) + T2 = constvalue(typeof(one(t))) + @OnDemandTableauExtract Vern7Tableau T T2 + k1 = f(uprev, p, t) + a = dt * a021 + k2 = f(uprev + a * k1, p, t + c2 * dt) + k3 = f(uprev + dt * (a031 * k1 + a032 * k2), p, t + c3 * dt) + k4 = f(uprev + dt * (a041 * k1 + a043 * k3), p, t + c4 * dt) + k5 = f(uprev + dt * (a051 * k1 + a053 * k3 + a054 * k4), p, t + c5 * dt) + k6 = f(uprev + dt * (a061 * k1 + a063 * k3 + a064 * k4 + a065 * k5), p, t + c6 * dt) + k7 = f(uprev + dt * (a071 * k1 + a073 * k3 + a074 * k4 + a075 * k5 + a076 * k6), p, + t + c7 * dt) + k8 = f( + uprev + + dt * (a081 * k1 + a083 * k3 + a084 * k4 + a085 * k5 + a086 * k6 + a087 * k7), + p, + t + c8 * dt) + g9 = uprev + + dt * + (a091 * k1 + a093 * k3 + a094 * k4 + a095 * k5 + a096 * k6 + a097 * k7 + a098 * k8) + g10 = uprev + + dt * (a101 * k1 + a103 * k3 + a104 * k4 + a105 * k5 + a106 * k6 + a107 * k7) + k9 = f(g9, p, t + dt) + k10 = f(g10, p, t + dt) + integrator.stats.nf += 10 + u = uprev + dt * (b1 * k1 + b4 * k4 + b5 * k5 + b6 * k6 + b7 * k7 + b8 * k8 + b9 * k9) + if integrator.alg isa CompositeAlgorithm + ϱu = integrator.opts.internalnorm(k10 - k9, t) + ϱd = integrator.opts.internalnorm(g10 - g9, t) + integrator.eigen_est = ϱu / ϱd + end + if integrator.opts.adaptive + utilde = dt * + (btilde1 * k1 + btilde4 * k4 + btilde5 * k5 + btilde6 * k6 + btilde7 * k7 + + btilde8 * k8 + btilde9 * k9 + btilde10 * k10) + atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.k[1] = k1 + integrator.k[2] = k2 + integrator.k[3] = k3 + integrator.k[4] = k4 + integrator.k[5] = k5 + integrator.k[6] = k6 + integrator.k[7] = k7 + integrator.k[8] = k8 + integrator.k[9] = k9 + integrator.k[10] = k10 + integrator.u = u + + alg = unwrap_alg(integrator, false) + if !alg.lazy && (integrator.opts.adaptive == false || + accept_step_controller(integrator, integrator.opts.controller)) + k = integrator.k + @OnDemandTableauExtract Vern7ExtraStages T T2 + k[11] = f( + uprev + + dt * (a1101 * k[1] + a1104 * k[4] + a1105 * k[5] + a1106 * k[6] + + a1107 * k[7] + a1108 * k[8] + a1109 * k[9]), + p, + t + c11 * dt) + k[12] = f( + uprev + + dt * (a1201 * k[1] + a1204 * k[4] + a1205 * k[5] + a1206 * k[6] + + a1207 * k[7] + a1208 * k[8] + a1209 * k[9] + a1211 * k[11]), + p, + t + c12 * dt) + k[13] = f( + uprev + + dt * (a1301 * k[1] + a1304 * k[4] + a1305 * k[5] + a1306 * k[6] + + a1307 * k[7] + a1308 * k[8] + a1309 * k[9] + a1311 * k[11] + + a1312 * k[12]), + p, + t + c13 * dt) + k[14] = f( + uprev + + dt * (a1401 * k[1] + a1404 * k[4] + a1405 * k[5] + a1406 * k[6] + + a1407 * k[7] + a1408 * k[8] + a1409 * k[9] + a1411 * k[11] + + a1412 * k[12] + a1413 * k[13]), + p, + t + c14 * dt) + k[15] = f( + uprev + + dt * (a1501 * k[1] + a1504 * k[4] + a1505 * k[5] + a1506 * k[6] + + a1507 * k[7] + a1508 * k[8] + a1509 * k[9] + a1511 * k[11] + + a1512 * k[12] + a1513 * k[13]), + p, + t + c15 * dt) + k[16] = f( + uprev + + dt * (a1601 * k[1] + a1604 * k[4] + a1605 * k[5] + a1606 * k[6] + + a1607 * k[7] + a1608 * k[8] + a1609 * k[9] + a1611 * k[11] + + a1612 * k[12] + a1613 * k[13]), + p, + t + c16 * dt) + integrator.stats.nf += 6 + end +end + +function initialize!(integrator, cache::Vern7Cache) + @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10 = cache + @unpack k = integrator + alg = unwrap_alg(integrator, false) + alg.lazy ? (integrator.kshortsize = 10) : (integrator.kshortsize = 16) + resize!(k, integrator.kshortsize) + k[1] = k1 + k[2] = k2 + k[3] = k3 + k[4] = k4 + k[5] = k5 + k[6] = k6 + k[7] = k7 + k[8] = k8 + k[9] = k9 + k[10] = k10 # Setup pointers + + if !alg.lazy + k[11] = similar(cache.k1) + k[12] = similar(cache.k1) + k[13] = similar(cache.k1) + k[14] = similar(cache.k1) + k[15] = similar(cache.k1) + k[16] = similar(cache.k1) + end +end + +@muladd function perform_step!(integrator, cache::Vern7Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + T = constvalue(recursive_unitless_bottom_eltype(u)) + T2 = constvalue(typeof(one(t))) + @OnDemandTableauExtract Vern7Tableau T T2 + @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, utilde, tmp, rtmp, atmp, stage_limiter!, step_limiter!, thread = cache + f(k1, uprev, p, t) + a = dt * a021 + @.. broadcast=false thread=thread tmp=uprev + a * k1 + stage_limiter!(tmp, integrator, p, t + c2 * dt) + f(k2, tmp, p, t + c2 * dt) + @.. broadcast=false thread=thread tmp=uprev + dt * (a031 * k1 + a032 * k2) + stage_limiter!(tmp, integrator, p, t + c3 * dt) + f(k3, tmp, p, t + c3 * dt) + @.. broadcast=false thread=thread tmp=uprev + dt * (a041 * k1 + a043 * k3) + stage_limiter!(tmp, integrator, p, t + c4 * dt) + f(k4, tmp, p, t + c4 * dt) + @.. broadcast=false thread=thread tmp=uprev + dt * (a051 * k1 + a053 * k3 + a054 * k4) + stage_limiter!(tmp, integrator, p, t + c5 * dt) + f(k5, tmp, p, t + c5 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a061 * k1 + a063 * k3 + a064 * k4 + a065 * k5) + stage_limiter!(tmp, integrator, p, t + c6 * dt) + f(k6, tmp, p, t + c6 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a071 * k1 + a073 * k3 + a074 * k4 + a075 * k5 + + a076 * k6) + stage_limiter!(tmp, integrator, p, t + c7 * dt) + f(k7, tmp, p, t + c7 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a081 * k1 + a083 * k3 + a084 * k4 + a085 * k5 + + a086 * k6 + + a087 * k7) + stage_limiter!(tmp, integrator, p, t + c8 * dt) + f(k8, tmp, p, t + c8 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a091 * k1 + a093 * k3 + a094 * k4 + a095 * k5 + + a096 * k6 + + a097 * k7 + a098 * k8) + stage_limiter!(tmp, integrator, p, t + dt) + f(k9, tmp, p, t + dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a101 * k1 + a103 * k3 + a104 * k4 + a105 * k5 + + a106 * k6 + + a107 * k7) + stage_limiter!(tmp, integrator, p, t + dt) + f(k10, tmp, p, t + dt) + @.. broadcast=false thread=thread u=uprev + + dt * + (b1 * k1 + b4 * k4 + b5 * k5 + b6 * k6 + b7 * k7 + + b8 * k8 + + b9 * k9) + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + integrator.stats.nf += 10 + if integrator.alg isa CompositeAlgorithm + g10 = u + g9 = tmp + @.. broadcast=false thread=thread rtmp=k10 - k9 + ϱu = integrator.opts.internalnorm(rtmp, t) + @.. broadcast=false thread=thread utilde=g10 - g9 + ϱd = integrator.opts.internalnorm(utilde, t) + integrator.eigen_est = ϱu / ϱd + end + if integrator.opts.adaptive + @.. broadcast=false thread=thread utilde=dt * (btilde1 * k1 + btilde4 * k4 + + btilde5 * k5 + + btilde6 * k6 + btilde7 * k7 + + btilde8 * k8 + + btilde9 * k9 + btilde10 * k10) + calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t, + thread) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + alg = unwrap_alg(integrator, false) + if !alg.lazy && (integrator.opts.adaptive == false || + accept_step_controller(integrator, integrator.opts.controller)) + k = integrator.k + @unpack tmp = cache + @OnDemandTableauExtract Vern7ExtraStages T T2 + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a1101 * k[1] + a1104 * k[4] + a1105 * k[5] + + a1106 * k[6] + + a1107 * k[7] + a1108 * k[8] + a1109 * k[9]) + f(k[11], tmp, p, t + c11 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a1201 * k[1] + a1204 * k[4] + a1205 * k[5] + + a1206 * k[6] + + a1207 * k[7] + a1208 * k[8] + a1209 * k[9] + + a1211 * k[11]) + f(k[12], tmp, p, t + c12 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a1301 * k[1] + a1304 * k[4] + a1305 * k[5] + + a1306 * k[6] + + a1307 * k[7] + a1308 * k[8] + a1309 * k[9] + + a1311 * k[11] + a1312 * k[12]) + f(k[13], tmp, p, t + c13 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a1401 * k[1] + a1404 * k[4] + a1405 * k[5] + + a1406 * k[6] + + a1407 * k[7] + a1408 * k[8] + a1409 * k[9] + + a1411 * k[11] + a1412 * k[12] + + a1413 * k[13]) + f(k[14], tmp, p, t + c14 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a1501 * k[1] + a1504 * k[4] + a1505 * k[5] + + a1506 * k[6] + + a1507 * k[7] + a1508 * k[8] + a1509 * k[9] + + a1511 * k[11] + a1512 * k[12] + + a1513 * k[13]) + f(k[15], tmp, p, t + c15 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a1601 * k[1] + a1604 * k[4] + a1605 * k[5] + + a1606 * k[6] + + a1607 * k[7] + a1608 * k[8] + a1609 * k[9] + + a1611 * k[11] + a1612 * k[12] + + a1613 * k[13]) + f(k[16], tmp, p, t + c16 * dt) + integrator.stats.nf += 6 + end + return nothing +end + +function initialize!(integrator, cache::Vern8ConstantCache) + alg = unwrap_alg(integrator, false) + alg.lazy ? (integrator.kshortsize = 13) : (integrator.kshortsize = 21) + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + @inbounds for i in eachindex(integrator.k) + integrator.k[i] = zero(integrator.uprev) ./ oneunit(integrator.t) + end +end + +@muladd function perform_step!(integrator, cache::Vern8ConstantCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + @unpack c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, a0201, a0301, a0302, a0401, a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, a0704, a0705, a0706, a0801, a0804, a0805, a0806, a0807, a0901, a0904, a0905, a0906, a0907, a0908, a1001, a1004, a1005, a1006, a1007, a1008, a1009, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211, a1301, a1304, a1305, a1306, a1307, a1308, a1309, a1310, b1, b6, b7, b8, b9, b10, b11, b12, btilde1, btilde6, btilde7, btilde8, btilde9, btilde10, btilde11, btilde12, btilde13 = cache.tab + k1 = f(uprev, p, t) + a = dt * a0201 + k2 = f(uprev + a * k1, p, t + c2 * dt) + k3 = f(uprev + dt * (a0301 * k1 + a0302 * k2), p, t + c3 * dt) + k4 = f(uprev + dt * (a0401 * k1 + a0403 * k3), p, t + c4 * dt) + k5 = f(uprev + dt * (a0501 * k1 + a0503 * k3 + a0504 * k4), p, t + c5 * dt) + k6 = f(uprev + dt * (a0601 * k1 + a0604 * k4 + a0605 * k5), p, t + c6 * dt) + k7 = f(uprev + dt * (a0701 * k1 + a0704 * k4 + a0705 * k5 + a0706 * k6), p, t + c7 * dt) + k8 = f( + uprev + dt * (a0801 * k1 + a0804 * k4 + a0805 * k5 + a0806 * k6 + a0807 * k7), p, + t + c8 * dt) + k9 = f( + uprev + + dt * + (a0901 * k1 + a0904 * k4 + a0905 * k5 + a0906 * k6 + a0907 * k7 + a0908 * k8), + p, + t + c9 * dt) + k10 = f( + uprev + + dt * + (a1001 * k1 + a1004 * k4 + a1005 * k5 + a1006 * k6 + a1007 * k7 + a1008 * k8 + + a1009 * k9), + p, + t + c10 * dt) + k11 = f( + uprev + + dt * + (a1101 * k1 + a1104 * k4 + a1105 * k5 + a1106 * k6 + a1107 * k7 + a1108 * k8 + + a1109 * k9 + a1110 * k10), + p, + t + c11 * dt) + g12 = uprev + + dt * + (a1201 * k1 + a1204 * k4 + a1205 * k5 + a1206 * k6 + a1207 * k7 + a1208 * k8 + + a1209 * k9 + a1210 * k10 + a1211 * k11) + g13 = uprev + + dt * + (a1301 * k1 + a1304 * k4 + a1305 * k5 + a1306 * k6 + a1307 * k7 + a1308 * k8 + + a1309 * k9 + a1310 * k10) + k12 = f(g12, p, t + dt) + k13 = f(g13, p, t + dt) + integrator.stats.nf += 13 + u = uprev + + dt * (b1 * k1 + b6 * k6 + b7 * k7 + b8 * k8 + b9 * k9 + b10 * k10 + b11 * k11 + + b12 * k12) + if integrator.alg isa CompositeAlgorithm + ϱu = integrator.opts.internalnorm(k13 - k12, t) + ϱd = integrator.opts.internalnorm(g13 - g12, t) + integrator.eigen_est = ϱu / ϱd + end + if integrator.opts.adaptive + utilde = dt * + (btilde1 * k1 + btilde6 * k6 + btilde7 * k7 + btilde8 * k8 + btilde9 * k9 + + btilde10 * k10 + btilde11 * k11 + btilde12 * k12 + btilde13 * k13) + atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + integrator.k[1] = k1 + integrator.k[2] = k2 + integrator.k[3] = k3 + integrator.k[4] = k4 + integrator.k[5] = k5 + integrator.k[6] = k6 + integrator.k[7] = k7 + integrator.k[8] = k8 + integrator.k[9] = k9 + integrator.k[10] = k10 + integrator.k[11] = k11 + integrator.k[12] = k12 + integrator.k[13] = k13 + integrator.u = u + + alg = unwrap_alg(integrator, false) + if !alg.lazy && (integrator.opts.adaptive == false || + accept_step_controller(integrator, integrator.opts.controller)) + k = integrator.k + @unpack c14, a1401, a1406, a1407, a1408, a1409, a1410, a1411, a1412, c15, a1501, a1506, a1507, a1508, a1509, a1510, a1511, a1512, a1514, c16, a1601, a1606, a1607, a1608, a1609, a1610, a1611, a1612, a1614, a1615, c17, a1701, a1706, a1707, a1708, a1709, a1710, a1711, a1712, a1714, a1715, a1716, c18, a1801, a1806, a1807, a1808, a1809, a1810, a1811, a1812, a1814, a1815, a1816, a1817, c19, a1901, a1906, a1907, a1908, a1909, a1910, a1911, a1912, a1914, a1915, a1916, a1917, c20, a2001, a2006, a2007, a2008, a2009, a2010, a2011, a2012, a2014, a2015, a2016, a2017, c21, a2101, a2106, a2107, a2108, a2109, a2110, a2111, a2112, a2114, a2115, a2116, a2117 = cache.tab.extra + k[14] = f( + uprev + + dt * (a1401 * k[1] + a1406 * k[6] + a1407 * k[7] + a1408 * k[8] + + a1409 * k[9] + a1410 * k[10] + a1411 * k[11] + a1412 * k[12]), + p, + t + c14 * dt) + k[15] = f( + uprev + + dt * (a1501 * k[1] + a1506 * k[6] + a1507 * k[7] + a1508 * k[8] + + a1509 * k[9] + a1510 * k[10] + a1511 * k[11] + a1512 * k[12] + + a1514 * k[14]), + p, + t + c15 * dt) + k[16] = f( + uprev + + dt * (a1601 * k[1] + a1606 * k[6] + a1607 * k[7] + a1608 * k[8] + + a1609 * k[9] + a1610 * k[10] + a1611 * k[11] + a1612 * k[12] + + a1614 * k[14] + a1615 * k[15]), + p, + t + c16 * dt) + k[17] = f( + uprev + + dt * (a1701 * k[1] + a1706 * k[6] + a1707 * k[7] + a1708 * k[8] + + a1709 * k[9] + a1710 * k[10] + a1711 * k[11] + a1712 * k[12] + + a1714 * k[14] + a1715 * k[15] + a1716 * k[16]), + p, + t + c17 * dt) + k[18] = f( + uprev + + dt * (a1801 * k[1] + a1806 * k[6] + a1807 * k[7] + a1808 * k[8] + + a1809 * k[9] + a1810 * k[10] + a1811 * k[11] + a1812 * k[12] + + a1814 * k[14] + a1815 * k[15] + a1816 * k[16] + a1817 * k[17]), + p, + t + c18 * dt) + k[19] = f( + uprev + + dt * (a1901 * k[1] + a1906 * k[6] + a1907 * k[7] + a1908 * k[8] + + a1909 * k[9] + a1910 * k[10] + a1911 * k[11] + a1912 * k[12] + + a1914 * k[14] + a1915 * k[15] + a1916 * k[16] + a1917 * k[17]), + p, + t + c19 * dt) + k[20] = f( + uprev + + dt * (a2001 * k[1] + a2006 * k[6] + a2007 * k[7] + a2008 * k[8] + + a2009 * k[9] + a2010 * k[10] + a2011 * k[11] + a2012 * k[12] + + a2014 * k[14] + a2015 * k[15] + a2016 * k[16] + a2017 * k[17]), + p, + t + c20 * dt) + k[21] = f( + uprev + + dt * (a2101 * k[1] + a2106 * k[6] + a2107 * k[7] + a2108 * k[8] + + a2109 * k[9] + a2110 * k[10] + a2111 * k[11] + a2112 * k[12] + + a2114 * k[14] + a2115 * k[15] + a2116 * k[16] + a2117 * k[17]), + p, + t + c21 * dt) + integrator.stats.nf += 8 + end +end + +function initialize!(integrator, cache::Vern8Cache) + @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13 = cache + @unpack k = integrator + alg = unwrap_alg(integrator, false) + alg.lazy ? (integrator.kshortsize = 13) : (integrator.kshortsize = 21) + resize!(k, integrator.kshortsize) + k[1] = k1 + k[2] = k2 + k[3] = k3 + k[4] = k4 + k[5] = k5 + k[6] = k6 + k[7] = k7 + k[8] = k8 + k[9] = k9 + k[10] = k10 + k[11] = k11 + k[12] = k12 + k[13] = k13 # Setup pointers + + if !alg.lazy + for i in 14:21 + k[i] = similar(cache.k1) + end + end +end + +@muladd function perform_step!(integrator, cache::Vern8Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + uidx = eachindex(integrator.uprev) + @unpack c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, a0201, a0301, a0302, a0401, a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, a0704, a0705, a0706, a0801, a0804, a0805, a0806, a0807, a0901, a0904, a0905, a0906, a0907, a0908, a1001, a1004, a1005, a1006, a1007, a1008, a1009, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211, a1301, a1304, a1305, a1306, a1307, a1308, a1309, a1310, b1, b6, b7, b8, b9, b10, b11, b12, btilde1, btilde6, btilde7, btilde8, btilde9, btilde10, btilde11, btilde12, btilde13 = cache.tab + @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, utilde, tmp, rtmp, atmp, stage_limiter!, step_limiter!, thread = cache + f(k1, uprev, p, t) + a = dt * a0201 + @.. broadcast=false thread=thread tmp=uprev + a * k1 + stage_limiter!(tmp, integrator, p, t + c2 * dt) + f(k2, tmp, p, t + c2 * dt) + @.. broadcast=false thread=thread tmp=uprev + dt * (a0301 * k1 + a0302 * k2) + stage_limiter!(tmp, integrator, p, t + c3 * dt) + f(k3, tmp, p, t + c3 * dt) + @.. broadcast=false thread=thread tmp=uprev + dt * (a0401 * k1 + a0403 * k3) + stage_limiter!(tmp, integrator, p, t + c4 * dt) + f(k4, tmp, p, t + c4 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a0501 * k1 + a0503 * k3 + a0504 * k4) + stage_limiter!(tmp, integrator, p, t + c5 * dt) + f(k5, tmp, p, t + c5 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a0601 * k1 + a0604 * k4 + a0605 * k5) + stage_limiter!(tmp, integrator, p, t + c6 * dt) + f(k6, tmp, p, t + c6 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a0701 * k1 + a0704 * k4 + a0705 * k5 + + a0706 * k6) + stage_limiter!(tmp, integrator, p, t + c7 * dt) + f(k7, tmp, p, t + c7 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a0801 * k1 + a0804 * k4 + a0805 * k5 + + a0806 * k6 + a0807 * k7) + stage_limiter!(tmp, integrator, p, t + c8 * dt) + f(k8, tmp, p, t + c8 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a0901 * k1 + a0904 * k4 + a0905 * k5 + + a0906 * k6 + + a0907 * k7 + a0908 * k8) + stage_limiter!(tmp, integrator, p, t + c9 * dt) + f(k9, tmp, p, t + c9 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a1001 * k1 + a1004 * k4 + a1005 * k5 + + a1006 * k6 + + a1007 * k7 + a1008 * k8 + a1009 * k9) + stage_limiter!(tmp, integrator, p, t + c10 * dt) + f(k10, tmp, p, t + c10 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a1101 * k1 + a1104 * k4 + a1105 * k5 + + a1106 * k6 + + a1107 * k7 + a1108 * k8 + a1109 * k9 + + a1110 * k10) + stage_limiter!(tmp, integrator, p, t + c11 * dt) + f(k11, tmp, p, t + c11 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a1201 * k1 + a1204 * k4 + a1205 * k5 + + a1206 * k6 + + a1207 * k7 + a1208 * k8 + a1209 * k9 + + a1210 * k10 + + a1211 * k11) + stage_limiter!(tmp, integrator, p, t + dt) + f(k12, tmp, p, t + dt) + @.. broadcast=false thread=thread u=uprev + + dt * + (a1301 * k1 + a1304 * k4 + a1305 * k5 + a1306 * k6 + + a1307 * k7 + + a1308 * k8 + a1309 * k9 + a1310 * k10) + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + f(k13, u, p, t + dt) + integrator.stats.nf += 13 + if integrator.alg isa CompositeAlgorithm + g13 = u + g12 = tmp + @.. broadcast=false thread=thread rtmp=k13 - k12 + ϱu = integrator.opts.internalnorm(rtmp, t) + @.. broadcast=false thread=thread utilde=g13 - g12 + ϱd = integrator.opts.internalnorm(utilde, t) + integrator.eigen_est = ϱu / ϱd + end + @.. broadcast=false thread=thread u=uprev + + dt * + (b1 * k1 + b6 * k6 + b7 * k7 + b8 * k8 + b9 * k9 + + b10 * k10 + + b11 * k11 + b12 * k12) + if integrator.opts.adaptive + @.. broadcast=false thread=thread utilde=dt * (btilde1 * k1 + btilde6 * k6 + + btilde7 * k7 + + btilde8 * k8 + btilde9 * k9 + + btilde10 * k10 + + btilde11 * k11 + btilde12 * k12 + + btilde13 * k13) + calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t, + thread) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + + alg = unwrap_alg(integrator, false) + if !alg.lazy && (integrator.opts.adaptive == false || + accept_step_controller(integrator, integrator.opts.controller)) + k = integrator.k + @unpack c14, a1401, a1406, a1407, a1408, a1409, a1410, a1411, a1412, c15, a1501, a1506, a1507, a1508, a1509, a1510, a1511, a1512, a1514, c16, a1601, a1606, a1607, a1608, a1609, a1610, a1611, a1612, a1614, a1615, c17, a1701, a1706, a1707, a1708, a1709, a1710, a1711, a1712, a1714, a1715, a1716, c18, a1801, a1806, a1807, a1808, a1809, a1810, a1811, a1812, a1814, a1815, a1816, a1817, c19, a1901, a1906, a1907, a1908, a1909, a1910, a1911, a1912, a1914, a1915, a1916, a1917, c20, a2001, a2006, a2007, a2008, a2009, a2010, a2011, a2012, a2014, a2015, a2016, a2017, c21, a2101, a2106, a2107, a2108, a2109, a2110, a2111, a2112, a2114, a2115, a2116, a2117 = cache.tab.extra + @unpack tmp = cache + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a1401 * k[1] + a1406 * k[6] + a1407 * k[7] + + a1408 * k[8] + + a1409 * k[9] + a1410 * k[10] + + a1411 * k[11] + + a1412 * k[12]) + f(k[14], tmp, p, t + c14 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a1501 * k[1] + a1506 * k[6] + a1507 * k[7] + + a1508 * k[8] + + a1509 * k[9] + a1510 * k[10] + + a1511 * k[11] + + a1512 * k[12] + a1514 * k[14]) + f(k[15], tmp, p, t + c15 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a1601 * k[1] + a1606 * k[6] + a1607 * k[7] + + a1608 * k[8] + + a1609 * k[9] + a1610 * k[10] + + a1611 * k[11] + + a1612 * k[12] + a1614 * k[14] + + a1615 * k[15]) + f(k[16], tmp, p, t + c16 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a1701 * k[1] + a1706 * k[6] + a1707 * k[7] + + a1708 * k[8] + + a1709 * k[9] + a1710 * k[10] + + a1711 * k[11] + + a1712 * k[12] + a1714 * k[14] + + a1715 * k[15] + + a1716 * k[16]) + f(k[17], tmp, p, t + c17 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a1801 * k[1] + a1806 * k[6] + a1807 * k[7] + + a1808 * k[8] + + a1809 * k[9] + a1810 * k[10] + + a1811 * k[11] + + a1812 * k[12] + a1814 * k[14] + + a1815 * k[15] + + a1816 * k[16] + a1817 * k[17]) + f(k[18], tmp, p, t + c18 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a1901 * k[1] + a1906 * k[6] + a1907 * k[7] + + a1908 * k[8] + + a1909 * k[9] + a1910 * k[10] + + a1911 * k[11] + + a1912 * k[12] + a1914 * k[14] + + a1915 * k[15] + + a1916 * k[16] + a1917 * k[17]) + f(k[19], tmp, p, t + c19 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a2001 * k[1] + a2006 * k[6] + a2007 * k[7] + + a2008 * k[8] + + a2009 * k[9] + a2010 * k[10] + + a2011 * k[11] + + a2012 * k[12] + a2014 * k[14] + + a2015 * k[15] + + a2016 * k[16] + a2017 * k[17]) + f(k[20], tmp, p, t + c20 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a2101 * k[1] + a2106 * k[6] + a2107 * k[7] + + a2108 * k[8] + + a2109 * k[9] + a2110 * k[10] + + a2111 * k[11] + + a2112 * k[12] + a2114 * k[14] + + a2115 * k[15] + + a2116 * k[16] + a2117 * k[17]) + integrator.stats.nf += 8 + f(k[21], tmp, p, t + c21 * dt) + end + return nothing +end + +function initialize!(integrator, cache::Vern9ConstantCache) + alg = unwrap_alg(integrator, false) + alg.lazy ? (integrator.kshortsize = 10) : (integrator.kshortsize = 20) + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + + # Avoid undefined entries if k is an array of arrays + @inbounds for i in eachindex(integrator.k) + integrator.k[i] = zero(integrator.uprev) ./ oneunit(integrator.t) + end +end + +@muladd function perform_step!(integrator, cache::Vern9ConstantCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + T = constvalue(recursive_unitless_bottom_eltype(u)) + T2 = constvalue(typeof(one(t))) + @OnDemandTableauExtract Vern9Tableau T T2 + k1 = f(uprev, p, t) + a = dt * a0201 + k2 = f(uprev + a * k1, p, t + c1 * dt) + k3 = f(uprev + dt * (a0301 * k1 + a0302 * k2), p, t + c2 * dt) + k4 = f(uprev + dt * (a0401 * k1 + a0403 * k3), p, t + c3 * dt) + k5 = f(uprev + dt * (a0501 * k1 + a0503 * k3 + a0504 * k4), p, t + c4 * dt) + k6 = f(uprev + dt * (a0601 * k1 + a0604 * k4 + a0605 * k5), p, t + c5 * dt) + k7 = f(uprev + dt * (a0701 * k1 + a0704 * k4 + a0705 * k5 + a0706 * k6), p, t + c6 * dt) + k8 = f(uprev + dt * (a0801 * k1 + a0806 * k6 + a0807 * k7), p, t + c7 * dt) + k9 = f(uprev + dt * (a0901 * k1 + a0906 * k6 + a0907 * k7 + a0908 * k8), p, t + c8 * dt) + k10 = f(uprev + dt * (a1001 * k1 + a1006 * k6 + a1007 * k7 + a1008 * k8 + a1009 * k9), + p, t + c9 * dt) + k11 = f( + uprev + + dt * + (a1101 * k1 + a1106 * k6 + a1107 * k7 + a1108 * k8 + a1109 * k9 + a1110 * k10), + p, t + c10 * dt) + k12 = f( + uprev + + dt * + (a1201 * k1 + a1206 * k6 + a1207 * k7 + a1208 * k8 + a1209 * k9 + a1210 * k10 + + a1211 * k11), + p, + t + c11 * dt) + k13 = f( + uprev + + dt * + (a1301 * k1 + a1306 * k6 + a1307 * k7 + a1308 * k8 + a1309 * k9 + a1310 * k10 + + a1311 * k11 + a1312 * k12), + p, + t + c12 * dt) + k14 = f( + uprev + + dt * + (a1401 * k1 + a1406 * k6 + a1407 * k7 + a1408 * k8 + a1409 * k9 + a1410 * k10 + + a1411 * k11 + a1412 * k12 + a1413 * k13), + p, + t + c13 * dt) + g15 = uprev + + dt * + (a1501 * k1 + a1506 * k6 + a1507 * k7 + a1508 * k8 + a1509 * k9 + a1510 * k10 + + a1511 * k11 + a1512 * k12 + a1513 * k13 + a1514 * k14) + g16 = uprev + + dt * + (a1601 * k1 + a1606 * k6 + a1607 * k7 + a1608 * k8 + a1609 * k9 + a1610 * k10 + + a1611 * k11 + a1612 * k12 + a1613 * k13) + k15 = f(g15, p, t + dt) + k16 = f(g16, p, t + dt) + integrator.stats.nf += 16 + u = uprev + + dt * (b1 * k1 + b8 * k8 + b9 * k9 + b10 * k10 + b11 * k11 + b12 * k12 + b13 * k13 + + b14 * k14 + b15 * k15) + if integrator.alg isa CompositeAlgorithm + ϱu = integrator.opts.internalnorm(k16 - k15, t) + ϱd = integrator.opts.internalnorm(g16 - g15, t) + integrator.eigen_est = ϱu / ϱd + end + if integrator.opts.adaptive + utilde = dt * (btilde1 * k1 + btilde8 * k8 + btilde9 * k9 + btilde10 * k10 + + btilde11 * k11 + btilde12 * k12 + btilde13 * k13 + btilde14 * k14 + + btilde15 * k15 + btilde16 * k16) + atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + # k2, k3,k4,k5,k6,k7 are not used in the code (not even in interpolations), we dont need their pointers. + # So we mapped k[2] (from integrator) with k8 (from cache), k[3] with k9 and so on. + integrator.k[1] = k1 + integrator.k[2] = k8 + integrator.k[3] = k9 + integrator.k[4] = k10 + integrator.k[5] = k11 + integrator.k[6] = k12 + integrator.k[7] = k13 + integrator.k[8] = k14 + integrator.k[9] = k15 + integrator.k[10] = k16 + integrator.u = u + + alg = unwrap_alg(integrator, false) + if !alg.lazy && (integrator.opts.adaptive == false || + accept_step_controller(integrator, integrator.opts.controller)) + k = integrator.k + @OnDemandTableauExtract Vern9ExtraStages T T2 + k[11] = f( + uprev + + dt * (a1701 * k[1] + a1708 * k[2] + a1709 * k[3] + a1710 * k[4] + + a1711 * k[5] + a1712 * k[6] + a1713 * k[7] + a1714 * k[8] + + a1715 * k[9]), + p, t + c17 * dt) + k[12] = f( + uprev + + dt * (a1801 * k[1] + a1808 * k[2] + a1809 * k[3] + a1810 * k[4] + + a1811 * k[5] + a1812 * k[6] + a1813 * k[7] + a1814 * k[8] + + a1815 * k[9] + a1817 * k[11]), + p, + t + c18 * dt) + k[13] = f( + uprev + + dt * (a1901 * k[1] + a1908 * k[2] + a1909 * k[3] + a1910 * k[4] + + a1911 * k[5] + a1912 * k[6] + a1913 * k[7] + a1914 * k[8] + + a1915 * k[9] + a1917 * k[11] + a1918 * k[12]), + p, + t + c19 * dt) + k[14] = f( + uprev + + dt * (a2001 * k[1] + a2008 * k[2] + a2009 * k[3] + a2010 * k[4] + + a2011 * k[5] + a2012 * k[6] + a2013 * k[7] + a2014 * k[8] + + a2015 * k[9] + a2017 * k[11] + a2018 * k[12] + a2019 * k[13]), + p, + t + c20 * dt) + k[15] = f( + uprev + + dt * (a2101 * k[1] + a2108 * k[2] + a2109 * k[3] + a2110 * k[4] + + a2111 * k[5] + a2112 * k[6] + a2113 * k[7] + a2114 * k[8] + + a2115 * k[9] + a2117 * k[11] + a2118 * k[12] + a2119 * k[13] + + a2120 * k[14]), + p, + t + c21 * dt) + k[16] = f( + uprev + + dt * (a2201 * k[1] + a2208 * k[2] + a2209 * k[3] + a2210 * k[4] + + a2211 * k[5] + a2212 * k[6] + a2213 * k[7] + a2214 * k[8] + + a2215 * k[9] + a2217 * k[11] + a2218 * k[12] + a2219 * k[13] + + a2220 * k[14] + a2221 * k[15]), + p, + t + c22 * dt) + k[17] = f( + uprev + + dt * (a2301 * k[1] + a2308 * k[2] + a2309 * k[3] + a2310 * k[4] + + a2311 * k[5] + a2312 * k[6] + a2313 * k[7] + a2314 * k[8] + + a2315 * k[9] + a2317 * k[11] + a2318 * k[12] + a2319 * k[13] + + a2320 * k[14] + a2321 * k[15]), + p, + t + c23 * dt) + k[18] = f( + uprev + + dt * (a2401 * k[1] + a2408 * k[2] + a2409 * k[3] + a2410 * k[4] + + a2411 * k[5] + a2412 * k[6] + a2413 * k[7] + a2414 * k[8] + + a2415 * k[9] + a2417 * k[11] + a2418 * k[12] + a2419 * k[13] + + a2420 * k[14] + a2421 * k[15]), + p, + t + c24 * dt) + k[19] = f( + uprev + + dt * (a2501 * k[1] + a2508 * k[2] + a2509 * k[3] + a2510 * k[4] + + a2511 * k[5] + a2512 * k[6] + a2513 * k[7] + a2514 * k[8] + + a2515 * k[9] + a2517 * k[11] + a2518 * k[12] + a2519 * k[13] + + a2520 * k[14] + a2521 * k[15]), + p, + t + c25 * dt) + k[20] = f( + uprev + + dt * (a2601 * k[1] + a2608 * k[2] + a2609 * k[3] + a2610 * k[4] + + a2611 * k[5] + a2612 * k[6] + a2613 * k[7] + a2614 * k[8] + + a2615 * k[9] + a2617 * k[11] + a2618 * k[12] + a2619 * k[13] + + a2620 * k[14] + a2621 * k[15]), + p, + t + c26 * dt) + integrator.stats.nf += 10 + end +end + +function initialize!(integrator, cache::Vern9Cache) + @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16 = cache + @unpack k = integrator + alg = unwrap_alg(integrator, false) + alg.lazy ? (integrator.kshortsize = 10) : (integrator.kshortsize = 20) + resize!(k, integrator.kshortsize) + # k2, k3,k4,k5,k6,k7 are not used in the code (not even in interpolations), we dont need their pointers. + # So we mapped k[2] (from integrator) with k8 (from cache), k[3] with k9 and so on. + k[1] = k1 + k[2] = k8 + k[3] = k9 + k[4] = k10 + k[5] = k11 + k[6] = k12 + k[7] = k13 + k[8] = k14 + k[9] = k15 + k[10] = k16 # Setup pointers + + if !alg.lazy + for i in 11:20 + k[i] = similar(cache.k1) + end + end +end + +@muladd function perform_step!(integrator, cache::Vern9Cache, repeat_step = false) + @unpack t, dt, uprev, u, f, p = integrator + uidx = eachindex(integrator.uprev) + T = constvalue(recursive_unitless_bottom_eltype(u)) + T2 = constvalue(typeof(one(t))) + @OnDemandTableauExtract Vern9Tableau T T2 + @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, utilde, tmp, rtmp, atmp, stage_limiter!, step_limiter!, thread = cache + f(k1, uprev, p, t) + a = dt * a0201 + @.. broadcast=false thread=thread tmp=uprev + a * k1 + stage_limiter!(tmp, integrator, p, t + c1 * dt) + f(k2, tmp, p, t + c1 * dt) + @.. broadcast=false thread=thread tmp=uprev + dt * (a0301 * k1 + a0302 * k2) + stage_limiter!(tmp, integrator, p, t + c2 * dt) + f(k3, tmp, p, t + c2 * dt) + @.. broadcast=false thread=thread tmp=uprev + dt * (a0401 * k1 + a0403 * k3) + stage_limiter!(tmp, integrator, p, t + c3 * dt) + f(k4, tmp, p, t + c3 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a0501 * k1 + a0503 * k3 + a0504 * k4) + stage_limiter!(tmp, integrator, p, t + c4 * dt) + f(k5, tmp, p, t + c4 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a0601 * k1 + a0604 * k4 + a0605 * k5) + stage_limiter!(tmp, integrator, p, t + c5 * dt) + f(k6, tmp, p, t + c5 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a0701 * k1 + a0704 * k4 + a0705 * k5 + + a0706 * k6) + stage_limiter!(tmp, integrator, p, t + c6 * dt) + f(k7, tmp, p, t + c6 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a0801 * k1 + a0806 * k6 + a0807 * k7) + stage_limiter!(tmp, integrator, p, t + c7 * dt) + f(k8, tmp, p, t + c7 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a0901 * k1 + a0906 * k6 + a0907 * k7 + + a0908 * k8) + stage_limiter!(tmp, integrator, p, t + c8 * dt) + f(k9, tmp, p, t + c8 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a1001 * k1 + a1006 * k6 + a1007 * k7 + + a1008 * k8 + a1009 * k9) + stage_limiter!(tmp, integrator, p, t + c9 * dt) + f(k10, tmp, p, t + c9 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a1101 * k1 + a1106 * k6 + a1107 * k7 + + a1108 * k8 + + a1109 * k9 + a1110 * k10) + stage_limiter!(tmp, integrator, p, t + c10 * dt) + f(k11, tmp, p, t + c10 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a1201 * k1 + a1206 * k6 + a1207 * k7 + + a1208 * k8 + + a1209 * k9 + a1210 * k10 + a1211 * k11) + stage_limiter!(tmp, integrator, p, t + c11 * dt) + f(k12, tmp, p, t + c11 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a1301 * k1 + a1306 * k6 + a1307 * k7 + + a1308 * k8 + + a1309 * k9 + a1310 * k10 + a1311 * k11 + + a1312 * k12) + stage_limiter!(tmp, integrator, p, t + c12 * dt) + f(k13, tmp, p, t + c12 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a1401 * k1 + a1406 * k6 + a1407 * k7 + + a1408 * k8 + + a1409 * k9 + a1410 * k10 + a1411 * k11 + + a1412 * k12 + + a1413 * k13) + stage_limiter!(tmp, integrator, p, t + c13 * dt) + f(k14, tmp, p, t + c13 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * (a1501 * k1 + a1506 * k6 + a1507 * k7 + + a1508 * k8 + + a1509 * k9 + a1510 * k10 + a1511 * k11 + + a1512 * k12 + + a1513 * k13 + a1514 * k14) + stage_limiter!(tmp, integrator, p, t + dt) + f(k15, tmp, p, t + dt) + @.. broadcast=false thread=thread u=uprev + + dt * + (a1601 * k1 + a1606 * k6 + a1607 * k7 + a1608 * k8 + + a1609 * k9 + + a1610 * k10 + a1611 * k11 + a1612 * k12 + + a1613 * k13) + stage_limiter!(u, integrator, p, t + dt) + step_limiter!(u, integrator, p, t + dt) + f(k16, u, p, t + dt) + integrator.stats.nf += 16 + if integrator.alg isa CompositeAlgorithm + g16 = u + g15 = tmp + @.. broadcast=false thread=thread rtmp=k16 - k15 + ϱu = integrator.opts.internalnorm(rtmp, t) + @.. broadcast=false thread=thread utilde=g16 - g15 + ϱd = integrator.opts.internalnorm(utilde, t) + integrator.eigen_est = ϱu / ϱd + end + @.. broadcast=false thread=thread u=uprev + + dt * + (b1 * k1 + b8 * k8 + b9 * k9 + b10 * k10 + + b11 * k11 + b12 * k12 + + b13 * k13 + b14 * k14 + b15 * k15) + if integrator.opts.adaptive + @.. broadcast=false thread=thread utilde=dt * (btilde1 * k1 + btilde8 * k8 + + btilde9 * k9 + + btilde10 * k10 + btilde11 * k11 + + btilde12 * k12 + + btilde13 * k13 + btilde14 * k14 + + btilde15 * k15 + + btilde16 * k16) + calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, + integrator.opts.reltol, integrator.opts.internalnorm, t, + thread) + integrator.EEst = integrator.opts.internalnorm(atmp, t) + end + + alg = unwrap_alg(integrator, false) + if !alg.lazy && (integrator.opts.adaptive == false || + accept_step_controller(integrator, integrator.opts.controller)) + k = integrator.k + @unpack tmp = cache + @OnDemandTableauExtract Vern9ExtraStages T T2 + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a1701 * k[1] + a1708 * k[2] + a1709 * k[3] + + a1710 * k[4] + + a1711 * k[5] + a1712 * k[6] + a1713 * k[7] + + a1714 * k[8] + + a1715 * k[9]) + f(k[11], tmp, p, t + c17 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a1801 * k[1] + a1808 * k[2] + a1809 * k[3] + + a1810 * k[4] + + a1811 * k[5] + a1812 * k[6] + a1813 * k[7] + + a1814 * k[8] + + a1815 * k[9] + a1817 * k[11]) + f(k[12], tmp, p, t + c18 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a1901 * k[1] + a1908 * k[2] + a1909 * k[3] + + a1910 * k[4] + + a1911 * k[5] + a1912 * k[6] + a1913 * k[7] + + a1914 * k[8] + + a1915 * k[9] + a1917 * k[11] + a1918 * k[12]) + f(k[13], tmp, p, t + c19 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a2001 * k[1] + a2008 * k[2] + a2009 * k[3] + + a2010 * k[4] + + a2011 * k[5] + a2012 * k[6] + a2013 * k[7] + + a2014 * k[8] + + a2015 * k[9] + a2017 * k[11] + + a2018 * k[12] + + a2019 * k[13]) + f(k[14], tmp, p, t + c20 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a2101 * k[1] + a2108 * k[2] + a2109 * k[3] + + a2110 * k[4] + + a2111 * k[5] + a2112 * k[6] + a2113 * k[7] + + a2114 * k[8] + + a2115 * k[9] + a2117 * k[11] + + a2118 * k[12] + + a2119 * k[13] + a2120 * k[14]) + f(k[15], tmp, p, t + c21 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a2201 * k[1] + a2208 * k[2] + a2209 * k[3] + + a2210 * k[4] + + a2211 * k[5] + a2212 * k[6] + a2213 * k[7] + + a2214 * k[8] + + a2215 * k[9] + a2217 * k[11] + + a2218 * k[12] + + a2219 * k[13] + a2220 * k[14] + + a2221 * k[15]) + f(k[16], tmp, p, t + c22 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a2301 * k[1] + a2308 * k[2] + a2309 * k[3] + + a2310 * k[4] + + a2311 * k[5] + a2312 * k[6] + a2313 * k[7] + + a2314 * k[8] + + a2315 * k[9] + a2317 * k[11] + + a2318 * k[12] + + a2319 * k[13] + a2320 * k[14] + + a2321 * k[15]) + f(k[17], tmp, p, t + c23 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a2401 * k[1] + a2408 * k[2] + a2409 * k[3] + + a2410 * k[4] + + a2411 * k[5] + a2412 * k[6] + a2413 * k[7] + + a2414 * k[8] + + a2415 * k[9] + a2417 * k[11] + + a2418 * k[12] + + a2419 * k[13] + a2420 * k[14] + + a2421 * k[15]) + f(k[18], tmp, p, t + c24 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a2501 * k[1] + a2508 * k[2] + a2509 * k[3] + + a2510 * k[4] + + a2511 * k[5] + a2512 * k[6] + a2513 * k[7] + + a2514 * k[8] + + a2515 * k[9] + a2517 * k[11] + + a2518 * k[12] + + a2519 * k[13] + a2520 * k[14] + + a2521 * k[15]) + f(k[19], tmp, p, t + c25 * dt) + @.. broadcast=false thread=thread tmp=uprev + + dt * + (a2601 * k[1] + a2608 * k[2] + a2609 * k[3] + + a2610 * k[4] + + a2611 * k[5] + a2612 * k[6] + a2613 * k[7] + + a2614 * k[8] + + a2615 * k[9] + a2617 * k[11] + + a2618 * k[12] + + a2619 * k[13] + a2620 * k[14] + + a2621 * k[15]) + integrator.stats.nf += 10 + f(k[20], tmp, p, t + c26 * dt) + end + return nothing +end diff --git a/src/rkc_utils.jl b/src/rkc_utils.jl new file mode 100644 index 0000000000..661197f5a7 --- /dev/null +++ b/src/rkc_utils.jl @@ -0,0 +1,276 @@ +# This function calculates the largest eigenvalue +# (absolute value wise) by power iteration. +const RKCAlgs = Union{RKC, IRKC, ESERK4, ESERK5, SERK2} +function maxeig!(integrator, cache::OrdinaryDiffEqConstantCache) + isfirst = integrator.iter == 1 || integrator.u_modified + @unpack t, dt, uprev, u, f, p, fsalfirst = integrator + maxiter = (integrator.alg isa Union{ESERK4, ESERK5, SERK2}) ? 100 : 50 + + safe = (integrator.alg isa RKCAlgs) ? 1.0 : 1.2 + # Initial guess for eigenvector `z` + if isfirst + if integrator.alg isa RKCAlgs + if integrator.alg isa IRKC + z = cache.du₂ + else + z = fsalfirst + end + else + fz = fsalfirst + z = f(fz, p, t) + integrator.stats.nf += 1 + end + else + z = cache.zprev + end + # Perturbation + u_norm = integrator.opts.internalnorm(uprev, t) + z_norm = integrator.opts.internalnorm(z, t) + pert = eps(u_norm) + sqrt_pert = sqrt(pert) + is_u_zero = u_norm == zero(u_norm) + is_z_zero = z_norm == zero(z_norm) + # Normalize `z` such that z-u lie in a circle + if (!is_u_zero && !is_z_zero) + dz_u = u_norm * sqrt_pert + quot = dz_u / z_norm + z = uprev + quot * z + elseif !is_u_zero + dz_u = u_norm * sqrt_pert + z = uprev + uprev * dz_u + elseif !is_z_zero + dz_u = pert + quot = dz_u / z_norm + z *= quot + else + dz_u = pert + z = dz_u * ones(z) + end # endif + # Start power iteration + integrator.eigen_est = 0 + for iter in 1:maxiter + if integrator.alg isa IRKC + fz = f.f2(z, p, t) + integrator.stats.nf2 += 1 + tmp = fz - cache.du₂ + else + fz = f(z, p, t) + integrator.stats.nf += 1 + tmp = fz - fsalfirst + end + Δ = integrator.opts.internalnorm(tmp, t) + eig_prev = integrator.eigen_est + integrator.eigen_est = Δ / dz_u * safe + # Convergence + if integrator.alg isa RKCAlgs # To match the constants given in the paper + if iter >= 2 && + abs(eig_prev - integrator.eigen_est) < + max(integrator.eigen_est, 1.0 / integrator.opts.dtmax) * 0.01 + integrator.eigen_est *= 1.2 + # Store the eigenvector + cache.zprev = z - uprev + return true + end + else + if iter >= 2 && + abs(eig_prev - integrator.eigen_est) < integrator.eigen_est * 0.05 + # Store the eigenvector + cache.zprev = z - uprev + return true + end + end + + # Next `z` + if Δ != zero(Δ) + quot = dz_u / Δ + z = uprev + quot * tmp + else + # An arbitrary change on `z` + nind = length(z) + if (nind != 1) + ind = 1 + iter % nind + # val = (uprev[ind] - (z[ind] - uprev[ind]))*one(eltype(z))*2 + _vec(z) .= _vec(z) .* (1 .- 2 .* ((1:length(z)) .== ind)) + else + z = -z + end + end + end + return false +end + +function maxeig!(integrator, cache::OrdinaryDiffEqMutableCache) + isfirst = integrator.iter == 1 || integrator.u_modified + @unpack t, dt, uprev, u, f, p, fsalfirst = integrator + if cache isa IRKCCache + fz, z, atmp = integrator.fsallast, cache.nlsolver.tmp, cache.atmp + else + fz, z, atmp = cache.k, cache.tmp, cache.atmp + end + ccache = cache.constantcache + maxiter = (integrator.alg isa Union{ESERK4, ESERK5, SERK2}) ? 100 : 50 + safe = (integrator.alg isa RKCAlgs) ? 1.0 : 1.2 + # Initial guess for eigenvector `z` + if isfirst + if integrator.alg isa RKCAlgs + if integrator.alg isa IRKC + @.. broadcast=false z=cache.du₂ + else + @.. broadcast=false z=fsalfirst + end + else + @.. broadcast=false fz=fsalfirst + f(z, fz, p, t) + integrator.stats.nf += 1 + end + else + @.. broadcast=false z=ccache.zprev + end + # Perturbation + u_norm = integrator.opts.internalnorm(uprev, t) + z_norm = integrator.opts.internalnorm(z, t) + pert = eps(u_norm) + sqrt_pert = sqrt(pert) + is_u_zero = u_norm == zero(u_norm) + is_z_zero = z_norm == zero(z_norm) + # Normalize `z` such that z-u lie in a circle + if (!is_u_zero && !is_z_zero) + dz_u = u_norm * sqrt_pert + quot = dz_u / z_norm + @.. broadcast=false z=uprev + quot * z + elseif !is_u_zero + dz_u = u_norm * sqrt_pert + @.. broadcast=false z=uprev + uprev * dz_u + elseif !is_z_zero + dz_u = pert + quot = dz_u / z_norm + @.. broadcast=false z*=quot + else + dz_u = pert + @.. broadcast=false z=dz_u * one(eltype(z)) + end # endif + # Start power iteration + integrator.eigen_est = 0 + for iter in 1:maxiter + if integrator.alg isa IRKC + f.f2(fz, z, p, t) + integrator.stats.nf2 += 1 + @.. broadcast=false atmp=fz - cache.du₂ + else + f(fz, z, p, t) + integrator.stats.nf += 1 + @.. broadcast=false atmp=fz - fsalfirst + end + Δ = integrator.opts.internalnorm(atmp, t) + eig_prev = integrator.eigen_est + integrator.eigen_est = Δ / dz_u * safe + # Convergence + if integrator.alg isa RKCAlgs # To match the constants given in the paper + if iter >= 2 && + abs(eig_prev - integrator.eigen_est) < + max(integrator.eigen_est, 1.0 / integrator.opts.dtmax) * 0.01 + integrator.eigen_est *= 1.2 + # Store the eigenvector + @.. broadcast=false ccache.zprev=z - uprev + return true + end + else + if iter >= 2 && + abs(eig_prev - integrator.eigen_est) < integrator.eigen_est * 0.05 + # Store the eigenvector + @.. broadcast=false ccache.zprev=z - uprev + return true + end + end + # Next `z` + if Δ != zero(Δ) + quot = dz_u / Δ + @.. broadcast=false z=uprev + quot * atmp + else + # An arbitrary change on `z` + nind = length(uprev) + if (nind != 1) + ind = 1 + iter % nind + # val = (uprev[ind] - (z[ind] - uprev[ind]))*one(eltype(z)) + _vec(z) .= _vec(z) .* (1 .- 2 .* ((1:length(z)) .== ind)) + else + z = -z + end + end + end + return false +end +""" + choosedeg!(cache) -> nothing + +Calculate `mdeg = ms[deg_index]` (the degree of the Chebyshev polynomial) +and `cache.start` (the start index of recurrence parameters for that +degree), where `recf` are the `μ,κ` pairs +for the `mdeg` degree method. The `κ` for `stage-1` for every degree +is 0 therefore it's not included in `recf` +""" +function choosedeg!(cache::T) where {T} + isconst = T <: OrdinaryDiffEqConstantCache + isconst || (cache = cache.constantcache) + start = 1 + @inbounds for i in 1:size(cache.ms, 1) + if cache.ms[i] >= cache.mdeg + cache.deg_index = i + cache.mdeg = cache.ms[i] + cache.start = start + break + end + start += cache.ms[i] * 2 - 1 + end + return nothing +end + +function choosedeg_SERK!(integrator, cache::T) where {T} + isconst = T <: OrdinaryDiffEqConstantCache + isconst || (cache = cache.constantcache) + @unpack ms = cache + start = 1 + @inbounds for i in 1:size(ms, 1) + if ms[i] < cache.mdeg + start += ms[i] + 1 + else + cache.start = start + cache.mdeg = ms[i] + break + end + end + if integrator.alg isa ESERK5 + if cache.mdeg <= 20 + cache.internal_deg = 2 + elseif cache.mdeg <= 50 + cache.internal_deg = 5 + elseif cache.mdeg <= 100 + cache.internal_deg = 10 + elseif cache.mdeg <= 500 + cache.internal_deg = 50 + elseif cache.mdeg <= 1000 + cache.internal_deg = 100 + elseif cache.mdeg <= 2000 + cache.internal_deg = 200 + end + end + + if integrator.alg isa ESERK4 + if cache.mdeg <= 20 + cache.internal_deg = 2 + elseif cache.mdeg <= 100 + cache.internal_deg = 10 + elseif cache.mdeg <= 500 + cache.internal_deg = 25 + elseif cache.mdeg <= 1000 + cache.internal_deg = 100 + elseif cache.mdeg <= 4000 + cache.internal_deg = 200 + end + end + + if integrator.alg isa SERK2 + cache.internal_deg = cache.mdeg / 10 + end + return nothing +end diff --git a/src/tableaus/feagin_tableaus.jl b/src/tableaus/feagin_tableaus.jl new file mode 100644 index 0000000000..64a056e0c9 --- /dev/null +++ b/src/tableaus/feagin_tableaus.jl @@ -0,0 +1,2650 @@ +struct Feagin10ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + adaptiveConst::T + a0100::T + a0200::T + a0201::T + a0300::T + a0302::T + a0400::T + a0402::T + a0403::T + a0500::T + a0503::T + a0504::T + a0600::T + a0603::T + a0604::T + a0605::T + a0700::T + a0704::T + a0705::T + a0706::T + a0800::T + a0805::T + a0806::T + a0807::T + a0900::T + a0905::T + a0906::T + a0907::T + a0908::T + a1000::T + a1005::T + a1006::T + a1007::T + a1008::T + a1009::T + a1100::T + a1105::T + a1106::T + a1107::T + a1108::T + a1109::T + a1110::T + a1200::T + a1203::T + a1204::T + a1205::T + a1206::T + a1207::T + a1208::T + a1209::T + a1210::T + a1211::T + a1300::T + a1302::T + a1303::T + a1305::T + a1306::T + a1307::T + a1308::T + a1309::T + a1310::T + a1311::T + a1312::T + a1400::T + a1401::T + a1404::T + a1406::T + a1412::T + a1413::T + a1500::T + a1502::T + a1514::T + a1600::T + a1601::T + a1602::T + a1604::T + a1605::T + a1606::T + a1607::T + a1608::T + a1609::T + a1610::T + a1611::T + a1612::T + a1613::T + a1614::T + a1615::T + b1::T + b2::T + b3::T + b4::T + b5::T + b6::T + b7::T + b8::T + b9::T + b10::T + b11::T + b12::T + b13::T + b14::T + b15::T + b16::T + b17::T + c1::T2 + c2::T2 + c3::T2 + c4::T2 + c5::T2 + c6::T2 + c7::T2 + c8::T2 + c9::T2 + c10::T2 + c11::T2 + c12::T2 + c13::T2 + c14::T2 + c15::T2 + c16::T2 +end + +""" +constructFeagin10 +""" +function Feagin10ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + adaptiveConst = convert(T, 0.002777777777777778) + a0100 = convert(T, 0.1) + + a0200 = convert(T, -0.9151765613752915) + a0201 = convert(T, 1.4545344021782731) + + a0300 = convert(T, 0.20225919030111816) + a0302 = convert(T, 0.6067775709033545) + + a0400 = convert(T, 0.18402471470864357) + a0402 = convert(T, 0.19796683122719236) + a0403 = convert(T, -0.07295478473136326) + + a0500 = convert(T, 0.08790073402066813) + a0503 = convert(T, 0.41045970252026065) + a0504 = convert(T, 0.4827137536788665) + + a0600 = convert(T, 0.08597005049024603) + a0603 = convert(T, 0.3308859630407222) + a0604 = convert(T, 0.4896629573094502) + a0605 = convert(T, -0.07318563750708508) + + a0700 = convert(T, 0.12093044912533372) + a0704 = convert(T, 0.2601246757582956) + a0705 = convert(T, 0.032540262154909134) + a0706 = convert(T, -0.0595780211817361) + + a0800 = convert(T, 0.11085437958039149) + a0805 = convert(T, -0.06057614882550056) + a0806 = convert(T, 0.3217637056017784) + a0807 = convert(T, 0.510485725608063) + + a0900 = convert(T, 0.112054414752879) + a0905 = convert(T, -0.14494277590286592) + a0906 = convert(T, -0.3332697190962567) + a0907 = convert(T, 0.4992692295568801) + a0908 = convert(T, 0.5095046089296861) + + a1000 = convert(T, 0.11397678396418598) + a1005 = convert(T, -0.07688133642033569) + a1006 = convert(T, 0.23952736032439065) + a1007 = convert(T, 0.3977746623680946) + a1008 = convert(T, 0.010755895687360746) + a1009 = convert(T, -0.3277691241640189) + + a1100 = convert(T, 0.07983145282801961) + a1105 = convert(T, -0.052032968680060306) + a1106 = convert(T, -0.05769541461685489) + a1107 = convert(T, 0.19478191571210415) + a1108 = convert(T, 0.14538492318832508) + a1109 = convert(T, -0.07829427103516708) + a1110 = convert(T, -0.11450329936109892) + + a1200 = convert(T, 0.9851156101648573) + a1203 = convert(T, 0.3308859630407222) + a1204 = convert(T, 0.4896629573094502) + a1205 = convert(T, -1.3789648657484357) + a1206 = convert(T, -0.8611641950276356) + a1207 = convert(T, 5.784288136375372) + a1208 = convert(T, 3.2880776198510357) + a1209 = convert(T, -2.386339050931364) + a1210 = convert(T, -3.254793424836439) + a1211 = convert(T, -2.16343541686423) + + a1300 = convert(T, 0.8950802957716328) + a1302 = convert(T, 0.19796683122719236) + a1303 = convert(T, -0.07295478473136326) + a1305 = convert(T, -0.8512362396620076) + a1306 = convert(T, 0.3983201123185333) + a1307 = convert(T, 3.639372631810356) + a1308 = convert(T, 1.5482287703983033) + a1309 = convert(T, -2.122217147040537) + a1310 = convert(T, -1.5835039854532618) + a1311 = convert(T, -1.7156160828593627) + a1312 = convert(T, -0.024403640575012746) + + a1400 = convert(T, -0.9151765613752915) + a1401 = convert(T, 1.4545344021782731) + a1404 = convert(T, -0.7773336436449683) + a1406 = convert(T, -0.0910895662155176) + a1412 = convert(T, 0.0910895662155176) + a1413 = convert(T, 0.7773336436449683) + + a1500 = convert(T, 0.1) + a1502 = convert(T, -0.15717866579977116) + a1514 = convert(T, 0.15717866579977116) + + a1600 = convert(T, 0.1817813007000953) + a1601 = convert(T, 0.675) + a1602 = convert(T, 0.3427581598471898) + a1604 = convert(T, 0.25911121454832275) + a1605 = convert(T, -0.35827896671795206) + a1606 = convert(T, -1.0459489594088331) + a1607 = convert(T, 0.930327845415627) + a1608 = convert(T, 1.7795095943170811) + a1609 = convert(T, 0.1) + a1610 = convert(T, -0.2825475695390441) + a1611 = convert(T, -0.15932735011997254) + a1612 = convert(T, -0.14551589464700151) + a1613 = convert(T, -0.25911121454832275) + a1614 = convert(T, -0.3427581598471898) + a1615 = convert(T, -0.675) + + b1 = convert(T, 0.03333333333333333) + b2 = convert(T, 0.025) + b3 = convert(T, 0.03333333333333333) + b4 = convert(T, 0) + b5 = convert(T, 0.05) + b6 = convert(T, 0) + b7 = convert(T, 0.04) + b8 = convert(T, 0) + b9 = convert(T, 0.1892374781489235) + b10 = convert(T, 0.2774291885177432) + b11 = convert(T, 0.2774291885177432) + b12 = convert(T, 0.1892374781489235) + b13 = convert(T, -0.04) + b14 = convert(T, -0.05) + b15 = convert(T, -0.03333333333333333) + b16 = convert(T, -0.025) + b17 = convert(T, 0.03333333333333333) + + c1 = convert(T2, 0.1) + c2 = convert(T2, 0.5393578408029818) + c3 = convert(T2, 0.8090367612044727) + c4 = convert(T2, 0.30903676120447265) + c5 = convert(T2, 0.9810741902197953) + c6 = convert(T2, 0.8333333333333334) + c7 = convert(T2, 0.3540173658568024) + c8 = convert(T2, 0.8825276619647323) + c9 = convert(T2, 0.6426157582403226) + c10 = convert(T2, 0.3573842417596775) + c11 = convert(T2, 0.11747233803526766) + c12 = convert(T2, 0.8333333333333334) + c13 = convert(T2, 0.30903676120447265) + c14 = convert(T2, 0.5393578408029818) + c15 = convert(T2, 0.1) + c16 = convert(T2, 1) + Feagin10ConstantCache(adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, + a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, + a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, + a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, + a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1203, + a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211, a1300, + a1302, a1303, a1305, a1306, a1307, a1308, a1309, a1310, a1311, + a1312, a1400, a1401, a1404, a1406, a1412, a1413, a1500, a1502, + a1514, a1600, a1601, a1602, a1604, a1605, a1606, a1607, a1608, + a1609, a1610, a1611, a1612, a1613, a1614, a1615, b1, b2, b3, b4, + b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, c1, + c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16) +end + +""" +constructFeagin10 +""" +function Feagin10ConstantCache(T::Type, T2::Type) + adaptiveConst = convert(T, 1 // 360) + a0100 = convert(T, 1 // 10) + + a0200 = convert(T, big"-0.915176561375291440520015019275342154318951387664369720564660") + a0201 = convert(T, big"1.45453440217827322805250021715664459117622483736537873607016") + + a0300 = convert(T, big"0.202259190301118170324681949205488413821477543637878380814562") + a0302 = convert(T, big"0.606777570903354510974045847616465241464432630913635142443687") + + a0400 = convert(T, big"0.184024714708643575149100693471120664216774047979591417844635") + a0402 = convert(T, big"0.197966831227192369068141770510388793370637287463360401555746") + a0403 = convert(T, + big"-0.0729547847313632629185146671595558023015011608914382961421311") + + a0500 = convert(T, big"0.0879007340206681337319777094132125475918886824944548534041378") + a0503 = convert(T, big"0.410459702520260645318174895920453426088035325902848695210406") + a0504 = convert(T, big"0.482713753678866489204726942976896106809132737721421333413261") + + a0600 = convert(T, big"0.0859700504902460302188480225945808401411132615636600222593880") + a0603 = convert(T, big"0.330885963040722183948884057658753173648240154838402033448632") + a0604 = convert(T, big"0.489662957309450192844507011135898201178015478433790097210790") + a0605 = convert(T, + big"-0.0731856375070850736789057580558988816340355615025188195854775") + + a0700 = convert(T, big"0.120930449125333720660378854927668953958938996999703678812621") + a0704 = convert(T, big"0.260124675758295622809007617838335174368108756484693361887839") + a0705 = convert(T, big"0.0325402621549091330158899334391231259332716675992700000776101") + a0706 = convert(T, + big"-0.0595780211817361001560122202563305121444953672762930724538856") + + a0800 = convert(T, big"0.110854379580391483508936171010218441909425780168656559807038") + a0805 = convert(T, + big"-0.0605761488255005587620924953655516875526344415354339234619466") + a0806 = convert(T, big"0.321763705601778390100898799049878904081404368603077129251110") + a0807 = convert(T, big"0.510485725608063031577759012285123416744672137031752354067590") + + a0900 = convert(T, big"0.112054414752879004829715002761802363003717611158172229329393") + a0905 = convert(T, big"-0.144942775902865915672349828340980777181668499748506838876185") + a0906 = convert(T, big"-0.333269719096256706589705211415746871709467423992115497968724") + a0907 = convert(T, big"0.499269229556880061353316843969978567860276816592673201240332") + a0908 = convert(T, big"0.509504608929686104236098690045386253986643232352989602185060") + + a1000 = convert(T, big"0.113976783964185986138004186736901163890724752541486831640341") + a1005 = convert(T, + big"-0.0768813364203356938586214289120895270821349023390922987406384") + a1006 = convert(T, big"0.239527360324390649107711455271882373019741311201004119339563") + a1007 = convert(T, big"0.397774662368094639047830462488952104564716416343454639902613") + a1008 = convert(T, big"0.0107558956873607455550609147441477450257136782823280838547024") + a1009 = convert(T, big"-0.327769124164018874147061087350233395378262992392394071906457") + + a1100 = convert(T, big"0.0798314528280196046351426864486400322758737630423413945356284") + a1105 = convert(T, + big"-0.0520329686800603076514949887612959068721311443881683526937298") + a1106 = convert(T, + big"-0.0576954146168548881732784355283433509066159287152968723021864") + a1107 = convert(T, big"0.194781915712104164976306262147382871156142921354409364738090") + a1108 = convert(T, big"0.145384923188325069727524825977071194859203467568236523866582") + a1109 = convert(T, + big"-0.0782942710351670777553986729725692447252077047239160551335016") + a1110 = convert(T, big"-0.114503299361098912184303164290554670970133218405658122674674") + + a1200 = convert(T, big"0.985115610164857280120041500306517278413646677314195559520529") + a1203 = convert(T, big"0.330885963040722183948884057658753173648240154838402033448632") + a1204 = convert(T, big"0.489662957309450192844507011135898201178015478433790097210790") + a1205 = convert(T, big"-1.37896486574843567582112720930751902353904327148559471526397") + a1206 = convert(T, big"-0.861164195027635666673916999665534573351026060987427093314412") + a1207 = convert(T, big"5.78428813637537220022999785486578436006872789689499172601856") + a1208 = convert(T, big"3.28807761985103566890460615937314805477268252903342356581925") + a1209 = convert(T, big"-2.38633905093136384013422325215527866148401465975954104585807") + a1210 = convert(T, big"-3.25479342483643918654589367587788726747711504674780680269911") + a1211 = convert(T, big"-2.16343541686422982353954211300054820889678036420109999154887") + + a1300 = convert(T, big"0.895080295771632891049613132336585138148156279241561345991710") + a1302 = convert(T, big"0.197966831227192369068141770510388793370637287463360401555746") + a1303 = convert(T, + big"-0.0729547847313632629185146671595558023015011608914382961421311") + a1305 = convert(T, big"-0.851236239662007619739049371445966793289359722875702227166105") + a1306 = convert(T, big"0.398320112318533301719718614174373643336480918103773904231856") + a1307 = convert(T, big"3.63937263181035606029412920047090044132027387893977804176229") + a1308 = convert(T, big"1.54822877039830322365301663075174564919981736348973496313065") + a1309 = convert(T, big"-2.12221714704053716026062427460427261025318461146260124401561") + a1310 = convert(T, big"-1.58350398545326172713384349625753212757269188934434237975291") + a1311 = convert(T, big"-1.71561608285936264922031819751349098912615880827551992973034") + a1312 = convert(T, + big"-0.0244036405750127452135415444412216875465593598370910566069132") + + a1400 = convert(T, big"-0.915176561375291440520015019275342154318951387664369720564660") + a1401 = convert(T, big"1.45453440217827322805250021715664459117622483736537873607016") + a1404 = convert(T, big"-0.777333643644968233538931228575302137803351053629547286334469") + a1406 = convert(T, + big"-0.0910895662155176069593203555807484200111889091770101799647985") + a1412 = convert(T, big"0.0910895662155176069593203555807484200111889091770101799647985") + a1413 = convert(T, big"0.777333643644968233538931228575302137803351053629547286334469") + + a1500 = convert(T, 1 // 10) + a1502 = convert(T, big"-0.157178665799771163367058998273128921867183754126709419409654") + a1514 = convert(T, big"0.157178665799771163367058998273128921867183754126709419409654") + + a1600 = convert(T, big"0.181781300700095283888472062582262379650443831463199521664945") + a1601 = convert(T, 27 // 40) + a1602 = convert(T, big"0.342758159847189839942220553413850871742338734703958919937260") + a1604 = convert(T, big"0.259111214548322744512977076191767379267783684543182428778156") + a1605 = convert(T, big"-0.358278966717952089048961276721979397739750634673268802484271") + a1606 = convert(T, big"-1.04594895940883306095050068756409905131588123172378489286080") + a1607 = convert(T, big"0.930327845415626983292300564432428777137601651182965794680397") + a1608 = convert(T, big"1.77950959431708102446142106794824453926275743243327790536000") + a1609 = convert(T, 1 // 10) + a1610 = convert(T, big"-0.282547569539044081612477785222287276408489375976211189952877") + a1611 = convert(T, big"-0.159327350119972549169261984373485859278031542127551931461821") + a1612 = convert(T, big"-0.145515894647001510860991961081084111308650130578626404945571") + a1613 = convert(T, big"-0.259111214548322744512977076191767379267783684543182428778156") + a1614 = convert(T, big"-0.342758159847189839942220553413850871742338734703958919937260") + a1615 = convert(T, -27 // 40) + + b1 = convert(T, 1 // 30) + b2 = convert(T, 1 // 40) + b3 = convert(T, 1 // 30) + b4 = convert(T, 0) + b5 = convert(T, 1 // 20) + b6 = convert(T, 0) + b7 = convert(T, 1 // 25) + b8 = convert(T, 0) + b9 = convert(T, big"0.189237478148923490158306404106012326238162346948625830327194") + b10 = convert(T, big"0.277429188517743176508360262560654340428504319718040836339472") + b11 = convert(T, big"0.277429188517743176508360262560654340428504319718040836339472") + b12 = convert(T, big"0.189237478148923490158306404106012326238162346948625830327194") + b13 = convert(T, -1 // 25) + b14 = convert(T, -1 // 20) + b15 = convert(T, -1 // 30) + b16 = convert(T, -1 // 40) + b17 = convert(T, 1 // 30) + + c1 = convert(T2, 1 // 10) + c2 = convert(T2, big"0.539357840802981787532485197881302436857273449701009015505500") + c3 = convert(T2, big"0.809036761204472681298727796821953655285910174551513523258250") + c4 = convert(T2, big"0.309036761204472681298727796821953655285910174551513523258250") + c5 = convert(T2, big"0.981074190219795268254879548310562080489056746118724882027805") + c6 = convert(T2, 5 // 6) + c7 = convert(T2, big"0.354017365856802376329264185948796742115824053807373968324184") + c8 = convert(T2, big"0.882527661964732346425501486979669075182867844268052119663791") + c9 = convert(T2, big"0.642615758240322548157075497020439535959501736363212695909875") + c10 = convert(T2, big"0.357384241759677451842924502979560464040498263636787304090125") + c11 = convert(T2, big"0.117472338035267653574498513020330924817132155731947880336209") + c12 = convert(T2, 5 // 6) + c13 = convert(T2, big"0.309036761204472681298727796821953655285910174551513523258250") + c14 = convert(T2, big"0.539357840802981787532485197881302436857273449701009015505500") + c15 = convert(T2, 1 // 10) + c16 = convert(T2, 1) + Feagin10ConstantCache(adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, + a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, + a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, + a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, + a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1203, + a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211, a1300, + a1302, a1303, a1305, a1306, a1307, a1308, a1309, a1310, a1311, + a1312, a1400, a1401, a1404, a1406, a1412, a1413, a1500, a1502, + a1514, a1600, a1601, a1602, a1604, a1605, a1606, a1607, a1608, + a1609, a1610, a1611, a1612, a1613, a1614, a1615, b1, b2, b3, b4, + b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, c1, + c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16) +end + +struct Feagin12ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + adaptiveConst::T + a0100::T + a0200::T + a0201::T + a0300::T + a0302::T + a0400::T + a0402::T + a0403::T + a0500::T + a0503::T + a0504::T + a0600::T + a0603::T + a0604::T + a0605::T + a0700::T + a0704::T + a0705::T + a0706::T + a0800::T + a0805::T + a0806::T + a0807::T + a0900::T + a0905::T + a0906::T + a0907::T + a0908::T + a1000::T + a1005::T + a1006::T + a1007::T + a1008::T + a1009::T + a1100::T + a1105::T + a1106::T + a1107::T + a1108::T + a1109::T + a1110::T + a1200::T + a1208::T + a1209::T + a1210::T + a1211::T + a1300::T + a1308::T + a1309::T + a1310::T + a1311::T + a1312::T + a1400::T + a1408::T + a1409::T + a1410::T + a1411::T + a1412::T + a1413::T + a1500::T + a1508::T + a1509::T + a1510::T + a1511::T + a1512::T + a1513::T + a1514::T + a1600::T + a1608::T + a1609::T + a1610::T + a1611::T + a1612::T + a1613::T + a1614::T + a1615::T + a1700::T + a1705::T + a1706::T + a1707::T + a1708::T + a1709::T + a1710::T + a1711::T + a1712::T + a1713::T + a1714::T + a1715::T + a1716::T + a1800::T + a1805::T + a1806::T + a1807::T + a1808::T + a1809::T + a1810::T + a1811::T + a1812::T + a1813::T + a1814::T + a1815::T + a1816::T + a1817::T + a1900::T + a1904::T + a1905::T + a1906::T + a1908::T + a1909::T + a1910::T + a1911::T + a1912::T + a1913::T + a1914::T + a1915::T + a1916::T + a1917::T + a1918::T + a2000::T + a2003::T + a2004::T + a2005::T + a2007::T + a2009::T + a2010::T + a2017::T + a2018::T + a2019::T + a2100::T + a2102::T + a2103::T + a2106::T + a2107::T + a2109::T + a2110::T + a2117::T + a2118::T + a2119::T + a2120::T + a2200::T + a2201::T + a2204::T + a2206::T + a2220::T + a2221::T + a2300::T + a2302::T + a2322::T + a2400::T + a2401::T + a2402::T + a2404::T + a2406::T + a2407::T + a2408::T + a2409::T + a2410::T + a2411::T + a2412::T + a2413::T + a2414::T + a2415::T + a2416::T + a2417::T + a2418::T + a2419::T + a2420::T + a2421::T + a2422::T + a2423::T + c1::T2 + c2::T2 + c3::T2 + c4::T2 + c5::T2 + c6::T2 + c7::T2 + c8::T2 + c9::T2 + c10::T2 + c11::T2 + c12::T2 + c13::T2 + c14::T2 + c15::T2 + c16::T2 + c17::T2 + c18::T2 + c19::T2 + c20::T2 + c21::T2 + c22::T2 + c23::T2 + c24::T2 + b1::T + b2::T + b3::T + b4::T + b5::T + b6::T + b7::T + b8::T + b9::T + b10::T + b11::T + b12::T + b13::T + b14::T + b15::T + b16::T + b17::T + b18::T + b19::T + b20::T + b21::T + b22::T + b23::T + b24::T + b25::T +end + +""" +constructFeagin12 +""" +function Feagin12ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + adaptiveConst = convert(T, 49 // 640) + c1 = convert(T2, 1 // 5) + c2 = convert(T2, 5 // 9) + c3 = convert(T2, 5 // 6) + c4 = convert(T2, 1 // 3) + c5 = convert(T2, 1) + c6 = convert(T2, 0.671835709170513812712245661002797570438953420568682550710222) + c7 = convert(T2, 0.288724941110620201935458488967024976908118598341806976469674) + c8 = convert(T2, 9 // 16) + c9 = convert(T2, 5 // 6) + c10 = convert(T2, 0.947695431179199287562380162101836721649589325892740646458322) + c11 = convert(T2, 0.0548112876863802643887753674810754475842153612931128785028369) + c12 = convert(T2, 0.0848880518607165350639838930162674302064148175640019542045934) + c13 = convert(T2, 0.265575603264642893098114059045616835297201264164077621448665) + c14 = convert(T2, 1 // 2) + c15 = convert(T2, 0.734424396735357106901885940954383164702798735835922378551335) + c16 = convert(T2, 0.915111948139283464936016106983732569793585182435998045795407) + c17 = convert(T2, 0.947695431179199287562380162101836721649589325892740646458322) + c18 = convert(T2, 5 // 6) + c19 = convert(T2, 0.288724941110620201935458488967024976908118598341806976469674) + c20 = convert(T2, 0.671835709170513812712245661002797570438953420568682550710222) + c21 = convert(T2, 1 // 3) + c22 = convert(T2, 5 // 9) + c23 = convert(T2, 1 // 5) + c24 = convert(T2, 1) + + b1 = convert(T, 1 // 42) + b2 = convert(T, 234375 // 10000000) + b3 = convert(T, 3125 // 100000) + b4 = convert(T, 0) + b5 = convert(T, 1 // 24) + b6 = convert(T, 0) + b7 = convert(T, 1 // 20) + b8 = convert(T, 1 // 20) + b9 = convert(T, 0) + b10 = convert(T, 1 // 10) + b11 = convert(T, 1 // 14) + b12 = convert(T, 0) + b13 = convert(T, 0.138413023680782974005350203145033146748813640089941234591267) + b14 = convert(T, 0.215872690604931311708935511140681138965472074195773051123019) + b15 = convert(T, 0.243809523809523809523809523809523809523809523809523809523810) + b16 = convert(T, 0.215872690604931311708935511140681138965472074195773051123019) + b17 = convert(T, 0.138413023680782974005350203145033146748813640089941234591267) + b18 = convert(T, -0.0714285714285714285714285714285714285714285714285714285714286) + b19 = convert(T, -1 // 10) + b20 = convert(T, -1 // 20) + b21 = convert(T, -1 // 20) + b22 = convert(T, -1 // 24) + b23 = convert(T, -3125 // 100000) + b24 = convert(T, -234375 // 10000000) + b25 = convert(T, 1 // 42) + + a0100 = convert(T, 1 // 5) + + a0200 = convert(T, -0.216049382716049382716049382716049382716049382716049382716049) + a0201 = convert(T, 0.771604938271604938271604938271604938271604938271604938271605) + + a0300 = convert(T, 5 // 24) + a0302 = convert(T, 5 // 8) + + a0400 = convert(T, 29 // 150) + a0402 = convert(T, 11 // 50) + a0403 = convert(T, -2 // 25) + + a0500 = convert(T, 1 // 10) + a0503 = convert(T, 2 // 5) + a0504 = convert(T, 1 // 2) + + a0600 = convert(T, 0.103364471650010477570395435690481791543342708330349879244197) + a0603 = convert(T, 0.124053094528946761061581889237115328211074784955180298044074) + a0604 = convert(T, 0.483171167561032899288836480451962508724109257517289177302380) + a0605 = convert(T, -0.0387530245694763252085681443767620580395733302341368038804290) + + a0700 = convert(T, 0.124038261431833324081904585980175168140024670698633612292480) + a0704 = convert(T, 0.217050632197958486317846256953159942875916353757734167684657) + a0705 = convert(T, 0.0137455792075966759812907801835048190594443990939408530842918) + a0706 = convert(T, -0.0661095317267682844455831341498149531672668252085016565917546) + + a0800 = convert(T, 0.0914774894856882983144991846980432197088832099976660100090486) + a0805 = convert(T, -0.00544348523717469689965754944144838611346156873847009178068318) + a0806 = convert(T, 0.0680716801688453518578515120895103863112751730758794372203952) + a0807 = convert(T, 0.408394315582641046727306852653894780093303185664924644551239) + + a0900 = convert(T, 0.0890013652502551018954509355423841780143232697403434118692699) + a0905 = convert(T, 0.00499528226645532360197793408420692800405891149406814091955810) + a0906 = convert(T, 0.397918238819828997341739603001347156083435060931424970826304) + a0907 = convert(T, 0.427930210752576611068192608300897981558240730580396406312359) + a0908 = convert(T, -0.0865117637557827005740277475955029103267246394128995965941585) + + a1000 = convert(T, 0.0695087624134907543112693906409809822706021061685544615255758) + a1005 = convert(T, 0.129146941900176461970759579482746551122871751501482634045487) + a1006 = convert(T, 1.53073638102311295076342566143214939031177504112433874313011) + a1007 = convert(T, 0.577874761129140052546751349454576715334892100418571882718036) + a1008 = convert(T, -0.951294772321088980532340837388859453930924498799228648050949) + a1009 = convert(T, -0.408276642965631951497484981519757463459627174520978426909934) + + a1100 = convert(T, 0.0444861403295135866269453507092463581620165501018684152933313) + a1105 = convert(T, -0.00380476867056961731984232686574547203016331563626856065717964) + a1106 = convert(T, 0.0106955064029624200721262602809059154469206077644957399593972) + a1107 = convert(T, 0.0209616244499904333296674205928919920806734650660039898074652) + a1108 = convert(T, -0.0233146023259321786648561431551978077665337818756053603898847) + a1109 = convert(T, 0.00263265981064536974369934736325334761174975280887405725010964) + a1110 = convert(T, 0.00315472768977025060103545855572111407955208306374459723959783) + + a1200 = convert(T, 0.0194588815119755475588801096525317761242073762016273186231215) + a1208 = convert(T, 0.0000678512949171812509306121653452367476194364781259165332321534) + a1209 = convert(T, -0.0000429795859049273623271005330230162343568863387724883603675550) + a1210 = convert(T, 0.0000176358982260285155407485928953302139937553442829975734148981) + a1211 = convert(T, 0.0653866627415027051009595231385181033549511358787382098351924) + + a1300 = convert(T, 0.206836835664277105916828174798272361078909196043446411598231) + a1308 = convert(T, 0.0166796067104156472828045866664696450306326505094792505215514) + a1309 = convert(T, -0.00879501563200710214457024178249986591130234990219959208704979) + a1310 = convert(T, 0.00346675455362463910824462315246379209427513654098596403637231) + a1311 = convert(T, -0.861264460105717678161432562258351242030270498966891201799225) + a1312 = convert(T, 0.908651882074050281096239478469262145034957129939256789178785) + + a1400 = convert(T, 0.0203926084654484010091511314676925686038504449562413004562382) + a1408 = convert(T, 0.0869469392016685948675400555583947505833954460930940959577347) + a1409 = convert(T, -0.0191649630410149842286436611791405053287170076602337673587681) + a1410 = convert(T, 0.00655629159493663287364871573244244516034828755253746024098838) + a1411 = convert(T, 0.0987476128127434780903798528674033899738924968006632201445462) + a1412 = convert(T, 0.00535364695524996055083260173615567408717110247274021056118319) + a1413 = convert(T, 0.301167864010967916837091303817051676920059229784957479998077) + + a1500 = convert(T, 0.228410433917778099547115412893004398779136994596948545722283) + a1508 = convert(T, -0.498707400793025250635016567442511512138603770959682292383042) + a1509 = convert(T, 0.134841168335724478552596703792570104791700727205981058201689) + a1510 = convert(T, -0.0387458244055834158439904226924029230935161059142806805674360) + a1511 = convert(T, -1.27473257473474844240388430824908952380979292713250350199641) + a1512 = convert(T, 1.43916364462877165201184452437038081875299303577911839630524) + a1513 = convert(T, -0.214007467967990254219503540827349569639028092344812795499026) + a1514 = convert(T, 0.958202417754430239892724139109781371059908874605153648768037) + + a1600 = convert(T, 2.00222477655974203614249646012506747121440306225711721209798) + a1608 = convert(T, 2.06701809961524912091954656438138595825411859673341600679555) + a1609 = convert(T, 0.623978136086139541957471279831494466155292316167021080663140) + a1610 = convert(T, -0.0462283685500311430283203554129062069391947101880112723185773) + a1611 = convert(T, -8.84973288362649614860075246727118949286604835457092701094630) + a1612 = convert(T, 7.74257707850855976227437225791835589560188590785037197433615) + a1613 = convert(T, -0.588358519250869210993353314127711745644125882130941202896436) + a1614 = convert(T, -1.10683733362380649395704708016953056176195769617014899442903) + a1615 = convert(T, -0.929529037579203999778397238291233214220788057511899747507074) + + a1700 = convert(T, 3.13789533412073442934451608989888796808161259330322100268310) + a1705 = convert(T, 0.129146941900176461970759579482746551122871751501482634045487) + a1706 = convert(T, 1.53073638102311295076342566143214939031177504112433874313011) + a1707 = convert(T, 0.577874761129140052546751349454576715334892100418571882718036) + a1708 = convert(T, 5.42088263055126683050056840891857421941300558851862156403363) + a1709 = convert(T, 0.231546926034829304872663800877643660904880180835945693836936) + a1710 = convert(T, 0.0759292995578913560162301311785251873561801342333194895292058) + a1711 = convert(T, -12.3729973380186513287414553402595806591349822617535905976253) + a1712 = convert(T, 9.85455883464769543935957209317369202080367765721777101906955) + a1713 = convert(T, 0.0859111431370436529579357709052367772889980495122329601159540) + a1714 = convert(T, -5.65242752862643921117182090081762761180392602644189218673969) + a1715 = convert(T, -1.94300935242819610883833776782364287728724899124166920477873) + a1716 = convert(T, -0.128352601849404542018428714319344620742146491335612353559923) + + a1800 = convert(T, 1.38360054432196014878538118298167716825163268489922519995564) + a1805 = convert(T, 0.00499528226645532360197793408420692800405891149406814091955810) + a1806 = convert(T, 0.397918238819828997341739603001347156083435060931424970826304) + a1807 = convert(T, 0.427930210752576611068192608300897981558240730580396406312359) + a1808 = convert(T, -1.30299107424475770916551439123047573342071475998399645982146) + a1809 = convert(T, 0.661292278669377029097112528107513072734573412294008071500699) + a1810 = convert(T, -0.144559774306954349765969393688703463900585822441545655530145) + a1811 = convert(T, -6.96576034731798203467853867461083919356792248105919255460819) + a1812 = convert(T, 6.65808543235991748353408295542210450632193197576935120716437) + a1813 = convert(T, -1.66997375108841486404695805725510845049807969199236227575796) + a1814 = convert(T, 2.06413702318035263832289040301832647130604651223986452170089) + a1815 = convert(T, -0.674743962644306471862958129570837723192079875998405058648892) + a1816 = convert(T, -0.00115618834794939500490703608435907610059605754935305582045729) + a1817 = convert(T, -0.00544057908677007389319819914241631024660726585015012485938593) + + a1900 = convert(T, 0.951236297048287669474637975894973552166903378983475425758226) + a1904 = convert(T, 0.217050632197958486317846256953159942875916353757734167684657) + a1905 = convert(T, 0.0137455792075966759812907801835048190594443990939408530842918) + a1906 = convert(T, -0.0661095317267682844455831341498149531672668252085016565917546) + a1908 = convert(T, 0.152281696736414447136604697040747131921486432699422112099617) + a1909 = convert(T, -0.337741018357599840802300793133998004354643424457539667670080) + a1910 = convert(T, -0.0192825981633995781534949199286824400469353110630787982121133) + a1911 = convert(T, -3.68259269696866809932409015535499603576312120746888880201882) + a1912 = convert(T, 3.16197870406982063541533528419683854018352080342887002331312) + a1913 = convert(T, -0.370462522106885290716991856022051125477943482284080569177386) + a1914 = convert(T, -0.0514974200365440434996434456698127984941168616474316871020314) + a1915 = convert(T, -0.000829625532120152946787043541792848416659382675202720677536554) + a1916 = convert(T, 0.00000279801041419278598986586589070027583961355402640879503213503) + a1917 = convert(T, 0.0418603916412360287969841020776788461794119440689356178942252) + a1918 = convert(T, 0.279084255090877355915660874555379649966282167560126269290222) + + a2000 = convert(T, 0.103364471650010477570395435690481791543342708330349879244197) + a2003 = convert(T, 0.124053094528946761061581889237115328211074784955180298044074) + a2004 = convert(T, 0.483171167561032899288836480451962508724109257517289177302380) + a2005 = convert(T, -0.0387530245694763252085681443767620580395733302341368038804290) + a2007 = convert(T, -0.438313820361122420391059788940960176420682836652600698580091) + a2009 = convert(T, -0.218636633721676647685111485017151199362509373698288330593486) + a2010 = convert(T, -0.0312334764394719229981634995206440349766174759626578122323015) + a2017 = convert(T, 0.0312334764394719229981634995206440349766174759626578122323015) + a2018 = convert(T, 0.218636633721676647685111485017151199362509373698288330593486) + a2019 = convert(T, 0.438313820361122420391059788940960176420682836652600698580091) + + a2100 = convert(T, 29 // 150) + a2102 = convert(T, 11 // 50) + a2103 = convert(T, -2 // 25) + a2106 = convert(T, 0.0984256130499315928152900286856048243348202521491288575952143) + a2107 = convert(T, -0.196410889223054653446526504390100417677539095340135532418849) + a2109 = convert(T, 0.436457930493068729391826122587949137609670676712525034763317) + a2110 = convert(T, 0.0652613721675721098560370939805555698350543810708414716730270) + a2117 = convert(T, -0.0652613721675721098560370939805555698350543810708414716730270) + a2118 = convert(T, -0.436457930493068729391826122587949137609670676712525034763317) + a2119 = convert(T, 0.196410889223054653446526504390100417677539095340135532418849) + a2120 = convert(T, -0.0984256130499315928152900286856048243348202521491288575952143) + + a2200 = convert(T, -0.216049382716049382716049382716049382716049382716049382716049) + a2201 = convert(T, 0.771604938271604938271604938271604938271604938271604938271605) + a2204 = convert(T, -2 // 3) + a2206 = convert(T, -0.390696469295978451446999802258495981249099665294395945559163) + a2220 = convert(T, 0.390696469295978451446999802258495981249099665294395945559163) + a2221 = convert(T, 2 // 3) + + a2300 = convert(T, 1 // 5) + a2302 = convert(T, -0.164609053497942386831275720164609053497942386831275720164609) + a2322 = convert(T, 0.164609053497942386831275720164609053497942386831275720164609) + + a2400 = convert(T, 1.47178724881110408452949550989023611293535315518571691939396) + a2401 = convert(T, 63 // 80) + a2402 = convert(T, 91 // 216) + a2404 = convert(T, 7 // 24) + a2406 = convert(T, 0.348600717628329563206854421629657569274689947367847465753757) + a2407 = convert(T, 0.229499544768994849582890233710555447073823569666506700662510) + a2408 = convert(T, 5.79046485790481979159831978177003471098279506036722411333192) + a2409 = convert(T, 0.418587511856506868874073759426596207226461447604248151080016) + a2410 = convert(T, 0.307039880222474002649653817490106690389251482313213999386651) + a2411 = convert(T, -4.68700905350603332214256344683853248065574415794742040470287) + a2412 = convert(T, 3.13571665593802262152038152399873856554395436199962915429076) + a2413 = convert(T, 1.40134829710965720817510506275620441055845017313930508348898) + a2414 = convert(T, -5.52931101439499023629010306005764336421276055777658156400910) + a2415 = convert(T, -0.853138235508063349309546894974784906188927508039552519557498) + a2416 = convert(T, 0.103575780373610140411804607167772795518293914458500175573749) + a2417 = convert(T, -0.140474416950600941142546901202132534870665923700034957196546) + a2418 = convert(T, -0.418587511856506868874073759426596207226461447604248151080016) + a2419 = convert(T, -0.229499544768994849582890233710555447073823569666506700662510) + a2420 = convert(T, -0.348600717628329563206854421629657569274689947367847465753757) + a2421 = convert(T, -7 // 24) + a2422 = convert(T, -91 // 216) + a2423 = convert(T, -63 // 80) + Feagin12ConstantCache(adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, + a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, + a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, + a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, + a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1208, + a1209, a1210, a1211, a1300, a1308, a1309, a1310, a1311, a1312, + a1400, a1408, a1409, a1410, a1411, a1412, a1413, a1500, a1508, + a1509, a1510, a1511, a1512, a1513, a1514, a1600, a1608, a1609, + a1610, a1611, a1612, a1613, a1614, a1615, a1700, a1705, a1706, + a1707, a1708, a1709, a1710, a1711, a1712, a1713, a1714, a1715, + a1716, a1800, a1805, a1806, a1807, a1808, a1809, a1810, a1811, + a1812, a1813, a1814, a1815, a1816, a1817, a1900, a1904, a1905, + a1906, a1908, a1909, a1910, a1911, a1912, a1913, a1914, a1915, + a1916, a1917, a1918, a2000, a2003, a2004, a2005, a2007, a2009, + a2010, a2017, a2018, a2019, a2100, a2102, a2103, a2106, a2107, + a2109, a2110, a2117, a2118, a2119, a2120, a2200, a2201, a2204, + a2206, a2220, a2221, a2300, a2302, a2322, a2400, a2401, a2402, + a2404, a2406, a2407, a2408, a2409, a2410, a2411, a2412, a2413, + a2414, a2415, a2416, a2417, a2418, a2419, a2420, a2421, a2422, + a2423, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, + c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, b1, b2, b3, + b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, + b18, b19, b20, b21, b22, b23, b24, b25) +end + +""" +constructFeagin12 +""" +function Feagin12ConstantCache(T::Type, T2::Type) + adaptiveConst = convert(T, 49 // 640) + c1 = convert(T2, 1 // 5) + c2 = convert(T2, 5 // 9) + c3 = convert(T2, 5 // 6) + c4 = convert(T2, 1 // 3) + c5 = convert(T2, 1) + c6 = convert(T2, big"0.671835709170513812712245661002797570438953420568682550710222") + c7 = convert(T2, big"0.288724941110620201935458488967024976908118598341806976469674") + c8 = convert(T2, 9 // 16) + c9 = convert(T2, 5 // 6) + c10 = convert(T2, big"0.947695431179199287562380162101836721649589325892740646458322") + c11 = convert(T2, big"0.0548112876863802643887753674810754475842153612931128785028369") + c12 = convert(T2, big"0.0848880518607165350639838930162674302064148175640019542045934") + c13 = convert(T2, big"0.265575603264642893098114059045616835297201264164077621448665") + c14 = convert(T2, 1 // 2) + c15 = convert(T2, big"0.734424396735357106901885940954383164702798735835922378551335") + c16 = convert(T2, big"0.915111948139283464936016106983732569793585182435998045795407") + c17 = convert(T2, big"0.947695431179199287562380162101836721649589325892740646458322") + c18 = convert(T2, 5 // 6) + c19 = convert(T2, big"0.288724941110620201935458488967024976908118598341806976469674") + c20 = convert(T2, big"0.671835709170513812712245661002797570438953420568682550710222") + c21 = convert(T2, 1 // 3) + c22 = convert(T2, 5 // 9) + c23 = convert(T2, 1 // 5) + c24 = convert(T2, 1) + + b1 = convert(T, 1 // 42) + b2 = convert(T, 234375 // 10000000) + b3 = convert(T, 3125 // 100000) + b4 = convert(T, 0) + b5 = convert(T, 1 // 24) + b6 = convert(T, 0) + b7 = convert(T, 1 // 20) + b8 = convert(T, 1 // 20) + b9 = convert(T, 0) + b10 = convert(T, 1 // 10) + b11 = convert(T, 1 // 14) + b12 = convert(T, 0) + b13 = convert(T, big"0.138413023680782974005350203145033146748813640089941234591267") + b14 = convert(T, big"0.215872690604931311708935511140681138965472074195773051123019") + b15 = convert(T, big"0.243809523809523809523809523809523809523809523809523809523810") + b16 = convert(T, big"0.215872690604931311708935511140681138965472074195773051123019") + b17 = convert(T, big"0.138413023680782974005350203145033146748813640089941234591267") + b18 = convert(T, big"-0.0714285714285714285714285714285714285714285714285714285714286") + b19 = convert(T, -1 // 10) + b20 = convert(T, -1 // 20) + b21 = convert(T, -1 // 20) + b22 = convert(T, -1 // 24) + b23 = convert(T, -3125 // 100000) + b24 = convert(T, -234375 // 10000000) + b25 = convert(T, 1 // 42) + + a0100 = convert(T, 1 // 5) + + a0200 = convert(T, big"-0.216049382716049382716049382716049382716049382716049382716049") + a0201 = convert(T, big"0.771604938271604938271604938271604938271604938271604938271605") + + a0300 = convert(T, 5 // 24) + a0302 = convert(T, 5 // 8) + + a0400 = convert(T, 29 // 150) + a0402 = convert(T, 11 // 50) + a0403 = convert(T, -2 // 25) + + a0500 = convert(T, 1 // 10) + a0503 = convert(T, 2 // 5) + a0504 = convert(T, 1 // 2) + + a0600 = convert(T, big"0.103364471650010477570395435690481791543342708330349879244197") + a0603 = convert(T, big"0.124053094528946761061581889237115328211074784955180298044074") + a0604 = convert(T, big"0.483171167561032899288836480451962508724109257517289177302380") + a0605 = convert(T, + big"-0.0387530245694763252085681443767620580395733302341368038804290") + + a0700 = convert(T, big"0.124038261431833324081904585980175168140024670698633612292480") + a0704 = convert(T, big"0.217050632197958486317846256953159942875916353757734167684657") + a0705 = convert(T, big"0.0137455792075966759812907801835048190594443990939408530842918") + a0706 = convert(T, + big"-0.0661095317267682844455831341498149531672668252085016565917546") + + a0800 = convert(T, big"0.0914774894856882983144991846980432197088832099976660100090486") + a0805 = convert(T, + big"-0.00544348523717469689965754944144838611346156873847009178068318") + a0806 = convert(T, big"0.0680716801688453518578515120895103863112751730758794372203952") + a0807 = convert(T, big"0.408394315582641046727306852653894780093303185664924644551239") + + a0900 = convert(T, big"0.0890013652502551018954509355423841780143232697403434118692699") + a0905 = convert(T, + big"0.00499528226645532360197793408420692800405891149406814091955810") + a0906 = convert(T, big"0.397918238819828997341739603001347156083435060931424970826304") + a0907 = convert(T, big"0.427930210752576611068192608300897981558240730580396406312359") + a0908 = convert(T, + big"-0.0865117637557827005740277475955029103267246394128995965941585") + + a1000 = convert(T, big"0.0695087624134907543112693906409809822706021061685544615255758") + a1005 = convert(T, big"0.129146941900176461970759579482746551122871751501482634045487") + a1006 = convert(T, big"1.53073638102311295076342566143214939031177504112433874313011") + a1007 = convert(T, big"0.577874761129140052546751349454576715334892100418571882718036") + a1008 = convert(T, big"-0.951294772321088980532340837388859453930924498799228648050949") + a1009 = convert(T, big"-0.408276642965631951497484981519757463459627174520978426909934") + + a1100 = convert(T, big"0.0444861403295135866269453507092463581620165501018684152933313") + a1105 = convert(T, + big"-0.00380476867056961731984232686574547203016331563626856065717964") + a1106 = convert(T, big"0.0106955064029624200721262602809059154469206077644957399593972") + a1107 = convert(T, big"0.0209616244499904333296674205928919920806734650660039898074652") + a1108 = convert(T, + big"-0.0233146023259321786648561431551978077665337818756053603898847") + a1109 = convert(T, + big"0.00263265981064536974369934736325334761174975280887405725010964") + a1110 = convert(T, + big"0.00315472768977025060103545855572111407955208306374459723959783") + + a1200 = convert(T, big"0.0194588815119755475588801096525317761242073762016273186231215") + a1208 = convert(T, + big"0.0000678512949171812509306121653452367476194364781259165332321534") + a1209 = convert(T, + big"-0.0000429795859049273623271005330230162343568863387724883603675550") + a1210 = convert(T, + big"0.0000176358982260285155407485928953302139937553442829975734148981") + a1211 = convert(T, big"0.0653866627415027051009595231385181033549511358787382098351924") + + a1300 = convert(T, big"0.206836835664277105916828174798272361078909196043446411598231") + a1308 = convert(T, big"0.0166796067104156472828045866664696450306326505094792505215514") + a1309 = convert(T, + big"-0.00879501563200710214457024178249986591130234990219959208704979") + a1310 = convert(T, + big"0.00346675455362463910824462315246379209427513654098596403637231") + a1311 = convert(T, big"-0.861264460105717678161432562258351242030270498966891201799225") + a1312 = convert(T, big"0.908651882074050281096239478469262145034957129939256789178785") + + a1400 = convert(T, big"0.0203926084654484010091511314676925686038504449562413004562382") + a1408 = convert(T, big"0.0869469392016685948675400555583947505833954460930940959577347") + a1409 = convert(T, + big"-0.0191649630410149842286436611791405053287170076602337673587681") + a1410 = convert(T, + big"0.00655629159493663287364871573244244516034828755253746024098838") + a1411 = convert(T, big"0.0987476128127434780903798528674033899738924968006632201445462") + a1412 = convert(T, + big"0.00535364695524996055083260173615567408717110247274021056118319") + a1413 = convert(T, big"0.301167864010967916837091303817051676920059229784957479998077") + + a1500 = convert(T, big"0.228410433917778099547115412893004398779136994596948545722283") + a1508 = convert(T, big"-0.498707400793025250635016567442511512138603770959682292383042") + a1509 = convert(T, big"0.134841168335724478552596703792570104791700727205981058201689") + a1510 = convert(T, + big"-0.0387458244055834158439904226924029230935161059142806805674360") + a1511 = convert(T, big"-1.27473257473474844240388430824908952380979292713250350199641") + a1512 = convert(T, big"1.43916364462877165201184452437038081875299303577911839630524") + a1513 = convert(T, big"-0.214007467967990254219503540827349569639028092344812795499026") + a1514 = convert(T, big"0.958202417754430239892724139109781371059908874605153648768037") + + a1600 = convert(T, big"2.00222477655974203614249646012506747121440306225711721209798") + a1608 = convert(T, big"2.06701809961524912091954656438138595825411859673341600679555") + a1609 = convert(T, big"0.623978136086139541957471279831494466155292316167021080663140") + a1610 = convert(T, + big"-0.0462283685500311430283203554129062069391947101880112723185773") + a1611 = convert(T, big"-8.84973288362649614860075246727118949286604835457092701094630") + a1612 = convert(T, big"7.74257707850855976227437225791835589560188590785037197433615") + a1613 = convert(T, big"-0.588358519250869210993353314127711745644125882130941202896436") + a1614 = convert(T, big"-1.10683733362380649395704708016953056176195769617014899442903") + a1615 = convert(T, big"-0.929529037579203999778397238291233214220788057511899747507074") + + a1700 = convert(T, big"3.13789533412073442934451608989888796808161259330322100268310") + a1705 = convert(T, big"0.129146941900176461970759579482746551122871751501482634045487") + a1706 = convert(T, big"1.53073638102311295076342566143214939031177504112433874313011") + a1707 = convert(T, big"0.577874761129140052546751349454576715334892100418571882718036") + a1708 = convert(T, big"5.42088263055126683050056840891857421941300558851862156403363") + a1709 = convert(T, big"0.231546926034829304872663800877643660904880180835945693836936") + a1710 = convert(T, big"0.0759292995578913560162301311785251873561801342333194895292058") + a1711 = convert(T, big"-12.3729973380186513287414553402595806591349822617535905976253") + a1712 = convert(T, big"9.85455883464769543935957209317369202080367765721777101906955") + a1713 = convert(T, big"0.0859111431370436529579357709052367772889980495122329601159540") + a1714 = convert(T, big"-5.65242752862643921117182090081762761180392602644189218673969") + a1715 = convert(T, big"-1.94300935242819610883833776782364287728724899124166920477873") + a1716 = convert(T, big"-0.128352601849404542018428714319344620742146491335612353559923") + + a1800 = convert(T, big"1.38360054432196014878538118298167716825163268489922519995564") + a1805 = convert(T, + big"0.00499528226645532360197793408420692800405891149406814091955810") + a1806 = convert(T, big"0.397918238819828997341739603001347156083435060931424970826304") + a1807 = convert(T, big"0.427930210752576611068192608300897981558240730580396406312359") + a1808 = convert(T, big"-1.30299107424475770916551439123047573342071475998399645982146") + a1809 = convert(T, big"0.661292278669377029097112528107513072734573412294008071500699") + a1810 = convert(T, big"-0.144559774306954349765969393688703463900585822441545655530145") + a1811 = convert(T, big"-6.96576034731798203467853867461083919356792248105919255460819") + a1812 = convert(T, big"6.65808543235991748353408295542210450632193197576935120716437") + a1813 = convert(T, big"-1.66997375108841486404695805725510845049807969199236227575796") + a1814 = convert(T, big"2.06413702318035263832289040301832647130604651223986452170089") + a1815 = convert(T, big"-0.674743962644306471862958129570837723192079875998405058648892") + a1816 = convert(T, + big"-0.00115618834794939500490703608435907610059605754935305582045729") + a1817 = convert(T, + big"-0.00544057908677007389319819914241631024660726585015012485938593") + + a1900 = convert(T, big"0.951236297048287669474637975894973552166903378983475425758226") + a1904 = convert(T, big"0.217050632197958486317846256953159942875916353757734167684657") + a1905 = convert(T, big"0.0137455792075966759812907801835048190594443990939408530842918") + a1906 = convert(T, + big"-0.0661095317267682844455831341498149531672668252085016565917546") + a1908 = convert(T, big"0.152281696736414447136604697040747131921486432699422112099617") + a1909 = convert(T, big"-0.337741018357599840802300793133998004354643424457539667670080") + a1910 = convert(T, + big"-0.0192825981633995781534949199286824400469353110630787982121133") + a1911 = convert(T, big"-3.68259269696866809932409015535499603576312120746888880201882") + a1912 = convert(T, big"3.16197870406982063541533528419683854018352080342887002331312") + a1913 = convert(T, big"-0.370462522106885290716991856022051125477943482284080569177386") + a1914 = convert(T, + big"-0.0514974200365440434996434456698127984941168616474316871020314") + a1915 = convert(T, + big"-0.000829625532120152946787043541792848416659382675202720677536554") + a1916 = convert(T, + big"0.00000279801041419278598986586589070027583961355402640879503213503") + a1917 = convert(T, big"0.0418603916412360287969841020776788461794119440689356178942252") + a1918 = convert(T, big"0.279084255090877355915660874555379649966282167560126269290222") + + a2000 = convert(T, big"0.103364471650010477570395435690481791543342708330349879244197") + a2003 = convert(T, big"0.124053094528946761061581889237115328211074784955180298044074") + a2004 = convert(T, big"0.483171167561032899288836480451962508724109257517289177302380") + a2005 = convert(T, + big"-0.0387530245694763252085681443767620580395733302341368038804290") + a2007 = convert(T, big"-0.438313820361122420391059788940960176420682836652600698580091") + a2009 = convert(T, big"-0.218636633721676647685111485017151199362509373698288330593486") + a2010 = convert(T, + big"-0.0312334764394719229981634995206440349766174759626578122323015") + a2017 = convert(T, big"0.0312334764394719229981634995206440349766174759626578122323015") + a2018 = convert(T, big"0.218636633721676647685111485017151199362509373698288330593486") + a2019 = convert(T, big"0.438313820361122420391059788940960176420682836652600698580091") + + a2100 = convert(T, 29 // 150) + a2102 = convert(T, 11 // 50) + a2103 = convert(T, -2 // 25) + a2106 = convert(T, big"0.0984256130499315928152900286856048243348202521491288575952143") + a2107 = convert(T, big"-0.196410889223054653446526504390100417677539095340135532418849") + a2109 = convert(T, big"0.436457930493068729391826122587949137609670676712525034763317") + a2110 = convert(T, big"0.0652613721675721098560370939805555698350543810708414716730270") + a2117 = convert(T, + big"-0.0652613721675721098560370939805555698350543810708414716730270") + a2118 = convert(T, big"-0.436457930493068729391826122587949137609670676712525034763317") + a2119 = convert(T, big"0.196410889223054653446526504390100417677539095340135532418849") + a2120 = convert(T, + big"-0.0984256130499315928152900286856048243348202521491288575952143") + + a2200 = convert(T, big"-0.216049382716049382716049382716049382716049382716049382716049") + a2201 = convert(T, big"0.771604938271604938271604938271604938271604938271604938271605") + a2204 = convert(T, -2 // 3) + a2206 = convert(T, big"-0.390696469295978451446999802258495981249099665294395945559163") + a2220 = convert(T, big"0.390696469295978451446999802258495981249099665294395945559163") + a2221 = convert(T, 2 // 3) + + a2300 = convert(T, 1 // 5) + a2302 = convert(T, big"-0.164609053497942386831275720164609053497942386831275720164609") + a2322 = convert(T, big"0.164609053497942386831275720164609053497942386831275720164609") + + a2400 = convert(T, big"1.47178724881110408452949550989023611293535315518571691939396") + a2401 = convert(T, 63 // 80) + a2402 = convert(T, 91 // 216) + a2404 = convert(T, 7 // 24) + a2406 = convert(T, big"0.348600717628329563206854421629657569274689947367847465753757") + a2407 = convert(T, big"0.229499544768994849582890233710555447073823569666506700662510") + a2408 = convert(T, big"5.79046485790481979159831978177003471098279506036722411333192") + a2409 = convert(T, big"0.418587511856506868874073759426596207226461447604248151080016") + a2410 = convert(T, big"0.307039880222474002649653817490106690389251482313213999386651") + a2411 = convert(T, big"-4.68700905350603332214256344683853248065574415794742040470287") + a2412 = convert(T, big"3.13571665593802262152038152399873856554395436199962915429076") + a2413 = convert(T, big"1.40134829710965720817510506275620441055845017313930508348898") + a2414 = convert(T, big"-5.52931101439499023629010306005764336421276055777658156400910") + a2415 = convert(T, big"-0.853138235508063349309546894974784906188927508039552519557498") + a2416 = convert(T, big"0.103575780373610140411804607167772795518293914458500175573749") + a2417 = convert(T, big"-0.140474416950600941142546901202132534870665923700034957196546") + a2418 = convert(T, big"-0.418587511856506868874073759426596207226461447604248151080016") + a2419 = convert(T, big"-0.229499544768994849582890233710555447073823569666506700662510") + a2420 = convert(T, big"-0.348600717628329563206854421629657569274689947367847465753757") + a2421 = convert(T, -7 // 24) + a2422 = convert(T, -91 // 216) + a2423 = convert(T, -63 // 80) + Feagin12ConstantCache(adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, + a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, + a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, + a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, + a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1208, + a1209, a1210, a1211, a1300, a1308, a1309, a1310, a1311, a1312, + a1400, a1408, a1409, a1410, a1411, a1412, a1413, a1500, a1508, + a1509, a1510, a1511, a1512, a1513, a1514, a1600, a1608, a1609, + a1610, a1611, a1612, a1613, a1614, a1615, a1700, a1705, a1706, + a1707, a1708, a1709, a1710, a1711, a1712, a1713, a1714, a1715, + a1716, a1800, a1805, a1806, a1807, a1808, a1809, a1810, a1811, + a1812, a1813, a1814, a1815, a1816, a1817, a1900, a1904, a1905, + a1906, a1908, a1909, a1910, a1911, a1912, a1913, a1914, a1915, + a1916, a1917, a1918, a2000, a2003, a2004, a2005, a2007, a2009, + a2010, a2017, a2018, a2019, a2100, a2102, a2103, a2106, a2107, + a2109, a2110, a2117, a2118, a2119, a2120, a2200, a2201, a2204, + a2206, a2220, a2221, a2300, a2302, a2322, a2400, a2401, a2402, + a2404, a2406, a2407, a2408, a2409, a2410, a2411, a2412, a2413, + a2414, a2415, a2416, a2417, a2418, a2419, a2420, a2421, a2422, + a2423, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, + c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, b1, b2, b3, + b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, + b18, b19, b20, b21, b22, b23, b24, b25) +end + +struct Feagin14ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + adaptiveConst::T + a0100::T + a0200::T + a0201::T + a0300::T + a0302::T + a0400::T + a0402::T + a0403::T + a0500::T + a0503::T + a0504::T + a0600::T + a0603::T + a0604::T + a0605::T + a0700::T + a0704::T + a0705::T + a0706::T + a0800::T + a0805::T + a0806::T + a0807::T + a0900::T + a0905::T + a0906::T + a0907::T + a0908::T + a1000::T + a1005::T + a1006::T + a1007::T + a1008::T + a1009::T + a1100::T + a1105::T + a1106::T + a1107::T + a1108::T + a1109::T + a1110::T + a1200::T + a1208::T + a1209::T + a1210::T + a1211::T + a1300::T + a1308::T + a1309::T + a1310::T + a1311::T + a1312::T + a1400::T + a1408::T + a1409::T + a1410::T + a1411::T + a1412::T + a1413::T + a1500::T + a1508::T + a1509::T + a1510::T + a1511::T + a1512::T + a1513::T + a1514::T + a1600::T + a1608::T + a1609::T + a1610::T + a1611::T + a1612::T + a1613::T + a1614::T + a1615::T + a1700::T + a1712::T + a1713::T + a1714::T + a1715::T + a1716::T + a1800::T + a1812::T + a1813::T + a1814::T + a1815::T + a1816::T + a1817::T + a1900::T + a1912::T + a1913::T + a1914::T + a1915::T + a1916::T + a1917::T + a1918::T + a2000::T + a2012::T + a2013::T + a2014::T + a2015::T + a2016::T + a2017::T + a2018::T + a2019::T + a2100::T + a2112::T + a2113::T + a2114::T + a2115::T + a2116::T + a2117::T + a2118::T + a2119::T + a2120::T + a2200::T + a2212::T + a2213::T + a2214::T + a2215::T + a2216::T + a2217::T + a2218::T + a2219::T + a2220::T + a2221::T + a2300::T + a2308::T + a2309::T + a2310::T + a2311::T + a2312::T + a2313::T + a2314::T + a2315::T + a2316::T + a2317::T + a2318::T + a2319::T + a2320::T + a2321::T + a2322::T + a2400::T + a2408::T + a2409::T + a2410::T + a2411::T + a2412::T + a2413::T + a2414::T + a2415::T + a2416::T + a2417::T + a2418::T + a2419::T + a2420::T + a2421::T + a2422::T + a2423::T + a2500::T + a2508::T + a2509::T + a2510::T + a2511::T + a2512::T + a2513::T + a2514::T + a2515::T + a2516::T + a2517::T + a2518::T + a2519::T + a2520::T + a2521::T + a2522::T + a2523::T + a2524::T + a2600::T + a2605::T + a2606::T + a2607::T + a2608::T + a2609::T + a2610::T + a2612::T + a2613::T + a2614::T + a2615::T + a2616::T + a2617::T + a2618::T + a2619::T + a2620::T + a2621::T + a2622::T + a2623::T + a2624::T + a2625::T + a2700::T + a2705::T + a2706::T + a2707::T + a2708::T + a2709::T + a2711::T + a2712::T + a2713::T + a2714::T + a2715::T + a2716::T + a2717::T + a2718::T + a2719::T + a2720::T + a2721::T + a2722::T + a2723::T + a2724::T + a2725::T + a2726::T + a2800::T + a2805::T + a2806::T + a2807::T + a2808::T + a2810::T + a2811::T + a2813::T + a2814::T + a2815::T + a2823::T + a2824::T + a2825::T + a2826::T + a2827::T + a2900::T + a2904::T + a2905::T + a2906::T + a2909::T + a2910::T + a2911::T + a2913::T + a2914::T + a2915::T + a2923::T + a2924::T + a2925::T + a2926::T + a2927::T + a2928::T + a3000::T + a3003::T + a3004::T + a3005::T + a3007::T + a3009::T + a3010::T + a3013::T + a3014::T + a3015::T + a3023::T + a3024::T + a3025::T + a3027::T + a3028::T + a3029::T + a3100::T + a3102::T + a3103::T + a3106::T + a3107::T + a3109::T + a3110::T + a3113::T + a3114::T + a3115::T + a3123::T + a3124::T + a3125::T + a3127::T + a3128::T + a3129::T + a3130::T + a3200::T + a3201::T + a3204::T + a3206::T + a3230::T + a3231::T + a3300::T + a3302::T + a3332::T + a3400::T + a3401::T + a3402::T + a3404::T + a3406::T + a3407::T + a3409::T + a3410::T + a3411::T + a3412::T + a3413::T + a3414::T + a3415::T + a3416::T + a3417::T + a3418::T + a3419::T + a3420::T + a3421::T + a3422::T + a3423::T + a3424::T + a3425::T + a3426::T + a3427::T + a3428::T + a3429::T + a3430::T + a3431::T + a3432::T + a3433::T + c1::T2 + c2::T2 + c3::T2 + c4::T2 + c5::T2 + c6::T2 + c7::T2 + c8::T2 + c9::T2 + c10::T2 + c11::T2 + c12::T2 + c13::T2 + c14::T2 + c15::T2 + c16::T2 + c17::T2 + c18::T2 + c19::T2 + c20::T2 + c21::T2 + c22::T2 + c23::T2 + c24::T2 + c25::T2 + c26::T2 + c27::T2 + c28::T2 + c29::T2 + c30::T2 + c31::T2 + c32::T2 + c33::T2 + c34::T2 + b1::T + b2::T + b3::T + b4::T + b5::T + b6::T + b7::T + b8::T + b9::T + b10::T + b11::T + b12::T + b13::T + b14::T + b15::T + b16::T + b17::T + b18::T + b19::T + b20::T + b21::T + b22::T + b23::T + b24::T + b25::T + b26::T + b27::T + b28::T + b29::T + b30::T + b31::T + b32::T + b33::T + b34::T + b35::T +end + +""" +constructFeagin14 +""" +function Feagin14ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + adaptiveConst = convert(T, 1 // 1000) + c1 = convert(T2, 1 // 9) + c2 = convert(T2, 5 // 9) + c3 = convert(T2, 5 // 6) + c4 = convert(T2, 1 // 3) + c5 = convert(T2, 1) + c6 = convert(T2, 0.669986979272772921764683785505998513938845229638460353285142) + c7 = convert(T2, 0.297068384213818357389584716808219413223332094698915687379168) + c8 = convert(T2, 8 // 11) + c9 = convert(T2, 0.140152799042188765276187487966946717629806463082532936287323) + c10 = convert(T2, 0.700701039770150737151099854830749337941407049265546408969222) + c11 = convert(T2, 4 // 11) + c12 = convert(T2, 0.263157894736842105263157894736842105263157894736842105263158) + c13 = convert(T2, 0.0392172246650270859125196642501208648863714315266128052078483) + c14 = convert(T2, 0.812917502928376762983393159278036506189612372617238550774312) + c15 = convert(T2, 1 // 6) + c16 = convert(T2, 9 // 10) + c17 = convert(T2, 0.0641299257451966923312771193896682809481096651615083225402924) + c18 = convert(T2, 0.204149909283428848927744634301023405027149505241333751628870) + c19 = convert(T2, 0.395350391048760565615671369827324372352227297456659450554577) + c20 = convert(T2, 0.604649608951239434384328630172675627647772702543340549445423) + c21 = convert(T2, 0.795850090716571151072255365698976594972850494758666248371130) + c22 = convert(T2, 0.935870074254803307668722880610331719051890334838491677459708) + c23 = convert(T2, 1 // 6) + c24 = convert(T2, 0.812917502928376762983393159278036506189612372617238550774312) + c25 = convert(T2, 0.0392172246650270859125196642501208648863714315266128052078483) + c26 = convert(T2, 4 // 11) + c27 = convert(T2, 0.700701039770150737151099854830749337941407049265546408969222) + c28 = convert(T2, 0.140152799042188765276187487966946717629806463082532936287323) + c29 = convert(T2, 0.297068384213818357389584716808219413223332094698915687379168) + c30 = convert(T2, 0.669986979272772921764683785505998513938845229638460353285142) + c31 = convert(T2, 1 // 3) + c32 = convert(T2, 5 // 9) + c33 = convert(T2, 1 // 9) + c34 = convert(T2, 1) + + b1 = convert(T, 1 // 56) + b2 = convert(T, 3 // 512) + b3 = convert(T, 3 // 256) + b4 = convert(T, 0) + b5 = convert(T, 9 // 512) + b6 = convert(T, 0) + b7 = convert(T, 3 // 128) + b8 = convert(T, 15 // 512) + b9 = convert(T, 0) + b10 = convert(T, 9 // 256) + b11 = convert(T, 21 // 512) + b12 = convert(T, 3 // 64) + b13 = convert(T, 0) + b14 = convert(T, 27 // 512) + b15 = convert(T, 15 // 256) + b16 = convert(T, 33 // 512) + b17 = convert(T, 0) + b18 = convert(T, 0.105352113571753019691496032887878162227673083080523884041670) + b19 = convert(T, 0.170561346241752182382120338553874085887555487802790804737501) + b20 = convert(T, 0.206229397329351940783526485701104894741914286259542454077972) + b21 = convert(T, 0.206229397329351940783526485701104894741914286259542454077972) + b22 = convert(T, 0.170561346241752182382120338553874085887555487802790804737501) + b23 = convert(T, 0.105352113571753019691496032887878162227673083080523884041670) + b24 = convert(T, -33 // 512) + b25 = convert(T, -15 // 256) + b26 = convert(T, -27 // 512) + b27 = convert(T, -3 // 64) + b28 = convert(T, -21 // 512) + b29 = convert(T, -9 // 256) + b30 = convert(T, -15 // 512) + b31 = convert(T, -3 // 128) + b32 = convert(T, -9 // 512) + b33 = convert(T, -3 // 256) + b34 = convert(T, -3 // 512) + b35 = convert(T, 1 // 56) + + a0100 = convert(T, 1 // 9) + + a0200 = convert(T, -5 // 6) + a0201 = convert(T, 25 // 18) + + a0300 = convert(T, 5 // 24) + a0302 = convert(T, 5 // 8) + + a0400 = convert(T, 29 // 150) + a0402 = convert(T, 11 // 50) + a0403 = convert(T, -2 // 25) + + a0500 = convert(T, 1 // 10) + a0503 = convert(T, 2 // 5) + a0504 = convert(T, 1 // 2) + + a0600 = convert(T, 0.103484561636679776672993546511910344499744798201971316606663) + a0603 = convert(T, 0.122068887306407222589644082868962077139592714834162134741275) + a0604 = convert(T, 0.482574490331246622475134780125688112865919023850168049679402) + a0605 = convert(T, -0.0381409600015606999730886240005620205664113072478411477421970) + + a0700 = convert(T, 0.124380526654094412881516420868799316268491466359671423163289) + a0704 = convert(T, 0.226120282197584301422238662979202901196752320742633143965145) + a0705 = convert(T, 0.0137885887618080880607695837016477814530969417491493385363543) + a0706 = convert(T, -0.0672210133996684449749399507414305856950086341525382182856200) + a0800 = convert(T, 0.0936919065659673815530885456083005933866349695217750085655603) + a0805 = convert(T, -0.00613406843450510987229498995641664735620914507128858871007099) + a0806 = convert(T, 0.216019825625503063708860097659866573490979433278117320188668) + a0807 = convert(T, 0.423695063515761937337619073960976753205867469544123532683116) + + a0900 = convert(T, 0.0838479812409052664616968791372814085980533139224911131069335) + a0905 = convert(T, -0.0117949367100973814319755056031295775367961960590736150777613) + a0906 = convert(T, -0.247299020568812652339473838743194598325992840353340132697498) + a0907 = convert(T, 0.0978080858367729012259313014081291665503740655476733940756599) + a0908 = convert(T, 0.217590689243420631360008651767860318344168120024782176879989) + + a1000 = convert(T, 0.0615255359769428227954562389614314714333423969064821107453940) + a1005 = convert(T, 0.00592232780324503308042990005798046524738389560444257136834990) + a1006 = convert(T, 0.470326159963841112217224303205894113455362530746108825010848) + a1007 = convert(T, 0.299688863848679000853981837096192399136831121671781279184194) + a1008 = convert(T, -0.247656877593994914689992276329810825853958069263947095548189) + a1009 = convert(T, 0.110895029771437682893999851839061714522445173600678718208625) + + a1100 = convert(T, 0.0419700073362782579861792864787277787213483656543104611245994) + a1105 = convert(T, -0.00317987696266205093901912847692712407988609169703103952205634) + a1106 = convert(T, 0.806397714906192077260821711520379506393543111567419750119748) + a1107 = convert(T, 0.0975983126412388979093522850684288851314672048003054550357187) + a1108 = convert(T, 0.778575578158398909027512446452927238999763460594181964958853) + a1109 = convert(T, 0.204890423831599428189499202098105603312029235081420653574829) + a1110 = convert(T, -1.56261579627468188307070943950527825211462892236424360892806) + + a1200 = convert(T, 0.0437726782233730163574465242495339811688214967071614123256973) + a1208 = convert(T, 0.00624365027520195208794358628580933625281631216903095917201250) + a1209 = convert(T, 0.200043097109577314994435165469647856829066232218264969608768) + a1210 = convert(T, -0.00805328367804983036823857162048902911923392887337029314844206) + a1211 = convert(T, 0.0211517528067396521915711903523399601316877825157550573051221) + + a1300 = convert(T, 0.0283499250363514563095023591920717312247137654896477097768495) + a1308 = convert(T, 0.00249163204855817407538949148805995149459884653585417680098222) + a1309 = convert(T, 0.0230138787854593149638399846373742768772087122638142234223658) + a1310 = convert(T, -0.00322155956692977098724476092467120878189463604760620461043308) + a1311 = convert(T, 0.00988442549447664668946335414487885256040819982786014648129297) + a1312 = convert(T, -0.0213010771328887351384307642875927384886634565429572466632092) + + a1400 = convert(T, 0.343511894290243001049432234735147943083353174980701426268122) + a1408 = convert(T, 0.210451912023627385609097011999010655788807405225626700040882) + a1409 = convert(T, 1.03427452057230411936482926828825709938667999698324740166559) + a1410 = convert(T, 0.00600303645864422487051240448206640574939078092406156945568306) + a1411 = convert(T, 0.855938125099619537578012106002407728915062652616416005816477) + a1412 = convert(T, -0.977235005036766810872264852372525633013107656892839677696022) + a1413 = convert(T, -0.660026980479294694616225013856327693720573981219974874776419) + + a1500 = convert(T, 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a2928 = convert(T, 0.856238975085428354755349769879501772112121597411563802855067) + + a3000 = convert(T, 0.103484561636679776672993546511910344499744798201971316606663) + a3003 = convert(T, 0.122068887306407222589644082868962077139592714834162134741275) + a3004 = convert(T, 0.482574490331246622475134780125688112865919023850168049679402) + a3005 = convert(T, -0.0381409600015606999730886240005620205664113072478411477421970) + a3007 = convert(T, -0.550499525310802324138388507020508177411414311000037561712836) + a3009 = convert(T, -0.711915811585189227887648262043794387578291882406745570495765) + a3010 = convert(T, -0.584129605671551340432988730158480872095335329645227595707052) + a3013 = convert(T, 2.11046308125864932128717300046622750300375054278936987850718) + a3014 = convert(T, -0.0837494736739572135525742023001037992695260175335123517729291) + a3015 = convert(T, 5.10021499072320914075295969043344113107545060862804249161191) + a3023 = convert(T, -5.10021499072320914075295969043344113107545060862804249161191) + a3024 = convert(T, 0.0837494736739572135525742023001037992695260175335123517729291) + a3025 = convert(T, -2.11046308125864932128717300046622750300375054278936987850718) + a3027 = convert(T, 0.584129605671551340432988730158480872095335329645227595707052) + a3028 = convert(T, 0.711915811585189227887648262043794387578291882406745570495765) + a3029 = convert(T, 0.550499525310802324138388507020508177411414311000037561712836) + + a3100 = convert(T, 29 // 150) + a3102 = convert(T, 11 // 50) + a3103 = convert(T, -2 // 25) + a3106 = convert(T, 0.109993425580724703919462404865068340845119058295846426463652) + a3107 = convert(T, -0.254297048076270161384068506997153122141835626976703920846242) + a3109 = convert(T, 0.865570777116694254343770343821098281832847401233011859346737) + a3110 = convert(T, 3.32416449114093083106799552786572018336860092936986407160200) + a3113 = convert(T, -12.0102223315977933882352385148661841260301942633996815127277) + a3114 = convert(T, 0.476601466242493239430442776862061899602963782003580209476163) + a3115 = convert(T, -29.0243011221036390525802623213654099596251221332470910692353) + a3123 = convert(T, 29.0243011221036390525802623213654099596251221332470910692353) + a3124 = convert(T, -0.476601466242493239430442776862061899602963782003580209476163) + a3125 = convert(T, 12.0102223315977933882352385148661841260301942633996815127277) + a3127 = convert(T, -3.32416449114093083106799552786572018336860092936986407160200) + a3128 = convert(T, -0.865570777116694254343770343821098281832847401233011859346737) + a3129 = convert(T, 0.254297048076270161384068506997153122141835626976703920846242) + a3130 = convert(T, -0.109993425580724703919462404865068340845119058295846426463652) + + a3200 = convert(T, -5 // 6) + a3201 = convert(T, 25 // 18) + a3204 = convert(T, -3 // 4) + a3206 = convert(T, -0.492529543718026304422682049114021320200214681580657784719074) + a3230 = convert(T, 0.492529543718026304422682049114021320200214681580657784719074) + a3231 = convert(T, 3 // 4) + + a3300 = convert(T, 1 // 9) + a3302 = convert(T, -2 // 9) + a3332 = convert(T, 2 // 9) + + a3400 = convert(T, 0.285835140388971558796088842163836414852927537894596466840753) + a3401 = convert(T, 7 // 24) + a3402 = convert(T, 7 // 32) + a3404 = convert(T, 21 // 128) + a3406 = convert(T, 0.218194354945556658327188241581352107093288824322187941141516) + a3407 = convert(T, 0.180392898478697766863635221946775437719620053641849228562435) + a3409 = convert(T, 0.205713839404845018859120755122929542277570094982808905393991) + a3410 = convert(T, 0.242715791581770239970282927959446515762745971386670541948576) + a3411 = convert(T, 0.246465780813629305833609291181891407799228103869305705137021) + a3412 = convert(T, -3.44991940790890824979834154601622662060370460614931644223924) + a3413 = convert(T, 0.228875562160036081760729060738458584294220372552740218459295) + a3414 = convert(T, 0.283290599702151415321527419056733335978436595493855789831434) + a3415 = convert(T, 3.21085125837766640960131490544236787005557320332238705967955) + a3416 = convert(T, -0.223538777364845699920233756214162507964125230083674032084065) + a3417 = convert(T, -0.707121157204419073518727286207487212130091231955206160635271) + a3418 = convert(T, 3.21123345150287080408174729202856500893260034443022374267639) + a3419 = convert(T, 1.40954348309669766030414474301123175769045945573548986335553) + a3420 = convert(T, -0.151362053443742613121602276742518111090963026203676055891793) + a3421 = convert(T, 0.372350574527014276454724080214619984397121028202148298716575) + a3422 = convert(T, 0.252978746406361336722199907762141285915775728129414319261111) + a3423 = convert(T, -3.21085125837766640960131490544236787005557320332238705967955) + a3424 = convert(T, -0.283290599702151415321527419056733335978436595493855789831434) + a3425 = convert(T, -0.228875562160036081760729060738458584294220372552740218459295) + a3426 = convert(T, -0.246465780813629305833609291181891407799228103869305705137021) + a3427 = convert(T, -0.242715791581770239970282927959446515762745971386670541948576) + a3428 = convert(T, -0.205713839404845018859120755122929542277570094982808905393991) + a3429 = convert(T, -0.180392898478697766863635221946775437719620053641849228562435) + a3430 = convert(T, -0.218194354945556658327188241581352107093288824322187941141516) + a3431 = convert(T, -21 // 128) + a3432 = convert(T, -7 // 32) + a3433 = convert(T, -7 // 24) + Feagin14ConstantCache(adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, + a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, + a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, + a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, + a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1208, + a1209, a1210, a1211, a1300, a1308, a1309, a1310, a1311, a1312, + a1400, a1408, a1409, a1410, a1411, a1412, a1413, a1500, a1508, + a1509, a1510, a1511, a1512, a1513, a1514, a1600, a1608, a1609, + a1610, a1611, a1612, a1613, a1614, a1615, a1700, a1712, a1713, + a1714, a1715, a1716, a1800, a1812, a1813, a1814, a1815, a1816, + a1817, a1900, a1912, a1913, a1914, a1915, a1916, a1917, a1918, + a2000, a2012, a2013, a2014, a2015, a2016, a2017, a2018, a2019, + a2100, a2112, a2113, a2114, a2115, a2116, a2117, a2118, a2119, + a2120, a2200, a2212, a2213, a2214, a2215, a2216, a2217, a2218, + a2219, a2220, a2221, a2300, a2308, a2309, a2310, a2311, a2312, + a2313, a2314, a2315, a2316, a2317, a2318, a2319, a2320, a2321, + a2322, a2400, a2408, a2409, a2410, a2411, a2412, a2413, a2414, + a2415, a2416, a2417, a2418, a2419, a2420, a2421, a2422, a2423, + a2500, a2508, a2509, a2510, a2511, a2512, a2513, a2514, a2515, + a2516, a2517, a2518, a2519, a2520, a2521, a2522, a2523, a2524, + a2600, a2605, a2606, a2607, a2608, a2609, a2610, a2612, a2613, + a2614, a2615, a2616, a2617, a2618, a2619, a2620, a2621, a2622, + a2623, a2624, a2625, a2700, a2705, a2706, a2707, a2708, a2709, + a2711, a2712, a2713, a2714, a2715, a2716, a2717, a2718, a2719, + a2720, a2721, a2722, a2723, a2724, a2725, a2726, a2800, a2805, + a2806, a2807, a2808, a2810, a2811, a2813, a2814, a2815, a2823, + a2824, a2825, a2826, a2827, a2900, a2904, a2905, a2906, a2909, + a2910, a2911, a2913, a2914, a2915, a2923, a2924, a2925, a2926, + a2927, a2928, a3000, a3003, a3004, a3005, a3007, a3009, a3010, + a3013, a3014, a3015, a3023, a3024, a3025, a3027, a3028, a3029, + a3100, a3102, a3103, a3106, a3107, a3109, a3110, a3113, a3114, + a3115, a3123, a3124, a3125, a3127, a3128, a3129, a3130, a3200, + a3201, a3204, a3206, a3230, a3231, a3300, a3302, a3332, a3400, + a3401, a3402, a3404, a3406, a3407, a3409, a3410, a3411, a3412, + a3413, a3414, a3415, a3416, a3417, a3418, a3419, a3420, a3421, + a3422, a3423, a3424, a3425, a3426, a3427, a3428, a3429, a3430, + a3431, a3432, a3433, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, + c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, + c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, b1, b2, b3, b4, + b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, + b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31, + b32, b33, b34, b35) +end + +""" +constructFeagin14 +""" +function Feagin14ConstantCache(T::Type, T2::Type) + adaptiveConst = convert(T, 1 // 1000) + c1 = convert(T2, 1 // 9) + c2 = convert(T2, 5 // 9) + c3 = convert(T2, 5 // 6) + c4 = convert(T2, 1 // 3) + c5 = convert(T2, 1) + c6 = convert(T2, big"0.669986979272772921764683785505998513938845229638460353285142") + c7 = convert(T2, big"0.297068384213818357389584716808219413223332094698915687379168") + c8 = convert(T2, 8 // 11) + c9 = convert(T2, big"0.140152799042188765276187487966946717629806463082532936287323") + c10 = convert(T2, big"0.700701039770150737151099854830749337941407049265546408969222") + c11 = convert(T2, 4 // 11) + c12 = convert(T2, big"0.263157894736842105263157894736842105263157894736842105263158") + c13 = convert(T2, big"0.0392172246650270859125196642501208648863714315266128052078483") + c14 = convert(T2, big"0.812917502928376762983393159278036506189612372617238550774312") + c15 = convert(T2, 1 // 6) + c16 = convert(T2, 9 // 10) + c17 = convert(T2, big"0.0641299257451966923312771193896682809481096651615083225402924") + c18 = convert(T2, big"0.204149909283428848927744634301023405027149505241333751628870") + c19 = convert(T2, big"0.395350391048760565615671369827324372352227297456659450554577") + c20 = convert(T2, big"0.604649608951239434384328630172675627647772702543340549445423") + c21 = convert(T2, big"0.795850090716571151072255365698976594972850494758666248371130") + c22 = convert(T2, big"0.935870074254803307668722880610331719051890334838491677459708") + c23 = convert(T2, 1 // 6) + c24 = convert(T2, big"0.812917502928376762983393159278036506189612372617238550774312") + c25 = convert(T2, big"0.0392172246650270859125196642501208648863714315266128052078483") + c26 = convert(T2, 4 // 11) + c27 = convert(T2, big"0.700701039770150737151099854830749337941407049265546408969222") + c28 = convert(T2, big"0.140152799042188765276187487966946717629806463082532936287323") + c29 = convert(T2, big"0.297068384213818357389584716808219413223332094698915687379168") + c30 = convert(T2, big"0.669986979272772921764683785505998513938845229638460353285142") + c31 = convert(T2, 1 // 3) + c32 = convert(T2, 5 // 9) + c33 = convert(T2, 1 // 9) + c34 = convert(T2, 1) + + b1 = convert(T, 1 // 56) + b2 = convert(T, 3 // 512) + b3 = convert(T, 3 // 256) + b4 = convert(T, 0) + b5 = convert(T, 9 // 512) + b6 = convert(T, 0) + b7 = convert(T, 3 // 128) + b8 = convert(T, 15 // 512) + b9 = convert(T, 0) + b10 = convert(T, 9 // 256) + b11 = convert(T, 21 // 512) + b12 = convert(T, 3 // 64) + b13 = convert(T, 0) + b14 = convert(T, 27 // 512) + b15 = convert(T, 15 // 256) + b16 = convert(T, 33 // 512) + b17 = convert(T, 0) + b18 = convert(T, big"0.105352113571753019691496032887878162227673083080523884041670") + b19 = convert(T, big"0.170561346241752182382120338553874085887555487802790804737501") + b20 = convert(T, big"0.206229397329351940783526485701104894741914286259542454077972") + b21 = convert(T, big"0.206229397329351940783526485701104894741914286259542454077972") + b22 = convert(T, big"0.170561346241752182382120338553874085887555487802790804737501") + b23 = convert(T, big"0.105352113571753019691496032887878162227673083080523884041670") + b24 = convert(T, -33 // 512) + b25 = convert(T, -15 // 256) + b26 = convert(T, -27 // 512) + b27 = convert(T, -3 // 64) + b28 = convert(T, -21 // 512) + b29 = convert(T, -9 // 256) + b30 = convert(T, -15 // 512) + b31 = convert(T, -3 // 128) + b32 = convert(T, -9 // 512) + b33 = convert(T, -3 // 256) + b34 = convert(T, -3 // 512) + b35 = convert(T, 1 // 56) + + a0100 = convert(T, 1 // 9) + + a0200 = convert(T, -5 // 6) + a0201 = convert(T, 25 // 18) + + a0300 = convert(T, 5 // 24) + a0302 = convert(T, 5 // 8) + + a0400 = convert(T, 29 // 150) + a0402 = convert(T, 11 // 50) + a0403 = convert(T, -2 // 25) + + a0500 = convert(T, 1 // 10) + a0503 = convert(T, 2 // 5) + a0504 = convert(T, 1 // 2) + + a0600 = convert(T, big"0.103484561636679776672993546511910344499744798201971316606663") + a0603 = convert(T, big"0.122068887306407222589644082868962077139592714834162134741275") + a0604 = convert(T, big"0.482574490331246622475134780125688112865919023850168049679402") + a0605 = convert(T, + big"-0.0381409600015606999730886240005620205664113072478411477421970") + + a0700 = convert(T, big"0.124380526654094412881516420868799316268491466359671423163289") + a0704 = convert(T, big"0.226120282197584301422238662979202901196752320742633143965145") + a0705 = convert(T, big"0.0137885887618080880607695837016477814530969417491493385363543") + a0706 = convert(T, + big"-0.0672210133996684449749399507414305856950086341525382182856200") + a0800 = convert(T, big"0.0936919065659673815530885456083005933866349695217750085655603") + a0805 = convert(T, + big"-0.00613406843450510987229498995641664735620914507128858871007099") + a0806 = convert(T, big"0.216019825625503063708860097659866573490979433278117320188668") + a0807 = convert(T, big"0.423695063515761937337619073960976753205867469544123532683116") + + a0900 = convert(T, big"0.0838479812409052664616968791372814085980533139224911131069335") + a0905 = convert(T, + big"-0.0117949367100973814319755056031295775367961960590736150777613") + a0906 = convert(T, big"-0.247299020568812652339473838743194598325992840353340132697498") + a0907 = convert(T, big"0.0978080858367729012259313014081291665503740655476733940756599") + a0908 = convert(T, big"0.217590689243420631360008651767860318344168120024782176879989") + + a1000 = convert(T, big"0.0615255359769428227954562389614314714333423969064821107453940") + a1005 = convert(T, + big"0.00592232780324503308042990005798046524738389560444257136834990") + a1006 = convert(T, big"0.470326159963841112217224303205894113455362530746108825010848") + a1007 = convert(T, big"0.299688863848679000853981837096192399136831121671781279184194") + a1008 = convert(T, big"-0.247656877593994914689992276329810825853958069263947095548189") + a1009 = convert(T, big"0.110895029771437682893999851839061714522445173600678718208625") + + a1100 = convert(T, big"0.0419700073362782579861792864787277787213483656543104611245994") + a1105 = convert(T, + big"-0.00317987696266205093901912847692712407988609169703103952205634") + a1106 = convert(T, big"0.806397714906192077260821711520379506393543111567419750119748") + a1107 = convert(T, big"0.0975983126412388979093522850684288851314672048003054550357187") + a1108 = convert(T, big"0.778575578158398909027512446452927238999763460594181964958853") + a1109 = convert(T, big"0.204890423831599428189499202098105603312029235081420653574829") + a1110 = convert(T, big"-1.56261579627468188307070943950527825211462892236424360892806") + + a1200 = convert(T, big"0.0437726782233730163574465242495339811688214967071614123256973") + a1208 = convert(T, + big"0.00624365027520195208794358628580933625281631216903095917201250") + a1209 = convert(T, big"0.200043097109577314994435165469647856829066232218264969608768") + a1210 = convert(T, + big"-0.00805328367804983036823857162048902911923392887337029314844206") + a1211 = convert(T, big"0.0211517528067396521915711903523399601316877825157550573051221") + + a1300 = convert(T, big"0.0283499250363514563095023591920717312247137654896477097768495") + a1308 = convert(T, + big"0.00249163204855817407538949148805995149459884653585417680098222") + a1309 = convert(T, big"0.0230138787854593149638399846373742768772087122638142234223658") + a1310 = convert(T, + big"-0.00322155956692977098724476092467120878189463604760620461043308") + a1311 = convert(T, + 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convert(T, big"0.299688863848679000853981837096192399136831121671781279184194") + a2708 = convert(T, big"-0.247656877593994914689992276329810825853958069263947095548189") + a2709 = convert(T, big"0.110895029771437682893999851839061714522445173600678718208625") + a2711 = convert(T, big"-0.491719043846229147070666628704194097678081907210673044988866") + a2712 = convert(T, big"-11.4743154427289496968389492564352536350842454130853175250727") + a2713 = convert(T, big"80.2593166576230272541702485886484400152793366623589989106256") + a2714 = convert(T, big"-0.384132303980042847625312526759029103746926841342088219165648") + a2715 = convert(T, big"7.28147667468107583471326950926136115767612581862877764249646") + a2716 = convert(T, big"-0.132699384612248379510571708176035274836827341616751884314074") + a2717 = convert(T, big"-81.0799832525730726674679289752255240006070716633632990308935") + a2718 = convert(T, big"-1.25037492835620639521768185656179119962253747492403205797494") + a2719 = convert(T, big"2.59263594969543681023776379504377324994226447359296887778718") + a2720 = convert(T, big"-0.301440298346404539830163997260526875264431537275641495291993") + a2721 = convert(T, big"0.221384460789832337451706451572773791695246839057318414301020") + a2722 = convert(T, big"0.0827577274771892931955989870974693152996276435429809890551210") + a2723 = convert(T, big"18.9960662040611520464672450037243263998175161412237156872211") + a2724 = convert(T, big"0.269231946409639685623468015128334167460051910348912845121977") + a2725 = convert(T, big"1.62674827447066537462989364929628933988125029284183680279020") + a2726 = convert(T, big"0.491719043846229147070666628704194097678081907210673044988866") + + a2800 = convert(T, big"0.0838479812409052664616968791372814085980533139224911131069335") + a2805 = convert(T, + big"-0.0117949367100973814319755056031295775367961960590736150777613") + a2806 = convert(T, big"-0.247299020568812652339473838743194598325992840353340132697498") + a2807 = convert(T, big"0.0978080858367729012259313014081291665503740655476733940756599") + a2808 = convert(T, big"0.217590689243420631360008651767860318344168120024782176879989") + a2810 = convert(T, big"0.137585606763325224865659632196787746647447222975084865975440") + a2811 = convert(T, big"0.0439870229715046685058790092341545026046103890294261359042581") + a2813 = convert(T, big"-0.513700813768193341957004456618630303738757363641964030086972") + a2814 = convert(T, big"0.826355691151315508644211308399153458701423158616168576922372") + a2815 = convert(T, big"25.7018139719811832625873882972519939511136556341960074626615") + a2823 = convert(T, big"-25.7018139719811832625873882972519939511136556341960074626615") + a2824 = convert(T, big"-0.826355691151315508644211308399153458701423158616168576922372") + a2825 = convert(T, big"0.513700813768193341957004456618630303738757363641964030086972") + a2826 = convert(T, + big"-0.0439870229715046685058790092341545026046103890294261359042581") + a2827 = convert(T, big"-0.137585606763325224865659632196787746647447222975084865975440") + + a2900 = convert(T, big"0.124380526654094412881516420868799316268491466359671423163289") + a2904 = convert(T, big"0.226120282197584301422238662979202901196752320742633143965145") + a2905 = convert(T, big"0.0137885887618080880607695837016477814530969417491493385363543") + a2906 = convert(T, + big"-0.0672210133996684449749399507414305856950086341525382182856200") + a2909 = convert(T, big"-0.856238975085428354755349769879501772112121597411563802855067") + a2910 = convert(T, big"-1.96337522866858908928262850028093813988180440518267404553576") + a2911 = convert(T, big"-0.232332822724119401237246257308921847250108199230419994978218") + a2913 = convert(T, big"4.30660719086453349461668936876562947772432562053478092626764") + a2914 = convert(T, big"-2.92722963249465482659787911202390446687687394950633612630592") + a2915 = convert(T, big"-82.3131666397858944454492334105458707735761966428138676971041") + a2923 = convert(T, big"82.3131666397858944454492334105458707735761966428138676971041") + a2924 = convert(T, big"2.92722963249465482659787911202390446687687394950633612630592") + a2925 = convert(T, big"-4.30660719086453349461668936876562947772432562053478092626764") + a2926 = convert(T, big"0.232332822724119401237246257308921847250108199230419994978218") + a2927 = convert(T, big"1.96337522866858908928262850028093813988180440518267404553576") + a2928 = convert(T, big"0.856238975085428354755349769879501772112121597411563802855067") + + a3000 = convert(T, big"0.103484561636679776672993546511910344499744798201971316606663") + a3003 = convert(T, big"0.122068887306407222589644082868962077139592714834162134741275") + a3004 = convert(T, big"0.482574490331246622475134780125688112865919023850168049679402") + a3005 = convert(T, + big"-0.0381409600015606999730886240005620205664113072478411477421970") + a3007 = convert(T, big"-0.550499525310802324138388507020508177411414311000037561712836") + a3009 = convert(T, big"-0.711915811585189227887648262043794387578291882406745570495765") + a3010 = convert(T, big"-0.584129605671551340432988730158480872095335329645227595707052") + a3013 = convert(T, big"2.11046308125864932128717300046622750300375054278936987850718") + a3014 = convert(T, + big"-0.0837494736739572135525742023001037992695260175335123517729291") + a3015 = convert(T, big"5.10021499072320914075295969043344113107545060862804249161191") + a3023 = convert(T, big"-5.10021499072320914075295969043344113107545060862804249161191") + a3024 = convert(T, big"0.0837494736739572135525742023001037992695260175335123517729291") + a3025 = convert(T, big"-2.11046308125864932128717300046622750300375054278936987850718") + a3027 = convert(T, big"0.584129605671551340432988730158480872095335329645227595707052") + a3028 = convert(T, big"0.711915811585189227887648262043794387578291882406745570495765") + a3029 = convert(T, big"0.550499525310802324138388507020508177411414311000037561712836") + + a3100 = convert(T, 29 // 150) + a3102 = convert(T, 11 // 50) + a3103 = convert(T, -2 // 25) + a3106 = convert(T, big"0.109993425580724703919462404865068340845119058295846426463652") + a3107 = convert(T, big"-0.254297048076270161384068506997153122141835626976703920846242") + a3109 = convert(T, big"0.865570777116694254343770343821098281832847401233011859346737") + a3110 = convert(T, big"3.32416449114093083106799552786572018336860092936986407160200") + a3113 = convert(T, big"-12.0102223315977933882352385148661841260301942633996815127277") + a3114 = convert(T, big"0.476601466242493239430442776862061899602963782003580209476163") + a3115 = convert(T, big"-29.0243011221036390525802623213654099596251221332470910692353") + a3123 = convert(T, big"29.0243011221036390525802623213654099596251221332470910692353") + a3124 = convert(T, big"-0.476601466242493239430442776862061899602963782003580209476163") + a3125 = convert(T, big"12.0102223315977933882352385148661841260301942633996815127277") + a3127 = convert(T, big"-3.32416449114093083106799552786572018336860092936986407160200") + a3128 = convert(T, big"-0.865570777116694254343770343821098281832847401233011859346737") + a3129 = convert(T, big"0.254297048076270161384068506997153122141835626976703920846242") + a3130 = convert(T, big"-0.109993425580724703919462404865068340845119058295846426463652") + + a3200 = convert(T, -5 // 6) + a3201 = convert(T, 25 // 18) + a3204 = convert(T, -3 // 4) + a3206 = convert(T, big"-0.492529543718026304422682049114021320200214681580657784719074") + a3230 = convert(T, big"0.492529543718026304422682049114021320200214681580657784719074") + a3231 = convert(T, 3 // 4) + + a3300 = convert(T, 1 // 9) + a3302 = convert(T, -2 // 9) + a3332 = convert(T, 2 // 9) + + a3400 = convert(T, big"0.285835140388971558796088842163836414852927537894596466840753") + a3401 = convert(T, 7 // 24) + a3402 = convert(T, 7 // 32) + a3404 = convert(T, 21 // 128) + a3406 = convert(T, big"0.218194354945556658327188241581352107093288824322187941141516") + a3407 = convert(T, big"0.180392898478697766863635221946775437719620053641849228562435") + a3409 = convert(T, big"0.205713839404845018859120755122929542277570094982808905393991") + a3410 = convert(T, big"0.242715791581770239970282927959446515762745971386670541948576") + a3411 = convert(T, big"0.246465780813629305833609291181891407799228103869305705137021") + a3412 = convert(T, big"-3.44991940790890824979834154601622662060370460614931644223924") + a3413 = convert(T, big"0.228875562160036081760729060738458584294220372552740218459295") + a3414 = convert(T, big"0.283290599702151415321527419056733335978436595493855789831434") + a3415 = convert(T, big"3.21085125837766640960131490544236787005557320332238705967955") + a3416 = convert(T, big"-0.223538777364845699920233756214162507964125230083674032084065") + a3417 = convert(T, big"-0.707121157204419073518727286207487212130091231955206160635271") + a3418 = convert(T, big"3.21123345150287080408174729202856500893260034443022374267639") + a3419 = convert(T, big"1.40954348309669766030414474301123175769045945573548986335553") + a3420 = convert(T, big"-0.151362053443742613121602276742518111090963026203676055891793") + a3421 = convert(T, big"0.372350574527014276454724080214619984397121028202148298716575") + a3422 = convert(T, big"0.252978746406361336722199907762141285915775728129414319261111") + a3423 = convert(T, big"-3.21085125837766640960131490544236787005557320332238705967955") + a3424 = convert(T, big"-0.283290599702151415321527419056733335978436595493855789831434") + a3425 = convert(T, big"-0.228875562160036081760729060738458584294220372552740218459295") + a3426 = convert(T, big"-0.246465780813629305833609291181891407799228103869305705137021") + a3427 = convert(T, big"-0.242715791581770239970282927959446515762745971386670541948576") + a3428 = convert(T, big"-0.205713839404845018859120755122929542277570094982808905393991") + a3429 = convert(T, big"-0.180392898478697766863635221946775437719620053641849228562435") + a3430 = convert(T, big"-0.218194354945556658327188241581352107093288824322187941141516") + a3431 = convert(T, -21 // 128) + a3432 = convert(T, -7 // 32) + a3433 = convert(T, -7 // 24) + Feagin14ConstantCache(adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, + a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, + a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, + a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, + a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1208, + a1209, a1210, a1211, a1300, a1308, a1309, a1310, a1311, a1312, + a1400, a1408, a1409, a1410, a1411, a1412, a1413, a1500, a1508, + a1509, a1510, a1511, a1512, a1513, a1514, a1600, a1608, a1609, + a1610, a1611, a1612, a1613, a1614, a1615, a1700, a1712, a1713, + a1714, a1715, a1716, a1800, a1812, a1813, a1814, a1815, a1816, + a1817, a1900, a1912, a1913, a1914, a1915, a1916, a1917, a1918, + a2000, a2012, a2013, a2014, a2015, a2016, a2017, a2018, a2019, + a2100, a2112, a2113, a2114, a2115, a2116, a2117, a2118, a2119, + a2120, a2200, a2212, a2213, a2214, a2215, a2216, a2217, a2218, + a2219, a2220, a2221, a2300, a2308, a2309, a2310, a2311, a2312, + a2313, a2314, a2315, a2316, a2317, a2318, a2319, a2320, a2321, + a2322, a2400, a2408, a2409, a2410, a2411, a2412, a2413, a2414, + a2415, a2416, a2417, a2418, a2419, a2420, a2421, a2422, a2423, + a2500, a2508, a2509, a2510, a2511, a2512, a2513, a2514, a2515, + a2516, a2517, a2518, a2519, a2520, a2521, a2522, a2523, a2524, + a2600, a2605, a2606, a2607, a2608, a2609, a2610, a2612, a2613, + a2614, a2615, a2616, a2617, a2618, a2619, a2620, a2621, a2622, + a2623, a2624, a2625, a2700, a2705, a2706, a2707, a2708, a2709, + a2711, a2712, a2713, a2714, a2715, a2716, a2717, a2718, a2719, + a2720, a2721, a2722, a2723, a2724, a2725, a2726, a2800, a2805, + a2806, a2807, a2808, a2810, a2811, a2813, a2814, a2815, a2823, + a2824, a2825, a2826, a2827, a2900, a2904, a2905, a2906, a2909, + a2910, a2911, a2913, a2914, a2915, a2923, a2924, a2925, a2926, + a2927, a2928, a3000, a3003, a3004, a3005, a3007, a3009, a3010, + a3013, a3014, a3015, a3023, a3024, a3025, a3027, a3028, a3029, + a3100, a3102, a3103, a3106, a3107, a3109, a3110, a3113, a3114, + a3115, a3123, a3124, a3125, a3127, a3128, a3129, a3130, a3200, + a3201, a3204, a3206, a3230, a3231, a3300, a3302, a3332, a3400, + a3401, a3402, a3404, a3406, a3407, a3409, a3410, a3411, a3412, + a3413, a3414, a3415, a3416, a3417, a3418, a3419, a3420, a3421, + a3422, a3423, a3424, a3425, a3426, a3427, a3428, a3429, a3430, + a3431, a3432, a3433, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, + c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, + c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, b1, b2, b3, b4, + b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, + b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31, + b32, b33, b34, b35) +end diff --git a/src/tableaus/firk_tableaus.jl b/src/tableaus/firk_tableaus.jl index 0577811478..5427d3cef2 100644 --- a/src/tableaus/firk_tableaus.jl +++ b/src/tableaus/firk_tableaus.jl @@ -111,7 +111,7 @@ function RadauIIA5Tableau(T, T2) e1, e2, e3) end -struct RadauIIA7Tableau{T, T2} +struct RadauIIA9Tableau{T, T2} T11::T T12::T T13::T @@ -178,7 +178,7 @@ struct RadauIIA7Tableau{T, T2} e5::T end -function RadauIIA7Tableau(T, T2) +function RadauIIA9Tableau(T, T2) T11 = convert(T, -1.251758622050104589014e-2) T12 = convert(T, -1.024204781790882707009e-2) T13 = convert(T, 4.767387729029572386318e-2) @@ -248,7 +248,7 @@ function RadauIIA7Tableau(T, T2) e4 = convert(T, 5.920031671845428725662e-1) e5 = convert(T, -2.000000000000000000000e-1) - RadauIIA7Tableau{T, T2}(T11, T12, T13, T14, T15, + RadauIIA9Tableau{T, T2}(T11, T12, T13, T14, T15, T21, T22, T23, T24, T25, T31, T32, T33, T34, T35, T41, T42, T43, T44, T45, T51, #=T52, T53, T54, T55=# TI11, TI12, TI13, TI14, TI15, TI21, TI22, TI23, TI24, TI25, @@ -258,3 +258,5 @@ function RadauIIA7Tableau(T, T2) γ, α1, β1, α2, β2, e1, e2, e3, e4, e5) end + + diff --git a/src/tableaus/rkc_tableaus.jl b/src/tableaus/rkc_tableaus.jl new file mode 100644 index 0000000000..5142663360 --- /dev/null +++ b/src/tableaus/rkc_tableaus.jl @@ -0,0 +1,37731 @@ +function ROCK2ConstantCache(T, T2, zprev) + ms = SVector{46, Int}( + 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, + 20, + 22, 24, 26, 28, 30, 33, 36, 39, 43, 47, 51, 56, 61, 66, 72, 78, + 85, 93, + 102, 112, 123, 135, 148, 163, 180, 198) + fp1 = SVector{46, T}(0.4102693550421609e+00, 0.3889624104727243e+00, + 0.3804692420283886e+00, + 0.3760815680865637e+00, 0.3735177579729938e+00, + 0.3719340231904236e+00, + 0.3708571145968057e+00, 0.3700947006022557e+00, + 0.3695328931459086e+00, + 0.3691085831661758e+00, 0.3687813249652330e+00, + 0.3685244707068931e+00, + 0.3683185599507446e+00, 0.3681542178682514e+00, + 0.3680181997765286e+00, + 0.3679084456991284e+00, 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44, 47, 50, 53, 56, 59, + 63, 67, 71, 76, 81, 86, + 92, 98, 105, 112, 120, 129, 138, 148) + fpa = [(-0.149352078672699, 0.629768962985252, + -0.355201061573650, 0.0146745996307541, + -0.0558517281602565, 0.590312931352706) + (-0.179313593132677, 0.522354978881996, + -0.268020263243268, 0.0410644459848542, + -0.0673692676033641, 0.534974252895965) + (-0.182428104178289, 0.488581974232839, + -0.243999027372673, 0.0403844469216897, + -0.0621100542563179, 0.510891501054959) + (-0.177747282156689, 0.475598890858970, + -0.236544145857569, 0.0357873367680739, + -0.0561802405454197, 0.498502393780149) + (-0.171097214294784, 0.471021380996139, + -0.235432301175529, 0.0305165148305403, + -0.0508758913107147, 0.491537536121394) + (-0.164446145110292, 0.470315341552133, + -0.237054736024656, 0.0253636332272387, + -0.0462365759807733, 0.487394153808489) + (-0.158427655171257, 0.471468878620055, + -0.239853802450812, 0.0205746749952032, + -0.0421744356707249, 0.484829913014008) + 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+ a52::T + a53::T + a54::T + abar21::T + abar31::T + abar32::T + abar41::T + abar42::T + abar43::T + abar51::T + abar52::T + abar53::T + abar54::T + b1::T + #b2::T + b3::T + b4::T + b5::T + bbar1::T + #bbar2::T + bbar3::T + bbar4::T + bbar5::T + btilde1::T + #btilde2::T + btilde3::T + btilde4::T + btilde5::T + bptilde1::T + #bptilde2::T + bptilde3::T + bptilde4::T + bptilde5::T +end + +function FineRKN4ConstantCache(T::Type, T2::Type) + c1 = convert(T2, 1 // 1) + c2 = convert(T2, 2 // 9) + c3 = convert(T2, 1 // 3) + c4 = convert(T2, 3 // 4) + c5 = convert(T2, 1 // 1) + a21 = convert(T, 2 // 81) + a31 = convert(T, 1 // 36) + a32 = convert(T, 1 // 36) + a41 = convert(T, 9 // 128) + #a42 = convert(T, 0 // 1) + a43 = convert(T, 27 // 128) + a51 = convert(T, 11 // 60) + a52 = convert(T, -3 // 20) + a53 = convert(T, 9 // 25) + a54 = convert(T, 8 // 75) + abar21 = convert(T, 2 // 9) + abar31 = convert(T, 1 // 12) + abar32 = convert(T, 1 // 4) + abar41 = convert(T, 69 // 128) + abar42 = convert(T, -243 // 128) + abar43 = convert(T, 135 // 64) + abar51 = convert(T, -17 // 12) + abar52 = convert(T, 27 // 4) + abar53 = convert(T, -27 // 5) + abar54 = convert(T, 16 // 15) + b1 = convert(T, 19 // 180) + #b2 = convert(T, 0 // 1) + b3 = convert(T, 63 // 200) + b4 = convert(T, 16 // 225) + b5 = convert(T, 1 // 120) + bbar1 = convert(T, 1 // 9) + #bbar2 = convert(T, 0 // 1) + bbar3 = convert(T, 9 // 20) + bbar4 = convert(T, 16 // 45) + bbar5 = convert(T, 1 // 12) + btilde1 = convert(T, 25 // 1116) + #btilde2 = convert(T, 0 // 1) + btilde3 = convert(T, -63 // 1240) + btilde4 = convert(T, 64 // 1395) + btilde5 = convert(T, -13 // 744) + bptilde1 = convert(T, 2 // 125) + #bptilde2 = convert(T, 0 // 1) + bptilde3 = convert(T, -27 // 625) + bptilde4 = convert(T, 32 // 625) + bptilde5 = convert(T, -3 // 125) + FineRKN4ConstantCache(c1, c2, c3, c4, c5, a21, a31, a32, a41, a43, a51, + a52, a53, a54, abar21, abar31, abar32, abar41, abar42, abar43, abar51, + abar52, abar53, abar54, b1, b3, b4, b5, bbar1, bbar3, bbar4, bbar5, btilde1, + btilde3, btilde4, btilde5, bptilde1, + bptilde3, bptilde4, bptilde5) +end + +struct FineRKN5ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + c1::T2 + c2::T2 + c3::T2 + c4::T2 + c5::T2 + c6::T2 + c7::T2 + a21::T + a31::T + a32::T + a41::T + #a42::T + a43::T + a51::T + a52::T + a53::T + a54::T + a61::T + a62::T + a63::T + a64::T + #a65::T + a71::T + #a72::T + a73::T + a74::T + a75::T + #a76::T + abar21::T + abar31::T + abar32::T + abar41::T + abar42::T + abar43::T + abar51::T + abar52::T + abar53::T + abar54::T + abar61::T + abar62::T + abar63::T + abar64::T + abar65::T + abar71::T + #abar72::T + abar73::T + abar74::T + abar75::T + abar76::T + b1::T + #b2::T + b3::T + b4::T + b5::T + #b6::T + #b7::T + bbar1::T + #bbar2::T + bbar3::T + bbar4::T + bbar5::T + bbar6::T + #bbar7::T + btilde1::T + #btilde2::T + btilde3::T + btilde4::T + btilde5::T + #btilde6::T + #btilde7::T + bptilde1::T + #bptilde2::T + bptilde3::T + bptilde4::T + bptilde5::T + bptilde6::T + bptilde7::T +end + +function FineRKN5ConstantCache(T::Type, T2::Type) + c1 = convert(T2, 1 // 1) + c2 = convert(T2, 8 // 39) + c3 = convert(T2, 4 // 13) + c4 = convert(T2, 5 // 6) + c5 = convert(T2, 43 // 47) + c6 = convert(T2, 1 // 1) # 36463 // 36464 + c7 = convert(T2, 1 // 1) + a21 = convert(T, 32 // 1521) + a31 = convert(T, 4 // 169) + a32 = convert(T, 4 // 169) + a41 = convert(T, 175 // 5184) + #a42 = convert(T, 0 // 1) + a43 = convert(T, 1625 // 5184) + a51 = convert(T, -342497279 // 5618900760) + a52 = convert(T, 6827067 // 46824173) + a53 = convert(T, 35048741 // 102161832) + a54 = convert(T, -2201514 // 234120865) + a61 = convert(T, -7079 // 52152) + a62 = convert(T, 767 // 2173) + a63 = convert(T, 14027 // 52152) + a64 = convert(T, 30 // 2173) + #a65 = convert(T, 0 // 1) + a71 = convert(T, 4817 // 51600) + #a72 = convert(T, 0 // 1) + a73 = convert(T, 388869 // 1216880) + a74 = convert(T, 3276 // 23575) + a75 = convert(T, -1142053 // 22015140) + #a76 = convert(T, 0 // 1) + abar21 = convert(T, 8 // 39) + abar31 = convert(T, 1 // 13) + abar32 = convert(T, 3 // 13) + abar41 = convert(T, 7385 // 6912) + abar42 = convert(T, -9425 // 2304) + abar43 = convert(T, 13325 // 3456) + abar51 = convert(T, 223324757 // 91364240) + abar52 = convert(T, -174255393 // 18272848) + abar53 = convert(T, 382840094 // 46824173) + abar54 = convert(T, -39627252 // 234120865) + abar61 = convert(T, 108475 // 36464) + abar62 = convert(T, -9633 // 848) + abar63 = convert(T, 7624604 // 806183) + abar64 = convert(T, 8100 // 49979) + abar65 = convert(T, -4568212 // 19446707) + abar71 = convert(T, 4817 // 51600) + #abar72 = convert(T, 0 // 1) + abar73 = convert(T, 1685099 // 3650640) + abar74 = convert(T, 19656 // 23575) + abar75 = convert(T, -53676491 // 88060560) + abar76 = convert(T, 53 // 240) + b1 = convert(T, 4817 // 51600) + #b2 = convert(T, 0 // 1) + b3 = convert(T, 388869 // 1216880) + b4 = convert(T, 3276 // 23575) + b5 = convert(T, -1142053 // 22015140) + #b6 = convert(T, 0 // 1) + #b7 = convert(T, 0 // 1) + bbar1 = convert(T, 4817 // 51600) + #bbar2 = convert(T, 0 // 1) + bbar3 = convert(T, 1685099 // 3650640) + bbar4 = convert(T, 19656 // 23575) + bbar5 = convert(T, -53676491 // 88060560) + bbar6 = convert(T, 53 // 240) + #bbar7 = convert(T, 0 // 1) + btilde1 = convert(T, 8151 // 2633750) + #btilde2 = convert(T, 0 // 1) + btilde3 = convert(T, -1377519 // 186334750) + btilde4 = convert(T, 586872 // 28879375) + btilde5 = convert(T, -36011118 // 2247378875) + #btilde6 = convert(T, 0 // 1) + #btilde7 = convert(T, 0 // 1) + bptilde1 = convert(T, 8151 // 2633750) + #bptilde2 = convert(T, 0 // 1) + bptilde3 = convert(T, -5969249 // 559004250) + bptilde4 = convert(T, 3521232 // 28879375) + bptilde5 = convert(T, -846261273 // 4494757750) + bptilde6 = convert(T, 4187 // 36750) + bptilde7 = convert(T, -1 // 25) + FineRKN5ConstantCache(c1, c2, c3, c4, c5, c6, c7, a21, a31, a32, a41, a43, a51, + a52, a53, a54, a61, a62, a63, a64, a71, a73, a74, a75, + abar21, abar31, abar32, abar41, abar42, abar43, abar51, + abar52, abar53, abar54, abar61, abar62, abar63, abar64, abar65, + abar71, abar73, abar74, abar75, abar76, b1, b3, b4, + b5, bbar1, bbar3, bbar4, bbar5, bbar6, btilde1, btilde3, btilde4, btilde5, bptilde1, + bptilde3, bptilde4, bptilde5, bptilde6, bptilde7) +end + +struct IRKN3ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + bconst1::T + bconst2::T + c1::T2 + a21::T + b1::T + b2::T + bbar1::T + bbar2::T +end + +function IRKN3ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + bconst1 = convert(T, 1.5) + bconst2 = convert(T, -0.5) + c1 = convert(T2, 0.5) + a21 = convert(T, 0.125) + b1 = convert(T, 0.6666666666666666) + b2 = convert(T, 0.8333333333333334) + bbar1 = convert(T, 0.3333333333333333) + bbar2 = convert(T, 0.4166666666666667) + IRKN3ConstantCache(bconst1, bconst2, c1, a21, b1, b2, bbar1, bbar2) +end + +function IRKN3ConstantCache(T::Type, T2::Type) + bconst1 = convert(T, 3 // 2) + bconst2 = convert(T, -1 // 2) + c1 = convert(T2, 1 // 2) + a21 = convert(T, 1 // 8) + b1 = convert(T, 2 // 3) + b2 = convert(T, 5 // 6) + bbar1 = convert(T, 1 // 3) + bbar2 = convert(T, 5 // 12) + IRKN3ConstantCache(bconst1, bconst2, c1, a21, b1, b2, bbar1, bbar2) +end + +struct IRKN4ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + bconst1::T + bconst2::T + c1::T2 + c2::T2 + a21::T + # a31::T + a32::T + b1::T + b2::T + b3::T + bbar1::T + bbar2::T + bbar3::T +end + +function IRKN4ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + bconst1 = convert(T, 1.5) + bconst2 = convert(T, -0.5) + c1 = convert(T2, 0.25) + c2 = convert(T2, 0.75) + a21 = convert(T, 0.03125) + # a31 = convert(T,0) + a32 = convert(T, 0.28125) + b1 = convert(T, 1.0555555555555556) + b2 = convert(T, -0.16666666666666666) + b3 = convert(T, 0.6111111111111112) + bbar1 = convert(T, -0.05555555555555555) + bbar2 = convert(T, 0.2916666666666667) + bbar3 = convert(T, 0.125) + IRKN4ConstantCache(bconst1, bconst2, c1, c2, a21, a32, b1, b2, b3, bbar1, bbar2, bbar3) +end + +function IRKN4ConstantCache(T::Type, T2::Type) + bconst1 = convert(T, 3 // 2) + bconst2 = convert(T, -1 // 2) + c1 = convert(T2, 1 // 4) + c2 = convert(T2, 3 // 4) + a21 = convert(T, 1 // 32) + # a31 = convert(T,0) + a32 = convert(T, 9 // 32) + b1 = convert(T, 19 // 18) + b2 = convert(T, -1 // 6) + b3 = convert(T, 11 // 18) + bbar1 = convert(T, -1 // 18) + bbar2 = convert(T, 7 // 24) + bbar3 = convert(T, 1 // 8) + IRKN4ConstantCache(bconst1, bconst2, c1, c2, a21, a32, b1, b2, b3, bbar1, bbar2, bbar3) +end + +struct Nystrom5VelocityIndependentConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + c1::T2 + c2::T2 + a21::T + a31::T + a32::T + a41::T + a42::T + a43::T + bbar1::T + bbar2::T + bbar3::T + b1::T + b2::T + b3::T + b4::T +end + +function Nystrom5VelocityIndependentConstantCache(T::Type{<:CompiledFloats}, + T2::Type{<:CompiledFloats}) + c1 = convert(T2, 0.2) + c2 = convert(T2, 0.6666666666666666) + # c3 = convert(T2,1) + a21 = convert(T, 0.02) + a31 = convert(T, -0.037037037037037035) + a32 = convert(T, 0.25925925925925924) + a41 = convert(T, 0.3) + a42 = convert(T, -0.05714285714285714) + a43 = convert(T, 0.2571428571428571) + bbar1 = convert(T, 0.041666666666666664) + bbar2 = convert(T, 0.2976190476190476) + bbar3 = convert(T, 0.16071428571428573) + b1 = bbar1 + b2 = convert(T, 0.37202380952380953) + b3 = convert(T, 0.48214285714285715) + b4 = convert(T, 0.10416666666666667) + Nystrom5VelocityIndependentConstantCache(c1, c2, a21, a31, a32, a41, a42, a43, bbar1, + bbar2, bbar3, b1, b2, b3, b4) +end + +function Nystrom5VelocityIndependentConstantCache(T::Type, T2::Type) + c1 = convert(T2, 1 // 5) + c2 = convert(T2, 2 // 3) + # c3 = convert(T2,1) + a21 = convert(T, 1 // 50) + a31 = convert(T, -1 // 27) + a32 = convert(T, 7 // 27) + a41 = convert(T, 3 // 10) + a42 = convert(T, -2 // 35) + a43 = convert(T, 9 // 35) + bbar1 = convert(T, 14 // 336) + bbar2 = convert(T, 100 // 336) + bbar3 = convert(T, 54 // 336) + b1 = bbar1 + b2 = convert(T, 125 // 336) + b3 = convert(T, 162 // 336) + b4 = convert(T, 35 // 336) + Nystrom5VelocityIndependentConstantCache(c1, c2, a21, a31, a32, a41, a42, a43, bbar1, + bbar2, bbar3, b1, b2, b3, b4) +end + +struct ERKN4ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + c1::T2 + c2::T2 + c3::T2 + a21::T + a31::T + a32::T + a41::T + a42::T + a43::T + b1::T + b2::T + b3::T + b4::T + bp1::T # bp denotes bprime + bp2::T + bp3::T + bp4::T + btilde1::T + btilde2::T + btilde3::T + btilde4::T + bptilde1::T + bptilde2::T + bptilde3::T + bptilde4::T +end + +function ERKN4ConstantCache(T::Type, T2::Type) + c1 = convert(T2, 1 // 4) + c2 = convert(T2, 7 // 10) + c3 = convert(T2, 1) + a21 = convert(T, 1 // 32) + a31 = convert(T, 19 // 600) + a32 = convert(T, 16 // 75) + a41 = convert(T, 32 // 315) + a42 = convert(T, 58 // 315) + a43 = convert(T, 3 // 14) + btilde1 = convert(T, 1 // 21 - 14 // 375) + btilde2 = convert(T, 28 // 81 - 136 // 375) + btilde3 = convert(T, 50 // 567 - 2 // 25) + btilde4 = convert(T, 1 // 54 - 1 // 50) + bptilde1 = convert(T, 1 // 14 - 17 // 231) + bptilde2 = convert(T, 32 // 81 - 116 // 297) + bptilde3 = convert(T, 250 // 567 - 925 // 2079) + bptilde4 = convert(T, 5 // 54 - 1 // 11) + b1 = convert(T, 1 // 21) + b2 = convert(T, 28 // 81) + b3 = convert(T, 50 // 567) + b4 = convert(T, 1 // 54) + bp1 = convert(T, 1 // 14) + bp2 = convert(T, 32 // 81) + bp3 = convert(T, 250 // 567) + bp4 = convert(T, 5 // 54) + ERKN4ConstantCache(c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, b4, bp1, bp2, + bp3, bp4, btilde1, btilde2, btilde3, btilde4, bptilde1, bptilde2, + bptilde3, bptilde4) +end + +function ERKN4ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + ERKN4ConstantCache(convert(T2, 0.25), + convert(T2, 0.7), + convert(T2, 1.0), + convert(T, 0.03125), + convert(T, 0.03166666666666667), + convert(T, 0.21333333333333335), + convert(T, 0.10158730158730159), + convert(T, 0.18412698412698414), + convert(T, 0.21428571428571427), + convert(T, 0.047619047619047616), + convert(T, 0.345679012345679), + convert(T, 0.08818342151675485), + convert(T, 0.018518518518518517), + convert(T, 0.07142857142857142), + convert(T, 0.3950617283950617), + convert(T, 0.4409171075837742), + convert(T, 0.09259259259259259), + convert(T, 0.010285714285714285), + convert(T, -0.016987654320987654), + convert(T, 0.00818342151675485), + convert(T, -0.0014814814814814814), + convert(T, -0.0021645021645021645), + convert(T, 0.004489337822671156), + convert(T, -0.004008337341670675), + convert(T, 0.0016835016835016834)) +end + +struct ERKN5ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + c1::T2 + c2::T2 + c3::T2 + a21::T + a31::T + a32::T + a41::T + a42::T + a43::T + b1::T + b2::T + b3::T + b4::T + bp1::T # bp denotes bprime + bp2::T + bp3::T + bp4::T + btilde1::T + btilde2::T + btilde3::T + btilde4::T + # bptilde1::T + # bptilde2::T + # bptilde3::T + # bptilde4::T +end + +function ERKN5ConstantCache(T::Type, T2::Type) + c1 = convert(T2, 1 // 2) + c2 = convert(T2, 19 // 70) + c3 = convert(T2, 44 // 51) + a21 = convert(T, 1 // 8) + a31 = convert(T, 2907 // 343000) + a32 = convert(T, 1216 // 42875) + a41 = convert(T, 6624772 // Int64(128538819)) + a42 = convert(T, 6273905 // Int64(54121608)) + a43 = convert(T, Int64(210498365) // Int64(1028310552)) + b1 = convert(T, 479 // 5016) + b2 = convert(T, 235 // 1776) + b3 = convert(T, 145775 // 641744) + b4 = convert(T, 309519 // 6873416) + btilde1 = convert(T, 479 // 5016 - 184883 // 2021250) + btilde2 = convert(T, 235 // 1776 - 411163 // 3399375) + btilde3 = convert(T, 145775 // 641744 - 6 // 25) + btilde4 = convert(T, 309519 // 6873416 - 593028 // Int64(12464375)) + bp1 = b1 + bp2 = convert(T, 235 // 888) + bp3 = convert(T, 300125 // 962616) + bp4 = convert(T, 2255067 // 6873416) + # bptilde1 = convert(T,0) + # bptilde2 = convert(T,0) + # bptilde3 = convert(T,0) + # bptilde4 = convert(T,0) + ERKN5ConstantCache(c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, b4, bp1, bp2, + bp3, bp4, btilde1, btilde2, btilde3, btilde4) +end + +function ERKN5ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + ERKN5ConstantCache(convert(T2, 0.5), + convert(T2, 0.2714285714285714), + convert(T2, 0.8627450980392157), + convert(T, 0.125), + convert(T, 0.008475218658892128), + convert(T, 0.028361516034985424), + convert(T, 0.051539076300366506), + convert(T, 0.11592236875149756), + convert(T, 0.20470310704348388), + convert(T, 0.09549441786283891), + convert(T, 0.13231981981981983), + convert(T, 0.22715444164651324), + convert(T, 0.04503132067082801), + convert(T, 0.09549441786283891), + convert(T, 0.26463963963963966), + convert(T, 0.3117806061814888), + convert(T, 0.32808533631603265), + convert(T, 0.004024782736060931), + convert(T, 0.011367291781577495), + convert(T, -0.012845558353486749), + convert(T, -0.0025465161641516788)) +end + +struct ERKN7ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + c1::T2 + c2::T2 + c3::T2 + c4::T2 + c5::T2 + c6::T2 + a21::T + a31::T + a32::T + a41::T + a42::T + a43::T + a51::T + a52::T + a53::T + a54::T + a61::T + a62::T + a63::T + a64::T + a65::T + a71::T + a73::T + a74::T + a75::T + a76::T + b1::T + b3::T + b4::T + b5::T + b6::T + bp1::T # bp denotes bprime + bp3::T + bp4::T + bp5::T + bp6::T + bp7::T + btilde1::T + btilde3::T + btilde4::T + btilde5::T + btilde6::T + bptilde1::T + bptilde3::T + bptilde4::T + bptilde5::T + bptilde6::T + bptilde7::T +end + +function ERKN7ConstantCache(T::Type, T2::Type) + c1 = convert(T2, 108816483 // 943181462) + c2 = convert(T2, 108816483 // 471590731) + c3 = convert(T2, 151401202 // 200292705) + c4 = convert(T2, 682035803 // 631524599) + c5 = convert(T2, 493263404 // 781610081) + c6 = convert(T2, 1) + a21 = convert(T, 5107771 // 767472028) + a31 = convert(T, 5107771 // 575604021) + a32 = convert(T, 16661485 // 938806552) + a41 = convert(T, 325996677 // 876867260) + a42 = convert(T, -397622579 // 499461366) + a43 = convert(T, 541212017 // 762248206) + a51 = convert(T, 82243160 // 364375691) + a52 = convert(T, -515873404 // 1213273815) + a53 = convert(T, 820109726 // 1294837243) + a54 = convert(T, 36245507 // 242779260) + a61 = convert(T, 3579594 // 351273191) + a62 = convert(T, 34292133 // 461028419) + a63 = convert(T, 267156948 // 2671391749) + a64 = convert(T, 22665163 // 1338599875) + a65 = convert(T, -3836509 // 1614789462) + a71 = convert(T, 53103334 // 780726093) + a73 = convert(T, 352190060 // 1283966121) + a74 = convert(T, 37088117 // 2206150964) + a75 = convert(T, 7183323 // 1828127386) + a76 = convert(T, 187705681 // 1370684829) + b1 = convert(T, 53103334 // 780726093) + b3 = convert(T, 352190060 // 1283966121) + b4 = convert(T, 37088117 // 2206150964) + b5 = convert(T, 7183323 // 1828127386) + b6 = convert(T, 187705681 // 1370684829) + bp1 = convert(T, 53103334 // 780726093) + bp3 = convert(T, 244481296 // 685635505) + bp4 = convert(T, 41493456 // 602487871) + bp5 = convert(T, -45498718 // 926142189) + bp6 = convert(T, 1625563237 // 4379140271) + bp7 = convert(T, 191595797 // 1038702495) + btilde1 = convert(T, 53103334 // 780726093 - 41808761 // 935030896) + btilde3 = convert(T, 352190060 // 1283966121 - 46261019 // 135447428) + btilde4 = convert(T, 37088117 // 2206150964 - 289298425 // 1527932372) + btilde5 = convert(T, 7183323 // 1828127386 + 52260067 // 3104571287) + btilde6 = convert(T, 187705681 // 1370684829 + 49872919 // 848719175) + bptilde1 = convert(T, 53103334 // 780726093 - 41808761 // 935030896) + bptilde3 = convert(T, 244481296 // 685635505 - 224724272 // 506147085) + bptilde4 = convert(T, 41493456 // 602487871 - 2995752066 // 3862177123) + bptilde5 = convert(T, -45498718 // 926142189 - 170795979 // 811534085) + bptilde6 = convert(T, 1625563237 // 4379140271 + 177906423 // 1116903503) + bptilde7 = convert(T, 191595797 // 1038702495 + 655510901 // 2077404990) + ERKN7ConstantCache(c1, c2, c3, c4, c5, c6, a21, a31, a32, a41, a42, a43, a51, a52, a53, + a54, a61, a62, a63, a64, a65, a71, a73, a74, a75, a76, b1, b3, b4, + b5, + b6, bp1, bp3, bp4, bp5, bp6, bp7, btilde1, btilde3, btilde4, btilde5, + btilde6, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6, bptilde7) +end + +function ERKN7ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + ERKN7ConstantCache(convert(T2, 108816483 // 943181462), + convert(T2, 0.23074347277618568), + convert(T2, 0.7558997318449516), + convert(T2, 1.0799829556599743), + convert(T2, 0.6310862871278652), + convert(T2, 1.0), + convert(T, 0.006655318778601792), + convert(T, 0.008873758371469056), + convert(T, 0.01774751674293811), + convert(T, 0.37177426033673555), + convert(T, -0.796102774043188), + convert(T, 0.7100207160080872), + convert(T, 0.2257097880879216), + convert(T, -0.4251912450611983), + convert(T, 0.6333689662029593), + convert(T, 0.14929408302834435), + convert(T, 0.010190342137439119), + convert(T, 0.07438182026691938), + convert(T, 0.10000665312379087), + convert(T, 0.016931992467129134), + convert(T, -0.002375857094861324), + convert(T, 0.06801788037587723), + convert(T, 0.2742985614960786), + convert(T, 0.01681123259704543), + convert(T, 0.003929333948504177), + convert(T, 0.13694299158249457), + convert(T, 0.06801788037587723), + convert(T, 0.2742985614960786), + convert(T, 0.01681123259704543), + convert(T, 0.003929333948504177), + convert(T, 0.13694299158249457), + convert(T, 0.06801788037587723), + convert(T, 0.35657618985177847), + convert(T, 0.06887019307314819), + convert(T, -0.049127141102520276), + convert(T, 0.371206021365649), + convert(T, 0.18445685643606738), + convert(T, 0.023304105484742516), + convert(T, -0.06724368617214582), + convert(T, -0.1725285773981577), + convert(T, 0.020762597600343137), + convert(T, 0.1957055604852179), + convert(T, 0.023304105484742516), + convert(T, -0.08741386493634701), + convert(T, -0.7067938872093759), + convert(T, -0.25958777628335805), + convert(T, 0.5304914229443385), + convert(T, 0.5)) +end + +struct DPRKN4ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + c1::T2 + c2::T2 + c3::T2 + a21::T + a31::T + a32::T + a41::T + a42::T + a43::T + b1::T + b2::T + b3::T + bp1::T # bp denotes bprime + bp2::T + bp3::T + bp4::T + btilde1::T + btilde2::T + btilde3::T + btilde4::T + bptilde1::T + bptilde2::T + bptilde3::T + bptilde4::T +end + +function DPRKN4ConstantCache(T::Type, T2::Type) + c1 = convert(T2, 1 // 4) + c2 = convert(T2, 7 // 10) + c3 = convert(T2, 1) + a21 = convert(T, 1 // 32) + a31 = convert(T, 7 // 1000) + a32 = convert(T, 119 // 500) + a41 = convert(T, 1 // 14) + a42 = convert(T, 8 // 27) + a43 = convert(T, 25 // 189) + b1 = convert(T, 1 // 14) + b2 = convert(T, 8 // 27) + b3 = convert(T, 25 // 189) + # b4 = convert(T, 0) + bp1 = convert(T, 1 // 14) + bp2 = convert(T, 32 // 81) + bp3 = convert(T, 250 // 567) + bp4 = convert(T, 5 // 54) + btilde1 = convert(T, 1 // 14 + 7 // 150) + btilde2 = convert(T, 8 // 27 - 67 // 150) + btilde3 = convert(T, 25 // 189 - 3 // 20) + btilde4 = convert(T, 1 // 20) + bptilde1 = convert(T, 1 // 14 - 13 // 21) + bptilde2 = convert(T, 32 // 81 + 20 // 27) + bptilde3 = convert(T, 250 // 567 - 275 // 189) + bptilde4 = convert(T, 5 // 54 + 1 // 3) + DPRKN4ConstantCache(c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, + bp1, bp2, bp3, bp4, btilde1, btilde2, btilde3, btilde4, + bptilde1, bptilde2, bptilde3, bptilde4) +end + +function DPRKN4ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + c1 = convert(T2, 0.25) + c2 = convert(T2, 0.7) + c3 = convert(T2, 1.0) + a21 = convert(T, 0.03125) + a31 = convert(T, 0.007) + a32 = convert(T, 0.238) + a41 = convert(T, 0.07142857142857142) + a42 = convert(T, 0.2962962962962963) + a43 = convert(T, 0.13227513227513227) + b1 = convert(T, 0.07142857142857142) + b2 = convert(T, 0.2962962962962963) + b3 = convert(T, 0.13227513227513227) + bp1 = convert(T, 0.07142857142857142) + bp2 = convert(T, 0.3950617283950617) + bp3 = convert(T, 0.4409171075837742) + bp4 = convert(T, 0.09259259259259259) + btilde1 = convert(T, 0.11809523809523809) + btilde2 = convert(T, -0.15037037037037038) + btilde3 = convert(T, -0.017724867724867727) + btilde4 = convert(T, 0.05) + bptilde1 = convert(T, -0.5476190476190477) + bptilde2 = convert(T, 1.1358024691358024) + bptilde3 = convert(T, -1.0141093474426808) + bptilde4 = convert(T, 0.42592592592592593) + DPRKN4ConstantCache(c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, + bp1, bp2, bp3, bp4, btilde1, btilde2, btilde3, btilde4, + bptilde1, bptilde2, bptilde3, bptilde4) +end +struct DPRKN5ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + c1::T2 + c2::T2 + c3::T2 + c4::T2 + c5::T2 + a21::T + a31::T + a32::T + a41::T + # a42::T + a43::T + a51::T + # a52::T + a53::T + a54::T + a61::T + # a62::T + a63::T + a64::T + a65::T + b1::T + # b2::T + b3::T + b4::T + b5::T + # b6::T + bp1::T # bp denotes bprime + # bp2::T + bp3::T + bp4::T + bp5::T + bp6::T + btilde1::T + # btilde2::T + btilde3::T + btilde4::T + btilde5::T + # btilde6::T + bptilde1::T + # bptilde2::T + bptilde3::T + bptilde4::T + bptilde5::T + bptilde6::T +end + +function DPRKN5ConstantCache(T::Type, T2::Type) + c1 = convert(T2, 1 // 8) + c2 = convert(T2, 1 // 4) + c3 = convert(T2, 1 // 2) + c4 = convert(T2, 3 // 4) + c5 = convert(T2, 1) + a21 = convert(T, 1 // 128) + a31 = convert(T, 1 // 96) + a32 = convert(T, 1 // 48) + a41 = convert(T, 1 // 24) + # a42 = convert(T, 0) + a43 = convert(T, 1 // 12) + a51 = convert(T, 9 // 128) + # a52 = convert(T, 0) + a53 = convert(T, 9 // 64) + a54 = convert(T, 9 // 128) + a61 = convert(T, 7 // 90) + # a62 = convert(T, 0) + a63 = convert(T, 4 // 15) + a64 = convert(T, 1 // 15) + a65 = convert(T, 4 // 45) + b1 = convert(T, 7 // 90) + # b2 = convert(T,0) + b3 = convert(T, 4 // 15) + b4 = convert(T, 1 // 15) + b5 = convert(T, 4 // 45) + # b6 = convert(T, 0) + bp1 = convert(T, 7 // 90) + # bp2 = convert(T,0) + bp3 = convert(T, 16 // 45) + bp4 = convert(T, 2 // 15) + bp5 = convert(T, 16 // 45) + bp6 = convert(T, 7 // 90) + btilde1 = convert(T, 7 // 90 - 1 // 6) + # btilde2 = convert(T,0) + btilde3 = convert(T, 4 // 15) + btilde4 = convert(T, 1 // 15 - 1 // 3) + btilde5 = convert(T, 4 // 45) + #btilde6 = convert(T, 0) + bptilde1 = convert(T, 7 // 90) + # bptilde2 = convert(T,0) + bptilde3 = convert(T, 16 // 45 - 2 // 3) + bptilde4 = convert(T, 2 // 15 + 1 // 3) + bptilde5 = convert(T, 16 // 45 - 2 // 3) + bptilde6 = convert(T, 7 // 90) + DPRKN5ConstantCache(c1, c2, c3, c4, c5, a21, a31, a32, a41, a43, a51, + a53, a54, a61, a63, a64, a65, b1, b3, b4, b5, bp1, + bp3, bp4, bp5, bp6, btilde1, btilde3, btilde4, btilde5, + bptilde1, bptilde3, bptilde4, bptilde5, bptilde6) +end + +function DPRKN5ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + c1 = convert(T2, 0.125) + c2 = convert(T2, 0.25) + c3 = convert(T2, 0.5) + c4 = convert(T2, 0.75) + c5 = convert(T2, 1.0) + a21 = convert(T, 1 // 128) + a31 = convert(T, 1 // 96) + a32 = convert(T, 1 // 48) + a41 = convert(T, 1 // 24) + a43 = convert(T, 1 // 12) + a51 = convert(T, 7 // 90) + a53 = convert(T, 4 // 15) + a54 = convert(T, 1 // 15) + a61 = convert(T, 0.07777777777777778) + a63 = convert(T, 0.26666666666666666) + a64 = convert(T, 0.06666666666666667) + a65 = convert(T, 0.08888888888888889) + b1 = convert(T, 0.07777777777777778) + b3 = convert(T, 0.26666666666666666) + b4 = convert(T, 0.06666666666666667) + b5 = convert(T, 0.08888888888888889) + bp1 = convert(T, 0.07777777777777778) + bp3 = convert(T, 0.35555555555555557) + bp4 = convert(T, 0.13333333333333333) + bp5 = convert(T, 0.35555555555555557) + bp6 = convert(T, 0.07777777777777778) + btilde1 = convert(T, -0.08888888888888888) + btilde3 = convert(T, 0.26666666666666666) + btilde4 = convert(T, -0.26666666666666666) + btilde5 = convert(T, 0.08888888888888889) + bptilde1 = convert(T, 0.07777777777777778) + bptilde3 = convert(T, -0.31111111111111106) + bptilde4 = convert(T, 0.4666666666666667) + bptilde5 = convert(T, -0.31111111111111106) + bptilde6 = convert(T, 0.07777777777777778) + DPRKN5ConstantCache(c1, c2, c3, c4, c5, a21, a31, a32, a41, a43, a51, + a53, a54, a61, a63, a64, a65, b1, b3, b4, b5, bp1, + bp3, bp4, bp5, bp6, btilde1, btilde3, btilde4, btilde5, + bptilde1, bptilde3, bptilde4, bptilde5, bptilde6) +end + +struct DPRKN6ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + c1::T2 + c2::T2 + c3::T2 + c4::T2 + c5::T2 + a21::T + a31::T + a32::T + a41::T + a42::T + a43::T + a51::T + a52::T + a53::T + a54::T + a61::T + # a62::T + a63::T + a64::T + a65::T + b1::T + # b2::T + b3::T + b4::T + b5::T + # b6::T + bp1::T # bp denotes bprime + # bp2::T + bp3::T + bp4::T + bp5::T + bp6::T + btilde1::T + btilde2::T + btilde3::T + btilde4::T + btilde5::T + # btilde6::T + bptilde1::T + # bptilde2::T + bptilde3::T + bptilde4::T + bptilde5::T + bptilde6::T + r14::T + r13::T + r12::T + r11::T + r10::T + r34::T + r33::T + r32::T + r31::T + r44::T + r43::T + r42::T + r41::T + r54::T + r53::T + r52::T + r51::T + r64::T + r63::T + r62::T + r61::T + rp14::T + rp13::T + rp12::T + rp11::T + rp10::T + rp34::T + rp33::T + rp32::T + rp31::T + rp44::T + rp43::T + rp42::T + rp41::T + rp54::T + rp53::T + rp52::T + rp51::T + rp64::T + rp63::T + rp62::T + rp61::T +end + +function DPRKN6ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + c1 = convert(T2, 0.12929590313670442) + c2 = convert(T2, 0.25859180627340883) + c3 = convert(T2, 0.67029708261548) + c4 = convert(T2, 0.9) + c5 = convert(T2, 1.0) + a21 = convert(T, 0.008358715283968025) + a31 = convert(T, 0.011144953711957367) + a32 = convert(T, 0.022289907423914734) + a41 = convert(T, 0.1454747428010918) + a42 = convert(T, -0.22986064052264749) + a43 = convert(T, 0.3090349872029675) + a51 = convert(T, -0.20766826295078997) + a52 = convert(T, 0.6863667842925143) + a53 = convert(T, -0.19954927787234925) + a54 = convert(T, 0.12585075653062489) + a61 = convert(T, 0.07811016144349478) + a63 = convert(T, 0.2882917411897668) + a64 = convert(T, 0.12242553717457041) + a65 = convert(T, 0.011172560192168035) + b1 = convert(T, 0.07811016144349478) + b3 = convert(T, 0.2882917411897668) + b4 = convert(T, 0.12242553717457041) + b5 = convert(T, 0.011172560192168035) + bp1 = convert(T, 0.07811016144349478) + bp3 = convert(T, 0.3888434787059826) + bp4 = convert(T, 0.3713207579288423) + bp5 = convert(T, 0.11172560192168035) + bp6 = convert(T, 0.05) + btilde1 = convert(T, -0.9807490989269235) + btilde2 = convert(T, 2.406751371924452) + btilde3 = convert(T, -1.559600370364267) + btilde4 = convert(T, 0.12242553717457041) + btilde5 = convert(T, 0.011172560192168035) + bptilde1 = convert(T, 0.023504273504273504) + bptilde3 = convert(T, -0.07242330719764424) + bptilde4 = convert(T, 0.17543989844952962) + bptilde5 = convert(T, -0.2765208647561589) + bptilde6 = convert(T, 0.15) + r14 = convert(T, 0.21367521367521367) + r13 = convert(T, -0.9066951566951567) + r12 = convert(T, 1.5161443494776827) + r11 = convert(T, -1.245014245014245) + r10 = convert(T, 0.5) + r34 = convert(T, -0.6583937017967658) + r33 = convert(T, 2.5384011164109506) + r32 = convert(T, -3.577652872294921) + r31 = convert(T, 1.9859371988705032) + r44 = convert(T, 1.5949081677229964) + r43 = convert(T, -5.164133553908094) + r42 = convert(T, 5.547586751052329) + r41 = convert(T, -1.8559358276926614) + r54 = convert(T, -2.513826043237808) + r53 = convert(T, 7.273336685101391) + r52 = convert(T, -6.926987319144182) + r51 = convert(T, 2.178649237472767) + r64 = convert(T, 1.3636363636363635) + r63 = convert(T, -3.7409090909090907) + r62 = convert(T, 3.440909090909091) + r61 = convert(T, -1.0636363636363637) + rp14 = convert(T, 1.2820512820512822) + rp13 = convert(T, -4.533475783475783) + rp12 = convert(T, 6.064577397910731) + rp11 = convert(T, -3.735042735042735) + rp10 = convert(T, 1) + rp34 = convert(T, -3.950362210780595) + rp33 = convert(T, 12.692005582054751) + rp32 = convert(T, -14.310611489179683) + rp31 = convert(T, 5.95781159661151) + rp44 = convert(T, 9.56944900633798) + rp43 = convert(T, -25.820667769540467) + rp42 = convert(T, 22.190347004209315) + rp41 = convert(T, -5.567807483077984) + rp54 = convert(T, -15.082956259426847) + rp53 = convert(T, 36.366683425506956) + rp52 = convert(T, -27.707949276576727) + rp51 = convert(T, 6.5359477124183005) + rp64 = convert(T, 8.181818181818182) + rp63 = convert(T, -18.704545454545453) + rp62 = convert(T, 13.763636363636364) + rp61 = convert(T, -3.190909090909091) + DPRKN6ConstantCache(c1, c2, c3, c4, c5, a21, a31, a32, a41, a42, a43, a51, + a52, a53, a54, a61, a63, a64, a65, b1, b3, b4, b5, bp1, + bp3, bp4, bp5, bp6, btilde1, btilde2, btilde3, btilde4, + btilde5, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6, + r14, r13, r12, r11, r10, r34, r33, r32, r31, r44, r43, r42, r41, + r54, + r53, r52, r51, r64, r63, r62, r61, rp14, rp13, rp12, rp11, rp10, + rp34, + rp33, rp32, rp31, rp44, rp43, rp42, rp41, rp54, rp53, rp52, rp51, + rp64, rp63, rp62, rp61) +end + +function DPRKN6ConstantCache(T::Type, T2::Type) + R = sqrt(big(8581)) + c1 = convert(T2, (209 - R) / 900) + c2 = convert(T2, (209 - R) / 450) + c3 = convert(T2, (209 + R) / 450) + c4 = convert(T2, 9 // 10) + c5 = convert(T2, 1) + a21 = convert(T, (26131 - 209R) / 81_0000) + a31 = convert(T, (26131 - 209R) / 60_7500) + a32 = convert(T, (26131 - 209R) / 30_3750) + a41 = convert(T, (980403512254 + 7781688431R) / 116944_6992_1875) + a42 = convert(T, -(126288_4486208 + 153854_81287R) / 116944_6992_1875) + a43 = convert(T, (7166_233_891_441 + 786_945_632_99R) / 46_777_879_687_500) + a51 = convert(T, -9(329260 + 3181R) / 2704_0000) + a52 = convert(T, 27(35129 + 3331R) / 1352_0000) + a53 = convert(T, -27(554358343 + 31040327R) / 46406048_0000) + a54 = convert(T, 153(8555_257 - 67973R) / 274592_0000) + a61 = convert(T, 329 // 4212) + # a62 = convert(T,0) + a63 = convert(T, (8411_9543 + 366_727R) / 4096_22616) + a64 = convert(T, (8411_9543 - 366_727R) / 4096_22616) + a65 = convert(T, 200 // 17901) + b1 = convert(T, 329 // 4212) + # b2 = convert(T,0) + b3 = a63 + b4 = a64 + b5 = convert(T, 200 // 17901) + # b6 = convert(T,0) + bp1 = b1 + # bp2 = b2 + bp3 = convert(T, (389225579 + 96856R) / 10_2405_6540) + bp4 = convert(T, (389225579 - 96856R) / 10_2405_6540) + bp5 = convert(T, 2000 // 17901) + bp6 = convert(T, 1 // 20) + btilde1 = convert(T, 329 // 4212 - (2701 + 23R) / 4563) + btilde2 = convert(T, (9829 + 131R) / 9126) + btilde3 = convert(T, (8411_9543 + 366_727R) / 4096_22616 - 5(1798 + 17R) / 9126) + btilde4 = b4 + btilde5 = b5 + # btilde6 = convert(T,0) + bptilde1 = convert(T, 329 // 4212 - 115 // 2106) + # btildep2 = convert(T,0) + bptilde3 = convert(T, + (389225579 + 96856R) / 10_2405_6540 - + (8411_9543 + 366_727R) / 2560_14135) + bptilde4 = convert(T, + (389225579 - 96856R) / 10_2405_6540 - + (8411_9543 - 366_727R) / 2560_14135) + bptilde5 = convert(T, 2000 // 17901 - 6950 // 17901) + bptilde6 = convert(T, 1 // 20 + 1 // 10) + r14 = convert(T, 900 // 4212) + r13 = convert(T, -3819 // 4212) + r12 = convert(T, 6386 // 4212) + r11 = convert(T, -5244 // 4212) + r10 = convert(T, 2106 // 4212) + r34 = convert(T, 1800 * (5860823 - 152228R) / 22529243880) + r33 = convert(T, -6 * (4929647204 - 156109769R) / 22529243880) + r32 = convert(T, (22190560391 - 1109665151R) / 22529243880) + r31 = convert(T, 18 * (81356461 + 25954829R) / 22529243880) + r44 = convert(T, 1800 * (5860823 + 152228R) / 22529243880) + r43 = convert(T, -6 * (4929647204 + 156109769R) / 22529243880) + r42 = convert(T, (22190560391 + 1109665151R) / 22529243880) + r41 = convert(T, 18 * (81356461 - 25954829R) / 22529243880) + r54 = convert(T, -200 * 225 // 17901) + r53 = convert(T, 200 * 651 // 17901) + r52 = convert(T, -200 * 620 // 17901) + r51 = convert(T, 200 * 195 // 17901) + r64 = convert(T, 15 // 11) + r63 = convert(T, -823 // 220) + r62 = convert(T, 757 // 220) + r61 = convert(T, -117 // 110) + rp14 = convert(T, 5400 // 4212) + rp13 = convert(T, -19095 // 4212) + rp12 = convert(T, 25544 // 4212) + rp11 = convert(T, -15732 // 4212) + rp10 = convert(T, 1) + rp34 = convert(T, 5400 * (5860823 - 152228R) / 11264621940) + rp33 = convert(T, -15 * (4929647204 - 156109769R) / 11264621940) + rp32 = convert(T, 2 * (22190560391 - 1109665151R) / 11264621940) + rp31 = convert(T, 27 * (81356461 + 25954829R) / 11264621940) + rp44 = convert(T, 5400 * (5860823 + 152228R) / 11264621940) + rp43 = convert(T, -15 * (4929647204 + 156109769R) / 11264621940) + rp42 = convert(T, 2 * (22190560391 + 1109665151R) / 11264621940) + rp41 = convert(T, 27 * (81356461 - 25954829R) / 11264621940) + rp54 = convert(T, -1000 * 270 // 17901) + rp53 = convert(T, 1000 * 651 // 17901) + rp52 = convert(T, -1000 * 496 // 17901) + rp51 = convert(T, 1000 * 117 // 17901) + rp64 = convert(T, 1800 // 220) + rp63 = convert(T, -4115 // 220) + rp62 = convert(T, 3028 // 220) + rp61 = convert(T, -702 // 220) + DPRKN6ConstantCache(c1, c2, c3, c4, c5, a21, a31, a32, a41, a42, a43, a51, + a52, a53, a54, a61, a63, a64, a65, b1, b3, b4, b5, bp1, + bp3, bp4, bp5, bp6, btilde1, btilde2, btilde3, btilde4, + btilde5, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6, + r14, r13, r12, r11, r10, r34, r33, r32, r31, r44, r43, r42, r41, + r54, + r53, r52, r51, r64, r63, r62, r61, rp14, rp13, rp12, rp11, rp10, + rp34, + rp33, rp32, rp31, rp44, rp43, rp42, rp41, rp54, rp53, rp52, rp51, + rp64, rp63, rp62, rp61) +end + +struct DPRKN6FMConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + c1::T2 + c2::T2 + c3::T2 + c4::T2 + c5::T2 + a21::T + a31::T + a32::T + a41::T + a42::T + a43::T + a51::T + a52::T + a53::T + a54::T + a61::T + a62::T + a63::T + a64::T + a65::T + b1::T + b2::T + b3::T + b4::T + b5::T + # b6::T + bp1::T # bp denotes bprime + bp2::T + bp3::T + bp4::T + bp5::T + bp6::T + btilde1::T + btilde2::T + btilde3::T + btilde4::T + btilde5::T + # btilde6::T + bptilde1::T + bptilde2::T + bptilde3::T + bptilde4::T + bptilde5::T + # bptilde6::T +end + +function DPRKN6FMConstantCache(T::Type, T2::Type) + c1 = convert(T2, 1 // 10) + c2 = convert(T2, 3 // 10) + c3 = convert(T2, 7 // 10) + c4 = convert(T2, 17 // 25) + c5 = convert(T2, 1) + a21 = convert(T, 1 // 200) + a31 = convert(T, -1 // 2200) + a32 = convert(T, 1 // 22) + a41 = convert(T, 637 // 6600) + a42 = convert(T, -7 // 110) + a43 = convert(T, 7 // 33) + a51 = convert(T, 225437 // 1968750) + a52 = convert(T, -30073 // 281250) + a53 = convert(T, 65569 // 281250) + a54 = convert(T, -9367 // 984375) + a61 = convert(T, 151 // 2142) + a62 = convert(T, 5 // 116) + a63 = convert(T, 385 // 1368) + a64 = convert(T, 55 // 168) + a65 = convert(T, -6250 // 28101) + b1 = convert(T, 151 // 2142) + b2 = convert(T, 5 // 116) + b3 = convert(T, 385 // 1368) + b4 = convert(T, 55 // 168) + b5 = convert(T, -6250 // 28101) + # b6 = convert(T, 0) + bp1 = convert(T, 151 // 2142) + bp2 = convert(T, 25 // 522) + bp3 = convert(T, 275 // 684) + bp4 = convert(T, 275 // 252) + bp5 = convert(T, -78125 // 112404) + bp6 = convert(T, 1 // 12) + btilde1 = convert(T, 151 // 2142 - 1349 // 157500) + btilde2 = convert(T, 5 // 116 - 7873 // 50000) + btilde3 = convert(T, 385 // 1368 - 192199 // 900000) + btilde4 = convert(T, 55 // 168 - 521683 // 2100000) + btilde5 = convert(T, -6250 // 28101 + 16 // 125) + # btilde6 = convert(T, 0) + bptilde1 = convert(T, 151 // 2142 - 1349 // 157500) + bptilde2 = convert(T, 25 // 522 - 7873 // 45000) + bptilde3 = convert(T, 275 // 684 - 27457 // 90000) + bptilde4 = convert(T, 275 // 252 - 521683 // 630000) + bptilde5 = convert(T, -78125 // 112404 + 2 // 5) + # bptilde6 = convert(T, 0) + DPRKN6FMConstantCache(c1, c2, c3, c4, c5, a21, a31, a32, a41, a42, a43, a51, a52, + a53, a54, a61, a62, a63, a64, a65, b1, b2, b3, b4, b5, bp1, bp2, + bp3, bp4, bp5, bp6, btilde1, btilde2, btilde3, btilde4, btilde5, + bptilde1, bptilde2, bptilde3, bptilde4, bptilde5) +end + +function DPRKN6FMConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + c1 = convert(T2, 0.1) + c2 = convert(T2, 0.3) + c3 = convert(T2, 0.7) + c4 = convert(T2, 0.68) + c5 = convert(T2, 1.0) + a21 = convert(T, 0.005) + a31 = convert(T, -0.00045454545454545455) + a32 = convert(T, 0.045454545454545456) + a41 = convert(T, 0.09651515151515151) + a42 = convert(T, -0.06363636363636363) + a43 = convert(T, 0.21212121212121213) + a51 = convert(T, 0.11450768253968253) + a52 = convert(T, -0.10692622222222223) + a53 = convert(T, 0.23313422222222221) + a54 = convert(T, -0.00951568253968254) + a61 = convert(T, 0.07049486461251167) + a62 = convert(T, 0.04310344827586207) + a63 = convert(T, 0.2814327485380117) + a64 = convert(T, 0.3273809523809524) + a65 = convert(T, -0.22241201380733783) + b1 = convert(T, 0.07049486461251167) + b2 = convert(T, 0.04310344827586207) + b3 = convert(T, 0.2814327485380117) + b4 = convert(T, 0.3273809523809524) + b5 = convert(T, -0.22241201380733783) + bp1 = convert(T, 0.07049486461251167) + bp2 = convert(T, 0.04789272030651341) + bp3 = convert(T, 0.402046783625731) + bp4 = convert(T, 1.0912698412698412) + bp5 = convert(T, -0.6950375431479306) + bp6 = convert(T, 0.08333333333333333) + btilde1 = convert(T, 0.061929785247432305) + btilde2 = convert(T, -0.11435655172413792) + btilde3 = convert(T, 0.06787830409356727) + btilde4 = convert(T, 0.07896047619047619) + btilde5 = convert(T, -0.09441201380733782) + bptilde1 = convert(T, 0.061929785247432305) + bptilde2 = convert(T, -0.12706283524904216) + bptilde3 = convert(T, 0.0969690058479532) + bptilde4 = convert(T, 0.26320158730158716) + bptilde5 = convert(T, -0.2950375431479306) + DPRKN6FMConstantCache(c1, c2, c3, c4, c5, a21, a31, a32, a41, a42, a43, a51, a52, + a53, a54, a61, a62, a63, a64, a65, b1, b2, b3, b4, b5, bp1, bp2, + bp3, bp4, bp5, bp6, btilde1, btilde2, btilde3, btilde4, btilde5, + bptilde1, bptilde2, bptilde3, bptilde4, bptilde5) +end + +struct DPRKN8ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + c1::T2 + c2::T2 + c3::T2 + c4::T2 + c5::T2 + c6::T2 + c7::T2 + c8::T2 + a21::T + a31::T + a32::T + a41::T + a42::T + a43::T + a51::T + a52::T + a53::T + a54::T + a61::T + a62::T + a63::T + a64::T + a65::T + a71::T + a72::T + a73::T + a74::T + a75::T + a76::T + a81::T + a82::T + a83::T + a84::T + a85::T + a86::T + a87::T + a91::T + # a92::T + a93::T + a94::T + a95::T + a96::T + a97::T + # a98::T + b1::T + # b2::T + b3::T + b4::T + b5::T + b6::T + b7::T + # b8::T + # b9::T + bp1::T + # bp2::T + bp3::T + bp4::T + bp5::T + bp6::T + bp7::T + bp8::T + # bp9::T + btilde1::T + # btilde2::T + btilde3::T + btilde4::T + btilde5::T + btilde6::T + btilde7::T + # btilde8::T + # btilde9::T + bptilde1::T + # bptilde2::T + bptilde3::T + bptilde4::T + bptilde5::T + bptilde6::T + bptilde7::T + bptilde8::T + bptilde9::T +end + +function DPRKN8ConstantCache(T::Type, T2::Type) + c1 = convert(T2, 1 // 20) + c2 = convert(T2, 1 // 10) + c3 = convert(T2, 3 // 10) + c4 = convert(T2, 1 // 2) + c5 = convert(T2, 7 // 10) + c6 = convert(T2, 9 // 10) + c7 = convert(T2, 1) + c8 = convert(T2, 1) + a21 = convert(T, 1 // 800) + a31 = convert(T, 1 // 600) + a32 = convert(T, 1 // 300) + a41 = convert(T, 9 // 200) + a42 = convert(T, -9 // 100) + a43 = convert(T, 9 // 100) + a51 = convert(T, -66701 // 197352) + a52 = convert(T, 28325 // 32892) + a53 = convert(T, -2665 // 5482) + a54 = convert(T, 2170 // 24669) + a61 = convert(T, 2270_15747 // 30425_1000) + a62 = convert(T, -5489_7451 // 30425_100) + a63 = convert(T, 12942_349 // 10141_700) + a64 = convert(T, -9499 // 304_251) + a65 = convert(T, 539 // 9250) + a71 = convert(T, -11318_91597 // 9017_89000) + a72 = convert(T, 4196_4921 // 1288_2700) + a73 = convert(T, -6663_147 // 3220_675) + a74 = convert(T, 270_954 // 644_135) + a75 = convert(T, -108 // 5875) + a76 = convert(T, 114 // 1645) + a81 = convert(T, 138_369_59 // 3667458) + a82 = convert(T, -177_314_50 // 1833729) + a83 = convert(T, 106_3919_505 // 15647_8208) + a84 = convert(T, -332_138_45 // 3911_9552) + a85 = convert(T, 133_35 // 285_44) + a86 = convert(T, -705 // 14272) + a87 = convert(T, 1645 // 57088) + a91 = convert(T, 223 // 7938) + # a92 = convert(T,0) + a93 = convert(T, 1175 // 8064) + a94 = convert(T, 925 // 6048) + a95 = convert(T, 41 // 448) + a96 = convert(T, 925 // 14112) + a97 = convert(T, 1175 // 72576) + # a98 = convert(T,0) + b1 = convert(T, 223 // 7938) + # b2 = convert(T,0) + b3 = convert(T, 1175 // 8064) + b4 = convert(T, 925 // 6048) + b5 = convert(T, 41 // 448) + b6 = convert(T, 925 // 14112) + b7 = convert(T, 1175 // 72576) + # b8 = convert(T,0) + # b9 = convert(T,0) + bp1 = convert(T, 223 // 7938) + # bp2 = convert(T,0) + bp3 = convert(T, 5875 // 36288) + bp4 = convert(T, 4625 // 21168) + bp5 = convert(T, 41 // 224) + bp6 = convert(T, 4625 // 21168) + bp7 = convert(T, 5875 // 36288) + bp8 = convert(T, 223 // 7938) + # bp9 = convert(T,0) + btilde1 = convert(T, 223 // 7938 - 7987_313 // 10994_1300) + # btilde2 = convert(T,0) + btilde3 = convert(T, 1175 // 8064 - 1610_737 // 4467_4560) + btilde4 = convert(T, 925 // 6048 - 10023_263 // 3350_5920) + btilde5 = convert(T, 41 // 448 + 497_221 // 1240_9600) + btilde6 = convert(T, 925 // 14112 - 1002_3263 // 7818_0480) + btilde7 = convert(T, 1175 // 72576 - 1610_737 // 40207_1040) + # btilde8 = convert(T,0) + # btilde9 = convert(T,0) + bptilde1 = convert(T, 223 // 7938 - 7987_313 // 10994_1300) + # bptilde2 = convert(T,0) + bptilde3 = convert(T, 5875 // 36288 - 1610_737 // 4020_7104) + bptilde4 = convert(T, 4625 // 21168 - 1002_3263 // 2345_4144) + bptilde5 = convert(T, 41 // 224 + 497_221 // 620_4800) + bptilde6 = convert(T, 4625 // 21168 - 1002_3263 // 2345_4144) + bptilde7 = convert(T, 5875 // 36288 - 1610_737 // 40207_104) + bptilde8 = convert(T, 223 // 7938 + 4251_941 // 5497_0650) + bptilde9 = convert(T, -3 // 20) + DPRKN8ConstantCache(c1, c2, c3, c4, c5, c6, c7, c8, a21, a31, a32, a41, a42, a43, a51, + a52, a53, a54, a61, a62, a63, a64, a65, a71, a72, a73, a74, a75, + a76, a81, a82, a83, a84, a85, a86, a87, a91, a93, a94, a95, a96, + a97, b1, b3, b4, b5, b6, b7, bp1, bp3, bp4, bp5, bp6, bp7, bp8, + btilde1, btilde3, btilde4, btilde5, btilde6, btilde7, bptilde1, + bptilde3, bptilde4, bptilde5, bptilde6, bptilde7, bptilde8, + bptilde9) +end + +function DPRKN8ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + DPRKN8ConstantCache(convert(T2, 0.05), + convert(T2, 0.1), + convert(T2, 0.3), + convert(T2, 0.5), + convert(T2, 0.7), + convert(T2, 0.9), + convert(T2, 1.0), + convert(T2, 1.0), + convert(T, 0.00125), + convert(T, 0.0016666666666666668), + convert(T, 0.0033333333333333335), + convert(T, 0.045), + convert(T, -0.09), + convert(T, 0.09), + convert(T, -0.3379798532571243), + convert(T, 0.8611516478170984), + convert(T, -0.48613644655235316), + convert(T, 0.0879646519923791), + convert(T, 0.7461462641043086), + convert(T, -1.804347430246737), + convert(T, 1.2761518285888953), + convert(T, -0.031220932716737166), + convert(T, 0.05827027027027027), + convert(T, -1.2551623461807584), + convert(T, 3.257463187064823), + convert(T, -2.068866619575089), + convert(T, 0.4206478455603251), + convert(T, -0.018382978723404254), + convert(T, 0.06930091185410335), + convert(T, 3.772901830095941), + convert(T, -9.669613121677195), + convert(T, 6.7991544547851674), + convert(T, -0.8490343907823893), + convert(T, 0.4671734865470852), + convert(T, -0.04939742152466368), + convert(T, 0.028815162556053812), + convert(T, 0.028092718568909044), + convert(T, 0.1457093253968254), + convert(T, 0.1529431216931217), + convert(T, 0.09151785714285714), + convert(T, 0.06554705215419501), + convert(T, 0.01618992504409171), + convert(T, 0.028092718568909044), + convert(T, 0.1457093253968254), + convert(T, 0.1529431216931217), + convert(T, 0.09151785714285714), + convert(T, 0.06554705215419501), + convert(T, 0.01618992504409171), + convert(T, 0.028092718568909044), + convert(T, 0.1618992504409171), + convert(T, 0.2184901738473167), + convert(T, 0.18303571428571427), + convert(T, 0.2184901738473167), + convert(T, 0.1618992504409171), + convert(T, 0.028092718568909044), + convert(T, -0.044557986852984274), + convert(T, 0.10965442077101599), + convert(T, -0.14620589436135464), + convert(T, 0.1315853049252192), + convert(T, -0.06265966901200913), + convert(T, 0.012183824530112887), + convert(T, -0.044557986852984274), + convert(T, 0.12183824530112887), + convert(T, -0.2088655633733638), + convert(T, 0.2631706098504384), + convert(T, -0.2088655633733638), + convert(T, 0.12183824530112887), + convert(T, 0.10544201314701572), + convert(T, -0.15)) +end + +struct DPRKN12ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + c1::T2 + c2::T2 + c3::T2 + c4::T2 + c5::T2 + c6::T2 + c7::T2 + c8::T2 + c9::T2 + c10::T2 + c11::T2 + c12::T2 + c13::T2 + c14::T2 + c15::T2 + c16::T2 + a21::T + a31::T + a32::T + a41::T + a42::T + a43::T + a51::T + # a52::T + a53::T + a54::T + a61::T + # a62::T + a63::T + a64::T + a65::T + a71::T + # a72::T + a73::T + a74::T + a75::T + a76::T + a81::T + # a82::T + # a83::T + a84::T + a85::T + a86::T + a87::T + a91::T + # a92::T + a93::T + a94::T + a95::T + a96::T + a97::T + a98::T + a101::T + # a102::T + a103::T + a104::T + a105::T + a106::T + a107::T + a108::T + a109::T + a111::T + # a112::T + a113::T + a114::T + a115::T + a116::T + a117::T + a118::T + a119::T + a1110::T + a121::T + # a122::T + a123::T + a124::T + a125::T + a126::T + a127::T + a128::T + a129::T + a1210::T + a1211::T + a131::T + # a132::T + a133::T + a134::T + a135::T + a136::T + a137::T + a138::T + a139::T + a1310::T + a1311::T + a1312::T + a141::T + # a142::T + a143::T + a144::T + a145::T + a146::T + a147::T + a148::T + a149::T + a1410::T + a1411::T + a1412::T + a1413::T + a151::T + # a152::T + a153::T + a154::T + a155::T + a156::T + a157::T + a158::T + a159::T + a1510::T + a1511::T + a1512::T + a1513::T + a1514::T + a161::T + # a162::T + a163::T + a164::T + a165::T + a166::T + a167::T + a168::T + a169::T + a1610::T + a1611::T + a1612::T + a1613::T + a1614::T + a1615::T + a171::T + # a172::T + a173::T + a174::T + a175::T + a176::T + a177::T + a178::T + a179::T + a1710::T + a1711::T + a1712::T + a1713::T + a1714::T + a1715::T + # a1716::T + b1::T + # b2::T + # b3::T + # b4::T + # b5::T + # b6::T + b7::T + b8::T + b9::T + b10::T + b11::T + b12::T + b13::T + b14::T + b15::T + # b16::T + # b17::T + bp1::T + # bp2::T + # bp3::T + # bp4::T + # bp5::T + # bp6::T + bp7::T + bp8::T + bp9::T + bp10::T + bp11::T + bp12::T + bp13::T + bp14::T + bp15::T + bp16::T + bp17::T + btilde1::T + # btilde2::T + # btilde3::T + # btilde4::T + # btilde5::T + # btilde6::T + btilde7::T + btilde8::T + btilde9::T + btilde10::T + btilde11::T + btilde12::T + btilde13::T + btilde14::T + btilde15::T + # btilde16::T + # btilde17::T + bptilde1::T + # bptilde2::T + # bptilde3::T + # bptilde4::T + # bptilde5::T + # bptilde6::T + bptilde7::T + bptilde8::T + bptilde9::T + bptilde10::T + bptilde11::T + bptilde12::T + bptilde13::T + bptilde14::T + bptilde15::T + bptilde16::T + bptilde17::T +end + +function DPRKN12ConstantCache(T::Type, T2::Type) + c1 = convert(T2, 1 // 50) + c2 = convert(T2, 1 // 25) + c3 = convert(T2, 1 // 10) + c4 = convert(T2, 2 // 15) + c5 = convert(T2, 4 // 25) + c6 = convert(T2, 1 // 20) + c7 = convert(T2, 1 // 5) + c8 = convert(T2, 1 // 4) + c9 = convert(T2, 1 // 3) + c10 = convert(T2, 1 // 2) + c11 = convert(T2, 5 // 9) + c12 = convert(T2, 3 // 4) + c13 = convert(T2, 6 // 7) + c14 = convert(T2, 8437 // 8926) + c15 = convert(T2, 1) + c16 = convert(T2, 1) + a21 = convert(T, 1 // 5000) + a31 = convert(T, 1 // 3750) + a32 = convert(T, 1 // 1875) + a41 = convert(T, 7 // 2400) + a42 = convert(T, -1 // 240) + a43 = convert(T, 1 // 160) + a51 = convert(T, 2 // 1215) + # a52 = convert(T,0) + a53 = convert(T, 4 // 729) + a54 = convert(T, 32 // 18225) + a61 = convert(T, 152 // 78125) + # a62 = convert(T,0) + a63 = convert(T, 1408 // 196875) + a64 = convert(T, 2048 // 703125) + a65 = convert(T, 432 // 546875) + a71 = convert(T, 29 // 51200) + # a72 = convert(T,0) + a73 = convert(T, 341 // 387072) + a74 = convert(T, -151 // 345600) + a75 = convert(T, 243 // 716800) + a76 = convert(T, -11 // 110592) + a81 = convert(T, 37 // 12000) + # a82 = convert(T,0) + # a83 = convert(T,0) + a84 = convert(T, 2 // 1125) + a85 = convert(T, 27 // 10000) + a86 = convert(T, 5 // 3168) + a87 = convert(T, 224 // 20625) + a91 = convert(T, 100467472123373 // 27511470744477696) + # a92 = convert(T,0) + a93 = convert(T, 101066550784375 // 25488568483854336) + a94 = convert(T, 49478218404275 // 15475202293768704) + a95 = convert(T, 21990175014231 // 2674726322379776) + a96 = convert(T, -3576386017671875 // 2723635603703291904) + a97 = convert(T, 16163228153 // 1654104722787) + a98 = convert(T, 38747524076705 // 10316801529179136) + a101 = convert(T, 62178936641284701329 // 16772293867250014666848) + # a102 = convert(T,0) + a103 = convert(T, 46108564356250 // 9072835168325103) + a104 = convert(T, 1522561724950 // 1296119309760729) + a105 = convert(T, -45978886013453735443 // 2174186242050927827184) + a106 = convert(T, 299403512366617849203125 // 4981371278573254356053856) + a107 = convert(T, 15571226634087127616 // 774466927638876610083) + a108 = convert(T, -133736375367792139885 // 4717207650164066625051) + a109 = convert(T, 7461389216 // 501451974639) + a111 = convert(T, 501256914705531962342417557181 // 14270506505142656332600844507392) + # a112 = convert(T,0) + a113 = convert(T, -1143766215625 // 132752960853408) + a114 = convert(T, -6864570325 // 1185294293334) + a115 = convert(T, 194348369382310456605879163404183 // 99893545535998594328205911551744) + a116 = convert(T, + -94634958447010580589908066176109375 // + 27549212808177898050085930321520256) + a117 = convert(T, -17006472665356285286219618514 // 155584463413110817059022733377) + a118 = convert(T, 33530528814694461893884349656345 // 14270506505142656332600844507392) + a119 = convert(T, -13439782155791134368 // 17777268379678341919) + a1110 = convert(T, 1441341768767571 // 13159456712985856) + a121 = convert(T, + parse(BigInt, "105854110734231079069010159870911189747853") // + parse(BigInt, "5156624149476760916008179453333467046288864")) + # a122 = convert(T,0) + a123 = convert(T, -144579793509250000 // 19842290513127000261) + a124 = convert(T, -101935644099967250 // 48188419817594143491) + a125 = convert(T, + parse(BigInt, "1585474394319811696785932424388196965") // + parse(BigInt, "1709257457318830856936350991091849456")) + a126 = convert(T, + parse(BigInt, "-843499776333774172853009613469456309715703125") // + parse(BigInt, "510505790798199330684809765880013237582597536")) + a127 = convert(T, + parse(BigInt, "-15057703799298260121553794369056896088480") // + parse(BigInt, "714327132646734138085088291809720015274157")) + a128 = convert(T, + parse(BigInt, "1749840442221344572962864758990584360232600") // + parse(BigInt, "1450300542040339007627300471250037606768743")) + a129 = convert(T, -11255775246405733991656178432768 // 27206626483067760480757659602193) + a1210 = convert(T, 669010348769579696 // 7368057640845834597) + a1211 = convert(T, 4598083098752 // 858563707934367) + a131 = convert(T, + parse(BigInt, "-1639758773684715326849438048667467886824967397") // + parse(BigInt, "11447568726280607813664651120965112496134881280")) + # a132 = convert(T,0) + a133 = convert(T, 3942453384375 // 314673684985856) + a134 = convert(T, 11737114158175 // 1719466921529856) + a135 = convert(T, + -23710715033675876683332701739887457 // + 4940189888325748664958546898558976) + a136 = convert(T, + parse(BigInt, "498150575499633273684774666731162498301909124515625") // + parse(BigInt, "87415924307623977386706008889913792042985180430336")) + a137 = convert(T, + parse(BigInt, "64881557768202140428371179540010005713998551") // + parse(BigInt, "85896810580242200654071863296887242202224768")) + a138 = convert(T, + parse(BigInt, "-2336309182318568698279006266321563486172654055") // + parse(BigInt, "18316109962048972501863441793544179993815810048")) + a139 = convert(T, + -493399374030747471036018890494175 // 251658285736841065236836942273664) + a1310 = convert(T, 418285003077108927126515545155 // 455369916679568501838710898688) + a1311 = convert(T, -15171723902781457 // 63532954684873728) + a1312 = convert(T, 1501203688494867 // 9434957026426880) + a141 = convert(T, + parse(BigInt, "34188549803371802849576690267872548602326398788953") // + parse(BigInt, "42496542183406636759747616530102745233754251202880")) + # a142 = convert(T,0) + a143 = convert(T, -18971246281693750 // 1138830954584356089) + a144 = convert(T, -59230464334542700 // 2765732318276293359) + a145 = convert(T, + parse(BigInt, "5147939981309774383134903239728881770043") // + parse(BigInt, "305929030949718561059100251282184099064")) + a146 = convert(T, + parse(BigInt, + "-3625720213550267723370658302114678215563058405229078120") // + parse(BigInt, "324512095420929759624784749347170583153994213035432256")) + a147 = convert(T, + parse(BigInt, "-60305503318319653518547439098565661266182518307816") // + parse(BigInt, "17856872599361492097414471889911176856851308259643")) + a148 = convert(T, + parse(BigInt, "-1036461878759982363277481306266144563833492657780645") // + parse(BigInt, "67994467493450618815596186448164392374006801924608")) + a149 = convert(T, + parse(BigInt, "128398681100219349205889126776607047000") // + parse(BigInt, "7473801441221286756994805323613917077")) + a1410 = convert(T, -49156374556350058671822606102117 // 9039888303968618912866414995904) + a1411 = convert(T, 12253036339964386945 // 8828680926314891943) + a1412 = convert(T, -647188390508758231059 // 1092148506009694282240) + a1413 = convert(T, 10915833599872 // 368729913707897) + a151 = convert(T, + parse(BigInt, + "-4939337286263213195547765488387521892799075623007291241961609516532") // + parse(BigInt, + "5408250052307451520718178852915698257207815452080611897685945761264")) + # a152 = convert(T,0) + a153 = convert(T, + 7588799849596321243074032368290625 // + parse(BigInt, "3147217749590114939838670370597819616")) + a154 = convert(T, + 16870665568420512953501332587233725 // + 955405388268427749593882076788623812) + a155 = convert(T, + parse(BigInt, + "-808642515918378014850308582271476014669568437579087796060") // + parse(BigInt, + "54447992506702009927986632715967769032585338753056786562")) + a156 = convert(T, + parse(BigInt, + "4610328329649866588704236006423149172472141907645890762410296050212") // + parse(BigInt, + "2135428689710103309390449198881479603148467934048051598947383737508")) + a157 = convert(T, + parse(BigInt, + "4159963831215576225909381034291748993887819834160487158570788681") // + parse(BigInt, + "1040533184037697645660563795162185415624171583014576682740416336")) + a158 = convert(T, + parse(BigInt, + "7381392142124351279433801934148706553542137071890521365664606664449580") // + parse(BigInt, + "259596002510757672994472584939953516345975141699869371088925396540699")) + a159 = convert(T, + parse(BigInt, + "-3336834334584052813468828675971359774694437229547862706920") // + parse(BigInt, + "132102862435303266640535426836147775872819092781208127980")) + a1510 = convert(T, + parse(BigInt, + "426619379967412086875039012957475466130081426048213491790") // + parse(BigInt, + "55162410119399855550108207148248549410926885937244965785")) + a1511 = convert(T, + parse(BigInt, "-630755628691078947314733435975762542732598947") // + parse(BigInt, "333503232300511886435069380727586592765317456")) + a1512 = convert(T, + parse(BigInt, "1522350657470125698997653827133798314909646891") // + parse(BigInt, "1520094067152619944607524353149267399623188480")) + a1513 = convert(T, + 305575414262755427083262606101825880 // + parse(BigInt, "65839748482572312891297405431209259829")) + a1514 = convert(T, + parse(BigInt, "256624643108055110568255672032710477795") // + parse(BigInt, "22874609758516552135947898572671559986304")) + a161 = convert(T, + parse(BigInt, + "-571597862947184314270186718640978947715678864684269066846") // + parse(BigInt, + "2077055064880303907616135969012720011907767004397744786340")) + # a162 = convert(T,0) + a163 = convert(T, 66981514290625 // 1829501741761029) + a164 = convert(T, 43495576635800 // 4443075658562499) + a165 = convert(T, + -127865248353371207265315478623656127 // + 10401415428935853634424440540325344) + a166 = convert(T, + parse(BigInt, + "1316565142658075739557231574080234814338066993483960326560") // + parse(BigInt, + "92668695535091962564795912774190176478892159517481612467")) + a167 = convert(T, + parse(BigInt, + "3881494143728609118531066904799685950051960514138645179820") // + parse(BigInt, + "2446349095978358868919950548516272963929118212742344026549")) + a168 = convert(T, + parse(BigInt, + "162922667049680755852592453758428194006198229544701786842910") // + parse(BigInt, + "66288722243155885736983218667976563740242178853010092663614")) + a169 = convert(T, + parse(BigInt, "-43986024977384568043684084266385512680544563954") // + parse(BigInt, "4922783599524658241955780540171948284522386185")) + a1610 = convert(T, + parse(BigInt, "285912200202585226675651763671663063668290787") // + parse(BigInt, "65371192072964016939690070594254881767827200")) + a1611 = convert(T, -6776815256667778089672518929 // 3693654613173093729492918708) + a1612 = convert(T, + 398946554885847045598775476868169 // 344154261237450078839899047372800) + a1613 = convert(T, -76630698033396272 // 4432017119727044925) + a1614 = convert(T, 28401702316003037 // 1469612686944417840) + a1615 = convert(T, + 66049942462586341419969330578128801 // + parse(BigInt, "12691068622536592094919763114637498325")) + a171 = convert(T, + parse(BigInt, + "83940754497395557520874219603241359529066454343054832302344735") // + parse(BigInt, + "64192596456995578553872477759926464976144474354415663868673233")) + # a172 = convert(T,0) + a173 = convert(T, 892543892035485503125 // 51401651664490002607536) + a174 = convert(T, -12732238157949399705325 // 686579204375687891972088) + a175 = convert(T, + parse(BigInt, "5290376174838819557032232941734928484252549") // + parse(BigInt, "357179779572898187570048915214361602000384")) + a176 = convert(T, + parse(BigInt, + "26873229338017506937199991804717456666650215387938173031932210") // + parse(BigInt, + "2863980005760296740624015421425947092438943496681472214589916")) + a177 = convert(T, + parse(BigInt, + "-1976497866818803305857417297961598735637414137241493515492778650") // + parse(BigInt, + "378029217824623393200881653405474359138017953416246216408422692")) + a178 = convert(T, + parse(BigInt, + "-1002860756304839757040188283199900676042073362417943601440986856950") // + parse(BigInt, + "20486915674765670626893195919603679319429068544972409068469849579")) + a179 = convert(T, + parse(BigInt, + "87398661196965758104117684348440686081062878816711392590") // + parse(BigInt, "2282122412587168891929052689609009868137678763277087160")) + a1710 = convert(T, + parse(BigInt, + "-7922242431969626895355493632206885458496418610471389") // + parse(BigInt, "748272134517487495468365669337985635214015258726400")) + a1711 = convert(T, + parse(BigInt, "2777643183645212014464950387658055285") // + parse(BigInt, "1141545470045611737197667093465955392")) + a1712 = convert(T, + parse(BigInt, "-1372659703515496442825084239977218110461") // + parse(BigInt, "1313121960368535725613950174847107891200")) + a1713 = convert(T, 6144417902699179309851023 // 85608793932459282773805825) + a1714 = convert(T, 140294243355138853053241 // 64884622846351585391642880) + a1715 = convert(T, + parse(BigInt, "168671028523891369934964082754523881107337") // + parse(BigInt, "24062875279623260368388427013982199424119600")) + # a1716 = convert(T,0) + b1 = convert(T, 63818747 // 5262156900) + # b2 = convert(T,0) + # b3 = convert(T,0) + # b4 = convert(T,0) + # b5 = convert(T,0) + # b6 = convert(T,0) + b7 = convert(T, 22555300000000 // 261366897038247) + b8 = convert(T, 1696514453125 // 6717619827072) + b9 = convert(T, -45359872 // 229764843) + b10 = convert(T, 19174962087 // 94371046000) + b11 = convert(T, -19310468 // 929468925) + b12 = convert(T, 16089185487681 // 146694672924800) + b13 = convert(T, 1592709632 // 41841694125) + b14 = convert(T, 52675701958271 // 4527711056573100) + b15 = convert(T, + parse(BigInt, "12540904472870916741199505796420811396") // + parse(BigInt, "2692319557780977037279406889319526430375")) + # b16 = convert(T,0) + # b17 = convert(T,0) + bp1 = convert(T, 63818747 // 5262156900) + # bp2 = convert(T,0) + # bp3 = convert(T,0) + # bp4 = convert(T,0) + # bp5 = convert(T,0) + # bp6 = convert(T,0) + bp7 = convert(T, 451106000000000 // 4965971043726693) + bp8 = convert(T, 8482572265625 // 26870479308288) + bp9 = convert(T, -181439488 // 689294529) + bp10 = convert(T, 57524886261 // 188742092000) + bp11 = convert(T, -38620936 // 929468925) + bp12 = convert(T, 144802669389129 // 586778691699200) + bp13 = convert(T, 6370838528 // 41841694125) + bp14 = convert(T, 368729913707897 // 4527711056573100) + bp15 = convert(T, + parse(BigInt, "111940113324845802831946788738852162520696") // + parse(BigInt, "1316544263754897771229629968877248424453375")) + bp16 = convert(T, -113178587 // 12362232960) + bp17 = convert(T, 1 // 40) + + btilde1 = convert(T, + Int64(63818747) // Int64(5262156900) - + Int64(27121957) // Int64(1594593000)) + # btilde2 = convert(T,0) + # btilde3 = convert(T,0) + # btilde4 = convert(T,0) + # btilde5 = convert(T,0) + # btilde6 = convert(T,0) + btilde7 = convert(T, + Int64(22555300000000) // Int64(261366897038247) - + Int64(4006163300000) // Int64(55441463008113)) + btilde8 = convert(T, + Int64(1696514453125) // Int64(6717619827072) - + Int64(9466403125) // Int64(25445529648)) + btilde9 = convert(T, + Int64(-45359872) // Int64(229764843) + + Int64(163199648) // Int64(406149975)) + btilde10 = convert(T, + Int64(19174962087) // Int64(94371046000) - + Int64(23359833) // Int64(69636250)) + btilde11 = convert(T, + Int64(-19310468) // Int64(929468925) + + Int64(18491714) // Int64(140828625)) + btilde12 = convert(T, + Int64(16089185487681) // Int64(146694672924800) - + Int64(11052304606701) // Int64(58344472186000)) + btilde13 = convert(T, + Int64(1592709632) // Int64(41841694125) - + Int64(1191129152) // Int64(44377554375)) + btilde14 = convert(T, + Int64(52675701958271) // Int64(4527711056573100) - + Int64(2033811086741) // Int64(124730332137000)) + btilde15 = convert(T, + parse(BigInt, "12540904472870916741199505796420811396") // + parse(BigInt, "2692319557780977037279406889319526430375") - + parse(BigInt, "3616943474975740389660406409450169802") // + parse(BigInt, "951830146690244407118982233597812374375")) + # btilde16 = convert(T,0) + # btilde17 = convert(T,0) + bptilde1 = convert(T, + Int64(63818747) // Int64(5262156900) - + Int64(27121957) // Int64(1594593000)) + # bptilde2 = convert(T,0) + # bptilde3 = convert(T,0) + # bptilde4 = convert(T,0) + # bptilde5 = convert(T,0) + # bptilde6 = convert(T,0) + bptilde7 = convert(T, + Int64(451106000000000) // Int64(4965971043726693) - + Int64(4217014000000) // Int64(55441463008113)) + bptilde8 = convert(T, + Int64(8482572265625) // Int64(26870479308288) - + Int64(47332015625) // Int64(101782118592)) + bptilde9 = convert(T, + Int64(-181439488) // Int64(689294529) + + Int64(652798592) // Int64(1218449925)) + bptilde10 = convert(T, + Int64(57524886261) // Int64(188742092000) - + Int64(70079499) // Int64(139272500)) + bptilde11 = convert(T, + Int64(-38620936) // Int64(929468925) + + Int64(36983428) // Int64(140828625)) + bptilde12 = convert(T, + Int64(144802669389129) // Int64(586778691699200) - + Int64(99470741460309) // Int64(233377888744000)) + bptilde13 = convert(T, + Int64(6370838528) // Int64(41841694125) - + Int64(4764516608) // Int64(44377554375)) + bptilde14 = convert(T, + Int64(368729913707897) // Int64(4527711056573100) - + Int64(14236677607187) // Int64(124730332137000)) + bptilde15 = convert(T, + parse(BigInt, "111940113324845802831946788738852162520696") // + parse(BigInt, "1316544263754897771229629968877248424453375") - + parse(BigInt, "198066487470143918516004831967805004004") // + parse(BigInt, "2855490440070733221356946700793437123125")) + bptilde16 = convert(T, Int64(-113178587) // Int64(12362232960) - Int64(1) // Int64(50)) + bptilde17 = convert(T, 1 // 40) + DPRKN12ConstantCache(c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, + c16, a21, a31, a32, a41, a42, a43, a51, a53, a54, a61, a63, a64, + a65, a71, a73, a74, a75, a76, a81, a84, a85, a86, a87, a91, a93, + a94, a95, a96, a97, a98, a101, a103, a104, a105, a106, a107, a108, + a109, a111, a113, a114, a115, a116, a117, a118, a119, a1110, a121, + a123, a124, a125, a126, a127, a128, a129, a1210, a1211, a131, a133, + a134, a135, a136, a137, a138, a139, a1310, a1311, a1312, a141, + a143, a144, a145, a146, a147, a148, a149, a1410, a1411, a1412, + a1413, a151, a153, a154, a155, a156, a157, a158, a159, a1510, + a1511, a1512, a1513, a1514, a161, a163, a164, a165, a166, a167, + a168, a169, a1610, a1611, a1612, a1613, a1614, a1615, a171, a173, + a174, a175, a176, a177, a178, a179, a1710, a1711, a1712, a1713, + a1714, a1715, b1, b7, b8, b9, b10, b11, b12, b13, b14, b15, bp1, + bp7, bp8, bp9, bp10, bp11, bp12, bp13, bp14, bp15, bp16, bp17, + btilde1, btilde7, btilde8, btilde9, btilde10, btilde11, btilde12, + btilde13, btilde14, btilde15, bptilde1, bptilde7, bptilde8, + bptilde9, bptilde10, bptilde11, bptilde12, bptilde13, bptilde14, + bptilde15, bptilde16, bptilde17) +end + +function DPRKN12ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + DPRKN12ConstantCache(convert(T2, 2.0e-2), + convert(T2, 4.0e-2), + convert(T2, 1.0e-1), + convert(T2, 1.33333333333333333333333333333e-1), + convert(T2, 1.6e-1), + convert(T2, 5.0e-2), + convert(T2, 2.0e-1), + convert(T2, 2.5e-1), + convert(T2, 3.33333333333333333333333333333e-1), + convert(T2, 5.0e-1), + convert(T2, 5.55555555555555555555555555556e-1), + convert(T2, 7.5e-1), + convert(T2, 8.57142857142857142857142857143e-1), + convert(T2, 9.45216222272014340129957427739e-1), + convert(T2, 1.0e0), + convert(T2, 1.0e0), + convert(T, 2.0e-4), + convert(T, 2.66666666666666666666666666667e-4), + convert(T, 5.33333333333333333333333333333e-4), + convert(T, 2.91666666666666666666666666667e-3), + convert(T, -4.16666666666666666666666666667e-3), + convert(T, 6.25e-3), + convert(T, 1.64609053497942386831275720165e-3), + convert(T, 5.48696844993141289437585733882e-3), + convert(T, 1.75582990397805212620027434842e-3), + convert(T, 1.9456e-3), + convert(T, 7.15174603174603174603174603175e-3), + convert(T, 2.91271111111111111111111111111e-3), + convert(T, 7.89942857142857142857142857143e-4), + convert(T, 5.6640625e-4), + convert(T, 8.80973048941798941798941798942e-4), + convert(T, -4.36921296296296296296296296296e-4), + convert(T, 3.39006696428571428571428571429e-4), + convert(T, -9.94646990740740740740740740741e-5), + convert(T, 3.08333333333333333333333333333e-3), + convert(T, 1.77777777777777777777777777778e-3), + convert(T, 2.7e-3), + convert(T, 1.57828282828282828282828282828e-3), + convert(T, 1.08606060606060606060606060606e-2), + convert(T, 3.65183937480112971375119150338e-3), + convert(T, 3.96517171407234306617557289807e-3), + convert(T, 3.19725826293062822350093426091e-3), + convert(T, 8.22146730685543536968701883401e-3), + convert(T, -1.31309269595723798362013884863e-3), + convert(T, 9.77158696806486781562609494147e-3), + convert(T, 3.75576906923283379487932641079e-3), + convert(T, 3.70724106871850081019565530521e-3), + convert(T, 5.08204585455528598076108163479e-3), + convert(T, 1.17470800217541204473569104943e-3), + convert(T, -2.11476299151269914996229766362e-2), + convert(T, 6.01046369810788081222573525136e-2), + convert(T, 2.01057347685061881846748708777e-2), + convert(T, -2.83507501229335808430366774368e-2), + convert(T, 1.48795689185819327555905582479e-2), + convert(T, 3.51253765607334415311308293052e-2), + convert(T, -8.61574919513847910340576078545e-3), + convert(T, -5.79144805100791652167632252471e-3), + convert(T, 1.94555482378261584239438810411e0), + convert(T, -3.43512386745651359636787167574e0), + convert(T, -1.09307011074752217583892572001e-1), + convert(T, 2.3496383118995166394320161088e0), + convert(T, -7.56009408687022978027190729778e-1), + convert(T, 1.09528972221569264246502018618e-1), + convert(T, 2.05277925374824966509720571672e-2), + convert(T, -7.28644676448017991778247943149e-3), + convert(T, -2.11535560796184024069259562549e-3), + convert(T, 9.27580796872352224256768033235e-1), + convert(T, -1.65228248442573667907302673325e0), + convert(T, -2.10795630056865698191914366913e-2), + convert(T, 1.20653643262078715447708832536e0), + convert(T, -4.13714477001066141324662463645e-1), + convert(T, 9.07987398280965375956795739516e-2), + convert(T, 5.35555260053398504916870658215e-3), + convert(T, -1.43240788755455150458921091632e-1), + convert(T, 1.25287037730918172778464480231e-2), + convert(T, 6.82601916396982712868112411737e-3), + convert(T, -4.79955539557438726550216254291e0), + convert(T, 5.69862504395194143379169794156e0), + convert(T, 7.55343036952364522249444028716e-1), + convert(T, -1.27554878582810837175400796542e-1), + convert(T, -1.96059260511173843289133255423e0), + convert(T, 9.18560905663526240976234285341e-1), + convert(T, -2.38800855052844310534827013402e-1), + convert(T, 1.59110813572342155138740170963e-1), + convert(T, 8.04501920552048948697230778134e-1), + convert(T, -1.66585270670112451778516268261e-2), + convert(T, -2.1415834042629734811731437191e-2), + convert(T, 1.68272359289624658702009353564e1), + convert(T, -1.11728353571760979267882984241e1), + convert(T, -3.37715929722632374148856475521e0), + convert(T, -1.52433266553608456461817682939e1), + convert(T, 1.71798357382154165620247684026e1), + convert(T, -5.43771923982399464535413738556e0), + convert(T, 1.38786716183646557551256778839e0), + convert(T, -5.92582773265281165347677029181e-1), + convert(T, 2.96038731712973527961592794552e-2), + convert(T, -9.13296766697358082096250482648e-1), + convert(T, 2.41127257578051783924489946102e-3), + convert(T, 1.76581226938617419820698839226e-2), + convert(T, -1.48516497797203838246128557088e1), + convert(T, 2.15897086700457560030782161561e0), + convert(T, 3.99791558311787990115282754337e0), + convert(T, 2.84341518002322318984542514988e1), + convert(T, -2.52593643549415984378843352235e1), + convert(T, 7.7338785423622373655340014114e0), + convert(T, -1.8913028948478674610382580129e0), + convert(T, 1.00148450702247178036685959248e0), + convert(T, 4.64119959910905190510518247052e-3), + convert(T, 1.12187550221489570339750499063e-2), + convert(T, -2.75196297205593938206065227039e-1), + convert(T, 3.66118887791549201342293285553e-2), + convert(T, 9.7895196882315626246509967162e-3), + convert(T, -1.2293062345886210304214726509e1), + convert(T, 1.42072264539379026942929665966e1), + convert(T, 1.58664769067895368322481964272e0), + convert(T, 2.45777353275959454390324346975e0), + convert(T, -8.93519369440327190552259086374e0), + convert(T, 4.37367273161340694839327077512e0), + convert(T, -1.83471817654494916304344410264e0), + convert(T, 1.15920852890614912078083198373e0), + convert(T, -1.72902531653839221518003422953e-2), + convert(T, 1.93259779044607666727649875324e-2), + convert(T, 5.20444293755499311184926401526e-3), + convert(T, 1.30763918474040575879994562983e0), + convert(T, 1.73641091897458418670879991296e-2), + convert(T, -1.8544456454265795024362115588e-2), + convert(T, 1.48115220328677268968478356223e1), + convert(T, 9.38317630848247090787922177126e0), + convert(T, -5.2284261999445422541474024553e0), + convert(T, -4.89512805258476508040093482743e1), + convert(T, 3.82970960343379225625583875836e1), + convert(T, -1.05873813369759797091619037505e1), + convert(T, 2.43323043762262763585119618787e0), + convert(T, -1.04534060425754442848652456513e0), + convert(T, 7.17732095086725945198184857508e-2), + convert(T, 2.16221097080827826905505320027e-3), + convert(T, 7.00959575960251423699282781988e-3), + convert(T, 0.012127868517185414), + convert(T, 0.08629746251568875), + convert(T, 0.2525469581187147), + convert(T, -0.1974186799326823), + convert(T, 0.2031869190789726), + convert(T, -0.020775808077714918), + convert(T, 0.10967804874502014), + convert(T, 0.038065132526466504), + convert(T, 0.01163406880432423), + convert(T, 0.0046580297040248785), + convert(T, 0.012127868517185414), + convert(T, 0.09083943422704079), + convert(T, 0.3156836976483934), + convert(T, -0.2632249065769097), + convert(T, 0.3047803786184589), + convert(T, -0.041551616155429835), + convert(T, 0.2467756096762953), + convert(T, 0.15226053010586602), + convert(T, 0.08143848163026961), + convert(T, 0.08502571193890811), + convert(T, -0.009155189630077963), + convert(T, 0.025), + convert(T, -0.004880833389821577), + convert(T, 0.014038126584857338), + convert(T, -0.11947921920803832), + convert(T, 0.20440246507662121), + convert(T, -0.1322681492223791), + convert(T, 0.11053069299761689), + convert(T, -0.07975385787102851), + convert(T, 0.011224330486437457), + convert(T, -0.004671596801593694), + convert(T, 0.0008580413473282841), + convert(T, -0.004880833389821577), + convert(T, 0.014776975352481408), + convert(T, -0.1493490240100479), + convert(T, 0.2725366201021616), + convert(T, -0.19840222383356862), + convert(T, 0.22106138599523378), + convert(T, -0.17944618020981415), + convert(T, 0.04489732194574983), + convert(T, -0.03270117761115586), + convert(T, 0.015662325288859434), + convert(T, -0.029155189630077964), + convert(T, 0.025)) +end diff --git a/src/tableaus/symplectic_tableaus.jl b/src/tableaus/symplectic_tableaus.jl new file mode 100644 index 0000000000..98676979c3 --- /dev/null +++ b/src/tableaus/symplectic_tableaus.jl @@ -0,0 +1,807 @@ +struct Symplectic2ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + a1::T + a2::T + b1::T + b2::T +end + +function PseudoVerletLeapfrogConstantCache(T, T2) + a1 = convert(T, 1) + a2 = convert(T, 0) + b1 = convert(T, 1 // 2) + b2 = convert(T, 1 // 2) + Symplectic2ConstantCache{T, T2}(a1, a2, b1, b2) +end + +function McAte2ConstantCache(T, T2) + a2 = convert(T, 1 - (1 / 2) * sqrt(convert(T, 2))) + a1 = convert(T, 1 - a2) + b2 = convert(T, 1 / (2 * (1 - a2))) + b1 = convert(T, 1 - b2) + Symplectic2ConstantCache{T, T2}(a1, a2, b1, b2) +end + +function VerletLeapfrogConstantCache(T, T2) + a1 = convert(T, 1 // 2) + a2 = convert(T, 1 // 2) + b1 = convert(T, 0) + b2 = convert(T, 1) + Symplectic2ConstantCache{T, T2}(a1, a2, b1, b2) +end + +struct Symplectic3ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + a1::T + a2::T + a3::T + b1::T + b2::T + b3::T +end + +function Ruth3ConstantCache(T, T2) + a1 = convert(T, 2 // 3) + a2 = convert(T, -2 // 3) + a3 = convert(T, 1) + b1 = convert(T, 7 // 24) + b2 = convert(T, 3 // 4) + b3 = convert(T, -1 // 24) + Symplectic3ConstantCache{T, T2}(a1, a2, a3, b1, b2, b3) +end + +function McAte3ConstantCache(T, T2) + a1 = convert(T, 0.9196615230173999) + a2 = convert(T, 0.25 / a1 - a1 / 2) + a3 = convert(T, 1 - a1 - a2) + b1 = convert(T, a3) + b2 = convert(T, a2) + b3 = convert(T, a1) + Symplectic3ConstantCache{T, T2}(a1, a2, a3, b1, b2, b3) +end + +struct Symplectic4ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + a1::T + a2::T + a3::T + a4::T + b1::T + b2::T + b3::T + b4::T +end + +function CandyRoz4ConstantCache(T, T2) + a1 = convert(T, (2 + T(2)^(1 // 3) + convert(T, 2)^(-1 // 3)) / 6) + a2 = convert(T, (1 - T(2)^(1 // 3) - convert(T, 2)^(-1 // 3)) / 6) + a3 = convert(T, a2) + a4 = convert(T, a1) + b1 = convert(T, 0) + b2 = convert(T, (2 - T(2)^(1 // 3))^-1) + b3 = convert(T, (1 - T(2)^(2 // 3))^-1) + b4 = convert(T, b2) + Symplectic4ConstantCache{T, T2}(a1, a2, a3, a4, b1, b2, b3, b4) +end + +function McAte4ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + a1 = convert(T, 0.515352837431122936) + a2 = convert(T, -0.085782019412973646) + a3 = convert(T, 0.441583023616466524) + a4 = convert(T, 0.128846158365384185) + b1 = convert(T, 0.134496199277431089) + b2 = convert(T, -0.224819803079420806) + b3 = convert(T, 0.756320000515668291) + b4 = convert(T, 0.334003603286321425) + Symplectic4ConstantCache{T, T2}(a1, a2, a3, a4, b1, b2, b3, b4) +end + +function McAte4ConstantCache(T::Type, T2::Type) + a1 = convert(T, big"0.515352837431122936") + a2 = convert(T, big"-0.085782019412973646") + a3 = convert(T, big" 0.441583023616466524") + a4 = convert(T, big" 0.128846158365384185") + b1 = convert(T, big" 0.134496199277431089") + b2 = convert(T, big"-0.224819803079420806") + b3 = convert(T, big" 0.756320000515668291") + b4 = convert(T, big" 0.334003603286321425") + Symplectic4ConstantCache{T, T2}(a1, a2, a3, a4, b1, b2, b3, b4) +end + +struct Symplectic45ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + a1::T + a2::T + a3::T + a4::T + a5::T + b1::T + b2::T + b3::T + b4::T + b5::T +end + +function CalvoSanz4ConstantCache(T, T2) + a1 = convert(T, 0.205177661542290) + a2 = convert(T, 0.403021281604210) + a3 = -convert(T, 0.12092087633891) + a4 = convert(T, 0.512721933192410) + a5 = convert(T, 0.0) + b1 = convert(T, 0.061758858135626) + b2 = convert(T, 0.33897802655364) + b3 = convert(T, 0.61479130717558) + b4 = -convert(T, 0.14054801465937) + b5 = convert(T, 0.12501982279453) + Symplectic45ConstantCache{T, T2}(a1, a2, a3, a4, a5, b1, b2, b3, b4, b5) +end + +# Broken +# http://epubs.siam.org/doi/pdf/10.1137/0916010 +# On the numerical integration of ordinary differential equations by symmetric composition methods +function McAte42ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + a1 = convert(T, 0.40518861839525227722) + a2 = convert(T, -0.28714404081652408900) + a3 = 1 - 2a1 - 2a2 + a4 = a2 + a5 = a1 + b1 = convert(T, -3 // 73) + b2 = convert(T, 17 // 59) + b3 = 1 - 2b1 - 2b2 + b4 = b2 + b5 = b1 + Symplectic45ConstantCache{T, T2}(a1, a2, a3, a4, a5, b1, b2, b3, b4, b5) +end + +function McAte42ConstantCache(T::Type, T2::Type) + a1 = convert(T, big"0.40518861839525227722") + a2 = convert(T, big"-0.28714404081652408900") + a3 = 1 - 2a1 - 2a2 + a4 = a2 + a5 = a1 + b1 = convert(T, -3 // 73) + b2 = convert(T, 17 // 59) + b3 = 1 - 2b1 - 2b2 + b4 = b2 + b5 = b1 + Symplectic45ConstantCache{T, T2}(a1, a2, a3, a4, a5, b1, b2, b3, b4, b5) +end + +struct Symplectic5ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + a1::T + a2::T + a3::T + a4::T + a5::T + a6::T + b1::T + b2::T + b3::T + b4::T + b5::T + b6::T +end + +function McAte5ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + a1 = convert(T, 0.339839625839110000) + a2 = convert(T, -0.088601336903027329) + a3 = convert(T, 0.5858564768259621188) + a4 = convert(T, -0.603039356536491888) + a5 = convert(T, 0.3235807965546976394) + a6 = convert(T, 0.4423637942197494587) + b1 = convert(T, 0.1193900292875672758) + b2 = convert(T, 0.6989273703824752308) + b3 = convert(T, -0.1713123582716007754) + b4 = convert(T, 0.4012695022513534480) + b5 = convert(T, 0.0107050818482359840) + b6 = convert(T, -0.0589796254980311632) + Symplectic5ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, b1, b2, b3, b4, b5, b6) +end + +function McAte5ConstantCache(T::Type, T2::Type) + a1 = convert(T, big"0.339839625839110000") + a2 = convert(T, big"-0.088601336903027329") + a3 = convert(T, big"0.5858564768259621188") + a4 = convert(T, big"-0.603039356536491888") + a5 = convert(T, big"0.3235807965546976394") + a6 = convert(T, big"0.4423637942197494587") + b1 = convert(T, big"0.1193900292875672758") + b2 = convert(T, big"0.6989273703824752308") + b3 = convert(T, big"-0.1713123582716007754") + b4 = convert(T, big"0.4012695022513534480") + b5 = convert(T, big"0.0107050818482359840") + b6 = convert(T, big"-0.0589796254980311632") + Symplectic5ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, b1, b2, b3, b4, b5, b6) +end + +struct Symplectic6ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + a1::T + a2::T + a3::T + a4::T + a5::T + a6::T + a7::T + a8::T + b1::T + b2::T + b3::T + b4::T + b5::T + b6::T + b7::T + b8::T +end + +function Yoshida6ConstantCache(T, T2) + a1 = convert(T, 0.78451361047756) + a2 = convert(T, 0.23557321335936) + a3 = convert(T, -1.1776799841789) + a4 = convert(T, 1.3151863206839) + a5 = convert(T, a3) + a6 = convert(T, a2) + a7 = convert(T, a1) + a8 = convert(T, 0.0) + b1 = a1 / 2 + b2 = convert(T, (a1 + a2) / 2) + b3 = convert(T, (a2 + a3) / 2) + b4 = convert(T, (a3 + a4) / 2) + b5 = convert(T, b4) + b6 = convert(T, b3) + b7 = convert(T, b2) + b8 = convert(T, b1) + Symplectic6ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, a7, a8, b1, b2, b3, b4, b5, b6, + b7, b8) +end + +struct Symplectic62ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + a1::T + a2::T + a3::T + a4::T + a5::T + a6::T + a7::T + a8::T + a9::T + a10::T + b1::T + b2::T + b3::T + b4::T + b5::T + b6::T + b7::T + b8::T + b9::T + b10::T +end + +function KahanLi6ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + a1 = convert(T, 0.39216144400731413927925056) + a2 = convert(T, 0.33259913678935943859974864) + a3 = convert(T, -0.70624617255763935980996482) + a4 = convert(T, 0.08221359629355080023149045) + a5 = convert(T, 0.79854399093482996339895035) + a6 = a4 + a7 = a3 + a8 = a2 + a9 = a1 + a10 = convert(T, 0) + b1 = convert(T, a1 / 2) + b2 = convert(T, (a1 + a2) / 2) + b3 = convert(T, (a2 + a3) / 2) + b4 = convert(T, (a3 + a4) / 2) + b5 = convert(T, (a4 + a5) / 2) + b6 = b5 + b7 = b4 + b8 = b3 + b9 = b2 + b10 = b1 + Symplectic62ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, b1, b2, b3, + b4, b5, b6, b7, b8, b9, b10) +end + +function KahanLi6ConstantCache(T::Type, T2::Type) + a1 = convert(T, big"0.39216144400731413927925056") + a2 = convert(T, big"0.33259913678935943859974864") + a3 = convert(T, big"-0.70624617255763935980996482") + a4 = convert(T, big"0.08221359629355080023149045") + a5 = convert(T, big"0.79854399093482996339895035") + a6 = a4 + a7 = a3 + a8 = a2 + a9 = a1 + a10 = convert(T, 0) + b1 = convert(T, a1 / 2) + b2 = convert(T, (a1 + a2) / 2) + b3 = convert(T, (a2 + a3) / 2) + b4 = convert(T, (a3 + a4) / 2) + b5 = convert(T, (a4 + a5) / 2) + b6 = b5 + b7 = b4 + b8 = b3 + b9 = b2 + b10 = b1 + Symplectic62ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, b1, b2, b3, + b4, b5, b6, b7, b8, b9, b10) +end + +struct McAte8ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + a1::T + a2::T + a3::T + a4::T + a5::T + a6::T + a7::T + a8::T + a9::T + a10::T + a11::T + a12::T + a13::T + a14::T + a15::T + a16::T + b1::T + b2::T + b3::T + b4::T + b5::T + b6::T + b7::T + b8::T + b9::T + b10::T + b11::T + b12::T + b13::T + b14::T + b15::T + b16::T +end + +function McAte8ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + a1 = convert(T, 0.74167036435061295344822780) + a2 = convert(T, -0.40910082580003159399730010) + a3 = convert(T, 0.19075471029623837995387626) + a4 = convert(T, -0.57386247111608226665638773) + a5 = convert(T, 0.29906418130365592384446354) + a6 = convert(T, 0.33462491824529818378495798) + a7 = convert(T, 0.31529309239676659663205666) + a8 = convert(T, -0.79688793935291635401978884) + a9 = a7 + a10 = a6 + a11 = a5 + a12 = a4 + a13 = a3 + a14 = a2 + a15 = a1 + a16 = convert(T, 0) + b1 = convert(T, a1 / 2) + b2 = convert(T, (a1 + a2) / 2) + b3 = convert(T, (a2 + a3) / 2) + b4 = convert(T, (a3 + a4) / 2) + b5 = convert(T, (a4 + a5) / 2) + b6 = convert(T, (a5 + a6) / 2) + b7 = convert(T, (a6 + a7) / 2) + b8 = convert(T, (a7 + a8) / 2) + b9 = b8 + b10 = b7 + b11 = b6 + b12 = b5 + b13 = b4 + b14 = b3 + b15 = b2 + b16 = b1 + McAte8ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, + a15, a16, + b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, + b15, b16) +end + +function McAte8ConstantCache(T::Type, T2::Type) + a1 = convert(T, big"0.74167036435061295344822780") + a2 = convert(T, big"-0.40910082580003159399730010") + a3 = convert(T, big"0.19075471029623837995387626") + a4 = convert(T, big"-0.57386247111608226665638773") + a5 = convert(T, big"0.29906418130365592384446354") + a6 = convert(T, big"0.33462491824529818378495798") + a7 = convert(T, big"0.31529309239676659663205666") + a8 = convert(T, big"-0.79688793935291635401978884") + a9 = a7 + a10 = a6 + a11 = a5 + a12 = a4 + a13 = a3 + a14 = a2 + a15 = a1 + a16 = convert(T, 0) + b1 = convert(T, a1 / 2) + b2 = convert(T, (a1 + a2) / 2) + b3 = convert(T, (a2 + a3) / 2) + b4 = convert(T, (a3 + a4) / 2) + b5 = convert(T, (a4 + a5) / 2) + b6 = convert(T, (a5 + a6) / 2) + b7 = convert(T, (a6 + a7) / 2) + b8 = convert(T, (a7 + a8) / 2) + b9 = b8 + b10 = b7 + b11 = b6 + b12 = b5 + b13 = b4 + b14 = b3 + b15 = b2 + b16 = b1 + McAte8ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, + a15, a16, + b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, + b15, b16) +end + +struct KahanLi8ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + a1::T + a2::T + a3::T + a4::T + a5::T + a6::T + a7::T + a8::T + a9::T + a10::T + a11::T + a12::T + a13::T + a14::T + a15::T + a16::T + a17::T + a18::T + b1::T + b2::T + b3::T + b4::T + b5::T + b6::T + b7::T + b8::T + b9::T + b10::T + b11::T + b12::T + b13::T + b14::T + b15::T + b16::T + b17::T + b18::T +end + +function KahanLi8ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + a1 = convert(T, 0.13020248308889008087881763) + a2 = convert(T, 0.56116298177510838456196441) + a3 = convert(T, -0.38947496264484728640807860) + a4 = convert(T, 0.15884190655515560089621075) + a5 = convert(T, -0.39590389413323757733623154) + a6 = convert(T, 0.18453964097831570709183254) + a7 = convert(T, 0.25837438768632204729397911) + a8 = convert(T, 0.29501172360931029887096624) + a9 = convert(T, -0.60550853383003451169892108) + a10 = a8 + a11 = a7 + a12 = a6 + a13 = a5 + a14 = a4 + a15 = a3 + a16 = a2 + a17 = a1 + a18 = convert(T, 0) + b1 = convert(T, a1 / 2) + b2 = convert(T, (a1 + a2) / 2) + b3 = convert(T, (a2 + a3) / 2) + b4 = convert(T, (a3 + a4) / 2) + b5 = convert(T, (a4 + a5) / 2) + b6 = convert(T, (a5 + a6) / 2) + b7 = convert(T, (a6 + a7) / 2) + b8 = convert(T, (a7 + a8) / 2) + b9 = convert(T, (a8 + a9) / 2) + b10 = b9 + b11 = b8 + b12 = b7 + b13 = b6 + b14 = b5 + b15 = b4 + b16 = b3 + b17 = b2 + b18 = b1 + KahanLi8ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, + a14, a15, a16, a17, a18, + b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, + b14, b15, b16, b17, b18) +end + +function KahanLi8ConstantCache(T::Type, T2::Type) + a1 = convert(T, big"0.13020248308889008087881763") + a2 = convert(T, big"0.56116298177510838456196441") + a3 = convert(T, big"-0.38947496264484728640807860") + a4 = convert(T, big"0.15884190655515560089621075") + a5 = convert(T, big"-0.39590389413323757733623154") + a6 = convert(T, big"0.18453964097831570709183254") + a7 = convert(T, big"0.25837438768632204729397911") + a8 = convert(T, big"0.29501172360931029887096624") + a9 = convert(T, big"-0.60550853383003451169892108") + a10 = a8 + a11 = a7 + a12 = a6 + a13 = a5 + a14 = a4 + a15 = a3 + a16 = a2 + a17 = a1 + a18 = convert(T, 0) + b1 = convert(T, a1 / 2) + b2 = convert(T, (a1 + a2) / 2) + b3 = convert(T, (a2 + a3) / 2) + b4 = convert(T, (a3 + a4) / 2) + b5 = convert(T, (a4 + a5) / 2) + b6 = convert(T, (a5 + a6) / 2) + b7 = convert(T, (a6 + a7) / 2) + b8 = convert(T, (a7 + a8) / 2) + b9 = convert(T, (a8 + a9) / 2) + b10 = b9 + b11 = b8 + b12 = b7 + b13 = b6 + b14 = b5 + b15 = b4 + b16 = b3 + b17 = b2 + b18 = b1 + KahanLi8ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, + a14, a15, a16, a17, a18, + b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, + b14, b15, b16, b17, b18) +end + +struct SofSpa10ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache + a1::T + a2::T + a3::T + a4::T + a5::T + a6::T + a7::T + a8::T + a9::T + a10::T + a11::T + a12::T + a13::T + a14::T + a15::T + a16::T + a17::T + a18::T + a19::T + a20::T + a21::T + a22::T + a23::T + a24::T + a25::T + a26::T + a27::T + a28::T + a29::T + a30::T + a31::T + a32::T + a33::T + a34::T + a35::T + a36::T + b1::T + b2::T + b3::T + b4::T + b5::T + b6::T + b7::T + b8::T + b9::T + b10::T + b11::T + b12::T + b13::T + b14::T + b15::T + b16::T + b17::T + b18::T + b19::T + b20::T + b21::T + b22::T + b23::T + b24::T + b25::T + b26::T + b27::T + b28::T + b29::T + b30::T + b31::T + b32::T + b33::T + b34::T + b35::T + b36::T +end + +function SofSpa10ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + a1 = convert(T, 0.07879572252168641926390768) + a2 = convert(T, 0.31309610341510852776481247) + a3 = convert(T, 0.02791838323507806610952027) + a4 = convert(T, -0.22959284159390709415121340) + a5 = convert(T, 0.13096206107716486317465686) + a6 = convert(T, -0.26973340565451071434460973) + a7 = convert(T, 0.07497334315589143566613711) + a8 = convert(T, 0.11199342399981020488957508) + a9 = convert(T, 0.36613344954622675119314812) + a10 = convert(T, -0.39910563013603589787862981) + a11 = convert(T, 0.10308739852747107731580277) + a12 = convert(T, 0.41143087395589023782070412) + a13 = convert(T, -0.00486636058313526176219566) + a14 = convert(T, -0.39203335370863990644808194) + a15 = convert(T, 0.05194250296244964703718290) + a16 = convert(T, 0.05066509075992449633587434) + a17 = convert(T, 0.04967437063972987905456880) + a18 = convert(T, 0.04931773575959453791768001) + a19 = a17 + a20 = a16 + a21 = a15 + a22 = a14 + a23 = a13 + a24 = a12 + a25 = a11 + a26 = a10 + a27 = a9 + a28 = a8 + a29 = a7 + a30 = a6 + a31 = a5 + a32 = a4 + a33 = a3 + a34 = a2 + a35 = a1 + a36 = convert(T, 0) + b1 = convert(T, a1 / 2) + b2 = convert(T, (a1 + a2) / 2) + b3 = convert(T, (a2 + a3) / 2) + b4 = convert(T, (a3 + a4) / 2) + b5 = convert(T, (a4 + a5) / 2) + b6 = convert(T, (a5 + a6) / 2) + b7 = convert(T, (a6 + a7) / 2) + b8 = convert(T, (a7 + a8) / 2) + b9 = convert(T, (a8 + a9) / 2) + b10 = convert(T, (a9 + a10) / 2) + b11 = convert(T, (a10 + a11) / 2) + b12 = convert(T, (a11 + a12) / 2) + b13 = convert(T, (a12 + a13) / 2) + b14 = convert(T, (a13 + a14) / 2) + b15 = convert(T, (a14 + a15) / 2) + b16 = convert(T, (a15 + a16) / 2) + b17 = convert(T, (a16 + a17) / 2) + b18 = convert(T, (a17 + a18) / 2) + b19 = b18 + b20 = b17 + b21 = b16 + b22 = b15 + b23 = b14 + b24 = b13 + b25 = b12 + b26 = b11 + b27 = b10 + b28 = b9 + b29 = b8 + b30 = b7 + b31 = b6 + b32 = b5 + b33 = b4 + b34 = b3 + b35 = b2 + b36 = b1 + SofSpa10ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, + a14, a15, a16, a17, a18, + a19, a20, a21, a22, a23, a24, a25, a26, a27, a28, a29, a30, + a31, a32, a33, a34, + a35, a36, + b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, + b14, b15, b16, b17, b18, + b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, + b31, b32, b33, b34, + b35, b36) +end + +function SofSpa10ConstantCache(T::Type, T2::Type) + a1 = convert(T, big"0.07879572252168641926390768") + a2 = convert(T, big"0.31309610341510852776481247") + a3 = convert(T, big"0.02791838323507806610952027") + a4 = convert(T, big"-0.22959284159390709415121340") + a5 = convert(T, big"0.13096206107716486317465686") + a6 = convert(T, big"-0.26973340565451071434460973") + a7 = convert(T, big"0.07497334315589143566613711") + a8 = convert(T, big"0.11199342399981020488957508") + a9 = convert(T, big"0.36613344954622675119314812") + a10 = convert(T, big"-0.39910563013603589787862981") + a11 = convert(T, big"0.10308739852747107731580277") + a12 = convert(T, big"0.41143087395589023782070412") + a13 = convert(T, big"-0.00486636058313526176219566") + a14 = convert(T, big"-0.39203335370863990644808194") + a15 = convert(T, big"0.05194250296244964703718290") + a16 = convert(T, big"0.05066509075992449633587434") + a17 = convert(T, big"0.04967437063972987905456880") + a18 = convert(T, big"0.04931773575959453791768001") + a19 = a17 + a20 = a16 + a21 = a15 + a22 = a14 + a23 = a13 + a24 = a12 + a25 = a11 + a26 = a10 + a27 = a9 + a28 = a8 + a29 = a7 + a30 = a6 + a31 = a5 + a32 = a4 + a33 = a3 + a34 = a2 + a35 = a1 + a36 = convert(T, 0) + b1 = convert(T, a1 / 2) + b2 = convert(T, (a1 + a2) / 2) + b3 = convert(T, (a2 + a3) / 2) + b4 = convert(T, (a3 + a4) / 2) + b5 = convert(T, (a4 + a5) / 2) + b6 = convert(T, (a5 + a6) / 2) + b7 = convert(T, (a6 + a7) / 2) + b8 = convert(T, (a7 + a8) / 2) + b9 = convert(T, (a8 + a9) / 2) + b10 = convert(T, (a9 + a10) / 2) + b11 = convert(T, (a10 + a11) / 2) + b12 = convert(T, (a11 + a12) / 2) + b13 = convert(T, (a12 + a13) / 2) + b14 = convert(T, (a13 + a14) / 2) + b15 = convert(T, (a14 + a15) / 2) + b16 = convert(T, (a15 + a16) / 2) + b17 = convert(T, (a16 + a17) / 2) + b18 = convert(T, (a17 + a18) / 2) + b19 = b18 + b20 = b17 + b21 = b16 + b22 = b15 + b23 = b14 + b24 = b13 + b25 = b12 + b26 = b11 + b27 = b10 + b28 = b9 + b29 = b8 + b30 = b7 + b31 = b6 + b32 = b5 + b33 = b4 + b34 = b3 + b35 = b2 + b36 = b1 + SofSpa10ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, + a14, a15, a16, a17, a18, + a19, a20, a21, a22, a23, a24, a25, a26, a27, a28, a29, a30, + a31, a32, a33, a34, + a35, a36, + b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, + b14, b15, b16, b17, b18, + b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, + b31, b32, b33, b34, + b35, b36) +end diff --git a/src/tableaus/verner_tableaus.jl b/src/tableaus/verner_tableaus.jl new file mode 100644 index 0000000000..1773305838 --- /dev/null +++ b/src/tableaus/verner_tableaus.jl @@ -0,0 +1,3894 @@ +## Vern6 +struct Vern6ExtraStages{T, T2} + c10::T2 + a1001::T + a1004::T + a1005::T + a1006::T + a1007::T + a1008::T + a1009::T + c11::T2 + a1101::T + a1104::T + a1105::T + a1106::T + a1107::T + a1108::T + a1109::T + a1110::T + c12::T2 + a1201::T + a1204::T + a1205::T + a1206::T + a1207::T + a1208::T + a1209::T + a1210::T + a1211::T +end + +function Vern6ExtraStages(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + # Extra stages for Order 5 + c10 = convert(T2, 0.5) + a1001 = convert(T, 0.016524159013572806) + a1004 = convert(T, 0.3053128187514179) + a1005 = convert(T, 0.2071200938201979) + a1006 = convert(T, -1.293879140655123) + a1007 = convert(T, 57.11988411588149) + a1008 = convert(T, -55.87979207510932) + a1009 = convert(T, 0.024830028297766014) + # Extra stages for Order 6 + c11 = convert(T2, 0.828) + a1101 = convert(T, 0.038150081818627744) + a1104 = convert(T, 0.2502358252513705) + a1105 = convert(T, 0.3249441447817608) + a1106 = convert(T, 1.8224606658327962) + a1107 = convert(T, -67.7137233269262) + a1108 = convert(T, 66.03587911808127) + a1109 = convert(T, -0.0363881087495127) + a1110 = convert(T, 0.106441599909888) + c12 = convert(T2, 0.28) + a1201 = convert(T, 0.11178168039666012) + a1204 = convert(T, 0.025757505109345213) + a1205 = convert(T, 3.785140856363646) + a1206 = convert(T, 92.34088993695727) + a1207 = convert(T, -3819.461508432344) + a1208 = convert(T, 3732.492711530704) + a1209 = convert(T, -1.0756940209963033) + a1210 = convert(T, -3.231539970732086) + a1211 = convert(T, -4.707539085458635) + + Vern6ExtraStages(c10, a1001, a1004, a1005, a1006, a1007, a1008, a1009, c11, a1101, + a1104, a1105, a1106, a1107, a1108, a1109, a1110, c12, a1201, a1204, + a1205, a1206, a1207, a1208, a1209, a1210, a1211) +end + +function Vern6ExtraStages(T, T2) + # Extra stages for Order 5 + c10 = convert(T2, 1 // 2) + a1001 = convert(T, + BigInt(35289331988986254405692535758830683) // + BigInt(2135620454874580332949729350544993288)) + a1004 = convert(T, + BigInt(313937014583068512255490687992212890625) // + BigInt(1028247080705354654473994781524199691557)) + a1005 = convert(T, + BigInt(1309307687253621245836726130885318359375) // + BigInt(6321490412177191231557635904400612215708)) + a1006 = convert(T, + -BigInt(35295844079877524186147726060781875) // + BigInt(27279088881521314684841470427640876)) + a1007 = convert(T, + BigInt(794353492803973228770716697389421875) // + BigInt(13906777037439977359946774228636361)) + a1008 = convert(T, + -BigInt(15228408956329265381787438679500067) // + BigInt(272520859345009876882656783678732)) + a1009 = convert(T, 28587810357600962662801 / 1151340224617184234295192) + # Extra stages for Order 6 + c11 = convert(T2, 207 // 250) + a1101 = convert(T, + BigInt(2486392061981208591025761263164027224438868971) // + BigInt(65173964076983042387381877152862343994140625000)) + a1104 = convert(T, + BigInt(2330654500023704838558579323179918419669) // + BigInt(9313832252765893609365894760182968220625)) + a1105 = convert(T, + BigInt(5283259505481013273874688940942473187741) // + BigInt(16258977397575080328080339260289640472500)) + a1106 = convert(T, + BigInt(9989685106081485386057729811605187743723) // + BigInt(5481427003263510055949691042076757812500)) + a1107 = convert(T, + -BigInt(65815640423883764662985178413751186161) // + BigInt(971969007022721623945108012714453125)) + a1108 = convert(T, + BigInt(183066350554023250298437927498791289370414247) // + BigInt(2772225538584491748887703284492309570312500)) + a1109 = convert(T, + -426178927623072052719640507155669 // + 11712038417736656029207275390625000) + a1110 = convert(T, 3248339841 // 30517578125) + c12 = convert(T2, 7 // 25) + a1201 = convert(T, + BigInt(4676747786898097735038451956075910033997933945857) // + BigInt(41838231186922043164464169766109251031526972656250)) + a1204 = convert(T, + BigInt(1320032412954312695441306548681592444623240) // + BigInt(51248457773784347881352490499724836575577977)) + a1205 = convert(T, + BigInt(2087002134582726310861746540254017903014374710) // + BigInt(551367099344274428347227263044005314054687829)) + a1206 = convert(T, + BigInt(3432932836484348829479408524345545011748570706) // + BigInt(37176735450871998946806722732624135633015625)) + a1207 = convert(T, + -BigInt(2316434358511265475362584844804601519943610264) // + BigInt(606481922490173339581866127622363581143375)) + a1208 = convert(T, + BigInt(82514605285282414051716141603447021470923168793) // + BigInt(22107104196177512751528507591142367597656250)) + a1209 = convert(T, + -BigInt(7560161019374651900153317984708038834) // + BigInt(7028170531590816328729091157353515625)) + a1210 = convert(T, + -BigInt(21655450552377696842870155771710589332) // + BigInt(6701278878958685336695179940732421875)) + a1211 = convert(T, + -3194830887993202085244614477336220 // + 678662636676110315314332975245759) + + Vern6ExtraStages(c10, a1001, a1004, a1005, a1006, a1007, a1008, a1009, c11, a1101, + a1104, a1105, a1106, a1107, a1108, a1109, a1110, c12, a1201, a1204, + a1205, a1206, a1207, a1208, a1209, a1210, a1211) +end + +""" +Coefficients for the polynomial +bᵢΘ = ri1*Θ + ri2*Θ^2 + ri3*Θ^3 + ... +""" +struct Vern6InterpolationCoefficients{T} + r011::T + r012::T + r013::T + r014::T + r015::T + r016::T + r042::T + r043::T + r044::T + r045::T + r046::T + r052::T + r053::T + r054::T + r055::T + r056::T + r062::T + r063::T + r064::T + r065::T + r066::T + r072::T + r073::T + r074::T + r075::T + r076::T + r082::T + r083::T + r084::T + r085::T + r086::T + r092::T + r093::T + r094::T + r095::T + r096::T + r102::T + r103::T + r104::T + r105::T + r106::T + r112::T + r113::T + r114::T + r115::T + r116::T + r122::T + r123::T + r124::T + r125::T + r126::T +end + +function Vern6InterpolationCoefficients(T::Type{<:CompiledFloats}) + r011 = convert(T, 1) + r012 = convert(T, -7.778593856495576) + r013 = convert(T, 27.0524385722671) + r014 = convert(T, -45.780190114576975) + r015 = convert(T, 36.723777410436384) + r016 = convert(T, -11.183042432947357) + r042 = convert(T, 16.632102138279762) + r043 = convert(T, -86.25583404770623) + r044 = convert(T, 171.73305461826962) + r045 = convert(T, -149.67744091315947) + r046 = convert(T, 47.826380659879696) + r052 = convert(T, 27.10835046149758) + r053 = convert(T, -140.58676162962996) + r054 = convert(T, 279.90447579689163) + r055 = convert(T, -243.95644583707966) + r056 = convert(T, 77.95131832728772) + r062 = convert(T, 283.70753264670356) + r063 = convert(T, -1471.3371557366656) + r064 = convert(T, 2929.3928569314394) + r065 = convert(T, -2553.17199842168) + r066 = convert(T, 815.8141610498723) + r072 = convert(T, -11365.512865164834) + r073 = convert(T, 58942.74718938947) + r074 = convert(T, -117353.43045697975) + r075 = convert(T, 102281.77209230464) + r076 = convert(T, -32682.059078573824) + r082 = convert(T, 11100.250191051131) + r083 = convert(T, -57567.067013355576) + r084 = convert(T, 114614.48808378985) + r085 = convert(T, -99894.591091309) + r086 = convert(T, 31919.283963225014) + r092 = convert(T, -3.0022825150732126) + r093 = convert(T, 14.946122435958785) + r094 = convert(T, -27.826954732510288) + r095 = convert(T, 21.824672217437076) + r096 = convert(T, -5.941557405812358) + r102 = convert(T, -19.610347376201034) + r103 = convert(T, 93.13370014508226) + r104 = convert(T, -165.3493635542416) + r105 = convert(T, 129.73901617804057) + r106 = convert(T, -37.91300539268019) + r112 = convert(T, -18.23029074639409) + r113 = convert(T, 96.74593449012313) + r114 = convert(T, -199.08634973839895) + r115 = convert(T, 180.85605899200485) + r116 = convert(T, -60.285352997334954) + r122 = convert(T, -13.563796638614157) + r123 = convert(T, 90.62137973668116) + r124 = convert(T, -204.04515601697273) + r125 = convert(T, 190.48135937835858) + r126 = convert(T, -63.493786459452856) + + Vern6InterpolationCoefficients(r011, r012, r013, r014, r015, r016, r042, r043, r044, + r045, r046, r052, r053, r054, r055, r056, r062, r063, + r064, r065, r066, r072, r073, r074, r075, r076, r082, + r083, r084, r085, r086, r092, r093, r094, r095, r096, + r102, r103, r104, r105, r106, r112, r113, r114, r115, + r116, r122, r123, r124, r125, r126) +end + +function Vern6InterpolationCoefficients(T) + r011 = convert(T, 1) + r012 = convert(T, -940811006205413129 // 120948724610397495) + r013 = convert(T, 88342864458754360181 // 3265615564480732365) + r014 = convert(T, -99667000922033025307 // 2177077042987154910) + r015 = convert(T, 7995049273203130972 // 217707704298715491) + r016 = convert(T, -7303903485456272500 // 653123112896146473) + r042 = convert(T, 2214248281250000 // 133130993475189) + r043 = convert(T, -49918013252500000000 // 578720428636646583) + r044 = convert(T, 1440368506953125000 // 8387252588936907) + r045 = convert(T, -28873797587500000000 // 192906809545548861) + r046 = convert(T, 27678103515625000000 // 578720428636646583) + r052 = convert(T, 893038428789062500 // 32943296570459319) + r053 = convert(T, -125047567320625000000 // 889469007402401613) + r054 = convert(T, 82988785418183593750 // 296489669134133871) + r055 = convert(T, -72330565909375000000 // 296489669134133871) + r056 = convert(T, 69335281738281250000 // 889469007402401613) + r062 = convert(T, 40331864555500 // 142160006043) + r063 = convert(T, -5647463071672000 // 3838320163161) + r064 = convert(T, 3747982556193250 // 1279440054387) + r065 = convert(T, -3266630520520000 // 1279440054387) + r066 = convert(T, 3131355943750000 // 3838320163161) + r072 = convert(T, -143250206750000 // 12603936879) + r073 = convert(T, 461347522996000000 // 7827044801859) + r074 = convert(T, -13312037070125000 // 113435431911) + r075 = convert(T, 266854670860000000 // 2609014933953) + r076 = convert(T, -255803940625000000 // 7827044801859) + r082 = convert(T, 3753451420391 // 338141155) + r083 = convert(T, -3679035166143248 // 63908678295) + r084 = convert(T, 4883240297928691 // 42605785530) + r085 = convert(T, -425608752364336 // 4260578553) + r086 = convert(T, 407983850042500 // 12781735659) + r092 = convert(T, -69713 // 23220) + r093 = convert(T, 4685161 // 313470) + r094 = convert(T, -135239 // 4860) + r095 = convert(T, 228046 // 10449) + r096 = convert(T, -186250 // 31347) + r102 = convert(T, -132664 // 6765) + r103 = convert(T, 17011336 // 182655) + r104 = convert(T, -10067296 // 60885) + r105 = convert(T, 1579832 // 12177) + r106 = convert(T, -1385000 // 36531) + r112 = convert(T, -2734375000 // 149990751) + r113 = convert(T, 391796875000 // 4049750277) + r114 = convert(T, -6250000000 // 31393413) + r115 = convert(T, 244140625000 // 1349916759) + r116 = convert(T, -244140625000 // 4049750277) + r122 = convert(T, -15453125 // 1139292) + r123 = convert(T, 1393796875 // 15380442) + r124 = convert(T, -2092203125 // 10253628) + r125 = convert(T, 488281250 // 2563407) + r126 = convert(T, -488281250 // 7690221) + + Vern6InterpolationCoefficients(r011, r012, r013, r014, r015, r016, r042, r043, r044, + r045, r046, r052, r053, r054, r055, r056, r062, r063, + r064, r065, r066, r072, r073, r074, r075, r076, r082, + r083, r084, r085, r086, r092, r093, r094, r095, r096, + r102, r103, r104, r105, r106, r112, r113, r114, r115, + r116, r122, r123, r124, r125, r126) +end + +""" +From Verner's Website +""" +struct Vern6Tableau{T, T2} + c1::T2 + c2::T2 + c3::T2 + c4::T2 + c5::T2 + c6::T2 + a21::T + a31::T + a32::T + a41::T + a43::T + a51::T + a53::T + a54::T + a61::T + a63::T + a64::T + a65::T + a71::T + a73::T + a74::T + a75::T + a76::T + a81::T + a83::T + a84::T + a85::T + a86::T + a87::T + a91::T + a94::T + a95::T + a96::T + a97::T + a98::T + btilde1::T + btilde4::T + btilde5::T + btilde6::T + btilde7::T + btilde8::T + btilde9::T + extra::Vern6ExtraStages{T, T2} + interp::Vern6InterpolationCoefficients{T} +end + +function Vern6Tableau(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + c1 = convert(T2, 0.06) + c2 = convert(T2, 0.09593333333333333) + c3 = convert(T2, 0.1439) + c4 = convert(T2, 0.4973) + c5 = convert(T2, 0.9725) + c6 = convert(T2, 0.9995) + a21 = convert(T, 0.06) + a31 = convert(T, 0.019239962962962962) + a32 = convert(T, 0.07669337037037037) + a41 = convert(T, 0.035975) + a43 = convert(T, 0.107925) + a51 = convert(T, 1.3186834152331484) + a53 = convert(T, -5.042058063628562) + a54 = convert(T, 4.220674648395414) + a61 = convert(T, -41.87259166432751) + a63 = convert(T, 159.43256216313748) + a64 = convert(T, -122.11921356501004) + a65 = convert(T, 5.531743066200053) + a71 = convert(T, -54.430156935316504) + a73 = convert(T, 207.06725136501848) + a74 = convert(T, -158.61081378459) + a75 = convert(T, 6.991816585950242) + a76 = convert(T, -0.01859723106220323) + a81 = convert(T, -54.66374178728198) + a83 = convert(T, 207.95280625538936) + a84 = convert(T, -159.2889574744995) + a85 = convert(T, 7.018743740796944) + a86 = convert(T, -0.018338785905045722) + a87 = convert(T, -0.0005119484997882099) + a91 = convert(T, 0.03438957868357036) + a94 = convert(T, 0.25826245556335037) + a95 = convert(T, 0.4209371189673537) + a96 = convert(T, 4.40539646966931) + a97 = convert(T, -176.48311902429865) + a98 = convert(T, 172.36413340141507) + # b1 =convert(T,0.04301298296577122) + # b4 =convert(T,0.23882842561019763) + # b5 =convert(T,0.44938719155539175) + # b6 =convert(T,2.2956854086040193) + # b7 =convert(T,-73.02457612433467) + # b8 =convert(T,70.96432878226597) + # b9 =convert(T,0.03333333333333333) + btilde1 = convert(T, 0.008623404282200854) + btilde4 = convert(T, -0.019434029953152708) + btilde5 = convert(T, 0.028450072588037983) + btilde6 = convert(T, -2.1097110610652914) + btilde7 = convert(T, 103.45854289996397) + btilde8 = convert(T, -101.39980461914912) + btilde9 = convert(T, 0.03333333333333333) + + extra = Vern6ExtraStages(T, T2) + interp = Vern6InterpolationCoefficients(T) + + Vern6Tableau(c1, c2, c3, c4, c5, c6, a21, a31, a32, a41, a43, a51, a53, a54, a61, a63, + a64, a65, a71, a73, a74, a75, a76, a81, a83, a84, a85, a86, a87, a91, a94, + a95, a96, a97, a98, btilde1, btilde4, btilde5, btilde6, btilde7, btilde8, + btilde9, extra, interp) +end + +function Vern6Tableau(T, T2) + c1 = convert(T2, 3 // 50) + c2 = convert(T2, 1439 // 15000) + c3 = convert(T2, 1439 // 10000) + c4 = convert(T2, 4973 // 10000) + c5 = convert(T2, 389 // 400) + c6 = convert(T2, 1999 // 2000) + a21 = convert(T, 3 // 50) + a31 = convert(T, 519479 // 27000000) + a32 = convert(T, 2070721 // 27000000) + a41 = convert(T, 1439 // 40000) + a43 = convert(T, 4317 // 40000) + a51 = convert(T, 109225017611 // 82828840000) + a53 = convert(T, -417627820623 // 82828840000) + a54 = convert(T, 43699198143 // 10353605000) + a61 = convert(T, -8036815292643907349452552172369 // 191934985946683241245914401600) + a63 = convert(T, 246134619571490020064824665 // 1543816496655405117602368) + a64 = convert(T, -13880495956885686234074067279 // 113663489566254201783474344) + a65 = convert(T, 755005057777788994734129 // 136485922925633667082436) + a71 = convert(T, + -BigInt(1663299841566102097180506666498880934230261) // + BigInt(30558424506156170307020957791311384232000)) + a73 = convert(T, + 130838124195285491799043628811093033 // 631862949514135618861563657970240) + a74 = convert(T, + -BigInt(3287100453856023634160618787153901962873) // + BigInt(20724314915376755629135711026851409200)) + a75 = convert(T, + 2771826790140332140865242520369241 // 396438716042723436917079980147600) + a76 = convert(T, -1799166916139193 // 96743806114007800) + a81 = convert(T, + -BigInt(832144750039369683895428386437986853923637763) // + BigInt(15222974550069600748763651844667619945204887)) + a83 = convert(T, + 818622075710363565982285196611368750 // + 3936576237903728151856072395343129) + a84 = convert(T, + -BigInt(9818985165491658464841194581385463434793741875) // + BigInt(61642597962658994069869370923196463581866011)) + a85 = convert(T, + BigInt(31796692141848558720425711042548134769375) // + BigInt(4530254033500045975557858016006308628092)) + a86 = convert(T, -14064542118843830075 // 766928748264306853644) + a87 = convert(T, -1424670304836288125 // 2782839104764768088217) + a91 = convert(T, 382735282417 // 11129397249634) + a94 = convert(T, 5535620703125000 // 21434089949505429) + a95 = convert(T, 13867056347656250 // 32943296570459319) + a96 = convert(T, 626271188750 // 142160006043) + a97 = convert(T, -51160788125000 // 289890548217) + a98 = convert(T, 163193540017 // 946795234) + # b1 =convert(T,124310637869885675646798613//2890072468789466426596827670) + # b4 =convert(T,265863151737164990361330921875//1113197271463372303940319369579) + # b5 =convert(T,3075493557174030806536302953125//6843749922042323876546949699876) + # b6 =convert(T,67798000008733879813263055//29532792147666737550036372) + # b7 =convert(T,-1099436585155390846238326375//15055706496446408859196167) + # b8 =convert(T,26171252653086373181571802//368794478890732346033505) + # b9 =convert(T,1//30) + btilde1 = convert(T, 12461131651614938103148389 // 1445036234394733213298413835) + btilde4 = convert(T, -21633909117387045317965953125 // 1113197271463372303940319369579) + btilde5 = convert(T, 21633909117387045317965953125 // 760416658004702652949661077764) + btilde6 = convert(T, -6922850917563854501749105 // 3281421349740748616670708) + btilde7 = convert(T, 173071272939096362543727625 // 1672856277382934317688463) + btilde8 = convert(T, -74791376208282344108625901 // 737588957781464692067010) + btilde9 = convert(T, 1 // 30) + + extra = Vern6ExtraStages(T, T2) + interp = Vern6InterpolationCoefficients(T) + + Vern6Tableau(c1, c2, c3, c4, c5, c6, a21, a31, a32, a41, a43, a51, a53, a54, a61, a63, + a64, a65, a71, a73, a74, a75, a76, a81, a83, a84, a85, a86, a87, a91, a94, + a95, a96, a97, a98, btilde1, btilde4, btilde5, btilde6, btilde7, btilde8, + btilde9, extra, interp) +end + +## Vern7 +struct Vern7ExtraStages{T, T2} + c11::T2 + a1101::T + a1104::T + a1105::T + a1106::T + a1107::T + a1108::T + a1109::T + c12::T2 + a1201::T + a1204::T + a1205::T + a1206::T + a1207::T + a1208::T + a1209::T + a1211::T + c13::T2 + a1301::T + a1304::T + a1305::T + a1306::T + a1307::T + a1308::T + a1309::T + a1311::T + a1312::T + c14::T2 + a1401::T + a1404::T + a1405::T + a1406::T + a1407::T + a1408::T + a1409::T + a1411::T + a1412::T + a1413::T + c15::T2 + a1501::T + a1504::T + a1505::T + a1506::T + a1507::T + a1508::T + a1509::T + a1511::T + a1512::T + a1513::T + c16::T2 + a1601::T + a1604::T + a1605::T + a1606::T + a1607::T + a1608::T + a1609::T + a1611::T + a1612::T + a1613::T +end + +@fold function Vern7ExtraStages(::Type{T}, + ::Type{T2}) where {T <: CompiledFloats, + T2 <: CompiledFloats} + c11 = convert(T2, 1) + a1101 = convert(T, 0.04715561848627222) + a1104 = convert(T, 0.25750564298434153) + a1105 = convert(T, 0.2621665397741262) + a1106 = convert(T, 0.15216092656738558) + a1107 = convert(T, 0.49399691700324844) + a1108 = convert(T, -0.29430311714032503) + a1109 = convert(T, 0.0813174723249511) + c12 = convert(T2, 0.29) + a1201 = convert(T, 0.0523222769159969) + a1204 = convert(T, 0.22495861826705715) + a1205 = convert(T, 0.017443709248776376) + a1206 = convert(T, -0.007669379876829393) + a1207 = convert(T, 0.03435896044073285) + a1208 = convert(T, -0.0410209723009395) + a1209 = convert(T, 0.025651133005205617) + a1211 = convert(T, -0.0160443457) + c13 = convert(T2, 0.125) + a1301 = convert(T, 0.053053341257859085) + a1304 = convert(T, 0.12195301011401886) + a1305 = convert(T, 0.017746840737602496) + a1306 = convert(T, -0.0005928372667681495) + a1307 = convert(T, 0.008381833970853752) + a1308 = convert(T, -0.01293369259698612) + a1309 = convert(T, 0.009412056815253861) + a1311 = convert(T, -0.005353253107275676) + a1312 = convert(T, -0.06666729992455811) + c14 = convert(T2, 0.25) + a1401 = convert(T, 0.03887903257436304) + a1404 = convert(T, -0.0024403203308301317) + a1405 = convert(T, -0.0013928917214672623) + a1406 = convert(T, -0.00047446291558680135) + a1407 = convert(T, 0.00039207932413159514) + a1408 = convert(T, -0.00040554733285128004) + a1409 = convert(T, 0.00019897093147716726) + a1411 = convert(T, -0.00010278198793179169) + a1412 = convert(T, 0.03385661513870267) + a1413 = convert(T, 0.1814893063199928) + c15 = convert(T2, 0.53) + a1501 = convert(T, 0.05723681204690013) + a1504 = convert(T, 0.22265948066761182) + a1505 = convert(T, 0.12344864200186899) + a1506 = convert(T, 0.04006332526666491) + a1507 = convert(T, -0.05269894848581452) + a1508 = convert(T, 0.04765971214244523) + a1509 = convert(T, -0.02138895885042213) + a1511 = convert(T, 0.015193891064036402) + a1512 = convert(T, 0.12060546716289655) + a1513 = convert(T, -0.022779423016187374) + c16 = convert(T2, 0.79) + a1601 = convert(T, 0.051372038802756814) + a1604 = convert(T, 0.5414214473439406) + a1605 = convert(T, 0.350399806692184) + a1606 = convert(T, 0.14193112269692182) + a1607 = convert(T, 0.10527377478429423) + a1608 = convert(T, -0.031081847805874016) + a1609 = convert(T, -0.007401883149519145) + a1611 = convert(T, -0.006377932504865363) + a1612 = convert(T, -0.17325495908361865) + a1613 = convert(T, -0.18228156777622026) + + Vern7ExtraStages(c11, a1101, a1104, a1105, a1106, a1107, a1108, a1109, c12, a1201, + a1204, a1205, a1206, a1207, a1208, a1209, a1211, c13, a1301, a1304, + a1305, a1306, a1307, a1308, a1309, a1311, a1312, c14, a1401, a1404, + a1405, a1406, a1407, a1408, a1409, a1411, a1412, a1413, c15, a1501, + a1504, a1505, a1506, a1507, a1508, a1509, a1511, a1512, a1513, c16, + a1601, a1604, a1605, a1606, a1607, a1608, a1609, a1611, a1612, a1613) +end + +@fold function Vern7ExtraStages(::Type{T}, ::Type{T2}) where {T, T2} + c11 = convert(T2, 1) + a1101 = convert(T, big" .4715561848627222170431765108838175679569e-1") + a1104 = convert(T, big" .2575056429843415189596436101037687580986") + a1105 = convert(T, big" .2621665397741262047713863095764527711129") + a1106 = convert(T, big" .1521609265673855740323133199165117535523") + a1107 = convert(T, big" .4939969170032484246907175893227876844296") + a1108 = convert(T, big"-.2943031171403250441557244744092703429139") + a1109 = convert(T, big" .8131747232495109999734599440136761892478e-1") + c12 = convert(T2, 29 // 100) + a1201 = convert(T, big" .5232227691599689815470932256735029887614e-1") + a1204 = convert(T, big" .2249586182670571550244187743667190903405") + a1205 = convert(T, big" .1744370924877637539031751304611402542578e-1") + a1206 = convert(T, big"-.7669379876829393188009028209348812321417e-2") + a1207 = convert(T, big" .3435896044073284645684381456417912794447e-1") + a1208 = convert(T, big"-.4102097230093949839125144540100346681769e-1") + a1209 = convert(T, big" .2565113300520561655297104906598973655221e-1") + a1211 = convert(T, big"-.160443457e-1") + c13 = convert(T2, 1 // 8) + a1301 = convert(T, big" .5305334125785908638834747243817578898946e-1") + a1304 = convert(T, big" .1219530101140188607092225622195251463666") + a1305 = convert(T, big" .1774684073760249704011573985936092552347e-1") + a1306 = convert(T, big"-.5928372667681494328907467430302313286925e-3") + a1307 = convert(T, big" .8381833970853750873624781948796072714855e-2") + a1308 = convert(T, big"-.1293369259698611956700998079778496462996e-1") + a1309 = convert(T, big" .9412056815253860804791356641605087829772e-2") + a1311 = convert(T, big"-.5353253107275676032399320754008272222345e-2") + a1312 = convert(T, big"-.6666729992455811078380186481263955324311e-1") + c14 = convert(T2, 1 // 4) + a1401 = convert(T, big" .3887903257436303686399931060834951327899e-1") + a1404 = convert(T, big"-.2440320330830131517910045090190069290791e-2") + a1405 = convert(T, big"-.1392891721467262281273220992320214734208e-2") + a1406 = convert(T, big"-.4744629155868013465038358934145339168472e-3") + a1407 = convert(T, big" .3920793241315951369383517310870803393356e-3") + a1408 = convert(T, big"-.4055473328512800136385880031750264996936e-3") + a1409 = convert(T, big" .1989709314771672628794304728258886009267e-3") + a1411 = convert(T, big"-.1027819879317916884712606136811051029682e-3") + a1412 = convert(T, big" .3385661513870266715302548402957613704604e-1") + a1413 = convert(T, big" .1814893063199928004309543737509423302792") + c15 = convert(T2, 53 // 100) + a1501 = convert(T, big" .5723681204690012909606837582140921695189e-1") + a1504 = convert(T, big" .2226594806676118099285816235023183680020") + a1505 = convert(T, big" .1234486420018689904911221497830317287757") + a1506 = convert(T, big" .4006332526666490875113688731927762275433e-1") + a1507 = convert(T, big"-.5269894848581452066926326838943832327366e-1") + a1508 = convert(T, big" .4765971214244522856887315416093212596338e-1") + a1509 = convert(T, big"-.2138895885042213036387863538386958914368e-1") + a1511 = convert(T, big" .1519389106403640165459624646184297766866e-1") + a1512 = convert(T, big" .1206054671628965554251364472502413614358") + a1513 = convert(T, big"-.2277942301618737288237298052574548913451e-1") + c16 = convert(T2, 79 // 100) + a1601 = convert(T, big" .5137203880275681426595607279552927584506e-1") + a1604 = convert(T, big" .5414214473439405582401399378307410450482") + a1605 = convert(T, big" .3503998066921840081154745647747846804810") + a1606 = convert(T, big" .1419311226969218216861835872156617148040") + a1607 = convert(T, big" .1052737747842942254816302629823570359198") + a1608 = convert(T, big"-.3108184780587401700842726199589213259835e-1") + a1609 = convert(T, big"-.7401883149519145061791854716430279714483e-2") + a1611 = convert(T, big"-.6377932504865363437569726480040013149706e-2") + a1612 = convert(T, big"-.1732549590836186403386348310205265959935") + a1613 = convert(T, big"-.1822815677762202619429607513861847306420") + + Vern7ExtraStages(c11, a1101, a1104, a1105, a1106, a1107, a1108, a1109, c12, a1201, + a1204, a1205, a1206, a1207, a1208, a1209, a1211, c13, a1301, a1304, + a1305, a1306, a1307, a1308, a1309, a1311, a1312, c14, a1401, a1404, + a1405, a1406, a1407, a1408, a1409, a1411, a1412, a1413, c15, a1501, + a1504, a1505, a1506, a1507, a1508, a1509, a1511, a1512, a1513, c16, + a1601, a1604, a1605, a1606, a1607, a1608, a1609, a1611, a1612, a1613) +end + +struct Vern7InterpolationCoefficients{T} + r011::T + r012::T + r013::T + r014::T + r015::T + r016::T + r017::T + r042::T + r043::T + r044::T + r045::T + r046::T + r047::T + r052::T + r053::T + r054::T + r055::T + r056::T + r057::T + r062::T + r063::T + r064::T + r065::T + r066::T + r067::T + r072::T + r073::T + r074::T + r075::T + r076::T + r077::T + r082::T + r083::T + r084::T + r085::T + r086::T + r087::T + r092::T + r093::T + r094::T + r095::T + r096::T + r097::T + r112::T + r113::T + r114::T + r115::T + r116::T + r117::T + r122::T + r123::T + r124::T + r125::T + r126::T + r127::T + r132::T + r133::T + r134::T + r135::T + r136::T + r137::T + r142::T + r143::T + r144::T + r145::T + r146::T + r147::T + r152::T + r153::T + r154::T + r155::T + r156::T + r157::T + r162::T + r163::T + r164::T + r165::T + r166::T + r167::T +end + +@fold function Vern7InterpolationCoefficients(::Type{T}) where {T <: CompiledFloats} + r011 = convert(T, 1) + r012 = convert(T, -8.413387198332767) + r013 = convert(T, 33.675508884490895) + r014 = convert(T, -70.80159089484886) + r015 = convert(T, 80.64695108301298) + r016 = convert(T, -47.19413969837522) + r017 = convert(T, 11.133813442539243) + r042 = convert(T, 8.754921980674396) + r043 = convert(T, -88.4596828699771) + r044 = convert(T, 346.9017638429916) + r045 = convert(T, -629.2580030059837) + r046 = convert(T, 529.6773755604193) + r047 = convert(T, -167.35886986514018) + r052 = convert(T, 8.913387586637922) + r053 = convert(T, -90.06081846893218) + r054 = convert(T, 353.1807459217058) + r055 = convert(T, -640.6476819744374) + r056 = convert(T, 539.2646279047156) + r057 = convert(T, -170.38809442991547) + r062 = convert(T, 5.1733120298478) + r063 = convert(T, -52.271115900055385) + r064 = convert(T, 204.9853867374073) + r065 = convert(T, -371.8306118563603) + r066 = convert(T, 312.9880934374529) + r067 = convert(T, -98.89290352172495) + r072 = convert(T, 16.79537744079696) + r073 = convert(T, -169.70040000059728) + r074 = convert(T, 665.4937727009246) + r075 = convert(T, -1207.1638892336007) + r076 = convert(T, 1016.1291515818546) + r077 = convert(T, -321.06001557237494) + r082 = convert(T, -10.005997536098665) + r083 = convert(T, 101.1005433052275) + r084 = convert(T, -396.47391512378437) + r085 = convert(T, 719.1787707014183) + r086 = convert(T, -605.3681033918824) + r087 = convert(T, 191.27439892797935) + r092 = convert(T, 2.764708833638599) + r093 = convert(T, -27.934602637390462) + r094 = convert(T, 109.54779186137893) + r095 = convert(T, -198.7128113064482) + r096 = convert(T, 167.26633571640318) + r097 = convert(T, -52.85010499525706) + r112 = convert(T, -2.1696320280163506) + r113 = convert(T, 22.016696037569876) + r114 = convert(T, -86.90152427798948) + r115 = convert(T, 159.22388973861476) + r116 = convert(T, -135.9618306534588) + r117 = convert(T, 43.792401183280006) + r122 = convert(T, -4.890070188793804) + r123 = convert(T, 22.75407737425176) + r124 = convert(T, -30.78034218537731) + r125 = convert(T, -2.797194317207249) + r126 = convert(T, 31.369456637508403) + r127 = convert(T, -15.655927320381801) + r132 = convert(T, 10.862170929551967) + r133 = convert(T, -50.542971417827104) + r134 = convert(T, 68.37148040407511) + r135 = convert(T, 6.213326521632409) + r136 = convert(T, -69.68006323194157) + r137 = convert(T, 34.776056794509195) + r142 = convert(T, -11.37286691922923) + r143 = convert(T, 130.79058078246717) + r144 = convert(T, -488.65113677785604) + r145 = convert(T, 832.2148793276441) + r146 = convert(T, -664.7743368554426) + r147 = convert(T, 201.79288044241662) + r152 = convert(T, -5.919778732715007) + r153 = convert(T, 63.27679965889219) + r154 = convert(T, -265.432682088738) + r155 = convert(T, 520.1009254140611) + r156 = convert(T, -467.412109533902) + r157 = convert(T, 155.3868452824017) + r162 = convert(T, -10.492146197961823) + r163 = convert(T, 105.35538525188011) + r164 = convert(T, -409.43975011988937) + r165 = convert(T, 732.831448907654) + r166 = convert(T, -606.3044574733512) + r167 = convert(T, 188.0495196316683) + + Vern7InterpolationCoefficients(r011, r012, r013, r014, r015, r016, r017, r042, r043, + r044, r045, r046, r047, r052, r053, r054, r055, r056, + r057, r062, r063, r064, r065, r066, r067, r072, r073, + r074, r075, r076, r077, r082, r083, r084, r085, r086, + r087, r092, r093, r094, r095, r096, r097, r112, r113, + r114, r115, r116, r117, r122, r123, r124, r125, r126, + r127, r132, r133, r134, r135, r136, r137, r142, r143, + r144, r145, r146, r147, r152, r153, r154, r155, r156, + r157, r162, r163, r164, r165, r166, r167) +end + +@fold function Vern7InterpolationCoefficients(::Type{T}) where {T} + r011 = convert(T, big" 1") + r012 = convert(T, big"-8.413387198332767469319987751201351965810") + r013 = convert(T, big" 33.67550888449089654479469983556967202215") + r014 = convert(T, big"-70.80159089484886164618905961010838757357") + r015 = convert(T, big" 80.64695108301297872968868805293298389704") + r016 = convert(T, big"-47.19413969837521580145883430419406103536") + r017 = convert(T, big" 11.13381344253924186418881142808952641234") + r042 = convert(T, big" 8.754921980674397160629587282876763437696") + r043 = convert(T, big"-88.45968286997709426134300934922618655402") + r044 = convert(T, big" 346.9017638429916309499891288356321692825") + r045 = convert(T, big"-629.2580030059837046812187141184986252218") + r046 = convert(T, big" 529.6773755604192983874116479833480529304") + r047 = convert(T, big"-167.3588698651401860365089970240284051167") + r052 = convert(T, big" 8.913387586637921662996190126913331844214") + r053 = convert(T, big"-90.06081846893217794712014609702916991513") + r054 = convert(T, big" 353.1807459217057824951538014683541349020") + r055 = convert(T, big"-640.6476819744374433668701027882567716886") + r056 = convert(T, big" 539.2646279047155261551781390920363285084") + r057 = convert(T, big"-170.3880944299154827945664954924414008798") + r062 = convert(T, big" 5.173312029847800338889849068990984974299") + r063 = convert(T, big"-52.27111590005538823385270070373176751689") + r064 = convert(T, big" 204.9853867374073094711024260808085419491") + r065 = convert(T, big"-371.8306118563602890875634623992262437796") + r066 = convert(T, big" 312.9880934374529000210073972654145891826") + r067 = convert(T, big"-98.89290352172494693555119599233959305606") + r072 = convert(T, big" 16.79537744079695986364946329034055578253") + r073 = convert(T, big"-169.7004000005972744435739149730966805754") + r074 = convert(T, big" 665.4937727009246303131700313781960584913") + r075 = convert(T, big"-1207.163889233600728395392916633015853882") + r076 = convert(T, big" 1016.129151581854603280159105697386989470") + r077 = convert(T, big"-321.0600155723749421933210511704882816019") + r082 = convert(T, big"-10.00599753609866476866352971232058330270") + r083 = convert(T, big" 101.1005433052275068199636113246449312792") + r084 = convert(T, big"-396.4739151237843754958939772727577263768") + r085 = convert(T, big" 719.1787707014182914108130834128646525498") + r086 = convert(T, big"-605.3681033918824350795711030652978269725") + r087 = convert(T, big" 191.2743989279793520691961908384572824802") + r092 = convert(T, big" 2.764708833638599139713222853969606774131") + r093 = convert(T, big"-27.93460263739046178114640484830267988046") + r094 = convert(T, big" 109.5477918613789217803046856340175757800") + r095 = convert(T, big"-198.7128113064482116421691972646370773711") + r096 = convert(T, big" 167.2663357164031670694252647113936863857") + r097 = convert(T, big"-52.85010499525706346613022509203974406942") + r112 = convert(T, big"-2.169632028016350481156919876642428429100") + r113 = convert(T, big" 22.01669603756987625585768587320929912766") + r114 = convert(T, big"-86.90152427798948350846176288615482496306") + r115 = convert(T, big" 159.2238897386147443720253338471077193471") + r116 = convert(T, big"-135.9618306534587908363115231453760181702") + r117 = convert(T, big" 43.79240118328000419804718618785625308759") + r122 = convert(T, big"-4.890070188793803933769786966428026149549") + r123 = convert(T, big" 22.75407737425176120799532459991506803585") + r124 = convert(T, big"-30.78034218537730965082079824005797506535") + r125 = convert(T, big"-2.797194317207249021142015125037024035537") + r126 = convert(T, big" 31.36945663750840183161406140272783187147") + r127 = convert(T, big"-15.65592732038180043387678567111987465689") + r132 = convert(T, big" 10.86217092955196715517224349929627754387") + r133 = convert(T, big"-50.54297141782710697188187875653305700081") + r134 = convert(T, big" 68.37148040407511827604242008548181691494") + r135 = convert(T, big" 6.213326521632409162585500428935637861213") + r136 = convert(T, big"-69.68006323194158104163196358466588618336") + r137 = convert(T, big" 34.77605679450919341971367832748521086414") + r142 = convert(T, big"-11.37286691922922915922346687401389055763") + r143 = convert(T, big" 130.7905807824671644130452602841032046030") + r144 = convert(T, big"-488.6511367778560207543260583489312609826") + r145 = convert(T, big" 832.2148793276440873476229585070779183432") + r146 = convert(T, big"-664.7743368554426242883314487337054193624") + r147 = convert(T, big" 201.7928804424166224412127551654694479565") + r152 = convert(T, big"-5.919778732715006698693070786679427540601") + r153 = convert(T, big" 63.27679965889218829298274978013773800731") + r154 = convert(T, big"-265.4326820887379575820873554556433306580") + r155 = convert(T, big" 520.1009254140610824835871087519714692468") + r156 = convert(T, big"-467.4121095339020118993777963241667608460") + r157 = convert(T, big" 155.3868452824017054035883640343803117904") + r162 = convert(T, big"-10.49214619796182281022379415510181241136") + r163 = convert(T, big" 105.3553852518801101042787230303396283676") + r164 = convert(T, big"-409.4397501198893846479834816688367917005") + r165 = convert(T, big" 732.8314489076540326880337353277812147333") + r166 = convert(T, big"-606.3044574733512377981129469949015057785") + r167 = convert(T, big" 188.0495196316683024640077644607192667895") + + Vern7InterpolationCoefficients(r011, r012, r013, r014, r015, r016, r017, r042, r043, + r044, r045, r046, r047, r052, r053, r054, r055, r056, + r057, r062, r063, r064, r065, r066, r067, r072, r073, + r074, r075, r076, r077, r082, r083, r084, r085, r086, + r087, r092, r093, r094, r095, r096, r097, r112, r113, + r114, r115, r116, r117, r122, r123, r124, r125, r126, + r127, r132, r133, r134, r135, r136, r137, r142, r143, + r144, r145, r146, r147, r152, r153, r154, r155, r156, + r157, r162, r163, r164, r165, r166, r167) +end + +struct Vern7Tableau{T, T2} + c2::T2 + c3::T2 + c4::T2 + c5::T2 + c6::T2 + c7::T2 + c8::T2 + a021::T + a031::T + a032::T + a041::T + a043::T + a051::T + a053::T + a054::T + a061::T + a063::T + a064::T + a065::T + a071::T + a073::T + a074::T + a075::T + a076::T + a081::T + a083::T + a084::T + a085::T + a086::T + a087::T + a091::T + a093::T + a094::T + a095::T + a096::T + a097::T + a098::T + a101::T + a103::T + a104::T + a105::T + a106::T + a107::T + b1::T + b4::T + b5::T + b6::T + b7::T + b8::T + b9::T + btilde1::T + btilde4::T + btilde5::T + btilde6::T + btilde7::T + btilde8::T + btilde9::T + btilde10::T +end + +@fold function Vern7Tableau(::Type{T}, + ::Type{T2}) where {T <: CompiledFloats, T2 <: CompiledFloats} + c2 = convert(T2, 0.005) + c3 = convert(T2, 0.10888888888888888) + c4 = convert(T2, 0.16333333333333333) + c5 = convert(T2, 0.4555) + c6 = convert(T2, 0.6095094489978381) + c7 = convert(T2, 0.884) + c8 = convert(T2, 0.925) + a021 = convert(T, 0.005) + a031 = convert(T, -1.07679012345679) + a032 = convert(T, 1.185679012345679) + a041 = convert(T, 0.04083333333333333) + a043 = convert(T, 0.1225) + a051 = convert(T, 0.6389139236255726) + a053 = convert(T, -2.455672638223657) + a054 = convert(T, 2.272258714598084) + a061 = convert(T, -2.6615773750187572) + a063 = convert(T, 10.804513886456137) + a064 = convert(T, -8.3539146573962) + a065 = convert(T, 0.820487594956657) + a071 = convert(T, 6.067741434696772) + a073 = convert(T, -24.711273635911088) + a074 = convert(T, 20.427517930788895) + a075 = convert(T, -1.9061579788166472) + a076 = convert(T, 1.006172249242068) + a081 = convert(T, 12.054670076253203) + a083 = convert(T, -49.75478495046899) + a084 = convert(T, 41.142888638604674) + a085 = convert(T, -4.461760149974004) + a086 = convert(T, 2.042334822239175) + a087 = convert(T, -0.09834843665406107) + a091 = convert(T, 10.138146522881808) + a093 = convert(T, -42.6411360317175) + a094 = convert(T, 35.76384003992257) + a095 = convert(T, -4.3480228403929075) + a096 = convert(T, 2.0098622683770357) + a097 = convert(T, 0.3487490460338272) + a098 = convert(T, -0.27143900510483127) + a101 = convert(T, -45.030072034298676) + a103 = convert(T, 187.3272437654589) + a104 = convert(T, -154.02882369350186) + a105 = convert(T, 18.56465306347536) + a106 = convert(T, -7.141809679295079) + a107 = convert(T, 1.3088085781613787) + b1 = convert(T, 0.04715561848627222) + b4 = convert(T, 0.25750564298434153) + b5 = convert(T, 0.26216653977412624) + b6 = convert(T, 0.15216092656738558) + b7 = convert(T, 0.4939969170032485) + b8 = convert(T, -0.29430311714032503) + b9 = convert(T, 0.08131747232495111) + # bhat1 = convert(T,0.044608606606341174) + # bhat4 = convert(T,0.26716403785713727) + # bhat5 = convert(T,0.22010183001772932) + # bhat6 = convert(T,0.2188431703143157) + # bhat7 = convert(T,0.22898717054112028) + # bhat10 = convert(T,0.02029518466335628) + btilde1 = convert(T, 0.002547011879931045) + btilde4 = convert(T, -0.00965839487279575) + btilde5 = convert(T, 0.04206470975639691) + btilde6 = convert(T, -0.0666822437469301) + btilde7 = convert(T, 0.2650097464621281) + btilde8 = convert(T, -0.29430311714032503) + btilde9 = convert(T, 0.08131747232495111) + btilde10 = convert(T, -0.02029518466335628) + + Vern7Tableau( + c2, c3, c4, c5, c6, c7, c8, a021, a031, a032, a041, a043, a051, a053, a054, + a061, a063, a064, a065, a071, a073, a074, a075, a076, a081, a083, a084, + a085, a086, a087, a091, a093, a094, a095, a096, a097, a098, a101, a103, + a104, a105, a106, a107, b1, b4, b5, b6, b7, b8, b9, btilde1, btilde4, + btilde5, btilde6, btilde7, btilde8, btilde9, btilde10) +end + +@fold function Vern7Tableau(::Type{T}, ::Type{T2}) where {T, T2} + c2 = convert(T2, 1 // 200) + c3 = convert(T2, 49 // 450) + c4 = convert(T2, 49 // 300) + c5 = convert(T2, 911 // 2000) + c6 = convert(T2, 3480084980 // 5709648941) + c7 = convert(T2, 221 // 250) + c8 = convert(T2, 37 // 40) + a021 = convert(T, 1 // 200) + a031 = convert(T, -4361 // 4050) + a032 = convert(T, 2401 // 2025) + a041 = convert(T, 49 // 1200) + a043 = convert(T, 49 // 400) + a051 = convert(T, 2454451729 // 3841600000) + a053 = convert(T, -9433712007 // 3841600000) + a054 = convert(T, 4364554539 // 1920800000) + a061 = convert(T, + -BigInt(6187101755456742839167388910402379177523537620) // + BigInt(2324599620333464857202963610201679332423082271)) + a063 = convert(T, + BigInt(27569888999279458303270493567994248533230000) // + BigInt(2551701010245296220859455115479340650299761)) + a064 = convert(T, + -BigInt(37368161901278864592027018689858091583238040000) // + BigInt(4473131870960004275166624817435284159975481033)) + a065 = convert(T, + BigInt(1392547243220807196190880383038194667840000000) // + BigInt(1697219131380493083996999253929006193143549863)) + a071 = convert(T, 11272026205260557297236918526339 // 1857697188743815510261537500000) + a073 = convert(T, -48265918242888069 // 1953194276993750) + a074 = convert(T, 26726983360888651136155661781228 // 1308381343805114800955157615625) + a075 = convert(T, -2090453318815827627666994432 // 1096684189897834170412307919) + a076 = convert(T, + BigInt(1148577938985388929671582486744843844943428041509) // + BigInt(1141532118233823914568777901158338927629837500000)) + a081 = convert(T, + BigInt(1304457204588839386329181466225966641) // + BigInt(108211771565488329642169667802016000)) + a083 = convert(T, -1990261989751005 // 40001418792832) + a084 = convert(T, + BigInt(2392691599894847687194643439066780106875) // + BigInt(58155654089143548047476915856270826016)) + a085 = convert(T, + -BigInt(1870932273351008733802814881998561250) // + BigInt(419326053051486744762255151208232123)) + a086 = convert(T, + BigInt(1043329047173803328972823866240311074041739158858792987034783181) // + BigInt(510851127745017966999893975119259285040213723744255237522144000)) + a087 = convert(T, -311918858557595100410788125 // 3171569057622789618800376448) + a091 = convert(T, + BigInt(17579784273699839132265404100877911157) // + BigInt(1734023495717116205617154737841023480)) + a093 = convert(T, -18539365951217471064750 // 434776548575709731377) + a094 = convert(T, + BigInt(447448655912568142291911830292656995992000) // + BigInt(12511202807447096607487664209063950964109)) + a095 = convert(T, + -BigInt(65907597316483030274308429593905808000000) // + BigInt(15158061430635748897861852383197382130691)) + a096 = convert(T, + BigInt(273847823027445129865693702689010278588244606493753883568739168819449761) // + BigInt(136252034448398939768371761610231099586032870552034688235302796640584360)) + a097 = convert(T, + BigInt(694664732797172504668206847646718750) // + BigInt(1991875650119463976442052358853258111)) + a098 = convert(T, + -19705319055289176355560129234220800 // + 72595753317320295604316217197876507) + a101 = convert(T, + -511858190895337044664743508805671 // 11367030248263048398341724647960) + a103 = convert(T, 2822037469238841750 // 15064746656776439) + a104 = convert(T, + -BigInt(23523744880286194122061074624512868000) // + BigInt(152723005449262599342117017051789699)) + a105 = convert(T, + BigInt(10685036369693854448650967542704000000) // + BigInt(575558095977344459903303055137999707)) + a106 = convert(T, + -BigInt(6259648732772142303029374363607629515525848829303541906422993) // + BigInt(876479353814142962817551241844706205620792843316435566420120)) + a107 = convert(T, + 17380896627486168667542032602031250 // + 13279937889697320236613879977356033) + b1 = convert(T, 96762636172307789 // 2051985304794103980) + b4 = convert(T, 312188947591288252500000 // 1212357694274963646019729) + b5 = convert(T, 13550580884964304000000000000 // 51686919683339547115937980629) + b6 = convert(T, + BigInt(72367769693133178898676076432831566019684378142853445230956642801) // + BigInt(475600216991873963561768100160364792981629064220601844848928537580)) + b7 = convert(T, 1619421054120605468750 // 3278200730370057108183) + b8 = convert(T, -66898316144057728000 // 227310933007074849597) + b9 = convert(T, 181081444637946577 // 2226845467039736466) + # bhat1 = convert(T,117807213929927//2640907728177740) + # bhat4 = convert(T,4758744518816629500000//17812069906509312711137) + # bhat5 = convert(T,1730775233574080000000000//7863520414322158392809673) + # bhat6 = convert(T,BigInt(2682653613028767167314032381891560552585218935572349997)//BigInt(12258338284789875762081637252125169126464880985167722660)) + # bhat7 = convert(T,40977117022675781250//178949401077111131341) + # bhat10 = convert(T,2152106665253777//106040260335225546) + btilde1 = convert(T, 522643094875451 // 205198530479410398) + btilde4 = convert(T, -550343178903849903000000 // 56980811630923291362927263) + btilde5 = convert(T, 197654115880170560000000000 // 4698810880303595192357998239) + btilde6 = convert(T, + BigInt(-3171408959554499061315206389277085667739969057641653677018211151) // + BigInt(47560021699187396356176810016036479298162906422060184484892853758)) + btilde7 = convert(T, 40831491787144609375000 // 154075434327392684084601) + btilde8 = convert(T, -66898316144057728000 // 227310933007074849597) + btilde9 = convert(T, 181081444637946577 // 2226845467039736466) + btilde10 = convert(T, -2152106665253777 // 106040260335225546) + + Vern7Tableau( + c2, c3, c4, c5, c6, c7, c8, a021, a031, a032, a041, a043, a051, a053, a054, + a061, a063, a064, a065, a071, a073, a074, a075, a076, a081, a083, a084, + a085, a086, a087, a091, a093, a094, a095, a096, a097, a098, a101, a103, + a104, a105, a106, a107, b1, b4, b5, b6, b7, b8, b9, btilde1, btilde4, + btilde5, btilde6, btilde7, btilde8, btilde9, btilde10) +end + +## Vern8 +struct Vern8ExtraStages{T, T2} + c14::T2 + a1401::T + a1406::T + a1407::T + a1408::T + a1409::T + a1410::T + a1411::T + a1412::T + c15::T2 + a1501::T + a1506::T + a1507::T + a1508::T + a1509::T + a1510::T + a1511::T + a1512::T + a1514::T + c16::T2 + a1601::T + a1606::T + a1607::T + a1608::T + a1609::T + a1610::T + a1611::T + a1612::T + a1614::T + a1615::T + c17::T2 + a1701::T + a1706::T + a1707::T + a1708::T + a1709::T + a1710::T + a1711::T + a1712::T + a1714::T + a1715::T + a1716::T + c18::T2 + a1801::T + a1806::T + a1807::T + a1808::T + a1809::T + a1810::T + a1811::T + a1812::T + a1814::T + a1815::T + a1816::T + a1817::T + c19::T2 + a1901::T + a1906::T + a1907::T + a1908::T + a1909::T + a1910::T + a1911::T + a1912::T + a1914::T + a1915::T + a1916::T + a1917::T + c20::T2 + a2001::T + a2006::T + a2007::T + a2008::T + a2009::T + a2010::T + a2011::T + a2012::T + a2014::T + a2015::T + a2016::T + a2017::T + c21::T2 + a2101::T + a2106::T + a2107::T + a2108::T + a2109::T + a2110::T + a2111::T + a2112::T + a2114::T + a2115::T + a2116::T + a2117::T +end + +function Vern8ExtraStages(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + c14 = convert(T2, 1) + a1401 = convert(T, 0.04427989419007951) + a1406 = convert(T, 0.3541049391724449) + a1407 = convert(T, 0.2479692154956438) + a1408 = convert(T, -15.694202038838084) + a1409 = convert(T, 25.084064965558564) + a1410 = convert(T, -31.738367786260277) + a1411 = convert(T, 22.938283273988784) + a1412 = convert(T, -0.2361324633071542) + c15 = convert(T2, 0.3110177634953864) + a1501 = convert(T, 0.04620700646754963) + a1506 = convert(T, 0.045039041608424805) + a1507 = convert(T, 0.23368166977134244) + a1508 = convert(T, 37.83901368421068) + a1509 = convert(T, -15.949113289454246) + a1510 = convert(T, 23.028368351816102) + a1511 = convert(T, -44.85578507769412) + a1512 = convert(T, -0.06379858768647444) + a1514 = convert(T, -0.012595035543861663) + c16 = convert(T2, 0.1725) + a1601 = convert(T, 0.05037946855482041) + a1606 = convert(T, 0.041098361310460796) + a1607 = convert(T, 0.17180541533481958) + a1608 = convert(T, 4.614105319981519) + a1609 = convert(T, -1.7916678830853965) + a1610 = convert(T, 2.531658930485041) + a1611 = convert(T, -5.324977860205731) + a1612 = convert(T, -0.03065532595385635) + a1614 = convert(T, -0.005254479979429613) + a1615 = convert(T, -0.08399194644224793) + c17 = convert(T2, 0.7846) + a1701 = convert(T, 0.0408289713299708) + a1706 = convert(T, 0.4244479514247632) + a1707 = convert(T, 0.23260915312752345) + a1708 = convert(T, 2.677982520711806) + a1709 = convert(T, 0.7420826657338945) + a1710 = convert(T, 0.1460377847941461) + a1711 = convert(T, -3.579344509890565) + a1712 = convert(T, 0.11388443896001738) + a1714 = convert(T, 0.012677906510331901) + a1715 = convert(T, -0.07443436349946675) + a1716 = convert(T, 0.047827480797578516) + c18 = convert(T2, 0.37) + a1801 = convert(T, 0.052126823936684136) + a1806 = convert(T, 0.053925083967447975) + a1807 = convert(T, 0.01660758097434641) + a1808 = convert(T, -4.45448575792678) + a1809 = convert(T, 6.835218278632146) + a1810 = convert(T, -8.711334822181994) + a1811 = convert(T, 6.491635839232917) + a1812 = convert(T, -0.07072551809844346) + a1814 = convert(T, -0.018540314919932164) + a1815 = convert(T, 0.023504021054353848) + a1816 = convert(T, 0.2344795103407822) + a1817 = convert(T, -0.08241072501152899) + c19 = convert(T2, 0.5) + a1901 = convert(T, 0.05020102870355714) + a1906 = convert(T, 0.1552209034795498) + a1907 = convert(T, 0.1264268424089235) + a1908 = convert(T, -5.149206303539847) + a1909 = convert(T, 8.46834099903693) + a1910 = convert(T, -10.662130681081495) + a1911 = convert(T, 7.541833224959729) + a1912 = convert(T, -0.07436968113832143) + a1914 = convert(T, -0.020558876866183826) + a1915 = convert(T, 0.07753795264710298) + a1916 = convert(T, 0.10462592203525443) + a1917 = convert(T, -0.11792133064519794) + c20 = convert(T2, 0.7) + a2001 = convert(T, 0.03737341446457826) + a2006 = convert(T, 0.35049307053383166) + a2007 = convert(T, 0.49226528193730257) + a2008 = convert(T, 8.553695439359313) + a2009 = convert(T, -10.353172990305913) + a2010 = convert(T, 13.83320427252915) + a2011 = convert(T, -12.280924330784618) + a2012 = convert(T, 0.17191515956565098) + a2014 = convert(T, 0.036415831143144964) + a2015 = convert(T, 0.02961920580288763) + a2016 = convert(T, -0.2651793938627067) + a2017 = convert(T, 0.09429503961738067) + c21 = convert(T2, 0.9) + a2101 = convert(T, 0.039390583455282506) + a2106 = convert(T, 0.3558516141234424) + a2107 = convert(T, 0.419738222595261) + a2108 = convert(T, 0.8720449778071941) + a2109 = convert(T, 0.8989520834876595) + a2110 = convert(T, -0.6305806161059884) + a2111 = convert(T, -1.1218872205954835) + a2112 = convert(T, 0.04298219512400197) + a2114 = convert(T, 0.013325575668739157) + a2115 = convert(T, 0.018762270539641482) + a2116 = convert(T, -0.18594111329221055) + a2117 = convert(T, 0.17736142719246029) + + Vern8ExtraStages(c14, a1401, a1406, a1407, a1408, a1409, a1410, a1411, a1412, c15, + a1501, a1506, a1507, a1508, a1509, a1510, a1511, a1512, a1514, c16, + a1601, a1606, a1607, a1608, a1609, a1610, a1611, a1612, a1614, a1615, + c17, a1701, a1706, a1707, a1708, a1709, a1710, a1711, a1712, a1714, + a1715, a1716, c18, a1801, a1806, a1807, a1808, a1809, a1810, a1811, + a1812, a1814, a1815, a1816, a1817, c19, a1901, a1906, a1907, a1908, + a1909, a1910, a1911, a1912, a1914, a1915, a1916, a1917, c20, a2001, + a2006, a2007, a2008, a2009, a2010, a2011, a2012, a2014, a2015, a2016, + a2017, c21, a2101, a2106, a2107, a2108, a2109, a2110, a2111, a2112, + a2114, a2115, a2116, a2117) +end + +function Vern8ExtraStages(T, T2) + c14 = convert(T2, 1) + a1401 = convert(T, big" .4427989419007951074716746668098518862111e-1") + a1406 = convert(T, big" .3541049391724448744815552028733568354121") + a1407 = convert(T, big" .2479692154956437828667629415370663023884") + a1408 = convert(T, big"-15.69420203883808405099207034271191213468") + a1409 = convert(T, big" 25.08406496555856261343930031237186278518") + a1410 = convert(T, big"-31.73836778626027646833156112007297739997") + a1411 = convert(T, big" 22.93828327398878395231483560344797018313") + a1412 = convert(T, big"-.2361324633071542145259900641263517600737") + c15 = convert(T2, big" .3110177634953863863927417318829099695921") + a1501 = convert(T, big" .4620700646754963101730413150238116432863e-1") + a1506 = convert(T, big" .4503904160842480866828520384400679697151e-1") + a1507 = convert(T, big" .2336816697713424410788701065340221126565") + a1508 = convert(T, big" 37.83901368421067410780338220861855254153") + a1509 = convert(T, big"-15.94911328945424610266139490307397370835") + a1510 = convert(T, big" 23.02836835181610285142510596329590091940") + a1511 = convert(T, big"-44.85578507769412524816130998016948002745") + a1512 = convert(T, big"-.6379858768647444009509067402330140781326e-1") + a1514 = convert(T, big"-.1259503554386166268241032464519842162533e-1") + c16 = convert(T2, 69 // 400) + a1601 = convert(T, big" .5037946855482040993065158747220696112586e-1") + a1606 = convert(T, big" .4109836131046079339916530614028848248545e-1") + a1607 = convert(T, big" .1718054153348195783296309209549424619697") + a1608 = convert(T, big" 4.61410531998151886974342237185977124648") + a1609 = convert(T, big"-1.791667883085396449712744996746836471721") + a1610 = convert(T, big" 2.531658930485041408462243518792913614971") + a1611 = convert(T, big"-5.32497786020573071925718815977276269909") + a1612 = convert(T, big"-.3065532595385634734924449496356513113607e-1") + a1614 = convert(T, big"-.5254479979429613570549519094377878106127e-2") + a1615 = convert(T, big"-.8399194644224792997538653464258058697156e-1") + c17 = convert(T2, 7846 // 10000) + a1701 = convert(T, big" .4082897132997079620207118756242653796386e-1") + a1706 = convert(T, big" .4244479514247632218892086657732332485609") + a1707 = convert(T, big" .2326091531275234539465100096964845486081") + a1708 = convert(T, big" 2.677982520711806062780528871014035962908") + a1709 = convert(T, big" .7420826657338945216477607044022963622057") + a1710 = convert(T, big" .1460377847941461193920992339731312296021") + a1711 = convert(T, big"-3.579344509890565218033356743825917680543") + a1712 = convert(T, big" .1138844389600173704531638716149985665239") + a1714 = convert(T, big" .1267790651033190047378693537615687232109e-1") + a1715 = convert(T, big"-.7443436349946674429752785032561552478382e-1") + a1716 = convert(T, big" .4782748079757851554575511473876987663388e-1") + c18 = convert(T2, 37 // 100) + a1801 = convert(T, big" .5212682393668413629928136927994514676607e-1") + a1806 = convert(T, big" .5392508396744797718209106862347065628649e-1") + a1807 = convert(T, big" .1660758097434640828541930599928251901718e-1") + a1808 = convert(T, big"-4.454485757926779655418936993298463071587") + a1809 = convert(T, big" 6.835218278632146381711296817968152631469") + a1810 = convert(T, big"-8.711334822181993739847172734848837971169") + a1811 = convert(T, big" 6.491635839232917053651267142703105653517") + a1812 = convert(T, big"-.7072551809844346422069985227700294651922e-1") + a1814 = convert(T, big"-.1854031491993216429111842937941202966440e-1") + a1815 = convert(T, big" .2350402105435384645116542087045962190647e-1") + a1816 = convert(T, big" .2344795103407822090556377813402774776461") + a1817 = convert(T, big"-.8241072501152898885823089698097768766651e-1") + c19 = convert(T2, 1 // 2) + a1901 = convert(T, big" .5020102870355713598699964419977883461362e-1") + a1906 = convert(T, big" .1552209034795498114932226104700567642339") + a1907 = convert(T, big" .1264268424089234914713091134864747506300") + a1908 = convert(T, big"-5.14920630353984701704917414605721854951") + a1909 = convert(T, big" 8.46834099903692926607453176331494311551") + a1910 = convert(T, big"-10.66213068108149527544209836207095498430") + a1911 = convert(T, big" 7.54183322495972836290996201569018333903") + a1912 = convert(T, big"-.743696811383214243944066492459357053774e-1") + a1914 = convert(T, big"-.2055887686618382619339821759221121764364e-1") + a1915 = convert(T, big" .775379526471029807261782993777862395844e-1") + a1916 = convert(T, big" .1046259220352544296313761971333987587377") + a1917 = convert(T, big"-.1179213306451979352145022687063013455111") + c20 = convert(T2, 7 // 10) + a2001 = convert(T, big" .3737341446457825692757506548800094134977e-1") + a2006 = convert(T, big" .3504930705338316406767087468339071089224") + a2007 = convert(T, big" .4922652819373025433298989824173484805373") + a2008 = convert(T, big" 8.553695439359312242284304421725315855379") + a2009 = convert(T, big"-10.35317299030591348532574006719207803272") + a2010 = convert(T, big" 13.83320427252914990351082875460544773493") + a2011 = convert(T, big"-12.28092433078461863729523583784519048012") + a2012 = convert(T, big" .1719151595656509762746810113378644307112") + a2014 = convert(T, big" .3641583114314496380113822384214528216140e-1") + a2015 = convert(T, big" .2961920580288763054890146412520723429115e-1") + a2016 = convert(T, big"-.2651793938627067002647615623738425030047") + a2017 = convert(T, big" .942950396173806655317007970358739475630e-1") + c21 = convert(T2, 9 // 10) + a2101 = convert(T, big" .3939058345528250943410670634923521987132e-1") + a2106 = convert(T, big" .3558516141234424183136697322755323715063") + a2107 = convert(T, big" .4197382225952610029372225526720065366258") + a2108 = convert(T, big" .872044977807194166293172525204036071060") + a2109 = convert(T, big" .898952083487659486126627160171417043611") + a2110 = convert(T, big"-.630580616105988359023456649527853470403") + a2111 = convert(T, big"-1.121887220595483550736681645425215081433") + a2112 = convert(T, big" .4298219512400197176967511031829197714867e-1") + a2114 = convert(T, big" .1332557566873915707013495891889190564164e-1") + a2115 = convert(T, big" .1876227053964148034446101291928097773800e-1") + a2116 = convert(T, big"-.1859411132922105570515379368592596513699") + a2117 = convert(T, big" .1773614271924602745226064729836361000042") + + Vern8ExtraStages(c14, a1401, a1406, a1407, a1408, a1409, a1410, a1411, a1412, c15, + a1501, a1506, a1507, a1508, a1509, a1510, a1511, a1512, a1514, c16, + a1601, a1606, a1607, a1608, a1609, a1610, a1611, a1612, a1614, a1615, + c17, a1701, a1706, a1707, a1708, a1709, a1710, a1711, a1712, a1714, + a1715, a1716, c18, a1801, a1806, a1807, a1808, a1809, a1810, a1811, + a1812, a1814, a1815, a1816, a1817, c19, a1901, a1906, a1907, a1908, + a1909, a1910, a1911, a1912, a1914, a1915, a1916, a1917, c20, a2001, + a2006, a2007, a2008, a2009, a2010, a2011, a2012, a2014, a2015, a2016, + a2017, c21, a2101, a2106, a2107, a2108, a2109, a2110, a2111, a2112, + a2114, a2115, a2116, a2117) +end + +struct Vern8InterpolationCoefficients{T} + r011::T + r012::T + r013::T + r014::T + r015::T + r016::T + r017::T + r018::T + r062::T + r063::T + r064::T + r065::T + r066::T + r067::T + r068::T + r072::T + r073::T + r074::T + r075::T + r076::T + r077::T + r078::T + r082::T + r083::T + r084::T + r085::T + r086::T + r087::T + r088::T + r092::T + r093::T + r094::T + r095::T + r096::T + r097::T + r098::T + r102::T + r103::T + r104::T + r105::T + r106::T + r107::T + r108::T + r112::T + r113::T + r114::T + r115::T + r116::T + r117::T + r118::T + r122::T + r123::T + r124::T + r125::T + r126::T + r127::T + r128::T + r142::T + r143::T + r144::T + r145::T + r146::T + r147::T + r148::T + r152::T + r153::T + r154::T + r155::T + r156::T + r157::T + r158::T + r162::T + r163::T + r164::T + r165::T + r166::T + r167::T + r168::T + r172::T + r173::T + r174::T + r175::T + r176::T + r177::T + r178::T + r182::T + r183::T + r184::T + r185::T + r186::T + r187::T + r188::T + r192::T + r193::T + r194::T + r195::T + r196::T + r197::T + r198::T + r202::T + r203::T + r204::T + r205::T + r206::T + r207::T + r208::T + r212::T + r213::T + r214::T + r215::T + r216::T + r217::T + r218::T +end + +function Vern8InterpolationCoefficients(T::Type{<:CompiledFloats}) + r011 = convert(T, 1) + r012 = convert(T, -10.039154650554519) + r013 = convert(T, 53.79210495862331) + r014 = convert(T, -165.0579057235472) + r015 = convert(T, 298.026456543461) + r016 = convert(T, -311.91254487079004) + r017 = convert(T, 174.60598526911716) + r018 = convert(T, -40.37066163211959) + r062 = convert(T, 158.1976739121776) + r063 = convert(T, -1543.96141721949) + r064 = convert(T, 6241.39874782878) + r065 = convert(T, -13136.516156406109) + r066 = convert(T, 15106.948493169599) + r067 = convert(T, -8996.489626298231) + r068 = convert(T, 2170.776389952444) + r072 = convert(T, 110.78115200797782) + r073 = convert(T, -1081.1905145356177) + r074 = convert(T, 4370.666940459977) + r075 = convert(T, -9199.113723922197) + r076 = convert(T, 10578.949209629855) + r077 = convert(T, -6299.975594978841) + r078 = convert(T, 1520.1305005543413) + r082 = convert(T, -7011.442038211314) + r083 = convert(T, 68429.55220744078) + r084 = convert(T, -276623.5714822198) + r085 = convert(T, 582220.4545548494) + r086 = convert(T, -669551.5244611246) + r087 = convert(T, 398731.3087623333) + r088 = convert(T, -96210.47174510667) + r092 = convert(T, 11206.397569848148) + r093 = convert(T, -109371.04854950662) + r094 = convert(T, 442127.8393698155) + r095 = convert(T, -930563.7629864562) + r096 = convert(T, 1.0701451335855902e6) + r097 = convert(T, -637292.8058429047) + r098 = convert(T, 153773.3309185794) + r102 = convert(T, -14179.231640455684) + r103 = convert(T, 138385.00931963572) + r104 = convert(T, -559415.549024087) + r105 = convert(T, 1.1774237946992505e6) + r106 = convert(T, -1.3540333227908213e6) + r107 = convert(T, 806353.893882505) + r108 = convert(T, -194566.3328138133) + r112 = convert(T, 10247.761767921746) + r113 = convert(T, -100015.05326375231) + r114 = convert(T, 404306.62401434296) + r115 = convert(T, -850959.9711689702) + r116 = convert(T, 978601.0462088685) + r117 = convert(T, -582776.4729907749) + r118 = convert(T, 140619.0037156383) + r122 = convert(T, -105.49303976850968) + r123 = convert(T, 1029.5801395803103) + r124 = convert(T, -4162.034181876453) + r125 = convert(T, 8759.996193602336) + r126 = convert(T, -10073.965556886049) + r127 = convert(T, 5999.247741473951) + r128 = convert(T, -1447.5674285888924) + r142 = convert(T, -14.863613373267432) + r143 = convert(T, 145.76359364894867) + r144 = convert(T, -587.6557063401914) + r145 = convert(T, 1227.3721512545558) + r146 = convert(T, -1394.4931057405536) + r147 = convert(T, 816.8562950730669) + r148 = convert(T, -192.97961452255882) + r152 = convert(T, 14.349685752905462) + r153 = convert(T, -150.29493444816657) + r154 = convert(T, 629.481242570029) + r155 = convert(T, -1352.5182073090607) + r156 = convert(T, 1575.8969337088804) + r157 = convert(T, -946.7876580472948) + r158 = convert(T, 229.87293777270722) + r162 = convert(T, -102.54524701110401) + r163 = convert(T, 1074.0326612646807) + r164 = convert(T, -4498.377917100411) + r165 = convert(T, 9665.320624003281) + r166 = convert(T, -11261.62224831288) + r167 = convert(T, 6765.902468760784) + r168 = convert(T, -1642.7103416043497) + r172 = convert(T, -38.13206313286474) + r173 = convert(T, 399.3854658292329) + r174 = convert(T, -1672.7487204919717) + r175 = convert(T, 3594.1072548585666) + r176 = convert(T, -4187.7015568029265) + r177 = convert(T, 2515.9412806490636) + r178 = convert(T, -610.8516609091005) + r182 = convert(T, -66.38279583069588) + r183 = convert(T, 595.8297683881103) + r184 = convert(T, -2188.7370600929717) + r185 = convert(T, 4213.839795282853) + r186 = convert(T, -4484.035731929197) + r187 = convert(T, 2500.6482514253466) + r188 = convert(T, -571.1622272434449) + r192 = convert(T, -90.4188757317306) + r193 = convert(T, 931.9503884048154) + r194 = convert(T, -3962.898377713156) + r195 = convert(T, 8733.31742002555) + r196 = convert(T, -10445.908189887661) + r197 = convert(T, 6426.218942917599) + r198 = convert(T, -1592.261308015418) + r202 = convert(T, -59.738843630388715) + r203 = convert(T, 544.8870146891725) + r204 = convert(T, -2090.4303749263127) + r205 = convert(T, 4194.418982707227) + r206 = convert(T, -4603.369436819628) + r207 = convert(T, 2619.2014135592976) + r208 = convert(T, -604.9687555793671) + r212 = convert(T, -59.20053764683937) + r213 = convert(T, 571.7660156218088) + r214 = convert(T, -2308.9495644453605) + r215 = convert(T, 4881.2341106861395) + r216 = convert(T, -5660.118807771202) + r217 = convert(T, 3408.7066890374217) + r218 = convert(T, -833.4379054819676) + + Vern8InterpolationCoefficients(r011, r012, r013, r014, r015, r016, r017, r018, r062, + r063, r064, r065, r066, r067, r068, r072, r073, r074, + r075, r076, r077, r078, r082, r083, r084, r085, r086, + r087, r088, r092, r093, r094, r095, r096, r097, r098, + r102, r103, r104, r105, r106, r107, r108, r112, r113, + r114, r115, r116, r117, r118, r122, r123, r124, r125, + r126, r127, r128, r142, r143, r144, r145, r146, r147, + r148, r152, r153, r154, r155, r156, r157, r158, r162, + r163, r164, r165, r166, r167, r168, r172, r173, r174, + r175, r176, r177, r178, r182, r183, r184, r185, r186, + r187, r188, r192, r193, r194, r195, r196, r197, r198, + r202, r203, r204, r205, r206, r207, r208, r212, r213, + r214, r215, r216, r217, r218) +end + +function Vern8InterpolationCoefficients(T) + r011 = convert(T, big" 1") + r012 = convert(T, big"-10.03915465055451898280745009553727015838") + r013 = convert(T, big" 53.79210495862331394937504547285261606206") + r014 = convert(T, big"-165.0579057235472167092186792753028629327") + r015 = convert(T, big" 298.0264565434610102489744601822776142620") + r016 = convert(T, big"-311.9125448707900689751032283191627986699") + r017 = convert(T, big" 174.6059852691171542761046061351126284335") + r018 = convert(T, big"-40.37066163211959429657758663355894180800") + r062 = convert(T, big" 158.1976739121776138067531004299642556045") + r063 = convert(T, big"-1543.961417219490013383329186557376850919") + r064 = convert(T, big" 6241.398747828780065219699818963300847515") + r065 = convert(T, big"-13136.51615640610824674042591770724411138") + r066 = convert(T, big" 15106.94849316959941770760848348143558467") + r067 = convert(T, big"-8996.489626298230413000758717864256649583") + r068 = convert(T, big" 2170.776389952444021264933974457050280938") + r072 = convert(T, big" 110.7811520079778201620910891542159716196") + r073 = convert(T, big"-1081.190514535617748557462051373884811281") + r074 = convert(T, big" 4370.666940459977376891679103587685016930") + r075 = convert(T, big"-9199.113723922197066947453657458673365167") + r076 = convert(T, big" 10578.94920962985483690180716390515207397") + r077 = convert(T, big"-6299.975594978841008450271944308599363057") + r078 = convert(T, big" 1520.130500554341433782477059435641543286") + r082 = convert(T, big"-7011.442038211314089634068023254940106045") + r083 = convert(T, big" 68429.55220744077890209519664603903716349") + r084 = convert(T, big"-276623.5714822198169288202316196287008724") + r085 = convert(T, big" 582220.4545548494658856503006312634684934") + r086 = convert(T, big"-669551.5244611245601905652331468068626208") + r087 = convert(T, big" 398731.3087623332757943809792249308827732") + r088 = convert(T, big"-96210.47174510666745715793578288559674281") + r092 = convert(T, big" 11206.39756984814734031374482605836502113") + r093 = convert(T, big"-109371.0485495066182770525095928736321803") + r094 = convert(T, big" 442127.8393698154661543505844693555049508") + r095 = convert(T, big"-930563.7629864562145364082427559715712707") + r096 = convert(T, big" 1070145.133585590072636708771436125254933") + r097 = convert(T, big"-637292.8058429046904373075590712408701797") + r098 = convert(T, big" 153773.3309185793956820086499888593205888") + r102 = convert(T, big"-14179.23164045568390825368995504736244876") + r103 = convert(T, big" 138385.0093196357218693716546019209270760") + r104 = convert(T, big"-559415.5490240869974273158302752589638112") + r105 = convert(T, big" 1177423.794699250413603625249340565972051") + r106 = convert(T, big"-1354033.322790821429356166591306087001182") + r107 = convert(T, big" 806353.8938825050195016379699232308969498") + r108 = convert(T, big"-194566.3328138133045593670938904445416121") + r112 = convert(T, big" 10247.76176792174468727263230424253072668") + r113 = convert(T, big"-100015.0532637523107509874155382267979521") + r114 = convert(T, big" 404306.6240143429367125014776377339233105") + r115 = convert(T, big"-850959.9711689702682710993795157496434280") + r116 = convert(T, big" 978601.0462088684697300958464199995189771") + r117 = convert(T, big"-582776.4729907748855939796622931794117500") + r118 = convert(T, big" 140619.0037156383022701488158207833280861") + r122 = convert(T, big"-105.4930397685096787379931952745881034169") + r123 = convert(T, big" 1029.580139580310194120073236423148130618") + r124 = convert(T, big"-4162.034181876452751021493197688100770349") + r125 = convert(T, big" 8759.996193602336131526447045580160767641") + r126 = convert(T, big"-10073.96555688604885441046004449728532151") + r127 = convert(T, big" 5999.247741473950186438936812025268574829") + r128 = convert(T, big"-1447.567428588892382130036646632729629570") + r142 = convert(T, big"-14.86361337326743122469601010648237947608") + r143 = convert(T, big" 145.7635936489486611601020590400812969906") + r144 = convert(T, big"-587.6557063401913588520708808169444817103") + r145 = convert(T, big" 1227.372151254555709980234511427063838550") + r146 = convert(T, big"-1394.493105740553645217117387304216418608") + r147 = convert(T, big" 816.8562950730668774494805290335070403105") + r148 = convert(T, big"-192.9796145225588132959328212730088960570") + r152 = convert(T, big" 14.34968575290546223276673100484047073648") + r153 = convert(T, big"-150.2949344481665658851785896351738227010") + r154 = convert(T, big" 629.4812425700290706612346725243246098946") + r155 = convert(T, big"-1352.518207309060677914698908083510085133") + r156 = convert(T, big" 1575.896933708880305858556996706058962503") + r157 = convert(T, big"-946.7876580472948045886633971120598201035") + r158 = convert(T, big" 229.8729377727072096359824945955196848017") + r162 = convert(T, big"-102.5452470111040085560664290210906322518") + r163 = convert(T, big" 1074.032661264680594125263250545103109541") + r164 = convert(T, big"-4498.377917100410634753487685261882069653") + r165 = convert(T, big" 9665.320624003280508099125255751992581938") + r166 = convert(T, big"-11261.62224831288113545795903649800929060") + r167 = convert(T, big" 6765.902468760784366342575368188597359812") + r168 = convert(T, big"-1642.710341604349689799450723704711058784") + r172 = convert(T, big"-38.13206313286473398334122725888547021750") + r173 = convert(T, big" 399.3854658292328681862496726489289700594") + r174 = convert(T, big"-1672.748720491971752312231602599596419744") + r175 = convert(T, big" 3594.107254858566583822606674735752304040") + r176 = convert(T, big"-4187.701556802926199931725021751236897492") + r177 = convert(T, big" 2515.941280649063720613355430002270532846") + r178 = convert(T, big"-610.8516609091004863949139257772330194915") + r182 = convert(T, big"-66.38279583069588062871084016403504860018") + r183 = convert(T, big" 595.8297683881103280237377269355990794854") + r184 = convert(T, big"-2188.737060092971609278770563269347103559") + r185 = convert(T, big" 4213.839795282852421559730676511794767863") + r186 = convert(T, big"-4484.035731929196864370162258757955490985") + r187 = convert(T, big" 2500.648251425346544829791147364129986790") + r188 = convert(T, big"-571.1622272434449401356158886201861909946") + r192 = convert(T, big"-90.41887573173058787343992868450872085904") + r193 = convert(T, big" 931.9503884048153706496188381219698380844") + r194 = convert(T, big"-3962.898377713156165984683269799703910403") + r195 = convert(T, big" 8733.317420025551238329244389917866097896") + r196 = convert(T, big"-10445.90818988766053535212385670877957360") + r197 = convert(T, big" 6426.218942917598693647793004359979629852") + r198 = convert(T, big"-1592.261308015418013416409177206823360972") + r202 = convert(T, big"-59.73884363038871206457816967313835076801") + r203 = convert(T, big" 544.8870146891724527559861176467523778088") + r204 = convert(T, big"-2090.430374926312850791322527518588562537") + r205 = convert(T, big" 4194.418982707226648046953315742901721971") + r206 = convert(T, big"-4603.369436819628073439413527693451638704") + r207 = convert(T, big" 2619.201413559297614510795648037620577207") + r208 = convert(T, big"-604.9687555793670790184208565420961249773") + r212 = convert(T, big"-59.20053764683937384859682230934791521325") + r213 = convert(T, big" 571.7660156218088014286377638724659591261") + r214 = convert(T, big"-2308.949564445360683785335401047607870804") + r215 = convert(T, big" 4881.234110686139058221334453291392021952") + r216 = convert(T, big"-5660.118807771202003386701685793459298252") + r217 = convert(T, big" 3408.706689037421803199133730396931709513") + r218 = convert(T, big"-833.4379054819676018284720384103746063216") + + Vern8InterpolationCoefficients(r011, r012, r013, r014, r015, r016, r017, r018, r062, + r063, r064, r065, r066, r067, r068, r072, r073, r074, + r075, r076, r077, r078, r082, r083, r084, r085, r086, + r087, r088, r092, r093, r094, r095, r096, r097, r098, + r102, r103, r104, r105, r106, r107, r108, r112, r113, + r114, r115, r116, r117, r118, r122, r123, r124, r125, + r126, r127, r128, r142, r143, r144, r145, r146, r147, + r148, r152, r153, r154, r155, r156, r157, r158, r162, + r163, r164, r165, r166, r167, r168, r172, r173, r174, + r175, r176, r177, r178, r182, r183, r184, r185, r186, + r187, r188, r192, r193, r194, r195, r196, r197, r198, + r202, r203, r204, r205, r206, r207, r208, r212, r213, + r214, r215, r216, r217, r218) +end + +struct Vern8Tableau{T, T2} + c2::T2 + c3::T2 + c4::T2 + c5::T2 + c6::T2 + c7::T2 + c8::T2 + c9::T2 + c10::T2 + c11::T2 + a0201::T + a0301::T + a0302::T + a0401::T + a0403::T + a0501::T + a0503::T + a0504::T + a0601::T + a0604::T + a0605::T + a0701::T + a0704::T + a0705::T + a0706::T + a0801::T + a0804::T + a0805::T + a0806::T + a0807::T + a0901::T + a0904::T + a0905::T + a0906::T + a0907::T + a0908::T + a1001::T + a1004::T + a1005::T + a1006::T + a1007::T + a1008::T + a1009::T + a1101::T + a1104::T + a1105::T + a1106::T + a1107::T + a1108::T + a1109::T + a1110::T + a1201::T + a1204::T + a1205::T + a1206::T + a1207::T + a1208::T + a1209::T + a1210::T + a1211::T + a1301::T + a1304::T + a1305::T + a1306::T + a1307::T + a1308::T + a1309::T + a1310::T + b1::T + b6::T + b7::T + b8::T + b9::T + b10::T + b11::T + b12::T + btilde1::T + btilde6::T + btilde7::T + btilde8::T + btilde9::T + btilde10::T + btilde11::T + btilde12::T + btilde13::T + extra::Vern8ExtraStages{T, T2} + interp::Vern8InterpolationCoefficients{T} +end + +function Vern8Tableau(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) + c2 = convert(T2, 0.05) + c3 = convert(T2, 0.1065625) + c4 = convert(T2, 0.15984375) + c5 = convert(T2, 0.39) + c6 = convert(T2, 0.465) + c7 = convert(T2, 0.155) + c8 = convert(T2, 0.943) + c9 = convert(T2, 0.901802041735857) + c10 = convert(T2, 0.909) + c11 = convert(T2, 0.94) + #c12 =convert(T2, 1) + #c13 =convert(T2, 1) + a0201 = convert(T, 0.05) + a0301 = convert(T, -0.0069931640625) + a0302 = convert(T, 0.1135556640625) + a0401 = convert(T, 0.0399609375) + a0403 = convert(T, 0.1198828125) + a0501 = convert(T, 0.36139756280045754) + a0503 = convert(T, -1.3415240667004928) + a0504 = convert(T, 1.3701265039000352) + a0601 = convert(T, 0.049047202797202795) + a0604 = convert(T, 0.23509720422144048) + a0605 = convert(T, 0.18085559298135673) + a0701 = convert(T, 0.06169289044289044) + a0704 = convert(T, 0.11236568314640277) + a0705 = convert(T, -0.03885046071451367) + a0706 = convert(T, 0.01979188712522046) + a0801 = convert(T, -1.767630240222327) + a0804 = convert(T, -62.5) + a0805 = convert(T, -6.061889377376669) + a0806 = convert(T, 5.6508231982227635) + a0807 = convert(T, 65.62169641937624) + a0901 = convert(T, -1.1809450665549708) + a0904 = convert(T, -41.50473441114321) + a0905 = convert(T, -4.434438319103725) + a0906 = convert(T, 4.260408188586133) + a0907 = convert(T, 43.75364022446172) + a0908 = convert(T, 0.00787142548991231) + a1001 = convert(T, -1.2814059994414884) + a1004 = convert(T, -45.047139960139866) + a1005 = convert(T, -4.731362069449576) + a1006 = convert(T, 4.514967016593808) + a1007 = convert(T, 47.44909557172985) + a1008 = convert(T, 0.01059228297111661) + a1009 = convert(T, -0.0057468422638446166) + a1101 = convert(T, -1.7244701342624853) + a1104 = convert(T, -60.92349008483054) + a1105 = convert(T, -5.951518376222392) + a1106 = convert(T, 5.556523730698456) + a1107 = convert(T, 63.98301198033305) + a1108 = convert(T, 0.014642028250414961) + a1109 = convert(T, 0.06460408772358203) + a1110 = convert(T, -0.0793032316900888) + a1201 = convert(T, -3.301622667747079) + a1204 = convert(T, -118.01127235975251) + a1205 = convert(T, -10.141422388456112) + a1206 = convert(T, 9.139311332232058) + a1207 = convert(T, 123.37594282840426) + a1208 = convert(T, 4.62324437887458) + a1209 = convert(T, -3.3832777380682018) + a1210 = convert(T, 4.527592100324618) + a1211 = convert(T, -5.828495485811623) + a1301 = convert(T, -3.039515033766309) + a1304 = convert(T, -109.26086808941763) + a1305 = convert(T, -9.290642497400293) + a1306 = convert(T, 8.43050498176491) + a1307 = convert(T, 114.20100103783314) + a1308 = convert(T, -0.9637271342145479) + a1309 = convert(T, -5.0348840888021895) + a1310 = convert(T, 5.958130824002923) + b1 = convert(T, 0.04427989419007951) + b6 = convert(T, 0.3541049391724449) + b7 = convert(T, 0.24796921549564377) + b8 = convert(T, -15.694202038838085) + b9 = convert(T, 25.084064965558564) + b10 = convert(T, -31.738367786260277) + b11 = convert(T, 22.938283273988784) + b12 = convert(T, -0.2361324633071542) + # bhat1 = convert(T,0.044312615229089795) + # bhat6 = convert(T,0.35460956423432266) + # bhat7 = convert(T,0.2478480431366653) + # bhat8 = convert(T,4.4481347324757845) + # bhat9 = convert(T,19.846886366118735) + # bhat10= convert(T,-23.58162337746562) + # bhat13= convert(T,-0.36016794372897754) + btilde1 = convert(T, -3.272103901028138e-5) + btilde6 = convert(T, -0.0005046250618777704) + btilde7 = convert(T, 0.0001211723589784759) + btilde8 = convert(T, -20.142336771313868) + btilde9 = convert(T, 5.2371785994398286) + btilde10 = convert(T, -8.156744408794658) + btilde11 = convert(T, 22.938283273988784) + btilde12 = convert(T, -0.2361324633071542) + btilde13 = convert(T, 0.36016794372897754) + + extra = Vern8ExtraStages(T, T2) + interp = Vern8InterpolationCoefficients(T) + + Vern8Tableau(c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, a0201, a0301, a0302, a0401, + a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, a0704, a0705, + a0706, a0801, a0804, a0805, a0806, a0807, a0901, a0904, a0905, a0906, + a0907, a0908, a1001, a1004, a1005, a1006, a1007, a1008, a1009, a1101, + a1104, a1105, a1106, a1107, a1108, a1109, a1110, a1201, a1204, a1205, + a1206, a1207, a1208, a1209, a1210, a1211, a1301, a1304, a1305, a1306, + a1307, a1308, a1309, a1310, b1, b6, b7, b8, b9, b10, b11, b12, btilde1, + btilde6, btilde7, btilde8, btilde9, btilde10, btilde11, btilde12, btilde13, + extra, interp) +end + +function Vern8Tableau(T, T2) + c2 = convert(T2, 1 // 20) + c3 = convert(T2, 341 // 3200) + c4 = convert(T2, 1023 // 6400) + c5 = convert(T2, 39 // 100) + c6 = convert(T2, 93 // 200) + c7 = convert(T2, 31 // 200) + c8 = convert(T2, 943 // 1000) + c9 = convert(T2, 7067558016280 // 7837150160667) + c10 = convert(T2, 909 // 1000) + c11 = convert(T2, 47 // 50) + #c12 =convert(T2, 1) + #c13 =convert(T2, 1) + a0201 = convert(T, 1 // 20) + a0301 = convert(T, -7161 // 1024000) + a0302 = convert(T, 116281 // 1024000) + a0401 = convert(T, 1023 // 25600) + a0403 = convert(T, 3069 // 25600) + a0501 = convert(T, 4202367 // 11628100) + a0503 = convert(T, -3899844 // 2907025) + a0504 = convert(T, 3982992 // 2907025) + a0601 = convert(T, 5611 // 114400) + a0604 = convert(T, 31744 // 135025) + a0605 = convert(T, 923521 // 5106400) + a0701 = convert(T, 21173 // 343200) + a0704 = convert(T, 8602624 // 76559175) + a0705 = convert(T, -26782109 // 689364000) + a0706 = convert(T, 5611 // 283500) + a0801 = convert(T, -1221101821869329 // 690812928000000) + a0804 = convert(T, -125 // 2) + a0805 = convert(T, -1024030607959889 // 168929280000000) + a0806 = convert(T, 1501408353528689 // 265697280000000) + a0807 = convert(T, 6070139212132283 // 92502016000000) + a0901 = convert(T, + -BigInt(1472514264486215803881384708877264246346044433307094207829051978044531801133057155) // + BigInt(1246894801620032001157059621643986024803301558393487900440453636168046069686436608)) + a0904 = convert(T, + -BigInt(5172294311085668458375175655246981230039025336933699114138315270772319372469280000) // + BigInt(124619381004809145897278630571215298365257079410236252921850936749076487132995191)) + a0905 = convert(T, + -BigInt(12070679258469254807978936441733187949484571516120469966534514296406891652614970375) // + BigInt(2722031154761657221710478184531100699497284085048389015085076961673446140398628096)) + a0906 = convert(T, + BigInt(780125155843893641323090552530431036567795592568497182701460674803126770111481625) // + BigInt(183110425412731972197889874507158786859226102980861859505241443073629143100805376)) + a0907 = convert(T, + BigInt(664113122959911642134782135839106469928140328160577035357155340392950009492511875) // + BigInt(15178465598586248136333023107295349175279765150089078301139943253016877823170816)) + a0908 = convert(T, + BigInt(10332848184452015604056836767286656859124007796970668046446015775000000) // + BigInt(1312703550036033648073834248740727914537972028638950165249582733679393783)) + a1001 = convert(T, + -BigInt(29055573360337415088538618442231036441314060511) // + BigInt(22674759891089577691327962602370597632000000000)) + a1004 = convert(T, -20462749524591049105403365239069 // 454251913499893469596231268750) + a1005 = convert(T, + -180269259803172281163724663224981097 // + 38100922558256871086579832832000000) + a1006 = convert(T, + BigInt(21127670214172802870128286992003940810655221489) // + BigInt(4679473877997892906145822697976708633673728000)) + a1007 = convert(T, + BigInt(318607235173649312405151265849660869927653414425413) // + BigInt(6714716715558965303132938072935465423910912000000)) + a1008 = convert(T, + 212083202434519082281842245535894 // + 20022426044775672563822865371173879) + a1009 = convert(T, + -BigInt(2698404929400842518721166485087129798562269848229517793703413951226714583) // + BigInt(469545674913934315077000442080871141884676035902717550325616728175875000000)) + a1101 = convert(T, + -BigInt(2342659845814086836951207140065609179073838476242943917) // + BigInt(1358480961351056777022231400139158760857532162795520000)) + a1104 = convert(T, -996286030132538159613930889652 // 16353068885996164905464325675) + a1105 = convert(T, -26053085959256534152588089363841 // 4377552804565683061011299942400) + a1106 = convert(T, + BigInt(20980822345096760292224086794978105312644533925634933539) // + BigInt(3775889992007550803878727839115494641972212962174156800)) + a1107 = convert(T, + BigInt(890722993756379186418929622095833835264322635782294899) // + BigInt(13921242001395112657501941955594013822830119803764736)) + a1108 = convert(T, + BigInt(161021426143124178389075121929246710833125) // + BigInt(10997207722131034650667041364346422894371443)) + a1109 = convert(T, + BigInt(300760669768102517834232497565452434946672266195876496371874262392684852243925359864884962513) // + BigInt(4655443337501346455585065336604505603760824779615521285751892810315680492364106674524398280000)) + a1110 = convert(T, -31155237437111730665923206875 // 392862141594230515010338956291) + a1201 = convert(T, + -BigInt(2866556991825663971778295329101033887534912787724034363) // + BigInt(868226711619262703011213925016143612030669233795338240)) + a1204 = convert(T, + -BigInt(16957088714171468676387054358954754000) // + BigInt(143690415119654683326368228101570221)) + a1205 = convert(T, + -BigInt(4583493974484572912949314673356033540575) // + BigInt(451957703655250747157313034270335135744)) + a1206 = convert(T, + BigInt(2346305388553404258656258473446184419154740172519949575) // + BigInt(256726716407895402892744978301151486254183185289662464)) + a1207 = convert(T, + BigInt(1657121559319846802171283690913610698586256573484808662625) // + BigInt(13431480411255146477259155104956093505361644432088109056)) + a1208 = convert(T, + BigInt(345685379554677052215495825476969226377187500) // + BigInt(74771167436930077221667203179551347546362089)) + a1209 = convert(T, + -BigInt(3205890962717072542791434312152727534008102774023210240571361570757249056167015230160352087048674542196011) // + BigInt(947569549683965814783015124451273604984657747127257615372449205973192657306017239103491074738324033259120)) + a1210 = convert(T, + BigInt(40279545832706233433100438588458933210937500) // + BigInt(8896460842799482846916972126377338947215101)) + a1211 = convert(T, + -BigInt(6122933601070769591613093993993358877250) // + BigInt(1050517001510235513198246721302027675953)) + a1301 = convert(T, + -BigInt(618675905535482500672800859344538410358660153899637) // + BigInt(203544282118214047100119475340667684874292102389760)) + a1304 = convert(T, + -BigInt(4411194916804718600478400319122931000) // + BigInt(40373053902469967450761491269633019)) + a1305 = convert(T, + -BigInt(16734711409449292534539422531728520225) // + BigInt(1801243715290088669307203927210237952)) + a1306 = convert(T, + BigInt(135137519757054679098042184152749677761254751865630525) // + BigInt(16029587794486289597771326361911895112703716593983488)) + a1307 = convert(T, + BigInt(38937568367409876012548551903492196137929710431584875) // + BigInt(340956454090191606099548798001469306974758443147264)) + a1308 = convert(T, + -BigInt(6748865855011993037732355335815350667265625) // + BigInt(7002880395717424621213565406715087764770357)) + a1309 = convert(T, + -BigInt(1756005520307450928195422767042525091954178296002788308926563193523662404739779789732685671) // + BigInt(348767814578469983605688098046186480904607278021030540735333862087061574934154942830062320)) + a1310 = convert(T, + BigInt(53381024589235611084013897674181629296875) // + BigInt(8959357584795694524874969598508592944141)) + b1 = convert(T, 44901867737754616851973 // 1014046409980231013380680) + b6 = convert(T, 791638675191615279648100000 // 2235604725089973126411512319) + b7 = convert(T, 3847749490868980348119500000 // 15517045062138271618141237517) + b8 = convert(T, -13734512432397741476562500000 // 875132892924995907746928783) + b9 = convert(T, + BigInt(12274765470313196878428812037740635050319234276006986398294443554969616342274215316330684448207141) // + BigInt(489345147493715517650385834143510934888829280686609654482896526796523353052166757299452852166040)) + b10 = convert(T, -9798363684577739445312500000 // 308722986341456031822630699) + b11 = convert(T, 282035543183190840068750 // 12295407629873040425991) + b12 = convert(T, -306814272936976936753 // 1299331183183744997286) + # bhat1 = convert(T, 10835401739407019406577//244521829356935137978320) + # bhat6 = convert(T, 13908189778321895491375000//39221135527894265375640567) + # bhat7 = convert(T, 73487947527027243487625000//296504045773342769773399443) + # bhat8 = convert(T, 68293140641257649609375000//15353208647806945749946119) + # bhat9 = convert(T, BigInt(22060647948996678611017711379974578860522018208949721559448560203338437626022142776381)//BigInt(1111542009262325874512959185795727215759010577565736079641376621381577236680929558640)) + # bhat10= convert(T,-547971229495642458203125000//23237214025700991642563601) + # bhat13= convert(T,-28735456870978964189//79783493704265043693) + btilde1 = convert(T, -225628434546552672055 // 6895515587865570890988624) + btilde6 = convert(T, -1128142172732763360275000 // 2235604725089973126411512319) + btilde7 = convert(T, 5640710863663816801375000 // 46551135186414814854423712551) + btilde8 = convert(T, -17627221448949427504296875000 // 875132892924995907746928783) + btilde9 = convert(T, + BigInt(17426957952517932078050241885889670195876481434157580946550703126433816616672116622859678756257765) // + BigInt(3327547002957265520022623672175874357244039108668945650483696382216358800754733949636279394729072)) + btilde10 = convert(T, -17627221448949427504296875000 // 2161060904390192222758414893) + btilde11 = convert(T, 282035543183190840068750 // 12295407629873040425991) + btilde12 = convert(T, -306814272936976936753 // 1299331183183744997286) + btilde13 = convert(T, 28735456870978964189 // 79783493704265043693) + + extra = Vern8ExtraStages(T, T2) + interp = Vern8InterpolationCoefficients(T) + + Vern8Tableau(c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, a0201, a0301, a0302, a0401, + a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, a0704, a0705, + a0706, a0801, a0804, a0805, a0806, a0807, a0901, a0904, a0905, a0906, + a0907, a0908, a1001, a1004, a1005, a1006, a1007, a1008, a1009, a1101, + a1104, a1105, a1106, a1107, a1108, a1109, a1110, a1201, a1204, a1205, + a1206, a1207, a1208, a1209, a1210, a1211, a1301, a1304, a1305, a1306, + a1307, a1308, a1309, a1310, b1, b6, b7, b8, b9, b10, b11, b12, btilde1, + btilde6, btilde7, btilde8, btilde9, btilde10, btilde11, btilde12, btilde13, + extra, interp) +end + +## Vern9 +struct Vern9ExtraStages{T, T2} + c17::T2 + a1701::T + a1708::T + a1709::T + a1710::T + a1711::T + a1712::T + a1713::T + a1714::T + a1715::T + c18::T2 + a1801::T + a1808::T + a1809::T + a1810::T + a1811::T + a1812::T + a1813::T + a1814::T + a1815::T + a1817::T + c19::T2 + a1901::T + a1908::T + a1909::T + a1910::T + a1911::T + a1912::T + a1913::T + a1914::T + a1915::T + a1917::T + a1918::T + c20::T2 + a2001::T + a2008::T + a2009::T + a2010::T + a2011::T + a2012::T + a2013::T + a2014::T + a2015::T + a2017::T + a2018::T + a2019::T + c21::T2 + a2101::T + a2108::T + a2109::T + a2110::T + a2111::T + a2112::T + a2113::T + a2114::T + a2115::T + a2117::T + a2118::T + a2119::T + a2120::T + c22::T2 + a2201::T + a2208::T + a2209::T + a2210::T + a2211::T + a2212::T + a2213::T + a2214::T + a2215::T + a2217::T + a2218::T + a2219::T + a2220::T + a2221::T + c23::T2 + a2301::T + a2308::T + a2309::T + a2310::T + a2311::T + a2312::T + a2313::T + a2314::T + a2315::T + a2317::T + a2318::T + a2319::T + a2320::T + a2321::T + c24::T2 + a2401::T + a2408::T + a2409::T + a2410::T + a2411::T + a2412::T + a2413::T + a2414::T + a2415::T + a2417::T + a2418::T + a2419::T + a2420::T + a2421::T + c25::T2 + a2501::T + a2508::T + a2509::T + a2510::T + a2511::T + a2512::T + a2513::T + a2514::T + a2515::T + a2517::T + a2518::T + a2519::T + a2520::T + a2521::T + c26::T2 + a2601::T + a2608::T + a2609::T + a2610::T + a2611::T + a2612::T + a2613::T + a2614::T + a2615::T + a2617::T + a2618::T + a2619::T + a2620::T + a2621::T +end + +@fold function Vern9ExtraStages(::Type{T}, + ::Type{T2}) where {T <: CompiledFloats, + T2 <: CompiledFloats} + # FIVE ADDITIONAL STAGES FOR INTERPOLANT OF ORDER 8 + c17 = convert(T2, 1) + a1701 = convert(T, 0.014611976858423152) + a1708 = convert(T, -0.3915211862331339) + a1709 = convert(T, 0.23109325002895065) + a1710 = convert(T, 0.12747667699928525) + a1711 = convert(T, 0.2246434176204158) + a1712 = convert(T, 0.5684352689748513) + a1713 = convert(T, 0.058258715572158275) + a1714 = convert(T, 0.13643174034822156) + a1715 = convert(T, 0.030570139830827976) + c18 = convert(T2, 0.7404185470631561) + a1801 = convert(T, 0.015499736681895594) + a1808 = convert(T, 0.3355153219059635) + a1809 = convert(T, 0.20036139441918607) + a1810 = convert(T, 0.12520606592835493) + a1811 = convert(T, 0.22986763931842066) + a1812 = convert(T, -0.20202506534761813) + a1813 = convert(T, 0.05917103230665457) + a1814 = convert(T, -0.026518347830476387) + a1815 = convert(T, -0.023840946021309713) + a1817 = convert(T, 0.027181715702085017) + c19 = convert(T2, 0.888) + a1901 = convert(T, 0.013024539431143383) + a1908 = convert(T, -0.7452850902413112) + a1909 = convert(T, 0.2643867896429301) + a1910 = convert(T, 0.1313961758372754) + a1911 = convert(T, 0.21672538151229273) + a1912 = convert(T, 0.8734117564076053) + a1913 = convert(T, 0.011859056439357767) + a1914 = convert(T, 0.05876002941689551) + a1915 = convert(T, 0.003266518630202088) + a1917 = convert(T, -0.00895930864841793) + a1918 = convert(T, 0.06941415157202692) + c20 = convert(T2, 0.696) + a2001 = convert(T, 0.013970899969259426) + a2008 = convert(T, -0.46657653359576745) + a2009 = convert(T, 0.24163727872162571) + a2010 = convert(T, 0.12903633413456747) + a2011 = convert(T, 0.22167006717351054) + a2012 = convert(T, 0.6257275123364645) + a2013 = convert(T, 0.04355312415679284) + a2014 = convert(T, 0.10119624916672908) + a2015 = convert(T, 0.01808582254679721) + a2017 = convert(T, -0.020798755876891697) + a2018 = convert(T, -0.09022232517086219) + a2019 = convert(T, -0.12127967356222542) + c21 = convert(T2, 0.487) + a2101 = convert(T, 0.016046388883181127) + a2108 = convert(T, 0.09517712399458336) + a2109 = convert(T, 0.13591872646553177) + a2110 = convert(T, 0.1237765280959854) + a2111 = convert(T, 0.2335656264102966) + a2112 = convert(T, -0.09051508172625873) + a2113 = convert(T, -0.02537574270006131) + a2114 = convert(T, -0.13596316968871622) + a2115 = convert(T, -0.04679214284145113) + a2117 = convert(T, 0.05177958859391748) + a2118 = convert(T, 0.09672595677476774) + a2119 = convert(T, 0.14773126903407427) + a2120 = convert(T, -0.11507507129585039) + + # FIVE ADDITIONAL STAGES FOR INTERPOLANT OF ORDER 9 + c22 = convert(T2, 0.025) + a2201 = convert(T, 0.018029186238936207) + a2208 = convert(T, 0.06983601042028874) + a2209 = convert(T, -0.025412476607916634) + a2210 = convert(T, 0.008487827035463275) + a2211 = convert(T, -0.002427525516089802) + a2212 = convert(T, -0.10478397528938199) + a2213 = convert(T, -0.014731477952480419) + a2214 = convert(T, -0.03916338390816177) + a2215 = convert(T, -0.010056573432939595) + a2217 = convert(T, 0.011025103922048344) + a2218 = convert(T, 0.005092830749095398) + a2219 = convert(T, 0.04759715599420645) + a2220 = convert(T, 0.03386307003288383) + a2221 = convert(T, 0.02764422831404798) + c23 = convert(T2, 0.15) + a2301 = convert(T, 0.01677431640522778) + a2308 = convert(T, 0.6220437408820475) + a2309 = convert(T, -0.2060859809768842) + a2310 = convert(T, 0.11563949897660589) + a2311 = convert(T, 0.026641017933783588) + a2312 = convert(T, -0.937681079341877) + a2313 = convert(T, -0.13678064667021603) + a2314 = convert(T, -0.3678480995268297) + a2315 = convert(T, -0.09547871314402478) + a2317 = convert(T, 0.10134920184223697) + a2318 = convert(T, -0.08911323084568594) + a2319 = convert(T, 0.46641409889747604) + a2320 = convert(T, 0.450273629235458) + a2321 = convert(T, 0.18385224633268188) + c24 = convert(T2, 0.32) + a2401 = convert(T, 0.010711497314914442) + a2408 = convert(T, -0.07094336118221108) + a2409 = convert(T, 0.10021649003400916) + a2410 = convert(T, 0.13834539804680251) + a2411 = convert(T, 0.17963306335781634) + a2412 = convert(T, 0.09048246545576182) + a2413 = convert(T, -0.005460662294523339) + a2414 = convert(T, -0.030004579051196197) + a2415 = convert(T, -0.011451920269627991) + a2417 = convert(T, 0.010033946861093851) + a2418 = convert(T, -0.09506485282809046) + a2419 = convert(T, 0.04853358804093592) + a2420 = convert(T, 0.08013325919783924) + a2421 = convert(T, -0.1251643326835242) + c25 = convert(T2, 0.78) + a2501 = convert(T, 0.014101720888692213) + a2508 = convert(T, -0.3713379753704491) + a2509 = convert(T, 0.22312655481171803) + a2510 = convert(T, 0.12870053459181202) + a2511 = convert(T, 0.22246006596754947) + a2512 = convert(T, 0.5382853042550702) + a2513 = convert(T, 0.05417202616988763) + a2514 = convert(T, 0.1256968791308744) + a2515 = convert(T, 0.027844927890020542) + a2517 = convert(T, -0.0307740924620506) + a2518 = convert(T, 0.008569805293689777) + a2519 = convert(T, -0.15351746905870445) + a2520 = convert(T, -0.021799570305481963) + a2521 = convert(T, 0.014471288197371868) + c26 = convert(T2, 0.96) + a2601 = convert(T, 0.014246004117356466) + a2608 = convert(T, -0.3767107393295407) + a2609 = convert(T, 0.22523997807304214) + a2610 = convert(T, 0.128360307629253) + a2611 = convert(T, 0.22302387052616926) + a2612 = convert(T, 0.5463127827750747) + a2613 = convert(T, 0.0552619079137578) + a2614 = convert(T, 0.12856135087499826) + a2615 = convert(T, 0.028572506812964065) + a2617 = convert(T, -0.02398761886357109) + a2618 = convert(T, 0.055562244589105095) + a2619 = convert(T, -0.017406756507628386) + a2620 = convert(T, -0.03815462365996979) + a2621 = convert(T, 0.011118785048989178) + + Vern9ExtraStages(c17, a1701, a1708, a1709, a1710, a1711, a1712, a1713, a1714, a1715, + c18, a1801, a1808, a1809, a1810, a1811, a1812, a1813, a1814, a1815, + a1817, c19, a1901, a1908, a1909, a1910, a1911, a1912, a1913, a1914, + a1915, a1917, a1918, c20, a2001, a2008, a2009, a2010, a2011, a2012, + a2013, a2014, a2015, a2017, a2018, a2019, c21, a2101, a2108, a2109, + a2110, a2111, a2112, a2113, a2114, a2115, a2117, a2118, a2119, a2120, + c22, a2201, a2208, a2209, a2210, a2211, a2212, a2213, a2214, a2215, + a2217, a2218, a2219, a2220, a2221, c23, a2301, a2308, a2309, a2310, + a2311, a2312, a2313, a2314, a2315, a2317, a2318, a2319, a2320, a2321, + c24, a2401, a2408, a2409, a2410, a2411, a2412, a2413, a2414, a2415, + a2417, a2418, a2419, a2420, a2421, c25, a2501, a2508, a2509, a2510, + a2511, a2512, a2513, a2514, a2515, a2517, a2518, a2519, a2520, a2521, + c26, a2601, a2608, a2609, a2610, a2611, a2612, a2613, a2614, a2615, + a2617, a2618, a2619, a2620, a2621) +end + +@fold function Vern9ExtraStages(::Type{T}, ::Type{T2}) where {T, T2} + # FIVE ADDITIONAL STAGES FOR INTERPOLANT OF ORDER 8 + c17 = convert(T2, 1) + a1701 = convert(T, big" .1461197685842315252051541915018784713459e-1") + a1708 = convert(T, big"-.3915211862331339089410228267288242030810") + a1709 = convert(T, big" .2310932500289506415909675644868993669908") + a1710 = convert(T, big" .1274766769992852382560589467488989175618") + a1711 = convert(T, big" .2246434176204157731566981937082069688984") + a1712 = convert(T, big" .5684352689748512932705226972873692126743") + a1713 = convert(T, big" .5825871557215827200814768021863420902155e-1") + a1714 = convert(T, big" .1364317403482215641609022744494239843327") + a1715 = convert(T, big" .3057013983082797397721005067920369646664e-1") + c18 = convert(T2, big" .7404185470631561083004100761798676215811") + a1801 = convert(T, big" .1549973668189559302279946863304789372788e-1") + a1808 = convert(T, big" .3355153219059635054403439303177105512242") + a1809 = convert(T, big" .2003613944191860651552622660712101217322") + a1810 = convert(T, big" .1252060659283549312946162355194540994211") + a1811 = convert(T, big" .2298676393184206750544046308957155868736") + a1812 = convert(T, big"-.2020250653476181447824906889122391003637") + a1813 = convert(T, big" .5917103230665456601422111997583025339897e-1") + a1814 = convert(T, big"-.2651834783047638681693835956996437528251e-1") + a1815 = convert(T, big"-.2384094602130971415278110567256446033405e-1") + a1817 = convert(T, big" .2718171570208501807097257892166705118335e-1") + c19 = convert(T2, 888 // 1000) + a1901 = convert(T, big" .1302453943114338366054520296881099431474e-1") + a1908 = convert(T, big"-.7452850902413112085299330666038981625179") + a1909 = convert(T, big" .2643867896429300961465132150322749722129") + a1910 = convert(T, big" .1313961758372753932588328082078842388890") + a1911 = convert(T, big" .2167253815122927263092467187957410643315") + a1912 = convert(T, big" .8734117564076052559016338094938888451419") + a1913 = convert(T, big" .1185905643935776688228545787724340848142e-1") + a1914 = convert(T, big" .5876002941689550612992712203494447529933e-1") + a1915 = convert(T, big" .3266518630202087866399279690939423159022e-2") + a1917 = convert(T, big"-.8959308648417929824525368306101792182274e-2") + a1918 = convert(T, big" .6941415157202692219907482080827253287034e-1") + c20 = convert(T2, 696 // 1000) + a2001 = convert(T, big" .1397089996925942721283716334050740168797e-1") + a2008 = convert(T, big"-.4665765335957674596054673402956853940520") + a2009 = convert(T, big" .2416372787216257077935214889875485248580") + a2010 = convert(T, big" .1290363341345674735721677437066933999929") + a2011 = convert(T, big" .2216700671735105311080225734522323922813") + a2012 = convert(T, big" .6257275123364644931771253383573999863003") + a2013 = convert(T, big" .4355312415679284117869124964829805160429e-1") + a2014 = convert(T, big" .1011962491667290833450024852274278874501") + a2015 = convert(T, big" .1808582254679721049279369742685497400353e-1") + a2017 = convert(T, big"-.2079875587689169691156509689282083267654e-1") + a2018 = convert(T, big"-.9022232517086218976198252891464664868640e-1") + a2019 = convert(T, big"-.1212796735622254216011467740438097427634") + c21 = convert(T2, 487 // 1000) + a2101 = convert(T, big" .1604638888318112738641232352800290501904e-1") + a2108 = convert(T, big" .9517712399458336651642257453589397190702e-1") + a2109 = convert(T, big" .1359187264655317806136927180199100622471") + a2110 = convert(T, big" .1237765280959854006935081364365637515893") + a2111 = convert(T, big" .2335656264102966047058755123098072346246") + a2112 = convert(T, big"-.9051508172625873314662090873741762206189e-1") + a2113 = convert(T, big"-.2537574270006131028513276914038326155331e-1") + a2114 = convert(T, big"-.1359631696887162048002744757083947500478") + a2115 = convert(T, big"-.4679214284145113075088049469061349990847e-1") + a2117 = convert(T, big" .5177958859391748239949773879090325427473e-1") + a2118 = convert(T, big" .9672595677476773313884172931875718705561e-1") + a2119 = convert(T, big" .1477312690340742769720989417101989769314") + a2120 = convert(T, big"-.1150750712958503934434410263732282100773") + + # FIVE ADDITIONAL STAGES FOR INTERPOLANT OF ORDER 9 + c22 = convert(T2, 1 // 40) + a2201 = convert(T, big" .1802918623893620731908165792176564180038e-1") + a2208 = convert(T, big" .6983601042028873702545973390560096201728e-1") + a2209 = convert(T, big"-.2541247660791663512384395986842781657182e-1") + a2210 = convert(T, big" .8487827035463274491721441398893680307535e-2") + a2211 = convert(T, big"-.2427525516089801645451101966852425715128e-2") + a2212 = convert(T, big"-.1047839752893819879012607694745789515746") + a2213 = convert(T, big"-.1473147795248041942353840372690095884761e-1") + a2214 = convert(T, big"-.3916338390816177165706892282751065537530e-1") + a2215 = convert(T, big"-.1005657343293959419073236542225421561652e-1") + a2217 = convert(T, big" .1102510392204834322538452331445716455061e-1") + a2218 = convert(T, big" .5092830749095398308703438556315975226108e-2") + a2219 = convert(T, big" .4759715599420644505591133410826632557391e-1") + a2220 = convert(T, big" .3386307003288382751110965442296681690349e-1") + a2221 = convert(T, big" .2764422831404797700452373965825845732168e-1") + c23 = convert(T2, 15 // 100) + a2301 = convert(T, big" .1677431640522778042988664067637191163626e-1") + a2308 = convert(T, big" .6220437408820475326702539861577894278533") + a2309 = convert(T, big"-.2060859809768841878234097076241307428139") + a2310 = convert(T, big" .1156394989766058889629372195583391792474") + a2311 = convert(T, big" .2664101793378358946544219293685167025971e-1") + a2312 = convert(T, big"-.9376810793418770527505892794460093668860") + a2313 = convert(T, big"-.1367806466702160302637074581619101741312") + a2314 = convert(T, big"-.3678480995268296672182605288991379118419") + a2315 = convert(T, big"-.9547871314402478902820445838193201497337e-1") + a2317 = convert(T, big" .1013492018422369748729008873270013785313") + a2318 = convert(T, big"-.8911323084568593396468400926074881389560e-1") + a2319 = convert(T, big" .4664140988974760478895528270623735057521") + a2320 = convert(T, big" .4502736292354579812232681662308722738519") + a2321 = convert(T, big" .1838522463326818655346135218242696774099") + c24 = convert(T2, 32 // 100) + a2401 = convert(T, big" .1071149731491444187554380927165768658192e-1") + a2408 = convert(T, big"-.7094336118221108191937165464264324417735e-1") + a2409 = convert(T, big" .1002164900340091596740582334112699697590") + a2410 = convert(T, big" .1383453980468025108839271214703390659581") + a2411 = convert(T, big" .1796330633578163411338104055485109917477") + a2412 = convert(T, big" .9048246545576180974879274948815422276563e-1") + a2413 = convert(T, big"-.5460662294523338383345981122023862069115e-2") + a2414 = convert(T, big"-.3000457905119619782973021046143166498567e-1") + a2415 = convert(T, big"-.1145192026962799093665613252151017277867e-1") + a2417 = convert(T, big" .1003394686109385076849515422360600302176e-1") + a2418 = convert(T, big"-.9506485282809046129031027932806241113157e-1") + a2419 = convert(T, big" .4853358804093591445756711642658478691640e-1") + a2420 = convert(T, big" .8013325919783924638483373011297347396327e-1") + a2421 = convert(T, big"-.1251643326835242045676140618774248455713") + c25 = convert(T2, 78 // 100) + a2501 = convert(T, big" .1410172088869221367153586187761994182069e-1") + a2508 = convert(T, big"-.3713379753704491105936205420001801316029") + a2509 = convert(T, big" .2231265548117180273161442520179150684520") + a2510 = convert(T, big" .1287005345918120122888629169443916280865") + a2511 = convert(T, big" .2224600659675494761192249831098918110654") + a2512 = convert(T, big" .5382853042550701952740528638168708946100") + a2513 = convert(T, big" .5417202616988763101781128062036252796548e-1") + a2514 = convert(T, big" .1256968791308743925752109039299467082975") + a2515 = convert(T, big" .2784492789002054061504430663197543089132e-1") + a2517 = convert(T, big"-.3077409246205059733390460511525401688205e-1") + a2518 = convert(T, big" .8569805293689777608077303071761466118035e-2") + a2519 = convert(T, big"-.1535174690587044615794997685221990516897") + a2520 = convert(T, big"-.2179957030548196497189489878038029238243e-1") + a2521 = convert(T, big" .1447128819737186799295514239727801525027e-1") + c26 = convert(T2, 96 // 100) + a2601 = convert(T, big" .1424600411735646609296566581447532773183e-1") + a2608 = convert(T, big"-.3767107393295407091303982522049390741260") + a2609 = convert(T, big" .2252399780730421480874737297000189000070") + a2610 = convert(T, big" .1283603076292529988314451246143633426068") + a2611 = convert(T, big" .2230238705261692544876826347415151339678") + a2612 = convert(T, big" .5463127827750747224899202176094949607118") + a2613 = convert(T, big" .5526190791375779994553849469706124289752e-1") + a2614 = convert(T, big" .1285613508749982456581494397108686240388") + a2615 = convert(T, big" .2857250681296406482698934635829147899039e-1") + a2617 = convert(T, big"-.2398761886357108720930416967644499057175e-1") + a2618 = convert(T, big" .5556224458910509454379297181908734648749e-1") + a2619 = convert(T, big"-.1740675650762838674257930398070760254668e-1") + a2620 = convert(T, big"-.3815462365996979065575121886854199471011e-1") + a2621 = convert(T, big" .1111878504898917877407531966545730451506e-1") + + Vern9ExtraStages(c17, a1701, a1708, a1709, a1710, a1711, a1712, a1713, a1714, a1715, + c18, a1801, a1808, a1809, a1810, a1811, a1812, a1813, a1814, a1815, + a1817, c19, a1901, a1908, a1909, a1910, a1911, a1912, a1913, a1914, + a1915, a1917, a1918, c20, a2001, a2008, a2009, a2010, a2011, a2012, + a2013, a2014, a2015, a2017, a2018, a2019, c21, a2101, a2108, a2109, + a2110, a2111, a2112, a2113, a2114, a2115, a2117, a2118, a2119, a2120, + c22, a2201, a2208, a2209, a2210, a2211, a2212, a2213, a2214, a2215, + a2217, a2218, a2219, a2220, a2221, c23, a2301, a2308, a2309, a2310, + a2311, a2312, a2313, a2314, a2315, a2317, a2318, a2319, a2320, a2321, + c24, a2401, a2408, a2409, a2410, a2411, a2412, a2413, a2414, a2415, + a2417, a2418, a2419, a2420, a2421, c25, a2501, a2508, a2509, a2510, + a2511, a2512, a2513, a2514, a2515, a2517, a2518, a2519, a2520, a2521, + c26, a2601, a2608, a2609, a2610, a2611, a2612, a2613, a2614, a2615, + a2617, a2618, a2619, a2620, a2621) +end + +struct Vern9InterpolationCoefficients{T} + r011::T + r012::T + r013::T + r014::T + r015::T + r016::T + r017::T + r018::T + r019::T + r082::T + r083::T + r084::T + r085::T + r086::T + r087::T + r088::T + r089::T + r092::T + r093::T + r094::T + r095::T + r096::T + r097::T + r098::T + r099::T + r102::T + r103::T + r104::T + r105::T + r106::T + r107::T + r108::T + r109::T + r112::T + r113::T + r114::T + r115::T + r116::T + r117::T + r118::T + r119::T + r122::T + r123::T + r124::T + r125::T + r126::T + r127::T + r128::T + r129::T + r132::T + r133::T + r134::T + r135::T + r136::T + r137::T + r138::T + r139::T + r142::T + r143::T + r144::T + r145::T + r146::T + r147::T + r148::T + r149::T + r152::T + r153::T + r154::T + r155::T + r156::T + r157::T + r158::T + r159::T + r172::T + r173::T + r174::T + r175::T + r176::T + r177::T + r178::T + r179::T + r182::T + r183::T + r184::T + r185::T + r186::T + r187::T + r188::T + r189::T + r192::T + r193::T + r194::T + r195::T + r196::T + r197::T + r198::T + r199::T + r202::T + r203::T + r204::T + r205::T + r206::T + r207::T + r208::T + r209::T + r212::T + r213::T + r214::T + r215::T + r216::T + r217::T + r218::T + r219::T + r222::T + r223::T + r224::T + r225::T + r226::T + r227::T + r228::T + r229::T + r232::T + r233::T + r234::T + r235::T + r236::T + r237::T + r238::T + r239::T + r242::T + r243::T + r244::T + r245::T + r246::T + r247::T + r248::T + r249::T + r252::T + r253::T + r254::T + r255::T + r256::T + r257::T + r258::T + r259::T + r262::T + r263::T + r264::T + r265::T + r266::T + r267::T + r268::T + r269::T +end + +@fold function Vern9InterpolationCoefficients(::Type{T}) where {T <: CompiledFloats} + r011 = convert(T, 1) + r012 = convert(T, -28.330488700617398) + r013 = convert(T, 257.6535452078578) + r014 = convert(T, -1152.1544557434572) + r015 = convert(T, 2909.390878345409) + r016 = convert(T, -4355.005172868188) + r017 = convert(T, 3834.083497036262) + r018 = convert(T, -1835.419052683407) + r019 = convert(T, 368.7958613829998) + r082 = convert(T, 2.649656243770091) + r083 = convert(T, -96.30312807816006) + r084 = convert(T, 869.3095462492796) + r085 = convert(T, -3395.688567551074) + r086 = convert(T, 6796.933987158715) + r087 = convert(T, -7340.848417712072) + r088 = convert(T, 4082.8488969923656) + r089 = convert(T, -919.2934944890586) + r092 = convert(T, -1.5639451819287329) + r093 = convert(T, 56.8423973927286) + r094 = convert(T, -513.1052300304285) + r095 = convert(T, 2004.2867021103232) + r096 = convert(T, -4011.8533059139295) + r097 = convert(T, 4332.895839278586) + r098 = convert(T, -2409.8793479371448) + r099 = convert(T, 542.6079835318221) + r102 = convert(T, -0.8627103334967224) + r103 = convert(T, 31.355653751851733) + r104 = convert(T, -283.0413682227354) + r105 = convert(T, 1105.613463426007) + r106 = convert(T, -2213.0362006784526) + r107 = convert(T, 2390.1310977541207) + r108 = convert(T, -1329.3482661468738) + r109 = convert(T, 299.31580712657853) + r112 = convert(T, -1.5202953379012147) + r113 = convert(T, 55.25592121120227) + r114 = convert(T, -498.7844190970741) + r115 = convert(T, 1948.346888525776) + r116 = convert(T, -3899.8821364075516) + r117 = convert(T, 4211.964345158858) + r118 = convert(T, -2342.619408856117) + r119 = convert(T, 527.4637482204279) + r122 = convert(T, -3.8469388441255234) + r123 = convert(T, 139.81898409868404) + r124 = convert(T, -1262.1186876216004) + r125 = convert(T, 4930.075848057311) + r126 = convert(T, -9868.21948606954) + r127 = convert(T, 10657.908924348867) + r128 = convert(T, -5927.738759872814) + r129 = convert(T, 1334.688551172191) + r132 = convert(T, -0.39427130612001415) + r133 = convert(T, 14.329994760676497) + r134 = convert(T, -129.35406659945582) + r135 = convert(T, 505.28160770025175) + r136 = convert(T, -1011.3900801394333) + r137 = convert(T, 1092.3250517818917) + r138 = convert(T, -607.531701930281) + r139 = convert(T, 136.79172444804232) + r142 = convert(T, -0.9233145622082102) + r143 = convert(T, 33.55834582309799) + r144 = convert(T, -302.9246397549736) + r145 = convert(T, 1183.2813069678675) + r146 = convert(T, -2368.4989867901113) + r147 = convert(T, 2558.034559755808) + r148 = convert(T, -1422.7331755778803) + r149 = convert(T, 320.3423358787482) + r152 = convert(T, -0.20688628029300538) + r153 = convert(T, 7.519388975651663) + r154 = convert(T, -67.87605708082904) + r155 = convert(T, 265.136799698415) + r156 = convert(T, -530.7074807559026) + r157 = convert(T, 573.176549564149) + r158 = convert(T, -318.7905688834869) + r159 = convert(T, 71.77882490212657) + r172 = convert(T, -0.44724419067440996) + r173 = convert(T, 16.44684676010504) + r174 = convert(T, -154.40861059212955) + r175 = convert(T, 641.8986298540249) + r176 = convert(T, -1391.9392256879823) + r177 = convert(T, 1643.890568302952) + r178 = convert(T, -1004.0652972233179) + r179 = convert(T, 248.6243327770223) + r182 = convert(T, -0.1507876007899798) + r183 = convert(T, 5.527328824824632) + r184 = convert(T, -51.33833743084619) + r185 = convert(T, 209.60220027032804) + r186 = convert(T, -442.7692650421826) + r187 = convert(T, 505.0579312588053) + r188 = convert(T, -295.63364106156195) + r189 = convert(T, 69.70457078142275) + r192 = convert(T, -0.6413652207435296) + r193 = convert(T, 23.510132486246846) + r194 = convert(T, -218.36426832469724) + r195 = convert(T, 891.5292818535365) + r196 = convert(T, -1883.290177206008) + r197 = convert(T, 2148.2309544883997) + r198 = convert(T, -1257.4584015217124) + r199 = convert(T, 296.4838434449778) + r202 = convert(T, 1.8107293134448457) + r203 = convert(T, -66.37479657295337) + r204 = convert(T, 616.4952025401107) + r205 = convert(T, -2517.0030307773227) + r206 = convert(T, 5316.984175781034) + r207 = convert(T, -6064.976140789574) + r208 = convert(T, 3550.1095388883914) + r209 = convert(T, -837.0456783831302) + r212 = convert(T, 0.05176008760353718) + r213 = convert(T, -1.8973378625803488) + r214 = convert(T, 17.622648207936294) + r215 = convert(T, -71.94907400242467) + r216 = convert(T, 151.9871383765666) + r217 = convert(T, -173.36864987478606) + r218 = convert(T, 101.4806461521468) + r219 = convert(T, -23.927131084462175) + r222 = convert(T, 31.321782556688) + r223 = convert(T, -355.6570858339106) + r224 = convert(T, 1752.6852824895159) + r225 = convert(T, -4708.092293138363) + r226 = convert(T, 7370.900776193489) + r227 = convert(T, -6716.504964764566) + r228 = convert(T, 3303.940398161186) + r229 = convert(T, -678.5938956640391) + r232 = convert(T, -2.7196073341859246) + r233 = convert(T, 86.64045615858264) + r234 = convert(T, -454.1926030939031) + r235 = convert(T, 1014.7492211005434) + r236 = convert(T, -1133.583456714544) + r237 = convert(T, 610.4671827718666) + r238 = convert(T, -109.02334994495438) + r239 = convert(T, -12.337842943405471) + r242 = convert(T, 3.1772148014329233) + r243 = convert(T, -113.8098697715143) + r244 = convert(T, 978.0935981825675) + r245 = convert(T, -3575.1293776236703) + r246 = convert(T, 6764.3615198384505) + r247 = convert(T, -6987.161043852012) + r248 = convert(T, 3751.9057627895713) + r249 = convert(T, -821.4378043648254) + r252 = convert(T, 0.877284308346553) + r253 = convert(T, -31.51810423988375) + r254 = convert(T, 273.1229151353221) + r255 = convert(T, -993.2198643101782) + r256 = convert(T, 1787.888078312664) + r257 = convert(T, -1677.394835799641) + r258 = convert(T, 781.3579535062688) + r259 = convert(T, -141.11342691289855) + r262 = convert(T, 1.7194275817987157) + r263 = convert(T, -62.89867309250732) + r264 = convert(T, 580.333550787398) + r265 = convert(T, -2348.110620506761) + r266 = convert(T, 4921.119298612906) + r267 = convert(T, -5597.912448707917) + r268 = convert(T, 3288.5977751496216) + r269 = convert(T, -782.8483098245397) + + Vern9InterpolationCoefficients(r011, r012, r013, r014, r015, r016, r017, r018, r019, + r082, r083, r084, r085, r086, r087, r088, r089, r092, + r093, r094, r095, r096, r097, r098, r099, r102, r103, + r104, r105, r106, r107, r108, r109, r112, r113, r114, + r115, r116, r117, r118, r119, r122, r123, r124, r125, + r126, r127, r128, r129, r132, r133, r134, r135, r136, + r137, r138, r139, r142, r143, r144, r145, r146, r147, + r148, r149, r152, r153, r154, r155, r156, r157, r158, + r159, r172, r173, r174, r175, r176, r177, r178, r179, + r182, r183, r184, r185, r186, r187, r188, r189, r192, + r193, r194, r195, r196, r197, r198, r199, r202, r203, + r204, r205, r206, r207, r208, r209, r212, r213, r214, + r215, r216, r217, r218, r219, r222, r223, r224, r225, + r226, r227, r228, r229, r232, r233, r234, r235, r236, + r237, r238, r239, r242, r243, r244, r245, r246, r247, + r248, r249, r252, r253, r254, r255, r256, r257, r258, + r259, r262, r263, r264, r265, r266, r267, r268, r269) +end + +function Vern9InterpolationCoefficients(T) + r011 = convert(T, 1) + r012 = convert(T, big"-28.33048870061739823290767301658881994700") + r013 = convert(T, big" 257.6535452078577977252092979905248156497") + r014 = convert(T, big"-1152.154455743457311528752964691951881858") + r015 = convert(T, big" 2909.390878345408890936564599116550031880") + r016 = convert(T, big"-4355.005172868188498048946108887283528629") + r017 = convert(T, big" 3834.083497036262189455855371796461857871") + r018 = convert(T, big"-1835.419052683407081215583427992189311730") + r019 = convert(T, big" 368.7958613829998340610814211036270246107") + r082 = convert(T, big" 2.649656243770091212685381903551424676261") + r083 = convert(T, big"-96.30312807816005963630382777245983513008") + r084 = convert(T, big" 869.3095462492795755338599928089438369769") + r085 = convert(T, big"-3395.688567551074115525201961265641584358") + r086 = convert(T, big" 6796.933987158715680563278170147156885480") + r087 = convert(T, big"-7340.848417712071304684606060804637321789") + r088 = convert(T, big" 4082.848896992365666259441580054990759905") + r089 = convert(T, big"-919.2934944890586676320942978986329899642") + r092 = convert(T, big"-1.563945181928732780647121505551017046606") + r093 = convert(T, big" 56.84239739272860000194549791973820565214") + r094 = convert(T, big"-513.1052300304284642178552372517916694426") + r095 = convert(T, big" 2004.286702110323162741493515173880535381") + r096 = convert(T, big"-4011.853305913929339500285683507736138334") + r097 = convert(T, big" 4332.895839278586189971336003691596594090") + r098 = convert(T, big"-2409.879347937144606091337260195738587773") + r099 = convert(T, big" 542.6079835318221405169412532400889768401") + r102 = convert(T, big"-.8627103334967223830653368770735555216700") + r103 = convert(T, big" 31.35565375185173442495465167501846267906") + r104 = convert(T, big"-283.0413682227354209126847112083546012674") + r105 = convert(T, big" 1105.613463426006937052739159664962261462") + r106 = convert(T, big"-2213.036200678452629288185991597653042989") + r107 = convert(T, big" 2390.131097754120588994847482867886207858") + r108 = convert(T, big"-1329.348266146873716496636094950745123424") + r109 = convert(T, big" 299.3158071265785138462868993727082901209") + r112 = convert(T, big"-1.520295337901214839055193576160469820911") + r113 = convert(T, big" 55.25592121120227100440616045452813504748") + r114 = convert(T, big"-498.7844190970740738969945498750124435385") + r115 = convert(T, big" 1948.346888525776056658403461666308795237") + r116 = convert(T, big"-3899.882136407551390287649940376076923682") + r117 = convert(T, big" 4211.964345158858030803618536151121927765") + r118 = convert(T, big"-2342.619408856117128087568672414857706561") + r119 = convert(T, big" 527.4637482204278644179968961638568925209") + r122 = convert(T, big"-3.846938844125523400516071820264700141179") + r123 = convert(T, big" 139.8189840986840520353362018994734906611") + r124 = convert(T, big"-1262.118687621600386514715930156791825893") + r125 = convert(T, big" 4930.075848057311658057235318456802793199") + r126 = convert(T, big"-9868.219486069539059368988308801366826185") + r127 = convert(T, big" 10657.90892434886730229746304583865145121") + r128 = convert(T, big"-5927.738759872814112912292792695856187255") + r129 = convert(T, big" 1334.688551172190921099749059976639173619") + r132 = convert(T, big"-.3942713061200141454309326713125653612517") + r133 = convert(T, big" 14.32999476067649707020689155180345562459") + r134 = convert(T, big"-129.3540665994558117853022852051786116929") + r135 = convert(T, big" 505.2816077002517600897861155496606850457") + r136 = convert(T, big"-1011.390080139433268878243655218566636574") + r137 = convert(T, big" 1092.325051781891697669369143688906543465") + r138 = convert(T, big"-607.5317019302810290917918493845279272648") + r139 = convert(T, big" 136.7917244480423273434147193694336909663") + r142 = convert(T, big"-.9233145622082101394378429409444333268499") + r143 = convert(T, big" 33.55834582309798808260613735851232640640") + r144 = convert(T, big"-302.9246397549735936661321348695774835448") + r145 = convert(T, big" 1183.281306967867553342903125095128753568") + r146 = convert(T, big"-2368.498986790111516106072390247333149007") + r147 = convert(T, big" 2558.034559755808027369106332027405169828") + r148 = convert(T, big"-1422.733175577880214903071122439856598476") + r149 = convert(T, big" 320.3423358787481875842587982911148385364") + r152 = convert(T, big"-.2068862802930053801253649628830330891017") + r153 = convert(T, big" 7.519388975651662772174695012120581518594") + r154 = convert(T, big"-67.87605708082904058354114755731111898667") + r155 = convert(T, big" 265.1367996984150421661637988925923843021") + r156 = convert(T, big"-530.7074807559025368587558119659212235622") + r157 = convert(T, big" 573.1765495641490277116961329189087439579") + r158 = convert(T, big"-318.7905688834868978004500126002971837241") + r159 = convert(T, big" 71.77882490212657594681492031347005327988") + r172 = convert(T, big"-.4472441906744099441704338175964823026105") + r173 = convert(T, big" 16.44684676010503791623763886833381020592") + r174 = convert(T, big"-154.4086105921295528355180056633078150675") + r175 = convert(T, big" 641.8986298540248497333509289273669726482") + r176 = convert(T, big"-1391.939225687982391028602609567895699003") + r177 = convert(T, big" 1643.890568302952013019278202625162156841") + r178 = convert(T, big"-1004.065297223317845596795060426393517046") + r179 = convert(T, big" 248.6243327770222987362193390543305737239") + r182 = convert(T, big"-.1507876007899797948720901584434839156279") + r183 = convert(T, big" 5.527328824824632235316362126620825363280") + r184 = convert(T, big"-51.33833743084618751433903968701557585387") + r185 = convert(T, big" 209.6022002703280347991393999433060881829") + r186 = convert(T, big"-442.7692650421825928714839983614217797969") + r187 = convert(T, big" 505.0579312588052893780948070449787925777") + r188 = convert(T, big"-295.6336410615619366143935619944592839974") + r189 = convert(T, big" 69.70457078142274038253812108643441743987") + r192 = convert(T, big"-.6413652207435296452288504944964177537185") + r193 = convert(T, big" 23.51013248624684600263471193689787394701") + r194 = convert(T, big"-218.3642683246972281497485359238725613162") + r195 = convert(T, big" 891.5292818535365634586829868055833114383") + r196 = convert(T, big"-1883.290177206007885518558760085145850658") + r197 = convert(T, big" 2148.230954488399755970660772306573864434") + r198 = convert(T, big"-1257.458401521712336970840850120592935471") + r199 = convert(T, big" 296.4838434449778148523985255750527153802") + r202 = convert(T, big" 1.810729313444845732964058528284532356045") + r203 = convert(T, big"-66.37479657295337371220255196726289169374") + r204 = convert(T, big" 616.4952025401106511929691356878863855003") + r205 = convert(T, big"-2517.003030777322559684753470471663859295") + r206 = convert(T, big" 5316.984175781033401491488704359579721604") + r207 = convert(T, big"-6064.976140789574108556866601189158423779") + r208 = convert(T, big" 3550.109538888391317555902194852386816092") + r209 = convert(T, big"-837.0456783831301740195014698000522807852") + r212 = convert(T, big".5176008760353717918864555990277480363987e-1") + r213 = convert(T, big"-1.897337862580348756406065418550014243949") + r214 = convert(T, big" 17.62264820793629244181715147639285955422") + r215 = convert(T, big"-71.94907400242465946110661282550878163878") + r216 = convert(T, big" 151.9871383765666045085018751235590550206") + r217 = convert(T, big"-173.3686498747860565970136435029707518663") + r218 = convert(T, big" 101.4806461521468075879782291473158292931") + r219 = convert(T, big"-23.92713108446217690295957956014097092250") + r222 = convert(T, big" 31.32178255668799909977422939838912846070") + r223 = convert(T, big"-355.6570858339106059687054319211280026146") + r224 = convert(T, big" 1752.685282489515979253875884672206842255") + r225 = convert(T, big"-4708.092293138363367969732154806019707156") + r226 = convert(T, big" 7370.900776193488713149861391844801840850") + r227 = convert(T, big"-6716.504964764565347011489385051202629762") + r228 = convert(T, big" 3303.940398161185772296756776169088470785") + r229 = convert(T, big"-678.5938956640391428503413103061359428182") + r232 = convert(T, big"-2.719607334185924760747802644504744092917") + r233 = convert(T, big" 86.64045615858264001154848875638486632034") + r234 = convert(T, big"-454.1926030939030807863651114984001402596") + r235 = convert(T, big" 1014.749221100543425314268817989377200147") + r236 = convert(T, big"-1133.583456714543865890388885909333783663") + r237 = convert(T, big" 610.4671827718666569168001429679645990946") + r238 = convert(T, big"-109.0233499449543802317396567002119357593") + r239 = convert(T, big"-12.33784294340547057337599296127606178639") + r242 = convert(T, big" 3.177214801432923432265738869490200556403") + r243 = convert(T, big"-113.8098697715142983214434051918276259885") + r244 = convert(T, big" 978.0935981825675014833003847211971070224") + r245 = convert(T, big"-3575.129377623670076451027372711378100786") + r246 = convert(T, big" 6764.361519838450570830405988615992045681") + r247 = convert(T, big"-6987.161043852012362644872233028628887679") + r248 = convert(T, big" 3751.905762789571137088934326513342858381") + r249 = convert(T, big"-821.4378043648253954175634277881875971878") + r252 = convert(T, big" .8772843083465530069477626269697233842708") + r253 = convert(T, big"-31.51810423988375104361582759389916060143") + r254 = convert(T, big" 273.1229151353221133842213845530391043248") + r255 = convert(T, big"-993.2198643101781966584366870874238565290") + r256 = convert(T, big" 1787.888078312663987193988385659681964836") + r257 = convert(T, big"-1677.394835799640950953367739332661886275") + r258 = convert(T, big" 781.3579535062687952504707744453846824540") + r259 = convert(T, big"-141.1134269128985501802080532710905715931") + r262 = convert(T, big" 1.719427581798715782378897599231938082126") + r263 = convert(T, big"-62.89867309250732184389962568482931880335") + r264 = convert(T, big" 580.3335507873980391019057196688995930872") + r265 = convert(T, big"-2348.110620506760958600472968113883922730") + r266 = convert(T, big" 4921.119298612906015908637628774963068611") + r267 = convert(T, big"-5597.912448707916639109910311016358007839") + r268 = convert(T, big" 3288.597775149621789973016480733216881572") + r269 = convert(T, big"-782.8483098245396412116558219612402319811") + + Vern9InterpolationCoefficients(r011, r012, r013, r014, r015, r016, r017, r018, r019, + r082, r083, r084, r085, r086, r087, r088, r089, r092, + r093, r094, r095, r096, r097, r098, r099, r102, r103, + r104, r105, r106, r107, r108, r109, r112, r113, r114, + r115, r116, r117, r118, r119, r122, r123, r124, r125, + r126, r127, r128, r129, r132, r133, r134, r135, r136, + r137, r138, r139, r142, r143, r144, r145, r146, r147, + r148, r149, r152, r153, r154, r155, r156, r157, r158, + r159, r172, r173, r174, r175, r176, r177, r178, r179, + r182, r183, r184, r185, r186, r187, r188, r189, r192, + r193, r194, r195, r196, r197, r198, r199, r202, r203, + r204, r205, r206, r207, r208, r209, r212, r213, r214, + r215, r216, r217, r218, r219, r222, r223, r224, r225, + r226, r227, r228, r229, r232, r233, r234, r235, r236, + r237, r238, r239, r242, r243, r244, r245, r246, r247, + r248, r249, r252, r253, r254, r255, r256, r257, r258, + r259, r262, r263, r264, r265, r266, r267, r268, r269) +end + +""" +From Verner's Website +""" +struct Vern9Tableau{T, T2} + c1::T2 + c2::T2 + c3::T2 + c4::T2 + c5::T2 + c6::T2 + c7::T2 + c8::T2 + c9::T2 + c10::T2 + c11::T2 + c12::T2 + c13::T2 + a0201::T + a0301::T + a0302::T + a0401::T + a0403::T + a0501::T + a0503::T + a0504::T + a0601::T + a0604::T + a0605::T + a0701::T + a0704::T + a0705::T + a0706::T + a0801::T + a0806::T + a0807::T + a0901::T + a0906::T + a0907::T + a0908::T + a1001::T + a1006::T + a1007::T + a1008::T + a1009::T + a1101::T + a1106::T + a1107::T + a1108::T + a1109::T + a1110::T + a1201::T + a1206::T + a1207::T + a1208::T + a1209::T + a1210::T + a1211::T + a1301::T + a1306::T + a1307::T + a1308::T + a1309::T + a1310::T + a1311::T + a1312::T + a1401::T + a1406::T + a1407::T + a1408::T + a1409::T + a1410::T + a1411::T + a1412::T + a1413::T + a1501::T + a1506::T + a1507::T + a1508::T + a1509::T + a1510::T + a1511::T + a1512::T + a1513::T + a1514::T + a1601::T + a1606::T + a1607::T + a1608::T + a1609::T + a1610::T + a1611::T + a1612::T + a1613::T + b1::T + b8::T + b9::T + b10::T + b11::T + b12::T + b13::T + b14::T + b15::T + btilde1::T + btilde8::T + btilde9::T + btilde10::T + btilde11::T + btilde12::T + btilde13::T + btilde14::T + btilde15::T + btilde16::T +end + +@fold function Vern9Tableau(::Type{T}, + ::Type{T2}) where {T <: CompiledFloats, T2 <: CompiledFloats} + c1 = convert(T2, 0.03462) + c2 = convert(T2, 0.09702435063878045) + c3 = convert(T2, 0.14553652595817068) + c4 = convert(T2, 0.561) + c5 = convert(T2, 0.22900791159048503) + c6 = convert(T2, 0.544992088409515) + c7 = convert(T2, 0.645) + c8 = convert(T2, 0.48375) + c9 = convert(T2, 0.06757) + c10 = convert(T2, 0.25) + c11 = convert(T2, 0.6590650618730999) + c12 = convert(T2, 0.8206) + c13 = convert(T2, 0.9012) + a0201 = convert(T, 0.03462) + a0301 = convert(T, -0.03893354388572875) + a0302 = convert(T, 0.13595789452450918) + a0401 = convert(T, 0.03638413148954267) + a0403 = convert(T, 0.10915239446862801) + a0501 = convert(T, 2.0257639143939694) + a0503 = convert(T, -7.638023836496291) + a0504 = convert(T, 6.173259922102322) + a0601 = convert(T, 0.05112275589406061) + a0604 = convert(T, 0.17708237945550218) + a0605 = convert(T, 0.0008027762409222536) + a0701 = convert(T, 0.13160063579752163) + a0704 = convert(T, -0.2957276252669636) + a0705 = convert(T, 0.08781378035642955) + a0706 = convert(T, 0.6213052975225274) + a0801 = convert(T, 0.07166666666666667) + a0806 = convert(T, 0.33055335789153195) + a0807 = convert(T, 0.2427799754418014) + a0901 = convert(T, 0.071806640625) + a0906 = convert(T, 0.3294380283228177) + a0907 = convert(T, 0.1165190029271823) + a0908 = convert(T, -0.034013671875) + a1001 = convert(T, 0.04836757646340646) + a1006 = convert(T, 0.03928989925676164) + a1007 = convert(T, 0.10547409458903446) + a1008 = convert(T, -0.021438652846483126) + a1009 = convert(T, -0.10412291746271944) + a1101 = convert(T, -0.026645614872014785) + a1106 = convert(T, 0.03333333333333333) + a1107 = convert(T, -0.1631072244872467) + a1108 = convert(T, 0.03396081684127761) + a1109 = convert(T, 0.1572319413814626) + a1110 = convert(T, 0.21522674780318796) + a1201 = convert(T, 0.03689009248708622) + a1206 = convert(T, -0.1465181576725543) + a1207 = convert(T, 0.2242577768172024) + a1208 = convert(T, 0.02294405717066073) + a1209 = convert(T, -0.0035850052905728597) + a1210 = convert(T, 0.08669223316444385) + a1211 = convert(T, 0.43838406519683376) + a1301 = convert(T, -0.4866012215113341) + a1306 = convert(T, -6.304602650282853) + a1307 = convert(T, -0.2812456182894729) + a1308 = convert(T, -2.679019236219849) + a1309 = convert(T, 0.5188156639241577) + a1310 = convert(T, 1.3653531876033418) + a1311 = convert(T, 5.8850910885039465) + a1312 = convert(T, 2.8028087862720628) + a1401 = convert(T, 0.4185367457753472) + a1406 = convert(T, 6.724547581906459) + a1407 = convert(T, -0.42544428016461133) + a1408 = convert(T, 3.3432791530012653) + a1409 = convert(T, 0.6170816631175374) + a1410 = convert(T, -0.9299661239399329) + a1411 = convert(T, -6.099948804751011) + a1412 = convert(T, -3.002206187889399) + a1413 = convert(T, 0.2553202529443446) + a1501 = convert(T, -0.7793740861228848) + a1506 = convert(T, -13.937342538107776) + a1507 = convert(T, 1.2520488533793563) + a1508 = convert(T, -14.691500408016868) + a1509 = convert(T, -0.494705058533141) + a1510 = convert(T, 2.2429749091462368) + a1511 = convert(T, 13.367893803828643) + a1512 = convert(T, 14.396650486650687) + a1513 = convert(T, -0.79758133317768) + a1514 = convert(T, 0.4409353709534278) + a1601 = convert(T, 2.0580513374668867) + a1606 = convert(T, 22.357937727968032) + a1607 = convert(T, 0.9094981099755646) + a1608 = convert(T, 35.89110098240264) + a1609 = convert(T, -3.442515027624454) + a1610 = convert(T, -4.865481358036369) + a1611 = convert(T, -18.909803813543427) + a1612 = convert(T, -34.26354448030452) + a1613 = convert(T, 1.2647565216956427) + b1 = convert(T, 0.014611976858423152) + b8 = convert(T, -0.3915211862331339) + b9 = convert(T, 0.23109325002895065) + b10 = convert(T, 0.12747667699928525) + b11 = convert(T, 0.2246434176204158) + b12 = convert(T, 0.5684352689748513) + b13 = convert(T, 0.058258715572158275) + b14 = convert(T, 0.13643174034822156) + b15 = convert(T, 0.030570139830827976) + # bhat1 =convert(T,0.01996996514886773) + # bhat8 =convert(T,2.19149930494933) + # bhat9 =convert(T,0.08857071848208438) + # bhat10 =convert(T,0.11405602348659656) + # bhat11 =convert(T,0.2533163805345107) + # bhat12 =convert(T,-2.056564386240941) + # bhat13 =convert(T,0.340809679901312) + # bhat16 =convert(T,0.04834231373823958) + btilde1 = convert(T, -0.005357988290444578) + btilde8 = convert(T, -2.583020491182464) + btilde9 = convert(T, 0.14252253154686625) + btilde10 = convert(T, 0.013420653512688676) + btilde11 = convert(T, -0.02867296291409493) + btilde12 = convert(T, 2.624999655215792) + btilde13 = convert(T, -0.2825509643291537) + btilde14 = convert(T, 0.13643174034822156) + btilde15 = convert(T, 0.030570139830827976) + btilde16 = convert(T, -0.04834231373823958) + + Vern9Tableau(c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, a0201, a0301, + a0302, a0401, a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, + a0704, a0705, a0706, a0801, a0806, a0807, a0901, a0906, a0907, a0908, + a1001, a1006, a1007, a1008, a1009, a1101, a1106, a1107, a1108, a1109, + a1110, a1201, a1206, a1207, a1208, a1209, a1210, a1211, a1301, a1306, + a1307, a1308, a1309, a1310, a1311, a1312, a1401, a1406, a1407, a1408, + a1409, a1410, a1411, a1412, a1413, a1501, a1506, a1507, a1508, a1509, + a1510, a1511, a1512, a1513, a1514, a1601, a1606, a1607, a1608, a1609, + a1610, a1611, a1612, a1613, b1, b8, b9, b10, b11, b12, b13, b14, b15, + btilde1, btilde8, btilde9, btilde10, btilde11, btilde12, btilde13, + btilde14, btilde15, btilde16) +end + +@fold function Vern9Tableau(::Type{T}, ::Type{T2}) where {T, T2} + c1 = convert(T2, 1731 // 50000) + c2 = convert(T2, + BigInt(7630049) // BigInt(53810000) - + BigInt(983539) // BigInt(53810000) * 6^(1 // 2)) + c3 = convert(T2, + BigInt(22890147) // BigInt(107620000) - + BigInt(2950617) // BigInt(107620000) * 6^(1 // 2)) + c4 = convert(T2, 561 // 1000) + c5 = convert(T2, BigInt(387) // BigInt(1000) - BigInt(129) // BigInt(2000) * 6^(1 // 2)) + c6 = convert(T2, BigInt(387) // BigInt(1000) + BigInt(129) // BigInt(2000) * 6^(1 // 2)) + c7 = convert(T2, 129 // 200) + c8 = convert(T2, 387 // 800) + c9 = convert(T2, 6757 // 100000) + c10 = convert(T2, 1 // 4) + c11 = convert(T2, 1427971650951258372 // 2166662646162554701) + c12 = convert(T2, 4103 // 5000) + c13 = convert(T2, 2253 // 2500) + a0201 = convert(T, 1731 // 50000) + a0301 = convert(T, + -BigInt(177968356965557) // BigInt(1002427673820000) + + BigInt(14180534491313) // BigInt(250606918455000) * 6^(1 // 2)) + a0302 = convert(T, + BigInt(64021741529527) // BigInt(200485534764000) - + BigInt(7504450763411) // BigInt(100242767382000) * 6^(1 // 2)) + a0401 = convert(T, + BigInt(22890147) // BigInt(430480000) - + BigInt(2950617) // BigInt(430480000) * 6^(1 // 2)) + a0403 = convert(T, + BigInt(68670441) // BigInt(430480000) - + BigInt(8851851) // BigInt(430480000) * 6^(1 // 2)) + a0501 = convert(T, + BigInt(592203994261020339) // BigInt(513126355505556250) + + BigInt(730386990293623641) // BigInt(2052505422022225000) * 6^(1 // 2)) + a0503 = convert(T, + -BigInt(8712153884182794903) // BigInt(2052505422022225000) - + BigInt(2843421359195851533) // BigInt(2052505422022225000) * 6^(1 // 2)) + a0504 = convert(T, + BigInt(1873698362223295443) // BigInt(513126355505556250) + + BigInt(528258592225556973) // BigInt(513126355505556250) * 6^(1 // 2)) + a0601 = convert(T, + BigInt(11380823631) // BigInt(157617812000) - + BigInt(339148869) // BigInt(39404453000) * 6^(1 // 2)) + a0604 = convert(T, + BigInt(16193232887091831) // BigInt(58864341808507450) - + BigInt(2355345717024309) // BigInt(58864341808507450) * 6^(1 // 2)) + a0605 = convert(T, + BigInt(165912282616977) // BigInt(4179075230308000) - + BigInt(33181894472511) // BigInt(2089537615154000) * 6^(1 // 2)) + a0701 = convert(T, + BigInt(26523528363) // BigInt(231790900000) + + BigInt(863255358) // BigInt(123138915625) * 6^(1 // 2)) + a0704 = convert(T, + -BigInt(38208748178016484817787) // BigInt(842517966262441068418750) - + BigInt(86118788556282369822807) // BigInt(842517966262441068418750) * + 6^(1 // 2)) + a0705 = convert(T, + BigInt(92362336407446913) // BigInt(290322814529044000) - + BigInt(232039320950012997) // BigInt(2467743923496874000) * 6^(1 // 2)) + a0706 = convert(T, + -BigInt(362925891) // BigInt(1690350537500) + + BigInt(857800423623) // BigInt(3380701075000) * 6^(1 // 2)) + a0801 = convert(T, 43 // 600) + a0806 = convert(T, BigInt(43) // BigInt(150) + BigInt(43) // BigInt(2400) * 6^(1 // 2)) + a0807 = convert(T, BigInt(43) // BigInt(150) - BigInt(43) // BigInt(2400) * 6^(1 // 2)) + a0901 = convert(T, 7353 // 102400) + a0906 = convert(T, + BigInt(22833) // BigInt(102400) + + BigInt(8901) // BigInt(204800) * 6^(1 // 2)) + a0907 = convert(T, + BigInt(22833) // BigInt(102400) - + BigInt(8901) // BigInt(204800) * 6^(1 // 2)) + a0908 = convert(T, -3483 // 102400) + a1001 = convert(T, 376708742472214988700853 // 7788456028125000000000000) + a1006 = convert(T, + BigInt(187914666753956840195279) // BigInt(2596152009375000000000000) - + BigInt(210440846556290693268911) // BigInt(15576912056250000000000000) * + 6^(1 // 2)) + a1007 = convert(T, + BigInt(187914666753956840195279) // BigInt(2596152009375000000000000) + + BigInt(210440846556290693268911) // BigInt(15576912056250000000000000) * + 6^(1 // 2)) + a1008 = convert(T, -18552667221896744226647 // 865384003125000000000000) + a1009 = convert(T, -3167799860072183913409 // 30423656359863281250000) + a1101 = convert(T, + -BigInt(426968570497) // BigInt(54394415898750) - + BigInt(92754382349) // BigInt(12087647977500) * 6^(1 // 2)) + a1106 = convert(T, 1 // 30) + a1107 = convert(T, + -BigInt(2865012129681958) // BigInt(114898584332330625) - + BigInt(12962517687655099) // BigInt(229797168664661250) * 6^(1 // 2)) + a1108 = convert(T, + BigInt(4389715333607) // BigInt(309890657317500) + + BigInt(92754382349) // BigInt(11477431752500) * 6^(1 // 2)) + a1109 = convert(T, + BigInt(4990058173976) // BigInt(83757096376875) + + BigInt(371017529396) // BigInt(9306344041875) * 6^(1 // 2)) + a1110 = convert(T, + BigInt(1099523524595993125000) // BigInt(6257667909869756018891) + + BigInt(100957348037989687500) // BigInt(6257667909869756018891) * + 6^(1 // 2)) + a1201 = convert(T, + BigInt(18382031104798403869938539009154656587521498573595595063164077882800315372787284683238439478955141517997198007108623761931447163756) // + BigInt(13974256944499724344918960993890933614161025322970450047932688998095008528620821239604734608111291769444706187497807869179550841329375) + + BigInt(407885778185158609210793892517582595305896470756467612636796259611491408260896413446883450891351622914818800693274034252252905536) // + BigInt(28084926388601226073624096169175002956970191576455110633226765141161372294098693275117181239385312198137508846535933127837167926875) * + 6^(1 // 2)) + a1206 = convert(T, + -BigInt(333881311789849411971573472868128281438202210721723123251742145367734582887577395547778228760174068758086134389952015563403904) // + BigInt(2270872004608103037127689848604039623086639035441372934050180593816493796129405349914148981460714202232988727738778494557727635) + + BigInt(4819272892477768171373308666720689121421091953625792970278044071549950640195056472955523769829034800621890424847009130000000) // + BigInt(23162894447002650978702436455761204155483718161502003927311842056928236720519934569124319610899284862776485022935540644488821877) * + 6^(1 // 2)) + a1207 = convert(T, + -BigInt(136666607496463622270135608863772076443625468798139480390426740993024803946981763209348364716108721312822619845726151693667598437699964416) // + BigInt(3719286465342404274788585327254180828195282427342057650194855634917821113563432870681372043512520401887141437067106105683944802332422369375) + + BigInt(169845085565361336805556009296394374527636952379388961026066628725155521832762086875632366996477567928657535912191396155566765457826139904) // + BigInt(1593979913718173260623679425966077497797978183146596135797795272107637620098614087434873732933937315094489187314474045293119200999609586875) * + 6^(1 // 2)) + a1208 = convert(T, + BigInt(5610987899273278525411960528081442902198567594809764379756195673673265700551076812883925583370253765702553235594764427173637673766208) // + BigInt(92881598198144033018278804740626334135423356791639598109358867770361609232846012626732332450844264293840456574956036349633197336361875) - + BigInt(5587476413495323413846491678323049250765705078855720721052003556321800113162964567765526724539063327600257543743479921263738432) // + BigInt(365303089362201664516413596925286161494473575337115296250511752859728108868696929614024803255122785403232359817965288739565550625) * + 6^(1 // 2)) + a1209 = convert(T, + BigInt(54598539818083615233566148602203244896696958910734339754065270985433507945162707737759469214674480807272210648148477499238783276259328) // + BigInt(301247919092298852634886875129959310794662932014184499827145075851637298698312074030567479239502011693447423026416040794479934024058125) - + BigInt(6526172450962537747372702280281321524894343532103481802188740153783862532174342615150135214261625966637100811092384548036046488576) // + BigInt(86490932843037281836028387921320502668579653176624892284566487468170341285762869374265713247057712228954184044334206372230816544375) * + 6^(1 // 2)) + a1210 = convert(T, + BigInt(9391667348404584010955422210328707125006120661611061908889750805619418785820948002455890360939221912190524731087070645107486913457760000000) // + BigInt(58157266968773020612419028503738708303515285854970725662326801531295387265784849843172223645193277229358434488742203091272981931739152584783) - + BigInt(8108825145085088104344721048166325225173729495689364696426720161112012414227752328969720658987315654179873760357725235734000399440000000) // + BigInt(265558296661064021061274102756797754810572081529546692522040189640618206693081506133206500662983001047298787619827411375675716583283801757) * + 6^(1 // 2)) + a1211 = convert(T, + BigInt(123461712659887915177271339396606860810479028777869348014870450606260914019560285661288212498128400476015695960341952) // + BigInt(281629106670320674754245209358840703704235147307838896741075511220826056829047205614324978253226176275078922716132461)) + a1301 = convert(T, + -BigInt(56042772675322042139227629978042586330633622706053363946766144416933631) // + BigInt(58808540772323190525590122613223430507352118534557342666015625000000000) + + BigInt(281404579734699232141455524604487724159024972527) // + BigInt(1478009944832743180452316204077188415527343750000) * 6^(1 // 2)) + a1306 = convert(T, + -BigInt(1027163900229750356561238237947225332675621517) // + BigInt(179261894431132664078747698292867431640625000) - + BigInt(2745292391641202525373103979336813513372321) // + BigInt(11702216468464340311060649744558385937500000) * 6^(1 // 2)) + a1307 = convert(T, + -BigInt(157229999853748227305165773364426925282378072238332930121) // + BigInt(36699907367985458573273204094330716033963413238525390625) + + BigInt(5757606442802795095318986067317837904184278650664590252101) // + BigInt(3523191107326604023034227593055748739260487670898437500000) * + 6^(1 // 2)) + a1308 = convert(T, + -BigInt(9311448168593934146015965019904013602133802943325818346622781285907057) // + BigInt(4255970849010124217193135449668739985401313363005576159362792968750000) - + BigInt(844213739204097696424366573813463172477074917581) // + BigInt(4210188359946578336976868164966163024902343750000) * 6^(1 // 2)) + a1309 = convert(T, + BigInt(885774233856672590222951867695327816457340130391639153070521335485617578) // + BigInt(301098541380295011015469248465465290112505656143757799934635162353515625) - + BigInt(281404579734699232141455524604487724159024972527) // + BigInt(284481916364737983221402322504830303192138671875) * 6^(1 // 2)) + a1310 = convert(T, + BigInt(315479116729780153956412124052199685097744239386639023787359107959254802182) // + BigInt(134481850506505848012587842215515574380212543200894932329128471154748828125) - + BigInt(2940396453647872276646068776592292229737651937934623) // + BigInt(7345465058781983710795837429530784777245286520703125) * + 6^(1 // 2)) + a1311 = convert(T, + BigInt(2250996163406545378616532039018846586217631599453822541) // + BigInt(382491303797095993563304148204275636433504028320312500)) + a1312 = convert(T, + BigInt(2689340957307691853294902388334454003959378146957529866233529251986359392336044151708949720958809747970514366293458424272174024493) // + BigInt(959516386019578808500569114780871708466894752280482835105408027815194895319055443842782227102120493960805649575561796875000000000)) + a1401 = convert(T, + BigInt(47342003848024391498707976847688893013083074441159779465719863625051668939887702630319) // + BigInt(44802546873926050730401222636656855760802419993852060264615320801485392456054687500000) - + BigInt(866369530987077991125562402829092187100493209601) // + BigInt(3325522375873672156017711459173673934936523437500) * 6^(1 // 2)) + a1406 = convert(T, + BigInt(871779321807802447463310035318238762878527157) // + BigInt(134446420823349498059060773719650573730468750) + + BigInt(107641268480999396081848975271849857994818) // + BigInt(1097082793918531904161935913552348681640625) * 6^(1 // 2)) + a1407 = convert(T, + BigInt(496103786351862292800034805114190705484800743513354117014) // + BigInt(110099722103956375719819612282992148101890239715576171875) - + BigInt(1329938412606197485769312599390307351191540891599374831099) // + BigInt(660598332623738254318917673697952888611341438293457031250) * + 6^(1 // 2)) + a1408 = convert(T, + BigInt(40774077277747636354598451708891165494123131383777235229538611989392175193285994266471) // + BigInt(15264290546248162101058985941588079518256741255377031736357946125713524703979492187500) + + BigInt(123767075855296855875080343261298883871499029943) // + BigInt(451091609994276250390378731960660324096679687500) * 6^(1 // 2)) + a1409 = convert(T, + -BigInt(10522038608500556459828649038302068473735749030796372764961618751973793724796364606986664) // + BigInt(3899417425005422254034574000397382862235892829653375835197340918271556055507659912109375) + + BigInt(3465478123948311964502249611316368748401972838404) // + BigInt(2560337247282641848992620902543472728729248046875) * 6^(1 // 2)) + a1410 = convert(T, + -BigInt(27843764471262693189365201135620670490328475323282820219474851621693895769527094334687108984) // + BigInt(12257041066285164222002594300605593929434139193022166317802121412999357024704596261133984375) + + BigInt(574774300271998598683873114105472016699241495055292) // + BigInt(1049352151254569101542262489932969253892183788671875) * + 6^(1 // 2)) + a1411 = convert(T, + -BigInt(34241134351848245624232809437676889009431930503529853032576417589898516) // + BigInt(5613347824358651981100985009024281007603230062439942682713165283203125)) + a1412 = convert(T, + -BigInt(3432044375893932378102368568052286501033850910516999202088532705211633432793920547702800961532438008401883737341854688972639605334600163938610268855705742764072609) // + BigInt(1143174106341682260971647690410567292143926198650927778920823267461111371275907599801714870165813394147519068210931766844494994616580258435518181434575195312500000)) + a1413 = convert(T, + BigInt(4746930876023919335079451612726717649218264199984) // + BigInt(18592065538407049755200144388134089346432755594877)) + a1501 = convert(T, + -BigInt(25188329249258825443748527038142409879923012133738985313265430932280250855708601) // + BigInt(11370641325574469312056961874077298550827642308774647316995717036347558064286250) + + BigInt(1234273058981860170179592598535508631343082535549881956) // + BigInt(2105633771469628744518390642968552144069898845895808125) * + 6^(1 // 2)) + a1506 = convert(T, + -BigInt(54821142119685055562477216205428613949905430396088) // + BigInt(3959439837009461289085587746748097947393101278095) - + BigInt(1511276753825982856072891469504471256664975925000) // + BigInt(40386286337496505148672995016830599063409633036569) * 6^(1 // 2)) + a1507 = convert(T, + -BigInt(60922424274061599918603524049390657305431262635197540405697952) // + BigInt(6484861747489032169774584624759953148531564032417461909516875) + + BigInt(84558575751635978733109961893984238786929550462615375699341616) // + BigInt(19454585242467096509323753874279859445594692097252385728550625) * + 6^(1 // 2)) + a1508 = convert(T, + -BigInt(116118147575045169733222875835719955334334798191459879782123534889390467935109772) // + BigInt(8810626901954835245672275131295870892503713957512170681453300814988417642493125) - + BigInt(176324722711694310025656085505072661620440362221411708) // + BigInt(285619406719829107485771207042040133465420149964555625) * + 6^(1 // 2)) + a1509 = convert(T, + BigInt(17769448722513898342276837490665097286927607247073335618566987143467294900183033216) // + BigInt(2551217008137889615056342146084561867122485163596619283719957742418751029506356875) - + BigInt(19748368943709762722873481576568138101489320568798111296) // + BigInt(6484554262322259071286545935997129135111813687175650625) * + 6^(1 // 2)) + a1510 = convert(T, + BigInt(97659266139124074818193264801929547781659926543786381510190954184218570746215033823993530000000) // + BigInt(18560076654469706205963482908787056850812308205603127326855360961727608242796551101182080033599) - + BigInt(85297084611782122474911131363078900058888025224607913745000000) // + BigInt(69210659450201393843166746722954036326338355649915383851733911) * + 6^(1 // 2)) + a1511 = convert(T, + BigInt(473389749049752963256114649231353822492912259509649519870869750525) // + BigInt(35412440882360341799798842428365422941216508121322622479260846291)) + a1512 = convert(T, + BigInt(33351439245158438248073494056784144097872912773415904536400728387690334563968394114702414108807505158106385116468732853458202899966748488718531545706559142895903144848764637) // + BigInt(2316611025327287427714802011322252886090793904989900621592365627649097578102163572190502232425490606773312310665593424982745744299371285598588298606088543376742054644818966)) + a1513 = convert(T, + -BigInt(38714992656958413389743252726016897599283911682945255636643554687500000) // + BigInt(48540494926971587499294589382572212036169135429877901702347521300421767)) + a1514 = convert(T, + BigInt(14800250200940323717124616175641261235119295795768814717803955078125) // + BigInt(33565577125141877760287380588632421223433194078156948298488471160489)) + a1601 = convert(T, + BigInt(2305785696086397561080858186939897173645641331085041313944389849986584101287) // + BigInt(617508244345282265819087370078275122671246164669900462139876057008239440000) - + BigInt(85404623305589712632165905233974183137607899140719) // + BigInt(124822287169084833758410283469525117460541643292500) * + 6^(1 // 2)) + a1606 = convert(T, + BigInt(102903996961580448264190625267026062654799259083) // + BigInt(5046398084890004857481629999673320438819484730) + + BigInt(41320925487304219313300272052128374567081128125) // + BigInt(51473260465878049546312625996667868475958744246) * 6^(1 // 2)) + a1607 = convert(T, + BigInt(62798443349876457506718920843975661399949564598018488144466) // + BigInt(4132553498782573324058263582553715220777051359780141380625) - + BigInt(72308807081932961554425711089716771013571419950657300729103) // + BigInt(12397660496347719972174790747661145662331154079340424141875) * + 6^(1 // 2)) + a1608 = convert(T, + BigInt(1794909142126482564390848522924225553221469019751470544959297614654661293377) // + BigInt(52596481193994264435601626109752988674679691644275456716633975785978672500) + + BigInt(12200660472227101804595129319139169019658271305817) // + BigInt(16931561456559959115207709344056578263397760602500) * 6^(1 // 2)) + a1609 = convert(T, + -BigInt(2775244732780109667342845612394739319115662636371477300455747022423270475907256) // + BigInt(228417153675584029725018045422706955827996328208181619436454383447149337555625) + + BigInt(341618493222358850528663620935896732550431596562876) // + BigInt(96101338378773357469245211954911505447551097205625) * 6^(1 // 2)) + a1610 = convert(T, + -BigInt(27680554659769016623530979176727448251292244310769996015342190819068970556083063125000) // + BigInt(3299557777429648960576561382256606844677258438797072955341581354051375036522231471437) + + BigInt(4426552127579895373479670356100179759944766558141730312500) // + BigInt(3077113738667320707748877199804636746494977000658967987677) * + 6^(1 // 2)) + a1611 = convert(T, + -BigInt(292603171929706291053929402159930330736639136252680853622275) // + BigInt(15473622826279161150227076887290262443510550964275858143964)) + a1612 = convert(T, + -BigInt(9815717129569106988569302193220999343824932084582093647596086931754666098662594153095258988516305165794739744873539829069617203523509136682216933020431) // + BigInt(286476991170934153076146641094402171801937250068596542931028678669501762253287693294397689327797388113854588113430063939405071979092547998950955940992)) + a1613 = convert(T, + BigInt(2729491144709837905799148766650782532906050298971406518524169921875) // + BigInt(2158115888622139473142775812109447802920656149243127309253686951469)) + b1 = convert(T, + 8198160366203173411119943711500331 // 561057579384085860167277847128765528) + b8 = convert(T, + -BigInt(455655493073428838813281446213740000000) // + BigInt(1163808011150910561240464225837312497869)) + b9 = convert(T, + BigInt(19965163648706008081135075746915614720000000) // + BigInt(86394404190537086868394686205782432516544599)) + b10 = convert(T, + BigInt(89231107919981418705566970804343750000000000000000000000) // + BigInt(699979870988335674445594679856445060562597693583175985391)) + b11 = convert(T, + 47104273954945906713184913871143492 // + 209684639122339601934631113492763467) + b12 = convert(T, + BigInt(20845004421404500464010584740796750650832176798370383084226351294730731196673647311062330972740734737279503119387627146381678677156136042524139311907482802844083) // + BigInt(36670849891136373020238225328265100250605144718501926305140966586758054847604681466336103169284755987753542321202462371554120593858149755539878561976786592389608)) + b13 = convert(T, + BigInt(6053037282142306509795911286909179687500000000) // + BigInt(103899257350518063455290077573775162739725126989)) + b14 = convert(T, + BigInt(917401104920993498360358406096725463867187500) // + BigInt(6724249815911346653315790737453607382989551463)) + b15 = convert(T, + 2585449557665268951371699596493957 // 84574345160764140163208606048427531) + # bhat1 =convert(T,552562031208180939317806684253//27669654257734667858523344041464) + # bhat8 =convert(T,221223388631423597589898601690000000//100946136798587090054685074667127461) + # bhat9 =convert(T,BigInt(101835408791305297984657812561920000000)//BigInt(1149763833200743759976506650241312100139)) + # bhat10 =convert(T,BigInt(1313720309077630014453239843750000000000000000000)//BigInt(11518201923215510989126466531107437037395719117133)) + # bhat11 =convert(T,4833611232701440504508086151728//19081321241454145230196661524503) + # bhat12 =convert(T,-BigInt(2129662374582324648106919795703373645353118273066742230724172731025813964712473647144010599206669825382719359113196238857709025512340589957)//BigInt(1035543739272367080885190546201097218891268728118207332592595987554851882972292670881794178380097716583123063485287435793657425889233080568)) + # bhat13 =convert(T,BigInt(1084761591753640855844358063964843750000000)//BigInt(3182895486031249071938549691320502488733423)) + # bhat16 =convert(T,1839190071060649887127895100784//38045139523510634351420875415397) + btilde1 = convert(T, + -1503069970302555747713611212548875 // + 280528789692042930083638923564382764) + btilde8 = convert(T, + BigInt(-3006139940605111495427222425097750000000) // + BigInt(1163808011150910561240464225837312497869)) + btilde9 = convert(T, + BigInt(12313149196718536685269903053200384000000000) // + BigInt(86394404190537086868394686205782432516544599)) + btilde10 = convert(T, + BigInt(9394187314390973423210070078430468750000000000000000000) // + BigInt(699979870988335674445594679856445060562597693583175985391)) + btilde11 = convert(T, + -6012279881210222990854444850195500 // + 209684639122339601934631113492763467) + btilde12 = convert(T, + BigInt(48130484160351526969737032053650002390763871764386160830857331738750104951318921056416737791402447075630390197043182920376678624912056972204118525928289962576625) // + BigInt(18335424945568186510119112664132550125302572359250963152570483293379027423802340733168051584642377993876771160601231185777060296929074877769939280988393296194804)) + btilde13 = convert(T, + BigInt(-29356835357471791947531468995095214843750000000) // + BigInt(103899257350518063455290077573775162739725126989)) + btilde14 = convert(T, + BigInt(917401104920993498360358406096725463867187500) // + BigInt(6724249815911346653315790737453607382989551463)) + btilde15 = convert(T, + 2585449557665268951371699596493957 // + 84574345160764140163208606048427531) + btilde16 = convert(T, + -1839190071060649887127895100784 // 38045139523510634351420875415397) + + Vern9Tableau(c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, a0201, a0301, + a0302, a0401, a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, + a0704, a0705, a0706, a0801, a0806, a0807, a0901, a0906, a0907, a0908, + a1001, a1006, a1007, a1008, a1009, a1101, a1106, a1107, a1108, a1109, + a1110, a1201, a1206, a1207, a1208, a1209, a1210, a1211, a1301, a1306, + a1307, a1308, a1309, a1310, a1311, a1312, a1401, a1406, a1407, a1408, + a1409, a1410, a1411, a1412, a1413, a1501, a1506, a1507, a1508, a1509, + a1510, a1511, a1512, a1513, a1514, a1601, a1606, a1607, a1608, a1609, + a1610, a1611, a1612, a1613, b1, b8, b9, b10, b11, b12, b13, b14, b15, + btilde1, btilde8, btilde9, btilde10, btilde11, btilde12, btilde13, + btilde14, btilde15, btilde16) +end diff --git a/test/algconvergence/ode_extrapolation_tests.jl b/test/algconvergence/ode_extrapolation_tests.jl new file mode 100644 index 0000000000..b265b3a753 --- /dev/null +++ b/test/algconvergence/ode_extrapolation_tests.jl @@ -0,0 +1,242 @@ +# Import packages +using OrdinaryDiffEq, DiffEqDevTools, Test, Random + +# Define test problems +# Note that the time span in ODEProblemLibrary is given by +# Float64 numbers + +linear = (u, p, t) -> (p * u) +linear_analytic = (u0, p, t) -> u0 * exp(p * t) +prob_ode_bigfloatlinear = ODEProblem(ODEFunction(linear, analytic = linear_analytic), + big"0.5", (big"0.0", big"1.0"), big"1.01") + +f_2dlinear = (du, u, p, t) -> (@. du = p * u) +f_2dlinear_analytic = (u0, p, t) -> @. u0 * exp(p * t) +prob_ode_bigfloat2Dlinear = ODEProblem( + ODEFunction(f_2dlinear, + analytic = f_2dlinear_analytic), + rand(BigFloat, (4, 2)), (big"0.0", big"1.0"), + big"1.01") + +# Prepare tests +Random.seed!(100) +problem_array = [prob_ode_bigfloatlinear, prob_ode_bigfloat2Dlinear] +dts = 1 .// 2 .^ (8:-1:1) + +testTol = 0.2 + +@testset "Testing extrapolation methods" begin + + # Test AitkenNeville + println("Testing AitkenNeville") + @testset "Testing AitkenNeville" begin + @testset "Testing sequential AitkenNeville" begin + for prob in problem_array + global dts + + # Convergence test + for j in 1:4 + sim = test_convergence(dts, prob, + AitkenNeville(max_order = j, + min_order = j, init_order = j, + threading = false)) + @test sim.𝒪est[:final]≈j atol=testTol + end + + # Regression test + sol = solve(prob, + AitkenNeville(max_order = 9, min_order = 1, + init_order = 9, threading = false), reltol = 1e-3) + @test length(sol.u) < 15 + sol = solve(prob, + AitkenNeville(max_order = 9, min_order = 1, + init_order = 9, threading = false), reltol = 1e-6) + @test length(sol.u) < 18 + end + end + end # AitkenNeville + + # Define the subdividing sequences + sequence_array = [:harmonic, :romberg, :bulirsch] + + println("Testing ImplicitEulerExtrapolation") + @testset "Testing ImplicitEulerExtrapolation" begin + for prob in problem_array, + seq in sequence_array + + global dts + + newTol = 0.35 + # Convergence test + for j in 1:4 + alg = ImplicitEulerExtrapolation(min_order = j, + init_order = j, max_order = j, + sequence = seq, threading = false) + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈alg.init_order + 1.1 atol=newTol #Superconvergence + end + # Regression test + sol = solve(prob, + ImplicitEulerExtrapolation(max_order = 9, min_order = 1, + init_order = 9, sequence = seq, + threading = false), reltol = 1e-3) + @test length(sol.u) < 15 + end + end + + println("Testing ImplicitEulerBarycentricExtrapolation") + @testset "Testing ImplicitEulerBarycentricExtrapolation" begin + for prob in problem_array, + seq in sequence_array + + global dts + + newTol = 0.35 + # Convergence test + for j in 1:4 + alg = ImplicitEulerBarycentricExtrapolation(min_order = j, + init_order = j, max_order = j, + sequence = seq, + threading = false) + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈alg.init_order + 0.5 atol=newTol #Superconvergence + end + # Regression test + sol = solve(prob, + ImplicitEulerBarycentricExtrapolation(max_order = 9, min_order = 1, + init_order = 9, + sequence = seq, + threading = false), + reltol = 1e-3) + @test length(sol.u) < 15 + end + end + + println("Testing ImplicitDeuflhardExtrapolation") + @testset "Testing ImplicitDeuflhardExtrapolation" begin + for prob in problem_array, + seq in sequence_array + + global dts + + # Convergence test + for j in 1:6 + alg = ImplicitDeuflhardExtrapolation(min_order = j, + init_order = j, max_order = j, + sequence = seq, threading = false) + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈2 * (alg.init_order + 1) atol=testTol + end + + # Regression test + alg = ImplicitDeuflhardExtrapolation(max_order = 9, min_order = 1, + init_order = 9, sequence = seq, + threading = false) + sol = solve(prob, alg, reltol = 1e-3) + @test length(sol.u) < 10 + end + end + + println("Testing ImplicitHairerWannerExtrapolation") + @testset "Testing ImplicitHairerWannerExtrapolation" begin + for prob in problem_array, + seq in sequence_array + + global dts + + # Convergence test + for j in 1:6 + alg = ImplicitHairerWannerExtrapolation(min_order = j, + init_order = j, max_order = j, + sequence = seq, threading = false) + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈2 * (alg.init_order + 1) - 1 atol=testTol + end + + alg = ImplicitHairerWannerExtrapolation(max_order = 9, min_order = 1, + init_order = 9, sequence = seq, + threading = false) + sol = solve(prob, alg, reltol = 1e-3) + @test length(sol.u) < 10 + end + end + + # Test ExtrapolationMidpointDeuflhard + + println("Testing ExtrapolationMidpointDeuflhard") + @testset "Testing ExtrapolationMidpointDeuflhard" begin + @testset "Testing sequential ExtrapolationMidpointDeuflhard" begin + for prob in problem_array, + seq in sequence_array + + global dts + + # Convergence test + for j in 1:6 + alg = ExtrapolationMidpointDeuflhard(min_order = j, + init_order = j, max_order = j, + sequence = seq, threading = false) + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈2 * (alg.init_order + 1) atol=testTol + end + + # Regression test + alg = ExtrapolationMidpointDeuflhard(max_order = 9, min_order = 1, + init_order = 9, sequence = seq, + threading = false) + sol = solve(prob, alg, reltol = 1e-3) + @test length(sol.u) < 10 + end + end + end # ExtrapolationMidpointDeuflhard + + # Test ExtrapolationMidpointHairerWanner + println("Testing ExtrapolationMidpointHairerWanner") + @testset "Testing ExtrapolationMidpointHairerWanner" begin + @testset "Testing sequential ExtrapolationMidpointHairerWanner" begin + for prob in problem_array, + seq in sequence_array + + global dts + + # Convergence test + for j in 1:6 + alg = ExtrapolationMidpointHairerWanner(min_order = j, + init_order = j, max_order = j, + sequence = seq, + threading = false) + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈2 * (alg.init_order + 1) atol=testTol + end + + # Regression test + alg = ExtrapolationMidpointHairerWanner(max_order = 9, min_order = 2, + init_order = 9, sequence = seq, + threading = false) + sol = solve(prob, alg, reltol = 1e-3) + @test length(sol.u) < 10 + end + end + end # ExtrapolationMidpointHairerWanner + + println("Regression Test Float32 and Float64 Fallbacks") + @testset "Regression Test Float32 and Float64 Fallbacks" begin + prob_ode_2Dlinear = ODEProblem( + ODEFunction(f_2dlinear, + analytic = f_2dlinear_analytic), + Float64.(prob_ode_bigfloat2Dlinear.u0), (0.0, 1.0), + 1.01) + s1 = solve(prob_ode_bigfloat2Dlinear, ExtrapolationMidpointDeuflhard()) + s2 = solve(prob_ode_2Dlinear, ExtrapolationMidpointDeuflhard()) + @test all(all(s1[i] - s2[i] .< 5e-14) for i in 1:length(s1)) + + prob_ode_2Dlinear = ODEProblem( + ODEFunction(f_2dlinear, + analytic = f_2dlinear_analytic), + Float32.(prob_ode_bigfloat2Dlinear.u0), + (0.0f0, 1.0f0), 1.01f0) + s1 = solve(prob_ode_bigfloat2Dlinear, ExtrapolationMidpointDeuflhard()) + s2 = solve(prob_ode_2Dlinear, ExtrapolationMidpointDeuflhard()) + @test all(all(s1[i] - s2[i] .< 5e-6) for i in 1:length(s1)) + end +end # Extrapolation methods diff --git a/test/algconvergence/ode_feagin_tests.jl b/test/algconvergence/ode_feagin_tests.jl new file mode 100644 index 0000000000..b156fcbfc6 --- /dev/null +++ b/test/algconvergence/ode_feagin_tests.jl @@ -0,0 +1,53 @@ +using OrdinaryDiffEq, DiffEqBase, Test, DiffEqDevTools, + Random + +import ODEProblemLibrary: prob_ode_bigfloatlinear, + prob_ode_bigfloat2Dlinear, + prob_ode_2Dlinear + +## Convergence Testing +println("Convergence Test on Linear") + +testTol = 1 +prob = prob_ode_2Dlinear +println("Feagin RKs") +dts = (1 // 2) .^ (4:-1:2) +sol = solve(prob, Feagin10(), dt = dts[1]) +prob = remake(prob_ode_bigfloat2Dlinear, tspan = (big(0) // 1, big(1) // 1)) +sol = solve(prob, Feagin10(), dt = dts[1]) + +prob = remake(prob_ode_bigfloat2Dlinear, tspan = (big(0.0), big(1.0))) +dts = (1 // 2) .^ (4:-1:2) +sim = test_convergence(dts, prob, Feagin10()) +@test abs(sim.𝒪est[:final] - 8) < testTol #Lowered due to low test dt + +sim = test_convergence(dts, prob, Feagin12()) +@test abs(sim.𝒪est[:final] - 12) < testTol + +sim = test_convergence(dts, prob, Feagin14()) +@test abs(sim.𝒪est[:final] - 15) < testTol #Upped to 15 for test + +prob = prob_ode_bigfloatlinear + +dts = (1 // 2) .^ (6:-1:3) +sim = test_convergence(dts, prob, Feagin10()) +@test abs(sim.𝒪est[:final] - 10) < testTol + +dts = (1 // 2) .^ (4:-1:2) +sim = test_convergence(dts, prob, Feagin12()) +@test abs(sim.𝒪est[:final] - 12) < testTol + +sim = test_convergence(dts, prob, Feagin14()) +@test abs(sim.𝒪est[:final] - 15) < testTol #Upped to 15 for test + +prob = prob_ode_bigfloat2Dlinear + +#compile +sol = solve(prob, Feagin10(), dt = dts[1]) +sol = solve(prob, Feagin12(), dt = dts[1]) +sol = solve(prob, Feagin14(), dt = dts[1]) + +#test +@time sol = solve(prob, Feagin10(), dt = dts[1]) +@time sol = solve(prob, Feagin12(), dt = dts[1]) +@time sol = solve(prob, Feagin14(), dt = dts[1]) diff --git a/test/algconvergence/ode_firk_tests.jl b/test/algconvergence/ode_firk_tests.jl index 3672e30fa9..f901b7c80e 100644 --- a/test/algconvergence/ode_firk_tests.jl +++ b/test/algconvergence/ode_firk_tests.jl @@ -8,11 +8,11 @@ for prob in [prob_ode_linear, prob_ode_2Dlinear] @test sim21.𝒪est[:final]≈5 atol=testTol end -sim21 = test_convergence(1 ./ 2 .^ (2.777:-1:0.777), prob_ode_linear, RadauIIA7()) -@test sim21.𝒪est[:final]≈7 atol=testTol +sim21 = test_convergence(1 ./ 2 .^ (2.75:-0.5:0.25), prob_ode_linear, RadauIIA9()) +@test sim21.𝒪est[:final]≈9 atol=testTol -sim21 = test_convergence(1 ./ 2 .^ (2.777:-1:0.777), prob_ode_2Dlinear, RadauIIA7()) -@test sim21.𝒪est[:final]≈8 atol=testTol +sim21 = test_convergence(1 ./ 2 .^ (2.75:-0.5:0.25), prob_ode_2Dlinear, RadauIIA0()) +@test sim21.𝒪est[:final]≈9 atol=testTol # test adaptivity for iip in (true, false) diff --git a/test/algconvergence/ode_low_storage_rk_tests.jl b/test/algconvergence/ode_low_storage_rk_tests.jl new file mode 100644 index 0000000000..7d28903ac9 --- /dev/null +++ b/test/algconvergence/ode_low_storage_rk_tests.jl @@ -0,0 +1,1567 @@ +using OrdinaryDiffEq, DiffEqDevTools, Test, Random +import ODEProblemLibrary: prob_ode_linear, prob_ode_2Dlinear, prob_ode_bigfloat2Dlinear + +Random.seed!(100) + +testTol = 0.25 + +f = (u, p, t) -> cos(t) +prob_ode_sin = ODEProblem(ODEFunction(f; analytic = (u0, p, t) -> sin(t)), 0.0, (0.0, 1.0)) + +f = (du, u, p, t) -> du[1] = cos(t) +prob_ode_sin_inplace = ODEProblem(ODEFunction(f; analytic = (u0, p, t) -> [sin(t)]), [0.0], + (0.0, 1.0)) + +f = (u, p, t) -> sin(u) +prob_ode_nonlinear = ODEProblem( + ODEFunction(f; + analytic = (u0, p, t) -> 2 * acot(exp(-t) * + cot(0.5))), 1.0, + (0.0, 0.5)) + +f = (du, u, p, t) -> du[1] = sin(u[1]) +prob_ode_nonlinear_inplace = ODEProblem( + ODEFunction(f; + analytic = (u0, p, t) -> [ + 2 * acot(exp(-t) * cot(0.5)) + ]), + [1.0], (0.0, 0.5)) + +test_problems_only_time = [prob_ode_sin, prob_ode_sin_inplace] +test_problems_linear = [prob_ode_linear, prob_ode_2Dlinear, prob_ode_bigfloat2Dlinear] +test_problems_nonlinear = [prob_ode_nonlinear, prob_ode_nonlinear_inplace] + +# Test the memory usage, cf. #640 +# Note: Basically, the size of the integrator should be the size of the cache +# plus the size of the initial condition (stored is integ.sol.prob.u0) if the +# keyword argument `alias_u0` is not set to `true` (default). +# Note: The memory requirements of the 2N methods can be reduced if an assignment +# of the form `tmp = A2end[i]*tmp + dt*f(u, p, t+c2end[i]*dt)` can be carried out +# without saving `f(u, p, t+c2end[i]*dt)` as `k`. +u0_large = rand(10^6) +prob_ode_large = ODEProblem((du, u, p, t) -> du .= u, u0_large, (0.0, 1.0)) + +@testset "ORK256" begin + alg = ORK256() + alg2 = ORK256(; williamson_condition = false) + dts = 1 ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 2 + integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "CarpenterKennedy2N54" begin + alg = CarpenterKennedy2N54() + alg2 = CarpenterKennedy2N54(; williamson_condition = false) + dts = 1 ./ 2 .^ (7:-1:3) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 2 + integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "SHLDDRK64" begin + alg = SHLDDRK64() + alg2 = SHLDDRK64(; williamson_condition = true) + dts = 1 ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 2 + integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "DGLDDRK73_C" begin + alg = DGLDDRK73_C() + alg2 = DGLDDRK73_C(; williamson_condition = false) + dts = 1 ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 2 + integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "DGLDDRK84_C" begin + alg = DGLDDRK84_C() + alg2 = DGLDDRK84_C(; williamson_condition = false) + dts = 1 ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 2 + integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "DGLDDRK84_F" begin + alg = DGLDDRK84_F() + alg2 = DGLDDRK84_F(; williamson_condition = false) + dts = 1 ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 2 + integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "NDBLSRK124" begin + alg = NDBLSRK124() + alg2 = NDBLSRK124(; williamson_condition = false) + dts = 1 ./ 2 .^ (7:-1:3) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 2 + integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "NDBLSRK134" begin + alg = NDBLSRK134() + alg2 = NDBLSRK134(; williamson_condition = false) + dts = 1 ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 2 + integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "NDBLSRK144" begin + alg = NDBLSRK144() + alg2 = NDBLSRK144(; williamson_condition = false) + dts = 1 ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + sim = test_convergence(dts, prob, alg2) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 2 + integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "CFRLDDRK64" begin + alg = CFRLDDRK64() + dts = 1 ./ 2 .^ (7:-1:4) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "TSLDDRK74" begin + alg = TSLDDRK74() + dts = 1 ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +# Methods from Carpenter, Kennedy, Lewis (2000) + +function RemakeNew(p::ODEProblem) + u1 = @. BigFloat(p.u0) + tsp1 = @. BigFloat(p.tspan) + remake(p; u0 = u1, tspan = tsp1) +end + +test_problems_only_time_BigFloat = @. RemakeNew(test_problems_only_time) +test_problems_linear_BigFloat = @. RemakeNew(test_problems_linear) +f = (u, p, t) -> sin(u) +prob_nonlinear_A = ODEProblem( + ODEFunction(f; + analytic = (u0, p, t) -> 2 * acot(exp(-t) * + cot(BigFloat(0.5)))), + BigFloat(1.0), (BigFloat(0.0), BigFloat(0.5))) + +f = (du, u, p, t) -> du[1] = sin(u[1]) +prob_nonlinear_B = ODEProblem( + ODEFunction(f; + analytic = (u0, p, t) -> [ + 2 * acot(exp(-t) * cot(BigFloat(0.5))) + ]), + [BigFloat(1.0)], + (BigFloat(0.0), BigFloat(0.5))) +test_problems_nonlinear_BigFloat = [prob_nonlinear_A, prob_nonlinear_B] + +@testset "CKLLSRK43_2" begin + alg = CKLLSRK43_2() + dts = BigFloat(1) ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol # This scheme has linear order of 4 + end + for prob in test_problems_nonlinear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 + integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 7 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "CKLLSRK54_3C" begin + alg = CKLLSRK54_3C() + dts = BigFloat(1) ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈1 atol=testTol # The CI plot is linear but the evaluated order is 1 + end + for prob in test_problems_linear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 + integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 7 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "CKLLSRK95_4S" begin + alg = CKLLSRK95_4S() + dts = BigFloat(1) ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 + integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 7 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "CKLLSRK95_4C" begin + alg = CKLLSRK95_4C() + dts = BigFloat(1) ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time_BigFloat + sim = test_convergence(dts, prob, alg) + @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear_BigFloat + sim = test_convergence(dts, prob, alg) + @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear_BigFloat + sim = test_convergence(dts, prob, alg) + @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 + integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 7 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "CKLLSRK95_4M" begin + alg = CKLLSRK95_4M() + dts = BigFloat(1) ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 + integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 7 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "CKLLSRK54_3C_3R" begin + alg = CKLLSRK54_3C_3R() + dts = BigFloat(1) ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 + integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 10 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "CKLLSRK54_3M_3R" begin + alg = CKLLSRK54_3M_3R() + dts = BigFloat(1) ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol + end + for prob in test_problems_nonlinear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 0.5 atol=testTol + end + integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 + integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 10 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "CKLLSRK54_3N_3R" begin + alg = CKLLSRK54_3N_3R() + dts = BigFloat(1) ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 + integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 10 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "CKLLSRK85_4C_3R" begin + alg = CKLLSRK85_4C_3R() + dts = BigFloat(1) ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 + integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 10 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "CKLLSRK85_4M_3R" begin + alg = CKLLSRK85_4M_3R() + dts = BigFloat(1) ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 + integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 10 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "CKLLSRK85_4P_3R" begin + alg = CKLLSRK85_4P_3R() + dts = BigFloat(1) ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 2 atol=testTol + end + for prob in test_problems_nonlinear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 + integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 10 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "CKLLSRK54_3N_4R" begin + alg = CKLLSRK54_3N_4R() + dts = BigFloat(1) ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 11 + integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 12 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 11 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "CKLLSRK54_3M_4R" begin + alg = CKLLSRK54_3M_4R() + dts = BigFloat(1) ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 0.5 atol=testTol # This scheme has linear orderof 4.5 + end + for prob in test_problems_nonlinear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 11 + integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 12 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 11 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "CKLLSRK65_4M_4R" begin + alg = CKLLSRK65_4M_4R() + dts = BigFloat(1) ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 11 + integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 12 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 11 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "CKLLSRK85_4FM_4R" begin + alg = CKLLSRK85_4FM_4R() + dts = BigFloat(1) ./ 2 .^ (10:-1:6) + for prob in test_problems_only_time_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol + end + for prob in test_problems_nonlinear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 11 + integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 12 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 11 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "CKLLSRK75_4M_5R" begin + alg = CKLLSRK75_4M_5R() + dts = BigFloat(1) ./ 2 .^ (8:-1:4) + for prob in test_problems_only_time_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear_BigFloat + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 13 + integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, + save_end = false, save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 14 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 13 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +# Methods from Parsani, Ketcheson, Deconinck (2013) + +@testset "ParsaniKetchesonDeconinck3S32" begin + alg = ParsaniKetchesonDeconinck3S32() + dts = 1 ./ 2 .^ (7:-1:3) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + # higher order as pure quadrature + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "ParsaniKetchesonDeconinck3S82" begin + alg = ParsaniKetchesonDeconinck3S82() + dts = 1 ./ 2 .^ (8:-1:5) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + # higher order as pure quadrature + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "ParsaniKetchesonDeconinck3S53" begin + alg = ParsaniKetchesonDeconinck3S53() + dts = 1 ./ 2 .^ (7:-1:3) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + # higher order as pure quadrature + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "ParsaniKetchesonDeconinck3S173" begin + alg = ParsaniKetchesonDeconinck3S173() + dts = 1 ./ 2 .^ (7:-1:3) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + # higher order as pure quadrature + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + dts = 1 ./ 2 .^ (6:-1:3) + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=1 + end + + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "ParsaniKetchesonDeconinck3S94" begin + alg = ParsaniKetchesonDeconinck3S94() + dts = 1 ./ 2 .^ (7:-1:3) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "ParsaniKetchesonDeconinck3S184" begin + alg = ParsaniKetchesonDeconinck3S184() + dts = 1 ./ 2 .^ (6:-1:2) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + dts = 1 ./ 2 .^ (7:-1:2) + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "ParsaniKetchesonDeconinck3S105" begin + alg = ParsaniKetchesonDeconinck3S105() + dts = 1 ./ 1.95 .^ (5:-1:1) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + dts = 1 ./ 2 .^ (5:-1:2) + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + dts = 1.5 ./ 2 .^ (5:-1:2) + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "ParsaniKetchesonDeconinck3S205" begin + alg = ParsaniKetchesonDeconinck3S205() + dts = 1 ./ 1.95 .^ (5:-1:1) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + dts = 1 ./ 2 .^ (5:-1:2) + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + dts = 1.5 ./ 2 .^ (5:-1:2) + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +# Methods from Ranocha, Dalcin, Parsani, Ketcheson (2021) + +@testset "RDPK3Sp35" begin + alg = RDPK3Sp35() + dts = 1 ./ 2 .^ (7:-1:3) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + # higher order as pure quadrature + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "RDPK3Sp49" begin + alg = RDPK3Sp49() + dts = 1 ./ 2 .^ (5:-1:2) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + # higher order as pure quadrature + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + dts = 1 ./ 2 .^ (8:-1:2) + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "RDPK3Sp510" begin + alg = RDPK3Sp510() + dts = 1 ./ 2 .^ (4.5:-1:1.5) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "RDPK3SpFSAL35" begin + alg = RDPK3SpFSAL35() + dts = 1 ./ 2 .^ (7:-1:3) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + # higher order as pure quadrature + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "RDPK3SpFSAL49" begin + alg = RDPK3SpFSAL49() + dts = 1 ./ 2 .^ (5:-1:2) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + # higher order as pure quadrature + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + dts = 1 ./ 2 .^ (8:-1:2) + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end + +@testset "RDPK3SpFSAL510" begin + alg = RDPK3SpFSAL510() + dts = 1 ./ 2 .^ (4.5:-1:1.5) + for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol + end + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 + integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) + @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 + # test whether aliasing u0 is bad + new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], + (0.0, 0.5)) + sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false) + sol_new = solve( + new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, + save_start = false, alias_u0 = true) + @test sol_old[end] ≈ sol_new[end] +end diff --git a/test/algconvergence/ode_ssprk_tests.jl b/test/algconvergence/ode_ssprk_tests.jl new file mode 100644 index 0000000000..aa0402c209 --- /dev/null +++ b/test/algconvergence/ode_ssprk_tests.jl @@ -0,0 +1,534 @@ +using OrdinaryDiffEq, DiffEqDevTools, Test, Random +import ODEProblemLibrary: prob_ode_linear, prob_ode_2Dlinear, prob_ode_bigfloat2Dlinear + +Random.seed!(100) + +dts = 1 .// 2 .^ (8:-1:4) +testTol = 0.25 + +f = (u, p, t) -> cos(t) +prob_ode_sin = ODEProblem(ODEFunction(f; analytic = (u0, p, t) -> sin(t)), 0.0, (0.0, 1.0)) + +f = (du, u, p, t) -> du[1] = cos(t) +prob_ode_sin_inplace = ODEProblem(ODEFunction(f; analytic = (u0, p, t) -> [sin(t)]), [0.0], + (0.0, 1.0)) + +f = (u, p, t) -> sin(u) +prob_ode_nonlinear = ODEProblem( + ODEFunction(f; + analytic = (u0, p, t) -> 2 * acot(exp(-t) * + cot(0.5))), 1.0, + (0.0, 0.5)) + +f = (du, u, p, t) -> du[1] = sin(u[1]) +prob_ode_nonlinear_inplace = ODEProblem( + ODEFunction(f; + analytic = (u0, p, t) -> [ + 2 * acot(exp(-t) * cot(0.5)) + ]), + [1.0], (0.0, 0.5)) + +test_problems_only_time = [prob_ode_sin, prob_ode_sin_inplace] +test_problems_linear = [prob_ode_linear, prob_ode_2Dlinear, prob_ode_bigfloat2Dlinear] +test_problems_nonlinear = [prob_ode_nonlinear, prob_ode_nonlinear_inplace] + +f_ssp = (u, p, t) -> begin + sin(10t) * u * (1 - u) +end +test_problem_ssp = ODEProblem(f_ssp, 0.1, (0.0, 8.0)) +test_problem_ssp_long = ODEProblem(f_ssp, 0.1, (0.0, 1.e3)) + +f_ssp_inplace = (du, u, p, t) -> begin + @. du = sin(10t) * u * (1 - u) +end +test_problem_ssp_inplace = ODEProblem(f_ssp_inplace, rand(3, 3), (0.0, 8.0)) + +# Test the memory usage, cf. #640 +# Note: Basically, the size of the integrator should be the size of the cache +# plus the size of the initial condition, stored is integ.sol.prob.u0. +u0_large = rand(10^6) +prob_ode_large = ODEProblem((du, u, p, t) -> du .= u, u0_large, (0.0, 1.0)) + +# test SSP coefficient for explicit Euler +alg = Euler() +sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), + dense = false) +@test all(sol.u .>= 0) +sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg) + 1.e-3, + dense = false) +@test any(sol.u .< 0) + +println("SSPRK22") +alg = SSPRK22() +for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +# test SSP coefficient +sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), + dense = false) +@test all(sol.u .>= 0) +# test SSP property of dense output +sol = solve(test_problem_ssp, alg, dt = 1.0) +@test mapreduce(t -> all(0 .<= sol(t) .<= 1), (u, v) -> u && v, + range(0, stop = 8, length = 50), init = true) +sol = solve(test_problem_ssp_inplace, alg, dt = 1.0) +@test mapreduce(t -> all(0 .<= sol(t) .<= 1), (u, v) -> u && v, + range(0, stop = 8, length = 50), init = true) +# test storage +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + +println("KYKSSPRK42") +alg = KYKSSPRK42() +for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +# test SSP coefficient +sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), + dense = false) +@test all(sol.u .>= 0) + +println("SHLDDRK52") +alg = SHLDDRK52() +for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end + +println("SHLDDRK_2N") +dts_SHLDDRK_2N = (1 / 2) .^ (0:3) +alg = SHLDDRK_2N() +for prob in test_problems_only_time + sim = test_convergence(dts_SHLDDRK_2N, prob, alg) + @test sim.𝒪est[:final]≈4 atol=0.46 +end +for prob in test_problems_linear + sim = test_convergence(dts_SHLDDRK_2N, prob, alg) + @test sim.𝒪est[:final]≈4 atol=0.46 +end +for prob in test_problems_nonlinear + sim = test_convergence(dts_SHLDDRK_2N, prob, alg) + @test sim.𝒪est[:final]≈4 atol=1 + # due to unusual saturation towards high dts(0.5 and onwards) and + # saturation towards low dts due to less precision in the provided values of weights , tolerance is kept so high +end + +println("SSPRK33") +alg = SSPRK33() +for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + # This corresponds to Simpson's rule; due to symmetric quadrature nodes, + # it is of degree 4 instead of 3, as would be expected. + @test abs(sim.𝒪est[:final] - 1 - OrdinaryDiffEq.alg_order(alg)) < testTol +end +for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +# test SSP coefficient +sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), + dense = false) +@test all(sol.u .>= 0) +# test SSP property of dense output +sol = solve(test_problem_ssp, alg, dt = 1.0) +@test mapreduce(t -> all(0 .<= sol(t) .<= 1), (u, v) -> u && v, + range(0, stop = 8, length = 50), init = true) +sol = solve(test_problem_ssp_inplace, alg, dt = 1.0) +@test mapreduce(t -> all(0 .<= sol(t) .<= 1), (u, v) -> u && v, + range(0, stop = 8, length = 50), init = true) +# test storage +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + +println("SSPRK53") +alg = SSPRK53() +for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +# test SSP coefficient +sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), + dense = false) +@test all(sol.u .>= 0) +# test storage +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + +println("SSPRK53_2N1") +alg = SSPRK53_2N1() +for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +# test SSP coefficient +sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), + dense = false) +@test all(sol.u .>= 0) +# test storage +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + +# for SSPRK53_2N2 to be in asymptotic range +dts = 1 .// 2 .^ (9:-1:5) +println("SSPRK53_2N2") +alg = SSPRK53_2N2() +for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +# test SSP coefficient +sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), + dense = false) +@test all(sol.u .>= 0) +# test storage +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 + +dts = 1 .// 2 .^ (9:-1:5) +println("SSPRK53_H") +alg = SSPRK53_H() +for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=0.4 +end +for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=0.4 +end +for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=0.4 +end +# test SSP coefficient +sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), + dense = false) +@test all(sol.u .>= 0) +# test storage +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 + +#reverting back to original dts +println("SSPRK63") +dts = 1 .// 2 .^ (8:-1:4) +alg = SSPRK63() +for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +# test SSP coefficient +sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), + dense = false) +@test all(sol.u .>= 0) + +println("SSPRK73") +alg = SSPRK73() +for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +# test SSP coefficient +sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), + dense = false) +@test all(sol.u .>= 0) + +println("SSPRK83") +alg = SSPRK83() +for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +# test SSP coefficient +sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), + dense = false) +@test all(sol.u .>= 0) + +println("SSPRK43") +alg = SSPRK43() +for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + # higher order as pure quadrature + @test abs(sim.𝒪est[:final] - 1 - OrdinaryDiffEq.alg_order(alg)) < testTol +end +for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +# test SSP coefficient +sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), + dense = false) +@test all(sol.u .>= 0) +# test SSP property of dense output +sol = solve(test_problem_ssp, alg, dt = 8 / 5, adaptive = false) +@test mapreduce(t -> all(0 .<= sol(t) .<= 1), (u, v) -> u && v, + range(0, stop = 8, length = 50), init = true) +sol = solve(test_problem_ssp_inplace, alg, dt = 8 / 5, adaptive = false) +@test mapreduce(t -> all(0 .<= sol(t) .<= 1), (u, v) -> u && v, + range(0, stop = 8, length = 50), init = true) +# test storage +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 + +println("SSPRK432") +alg = SSPRK432() +for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + # higher order as pure quadrature + @test abs(sim.𝒪est[:final] - 1 - OrdinaryDiffEq.alg_order(alg)) < testTol +end +for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +# test SSP coefficient +sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), + dense = false) +@test all(sol.u .>= 0) +# test SSP property of dense output +sol = solve(test_problem_ssp, alg, dt = 8 / 5, adaptive = false) +@test mapreduce(t -> all(0 .<= sol(t) .<= 1), (u, v) -> u && v, + range(0, stop = 8, length = 50), init = true) +sol = solve(test_problem_ssp_inplace, alg, dt = 8 / 5, adaptive = false) +@test mapreduce(t -> all(0 .<= sol(t) .<= 1), (u, v) -> u && v, + range(0, stop = 8, length = 50), init = true) +# test storage +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 + +alg = SSPRKMSVS32() +for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end + +println("SSPRKMSVS43") +alg = SSPRKMSVS43() +for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) #shows superconvergence to 4th order + @test abs(sim.𝒪est[:final] - 1 - OrdinaryDiffEq.alg_order(alg)) < testTol +end + +println("SSPRK932") +alg = SSPRK932() +for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +# test SSP coefficient +sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), + dense = false, maxiters = 1e7) +@test all(sol.u .>= 0) +# test storage +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 + +println("SSPRK54") +alg = SSPRK54() +for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + # convergence order seems to be worse for this problem + @test abs(sim.𝒪est[:final] + 0.25 - OrdinaryDiffEq.alg_order(alg)) < testTol +end +for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + # convergence order seems to be better for this problem + @test abs(sim.𝒪est[:final] - 0.5 - OrdinaryDiffEq.alg_order(alg)) < testTol +end +# test SSP coefficient +sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), + dense = false) +@test all(sol.u .>= 0) + +println("SSPRK104") +alg = SSPRK104() +for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol +end +# test SSP coefficient +sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), + dense = false) +@test all(sol.u .>= 0) +# test storage +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 +integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, + save_everystep = false, alias_u0 = true) +@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 + +println("KYK2014DGSSPRK_3S2") +alg = KYK2014DGSSPRK_3S2() +for prob in test_problems_only_time + sim = test_convergence(dts, prob, alg) + @test abs(sim.𝒪est[:final] - OrdinaryDiffEq.alg_order(alg)) < testTol +end +for prob in test_problems_linear + sim = test_convergence(dts, prob, alg) + @test abs(sim.𝒪est[:final] - OrdinaryDiffEq.alg_order(alg)) < testTol +end +for prob in test_problems_nonlinear + sim = test_convergence(dts, prob, alg) + @test abs(sim.𝒪est[:final] - OrdinaryDiffEq.alg_order(alg)) < testTol +end +# test SSP coefficient +sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), + dense = false) +@test all(sol.u .>= 0) diff --git a/test/algconvergence/rkc_tests.jl b/test/algconvergence/rkc_tests.jl new file mode 100644 index 0000000000..4121e2e345 --- /dev/null +++ b/test/algconvergence/rkc_tests.jl @@ -0,0 +1,97 @@ +using OrdinaryDiffEq, DiffEqDevTools, Test, LinearAlgebra, Random +using OrdinaryDiffEq: maxeig! +import ODEProblemLibrary: prob_ode_linear, prob_ode_2Dlinear +probArr = Vector{ODEProblem}(undef, 2) +probArr[1] = prob_ode_linear +probArr[2] = prob_ode_2Dlinear + +@testset "Power Iteration of Runge-Kutta-Chebyshev Tests" begin + Random.seed!(123) + eigen_est = (integrator) -> integrator.eigen_est = 1.5e2 + for iip in [true, false], alg in [ROCK4(), ROCK4(eigen_est = eigen_est)] + println(typeof(alg)) + A = randn(20, 20) + test_f(u, p, t) = A * u + test_f(du, u, p, t) = mul!(du, A, u) + prob = ODEProblem{iip}(test_f, randn(20), (0, 1.0)) + integrator = init(prob, alg) + eigm = maximum(abs.(eigvals(A))) + maxeig!(integrator, integrator.cache) + eigest = integrator.eigen_est + @test eigest≈eigm rtol=0.1eigm + + A = A - 1e2I + test_stiff(u, p, t) = A * u + test_stiff(du, u, p, t) = mul!(du, A, u) + prob = ODEProblem{iip}(test_stiff, ones(20), (0, 1.0)) + @test_nowarn solve(prob, alg) + end + + Random.seed!(123) + for iip in [true, false], Alg in [IRKC] + alg = Alg() + println(typeof(alg)) + A = randn(20, 20) + B = randn(20, 20) + test_f1 = !iip ? (u, p, t) -> A * u : (du, u, p, t) -> mul!(du, A, u) + test_f2 = !iip ? (u, p, t) -> B * u : (du, u, p, t) -> mul!(du, B, u) + ff_split = SplitFunction{iip}(test_f1, test_f2) + prob = SplitODEProblem{iip}(ff_split, randn(20, 1), (0.0, 1.0)) + integrator = init(prob, alg) + eigm = maximum(abs.(eigvals(A))) + maxeig!(integrator, integrator.cache) + eigest = integrator.eigen_est + @test eigest≈eigm rtol=0.1eigm + + A = A - 1e2I + test_f1 = !iip ? (u, p, t) -> A * u : (du, u, p, t) -> mul!(du, A, u) + prob = SplitODEProblem{iip}(SplitFunction{iip}(test_f1, test_f2), ones(20), + (0.0, 1.0)) + @test_nowarn solve(prob, alg) + end +end + +@testset "Runge-Kutta-Chebyshev Convergence Tests" begin + dts = 1 .// 2 .^ (8:-1:4) + testTol = 0.1 + for prob in probArr + println("ROCK2") + #default ROCK2 + sim = test_convergence(dts, prob, ROCK2()) + @test sim.𝒪est[:l∞]≈2 atol=testTol + #testing ROCK2 for different minimum stages to insure that the constants are right + sim = test_convergence(dts, prob, ROCK2(min_stages = 5)) + @test sim.𝒪est[:l∞]≈2 atol=testTol + sim = test_convergence(dts, prob, ROCK2(min_stages = 10)) + @test sim.𝒪est[:l∞]≈2 atol=testTol + sim = test_convergence(dts, prob, ROCK2(min_stages = 21)) + @test sim.𝒪est[:l∞]≈2 atol=testTol + #default ROCK4 + println("ROCK4") + sim = test_convergence(dts, prob, ROCK4()) + @test sim.𝒪est[:l∞]≈4 atol=testTol + #testing ROCK4 for different minimum stages to insure that the constants are right + sim = test_convergence(dts, prob, ROCK4(min_stages = 6)) + @test sim.𝒪est[:l∞]≈4 atol=testTol + sim = test_convergence(dts, prob, ROCK4(min_stages = 10)) + @test sim.𝒪est[:l∞]≈4 atol=testTol + sim = test_convergence(dts, prob, ROCK4(min_stages = 21)) + @test sim.𝒪est[:l∞]≈4 atol=testTol + + println("ROCKC") + sim = test_convergence(dts, prob, RKC()) + @test sim.𝒪est[:l∞]≈2 atol=testTol + println("SERK2") + sim = test_convergence(dts, prob, SERK2()) + @test sim.𝒪est[:l∞]≈2 atol=testTol + println("ESERK4") + sim = test_convergence(dts, prob, ESERK4()) + @test sim.𝒪est[:l∞]≈4 atol=testTol + end + dts = 1 .// 2 .^ (6:-1:2) + for prob in probArr + println("ESERK5") + sim = test_convergence(dts, prob, ESERK5()) + @test sim.𝒪est[:l∞]≈5 atol=testTol + end +end diff --git a/test/algconvergence/symplectic_tests.jl b/test/algconvergence/symplectic_tests.jl new file mode 100644 index 0000000000..489f86a9c5 --- /dev/null +++ b/test/algconvergence/symplectic_tests.jl @@ -0,0 +1,102 @@ + +using Test, LinearAlgebra +using OrdinaryDiffEq, DiffEqBase + +# algorithm, dq(p) != p, convergence order +const ALGOS = ((SymplecticEuler, true, 1), + (VelocityVerlet, false, 2), + (VerletLeapfrog, true, 2), + (PseudoVerletLeapfrog, true, 2), + (McAte2, true, 2), + (Ruth3, true, 3), + (McAte3, true, 3), + (CandyRoz4, true, 4), + (McAte4, true, 4), + (CalvoSanz4, true, 4), + (McAte42, true, 1), # known to be broken + (McAte5, true, 5), + (Yoshida6, true, 6), + (KahanLi6, true, 6), + (McAte8, true, 8), + (KahanLi8, true, 8), + (SofSpa10, true, 10)) + +function dp(p, q, pa, t) + 0q .+ pa[2] +end + +function dq(p, q, pa, t) + p .* pa[1] +end + +dp(res, p, q, pa, t) = (res .= dp(p, q, pa, t)) +dq(res, p, q, pa, t) = (res .= dq(p, q, pa, t)) + +dynode(iip, dp, dq) = DynamicalODEFunction{iip}(dp, dq) + +# [0:1] used in dp, dq; [3:4] start values for p0, q0 +const PARAMS = ((1.0, 0.1, 1.0, 0.0), (0.1, 1.0, 1.0, -1.0)) +const IIPS = (true, false) +const TSPAN = (0.0, 1.0) + +solution(t, w) = (w[2] * t + w[3], (w[2] / 2 * t + w[3]) * w[1] * t + w[4]) +apa(iip::Bool, x) = iip ? vcat.(x) : x +errorbound(dt, d, x) = 100 * abs(dt)^d + 1000 * eps(norm(x)) +function printerrors(text, calc, solution, pa, t1) + print(text, ": ") + print(norm(calc[1] - solution(t1, pa)[1]), " ") + print(norm(calc[2] - solution(t1, pa)[2])) + println() +end + +@testset "symplectic $alg-$iip-$pa" for (alg, x, d) in ALGOS, iip in IIPS, pa in PARAMS + dt = 0.01 + tspan = TSPAN + t0, t1 = tspan + dynfun = dynode(iip, dp, dq) + p0, q0 = apa(iip, solution(t0, pa)) + prob = DynamicalODEProblem(dynfun, p0, q0, tspan, pa) + + if x || pa[1] == 1 + sol = solve(prob, alg(); dt = dt) + calc = sol(t1) + # printerrors("$alg-$iip-$pa", calc, solution, pa, t1) + @test calc[1]≈solution(t1, pa)[1] rtol=errorbound(dt, d, calc[1]) + @test calc[2]≈solution(t1, pa)[2] rtol=errorbound(dt, d, calc[2]) + else + @test_throws ArgumentError solve(prob, alg(); dt = dt) + end +end + +function motionfuncDirect1(dv, v, u, p, t) + # 1:Electron, 2: Be + ω_1, ω_2, γ, m_1, m_2, η, ω_d = p + dv[1] = -ω_1^2 * u[1] * (1 + η * cos(ω_d * t)) - γ * u[2] / m_1 + dv[2] = -ω_2^2 * u[2] - γ * u[1] / m_2 +end + +function motionfuncDirect1(v, u, p, t) + # 1:Electron, 2: Be + ω_1, ω_2, γ, m_1, m_2, η, ω_d = p + [-ω_1^2 * u[1] * (1 + η * cos(ω_d * t)) - γ * u[2] / m_1, + -ω_2^2 * u[2] - γ * u[1] / m_2] +end + +param = [90386.15717208837, 3938.9288690708827, 8560.718748264337, 0.000544617021484666, + 8.947079933513658, 0.7596480420227258, 78778.57738141765] +u0_direct = zeros(2) # mm, mm +v0_direct = [0.0, 135.83668926684385] +tspan = (0.0, 1.321179076090661) +prob_direct = SecondOrderODEProblem(motionfuncDirect1, v0_direct, u0_direct, tspan, param) +dt = 2e-8 +ref = solve( + prob_direct, DPRKN12(), abstol = 1e-12, reltol = 1e-12, maxiters = 1e7, saveat = 0.01) + +@testset "symplectic time-dependent $alg" for (alg, x, d) in ALGOS + sol = solve(prob_direct, alg(), dt = dt, saveat = 0.01) + if alg <: Yoshida6 + @test maximum(ref[4, :] - sol[4, :]) < 9e-3 + else + @test maximum(ref[4, :] - sol[4, :]) < 3e-3 + end +end From fdc92bb45a135df16f9cd416083aef8b2098b8ba Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:52:41 -0400 Subject: [PATCH 02/71] Delete src/algorithms/explicit_rk_pde.jl --- src/algorithms/explicit_rk_pde.jl | 1230 ----------------------------- 1 file changed, 1230 deletions(-) delete mode 100644 src/algorithms/explicit_rk_pde.jl diff --git a/src/algorithms/explicit_rk_pde.jl b/src/algorithms/explicit_rk_pde.jl deleted file mode 100644 index 20fbeadeae..0000000000 --- a/src/algorithms/explicit_rk_pde.jl +++ /dev/null @@ -1,1230 +0,0 @@ -#Low Storage Explicit Runge-Kutta Methods - -@doc explicit_rk_docstring( - "A fourth-order, five-stage explicit low-storage method of Carpenter and Kennedy -(free 3rd order Hermite interpolant). Fixed timestep only. Designed for -hyperbolic PDEs (stability properties).", - "CarpenterKennedy2N54", - references = "@article{carpenter1994fourth, - title={Fourth-order 2N-storage Runge-Kutta schemes}, - author={Carpenter, Mark H and Kennedy, Christopher A}, - year={1994} - }", - extra_keyword_description = """- `williamson_condition`: allows for an optimization that allows fusing broadcast expressions with the function call `f`. However, it only works for `Array` types. - """, - extra_keyword_default = "williamson_condition = true") -Base.@kwdef struct CarpenterKennedy2N54{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() - williamson_condition::Bool = true -end -# for backwards compatibility -function CarpenterKennedy2N54(stage_limiter!, - step_limiter! = trivial_limiter!; - williamson_condition = true) - CarpenterKennedy2N54(stage_limiter!, step_limiter!, False(), williamson_condition) -end - -@doc explicit_rk_docstring( - "A fourth-order, six-stage explicit low-storage method. Fixed timestep only.", - "SHLDDRK64", - references = "D. Stanescu, W. G. Habashi. - 2N-Storage Low Dissipation and Dispersion Runge-Kutta Schemes for Computational - Acoustics. - Journal of Computational Physics, 143(2), pp 674-681, 1998. - doi: https://doi.org/10.1006/jcph.1998.5986 - }", - extra_keyword_description = """- `williamson_condition`: allows for an optimization that allows fusing broadcast expressions with the function call `f`. However, it only works for `Array` types. - """, - extra_keyword_default = "williamson_condition = true") -Base.@kwdef struct SHLDDRK64{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() - williamson_condition::Bool = true -end -# for backwards compatibility -function SHLDDRK64(stage_limiter!, - step_limiter! = trivial_limiter!; - williamson_condition = true) - SHLDDRK64(stage_limiter!, step_limiter!, False(), williamson_condition) -end - -@doc explicit_rk_docstring("TBD", "SHLDDRK52") -Base.@kwdef struct SHLDDRK52{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function SHLDDRK52(stage_limiter!, step_limiter! = trivial_limiter!) - SHLDDRK52(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring("TBD", "SHLDDRK_2N") -Base.@kwdef struct SHLDDRK_2N{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function SHLDDRK_2N(stage_limiter!, step_limiter! = trivial_limiter!) - SHLDDRK_2N(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring("Low-Storage Method -6-stage, fourth order low-stage, low-dissipation, low-dispersion scheme. -Fixed timestep only.", "HSLDDRK64", - references = "D. Stanescu, W. G. Habashi. - 2N-Storage Low Dissipation and Dispersion Runge-Kutta Schemes for Computational - Acoustics. - Journal of Computational Physics, 143(2), pp 674-681, 1998. - doi: https://doi.org/10.1006/jcph.1998.5986 - }", - extra_keyword_description = """- `williamson_condition`: allows for an optimization that allows fusing broadcast expressions with the function call `f`. However, it only works for `Array` types. - """, - extra_keyword_default = "williamson_condition = true") -struct HSLDDRK64{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread - williamson_condition::Bool - function HSLDDRK64(stage_limiter! = trivial_limiter!, step_limiter! = trivial_limiter!; - williamson_condition = true) - Base.depwarn("HSLDDRK64 is deprecated, use SHLDDRK64 instead.", :HSLDDRK64) - SHLDDRK64(stage_limiter!, step_limiter!, thread; - williamson_condition = williamson_condition) - end -end - -@doc explicit_rk_docstring( - "7-stage, third order low-storage low-dissipation, low-dispersion scheme for -discontinuous Galerkin space discretizations applied to wave propagation problems. -Optimized for PDE discretizations when maximum spatial step is small due to -geometric features of computational domain. Fixed timestep only.", - "DGLDDRK73_C", - references = "T. Toulorge, W. Desmet. - Optimal Runge–Kutta Schemes for Discontinuous Galerkin Space Discretizations - Applied to Wave Propagation Problems. - Journal of Computational Physics, 231(4), pp 2067-2091, 2012. - doi: https://doi.org/10.1016/j.jcp.2011.11.024", - extra_keyword_description = """- `williamson_condition`: allows for an optimization that allows fusing broadcast expressions with the function call `f`. However, it only works for `Array` types. - """, - extra_keyword_default = "williamson_condition = true") -Base.@kwdef struct DGLDDRK73_C{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() - williamson_condition::Bool = true -end -# for backwards compatibility -function DGLDDRK73_C(stage_limiter!, step_limiter! = trivial_limiter!; - williamson_condition = true) - DGLDDRK73_C(stage_limiter!, - step_limiter!, - False(), - williamson_condition) -end - -@doc explicit_rk_docstring( - "8-stage, fourth order low-storage low-dissipation, low-dispersion scheme for -discontinuous Galerkin space discretizations applied to wave propagation problems. -Optimized for PDE discretizations when maximum spatial step is small due to -geometric features of computational domain. Fixed timestep only.", - "DGLDDRK84_C", - references = "T. Toulorge, W. Desmet. - Optimal Runge–Kutta Schemes for Discontinuous Galerkin Space Discretizations - Applied to Wave Propagation Problems. - Journal of Computational Physics, 231(4), pp 2067-2091, 2012. - doi: https://doi.org/10.1016/j.jcp.2011.11.024", - extra_keyword_description = """- `williamson_condition`: allows for an optimization that allows fusing broadcast expressions with the function call `f`. However, it only works for `Array` types. - """, - extra_keyword_default = "williamson_condition = true") -Base.@kwdef struct DGLDDRK84_C{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() - williamson_condition::Bool = true -end -# for backwards compatibility -function DGLDDRK84_C(stage_limiter!, step_limiter! = trivial_limiter!; - williamson_condition = true) - DGLDDRK84_C(stage_limiter!, - step_limiter!, - False(), - williamson_condition) -end - -@doc explicit_rk_docstring( - "8-stage, fourth order low-storage low-dissipation, low-dispersion scheme for -discontinuous Galerkin space discretizations applied to wave propagation problems. -Optimized for PDE discretizations when the maximum spatial step size is not -constrained. Fixed timestep only.", - "DGLDDRK84_F", - references = "T. Toulorge, W. Desmet. - Optimal Runge–Kutta Schemes for Discontinuous Galerkin Space Discretizations - Applied to Wave Propagation Problems. - Journal of Computational Physics, 231(4), pp 2067-2091, 2012. - doi: https://doi.org/10.1016/j.jcp.2011.11.024", - extra_keyword_description = """- `williamson_condition`: allows for an optimization that allows fusing broadcast expressions with the function call `f`. However, it only works for `Array` types. - """, - extra_keyword_default = "williamson_condition = true") -Base.@kwdef struct DGLDDRK84_F{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() - williamson_condition::Bool = true -end -# for backwards compatibility -function DGLDDRK84_F(stage_limiter!, step_limiter! = trivial_limiter!; - williamson_condition = true) - DGLDDRK84_F(stage_limiter!, - step_limiter!, - False(), - williamson_condition) -end - -@doc explicit_rk_docstring( - "12-stage, fourth order low-storage method with optimized stability regions for -advection-dominated problems. Fixed timestep only.", - "NDBLSRK124", - references = "Jens Niegemann, Richard Diehl, Kurt Busch. - Efficient Low-Storage Runge–Kutta Schemes with Optimized Stability Regions. - Journal of Computational Physics, 231, pp 364-372, 2012. - doi: https://doi.org/10.1016/j.jcp.2011.09.003", - extra_keyword_description = """- `williamson_condition`: allows for an optimization that allows fusing broadcast expressions with the function call `f`. However, it only works for `Array` types. - """, - extra_keyword_default = "williamson_condition = true") -Base.@kwdef struct NDBLSRK124{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() - williamson_condition::Bool = true -end -# for backwards compatibility -function NDBLSRK124(stage_limiter!, step_limiter! = trivial_limiter!; - williamson_condition = true) - NDBLSRK124(stage_limiter!, - step_limiter!, False(), - williamson_condition) -end - -@doc explicit_rk_docstring( - "13-stage, fourth order low-storage method with optimized stability regions for -advection-dominated problems. Fixed timestep only.", - "NDBLSRK134", - references = "Jens Niegemann, Richard Diehl, Kurt Busch. - Efficient Low-Storage Runge–Kutta Schemes with Optimized Stability Regions. - Journal of Computational Physics, 231, pp 364-372, 2012. - doi: https://doi.org/10.1016/j.jcp.2011.09.003", - extra_keyword_description = """- `williamson_condition`: allows for an optimization that allows fusing broadcast expressions with the function call `f`. However, it only works for `Array` types. - """, - extra_keyword_default = "williamson_condition = true") -Base.@kwdef struct NDBLSRK134{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() - williamson_condition::Bool = true -end -# for backwards compatibility -function NDBLSRK134(stage_limiter!, step_limiter! = trivial_limiter!; - williamson_condition = true) - NDBLSRK134(stage_limiter!, - step_limiter!, False(), - williamson_condition) -end - -@doc explicit_rk_docstring( - "14-stage, fourth order low-storage method with optimized stability regions for -advection-dominated problems. Fixed timestep only.", - "NDBLSRK144", - references = "Jens Niegemann, Richard Diehl, Kurt Busch. - Efficient Low-Storage Runge–Kutta Schemes with Optimized Stability Regions. - Journal of Computational Physics, 231, pp 364-372, 2012. - doi: https://doi.org/10.1016/j.jcp.2011.09.003", - extra_keyword_description = """- `williamson_condition`: allows for an optimization that allows fusing broadcast expressions with the function call `f`. However, it only works for `Array` types. - """, - extra_keyword_default = "williamson_condition = true") -Base.@kwdef struct NDBLSRK144{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() - williamson_condition::Bool = true -end -# for backwards compatibility -function NDBLSRK144(stage_limiter!, step_limiter! = trivial_limiter!; - williamson_condition = true) - NDBLSRK144{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, False(), - williamson_condition) -end - -@doc explicit_rk_docstring("Low-Storage Method -6-stage, fourth order low-storage, low-dissipation, low-dispersion scheme. -Fixed timestep only.", "CFRLDDRK64", - references = "M. Calvo, J. M. Franco, L. Randez. A New Minimum Storage Runge–Kutta Scheme - for Computational Acoustics. Journal of Computational Physics, 201, pp 1-12, 2004. - doi: https://doi.org/10.1016/j.jcp.2004.05.012") -Base.@kwdef struct CFRLDDRK64{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function CFRLDDRK64(stage_limiter!, step_limiter! = trivial_limiter!) - CFRLDDRK64(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -7-stage, fourth order low-storage low-dissipation, low-dispersion scheme with maximal accuracy and stability limit along the imaginary axes. -Fixed timestep only.", - "TSLDDRK74", - references = "Kostas Tselios, T. E. Simos. Optimized Runge–Kutta Methods with Minimal Dispersion and Dissipation - for Problems arising from Computational Acoustics. Physics Letters A, 393(1-2), pp 38-47, 2007. - doi: https://doi.org/10.1016/j.physleta.2006.10.072") -Base.@kwdef struct TSLDDRK74{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function TSLDDRK74(stage_limiter!, step_limiter! = trivial_limiter!) - TSLDDRK74(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -4-stage, third order low-storage scheme, optimized for compressible Navier–Stokes equations. -", "CKLLSRK43_2") -Base.@kwdef struct CKLLSRK43_2{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function CKLLSRK43_2(stage_limiter!, step_limiter! = trivial_limiter!) - CKLLSRK43_2{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations. -", "CKLLSRK54_3C") -Base.@kwdef struct CKLLSRK54_3C{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function CKLLSRK54_3C(stage_limiter!, step_limiter! = trivial_limiter!) - CKLLSRK54_3C{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -9-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations. -", "CKLLSRK95_4S") -Base.@kwdef struct CKLLSRK95_4S{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function CKLLSRK95_4S(stage_limiter!, step_limiter! = trivial_limiter!) - CKLLSRK95_4S{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -9-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations. -", "CKLLSRK95_4C") -Base.@kwdef struct CKLLSRK95_4C{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function CKLLSRK95_4C(stage_limiter!, step_limiter! = trivial_limiter!) - CKLLSRK95_4C{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -9-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations. -", "CKLLSRK95_4M") -Base.@kwdef struct CKLLSRK95_4M{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function CKLLSRK95_4M(stage_limiter!, step_limiter! = trivial_limiter!) - CKLLSRK95_4M{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations. -", "CKLLSRK54_3C_3R") -Base.@kwdef struct CKLLSRK54_3C_3R{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function CKLLSRK54_3C_3R(stage_limiter!, step_limiter! = trivial_limiter!) - CKLLSRK54_3C_3R{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations. -", "CKLLSRK54_3M_3R") -Base.@kwdef struct CKLLSRK54_3M_3R{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function CKLLSRK54_3M_3R(stage_limiter!, step_limiter! = trivial_limiter!) - CKLLSRK54_3M_3R{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations. -", "CKLLSRK54_3N_3R") -Base.@kwdef struct CKLLSRK54_3N_3R{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function CKLLSRK54_3N_3R(stage_limiter!, step_limiter! = trivial_limiter!) - CKLLSRK54_3N_3R{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -8-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations. -", "CKLLSRK85_4C_3R") -Base.@kwdef struct CKLLSRK85_4C_3R{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function CKLLSRK85_4C_3R(stage_limiter!, step_limiter! = trivial_limiter!) - CKLLSRK85_4C_3R{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -8-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations. -", "CKLLSRK85_4M_3R") -Base.@kwdef struct CKLLSRK85_4M_3R{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function CKLLSRK85_4M_3R(stage_limiter!, step_limiter! = trivial_limiter!) - CKLLSRK85_4M_3R{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -8-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations. -", "CKLLSRK85_4P_3R") -Base.@kwdef struct CKLLSRK85_4P_3R{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function CKLLSRK85_4P_3R(stage_limiter!, step_limiter! = trivial_limiter!) - CKLLSRK85_4P_3R{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations. -", "CKLLSRK54_3N_4R") -Base.@kwdef struct CKLLSRK54_3N_4R{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function CKLLSRK54_3N_4R(stage_limiter!, step_limiter! = trivial_limiter!) - CKLLSRK54_3N_4R{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations. -", "CKLLSRK54_3M_4R") -Base.@kwdef struct CKLLSRK54_3M_4R{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function CKLLSRK54_3M_4R(stage_limiter!, step_limiter! = trivial_limiter!) - CKLLSRK54_3M_4R{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "6-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.", - "CKLLSRK65_4M_4R") -Base.@kwdef struct CKLLSRK65_4M_4R{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function CKLLSRK65_4M_4R(stage_limiter!, step_limiter! = trivial_limiter!) - CKLLSRK65_4M_4R(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -8-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.", - "CKLLSRK85_4FM_4R") -Base.@kwdef struct CKLLSRK85_4FM_4R{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function CKLLSRK85_4FM_4R(stage_limiter!, step_limiter! = trivial_limiter!) - CKLLSRK85_4FM_4R(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "CKLLSRK75_4M_5R: Low-Storage Method -7-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.", - "CKLLSRK75_4M_5R") -Base.@kwdef struct CKLLSRK75_4M_5R{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function CKLLSRK75_4M_5R(stage_limiter!, step_limiter! = trivial_limiter!) - CKLLSRK75_4M_5R{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -3-stage, second order (3S) low-storage scheme, optimized the spectral difference method applied to wave propagation problems.", - "ParsaniKetchesonDeconinck3S32", - references = "Parsani, Matteo, David I. Ketcheson, and W. Deconinck. - Optimized explicit Runge--Kutta schemes for the spectral difference method applied to wave propagation problems. - SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. - doi: https://doi.org/10.1137/120885899") -Base.@kwdef struct ParsaniKetchesonDeconinck3S32{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function ParsaniKetchesonDeconinck3S32(stage_limiter!, step_limiter! = trivial_limiter!) - ParsaniKetchesonDeconinck3S32{typeof(stage_limiter!), typeof(step_limiter!), False}( - stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -8-stage, second order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.", - "ParsaniKetchesonDeconinck3S82", - references = "Parsani, Matteo, David I. Ketcheson, and W. Deconinck. - Optimized explicit Runge--Kutta schemes for the spectral difference method applied to wave propagation problems. - SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. - doi: https://doi.org/10.1137/120885899") -Base.@kwdef struct ParsaniKetchesonDeconinck3S82{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function ParsaniKetchesonDeconinck3S82(stage_limiter!, step_limiter! = trivial_limiter!) - ParsaniKetchesonDeconinck3S82{typeof(stage_limiter!), typeof(step_limiter!), False}( - stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -5-stage, third order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.", - "ParsaniKetchesonDeconinck3S53", - references = "Parsani, Matteo, David I. Ketcheson, and W. Deconinck. - Optimized explicit Runge--Kutta schemes for the spectral difference method applied to wave propagation problems. - SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. - doi: https://doi.org/10.1137/120885899") -Base.@kwdef struct ParsaniKetchesonDeconinck3S53{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function ParsaniKetchesonDeconinck3S53(stage_limiter!, step_limiter! = trivial_limiter!) - ParsaniKetchesonDeconinck3S53{typeof(stage_limiter!), typeof(step_limiter!), False}( - stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -17-stage, third order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.", - "ParsaniKetchesonDeconinck3S173", - references = "Parsani, Matteo, David I. Ketcheson, and W. Deconinck. - Optimized explicit Runge--Kutta schemes for the spectral difference method applied to wave propagation problems. - SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. - doi: https://doi.org/10.1137/120885899") -Base.@kwdef struct ParsaniKetchesonDeconinck3S173{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function ParsaniKetchesonDeconinck3S173(stage_limiter!, step_limiter! = trivial_limiter!) - ParsaniKetchesonDeconinck3S173{typeof(stage_limiter!), typeof(step_limiter!), False}( - stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -9-stage, fourth order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.", - "ParsaniKetchesonDeconinck3S94", - references = "Parsani, Matteo, David I. Ketcheson, and W. Deconinck. - Optimized explicit Runge--Kutta schemes for the spectral difference method applied to wave propagation problems. - SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. - doi: https://doi.org/10.1137/120885899") -Base.@kwdef struct ParsaniKetchesonDeconinck3S94{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function ParsaniKetchesonDeconinck3S94(stage_limiter!, step_limiter! = trivial_limiter!) - ParsaniKetchesonDeconinck3S94{typeof(stage_limiter!), typeof(step_limiter!), False}( - stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -18-stage, fourth order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.", - "ParsaniKetchesonDeconinck3S184", - references = "Parsani, Matteo, David I. Ketcheson, and W. Deconinck. - Optimized explicit Runge--Kutta schemes for the spectral difference method applied to wave propagation problems. - SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. - doi: https://doi.org/10.1137/120885899") -Base.@kwdef struct ParsaniKetchesonDeconinck3S184{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function ParsaniKetchesonDeconinck3S184(stage_limiter!, step_limiter! = trivial_limiter!) - ParsaniKetchesonDeconinck3S184{typeof(stage_limiter!), typeof(step_limiter!), False}( - stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -10-stage, fifth order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.", - "ParsaniKetchesonDeconinck3S105", - references = "Parsani, Matteo, David I. Ketcheson, and W. Deconinck. - Optimized explicit Runge--Kutta schemes for the spectral difference method applied to wave propagation problems. - SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. - doi: https://doi.org/10.1137/120885899") -Base.@kwdef struct ParsaniKetchesonDeconinck3S105{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function ParsaniKetchesonDeconinck3S105(stage_limiter!, step_limiter! = trivial_limiter!) - ParsaniKetchesonDeconinck3S105{typeof(stage_limiter!), typeof(step_limiter!), False}( - stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "Low-Storage Method -20-stage, fifth order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.", - "ParsaniKetchesonDeconinck3S205", - references = "Parsani, Matteo, David I. Ketcheson, and W. Deconinck. - Optimized explicit Runge--Kutta schemes for the spectral difference method applied to wave propagation problems. - SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. - doi: https://doi.org/10.1137/120885899") -Base.@kwdef struct ParsaniKetchesonDeconinck3S205{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function ParsaniKetchesonDeconinck3S205(stage_limiter!, step_limiter! = trivial_limiter!) - ParsaniKetchesonDeconinck3S205{typeof(stage_limiter!), typeof(step_limiter!), False}( - stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "A third-order, five-stage explicit Runge-Kutta method with embedded error estimator -designed for spectral element discretizations of compressible fluid mechanics.", - "RDPK3Sp35", - references = "Ranocha, Dalcin, Parsani, Ketcheson (2021) - Optimized Runge-Kutta Methods with Automatic Step Size Control for - Compressible Computational Fluid Dynamics - [arXiv:2104.06836](https://arxiv.org/abs/2104.06836)") -Base.@kwdef struct RDPK3Sp35{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function RDPK3Sp35(stage_limiter!, step_limiter! = trivial_limiter!) - RDPK3Sp35{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, False()) -end - -@doc explicit_rk_docstring( - "A third-order, five-stage explicit Runge-Kutta method with embedded error estimator -using the FSAL property designed for spectral element discretizations of -compressible fluid mechanics.", - "RDPK3SpFSAL35", - references = "Ranocha, Dalcin, Parsani, Ketcheson (2021) - Optimized Runge-Kutta Methods with Automatic Step Size Control for - Compressible Computational Fluid Dynamics - [arXiv:2104.06836](https://arxiv.org/abs/2104.06836)") -Base.@kwdef struct RDPK3SpFSAL35{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function RDPK3SpFSAL35(stage_limiter!, step_limiter! = trivial_limiter!) - RDPK3SpFSAL35{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "A fourth-order, nine-stage explicit Runge-Kutta method with embedded error estimator -designed for spectral element discretizations of compressible fluid mechanics.", - "RDPK3Sp49", - references = "Ranocha, Dalcin, Parsani, Ketcheson (2021) - Optimized Runge-Kutta Methods with Automatic Step Size Control for - Compressible Computational Fluid Dynamics - [arXiv:2104.06836](https://arxiv.org/abs/2104.06836)") -Base.@kwdef struct RDPK3Sp49{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function RDPK3Sp49(stage_limiter!, step_limiter! = trivial_limiter!) - RDPK3Sp49{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, False()) -end - -@doc explicit_rk_docstring( - "A fourth-order, nine-stage explicit Runge-Kutta method with embedded error estimator -using the FSAL property designed for spectral element discretizations of -compressible fluid mechanics.", - "RDPK3SpFSAL49", - references = "Ranocha, Dalcin, Parsani, Ketcheson (2021) - Optimized Runge-Kutta Methods with Automatic Step Size Control for - Compressible Computational Fluid Dynamics - [arXiv:2104.06836](https://arxiv.org/abs/2104.06836)") -Base.@kwdef struct RDPK3SpFSAL49{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function RDPK3SpFSAL49(stage_limiter!, step_limiter! = trivial_limiter!) - RDPK3SpFSAL49{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "A fifth-order, ten-stage explicit Runge-Kutta method with embedded error estimator -designed for spectral element discretizations of compressible fluid mechanics.", - "RDPK3Sp510", - references = "Ranocha, Dalcin, Parsani, Ketcheson (2021) - Optimized Runge-Kutta Methods with Automatic Step Size Control for - Compressible Computational Fluid Dynamics - [arXiv:2104.06836](https://arxiv.org/abs/2104.06836)") -Base.@kwdef struct RDPK3Sp510{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function RDPK3Sp510(stage_limiter!, step_limiter! = trivial_limiter!) - RDPK3Sp510{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, False()) -end - -@doc explicit_rk_docstring( - "A fifth-order, ten-stage explicit Runge-Kutta method with embedded error estimator -using the FSAL property designed for spectral element discretizations of -compressible fluid mechanics.", - "RDPK3SpFSAL510", - references = "Ranocha, Dalcin, Parsani, Ketcheson (2021) - Optimized Runge-Kutta Methods with Automatic Step Size Control for - Compressible Computational Fluid Dynamics - [arXiv:2104.06836](https://arxiv.org/abs/2104.06836)") -Base.@kwdef struct RDPK3SpFSAL510{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function RDPK3SpFSAL510(stage_limiter!, step_limiter! = trivial_limiter!) - RDPK3SpFSAL510{typeof(stage_limiter!), typeof(step_limiter!), False}(stage_limiter!, - step_limiter!, - False()) -end - -#SSP Optimized Runge-Kutta Methods - -@doc explicit_rk_docstring("TBD", - "KYK2014DGSSPRK_3S2") -Base.@kwdef struct KYK2014DGSSPRK_3S2{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function KYK2014DGSSPRK_3S2(stage_limiter!, step_limiter! = trivial_limiter!) - KYK2014DGSSPRK_3S2(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "A second-order, two-stage explicit strong stability preserving (SSP) method. -Fixed timestep only.", - "SSPRK22", - references = "Shu, Chi-Wang, and Stanley Osher. - Efficient implementation of essentially non-oscillatory shock-capturing schemes. - Journal of Computational Physics 77.2 (1988): 439-471. - https://doi.org/10.1016/0021-9991(88)90177-5") -Base.@kwdef struct SSPRK22{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function SSPRK22(stage_limiter!, step_limiter! = trivial_limiter!) - SSPRK22(stage_limiter!, - step_limiter!, False()) -end - -@doc explicit_rk_docstring( - "A third-order, three-stage explicit strong stability preserving (SSP) method. -Fixed timestep only.", - "SSPRK33", - references = "Shu, Chi-Wang, and Stanley Osher. - Efficient implementation of essentially non-oscillatory shock-capturing schemes. - Journal of Computational Physics 77.2 (1988): 439-471. - https://doi.org/10.1016/0021-9991(88)90177-5") -Base.@kwdef struct SSPRK33{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function SSPRK33(stage_limiter!, step_limiter! = trivial_limiter!) - SSPRK33(stage_limiter!, - step_limiter!, False()) -end - -@doc explicit_rk_docstring( - "A third-order, five-stage explicit strong stability preserving (SSP) method. -Fixed timestep only.", - "SSPRK53", - references = "Ruuth, Steven. - Global optimization of explicit strong-stability-preserving Runge-Kutta methods. - Mathematics of Computation 75.253 (2006): 183-207") -Base.@kwdef struct SSPRK53{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function SSPRK53(stage_limiter!, step_limiter! = trivial_limiter!) - SSPRK53(stage_limiter!, - step_limiter!, False()) -end - -@doc explicit_rk_docstring("TBD", - "KYKSSPRK42") -Base.@kwdef struct KYKSSPRK42{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function KYKSSPRK42(stage_limiter!, step_limiter! = trivial_limiter!) - KYKSSPRK42(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "A third-order, five-stage explicit strong stability preserving (SSP) low-storage method. -Fixed timestep only.", - "SSPRK53_2N1", - references = "Higueras and T. Roldán. - New third order low-storage SSP explicit Runge–Kutta methods - arXiv:1809.04807v1.") -Base.@kwdef struct SSPRK53_2N1{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function SSPRK53_2N1(stage_limiter!, step_limiter! = trivial_limiter!) - SSPRK53_2N1(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "A third-order, five-stage explicit strong stability preserving (SSP) low-storage method. -Fixed timestep only.", - "SSPRK53_2N2", - references = "Higueras and T. Roldán. - New third order low-storage SSP explicit Runge–Kutta methods - arXiv:1809.04807v1.") -Base.@kwdef struct SSPRK53_2N2{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function SSPRK53_2N2(stage_limiter!, step_limiter! = trivial_limiter!) - SSPRK53_2N2(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "A third-order, five-stage explicit strong stability preserving (SSP) low-storage method. -Fixed timestep only.", - "SSPRK53_H", - references = "Higueras and T. Roldán. - New third order low-storage SSP explicit Runge–Kutta methods - arXiv:1809.04807v1.") -Base.@kwdef struct SSPRK53_H{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function SSPRK53_H(stage_limiter!, step_limiter! = trivial_limiter!) - SSPRK53_H(stage_limiter!, - step_limiter!, False()) -end - -@doc explicit_rk_docstring( - "A third-order, six-stage explicit strong stability preserving (SSP) method. -Fixed timestep only.", - "SSPRK63", - references = "Ruuth, Steven. - Global optimization of explicit strong-stability-preserving Runge-Kutta methods. - Mathematics of Computation 75.253 (2006): 183-207") -Base.@kwdef struct SSPRK63{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function SSPRK63(stage_limiter!, step_limiter! = trivial_limiter!) - SSPRK63(stage_limiter!, - step_limiter!, False()) -end - -@doc explicit_rk_docstring( - "A third-order, seven-stage explicit strong stability preserving (SSP) method. -Fixed timestep only.", - "SSPRK73", - references = "Ruuth, Steven. - Global optimization of explicit strong-stability-preserving Runge-Kutta methods. - Mathematics of Computation 75.253 (2006): 183-207") -Base.@kwdef struct SSPRK73{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function SSPRK73(stage_limiter!, step_limiter! = trivial_limiter!) - SSPRK73(stage_limiter!, - step_limiter!, False()) -end - -@doc explicit_rk_docstring( - "A third-order, eight-stage explicit strong stability preserving (SSP) method. -Fixed timestep only.", - "SSPRK83", - references = "Ruuth, Steven. - Global optimization of explicit strong-stability-preserving Runge-Kutta methods. - Mathematics of Computation 75.253 (2006): 183-207") -Base.@kwdef struct SSPRK83{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function SSPRK83(stage_limiter!, step_limiter! = trivial_limiter!) - SSPRK83(stage_limiter!, - step_limiter!, False()) -end - -@doc explicit_rk_docstring( - "A third-order, four-stage explicit strong stability preserving (SSP) method.", - "SSPRK43", - references = """Optimal third-order explicit SSP method with four stages discovered by - - - J. F. B. M. Kraaijevanger. - "Contractivity of Runge-Kutta methods." - In: BIT Numerical Mathematics 31.3 (1991), pp. 482–528. - [DOI: 10.1007/BF01933264](https://doi.org/10.1007/BF01933264). - - Embedded method constructed by - - - Sidafa Conde, Imre Fekete, John N. Shadid. - "Embedded error estimation and adaptive step-size control for - optimal explicit strong stability preserving Runge–Kutta methods." - [arXiv: 1806.08693](https://arXiv.org/abs/1806.08693) - - Efficient implementation (and optimized controller) developed by - - - Hendrik Ranocha, Lisandro Dalcin, Matteo Parsani, David I. Ketcheson (2021) - Optimized Runge-Kutta Methods with Automatic Step Size Control for - Compressible Computational Fluid Dynamics - [arXiv:2104.06836](https://arxiv.org/abs/2104.06836)""") -Base.@kwdef struct SSPRK43{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function SSPRK43(stage_limiter!, step_limiter! = trivial_limiter!) - SSPRK43(stage_limiter!, - step_limiter!, False()) -end - -@doc explicit_rk_docstring( - "A third-order, four-stage explicit strong stability preserving (SSP) method.", - "SSPRK432", - references = "Gottlieb, Sigal, David I. Ketcheson, and Chi-Wang Shu. - Strong stability preserving Runge-Kutta and multistep time discretizations. - World Scientific, 2011. - Example 6.1") -Base.@kwdef struct SSPRK432{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function SSPRK432(stage_limiter!, step_limiter! = trivial_limiter!) - SSPRK432(stage_limiter!, - step_limiter!, False()) -end - -@doc explicit_rk_docstring( - "A third-order, four-step explicit strong stability preserving (SSP) linear multistep method. -This method does not come with an error estimator and requires a fixed time step -size.", - "SSPRKMSVS43", - references = "Shu, Chi-Wang. - Total-variation-diminishing time discretizations. - SIAM Journal on Scientific and Statistical Computing 9, no. 6 (1988): 1073-1084. - [DOI: 10.1137/0909073](https://doi.org/10.1137/0909073)") -Base.@kwdef struct SSPRKMSVS43{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function SSPRKMSVS43(stage_limiter!, step_limiter! = trivial_limiter!) - SSPRKMSVS43(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "A second-order, three-step explicit strong stability preserving (SSP) linear multistep method. -This method does not come with an error estimator and requires a fixed time step -size.", - "SSPRKMSVS32", - references = "Shu, Chi-Wang. - Total-variation-diminishing time discretizations. - SIAM Journal on Scientific and Statistical Computing 9, no. 6 (1988): 1073-1084. - [DOI: 10.1137/0909073](https://doi.org/10.1137/0909073)") -Base.@kwdef struct SSPRKMSVS32{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function SSPRKMSVS32(stage_limiter!, step_limiter! = trivial_limiter!) - SSPRKMSVS32(stage_limiter!, - step_limiter!, - False()) -end - -@doc explicit_rk_docstring( - "A third-order, nine-stage explicit strong stability preserving (SSP) method. - -Consider using `SSPRK43` instead, which uses the same main method and an -improved embedded method.", - "SSPRK932", - references = "Gottlieb, Sigal, David I. Ketcheson, and Chi-Wang Shu. - Strong stability preserving Runge-Kutta and multistep time discretizations. - World Scientific, 2011.") -Base.@kwdef struct SSPRK932{StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqAdaptiveAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function SSPRK932(stage_limiter!, step_limiter! = trivial_limiter!) - SSPRK932(stage_limiter!, - step_limiter!, False()) -end - -@doc explicit_rk_docstring( - "A fourth-order, five-stage explicit strong stability preserving (SSP) method. -Fixed timestep only.", - "SSPRK54", - references = "Ruuth, Steven. - Global optimization of explicit strong-stability-preserving Runge-Kutta methods. - Mathematics of Computation 75.253 (2006): 183-207.") -Base.@kwdef struct SSPRK54{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function SSPRK54(stage_limiter!, step_limiter! = trivial_limiter!) - SSPRK54(stage_limiter!, - step_limiter!, False()) -end - -@doc explicit_rk_docstring( - "A fourth-order, ten-stage explicit strong stability preserving (SSP) method. -Fixed timestep only.", - "SSPRK104", - references = "Ketcheson, David I. - Highly efficient strong stability-preserving Runge–Kutta methods with - low-storage implementations. - SIAM Journal on Scientific Computing 30.4 (2008): 2113-2136.") -Base.@kwdef struct SSPRK104{StageLimiter, StepLimiter, Thread} <: OrdinaryDiffEqAlgorithm - stage_limiter!::StageLimiter = trivial_limiter! - step_limiter!::StepLimiter = trivial_limiter! - thread::Thread = False() -end -# for backwards compatibility -function SSPRK104(stage_limiter!, step_limiter! = trivial_limiter!) - SSPRK104(stage_limiter!, - step_limiter!, False()) -end From 3a48a6e6a330f2fcb9f332b97b26ac244a91e4af Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:52:57 -0400 Subject: [PATCH 03/71] Delete src/caches/extrapolation_caches.jl --- src/caches/extrapolation_caches.jl | 1704 ---------------------------- 1 file changed, 1704 deletions(-) delete mode 100644 src/caches/extrapolation_caches.jl diff --git a/src/caches/extrapolation_caches.jl b/src/caches/extrapolation_caches.jl deleted file mode 100644 index 34bb50d377..0000000000 --- a/src/caches/extrapolation_caches.jl +++ /dev/null @@ -1,1704 +0,0 @@ -@cache mutable struct AitkenNevilleCache{ - uType, - rateType, - arrayType, - dtType, - uNoUnitsType -} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - tmp::uType - k::rateType - utilde::uType - atmp::uNoUnitsType - fsalfirst::rateType - dtpropose::dtType - T::arrayType - cur_order::Int - work::dtType - A::Int - step_no::Int - u_tmps::Array{uType, 1} - k_tmps::Array{rateType, 1} -end - -@cache mutable struct AitkenNevilleConstantCache{dtType, arrayType} <: - OrdinaryDiffEqConstantCache - dtpropose::dtType - T::arrayType - cur_order::Int - work::dtType - A::Int - step_no::Int -end - -function alg_cache(alg::AitkenNeville, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - utilde = zero(u) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - cur_order = max(alg.init_order, alg.min_order) - dtpropose = zero(dt) - T = Array{typeof(u), 2}(undef, alg.max_order, alg.max_order) - # Array of arrays of length equal to number of threads to store intermediate - # values of u and k. [Thread Safety] - u_tmps = Array{typeof(u), 1}(undef, Threads.nthreads()) - k_tmps = Array{typeof(k), 1}(undef, Threads.nthreads()) - # Initialize each element of u_tmps and k_tmps to different instance of - # zeros array similar to u and k respectively - for i in 1:Threads.nthreads() - u_tmps[i] = zero(u) - k_tmps[i] = zero(rate_prototype) - end - # Initialize lower triangle of T to different instance of zeros array similar to u - for i in 1:(alg.max_order) - for j in 1:i - T[i, j] = zero(u) - end - end - work = zero(dt) - A = one(Int) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - step_no = zero(Int) - AitkenNevilleCache(u, uprev, tmp, k, utilde, atmp, fsalfirst, dtpropose, T, cur_order, - work, A, step_no, u_tmps, k_tmps) -end - -function alg_cache(alg::AitkenNeville, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - dtpropose = zero(dt) - cur_order = max(alg.init_order, alg.min_order) - T = Array{typeof(u), 2}(undef, alg.max_order, alg.max_order) - @.. broadcast=false T=u - work = zero(dt) - A = one(Int) - step_no = zero(Int) - AitkenNevilleConstantCache(dtpropose, T, cur_order, work, A, step_no) -end - -@cache mutable struct ImplicitEulerExtrapolationCache{uType, rateType, QType, arrayType, - dtType, JType, WType, F, JCType, - GCType, uNoUnitsType, TFType, UFType, - sequenceType} <: - OrdinaryDiffEqMutableCache - uprev::uType - u_tmps::Array{uType, 1} - u_tmps2::Array{uType, 1} - utilde::uType - tmp::uType - atmp::uNoUnitsType - k_tmps::Array{rateType, 1} - dtpropose::dtType - T::arrayType - A::Int - step_no::Int - du1::rateType - du2::rateType - J::JType - W::WType - tf::TFType - uf::UFType - linsolve_tmps::Array{rateType, 1} - linsolve::Array{F, 1} - jac_config::JCType - grad_config::GCType - sequence::sequenceType #support for different sequences - stage_number::Vector{Int} # stage_number[n] contains information for extrapolation order (n - 1) - - Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n - 1) - n_curr::Int # Storage for the current extrapolation order - n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter - sigma::Rational{Int} # Parameter for order selection - res::uNoUnitsType # Storage for the scaled residual of u and utilde - - #Stepsizing caches - work::Array{QType, 1} - dt_new::Array{QType, 1} - - # Values to check overflow in T1 computation - diff1::Array{uType, 1} - diff2::Array{uType, 1} -end - -@cache mutable struct ImplicitEulerExtrapolationConstantCache{QType, dtType, arrayType, TF, - UF, sequenceType} <: - OrdinaryDiffEqConstantCache - Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n) - dtpropose::dtType - T::arrayType - n_curr::Int - n_old::Int - A::Int - step_no::Int - sigma::Rational{Int} - - tf::TF - uf::UF - - sequence::sequenceType #support for different sequences - stage_number::Vector{Int} - - #Stepsizing caches - work::Array{QType, 1} - dt_new::Array{QType, 1} -end - -function alg_cache(alg::ImplicitEulerExtrapolation, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - dtpropose = zero(dt) - #cur_order = max(alg.init_order, alg.min_order) - QType = tTypeNoUnits <: Integer ? typeof(qmin_default(alg)) : tTypeNoUnits # Cf. DiffEqBase.__init in solve.jl - Q = fill(zero(QType), alg.max_order + 1) - n_curr = alg.init_order - n_old = alg.init_order - T = Array{typeof(u), 2}(undef, alg.max_order + 1, alg.max_order + 1) - for i in 1:(alg.max_order + 1) - for j in 1:i - T[i, j] = zero(u) - end - end - A = one(Int) - step_no = zero(Int) - tf = TimeDerivativeWrapper(f, u, p) - uf = UDerivativeWrapper(f, t, p) - sequence = generate_sequence(constvalue(uBottomEltypeNoUnits), alg) - stage_number = Vector{Int}(undef, alg.max_order + 1) - - for n in 1:length(stage_number) - s = zero(eltype(sequence)) - for i in 1:n - s += sequence[i] - end - stage_number[n] = 2 * Int(s) - n + 7 - end - sigma = 9 // 10 - work = fill(zero(eltype(Q)), alg.max_order + 1) - dt_new = fill(zero(eltype(Q)), alg.max_order + 1) - ImplicitEulerExtrapolationConstantCache(Q, dtpropose, T, n_curr, n_old, A, step_no, - sigma, tf, uf, sequence, stage_number, work, - dt_new) -end - -function alg_cache(alg::ImplicitEulerExtrapolation, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - u_tmp = zero(u) - u_tmps = Array{typeof(u_tmp), 1}(undef, Threads.nthreads()) - - u_tmps[1] = u_tmp - for i in 2:Threads.nthreads() - u_tmps[i] = zero(u_tmp) - end - - u_tmps2 = Array{typeof(u_tmp), 1}(undef, Threads.nthreads()) - - for i in 1:Threads.nthreads() - u_tmps2[i] = zero(u_tmp) - end - - utilde = zero(u) - tmp = zero(u) - k_tmp = zero(rate_prototype) - k_tmps = Array{typeof(k_tmp), 1}(undef, Threads.nthreads()) - - k_tmps[1] = k_tmp - for i in 2:Threads.nthreads() - k_tmps[i] = zero(rate_prototype) - end - - #cur_order = max(alg.init_order, alg.min_order) - dtpropose = zero(dt) - T = Array{typeof(u), 2}(undef, alg.max_order + 1, alg.max_order + 1) - # Initialize lower triangle of T to different instance of zeros array similar to u - for i in 1:(alg.max_order + 1) - for j in 1:i - T[i, j] = zero(u) - end - end - A = one(Int) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - step_no = zero(Int) - - du1 = zero(rate_prototype) - du2 = zero(rate_prototype) - - if DiffEqBase.has_jac(f) && !DiffEqBase.has_Wfact(f) && f.jac_prototype !== nothing - W_el = WOperator(f, dt, true) - J = nothing # is J = W.J better? - else - J = false .* _vec(rate_prototype) .* _vec(rate_prototype)' # uEltype? - W_el = zero(J) - end - - W = Array{typeof(W_el), 1}(undef, Threads.nthreads()) - W[1] = W_el - for i in 2:Threads.nthreads() - if W_el isa WOperator - W[i] = WOperator(f, dt, true) - else - W[i] = zero(W_el) - end - end - - tf = TimeGradientWrapper(f, uprev, p) - uf = UJacobianWrapper(f, t, p) - linsolve_tmp = zero(rate_prototype) - linsolve_tmps = Array{typeof(linsolve_tmp), 1}(undef, Threads.nthreads()) - - for i in 1:Threads.nthreads() - linsolve_tmps[i] = zero(rate_prototype) - end - - linprob = LinearProblem(W[1], _vec(linsolve_tmps[1]); u0 = _vec(k_tmps[1])) - linsolve1 = init(linprob, alg.linsolve, alias_A = true, alias_b = true) - #Pl = LinearSolve.InvPreconditioner(Diagonal(_vec(weight))), - #Pr = Diagonal(_vec(weight))) - - linsolve = Array{typeof(linsolve1), 1}(undef, Threads.nthreads()) - linsolve[1] = linsolve1 - for i in 2:Threads.nthreads() - linprob = LinearProblem(W[i], _vec(linsolve_tmps[i]); u0 = _vec(k_tmps[i])) - linsolve[i] = init(linprob, alg.linsolve, alias_A = true, alias_b = true) - #Pl = LinearSolve.InvPreconditioner(Diagonal(_vec(weight))), - #Pr = Diagonal(_vec(weight))) - end - - res = uEltypeNoUnits.(zero(u)) - grad_config = build_grad_config(alg, f, tf, du1, t) - jac_config = build_jac_config(alg, f, uf, du1, uprev, u, du1, du2) - sequence = generate_sequence(constvalue(uBottomEltypeNoUnits), alg) - cc = alg_cache(alg, u, rate_prototype, uEltypeNoUnits, uBottomEltypeNoUnits, - tTypeNoUnits, uprev, uprev2, f, t, dt, reltol, p, calck, Val(false)) - diff1 = Array{typeof(u), 1}(undef, Threads.nthreads()) - diff2 = Array{typeof(u), 1}(undef, Threads.nthreads()) - for i in 1:Threads.nthreads() - diff1[i] = zero(u) - diff2[i] = zero(u) - end - ImplicitEulerExtrapolationCache(uprev, u_tmps, u_tmps2, utilde, tmp, atmp, k_tmps, - dtpropose, T, A, step_no, - du1, du2, J, W, tf, uf, linsolve_tmps, linsolve, - jac_config, grad_config, sequence, cc.stage_number, - cc.Q, cc.n_curr, cc.n_old, cc.sigma, res, cc.work, - cc.dt_new, diff1, diff2) -end - -struct extrapolation_coefficients{T1, T2, T3} - # This structure is used by the caches of the algorithms - # ExtrapolationMidpointDeuflhard() and ExtrapolationMidpointHairerWanner(). - # It contains the constant coefficients used to extrapolate the internal discretisations - # in their perfom_step! function and some additional constant data. - - subdividing_sequence::T1 # subdividing_sequence[n] is used for the (n -1)th internal discretisation - - # Weights and Scaling factors for extrapolation operators - extrapolation_weights::T2 - extrapolation_scalars::T3 - - # Weights and scaling factors for internal extrapolation operators (used for error estimate) - extrapolation_weights_2::T2 - extrapolation_scalars_2::T3 -end - -function create_extrapolation_coefficients(T, - alg::Union{ExtrapolationMidpointDeuflhard, - ExtrapolationMidpointHairerWanner, - ImplicitDeuflhardExtrapolation, - ImplicitHairerWannerExtrapolation}) - # Compute and return extrapolation_coefficients - - @unpack min_order, init_order, max_order, sequence = alg - - # Initialize subdividing_sequence: - if sequence == :harmonic - subdividing_sequence = BigInt.(1:(max_order + 1)) - elseif sequence == :romberg - subdividing_sequence = BigInt(2) .^ (0:max_order) - else # sequence == :bulirsch - subdividing_sequence = [n == 0 ? BigInt(1) : - (isodd(n) ? BigInt(2)^((n + 1) ÷ 2) : - 3 * BigInt(2)^(n ÷ 2 - 1)) for n in 0:max_order] - end - - # Compute nodes corresponding to subdividing_sequence - nodes = BigInt(1) .// subdividing_sequence .^ 2 - - # Compute barycentric weights for internal extrapolation operators - extrapolation_weights_2 = zeros(Rational{BigInt}, max_order, max_order) - extrapolation_weights_2[1, :] = ones(Rational{BigInt}, 1, max_order) - for n in 2:max_order - distance = nodes[2:n] .- nodes[n + 1] - extrapolation_weights_2[1:(n - 1), n] = extrapolation_weights_2[1:(n - 1), - n - 1] .// distance - extrapolation_weights_2[n, n] = 1 // prod(-distance) - end - - # Compute barycentric weights for extrapolation operators - extrapolation_weights = zeros(Rational{BigInt}, max_order + 1, max_order + 1) - for n in 1:max_order - extrapolation_weights[n + 1, (n + 1):(max_order + 1)] = extrapolation_weights_2[n, - n:max_order] // - (nodes[n + 1] - nodes[1]) - extrapolation_weights[1, n] = 1 // prod(nodes[1] .- nodes[2:n]) - end - extrapolation_weights[1, max_order + 1] = 1 // - prod(nodes[1] .- nodes[2:(max_order + 1)]) - - # Rescale barycentric weights to obtain weights of 1. Barycentric Formula - for m in 1:(max_order + 1) - extrapolation_weights[1:m, m] = -extrapolation_weights[1:m, m] .// nodes[1:m] - if 2 <= m - extrapolation_weights_2[1:(m - 1), m - 1] = -extrapolation_weights_2[1:(m - 1), - m - 1] .// - nodes[2:m] - end - end - - # Compute scaling factors for internal extrapolation operators - extrapolation_scalars_2 = ones(Rational{BigInt}, max_order) - extrapolation_scalars_2[1] = -nodes[2] - for n in 1:(max_order - 1) - extrapolation_scalars_2[n + 1] = -extrapolation_scalars_2[n] * nodes[n + 2] - end - - # Compute scaling factors for extrapolation operators - extrapolation_scalars = -nodes[1] * [BigInt(1); extrapolation_scalars_2] - - # Initialize and return extrapolation_coefficients - extrapolation_coefficients(Int.(subdividing_sequence), - T.(extrapolation_weights), T.(extrapolation_scalars), - T.(extrapolation_weights_2), T.(extrapolation_scalars_2)) -end - -function create_extrapolation_coefficients(T, alg::ImplicitEulerBarycentricExtrapolation) - # Compute and return extrapolation_coefficients - - @unpack min_order, init_order, max_order, sequence = alg - - # Initialize subdividing_sequence: - if sequence == :harmonic - subdividing_sequence = BigInt.(1:(max_order + 1)) - elseif sequence == :romberg - subdividing_sequence = BigInt(2) .^ (0:max_order) - else # sequence == :bulirsch - subdividing_sequence = [n == 0 ? BigInt(1) : - (isodd(n) ? BigInt(2)^((n + 1) ÷ 2) : - 3 * BigInt(2)^(n ÷ 2 - 1)) for n in 0:max_order] - end - - # Compute nodes corresponding to subdividing_sequence - nodes = BigInt(1) .// subdividing_sequence - - # Compute barycentric weights for internal extrapolation operators - extrapolation_weights_2 = zeros(Rational{BigInt}, max_order, max_order) - extrapolation_weights_2[1, :] = ones(Rational{BigInt}, 1, max_order) - for n in 2:max_order - distance = nodes[2:n] .- nodes[n + 1] - extrapolation_weights_2[1:(n - 1), n] = extrapolation_weights_2[1:(n - 1), - n - 1] .// distance - extrapolation_weights_2[n, n] = 1 // prod(-distance) - end - - # Compute barycentric weights for extrapolation operators - extrapolation_weights = zeros(Rational{BigInt}, max_order + 1, max_order + 1) - for n in 1:max_order - extrapolation_weights[n + 1, (n + 1):(max_order + 1)] = extrapolation_weights_2[n, - n:max_order] // - (nodes[n + 1] - nodes[1]) - extrapolation_weights[1, n] = 1 // prod(nodes[1] .- nodes[2:n]) - end - extrapolation_weights[1, max_order + 1] = 1 // - prod(nodes[1] .- nodes[2:(max_order + 1)]) - - # Rescale barycentric weights to obtain weights of 1. Barycentric Formula - for m in 1:(max_order + 1) - extrapolation_weights[1:m, m] = -extrapolation_weights[1:m, m] .// nodes[1:m] - if 2 <= m - extrapolation_weights_2[1:(m - 1), m - 1] = -extrapolation_weights_2[1:(m - 1), - m - 1] .// - nodes[2:m] - end - end - - # Compute scaling factors for internal extrapolation operators - extrapolation_scalars_2 = ones(Rational{BigInt}, max_order) - extrapolation_scalars_2[1] = -nodes[2] - for n in 1:(max_order - 1) - extrapolation_scalars_2[n + 1] = -extrapolation_scalars_2[n] * nodes[n + 2] - end - - # Compute scaling factors for extrapolation operators - extrapolation_scalars = -nodes[1] * [BigInt(1); extrapolation_scalars_2] - - # Initialize and return extrapolation_coefficients - extrapolation_coefficients(Int.(subdividing_sequence), - T.(extrapolation_weights), T.(extrapolation_scalars), - T.(extrapolation_weights_2), T.(extrapolation_scalars_2)) -end - -function create_extrapolation_coefficients(T::Type{<:CompiledFloats}, - alg::ImplicitEulerBarycentricExtrapolation) - # Compute and return extrapolation_coefficients - - @unpack min_order, init_order, max_order, sequence = alg - - max_order > 15 && - error("max_order > 15 not allowed for Float32 or Float64 with this algorithm. That's a bad idea.") - - # Initialize subdividing_sequence: - if sequence == :harmonic - subdividing_sequence = [ - 1, - 2, - 3, - 4, - 5, - 6, - 7, - 8, - 9, - 10, - 11, - 12, - 13, - 14, - 15, - 16, - 17, - 18, - 19, - 20, - 21 - ] - extrapolation_weights = T[-1.0 -2.0 -3.0 -4.0 -5.0 -6.0 -7.0 -8.0 -9.0 -10.0 -11.0 -12.0 -13.0 -14.0 -15.0 -16.0; - 0.0 4.0 24.0 96.0 320.0 960.0 2688.0 7168.0 18432.0 46080.0 112640.0 270336.0 638976.0 1.490944e6 3.44064e6 7.86432e6; - 0.0 0.0 -27.0 -324.0 -2430.0 -14580.0 -76545.0 -367416.0 -1.653372e6 -7.08588e6 -2.9229255e7 -1.1691702e8 -4.55976378e8 -1.741000716e9 -6.528752685e9 -2.410616376e10; - 0.0 0.0 0.0 256.0 5120.0 61440.0 573440.0 4.58752e6 3.3030144e7 2.2020096e8 1.38412032e9 8.30472192e9 4.798283776e10 2.68703891456e11 1.46565758976e12 7.81684047872e12; - 0.0 0.0 0.0 0.0 -3125.0 -93750.0 -1.640625e6 -2.1875e7 -2.4609375e8 -2.4609375e9 -2.255859375e10 -1.93359375e11 -1.571044921875e12 -1.221923828125e13 -9.1644287109375e13 -6.6650390625e14; - 0.0 0.0 0.0 0.0 0.0 46656.0 1.959552e6 4.7029248e7 8.46526464e8 1.269789696e10 1.67612239872e11 2.011346878464e12 2.2412150931456e13 2.35327584780288e14 2.35327584780288e15 2.259144813890765e16; - 0.0 0.0 0.0 0.0 0.0 0.0 -823543.0 -4.6118408e7 -1.452729852e9 -3.389702988e10 -6.5251782519e11 -1.0962299463192e13 -1.66261541858412e14 -2.327661586017768e15 -3.0550558316483204e16 -3.8018472571623546e17; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.6777216e7 1.207959552e9 4.831838208e10 1.41733920768e12 3.401614098432e13 7.07535732473856e14 1.3207333672845312e16 2.2641143439163392e17 3.6225829502661427e18; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -3.87420489e8 -3.486784401e10 -1.725958278495e12 -6.213449802582e13 -1.817434067255235e15 -4.579933849483192e16 -1.0304851161337183e18 -2.119855096046506e19; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0e10 1.1e12 6.6e13 2.86e15 1.001e17 3.003e18 8.008e19; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.85311670611e11 -3.7661140520652e13 -2.692771547226618e15 -1.3822893942429973e17 -5.701943751252363e18 -2.007084200440832e20; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 8.916100448256e12 1.390911669927936e15 1.1683658027394662e17 7.010194816436797e18 3.364893511889663e20; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -3.02875106592253e14 -5.512326939979005e16 -5.37451876647953e18 -3.726333011425807e20; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.1112006825558016e16 2.3335214333671834e18 2.6135440053712454e20; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -4.378938903808594e17 -1.0509453369140625e20; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.8446744073709552e19] - extrapolation_weights_2 = T[-2.0 -12.0 -48.0 -160.0 -480.0 -1344.0 -3584.0 -9216.0 -23040.0 -56320.0 -135168.0 -319488.0 -745472.0 -1.72032e6 -3.93216e6; - 0.0 18.0 216.0 1620.0 9720.0 51030.0 244944.0 1.102248e6 4.72392e6 1.948617e7 7.794468e7 3.03984252e8 1.160667144e9 4.35250179e9 1.607077584e10; - 0.0 0.0 -192.0 -3840.0 -46080.0 -430080.0 -3.44064e6 -2.4772608e7 -1.6515072e8 -1.03809024e9 -6.22854144e9 -3.598712832e10 -2.01527918592e11 -1.09924319232e12 -5.86263035904e12; - 0.0 0.0 0.0 2500.0 75000.0 1.3125e6 1.75e7 1.96875e8 1.96875e9 1.8046875e10 1.546875e11 1.2568359375e12 9.775390625e12 7.33154296875e13 5.33203125e14; - 0.0 0.0 0.0 0.0 -38880.0 -1.63296e6 -3.919104e7 -7.0543872e8 -1.05815808e10 -1.3967686656e11 -1.67612239872e12 -1.867679244288e13 -1.9610632065024e14 -1.9610632065024e15 -1.882620678242304e16; - 0.0 0.0 0.0 0.0 0.0 705894.0 3.9530064e7 1.245197016e9 2.905459704e10 5.5930099302e11 9.396256682736e12 1.42509893021496e14 1.995138502300944e15 2.618619284269989e16 3.2587262204248755e17; - 0.0 0.0 0.0 0.0 0.0 0.0 -1.4680064e7 -1.056964608e9 -4.227858432e10 -1.24017180672e12 -2.976412336128e13 -6.19093765914624e14 -1.1556416963739648e16 -1.9811000509267968e17 -3.169760081482875e18; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.44373768e8 3.099363912e10 1.53418513644e12 5.523066491184e13 1.61549694867132e15 4.071052310651726e16 9.159867698966385e17 1.884315640930228e19; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -9.0e9 -9.9e11 -5.94e13 -2.574e15 -9.009e16 -2.7027e18 -7.2072e19; 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- 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0231987972010274e22] - extrapolation_scalars = T[-1.0, 0.5, -0.16666666666666666, 0.041666666666666664, - -0.006944444444444444, 0.0008680555555555555, - -7.233796296296296e-5, 4.521122685185185e-6, - -1.8838011188271604e-7, 5.886878496334876e-9, - -1.226433020069766e-10, 1.9163015938590095e-12, - -1.9961474936031345e-14, 1.5594902293774489e-16, - -8.122344944674213e-19, 3.1727909940133645e-21] - extrapolation_scalars_2 = T[-0.5, 0.16666666666666666, -0.041666666666666664, - 0.006944444444444444, -0.0008680555555555555, - 7.233796296296296e-5, -4.521122685185185e-6, - 1.8838011188271604e-7, -5.886878496334876e-9, - 1.226433020069766e-10, -1.9163015938590095e-12, - 1.9961474936031345e-14, -1.5594902293774489e-16, - 8.122344944674213e-19, -3.1727909940133645e-21] - end - extrapolation_coefficients(subdividing_sequence, - extrapolation_weights, extrapolation_scalars, - extrapolation_weights_2, extrapolation_scalars_2) -end - -function create_extrapolation_coefficients(T::Type{<:CompiledFloats}, - alg::Union{ExtrapolationMidpointDeuflhard, - ExtrapolationMidpointHairerWanner, - ImplicitDeuflhardExtrapolation, - ImplicitHairerWannerExtrapolation}) - # Compute and return extrapolation_coefficients - - @unpack min_order, init_order, max_order, sequence = alg - - max_order > 15 && - error("max_order > 15 not allowed for Float32 or Float64 with this algorithm. That's a bad idea.") - - # Initialize subdividing_sequence: - if sequence == :harmonic - subdividing_sequence = [ - 1, - 2, - 3, - 4, - 5, - 6, - 7, - 8, - 9, - 10, - 11, - 12, - 13, - 14, - 15, - 16, - 17, - 18, - 19, - 20, - 21 - ] - extrapolation_weights = T[-1.0 -1.3333333333333333 -1.5 -1.6 -1.6666666666666667 -1.7142857142857142 -1.75 -1.7777777777777777 -1.8 -1.8181818181818181 -1.8333333333333333 -1.8461538461538463 -1.8571428571428572 -1.8666666666666667 -1.875 -1.8823529411764706; - 0.0 5.333333333333333 38.4 204.8 975.2380952380952 4388.571428571428 19114.666666666668 81555.91111111111 343170.32727272727 1.4298763636363635e6 5.915044102564103e6 2.433618145054945e7 9.970459794285715e7 4.0712710826666665e8 1.6579836988235295e9 6.737203601568627e9; - 0.0 0.0 -72.9 -1499.6571428571428 -21088.928571428572 -253067.14285714287 -2.79006525e6 -2.9219592436363637e7 -2.9584837341818184e8 -2.925972923916084e9 -2.8449861733434067e10 -2.7311867264096704e11 -2.596334381793193e12 -2.449162486354648e13 -2.2960898309574828e14 -2.141777720860745e15; - 0.0 0.0 0.0 1872.4571428571428 83220.31746031746 2.3967451428571427e6 5.6940854303030305e7 1.214738225131313e9 2.422001138107972e10 4.613335501158042e11 8.50611193356378e12 1.5311001480414803e14 2.7059443139242895e15 4.7143563158147624e16 8.120422362168969e17 1.3858854164768373e19; - 0.0 0.0 0.0 0.0 -77504.96031746031 -6.341314935064935e6 -3.236712831439394e8 -1.3278821872571873e10 -4.80171683784965e11 -1.6005722792832168e13 -5.043469942533053e14 -1.525755612867142e16 -4.4766093502525523e17 -1.2827711003647664e19 -3.607793719775906e20 -9.995618963881296e21; - 0.0 0.0 0.0 0.0 0.0 4.711650077922078e6 6.393346721118882e8 5.260811016234965e10 3.4090055385202573e12 1.9175656154176447e14 9.826959789128542e15 4.7169406987817e17 2.15773437679608e19 9.515608601670712e20 4.078117972144591e22 1.708360692331116e24; - 0.0 0.0 0.0 0.0 0.0 0.0 -3.952348909376457e8 -8.263044119869713e10 -1.0248756909925902e13 -9.846844874242534e14 -8.108603230469998e16 -6.022558357283822e18 -4.1560671463889437e20 -2.715297202307443e22 -1.7009177076954297e24 -1.0307396968759164e26; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.3741255122091064e10 1.3338509797230594e13 2.371290630618772e15 3.221627130440662e17 3.711314454267642e19 3.8230073464151254e21 3.6330154661690406e23 3.249405137443117e25 2.772825717284793e27; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -6.174193142616171e12 -2.6321560239574205e15 -6.449440297701669e17 -1.1940678036887662e20 -1.8574538823517637e22 -2.5642554640188345e24 -3.245385821648838e26 -3.845504022726303e28; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.082508822446903e15 6.237312738860727e17 2.041302350899874e20 4.99971155510259e22 1.0207744425001122e25 1.837393996500202e27 3.015210660923408e29; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.30788366240374e17 -1.748372388422729e20 -7.448430618928414e22 -2.355293074113417e25 -6.165659032955555e27 -1.4147218829987503e30; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 5.87960511179021e19 5.723442800021062e22 3.1065086459191243e25 1.2426034583676497e28 4.089940525827236e30; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.7640007344435631e22 -2.1641022343595773e25 -1.4694640618129094e28 -7.307458985088932e30; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6.155890364150897e24 9.361198795139813e27 7.828458512415587e30; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.472332709198601e27 -4.593753679027078e30; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.1322357960170301e30] - extrapolation_weights_2 = T[-4.0 -28.8 -153.6 -731.4285714285714 -3291.4285714285716 -14336.0 -61166.933333333334 -257377.74545454545 -1.0724072727272727e6 -4.436283076923077e6 -1.8252136087912086e7 -7.477844845714286e7 -3.053453312e8 -1.2434877741176472e9 -5.052902701176471e9; - 0.0 64.8 1333.0285714285715 18745.714285714286 224948.57142857142 2.480058e6 2.5972971054545455e7 2.6297633192727274e8 2.6008648212587414e9 2.5288765985274727e10 2.4277215345863736e11 2.3078527838161714e12 2.1770333212041316e13 2.0409687386288734e14 1.9038024185428845e15; - 0.0 0.0 -1755.4285714285713 -78019.04761904762 -2.2469485714285714e6 -5.338205090909091e7 -1.138817086060606e9 -2.2706260669762238e10 -4.325002032335664e11 -7.974479937716044e12 -1.4354063887888878e14 -2.5368227943040215e15 -4.41970904607634e16 -7.612895964533408e17 -1.299267577947035e19; - 0.0 0.0 0.0 74404.76190476191 6.087662337662337e6 3.107244318181818e8 1.2747668997668997e10 4.609648164335664e11 1.536549388111888e13 4.8417311448317306e14 1.4647253883524564e16 4.29754497624245e17 1.2314602563501758e19 3.4634819709848696e20 9.595794205326044e21; - 0.0 0.0 0.0 0.0 -4.580770909090909e6 -6.215753756643356e8 -5.114677376895105e10 -3.314310940228028e12 -1.8642999038782656e14 -9.553988683874972e15 -4.585914568259986e17 -2.0977973107739664e19 -9.251286140513193e20 -3.964836917362797e22 -1.6609062286552515e24; - 0.0 0.0 0.0 0.0 0.0 3.8716887275524473e8 8.094410566402983e10 1.0039598605641701e13 9.64588885640085e14 7.943121531888978e16 5.899649003053539e18 4.071249449523863e20 2.659882973688924e22 1.6662051014159312e24 1.0097041928580407e26; - 0.0 0.0 0.0 0.0 0.0 0.0 -4.3057798010808395e10 -1.3130095581648865e13 -2.3342392145153535e15 -3.1712892065275264e17 -3.65332516591971e19 -3.763272856627389e21 -3.5762495995101494e23 -3.198633182170568e25 -2.729500315452218e27; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6.097968535917206e12 2.59966027057523e15 6.369817577976957e17 1.1793262258654482e20 1.8345223529400134e22 2.532597989154405e24 3.205319330023544e26 3.7980286644210397e28; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0716837342224339e15 -6.174939611472119e17 -2.0208893273908753e20 -4.949714439551565e22 -1.010566698075111e25 -1.8190200565352e27 -2.9850585543141743e29; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.2888102437061885e17 1.733923029840723e20 7.38687334108603e22 2.3358278420959505e25 6.114703173179063e27 1.4030299666103307e30; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -5.838774520736112e19 -5.6836966694653606e22 -3.0849356692113527e25 -1.233974267684541e28 -4.061538161064547e30; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.753562860275258e22 2.1512968956947278e25 1.4607690081927147e28 7.2642195828103e30; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -6.124482760252167e24 -9.313437576797262e27 -7.788517397556324e30; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.461344563824385e27 4.57333699600918e30; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.1278129999388386e30] - extrapolation_scalars = T[-1.0, 0.25, -0.027777777777777776, 0.001736111111111111, - -6.944444444444444e-5, 1.9290123456790124e-6, - -3.936759889140842e-8, 6.151187326782565e-10, - -7.594058428126624e-12, 7.594058428126623e-14, - -6.276081345559193e-16, 4.358389823304995e-18, - -2.5789288895295828e-20, 1.3157800456783586e-22, - -5.8479113141260385e-25, 2.2843403570804838e-27] - extrapolation_scalars_2 = T[-0.25, 0.027777777777777776, -0.001736111111111111, - 6.944444444444444e-5, -1.9290123456790124e-6, - 3.936759889140842e-8, -6.151187326782565e-10, - 7.594058428126624e-12, -7.594058428126623e-14, - 6.276081345559193e-16, -4.358389823304995e-18, - 2.5789288895295828e-20, -1.3157800456783586e-22, - 5.8479113141260385e-25, -2.2843403570804838e-27] - elseif sequence == :romberg - subdividing_sequence = [ - 1, - 2, - 4, - 8, - 16, - 32, - 64, - 128, - 256, - 512, - 1024, - 2048, - 4096, - 8192, - 16384, - 32768 - ] - extrapolation_weights = T[-1.0 -1.3333333333333333 -1.4222222222222223 -1.4447971781305116 -1.4504630494172979 -1.451880901860521 -1.452235451531305 -1.4523240943593299 -1.4523462554044868 -1.4523517956869105 -1.4523531807588372 -1.4523535270269017 -1.4523536135939228 -1.4523536352356785 -1.4523536406461173 -1.452353641998727; - 0.0 5.333333333333333 28.444444444444443 121.36296296296297 493.15743680188126 1980.3655501377505 7929.205565360925 31724.5675171852 126906.01579724405 507631.8090356717 2.0305349820189304e6 8.122147673959353e6 3.248859844172289e7 1.2995440151277749e8 5.19817613796996e8 2.07927046293387e9; - 0.0 0.0 -91.02222222222223 -1941.8074074074075 -33140.17975308642 -538659.4296374682 -8.652349112921841e6 -1.3857291091506496e8 -2.2177080072599993e9 -3.54854939788296e10 -5.677765672441477e11 -9.084459730370057e12 -1.4535149430390788e14 -2.325624463334606e15 -3.720999363124215e16 -5.953599069714284e17; - 0.0 0.0 0.0 5917.889241622575 504993.2152851264 3.4474203496797964e7 2.241370436871182e9 1.4401024799097037e11 9.225665310201598e12 5.905867660750885e14 3.77998601491761e16 2.4192279640364677e18 1.5483118033241417e20 9.909204991428803e21 6.341892706539483e23 4.05881157410929e25; - 0.0 0.0 0.0 0.0 -1.5209207425057925e6 -5.1914094677531046e8 -1.4176008786611145e11 -3.6866623485688414e13 -9.474866810815984e15 -2.4279369357326935e18 -6.217036386624773e20 -1.591658462098873e23 -4.074707838080507e25 -1.0431291857706623e28 -2.670413262277438e30 -6.836259581321538e32; - 0.0 0.0 0.0 0.0 0.0 1.5589452477944808e9 2.1284799116553977e12 2.3248676581708025e15 2.4184528070774876e18 2.486207422190278e21 2.5483650380553205e24 2.6101630458060033e27 2.6729701040532997e30 2.7371631523457504e33 2.8028657600863993e36 2.870137275504677e39; - 0.0 0.0 0.0 0.0 0.0 0.0 -6.386999060908798e12 -3.4881530871309916e16 -1.5239973381214444e20 -6.341377114357268e23 -2.607614058456583e27 -1.069122783562139e31 -4.380196305334128e34 -1.7942379182565492e38 -7.349310654759861e41 -3.010289127531343e45; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0465098000284594e17 2.2861355418221703e21 3.995311436502874e25 6.649821721972122e29 1.0937793665786103e34 1.7937998718897874e38 2.93967940527153e42 4.816664723480877e46 7.891743901406595e50; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -6.858511278043386e21 -5.993058601571351e26 -4.189451610800854e31 -2.7891799442838834e36 -1.835085270122301e41 -1.2038170852496654e46 -7.891262227584487e50 -5.171933283225826e55; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.7979244390088466e27 6.284201388527134e32 1.7571900680469942e38 4.679485289631606e43 1.2315095760466199e49 3.231484209329825e54 8.473210620642257e59; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.8852622144842938e33 -2.635787615753444e39 -2.948078543974702e45 -3.140352413792322e51 -3.305811498811932e57 -3.46978305819599e63; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7.907364732522996e39 4.422118870277351e46 1.9784224923818425e53 8.429821331796452e59 3.549588914822444e66; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.3266357401568573e47 -2.9676339154575293e54 -5.310787755579382e61 -9.051452272305827e68; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 8.902901879036164e54 7.966181752074431e62 5.702415016525277e70; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.389854534525231e63 -8.553622556652643e71; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.5660867693856473e72] - extrapolation_weights_2 = T[-4.0 -21.333333333333332 -91.02222222222223 -369.86807760141096 -1485.274162603313 -5946.904174020694 -23793.4256378889 -95179.51184793304 -380723.8567767538 -1.522901236514198e6 -6.091610755469514e6 -2.4366448831292167e7 -9.746580113458312e7 -3.89863210347747e8 -1.5594528472004025e9; - 0.0 85.33333333333333 1820.4444444444443 31068.91851851852 504993.2152851264 8.111577293364226e6 1.299121039828734e8 2.0791012568062494e9 3.3267650605152744e10 5.322905317913885e11 8.516680997221928e12 1.3626702590991364e14 2.1802729343761932e15 3.4884369029289516e16 5.5814991278571405e17; - 0.0 0.0 -5825.422222222222 -497102.6962962963 -3.3935544067160495e7 -2.2063490237950697e9 -1.4176008786611145e11 -9.081514289729697e12 -5.813588478551652e14 -3.7209237334345224e16 -2.3814275270983977e18 -1.524119431397202e20 -9.754373663437728e21 -6.242800632999802e23 -3.995392643263833e25; - 0.0 0.0 0.0 1.5149796458553793e6 5.1711305245196944e8 1.4120633752288446e11 3.6722613237697445e13 9.437855612336234e15 2.4184528070774876e18 6.19275108823952e20 1.585441046231299e23 4.058791010588005e25 1.0390544623887458e28 2.659981960471667e30 6.809555442332001e32; - 0.0 0.0 0.0 0.0 -1.5574228403259315e9 -2.1264013179916716e12 -2.32259727959837e15 -2.416091036758076e18 -2.4837794852545453e21 -2.545876400322845e24 -2.607614058456583e27 -2.6703597816860604e30 -2.7344901414547876e33 -2.8001285864925646e36 -2.867334407071567e39; - 0.0 0.0 0.0 0.0 0.0 6.385439734966193e12 3.4873014872562036e16 1.523625268458817e20 6.339828926585209e23 2.606977433930593e27 1.0688617672575583e31 4.379126921470521e34 1.7937998718897874e38 7.34751638946329e41 3.009554193662317e45; - 0.0 0.0 0.0 0.0 0.0 0.0 -1.0464459261392974e17 -2.2859960071821667e21 -3.995067582045079e25 -6.649415849064287e29 -1.093712607584068e34 -1.7936903870343255e38 -2.9394999814797044e42 -4.816370737596875e46 -7.891262227584487e50; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6.858406625466511e21 5.99296715475431e26 4.1893876848424375e31 2.789137384775456e36 1.8350572689432526e41 1.2037987164586916e46 7.89114181647872e50 5.171854365786813e55; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.7979175804714053e27 -6.284177416201281e32 -1.7571833648988464e38 -4.679467438811868e43 -1.2315048782104076e49 -3.231471882195848e54 -8.47317829790887e59; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.8852604165581403e33 2.6357851020704912e39 2.948075732467912e45 3.140349418918881e51 3.305808346144411e57 3.4697797491530044e63; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -7.907362847260331e39 -4.4221178159620535e46 -1.978422020689163e53 -8.429819321970427e59 -3.549588068534498e66; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.3266356610832054e47 2.967633738572764e54 5.310787439031764e61 9.051451732797232e68; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -8.902901746372587e54 -7.966181633369073e62 -5.702414931552672e70; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.3898545256223295e63 8.553622524787915e71; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.5660867669957927e72] - extrapolation_scalars = T[-1.0, 0.25, -0.015625, 0.000244140625, - -9.5367431640625e-7, 9.313225746154785e-10, - -2.2737367544323206e-13, 1.3877787807814457e-17, - -2.117582368135751e-22, 8.077935669463161e-28, - -7.703719777548943e-34, 1.8367099231598242e-40, - -1.0947644252537633e-47, 1.6313261169996311e-55, - -6.077163357286271e-64, 5.659799424266695e-73] - extrapolation_scalars_2 = T[-0.25, 0.015625, -0.000244140625, 9.5367431640625e-7, - -9.313225746154785e-10, 2.2737367544323206e-13, - -1.3877787807814457e-17, 2.117582368135751e-22, - -8.077935669463161e-28, 7.703719777548943e-34, - -1.8367099231598242e-40, 1.0947644252537633e-47, - -1.6313261169996311e-55, 6.077163357286271e-64, - -5.659799424266695e-73] - else # sequence == :bulirsch - subdividing_sequence = [1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256] - extrapolation_weights = T[-1.0 -1.3333333333333333 -1.5 -1.6 -1.6457142857142857 -1.6718367346938776 -1.6835279006707577 -1.6901299708694666 -1.693069327340544 -1.6947243315705933 -1.6954602083971546 -1.695874240194077 -1.6960582742950205 -1.6961617997954963 -1.6962078123772122 -1.6962336948493626; 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- 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.0269737017532947e20 -1.0674622648776207e24 -3.279244077704051e27 -8.791712994944155e30 -2.1606513856374756e34 -5.159530537984771e37; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.1022516982215851e24 8.126681320648103e27 4.438251558583284e31 2.0451463181951773e35 8.935380607282608e38; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -7.659880204931148e27 -1.6135647078547534e32 -1.9827483130119208e36 -2.126313710861715e40; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.665360734159382e32 4.911348648324117e36 1.0729004833885644e41; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -4.62766803500927e36 -3.8992995301161535e41; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.023990816545532e41] - extrapolation_weights_2 = T[-4.0 -28.8 -153.6 -691.2 -2949.12 -12133.522285714285 -49304.47151020408 -198597.0320970458 -797503.3759504899 -3.1955613533737888e6 -1.279474027704696e7 -5.120118384423134e7 -2.0485474874331778e8 -8.195079172733225e8 -3.27823175648077e9; - 0.0 64.8 1333.0285714285715 15996.342857142858 167525.33610389612 1.6082432265974027e6 1.5001588640001683e7 1.3715738185144395e8 1.2453620011260173e9 1.1252211963115074e10 1.0149291456038025e11 9.143291305850092e11 8.233484963636221e12 7.411946024407464e13 6.671667636089105e14; - 0.0 0.0 -1755.4285714285713 -50556.34285714286 -1.0785353142857142e6 -1.941363565714286e7 -3.313260485485714e8 -5.45268011325649e9 -8.862768945991501e10 -1.427959416193316e12 -2.2936948112658125e13 -3.6762941531523006e14 -5.887820469721143e15 -9.424603291176736e16 -1.508304765056309e18; - 0.0 0.0 0.0 55987.2 4.606946742857143e6 2.2113344365714285e8 9.263480985201038e9 3.557176698317199e11 1.327244552700053e13 4.853922935588765e14 1.7629065526851648e16 6.37135168217509e17 2.29873754256621e19 8.283544552215128e20 2.9837150424218233e22; - 0.0 0.0 0.0 0.0 -5.020091644675325e6 -5.783145574665974e8 -4.9349508903816315e10 -3.5531646410747744e12 -2.4256270616403794e14 -1.5967556428626954e16 -1.0381446211373969e18 -6.690587991889685e19 -4.2987683787890434e21 -2.755996478533553e23 -1.765561927831622e25; - 0.0 0.0 0.0 0.0 0.0 5.661016157622857e8 1.863283032451866e11 3.577503422307583e13 5.994594825452124e15 9.207697651894463e17 1.3742209159491396e20 2.0102888827598844e22 2.920484310307798e24 4.221989553536732e26 6.093053013029727e28; - 0.0 0.0 0.0 0.0 0.0 0.0 -1.9484826341819125e11 -8.978607978310253e13 -3.0646981899298996e16 -8.826330786998111e18 -2.410176726902951e21 -6.346339632896457e23 -1.6504512467519928e26 -4.254701731487095e28 -1.0934750300970127e31; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 8.539308868165419e13 1.1242610075573214e17 8.63432453804023e19 5.787195268551182e22 3.555652772997846e25 2.1226815194136454e28 1.2420719290740417e31 7.217771758563227e33; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.1639991919747662e17 -2.145483310647889e20 -2.929299880137918e23 -3.3745534619188814e26 -3.685912261338597e29 -3.882213417199601e32 -4.0384879128506835e35; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.0260939388619086e20 1.0669989566029343e24 3.277820794684214e27 8.787897147290099e30 2.1597136029180146e34 5.157291158410993e37; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.1019825938030739e24 -8.124697267591304e27 -4.437168001073864e31 -2.0446470148948364e35 -8.933199117876534e38; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7.6590490547353e27 1.6133896248786405e32 1.9825331710508737e36 2.126082991058019e40; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.66525908860676e32 -4.911048883391968e36 -1.07283499873992e41; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.627542501479674e36 3.8991937548467816e41; - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -4.023929415318473e41] - extrapolation_scalars = T[-1.0, 0.25, -0.027777777777777776, 0.001736111111111111, - -4.8225308641975306e-5, 7.535204475308642e-7, - -5.232780885631001e-9, 2.0440550334496098e-11, - -3.548706655294462e-14, 3.465533843060998e-17, - -1.5041379527174468e-20, 3.672211798626579e-24, - -3.9846048162180767e-28, 2.4320097755237285e-32, - -6.597248740027475e-37, 1.0066602691692314e-41] - extrapolation_scalars_2 = T[-0.25, 0.027777777777777776, -0.001736111111111111, - 4.8225308641975306e-5, -7.535204475308642e-7, - 5.232780885631001e-9, -2.0440550334496098e-11, - 3.548706655294462e-14, -3.465533843060998e-17, - 1.5041379527174468e-20, -3.672211798626579e-24, - 3.9846048162180767e-28, -2.4320097755237285e-32, - 6.597248740027475e-37, -1.0066602691692314e-41] - end - extrapolation_coefficients(subdividing_sequence, - extrapolation_weights, extrapolation_scalars, - extrapolation_weights_2, extrapolation_scalars_2) -end - -function generate_sequence(T, alg::ImplicitEulerExtrapolation) - # Compute and return extrapolation_coefficients - - @unpack min_order, init_order, max_order, sequence = alg - - # Initialize subdividing_sequence: - if sequence == :harmonic - subdividing_sequence = BigInt.(1:(max_order + 1)) - elseif sequence == :romberg - subdividing_sequence = BigInt(2) .^ (0:max_order) - else # sequence == :bulirsch - subdividing_sequence = [n == 0 ? BigInt(1) : - (isodd(n) ? BigInt(2)^((n + 1) ÷ 2) : - 3 * BigInt(2)^(n ÷ 2 - 1)) for n in 0:max_order] - end - - subdividing_sequence -end - -function generate_sequence(T::Type{<:CompiledFloats}, alg::ImplicitEulerExtrapolation) - # Compute and return extrapolation_coefficients - - @unpack min_order, init_order, max_order, sequence = alg - - # Initialize subdividing_sequence: - if sequence == :harmonic - subdividing_sequence = Int.(1:(max_order + 1)) - elseif sequence == :romberg - subdividing_sequence = Int(2) .^ (0:max_order) - else # sequence == :bulirsch - subdividing_sequence = [n == 0 ? Int(1) : - (isodd(n) ? Int(2)^((n + 1) ÷ 2) : 3 * Int(2)^(n ÷ 2 - 1)) - for n in 0:max_order] - end - - subdividing_sequence -end - -@cache mutable struct ExtrapolationMidpointDeuflhardConstantCache{QType, - extrapolation_coefficients -} <: - OrdinaryDiffEqConstantCache - # Values that are mutated - Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n + alg.min_order - 1) - n_curr::Int # Storage for the current extrapolation order - n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter - - # Constant values - coefficients::extrapolation_coefficients - stage_number::Vector{Int} # stage_number[n] contains information for extrapolation order (n + alg.min_order - 1) -end - -function alg_cache(alg::ExtrapolationMidpointDeuflhard, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - # Initialize cache's members - QType = tTypeNoUnits <: Integer ? typeof(qmin_default(alg)) : tTypeNoUnits # Cf. DiffEqBase.__init in solve.jl - - Q = fill(zero(QType), alg.max_order - alg.min_order + 1) - n_curr = alg.init_order - n_old = alg.init_order - sequence_factor = alg.sequence_factor - - coefficients = create_extrapolation_coefficients(constvalue(uBottomEltypeNoUnits), alg) - stage_number = Vector{Int}(undef, alg.max_order - alg.min_order + 1) - for n in 1:length(stage_number) - s = zero(eltype(coefficients.subdividing_sequence)) - for i in 1:(alg.min_order + n) - s += coefficients.subdividing_sequence[i] - end - stage_number[n] = sequence_factor * Int(s) - alg.min_order - n + 3 - sequence_factor - end - - # Initialize cache - ExtrapolationMidpointDeuflhardConstantCache(Q, n_curr, n_old, coefficients, - stage_number) -end - -@cache mutable struct ExtrapolationMidpointDeuflhardCache{uType, uNoUnitsType, rateType, - QType, extrapolation_coefficients -} <: OrdinaryDiffEqMutableCache - # Values that are mutated - utilde::uType - u_temp1::uType - u_temp2::uType - u_temp3::Array{uType, 1} - u_temp4::Array{uType, 1} - tmp::uType # for get_tmp_cache() - T::Array{uType, 1} # Storage for the internal discretisations obtained by the explicit midpoint rule - res::uNoUnitsType # Storage for the scaled residual of u and utilde - - fsalfirst::rateType - k::rateType - k_tmps::Array{rateType, 1} - - # Constant values - Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n + alg.min_order - 1) - n_curr::Int # Storage for the current extrapolation order - n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter - coefficients::extrapolation_coefficients - stage_number::Vector{Int} # Stage_number[n] contains information for extrapolation order (n + alg.min_order - 1) -end - -function alg_cache(alg::ExtrapolationMidpointDeuflhard, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - # Initialize cache's members - utilde = zero(u) - u_temp1 = zero(u) - u_temp2 = zero(u) - u_temp3 = Array{typeof(u), 1}(undef, Threads.nthreads()) - u_temp4 = Array{typeof(u), 1}(undef, Threads.nthreads()) - - for i in 1:Threads.nthreads() - u_temp3[i] = zero(u) - u_temp4[i] = zero(u) - end - - tmp = zero(u) - T = Vector{typeof(u)}(undef, alg.max_order + 1) - for i in 1:(alg.max_order + 1) - T[i] = zero(u) - end - res = uEltypeNoUnits.(zero(u)) - - fsalfirst = zero(rate_prototype) - k = zero(rate_prototype) - k_tmps = Array{typeof(k), 1}(undef, Threads.nthreads()) - for i in 1:Threads.nthreads() - k_tmps[i] = zero(rate_prototype) - end - - cc = alg_cache(alg::ExtrapolationMidpointDeuflhard, u, rate_prototype, uEltypeNoUnits, - uBottomEltypeNoUnits, tTypeNoUnits, uprev, uprev2, f, t, dt, reltol, p, - calck, Val(false)) - # Initialize cache - ExtrapolationMidpointDeuflhardCache(utilde, u_temp1, u_temp2, u_temp3, u_temp4, tmp, T, - res, fsalfirst, k, k_tmps, cc.Q, cc.n_curr, - cc.n_old, cc.coefficients, cc.stage_number) -end - -@cache mutable struct ImplicitDeuflhardExtrapolationConstantCache{QType, - extrapolation_coefficients, - TF, UF} <: - OrdinaryDiffEqConstantCache - # Values that are mutated - Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n + alg.min_order - 1) - n_curr::Int # Storage for the current extrapolation order - n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter - - # Constant values - coefficients::extrapolation_coefficients - stage_number::Vector{Int} # stage_number[n] contains information for extrapolation order (n + alg.min_order - 1) - - tf::TF - uf::UF -end - -@cache mutable struct ImplicitDeuflhardExtrapolationCache{uType, QType, - extrapolation_coefficients, - rateType, JType, WType, F, JCType, - GCType, uNoUnitsType, TFType, - UFType} <: - OrdinaryDiffEqMutableCache - # Values that are mutated - utilde::uType - u_temp1::uType - u_temp2::uType - u_temp3::Array{uType, 1} - u_temp4::Array{uType, 1} - tmp::uType # for get_tmp_cache() - T::Array{uType, 1} # Storage for the internal discretisations obtained by the explicit midpoint rule - res::uNoUnitsType # Storage for the scaled residual of u and utilde - - fsalfirst::rateType - k::rateType - k_tmps::Array{rateType, 1} - - # Constant values - Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n + alg.min_order - 1) - n_curr::Int # Storage for the current extrapolation order - n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter - coefficients::extrapolation_coefficients - stage_number::Vector{Int} # Stage_number[n] contains information for extrapolation order (n + alg.min_order - 1) - - du1::rateType - du2::rateType - J::JType - W::WType - tf::TFType - uf::UFType - linsolve_tmps::Array{rateType, 1} - linsolve::Array{F, 1} - jac_config::JCType - grad_config::GCType - # Values to check overflow in T1 computation - diff1::Array{uType, 1} - diff2::Array{uType, 1} -end - -function alg_cache(alg::ImplicitDeuflhardExtrapolation, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - # Initialize cache's members - QType = tTypeNoUnits <: Integer ? typeof(qmin_default(alg)) : tTypeNoUnits # Cf. DiffEqBase.__init in solve.jl - - Q = fill(zero(QType), alg.max_order - alg.min_order + 1) - n_curr = alg.init_order - n_old = alg.init_order - - coefficients = create_extrapolation_coefficients(constvalue(uBottomEltypeNoUnits), alg) - stage_number = Vector{Int}(undef, alg.max_order - alg.min_order + 1) - - #== - Work calculation in Deuflhard is referenced from here: https://link.springer.com/article/10.1007/BF01418332 - A[1] := CJAC + CLR + (N[1] + 1)(CF + CS) - A[J] := A[J-1] - N[J]*(CF + CS) + CLR + CS J = 2, 3, 4..... - CF = 1; CJ = n*CF ; CS = CLR = 0 - n = Dimension of the jacobian (particularly gaussian decomposition of I - hJ (n,n) matrix) - Since we are using 4*N sequence and doing 4*N - 1 Computations - A[J] := A[J-1] - (4*N[J] - 1)*(CF + CS) + CLR + CS J = 2, 3, 4..... - ===# - for n in 1:length(stage_number) - s = zero(eltype(coefficients.subdividing_sequence)) - for i in 1:(alg.min_order + n) - s += coefficients.subdividing_sequence[i] - end - stage_number[n] = 4 * Int(s) - alg.min_order - n - 1 - end - - #Update stage_number by the jacobian size - jac_dim = rate_prototype isa Union{CompiledFloats, BigFloat} ? 1 : - sum(size(rate_prototype)) - stage_number = stage_number .+ jac_dim - - tf = TimeDerivativeWrapper(f, u, p) - uf = UDerivativeWrapper(f, t, p) - ImplicitDeuflhardExtrapolationConstantCache(Q, n_curr, n_old, coefficients, - stage_number, tf, uf) -end - -function alg_cache(alg::ImplicitDeuflhardExtrapolation, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - utilde = zero(u) - u_temp1 = zero(u) - u_temp2 = zero(u) - u_temp3 = Array{typeof(u), 1}(undef, Threads.nthreads()) - u_temp4 = Array{typeof(u), 1}(undef, Threads.nthreads()) - - for i in 1:Threads.nthreads() - u_temp3[i] = zero(u) - u_temp4[i] = zero(u) - end - - tmp = zero(u) - T = Vector{typeof(u)}(undef, alg.max_order + 1) - for i in 1:(alg.max_order + 1) - T[i] = zero(u) - end - res = uEltypeNoUnits.(zero(u)) - - fsalfirst = zero(rate_prototype) - k = zero(rate_prototype) - k_tmps = Array{typeof(k), 1}(undef, Threads.nthreads()) - for i in 1:Threads.nthreads() - k_tmps[i] = zero(rate_prototype) - end - - cc = alg_cache(alg::ImplicitDeuflhardExtrapolation, u, rate_prototype, uEltypeNoUnits, - uBottomEltypeNoUnits, tTypeNoUnits, uprev, uprev2, f, t, dt, reltol, p, - calck, Val(false)) - - du1 = zero(rate_prototype) - du2 = zero(rate_prototype) - - if DiffEqBase.has_jac(f) && !DiffEqBase.has_Wfact(f) && f.jac_prototype !== nothing - W_el = WOperator(f, dt, true) - J = nothing # is J = W.J better? - else - J = false .* _vec(rate_prototype) .* _vec(rate_prototype)' # uEltype? - W_el = zero(J) - end - - W = Array{typeof(W_el), 1}(undef, Threads.nthreads()) - W[1] = W_el - for i in 2:Threads.nthreads() - if W_el isa WOperator - W[i] = WOperator(f, dt, true) - else - W[i] = zero(W_el) - end - end - tf = TimeGradientWrapper(f, uprev, p) - uf = UJacobianWrapper(f, t, p) - linsolve_tmp = zero(rate_prototype) - linsolve_tmps = Array{typeof(linsolve_tmp), 1}(undef, Threads.nthreads()) - - for i in 1:Threads.nthreads() - linsolve_tmps[i] = zero(rate_prototype) - end - - linprob = LinearProblem(W[1], _vec(linsolve_tmps[1]); u0 = _vec(k_tmps[1])) - linsolve1 = init(linprob, alg.linsolve, alias_A = true, alias_b = true) - #Pl = LinearSolve.InvPreconditioner(Diagonal(_vec(weight))), - #Pr = Diagonal(_vec(weight))) - - linsolve = Array{typeof(linsolve1), 1}(undef, Threads.nthreads()) - linsolve[1] = linsolve1 - for i in 2:Threads.nthreads() - linprob = LinearProblem(W[i], _vec(linsolve_tmps[i]); u0 = _vec(k_tmps[i])) - linsolve[i] = init(linprob, alg.linsolve, alias_A = true, alias_b = true) - #Pl = LinearSolve.InvPreconditioner(Diagonal(_vec(weight))), - #Pr = Diagonal(_vec(weight))) - end - grad_config = build_grad_config(alg, f, tf, du1, t) - jac_config = build_jac_config(alg, f, uf, du1, uprev, u, du1, du2) - - diff1 = Array{typeof(u), 1}(undef, Threads.nthreads()) - diff2 = Array{typeof(u), 1}(undef, Threads.nthreads()) - for i in 1:Threads.nthreads() - diff1[i] = zero(u) - diff2[i] = zero(u) - end - - ImplicitDeuflhardExtrapolationCache(utilde, u_temp1, u_temp2, u_temp3, u_temp4, tmp, T, - res, fsalfirst, k, k_tmps, cc.Q, cc.n_curr, - cc.n_old, cc.coefficients, cc.stage_number, - du1, du2, J, W, tf, uf, linsolve_tmps, linsolve, - jac_config, grad_config, diff1, diff2) -end - -@cache mutable struct ExtrapolationMidpointHairerWannerConstantCache{QType, - extrapolation_coefficients -} <: - OrdinaryDiffEqConstantCache - # Values that are mutated - Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n - 1) - n_curr::Int # Storage for the current extrapolation order - n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter - - # Constant values - coefficients::extrapolation_coefficients - stage_number::Vector{Int} # stage_number[n] contains information for extrapolation order (n - 1) - sigma::Rational{Int} # Parameter for order selection - - #Stepsizing caches - work::Array{QType, 1} - dt_new::Array{QType, 1} -end - -function alg_cache(alg::ExtrapolationMidpointHairerWanner, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - # Initialize cache's members - QType = tTypeNoUnits <: Integer ? typeof(qmin_default(alg)) : tTypeNoUnits # Cf. DiffEqBase.__init in solve.jl - - Q = fill(zero(QType), alg.max_order + 1) - n_curr = alg.init_order - n_old = alg.init_order - sequence_factor = alg.sequence_factor - - coefficients = create_extrapolation_coefficients(constvalue(uBottomEltypeNoUnits), alg) - stage_number = Vector{Int}(undef, alg.max_order + 1) - for n in 1:length(stage_number) - s = zero(eltype(coefficients.subdividing_sequence)) - for i in 1:n - s += coefficients.subdividing_sequence[i] - end - stage_number[n] = sequence_factor * Int(s) - n + 3 - sequence_factor - end - sigma = 9 // 10 - - work = fill(zero(eltype(Q)), alg.max_order + 1) - dt_new = fill(zero(eltype(Q)), alg.max_order + 1) - # Initialize the constant cache - ExtrapolationMidpointHairerWannerConstantCache(Q, n_curr, n_old, coefficients, - stage_number, sigma, work, dt_new) -end - -@cache mutable struct ExtrapolationMidpointHairerWannerCache{uType, uNoUnitsType, rateType, - QType, - extrapolation_coefficients} <: - OrdinaryDiffEqMutableCache - # Values that are mutated - utilde::uType - u_temp1::uType - u_temp2::uType - u_temp3::Array{uType, 1} - u_temp4::Array{uType, 1} - tmp::uType # for get_tmp_cache() - T::Array{uType, 1} # Storage for the internal discretisations obtained by the explicit midpoint rule - res::uNoUnitsType # Storage for the scaled residual of u and utilde - - fsalfirst::rateType - k::rateType - k_tmps::Array{rateType, 1} - - # Constant values - Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n - 1) - n_curr::Int # Storage for the current extrapolation order - n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter - coefficients::extrapolation_coefficients - stage_number::Vector{Int} # stage_number[n] contains information for extrapolation order (n - 1) - sigma::Rational{Int} # Parameter for order selection - - #Stepsizing caches - work::Array{QType, 1} - dt_new::Array{QType, 1} -end - -function alg_cache(alg::ExtrapolationMidpointHairerWanner, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - # Initialize cache's members - utilde = zero(u) - u_temp1 = zero(u) - u_temp2 = zero(u) - u_temp3 = Array{typeof(u), 1}(undef, Threads.nthreads()) - u_temp4 = Array{typeof(u), 1}(undef, Threads.nthreads()) - - for i in 1:Threads.nthreads() - u_temp3[i] = zero(u) - u_temp4[i] = zero(u) - end - tmp = zero(u) - T = Vector{typeof(u)}(undef, alg.max_order + 1) - for i in 1:(alg.max_order + 1) - T[i] = zero(u) - end - res = uEltypeNoUnits.(zero(u)) - fsalfirst = zero(rate_prototype) - k = zero(rate_prototype) - k_tmps = Array{typeof(k), 1}(undef, Threads.nthreads()) - for i in 1:Threads.nthreads() - k_tmps[i] = zero(rate_prototype) - end - - cc = alg_cache(alg, u, rate_prototype, uEltypeNoUnits, uBottomEltypeNoUnits, - tTypeNoUnits, uprev, uprev2, f, t, dt, reltol, p, calck, Val(false)) - - # Initialize the cache - ExtrapolationMidpointHairerWannerCache(utilde, u_temp1, u_temp2, u_temp3, u_temp4, tmp, - T, res, fsalfirst, k, k_tmps, - cc.Q, cc.n_curr, cc.n_old, cc.coefficients, - cc.stage_number, cc.sigma, cc.work, cc.dt_new) -end - -@cache mutable struct ImplicitHairerWannerExtrapolationConstantCache{QType, - extrapolation_coefficients, - TF, UF} <: - OrdinaryDiffEqConstantCache - # Values that are mutated - Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n - 1) - n_curr::Int # Storage for the current extrapolation order - n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter - - # Constant values - coefficients::extrapolation_coefficients - stage_number::Vector{Int} # stage_number[n] contains information for extrapolation order (n - 1) - sigma::Rational{Int} # Parameter for order selection - - tf::TF - uf::UF - - #Stepsizing caches - work::Array{QType, 1} - dt_new::Array{QType, 1} -end - -function alg_cache(alg::ImplicitHairerWannerExtrapolation, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - # Initialize cache's members - QType = tTypeNoUnits <: Integer ? typeof(qmin_default(alg)) : tTypeNoUnits # Cf. DiffEqBase.__init in solve.jl - - Q = fill(zero(QType), alg.max_order + 1) - n_curr = alg.init_order - n_old = alg.init_order - - coefficients = create_extrapolation_coefficients(constvalue(uBottomEltypeNoUnits), alg) - #==Work Calculation (A[J] denotes Jth order work) - Default values are used from https://github.com/luchr/ODEInterface.jl/blob/master/src/Seulex.jl#L393-L399 - - ║ WKFCN │ estimated works (complexity) │ 1.0 ║ - ║ WKJAC │ for a call to │ 5.0 ║ - ║ WKDEC │ WKFCN: right-hand side f │ 1.0 ║ - ║ WKSOL │ WKJAC: JACOBIMATRIX │ 1.0 ║ - ║ WKROW │ WKDEC: LU-decomposition │ 2.0 ║ - ║ │ WKSOL: Forward- and Backward subst. │ ║ - ║ | WKROW: Tot. work in one iteration | ║ - ╚════════════╧═════════════════════════════════════╧═════════╝ - WKROW = WKFCN + WKSOL - A[1] = WKJAC + (N[1] + 1)* WKROw + WKDEC - A[J] = A[J - 1] + N[J]* WKROW + WKDEC - - Since we are using 4*N Sequence and only performing 4*N - 1 computations, The modified Work Equation becomes: - A[J] = A[J - 1] + (4*N[J] - 1)* WKROW + WKDEC - ==# - stage_number = Vector{Int}(undef, alg.max_order + 1) - for n in 1:length(stage_number) - s = zero(eltype(coefficients.subdividing_sequence)) - for i in 1:n - s += coefficients.subdividing_sequence[i] - end - stage_number[n] = 8 * Int(s) - n + 3 - end - sigma = 9 // 10 - - # Initialize the constant cache - tf = TimeDerivativeWrapper(f, u, p) - uf = UDerivativeWrapper(f, t, p) - work = fill(zero(eltype(Q)), alg.max_order + 1) - dt_new = fill(zero(eltype(Q)), alg.max_order + 1) - ImplicitHairerWannerExtrapolationConstantCache(Q, n_curr, n_old, coefficients, - stage_number, sigma, tf, uf, work, - dt_new) -end - -@cache mutable struct ImplicitHairerWannerExtrapolationCache{uType, uNoUnitsType, rateType, - QType, - extrapolation_coefficients, - JType, WType, F, JCType, - GCType, TFType, UFType} <: - OrdinaryDiffEqMutableCache - # Values that are mutated - utilde::uType - u_temp1::uType - u_temp2::uType - u_temp3::Array{uType, 1} - u_temp4::Array{uType, 1} - tmp::uType # for get_tmp_cache() - T::Array{uType, 1} # Storage for the internal discretisations obtained by the explicit midpoint rule - res::uNoUnitsType # Storage for the scaled residual of u and utilde - - fsalfirst::rateType - k::rateType - k_tmps::Array{rateType, 1} - - # Constant values - Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n - 1) - n_curr::Int # Storage for the current extrapolation order - n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter - coefficients::extrapolation_coefficients - stage_number::Vector{Int} # stage_number[n] contains information for extrapolation order (n - 1) - sigma::Rational{Int} # Parameter for order selection - - du1::rateType - du2::rateType - J::JType - W::WType - tf::TFType - uf::UFType - linsolve_tmps::Array{rateType, 1} - linsolve::Array{F, 1} - jac_config::JCType - grad_config::GCType - # Values to check overflow in T1 computation - diff1::Array{uType, 1} - diff2::Array{uType, 1} - - #Stepsizing caches - work::Array{QType, 1} - dt_new::Array{QType, 1} -end - -function alg_cache(alg::ImplicitHairerWannerExtrapolation, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - # Initialize cache's members - utilde = zero(u) - u_temp1 = zero(u) - u_temp2 = zero(u) - u_temp3 = Array{typeof(u), 1}(undef, Threads.nthreads()) - u_temp4 = Array{typeof(u), 1}(undef, Threads.nthreads()) - - for i in 1:Threads.nthreads() - u_temp3[i] = zero(u) - u_temp4[i] = zero(u) - end - tmp = zero(u) - T = Vector{typeof(u)}(undef, alg.max_order + 1) - for i in 1:(alg.max_order + 1) - T[i] = zero(u) - end - res = uEltypeNoUnits.(zero(u)) - fsalfirst = zero(rate_prototype) - k = zero(rate_prototype) - k_tmps = Array{typeof(k), 1}(undef, Threads.nthreads()) - for i in 1:Threads.nthreads() - k_tmps[i] = zero(rate_prototype) - end - - cc = alg_cache(alg, u, rate_prototype, uEltypeNoUnits, uBottomEltypeNoUnits, - tTypeNoUnits, uprev, uprev2, f, t, dt, reltol, p, calck, Val(false)) - - du1 = zero(rate_prototype) - du2 = zero(rate_prototype) - - if DiffEqBase.has_jac(f) && !DiffEqBase.has_Wfact(f) && f.jac_prototype !== nothing - W_el = WOperator(f, dt, true) - J = nothing # is J = W.J better? - else - J = false .* _vec(rate_prototype) .* _vec(rate_prototype)' # uEltype? - W_el = zero(J) - end - - W = Array{typeof(W_el), 1}(undef, Threads.nthreads()) - W[1] = W_el - for i in 2:Threads.nthreads() - if W_el isa WOperator - W[i] = WOperator(f, dt, true) - else - W[i] = zero(W_el) - end - end - - tf = TimeGradientWrapper(f, uprev, p) - uf = UJacobianWrapper(f, t, p) - linsolve_tmp = zero(rate_prototype) - linsolve_tmps = Array{typeof(linsolve_tmp), 1}(undef, Threads.nthreads()) - - for i in 1:Threads.nthreads() - linsolve_tmps[i] = zero(rate_prototype) - end - - linprob = LinearProblem(W[1], _vec(linsolve_tmps[1]); u0 = _vec(k_tmps[1])) - linsolve1 = init(linprob, alg.linsolve, alias_A = true, alias_b = true) - #Pl = LinearSolve.InvPreconditioner(Diagonal(_vec(weight))), - #Pr = Diagonal(_vec(weight))) - - linsolve = Array{typeof(linsolve1), 1}(undef, Threads.nthreads()) - linsolve[1] = linsolve1 - for i in 2:Threads.nthreads() - linprob = LinearProblem(W[i], _vec(linsolve_tmps[i]); u0 = _vec(k_tmps[i])) - linsolve[i] = init(linprob, alg.linsolve, alias_A = true, alias_b = true) - #Pl = LinearSolve.InvPreconditioner(Diagonal(_vec(weight))), - #Pr = Diagonal(_vec(weight))) - end - grad_config = build_grad_config(alg, f, tf, du1, t) - jac_config = build_jac_config(alg, f, uf, du1, uprev, u, du1, du2) - - diff1 = Array{typeof(u), 1}(undef, Threads.nthreads()) - diff2 = Array{typeof(u), 1}(undef, Threads.nthreads()) - for i in 1:Threads.nthreads() - diff1[i] = zero(u) - diff2[i] = zero(u) - end - - # Initialize the cache - ImplicitHairerWannerExtrapolationCache(utilde, u_temp1, u_temp2, u_temp3, u_temp4, tmp, - T, res, fsalfirst, k, k_tmps, - cc.Q, cc.n_curr, cc.n_old, cc.coefficients, - cc.stage_number, cc.sigma, du1, du2, J, W, tf, - uf, linsolve_tmps, - linsolve, jac_config, grad_config, diff1, diff2, - cc.work, cc.dt_new) -end - -@cache mutable struct ImplicitEulerBarycentricExtrapolationConstantCache{QType, - extrapolation_coefficients, - TF, UF} <: - OrdinaryDiffEqConstantCache - # Values that are mutated - Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n - 1) - n_curr::Int # Storage for the current extrapolation order - n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter - - # Constant values - coefficients::extrapolation_coefficients - stage_number::Vector{Int} # stage_number[n] contains information for extrapolation order (n - 1) - sigma::Rational{Int} # Parameter for order selection - - tf::TF - uf::UF - - #Stepsizing caches - work::Array{QType, 1} - dt_new::Array{QType, 1} -end - -function alg_cache(alg::ImplicitEulerBarycentricExtrapolation, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - # Initialize cache's members - QType = tTypeNoUnits <: Integer ? typeof(qmin_default(alg)) : tTypeNoUnits # Cf. DiffEqBase.__init in solve.jl - - Q = fill(zero(QType), alg.max_order + 1) - n_curr = alg.init_order - n_old = alg.init_order - sequence_factor = alg.sequence_factor - - coefficients = create_extrapolation_coefficients(constvalue(uBottomEltypeNoUnits), alg) - - stage_number = Vector{Int}(undef, alg.max_order + 1) - for n in 1:length(stage_number) - s = zero(eltype(coefficients.subdividing_sequence)) - for i in 1:n - s += coefficients.subdividing_sequence[i] - end - stage_number[n] = 2 * sequence_factor * Int(s) - n + 7 - end - sigma = 9 // 10 - - work = fill(zero(eltype(Q)), alg.max_order + 1) - dt_new = fill(zero(eltype(Q)), alg.max_order + 1) - # Initialize the constant cache - tf = TimeDerivativeWrapper(f, u, p) - uf = UDerivativeWrapper(f, t, p) - ImplicitEulerBarycentricExtrapolationConstantCache(Q, n_curr, n_old, coefficients, - stage_number, sigma, tf, uf, work, - dt_new) -end - -@cache mutable struct ImplicitEulerBarycentricExtrapolationCache{uType, uNoUnitsType, - rateType, QType, - extrapolation_coefficients, - JType, WType, F, JCType, - GCType, TFType, UFType} <: - OrdinaryDiffEqMutableCache - # Values that are mutated - utilde::uType - u_temp1::uType - u_temp2::uType - u_temp3::Array{uType, 1} - u_temp4::Array{uType, 1} - tmp::uType # for get_tmp_cache() - T::Array{uType, 1} # Storage for the internal discretisations obtained by the explicit midpoint rule - res::uNoUnitsType # Storage for the scaled residual of u and utilde - - fsalfirst::rateType - k::rateType - k_tmps::Array{rateType, 1} - - # Constant values - Q::Vector{QType} # Storage for stepsize scaling factors. Q[n] contains information for extrapolation order (n - 1) - n_curr::Int # Storage for the current extrapolation order - n_old::Int # Storage for the extrapolation order n_curr before perfom_step! changes the latter - coefficients::extrapolation_coefficients - stage_number::Vector{Int} # stage_number[n] contains information for extrapolation order (n - 1) - sigma::Rational{Int} # Parameter for order selection - - du1::rateType - du2::rateType - J::JType - W::WType - tf::TFType - uf::UFType - linsolve_tmps::Array{rateType, 1} - linsolve::Array{F, 1} - jac_config::JCType - grad_config::GCType - # Values to check overflow in T1 computation - diff1::Array{uType, 1} - diff2::Array{uType, 1} - #Stepsizing caches - work::Array{QType, 1} - dt_new::Array{QType, 1} -end - -function alg_cache(alg::ImplicitEulerBarycentricExtrapolation, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - # Initialize cache's members - utilde = zero(u) - u_temp1 = zero(u) - u_temp2 = zero(u) - u_temp3 = Array{typeof(u), 1}(undef, Threads.nthreads()) - u_temp4 = Array{typeof(u), 1}(undef, Threads.nthreads()) - - for i in 1:Threads.nthreads() - u_temp3[i] = zero(u) - u_temp4[i] = zero(u) - end - tmp = zero(u) - T = Vector{typeof(u)}(undef, alg.max_order + 1) - for i in 1:(alg.max_order + 1) - T[i] = zero(u) - end - res = uEltypeNoUnits.(zero(u)) - fsalfirst = zero(rate_prototype) - k = zero(rate_prototype) - k_tmps = Array{typeof(k), 1}(undef, Threads.nthreads()) - for i in 1:Threads.nthreads() - k_tmps[i] = zero(rate_prototype) - end - - cc = alg_cache(alg, u, rate_prototype, uEltypeNoUnits, uBottomEltypeNoUnits, - tTypeNoUnits, uprev, uprev2, f, t, dt, reltol, p, calck, Val(false)) - - du1 = zero(rate_prototype) - du2 = zero(rate_prototype) - - if DiffEqBase.has_jac(f) && !DiffEqBase.has_Wfact(f) && f.jac_prototype !== nothing - W_el = WOperator(f, dt, true) - J = nothing # is J = W.J better? - else - J = false .* _vec(rate_prototype) .* _vec(rate_prototype)' # uEltype? - W_el = zero(J) - end - - W = Array{typeof(W_el), 1}(undef, Threads.nthreads()) - W[1] = W_el - for i in 2:Threads.nthreads() - if W_el isa WOperator - W[i] = WOperator(f, dt, true) - else - W[i] = zero(W_el) - end - end - - tf = TimeGradientWrapper(f, uprev, p) - uf = UJacobianWrapper(f, t, p) - linsolve_tmp = zero(rate_prototype) - linsolve_tmps = Array{typeof(linsolve_tmp), 1}(undef, Threads.nthreads()) - - for i in 1:Threads.nthreads() - linsolve_tmps[i] = zero(rate_prototype) - end - - linprob = LinearProblem(W[1], _vec(linsolve_tmps[1]); u0 = _vec(k_tmps[1])) - linsolve1 = init(linprob, alg.linsolve, alias_A = true, alias_b = true) - #Pl = LinearSolve.InvPreconditioner(Diagonal(_vec(weight))), - #Pr = Diagonal(_vec(weight))) - - linsolve = Array{typeof(linsolve1), 1}(undef, Threads.nthreads()) - linsolve[1] = linsolve1 - for i in 2:Threads.nthreads() - linprob = LinearProblem(W[i], _vec(linsolve_tmps[i]); u0 = _vec(k_tmps[i])) - linsolve[i] = init(linprob, alg.linsolve, alias_A = true, alias_b = true) - #Pl = LinearSolve.InvPreconditioner(Diagonal(_vec(weight))), - #Pr = Diagonal(_vec(weight))) - end - grad_config = build_grad_config(alg, f, tf, du1, t) - jac_config = build_jac_config(alg, f, uf, du1, uprev, u, du1, du2) - - diff1 = Array{typeof(u), 1}(undef, Threads.nthreads()) - diff2 = Array{typeof(u), 1}(undef, Threads.nthreads()) - for i in 1:Threads.nthreads() - diff1[i] = zero(u) - diff2[i] = zero(u) - end - - # Initialize the cache - ImplicitEulerBarycentricExtrapolationCache(utilde, u_temp1, u_temp2, u_temp3, u_temp4, - tmp, T, res, fsalfirst, k, k_tmps, - cc.Q, cc.n_curr, cc.n_old, cc.coefficients, - cc.stage_number, cc.sigma, du1, du2, J, W, - tf, uf, linsolve_tmps, - linsolve, jac_config, grad_config, diff1, - diff2, cc.work, cc.dt_new) -end From 5400ec803d871943b3e89946fbdd4ba88e990c74 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:53:26 -0400 Subject: [PATCH 04/71] Delete src/caches/feagin_caches.jl --- src/caches/feagin_caches.jl | 248 ------------------------------------ 1 file changed, 248 deletions(-) delete mode 100644 src/caches/feagin_caches.jl diff --git a/src/caches/feagin_caches.jl b/src/caches/feagin_caches.jl deleted file mode 100644 index 47defa81a2..0000000000 --- a/src/caches/feagin_caches.jl +++ /dev/null @@ -1,248 +0,0 @@ -@cache struct Feagin10Cache{uType, uNoUnitsType, rateType, TabType} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - k2::rateType - k3::rateType - k4::rateType - k5::rateType - k6::rateType - k7::rateType - k8::rateType - k9::rateType - k10::rateType - k11::rateType - k12::rateType - k13::rateType - k14::rateType - k15::rateType - k16::rateType - k17::rateType - tmp::uType - atmp::uNoUnitsType - k::rateType - tab::TabType -end - -function alg_cache(alg::Feagin10, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tab = Feagin10ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - k1 = zero(rate_prototype) - k2 = zero(rate_prototype) - k3 = zero(rate_prototype) - k4 = zero(rate_prototype) - k5 = zero(rate_prototype) - k6 = zero(rate_prototype) - k7 = zero(rate_prototype) - k8 = zero(rate_prototype) - k9 = zero(rate_prototype) - k10 = zero(rate_prototype) - k11 = zero(rate_prototype) - k12 = zero(rate_prototype) - k13 = zero(rate_prototype) - k14 = zero(rate_prototype) - k15 = zero(rate_prototype) - k16 = zero(rate_prototype) - k17 = zero(rate_prototype) - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - k = zero(rate_prototype) - - Feagin10Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, - k15, k16, k17, tmp, atmp, k, tab) -end - -function alg_cache(alg::Feagin10, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - Feagin10ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct Feagin12Cache{uType, uNoUnitsType, rateType, TabType} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - k2::rateType - k3::rateType - k4::rateType - k5::rateType - k6::rateType - k7::rateType - k8::rateType - k9::rateType - k10::rateType - k11::rateType - k12::rateType - k13::rateType - k14::rateType - k15::rateType - k16::rateType - k17::rateType - k18::rateType - k19::rateType - k20::rateType - k21::rateType - k22::rateType - k23::rateType - k24::rateType - k25::rateType - tmp::uType - atmp::uNoUnitsType - k::rateType - tab::TabType -end - -function alg_cache(alg::Feagin12, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tab = Feagin12ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - k1 = zero(rate_prototype) - k2 = zero(rate_prototype) - k3 = zero(rate_prototype) - k4 = zero(rate_prototype) - k5 = zero(rate_prototype) - k6 = zero(rate_prototype) - k7 = zero(rate_prototype) - k8 = zero(rate_prototype) - k9 = zero(rate_prototype) - k10 = zero(rate_prototype) - k11 = zero(rate_prototype) - k12 = zero(rate_prototype) - k13 = zero(rate_prototype) - k14 = zero(rate_prototype) - k15 = zero(rate_prototype) - k16 = zero(rate_prototype) - k17 = zero(rate_prototype) - k18 = zero(rate_prototype) - k19 = zero(rate_prototype) - k20 = zero(rate_prototype) - k21 = zero(rate_prototype) - k22 = zero(rate_prototype) - k23 = zero(rate_prototype) - k24 = zero(rate_prototype) - k25 = zero(rate_prototype) - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - k = zero(rate_prototype) - - Feagin12Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, - k15, k16, k17, k18, k19, k20, k21, k22, k23, k24, k25, tmp, atmp, k, tab) -end - -function alg_cache(alg::Feagin12, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - Feagin12ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct Feagin14Cache{uType, uNoUnitsType, rateType, TabType} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - k2::rateType - k3::rateType - k4::rateType - k5::rateType - k6::rateType - k7::rateType - k8::rateType - k9::rateType - k10::rateType - k11::rateType - k12::rateType - k13::rateType - k14::rateType - k15::rateType - k16::rateType - k17::rateType - k18::rateType - k19::rateType - k20::rateType - k21::rateType - k22::rateType - k23::rateType - k24::rateType - k25::rateType - k26::rateType - k27::rateType - k28::rateType - k29::rateType - k30::rateType - k31::rateType - k32::rateType - k33::rateType - k34::rateType - k35::rateType - tmp::uType - atmp::uNoUnitsType - k::rateType - tab::TabType -end - -function alg_cache(alg::Feagin14, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tab = Feagin14ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - k1 = zero(rate_prototype) - k2 = zero(rate_prototype) - k3 = zero(rate_prototype) - k4 = zero(rate_prototype) - k5 = zero(rate_prototype) - k6 = zero(rate_prototype) - k7 = zero(rate_prototype) - k8 = zero(rate_prototype) - k9 = zero(rate_prototype) - k10 = zero(rate_prototype) - k11 = zero(rate_prototype) - k12 = zero(rate_prototype) - k13 = zero(rate_prototype) - k14 = zero(rate_prototype) - k15 = zero(rate_prototype) - k16 = zero(rate_prototype) - k17 = zero(rate_prototype) - k18 = zero(rate_prototype) - k19 = zero(rate_prototype) - k20 = zero(rate_prototype) - k21 = zero(rate_prototype) - k22 = zero(rate_prototype) - k23 = zero(rate_prototype) - k24 = zero(rate_prototype) - k25 = zero(rate_prototype) - k26 = zero(rate_prototype) - k27 = zero(rate_prototype) - k28 = zero(rate_prototype) - k29 = zero(rate_prototype) - k30 = zero(rate_prototype) - k31 = zero(rate_prototype) - k32 = zero(rate_prototype) - k33 = zero(rate_prototype) - k34 = zero(rate_prototype) - k35 = zero(rate_prototype) - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - k = zero(rate_prototype) - - Feagin14Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, - k15, k16, - k17, k18, k19, k20, k21, k22, k23, k24, k25, k26, k27, k28, k29, k30, - k31, k32, k33, k34, k35, tmp, atmp, k, tab) -end - -function alg_cache(alg::Feagin14, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - Feagin14ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end From 38ad679a44f21d305145a48be3a140c71252a6d3 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:53:44 -0400 Subject: [PATCH 05/71] Delete src/caches/low_storage_rk_caches.jl --- src/caches/low_storage_rk_caches.jl | 3839 --------------------------- 1 file changed, 3839 deletions(-) delete mode 100644 src/caches/low_storage_rk_caches.jl diff --git a/src/caches/low_storage_rk_caches.jl b/src/caches/low_storage_rk_caches.jl deleted file mode 100644 index a903e155ad..0000000000 --- a/src/caches/low_storage_rk_caches.jl +++ /dev/null @@ -1,3839 +0,0 @@ - -# 2N low storage methods introduced by Williamson -@cache struct LowStorageRK2NCache{uType, rateType, TabType, StageLimiter, StepLimiter, - Thread} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - tmp::uType # tmp acts as second register and fsal both - tab::TabType - williamson_condition::Bool - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct LowStorageRK2NConstantCache{N, T, T2} <: OrdinaryDiffEqConstantCache - A2end::SVector{N, T} # A1 is always zero - B1::T - B2end::SVector{N, T} - c2end::SVector{N, T2} # c1 is always zero -end - -function ORK256ConstantCache(T, T2) - A2 = convert(T, -1.0) - A3 = convert(T, -1.55798) - A4 = convert(T, -1.0) - A5 = convert(T, -0.45031) - A2end = SVector(A2, A3, A4, A5) - - B1 = convert(T, 0.2) - B2 = convert(T, 0.83204) - B3 = convert(T, 0.6) - B4 = convert(T, 0.35394) - B5 = convert(T, 0.2) - B2end = SVector(B2, B3, B4, B5) - - c2 = convert(T2, 0.2) - c3 = convert(T2, 0.2) - c4 = convert(T2, 0.8) - c5 = convert(T2, 0.8) - c2end = SVector(c2, c3, c4, c5) - - LowStorageRK2NConstantCache{4, T, T2}(A2end, B1, B2end, c2end) -end - -function alg_cache(alg::ORK256, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tab = ORK256ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - tmp = zero(u) - williamson_condition = alg.williamson_condition - if calck - k = zero(rate_prototype) - williamson_condition = false - else - if williamson_condition - k = tmp - else - k = zero(rate_prototype) - end - end - LowStorageRK2NCache(u, uprev, k, tmp, tab, williamson_condition, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::ORK256, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - ORK256ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function CarpenterKennedy2N54ConstantCache(T, T2) - A2 = convert(T, -567301805773 // 1357537059087) - A3 = convert(T, -2404267990393 // 2016746695238) - A4 = convert(T, -3550918686646 // 2091501179385) - A5 = convert(T, -1275806237668 // 842570457699) - A2end = SVector(A2, A3, A4, A5) - - B1 = convert(T, 1432997174477 // 9575080441755) - B2 = convert(T, 5161836677717 // 13612068292357) - B3 = convert(T, 1720146321549 // 2090206949498) - B4 = convert(T, 3134564353537 // 4481467310338) - B5 = convert(T, 2277821191437 // 14882151754819) - B2end = SVector(B2, B3, B4, B5) - - c2 = convert(T2, 1432997174477 // 9575080441755) - c3 = convert(T2, 2526269341429 // 6820363962896) - c4 = convert(T2, 2006345519317 // 3224310063776) - c5 = convert(T2, 2802321613138 // 2924317926251) - c2end = SVector(c2, c3, c4, c5) - - LowStorageRK2NConstantCache{4, T, T2}(A2end, B1, B2end, c2end) -end - -function alg_cache(alg::CarpenterKennedy2N54, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tab = CarpenterKennedy2N54ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - tmp = zero(u) - williamson_condition = alg.williamson_condition - if calck - k = zero(rate_prototype) - williamson_condition = false - else - if williamson_condition - k = tmp - else - k = zero(rate_prototype) - end - end - LowStorageRK2NCache(u, uprev, k, tmp, tab, williamson_condition, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::CarpenterKennedy2N54, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - CarpenterKennedy2N54ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) -end - -function SHLDDRK64ConstantCache(T, T2) - #TODO: Solve the order conditions with more accuracy - A2 = convert(T, -0.4919575) - A3 = convert(T, -0.8946264) - A4 = convert(T, -1.5526678) - A5 = convert(T, -3.4077973) - A6 = convert(T, -1.0742640) - A2end = SVector(A2, A3, A4, A5, A6) - - B1 = convert(T, 0.1453095) - B2 = convert(T, 0.4653797) - B3 = convert(T, 0.4675397) - B4 = convert(T, 0.7795279) - B5 = convert(T, 0.3574327) - B6 = convert(T, 0.15) - B2end = SVector(B2, B3, B4, B5, B6) - - c2 = convert(T2, 0.1453095) - c3 = convert(T2, 0.3817422) - c4 = convert(T2, 0.6367813) - c5 = convert(T2, 0.7560744) - c6 = convert(T2, 0.9271047) - c2end = SVector(c2, c3, c4, c5, c6) - - LowStorageRK2NConstantCache{5, T, T2}(A2end, B1, B2end, c2end) -end - -function alg_cache(alg::SHLDDRK64, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tab = SHLDDRK64ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - tmp = zero(u) - williamson_condition = alg.williamson_condition - if calck - k = zero(rate_prototype) - williamson_condition = false - else - if williamson_condition - k = tmp - else - k = zero(rate_prototype) - end - end - LowStorageRK2NCache(u, uprev, k, tmp, tab, williamson_condition, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::SHLDDRK64, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SHLDDRK64ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function DGLDDRK73_CConstantCache(T, T2) - A2 = convert(T, -0.8083163874983830) - A3 = convert(T, -1.503407858773331) - A4 = convert(T, -1.053064525050744) - A5 = convert(T, -1.463149119280508) - A6 = convert(T, -0.6592881281087830) - A7 = convert(T, -1.667891931891068) - A2end = SVector(A2, A3, A4, A5, A6, A7) - - B1 = convert(T, 0.01197052673097840) - B2 = convert(T, 0.8886897793820711) - B3 = convert(T, 0.4578382089261419) - B4 = convert(T, 0.5790045253338471) - B5 = convert(T, 0.3160214638138484) - B6 = convert(T, 0.2483525368264122) - B7 = convert(T, 0.06771230959408840) - B2end = SVector(B2, B3, B4, B5, B6, B7) - - c2 = convert(T2, 0.01197052673097840) - c3 = convert(T2, 0.1823177940361990) - c4 = convert(T2, 0.5082168062551849) - c5 = convert(T2, 0.6532031220148590) - c6 = convert(T2, 0.8534401385678250) - c7 = convert(T2, 0.9980466084623790) - c2end = SVector(c2, c3, c4, c5, c6, c7) - - LowStorageRK2NConstantCache{6, T, T2}(A2end, B1, B2end, c2end) -end - -function alg_cache(alg::DGLDDRK73_C, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tab = DGLDDRK73_CConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - tmp = zero(u) - williamson_condition = alg.williamson_condition - if calck - k = zero(rate_prototype) - williamson_condition = false - else - if williamson_condition - k = tmp - else - k = zero(rate_prototype) - end - end - LowStorageRK2NCache(u, uprev, k, tmp, tab, williamson_condition, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::DGLDDRK73_C, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - DGLDDRK73_CConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function DGLDDRK84_CConstantCache(T, T2) - A2 = convert(T, -0.7212962482279240) - A3 = convert(T, -0.01077336571612980) - A4 = convert(T, -0.5162584698930970) - A5 = convert(T, -1.730100286632201) - A6 = convert(T, -5.200129304403076) - A7 = convert(T, 0.7837058945416420) - A8 = convert(T, -0.5445836094332190) - A2end = SVector(A2, A3, A4, A5, A6, A7, A8) - - B1 = convert(T, 0.2165936736758085) - B2 = convert(T, 0.1773950826411583) - B3 = convert(T, 0.01802538611623290) - B4 = convert(T, 0.08473476372541490) - B5 = convert(T, 0.8129106974622483) - B6 = convert(T, 1.903416030422760) - B7 = convert(T, 0.1314841743399048) - B8 = convert(T, 0.2082583170674149) - B2end = SVector(B2, B3, B4, B5, B6, B7, B8) - - c2 = convert(T2, 0.2165936736758085) - c3 = convert(T2, 0.2660343487538170) - c4 = convert(T2, 0.2840056122522720) - c5 = convert(T2, 0.3251266843788570) - c6 = convert(T2, 0.4555149599187530) - c7 = convert(T2, 0.7713219317101170) - c8 = convert(T2, 0.9199028964538660) - c2end = SVector(c2, c3, c4, c5, c6, c7, c8) - - LowStorageRK2NConstantCache{7, T, T2}(A2end, B1, B2end, c2end) -end - -function alg_cache(alg::DGLDDRK84_C, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tab = DGLDDRK84_CConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - tmp = zero(u) - williamson_condition = alg.williamson_condition - if calck - k = zero(rate_prototype) - williamson_condition = false - else - if williamson_condition - k = tmp - else - k = zero(rate_prototype) - end - end - LowStorageRK2NCache(u, uprev, k, tmp, tab, williamson_condition, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::DGLDDRK84_C, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - DGLDDRK84_CConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function DGLDDRK84_FConstantCache(T, T2) - A2 = convert(T, -0.5534431294501569) - A3 = convert(T, 0.01065987570203490) - A4 = convert(T, -0.5515812888932000) - A5 = convert(T, -1.885790377558741) - A6 = convert(T, -5.701295742793264) - A7 = convert(T, 2.113903965664793) - A8 = convert(T, -0.5339578826675280) - A2end = SVector(A2, A3, A4, A5, A6, A7, A8) - - B1 = convert(T, 0.08037936882736950) - B2 = convert(T, 0.5388497458569843) - B3 = convert(T, 0.01974974409031960) - B4 = convert(T, 0.09911841297339970) - B5 = convert(T, 0.7466920411064123) - B6 = convert(T, 1.679584245618894) - B7 = convert(T, 0.2433728067008188) - B8 = convert(T, 0.1422730459001373) - B2end = SVector(B2, B3, B4, B5, B6, B7, B8) - - c2 = convert(T2, 0.08037936882736950) - c3 = convert(T2, 0.3210064250338430) - c4 = convert(T2, 0.3408501826604660) - c5 = convert(T2, 0.3850364824285470) - c6 = convert(T2, 0.5040052477534100) - c7 = convert(T2, 0.6578977561168540) - c8 = convert(T2, 0.9484087623348481) - c2end = SVector(c2, c3, c4, c5, c6, c7, c8) - - LowStorageRK2NConstantCache{7, T, T2}(A2end, B1, B2end, c2end) -end - -function alg_cache(alg::DGLDDRK84_F, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tab = DGLDDRK84_FConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - tmp = zero(u) - williamson_condition = alg.williamson_condition - if calck - k = zero(rate_prototype) - williamson_condition = false - else - if williamson_condition - k = tmp - else - k = zero(rate_prototype) - end - end - LowStorageRK2NCache(u, uprev, k, tmp, tab, williamson_condition, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::DGLDDRK84_F, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - DGLDDRK84_FConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function NDBLSRK124ConstantCache(T, T2) - A2 = convert(T, -0.0923311242368072) - A3 = convert(T, -0.9441056581158819) - A4 = convert(T, -4.3271273247576394) - A5 = convert(T, -2.1557771329026072) - A6 = convert(T, -0.9770727190189062) - A7 = convert(T, -0.7581835342571139) - A8 = convert(T, -1.7977525470825499) - A9 = convert(T, -2.6915667972700770) - A10 = convert(T, -4.6466798960268143) - A11 = convert(T, -0.1539613783825189) - A12 = convert(T, -0.5943293901830616) - A2end = SVector(A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12) - - B1 = convert(T, 0.0650008435125904) - B2 = convert(T, 0.0161459902249842) - B3 = convert(T, 0.5758627178358159) - B4 = convert(T, 0.1649758848361671) - B5 = convert(T, 0.3934619494248182) - B6 = convert(T, 0.0443509641602719) - B7 = convert(T, 0.2074504268408778) - B8 = convert(T, 0.6914247433015102) - B9 = convert(T, 0.3766646883450449) - B10 = convert(T, 0.0757190350155483) - B11 = convert(T, 0.2027862031054088) - B12 = convert(T, 0.2167029365631842) - B2end = SVector(B2, B3, B4, B5, B6, B7, B8, B9, B10, B11, B12) - - c2 = convert(T2, 0.0650008435125904) - c3 = convert(T2, 0.0796560563081853) - c4 = convert(T2, 0.1620416710085376) - c5 = convert(T2, 0.2248877362907778) - c6 = convert(T2, 0.2952293985641261) - c7 = convert(T2, 0.3318332506149405) - c8 = convert(T2, 0.4094724050198658) - c9 = convert(T2, 0.6356954475753369) - c10 = convert(T2, 0.6806551557645497) - c11 = convert(T2, 0.7143773712418350) - c12 = convert(T2, 0.9032588871651854) - c2end = SVector(c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12) - - LowStorageRK2NConstantCache{11, T, T2}(A2end, B1, B2end, c2end) -end - -function alg_cache(alg::NDBLSRK124, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tab = NDBLSRK124ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - tmp = zero(u) - williamson_condition = alg.williamson_condition - if calck - k = zero(rate_prototype) - williamson_condition = false - else - if williamson_condition - k = tmp - else - k = zero(rate_prototype) - end - end - LowStorageRK2NCache(u, uprev, k, tmp, tab, williamson_condition, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::NDBLSRK124, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - NDBLSRK124ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function NDBLSRK134ConstantCache(T, T2) - A2 = convert(T, -0.6160178650170565) - A3 = convert(T, -0.4449487060774118) - A4 = convert(T, -1.0952033345276178) - A5 = convert(T, -1.2256030785959187) - A6 = convert(T, -0.2740182222332805) - A7 = convert(T, -0.0411952089052647) - A8 = convert(T, -0.1797084899153560) - A9 = convert(T, -1.1771530652064288) - A10 = convert(T, -0.4078831463120878) - A11 = convert(T, -0.8295636426191777) - A12 = convert(T, -4.7895970584252288) - A13 = convert(T, -0.6606671432964504) - A2end = SVector(A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12, A13) - - B1 = convert(T, 0.0271990297818803) - B2 = convert(T, 0.1772488819905108) - B3 = convert(T, 0.0378528418949694) - B4 = convert(T, 0.6086431830142991) - B5 = convert(T, 0.2154313974316100) - B6 = convert(T, 0.2066152563885843) - B7 = convert(T, 0.0415864076069797) - B8 = convert(T, 0.0219891884310925) - B9 = convert(T, 0.9893081222650993) - B10 = convert(T, 0.0063199019859826) - B11 = convert(T, 0.3749640721105318) - B12 = convert(T, 1.6080235151003195) - B13 = convert(T, 0.0961209123818189) - B2end = SVector(B2, B3, B4, B5, B6, B7, B8, B9, B10, B11, B12, B13) - - c2 = convert(T2, 0.0271990297818803) - c3 = convert(T2, 0.0952594339119365) - c4 = convert(T2, 0.1266450286591127) - c5 = convert(T2, 0.1825883045699772) - c6 = convert(T2, 0.3737511439063931) - c7 = convert(T2, 0.5301279418422206) - c8 = convert(T2, 0.5704177433952291) - c9 = convert(T2, 0.5885784947099155) - c10 = convert(T2, 0.6160769826246714) - c11 = convert(T2, 0.6223252334314046) - c12 = convert(T2, 0.6897593128753419) - c13 = convert(T2, 0.9126827615920843) - c2end = SVector(c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13) - - LowStorageRK2NConstantCache{12, T, T2}(A2end, B1, B2end, c2end) -end - -function alg_cache(alg::NDBLSRK134, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tab = NDBLSRK134ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - tmp = zero(u) - williamson_condition = alg.williamson_condition - if calck - k = zero(rate_prototype) - williamson_condition = false - else - if williamson_condition - k = tmp - else - k = zero(rate_prototype) - end - end - LowStorageRK2NCache(u, uprev, k, tmp, tab, williamson_condition, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::NDBLSRK134, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - NDBLSRK134ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function NDBLSRK144ConstantCache(T, T2) - A2 = convert(T, -0.7188012108672410) - A3 = convert(T, -0.7785331173421570) - A4 = convert(T, -0.0053282796654044) - A5 = convert(T, -0.8552979934029281) - A6 = convert(T, -3.9564138245774565) - A7 = convert(T, -1.5780575380587385) - A8 = convert(T, -2.0837094552574054) - A9 = convert(T, -0.7483334182761610) - A10 = convert(T, -0.7032861106563359) - A11 = convert(T, 0.0013917096117681) - A12 = convert(T, -0.0932075369637460) - A13 = convert(T, -0.9514200470875948) - A14 = convert(T, -7.1151571693922548) - A2end = SVector(A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12, A13, A14) - - B1 = convert(T, 0.0367762454319673) - B2 = convert(T, 0.3136296607553959) - B3 = convert(T, 0.1531848691869027) - B4 = convert(T, 0.0030097086818182) - B5 = convert(T, 0.3326293790646110) - B6 = convert(T, 0.2440251405350864) - B7 = convert(T, 0.3718879239592277) - B8 = convert(T, 0.6204126221582444) - B9 = convert(T, 0.1524043173028741) - B10 = convert(T, 0.0760894927419266) - B11 = convert(T, 0.0077604214040978) - B12 = convert(T, 0.0024647284755382) - B13 = convert(T, 0.0780348340049386) - B14 = convert(T, 5.5059777270269628) - B2end = SVector(B2, B3, B4, B5, B6, B7, B8, B9, B10, B11, B12, B13, B14) - - c2 = convert(T2, 0.0367762454319673) - c3 = convert(T2, 0.1249685262725025) - c4 = convert(T2, 0.2446177702277698) - c5 = convert(T2, 0.2476149531070420) - c6 = convert(T2, 0.2969311120382472) - c7 = convert(T2, 0.3978149645802642) - c8 = convert(T2, 0.5270854589440328) - c9 = convert(T2, 0.6981269994175695) - c10 = convert(T2, 0.8190890835352128) - c11 = convert(T2, 0.8527059887098624) - c12 = convert(T2, 0.8604711817462826) - c13 = convert(T2, 0.8627060376969976) - c14 = convert(T2, 0.8734213127600976) - c2end = SVector(c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14) - - LowStorageRK2NConstantCache{13, T, T2}(A2end, B1, B2end, c2end) -end - -function alg_cache(alg::NDBLSRK144, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tab = NDBLSRK144ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - tmp = zero(u) - williamson_condition = alg.williamson_condition - if calck - k = zero(rate_prototype) - williamson_condition = false - else - if williamson_condition - k = tmp - else - k = zero(rate_prototype) - end - end - LowStorageRK2NCache(u, uprev, k, tmp, tab, williamson_condition, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::NDBLSRK144, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - NDBLSRK144ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -# 2C low storage methods introduced by Calvo, Franco, Rández (2004) -@cache struct LowStorageRK2CCache{uType, rateType, TabType, StageLimiter, StepLimiter, - Thread} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - tmp::uType - fsalfirst::rateType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct LowStorageRK2CConstantCache{N, T, T2} <: OrdinaryDiffEqConstantCache - A2end::SVector{N, T} # A1 is always zero - B1::T - B2end::SVector{N, T} - c2end::SVector{N, T2} # c1 is always zero -end - -function CFRLDDRK64ConstantCache(T, T2) - A2 = convert(T, 0.17985400977138) - A3 = convert(T, 0.14081893152111) - A4 = convert(T, 0.08255631629428) - A5 = convert(T, 0.65804425034331) - A6 = convert(T, 0.31862993413251) - A2end = SVector(A2, A3, A4, A5, A6) - - B1 = convert(T, 0.10893125722541) - B2 = convert(T, 0.13201701492152) - B3 = convert(T, 0.38911623225517) - B4 = convert(T, -0.59203884581148) - B5 = convert(T, 0.47385028714844) - B6 = convert(T, 0.48812405426094) - B2end = SVector(B2, B3, B4, B5, B6) - - c2 = convert(T2, 0.28878526699679) - c3 = convert(T2, 0.38176720366804) - c4 = convert(T2, 0.71262082069639) - c5 = convert(T2, 0.69606990893393) - c6 = convert(T2, 0.83050587987157) - c2end = SVector(c2, c3, c4, c5, c6) - - LowStorageRK2CConstantCache{5, T, T2}(A2end, B1, B2end, c2end) -end - -function alg_cache(alg::CFRLDDRK64, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = CFRLDDRK64ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK2CCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::CFRLDDRK64, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - CFRLDDRK64ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function TSLDDRK74ConstantCache(T, T2) - A2 = convert(T, 0.241566650129646868) - A3 = convert(T, 0.0423866513027719953) - A4 = convert(T, 0.215602732678803776) - A5 = convert(T, 0.232328007537583987) - A6 = convert(T, 0.256223412574146438) - A7 = convert(T, 0.0978694102142697230) - A2end = SVector(A2, A3, A4, A5, A6, A7) - - B1 = convert(T, 0.0941840925477795334) - B2 = convert(T, 0.149683694803496998) - B3 = convert(T, 0.285204742060440058) - B4 = convert(T, -0.122201846148053668) - B5 = convert(T, 0.0605151571191401122) - B6 = convert(T, 0.345986987898399296) - B7 = convert(T, 0.186627171718797670) - B2end = SVector(B2, B3, B4, B5, B6, B7) - - c2 = convert(T2, 0.335750742677426401) - c3 = convert(T2, 0.286254438654048527) - c4 = convert(T2, 0.744675262090520366) - c5 = convert(T2, 0.639198690801246909) - c6 = convert(T2, 0.723609252956949472) - c7 = convert(T2, 0.91124223849547205) - c2end = SVector(c2, c3, c4, c5, c6, c7) - - LowStorageRK2CConstantCache{6, T, T2}(A2end, B1, B2end, c2end) -end - -function alg_cache(alg::TSLDDRK74, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = TSLDDRK74ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - LowStorageRK2CCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::TSLDDRK74, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - TSLDDRK74ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -# 3S low storage methods introduced by Ketcheson -@cache struct LowStorageRK3SCache{uType, rateType, TabType, StageLimiter, StepLimiter, - Thread} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - tmp::uType - fsalfirst::rateType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct LowStorageRK3SConstantCache{N, T, T2} <: OrdinaryDiffEqConstantCache - γ12end::SVector{N, T} # γ11 is always zero - γ22end::SVector{N, T} # γ21 is always one - γ32end::SVector{N, T} # γ31 is always zero - # TODO: γ302 == γ303 == 0 in all emthods implemented below -> possible optimisation? - δ2end::SVector{N, T} # δ1 is always one - β1::T - β2end::SVector{N, T} - c2end::SVector{N, T2} # c1 is always zero -end - -function ParsaniKetchesonDeconinck3S32ConstantCache(T, T2) - γ102 = convert(T, -1.2664395576322218e-1) - γ103 = convert(T, 1.1426980685848858e+0) - γ12end = SVector(γ102, γ103) - - γ202 = convert(T, 6.5427782599406470e-1) - γ203 = convert(T, -8.2869287683723744e-2) - γ22end = SVector(γ202, γ203) - - γ302 = convert(T, 0.0000000000000000e+0) - γ303 = convert(T, 0.0000000000000000e+0) - γ32end = SVector(γ302, γ303) - - δ02 = convert(T, 7.2196567116037724e-1) - δ03 = convert(T, 0.0000000000000000e+0) - δ2end = SVector(δ02, δ03) - - β1 = convert(T, 7.2366074728360086e-1) - β02 = convert(T, 3.4217876502651023e-1) - β03 = convert(T, 3.6640216242653251e-1) - β2end = SVector(β02, β03) - - c02 = convert(T2, 7.2366074728360086e-1) - c03 = convert(T2, 5.9236433182015646e-1) - c2end = SVector(c02, c03) - - LowStorageRK3SConstantCache{2, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end) -end - -function alg_cache(alg::ParsaniKetchesonDeconinck3S32, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = ParsaniKetchesonDeconinck3S32ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK3SCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::ParsaniKetchesonDeconinck3S32, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - ParsaniKetchesonDeconinck3S32ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) -end - -function ParsaniKetchesonDeconinck3S82ConstantCache(T, T2) - γ102 = convert(T, 4.2397552118208004e-1) - γ103 = convert(T, -2.3528852074619033e-1) - γ104 = convert(T, 7.9598685017877846e-1) - γ105 = convert(T, -1.3205224623823271e+0) - γ106 = convert(T, 2.1452956294251941e+0) - γ107 = convert(T, -9.5532770501880648e-1) - γ108 = convert(T, 2.5361391125131094e-1) - γ12end = SVector(γ102, γ103, γ104, γ105, γ106, γ107, γ108) - - γ202 = convert(T, 4.4390665802303775e-1) - γ203 = convert(T, 7.5333732286056154e-1) - γ204 = convert(T, 6.5885460813015481e-2) - γ205 = convert(T, 6.3976199384289623e-1) - γ206 = convert(T, -7.3823030755143193e-1) - γ207 = convert(T, 7.0177211879534529e-1) - γ208 = convert(T, 4.0185379950224559e-1) - γ22end = SVector(γ202, γ203, γ204, γ205, γ206, γ207, γ208) - - γ302 = convert(T, 0.0000000000000000e+0) - γ303 = convert(T, 0.0000000000000000e+0) - γ304 = convert(T, 5.8415358412023582e-2) - γ305 = convert(T, 6.4219008773865116e-1) - γ306 = convert(T, 6.8770305706885126e-1) - γ307 = convert(T, 6.3729822311671305e-2) - γ308 = convert(T, -3.3679429978131387e-1) - γ32end = SVector(γ302, γ303, γ304, γ305, γ306, γ307, γ308) - - δ02 = convert(T, 2.9762522910396538e-1) - δ03 = convert(T, 3.4212961014330662e-1) - δ04 = convert(T, 5.7010739154759105e-1) - δ05 = convert(T, 4.1350769551529132e-1) - δ06 = convert(T, -1.4040672669058066e-1) - δ07 = convert(T, 2.1249567092409008e-1) - δ08 = convert(T, 0.0000000000000000e+0) - δ2end = SVector(δ02, δ03, δ04, δ05, δ06, δ07, δ08) - - β1 = convert(T, 9.9292229393265474e-1) - β02 = convert(T, 5.2108385130005974e-1) - β03 = convert(T, 3.8505327083543915e-3) - β04 = convert(T, 7.9714199213087467e-1) - β05 = convert(T, -8.1822460276649120e-2) - β06 = convert(T, 8.4604310411858186e-1) - β07 = convert(T, -1.0191166090841246e-1) - β08 = convert(T, 6.3190236038107500e-2) - β2end = SVector(β02, β03, β04, β05, β06, β07, β08) - - c02 = convert(T2, 9.9292229393265474e-1) - c03 = convert(T2, 1.0732413280565014e+0) - c04 = convert(T2, 2.5057060509809409e-1) - c05 = convert(T2, 1.0496674928979783e+0) - c06 = convert(T2, -6.7488037049720317e-1) - c07 = convert(T2, -1.5868411612120166e+0) - c08 = convert(T2, 2.1138242369563969e+0) - c2end = SVector(c02, c03, c04, c05, c06, c07, c08) - - LowStorageRK3SConstantCache{7, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end) -end - -function alg_cache(alg::ParsaniKetchesonDeconinck3S82, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = ParsaniKetchesonDeconinck3S82ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK3SCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::ParsaniKetchesonDeconinck3S82, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - ParsaniKetchesonDeconinck3S82ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) -end - -function ParsaniKetchesonDeconinck3S53ConstantCache(T, T2) - γ102 = convert(T, 2.5876919610938998e-1) - γ103 = convert(T, -1.3243708384977859e-1) - γ104 = convert(T, 5.0556648948362981e-2) - γ105 = convert(T, 5.6705507883024708e-1) - γ12end = SVector(γ102, γ103, γ104, γ105) - - γ202 = convert(T, 5.5284013909611196e-1) - γ203 = convert(T, 6.7318513326032769e-1) - γ204 = convert(T, 2.8031054965521607e-1) - γ205 = convert(T, 5.5215115815918758e-1) - γ22end = SVector(γ202, γ203, γ204, γ205) - - γ302 = convert(T, 0.0000000000000000e+0) - γ303 = convert(T, 0.0000000000000000e+0) - γ304 = convert(T, 2.7525797946334213e-1) - γ305 = convert(T, -8.9505445022148511e-1) - γ32end = SVector(γ302, γ303, γ304, γ305) - - δ02 = convert(T, 3.4076878915216791e-1) - δ03 = convert(T, 3.4143871647890728e-1) - δ04 = convert(T, 7.2292984084963252e-1) - δ05 = convert(T, 0.0000000000000000e+0) - δ2end = SVector(δ02, δ03, δ04, δ05) - - β1 = convert(T, 2.3002859824852059e-1) - β02 = convert(T, 3.0214498165167158e-1) - β03 = convert(T, 8.0256010238856679e-1) - β04 = convert(T, 4.3621618871511753e-1) - β05 = convert(T, 1.1292705979513513e-1) - β2end = SVector(β02, β03, β04, β05) - - c02 = convert(T2, 2.3002859824852059e-1) - c03 = convert(T2, 4.0500453764839639e-1) - c04 = convert(T2, 8.9478204142351003e-1) - c05 = convert(T2, 7.2351146275625733e-1) - c2end = SVector(c02, c03, c04, c05) - - LowStorageRK3SConstantCache{4, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end) -end - -function alg_cache(alg::ParsaniKetchesonDeconinck3S53, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = ParsaniKetchesonDeconinck3S53ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK3SCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::ParsaniKetchesonDeconinck3S53, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - ParsaniKetchesonDeconinck3S53ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) -end - -function ParsaniKetchesonDeconinck3S173ConstantCache(T, T2) - γ102 = convert(T, 7.9377023961829174e-1) - γ103 = convert(T, -8.3475116244241754e-2) - γ104 = convert(T, -1.6706337980062214e-2) - γ105 = convert(T, 3.6410691500331427e-1) - γ106 = convert(T, 6.9178255181542780e-1) - γ107 = convert(T, 1.4887115004739182e+0) - γ108 = convert(T, 4.5336125560871188e-1) - γ109 = convert(T, -1.2705776046458739e-1) - γ110 = convert(T, 8.3749845457747696e-1) - γ111 = convert(T, 1.5709218393361746e-1) - γ112 = convert(T, -5.7768207086288348e-1) - γ113 = convert(T, -5.7340394122375393e-1) - γ114 = convert(T, -1.2050734846514470e+0) - γ115 = convert(T, -2.8100719513641002e+0) - γ116 = convert(T, 1.6142798657609492e-1) - γ117 = convert(T, -2.5801264756641613e+0) - γ12end = SVector( - γ102, γ103, γ104, γ105, γ106, γ107, γ108, γ109, γ110, γ111, γ112, γ113, - γ114, γ115, γ116, γ117) - - γ202 = convert(T, 3.2857861940811250e-1) - γ203 = convert(T, 1.1276843361180819e+0) - γ204 = convert(T, 1.3149447395238016e+0) - γ205 = convert(T, 5.2062891534209055e-1) - γ206 = convert(T, 8.8127462325164985e-1) - γ207 = convert(T, 4.2020606445856712e-1) - γ208 = convert(T, 7.6532635739246124e-2) - γ209 = convert(T, 4.4386734924685722e-1) - γ210 = convert(T, 6.6503093955199682e-2) - γ211 = convert(T, 1.5850209163184039e+0) - γ212 = convert(T, 1.1521721573462576e+0) - γ213 = convert(T, 1.1172750819374575e+0) - γ214 = convert(T, 7.7630223917584007e-1) - γ215 = convert(T, 1.0046657060652295e+0) - γ216 = convert(T, -1.9795868964959054e-1) - γ217 = convert(T, 1.3350583594705518e+0) - γ22end = SVector( - γ202, γ203, γ204, γ205, γ206, γ207, γ208, γ209, γ210, γ211, γ212, γ213, - γ214, γ215, γ216, γ217) - - γ302 = convert(T, 0.0000000000000000e+0) - γ303 = convert(T, 0.0000000000000000e+0) - γ304 = convert(T, 8.4034574578399479e-1) - γ305 = convert(T, 8.5047738439705145e-1) - γ306 = convert(T, 1.4082448501410852e-1) - γ307 = convert(T, -3.2678802469519369e-1) - γ308 = convert(T, 5.3716357620635535e-1) - γ309 = convert(T, 9.0228922115199051e-1) - γ310 = convert(T, 1.5960226946983552e-1) - γ311 = convert(T, 1.1038153140686748e+0) - γ312 = convert(T, 1.0843516423068365e-1) - γ313 = convert(T, 4.6212710442787724e-1) - γ314 = convert(T, -3.3448312125108398e-1) - γ315 = convert(T, 1.1153826567096696e+0) - γ316 = convert(T, 1.5503248734613539e+0) - γ317 = convert(T, -1.2200245424704212e+0) - γ32end = SVector( - γ302, γ303, γ304, γ305, γ306, γ307, γ308, γ309, γ310, γ311, γ312, γ313, - γ314, γ315, γ316, γ317) - - δ02 = convert(T, -3.7235794357769936e-1) - δ03 = convert(T, 3.3315440189685536e-1) - δ04 = convert(T, -8.2667630338402520e-1) - δ05 = convert(T, -5.4628377681035534e-1) - δ06 = convert(T, 6.0210777634642887e-1) - δ07 = convert(T, -5.7528717894031067e-1) - δ08 = convert(T, 5.0914861529202782e-1) - δ09 = convert(T, 3.8258114767897194e-1) - δ10 = convert(T, -4.6279063221185290e-1) - δ11 = convert(T, -2.0820434288562648e-1) - δ12 = convert(T, 1.4398056081552713e+0) - δ13 = convert(T, -2.8056600927348752e-1) - δ14 = convert(T, 2.2767189929551406e+0) - δ15 = convert(T, -5.8917530100546356e-1) - δ16 = convert(T, 9.1328651048418164e-1) - δ17 = convert(T, 0.0000000000000000e+0) - δ2end = SVector(δ02, δ03, δ04, δ05, δ06, δ07, δ08, δ09, δ10, δ11, δ12, δ13, δ14, δ15, - δ16, δ17) - - β1 = convert(T, 4.9565403010221741e-2) - β02 = convert(T, 9.7408718698159397e-2) - β03 = convert(T, -1.7620737976801870e-1) - β04 = convert(T, 1.4852069175460250e-1) - β05 = convert(T, -3.3127657103714951e-2) - β06 = convert(T, 4.8294609330498492e-2) - β07 = convert(T, 4.9622612199980112e-2) - β08 = convert(T, 8.7340766269850378e-1) - β09 = convert(T, -2.8692804399085370e-1) - β10 = convert(T, 1.2679897532256112e+0) - β11 = convert(T, -1.0217436118953449e-2) - β12 = convert(T, 8.4665570032598350e-2) - β13 = convert(T, 2.8253854742588246e-2) - β14 = convert(T, -9.2936733010804407e-2) - β15 = convert(T, -8.4798124766803512e-2) - β16 = convert(T, -1.6923145636158564e-2) - β17 = convert(T, -4.7305106233879957e-2) - β2end = SVector(β02, β03, β04, β05, β06, β07, β08, β09, β10, β11, β12, β13, β14, β15, - β16, β17) - - c02 = convert(T2, 4.9565403010221741e-2) - c03 = convert(T2, 1.3068799001687578e-1) - c04 = convert(T2, -1.5883063460310493e-1) - c05 = convert(T2, 3.5681144740196935e-1) - c06 = convert(T2, 7.6727123317642698e-2) - c07 = convert(T2, 1.0812579255374613e-1) - c08 = convert(T2, 1.8767228084815801e-1) - c09 = convert(T2, 9.6162976936182631e-1) - c10 = convert(T2, -2.2760719867560897e-1) - c11 = convert(T2, 1.1115681606027146e+0) - c12 = convert(T2, 6.1266845427676520e-1) - c13 = convert(T2, 1.0729473245077408e+0) - c14 = convert(T2, 3.7824186468104548e-1) - c15 = convert(T2, 7.9041891347646720e-1) - c16 = convert(T2, -1.0406955693161675e+0) - c17 = convert(T2, -2.4607146824557105e-1) - c2end = SVector(c02, c03, c04, c05, c06, c07, c08, c09, c10, c11, c12, c13, c14, c15, - c16, c17) - - LowStorageRK3SConstantCache{16, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end) -end - -function alg_cache(alg::ParsaniKetchesonDeconinck3S173, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = ParsaniKetchesonDeconinck3S173ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK3SCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::ParsaniKetchesonDeconinck3S173, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - ParsaniKetchesonDeconinck3S173ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) -end - -function ParsaniKetchesonDeconinck3S94ConstantCache(T, T2) - γ102 = convert(T, -4.6556413837561301e+0) - γ103 = convert(T, -7.7202649689034453e-1) - γ104 = convert(T, -4.0244202720632174e+0) - γ105 = convert(T, -2.1296873883702272e-2) - γ106 = convert(T, -2.4350219407769953e+0) - γ107 = convert(T, 1.9856336960249132e-2) - γ108 = convert(T, -2.8107894116913812e-1) - γ109 = convert(T, 1.6894354373677900e-1) - γ12end = SVector(γ102, γ103, γ104, γ105, γ106, γ107, γ108, γ109) - - γ202 = convert(T, 2.4992627683300688e+0) - γ203 = convert(T, 5.8668202764174726e-1) - γ204 = convert(T, 1.2051419816240785e+0) - γ205 = convert(T, 3.4747937498564541e-1) - γ206 = convert(T, 1.3213458736302766e+0) - γ207 = convert(T, 3.1196363453264964e-1) - γ208 = convert(T, 4.3514189245414447e-1) - γ209 = convert(T, 2.3596980658341213e-1) - γ22end = SVector(γ202, γ203, γ204, γ205, γ206, γ207, γ208, γ209) - - γ302 = convert(T, 0.0000000000000000e+0) - γ303 = convert(T, 0.0000000000000000e+0) - γ304 = convert(T, 7.6209857891449362e-1) - γ305 = convert(T, -1.9811817832965520e-1) - γ306 = convert(T, -6.2289587091629484e-1) - γ307 = convert(T, -3.7522475499063573e-1) - γ308 = convert(T, -3.3554373281046146e-1) - γ309 = convert(T, -4.5609629702116454e-2) - γ32end = SVector(γ302, γ303, γ304, γ305, γ306, γ307, γ308, γ309) - - δ02 = convert(T, 1.2629238731608268e+0) - δ03 = convert(T, 7.5749675232391733e-1) - δ04 = convert(T, 5.1635907196195419e-1) - δ05 = convert(T, -2.7463346616574083e-2) - δ06 = convert(T, -4.3826743572318672e-1) - δ07 = convert(T, 1.2735870231839268e+0) - δ08 = convert(T, -6.2947382217730230e-1) - δ09 = convert(T, 0.0000000000000000e+0) - δ2end = SVector(δ02, δ03, δ04, δ05, δ06, δ07, δ08, δ09) - - β1 = convert(T, 2.8363432481011769e-1) - β02 = convert(T, 9.7364980747486463e-1) - β03 = convert(T, 3.3823592364196498e-1) - β04 = convert(T, -3.5849518935750763e-1) - β05 = convert(T, -4.1139587569859462e-3) - β06 = convert(T, 1.4279689871485013e+0) - β07 = convert(T, 1.8084680519536503e-2) - β08 = convert(T, 1.6057708856060501e-1) - β09 = convert(T, 2.9522267863254809e-1) - β2end = SVector(β02, β03, β04, β05, β06, β07, β08, β09) - - c02 = convert(T2, 2.8363432481011769e-1) - c03 = convert(T2, 5.4840742446661772e-1) - c04 = convert(T2, 3.6872298094969475e-1) - c05 = convert(T2, -6.8061183026103156e-1) - c06 = convert(T2, 3.5185265855105619e-1) - c07 = convert(T2, 1.6659419385562171e+0) - c08 = convert(T2, 9.7152778807463247e-1) - c09 = convert(T2, 9.0515694340066954e-1) - c2end = SVector(c02, c03, c04, c05, c06, c07, c08, c09) - - LowStorageRK3SConstantCache{8, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end) -end - -function alg_cache(alg::ParsaniKetchesonDeconinck3S94, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = ParsaniKetchesonDeconinck3S94ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK3SCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::ParsaniKetchesonDeconinck3S94, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - ParsaniKetchesonDeconinck3S94ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) -end - -function ParsaniKetchesonDeconinck3S184ConstantCache(T, T2) - γ102 = convert(T, 1.1750819811951678e+0) - γ103 = convert(T, 3.0909017892654811e-1) - γ104 = convert(T, 1.4409117788115862e+0) - γ105 = convert(T, -4.3563049445694069e-1) - γ106 = convert(T, 2.0341503014683893e-1) - γ107 = convert(T, 4.9828356971917692e-1) - γ108 = convert(T, 3.5307737157745489e+0) - γ109 = convert(T, -7.9318790975894626e-1) - γ110 = convert(T, 8.9120513355345166e-1) - γ111 = convert(T, 5.7091009196320974e-1) - γ112 = convert(T, 1.6912188575015419e-2) - γ113 = convert(T, 1.0077912519329719e+0) - γ114 = convert(T, -6.8532953752099512e-1) - γ115 = convert(T, 1.0488165551884063e+0) - γ116 = convert(T, 8.3647761371829943e-1) - γ117 = convert(T, 1.3087909830445710e+0) - γ118 = convert(T, 9.0419681700177323e-1) - γ12end = SVector( - γ102, γ103, γ104, γ105, γ106, γ107, γ108, γ109, γ110, γ111, γ112, γ113, - γ114, γ115, γ116, γ117, γ118) - - γ202 = convert(T, -1.2891068509748144e-1) - γ203 = convert(T, 3.5609406666728954e-1) - γ204 = convert(T, -4.0648075226104241e-1) - γ205 = convert(T, 6.0714786995207426e-1) - γ206 = convert(T, 1.0253501186236846e+0) - γ207 = convert(T, 2.4411240760769423e-1) - γ208 = convert(T, -1.2813606970134104e+0) - γ209 = convert(T, 8.1625711892373898e-1) - γ210 = convert(T, 1.0171269354643386e-1) - γ211 = convert(T, 1.9379378662711269e-1) - γ212 = convert(T, 7.4408643544851782e-1) - γ213 = convert(T, -1.2591764563430008e-1) - γ214 = convert(T, 1.1996463179654226e+0) - γ215 = convert(T, 4.5772068865370406e-2) - γ216 = convert(T, 8.3622292077033844e-1) - γ217 = convert(T, -1.4179124272450148e+0) - γ218 = convert(T, 1.3661459065331649e-1) - γ22end = SVector( - γ202, γ203, γ204, γ205, γ206, γ207, γ208, γ209, γ210, γ211, γ212, γ213, - γ214, γ215, γ216, γ217, γ218) - - γ302 = convert(T, 0.0000000000000000e+0) - γ303 = convert(T, 0.0000000000000000e+0) - γ304 = convert(T, 2.5583378537249163e-1) - γ305 = convert(T, 5.2676794366988289e-1) - γ306 = convert(T, -2.5648375621792202e-1) - γ307 = convert(T, 3.1932438003236391e-1) - γ308 = convert(T, -3.1106815010852862e-1) - γ309 = convert(T, 4.7631196164025996e-1) - γ310 = convert(T, -9.8853727938895783e-2) - γ311 = convert(T, 1.9274726276883622e-1) - γ312 = convert(T, 3.2389860855971508e-2) - γ313 = convert(T, 7.5923980038397509e-2) - γ314 = convert(T, 2.0635456088664017e-1) - γ315 = convert(T, -8.9741032556032857e-2) - γ316 = convert(T, 2.6899932505676190e-2) - γ317 = convert(T, 4.1882069379552307e-2) - γ318 = convert(T, 6.2016148912381761e-2) - γ32end = SVector( - γ302, γ303, γ304, γ305, γ306, γ307, γ308, γ309, γ310, γ311, γ312, γ313, - γ314, γ315, γ316, γ317, γ318) - - δ02 = convert(T, 3.5816500441970289e-1) - δ03 = convert(T, 5.8208024465093577e-1) - δ04 = convert(T, -2.2615285894283538e-1) - δ05 = convert(T, -2.1715466578266213e-1) - δ06 = convert(T, -4.6990441450888265e-1) - δ07 = convert(T, -2.7986911594744995e-1) - δ08 = convert(T, 9.8513926355272197e-1) - δ09 = convert(T, -1.1899324232814899e-1) - δ10 = convert(T, 4.2821073124370562e-1) - δ11 = convert(T, -8.2196355299900403e-1) - δ12 = convert(T, 5.8113997057675074e-2) - δ13 = convert(T, -6.1283024325436919e-1) - δ14 = convert(T, 5.6800136190634054e-1) - δ15 = convert(T, -3.3874970570335106e-1) - δ16 = convert(T, -7.3071238125137772e-1) - δ17 = convert(T, 8.3936016960374532e-2) - δ18 = convert(T, 0.0000000000000000e+0) - δ2end = SVector(δ02, δ03, δ04, δ05, δ06, δ07, δ08, δ09, δ10, δ11, δ12, δ13, δ14, δ15, - δ16, δ17, δ18) - - β1 = convert(T, 1.2384169480626298e-1) - β02 = convert(T, 1.0176262534280349e+0) - β03 = convert(T, -6.9732026387527429e-2) - β04 = convert(T, 3.4239356067806476e-1) - β05 = convert(T, 1.8177707207807942e-2) - β06 = convert(T, -6.1188746289480445e-3) - β07 = convert(T, 7.8242308902580354e-2) - β08 = convert(T, -3.7642864750532951e-1) - β09 = convert(T, -4.5078383666690258e-2) - β10 = convert(T, -7.5734228201432585e-1) - β11 = convert(T, -2.7149222760935121e-1) - β12 = convert(T, 1.1833684341657344e-3) - β13 = convert(T, 2.8858319979308041e-2) - β14 = convert(T, 4.6005267586974657e-1) - β15 = convert(T, 1.8014887068775631e-2) - β16 = convert(T, -1.5508175395461857e-2) - β17 = convert(T, -4.0095737929274988e-1) - β18 = convert(T, 1.4949678367038011e-1) - β2end = SVector(β02, β03, β04, β05, β06, β07, β08, β09, β10, β11, β12, β13, β14, β15, - β16, β17, β18) - - c02 = convert(T2, 1.2384169480626298e-1) - c03 = convert(T2, 1.1574324659554065e+0) - c04 = convert(T2, 5.4372099141546926e-1) - c05 = convert(T2, 8.8394666834280744e-1) - c06 = convert(T2, -1.2212042176605774e-1) - c07 = convert(T2, 4.4125685133082082e-1) - c08 = convert(T2, 3.8039092095473748e-1) - c09 = convert(T2, 5.4591107347528367e-2) - c10 = convert(T2, 4.8731855535356028e-1) - c11 = convert(T2, -2.3007964303896034e-1) - c12 = convert(T2, -1.8907656662915873e-1) - c13 = convert(T2, 8.1059805668623763e-1) - c14 = convert(T2, 7.7080875997868803e-1) - c15 = convert(T2, 1.1712158507200179e+0) - c16 = convert(T2, 1.2755351018003545e+0) - c17 = convert(T2, 8.0422507946168564e-1) - c18 = convert(T2, 9.7508680250761848e-1) - c2end = SVector(c02, c03, c04, c05, c06, c07, c08, c09, c10, c11, c12, c13, c14, c15, - c16, c17, c18) - - LowStorageRK3SConstantCache{17, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end) -end - -function alg_cache(alg::ParsaniKetchesonDeconinck3S184, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = ParsaniKetchesonDeconinck3S184ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK3SCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::ParsaniKetchesonDeconinck3S184, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - ParsaniKetchesonDeconinck3S184ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) -end - -function ParsaniKetchesonDeconinck3S105ConstantCache(T, T2) - γ102 = convert(T, 4.0436600785287713e-1) - γ103 = convert(T, -8.5034274641295027e-1) - γ104 = convert(T, -6.9508941671218478e+0) - γ105 = convert(T, 9.2387652252320684e-1) - γ106 = convert(T, -2.5631780399589106e+0) - γ107 = convert(T, 2.5457448699988827e-1) - γ108 = convert(T, 3.1258317336761454e-1) - γ109 = convert(T, -7.0071148003175443e-1) - γ110 = convert(T, 4.8396209710057070e-1) - γ12end = SVector(γ102, γ103, γ104, γ105, γ106, γ107, γ108, γ109, γ110) - - γ202 = convert(T, 6.8714670697294733e-1) - γ203 = convert(T, 1.0930247604585732e+0) - γ204 = convert(T, 3.2259753823377983e+0) - γ205 = convert(T, 1.0411537008416110e+0) - γ206 = convert(T, 1.2928214888638039e+0) - γ207 = convert(T, 7.3914627692888835e-1) - γ208 = convert(T, 1.2391292570651462e-1) - γ209 = convert(T, 1.8427534793568445e-1) - γ210 = convert(T, 5.7127889427161162e-2) - γ22end = SVector(γ202, γ203, γ204, γ205, γ206, γ207, γ208, γ209, γ210) - - γ302 = convert(T, 0.0000000000000000e+0) - γ303 = convert(T, 0.0000000000000000e+0) - γ304 = convert(T, -2.3934051593398129e+0) - γ305 = convert(T, -1.9028544220991284e+0) - γ306 = convert(T, -2.8200422105835639e+0) - γ307 = convert(T, -1.8326984641282289e+0) - γ308 = convert(T, -2.1990945108072310e-1) - γ309 = convert(T, -4.0824306603783045e-1) - γ310 = convert(T, -1.3776697911236280e-1) - γ32end = SVector(γ302, γ303, γ304, γ305, γ306, γ307, γ308, γ309, γ310) - - δ02 = convert(T, -1.3317784091400336e-1) - δ03 = convert(T, 8.2604227852898304e-1) - δ04 = convert(T, 1.5137004305165804e+0) - δ05 = convert(T, -1.3058100631721905e+0) - δ06 = convert(T, 3.0366787893355149e+0) - δ07 = convert(T, -1.4494582670831953e+0) - δ08 = convert(T, 3.8343138733685103e+0) - δ09 = convert(T, 4.1222939718018692e+0) - δ10 = convert(T, 0.0000000000000000e+0) - δ2end = SVector(δ02, δ03, δ04, δ05, δ06, δ07, δ08, δ09, δ10) - - β1 = convert(T, 2.5978835757039448e-1) - β02 = convert(T, 1.7770088002098183e-2) - β03 = convert(T, 2.4816366373161344e-1) - β04 = convert(T, 7.9417368275785671e-1) - β05 = convert(T, 3.8853912968701337e-1) - β06 = convert(T, 1.4550516642704694e-1) - β07 = convert(T, 1.5875173794655811e-1) - β08 = convert(T, 1.6506056315937651e-1) - β09 = convert(T, 2.1180932999328042e-1) - β10 = convert(T, 1.5593923403495016e-1) - β2end = SVector(β02, β03, β04, β05, β06, β07, β08, β09, β10) - - c02 = convert(T2, 2.5978835757039448e-1) - c03 = convert(T2, 9.9045731158085557e-2) - c04 = convert(T2, 2.1555118823045644e-1) - c05 = convert(T2, 5.0079500784155040e-1) - c06 = convert(T2, 5.5922519148547800e-1) - c07 = convert(T2, 5.4499869734044426e-1) - c08 = convert(T2, 7.6152246625852738e-1) - c09 = convert(T2, 8.4270620830633836e-1) - c10 = convert(T2, 9.1522098071770008e-1) - c2end = SVector(c02, c03, c04, c05, c06, c07, c08, c09, c10) - - LowStorageRK3SConstantCache{9, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end) -end - -function alg_cache(alg::ParsaniKetchesonDeconinck3S105, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = ParsaniKetchesonDeconinck3S105ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK3SCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::ParsaniKetchesonDeconinck3S105, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - ParsaniKetchesonDeconinck3S105ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) -end - -function ParsaniKetchesonDeconinck3S205ConstantCache(T, T2) - γ102 = convert(T, -1.1682479703229380e+0) - γ103 = convert(T, -2.5112155037089772e+0) - γ104 = convert(T, -5.5259960154735988e-1) - γ105 = convert(T, 2.9243033509511740e-3) - γ106 = convert(T, -4.7948973385386493e+0) - γ107 = convert(T, -5.3095533497183016e+0) - γ108 = convert(T, -2.3624194456630736e+0) - γ109 = convert(T, 2.0068995756589547e-1) - γ110 = convert(T, -1.4985808661597710e+0) - γ111 = convert(T, 4.8941228502377687e-1) - γ112 = convert(T, -1.0387512755259576e-1) - γ113 = convert(T, -1.3287664273288191e-1) - γ114 = convert(T, 7.5858678822837511e-1) - γ115 = convert(T, -4.3321586294096939e+0) - γ116 = convert(T, 4.8199700138402146e-1) - γ117 = convert(T, -7.0924756614960671e-3) - γ118 = convert(T, -8.8422252029506054e-1) - γ119 = convert(T, -8.9129367099545231e-1) - γ120 = convert(T, 1.5297157134040762e+0) - γ12end = SVector( - γ102, γ103, γ104, γ105, γ106, γ107, γ108, γ109, γ110, γ111, γ112, γ113, - γ114, γ115, γ116, γ117, γ118, γ119, γ120) - - γ202 = convert(T, 8.8952052154583572e-1) - γ203 = convert(T, 8.8988129100385194e-1) - γ204 = convert(T, 3.5701564494677057e-1) - γ205 = convert(T, 2.4232462479216824e-1) - γ206 = convert(T, 1.2727083024258155e+0) - γ207 = convert(T, 1.1126977210342681e+0) - γ208 = convert(T, 5.1360709645409097e-1) - γ209 = convert(T, 1.1181089682044856e-1) - γ210 = convert(T, 2.7881272382085232e-1) - γ211 = convert(T, 4.9032886260666715e-2) - γ212 = convert(T, 4.1871051065897870e-2) - γ213 = convert(T, 4.4602463796686219e-2) - γ214 = convert(T, 1.4897271251154750e-2) - γ215 = convert(T, 2.6244269699436817e-1) - γ216 = convert(T, -4.7486056986590294e-3) - γ217 = convert(T, 2.3219312682036197e-2) - γ218 = convert(T, 6.2852588972458059e-2) - γ219 = convert(T, 5.4473719351268962e-2) - γ220 = convert(T, 2.4345446089014514e-2) - γ22end = SVector( - γ202, γ203, γ204, γ205, γ206, γ207, γ208, γ209, γ210, γ211, γ212, γ213, - γ214, γ215, γ216, γ217, γ218, γ219, γ220) - - γ302 = convert(T, 0.0000000000000000e+0) - γ303 = convert(T, 0.0000000000000000e+0) - γ304 = convert(T, 1.9595487007932735e-1) - γ305 = convert(T, -6.9871675039100595e-5) - γ306 = convert(T, 1.0592231169810050e-1) - γ307 = convert(T, 1.0730426871909635e+0) - γ308 = convert(T, 8.9257826744389124e-1) - γ309 = convert(T, -1.4078912484894415e-1) - γ310 = convert(T, -2.6869890558434262e-1) - γ311 = convert(T, -6.5175753568318007e-2) - γ312 = convert(T, 4.9177812903108553e-1) - γ313 = convert(T, 4.6017684776493678e-1) - γ314 = convert(T, -6.4689512947008251e-3) - γ315 = convert(T, 4.4034728024115377e-1) - γ316 = convert(T, 6.1086885767527943e-1) - γ317 = convert(T, 5.0546454457410162e-1) - γ318 = convert(T, 5.4668509293072887e-1) - γ319 = convert(T, 7.1414182420995431e-1) - γ320 = convert(T, -1.0558095282893749e+0) - γ32end = SVector( - γ302, γ303, γ304, γ305, γ306, γ307, γ308, γ309, γ310, γ311, γ312, γ313, - γ314, γ315, γ316, γ317, γ318, γ319, γ320) - - δ02 = convert(T, 1.4375468781258596e+0) - δ03 = convert(T, 1.5081653637261594e+0) - δ04 = convert(T, -1.4575347066062688e-1) - δ05 = convert(T, 3.1495761082838158e-1) - δ06 = convert(T, 3.5505919368536931e-1) - δ07 = convert(T, 2.3616389374566960e-1) - δ08 = convert(T, 1.0267488547302055e-1) - δ09 = convert(T, 3.5991243524519438e+0) - δ10 = convert(T, 1.5172890003890782e+0) - δ11 = convert(T, 1.8171662741779953e+0) - δ12 = convert(T, 2.8762263521436831e+0) - δ13 = convert(T, 4.6350154228218754e-1) - δ14 = convert(T, 1.5573122110727220e+0) - δ15 = convert(T, 2.0001066778080254e+0) - δ16 = convert(T, 9.1690694855534305e-1) - δ17 = convert(T, 2.0474618401365854e+0) - δ18 = convert(T, -3.2336329115436924e-1) - δ19 = convert(T, 3.2899060754742177e-1) - δ20 = convert(T, 0.0000000000000000e+0) - δ2end = SVector(δ02, δ03, δ04, δ05, δ06, δ07, δ08, δ09, δ10, δ11, δ12, δ13, δ14, δ15, - δ16, δ17, δ18, δ19, δ20) - - β1 = convert(T, 1.7342385375780556e-1) - β02 = convert(T, 2.8569004728564801e-1) - β03 = convert(T, 6.8727044379779589e-1) - β04 = convert(T, 1.2812121060977319e-1) - β05 = convert(T, 4.9137180740403122e-4) - β06 = convert(T, 4.7033584446956857e-2) - β07 = convert(T, 4.4539998128170821e-1) - β08 = convert(T, 1.2259824887343720e+0) - β09 = convert(T, 2.0616463985024421e-2) - β10 = convert(T, 1.5941162575324802e-1) - β11 = convert(T, 1.2953803678226099e+0) - β12 = convert(T, 1.7287352967302603e-3) - β13 = convert(T, 1.1660483420536467e-1) - β14 = convert(T, 7.7997036621815521e-2) - β15 = convert(T, 3.2563250234418012e-1) - β16 = convert(T, 1.0611520488333197e+0) - β17 = convert(T, 6.5891625628040993e-4) - β18 = convert(T, 8.3534647700054046e-2) - β19 = convert(T, 9.8972579458252483e-2) - β20 = convert(T, 4.3010116145097040e-2) - β2end = SVector(β02, β03, β04, β05, β06, β07, β08, β09, β10, β11, β12, β13, β14, β15, - β16, β17, β18, β19, β20) - - c02 = convert(T2, 1.7342385375780556e-1) - c03 = convert(T2, 3.0484982420032158e-1) - c04 = convert(T2, 5.5271395645729193e-1) - c05 = convert(T2, 4.7079204549750037e-2) - c06 = convert(T2, 1.5652540451324129e-1) - c07 = convert(T2, 1.8602224049074517e-1) - c08 = convert(T2, 2.8426620035751449e-1) - c09 = convert(T2, 9.5094727548792268e-1) - c10 = convert(T2, 6.8046501070096010e-1) - c11 = convert(T2, 5.9705366562360063e-1) - c12 = convert(T2, 1.8970821645077285e+0) - c13 = convert(T2, 2.9742664004529606e-1) - c14 = convert(T2, 6.0813463700134940e-1) - c15 = convert(T2, 7.3080004188477765e-1) - c16 = convert(T2, 9.1656999044951792e-1) - c17 = convert(T2, 1.4309687554614530e+0) - c18 = convert(T2, 4.1043824968249148e-1) - c19 = convert(T2, 8.4898255952298962e-1) - c20 = convert(T2, 3.3543896258348421e-1) - c2end = SVector(c02, c03, c04, c05, c06, c07, c08, c09, c10, c11, c12, c13, c14, c15, - c16, c17, c18, c19, c20) - - LowStorageRK3SConstantCache{19, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end) -end - -function alg_cache(alg::ParsaniKetchesonDeconinck3S205, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = ParsaniKetchesonDeconinck3S205ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK3SCache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::ParsaniKetchesonDeconinck3S205, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - ParsaniKetchesonDeconinck3S205ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) -end - -# 3S+ low storage methods: 3S methods adding another memory location for the embedded method (non-FSAL version) -# ## References -# - Ranocha, Dalcin, Parsani, Ketcheson (2021) -# Optimized Runge-Kutta Methods with Automatic Step Size Control for -# Compressible Computational Fluid Dynamics -# [arXiv:2104.06836](https://arxiv.org/abs/2104.06836) -@cache struct LowStorageRK3SpCache{uType, rateType, uNoUnitsType, TabType, StageLimiter, - StepLimiter, Thread} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - k::rateType - utilde::uType - tmp::uType - atmp::uNoUnitsType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct LowStorageRK3SpConstantCache{N, T, T2} <: OrdinaryDiffEqConstantCache - γ12end::SVector{N, T} # γ11 is always zero - γ22end::SVector{N, T} # γ21 is always one - γ32end::SVector{N, T} # γ31 is always zero - # TODO: γ302 == γ303 == 0 in all emthods implemented below -> possible optimization? - δ2end::SVector{N, T} # δ1 is always one - β1::T - β2end::SVector{N, T} - c2end::SVector{N, T2} # c1 is always zero - bhat1::T - bhat2end::SVector{N, T} -end - -function RDPK3Sp35ConstantCache(T, T2) - γ12end = SVector(convert(T, big"2.587669070352079020144955303389306026e-01"), - convert(T, big"-1.324366873994502973977035353758550057e-01"), - convert(T, big"5.055601231460399101814291350373559483e-02"), - convert(T, big"5.670552807902877312521811889846000976e-01")) - - γ22end = SVector(convert(T, big"5.528418745102160639901976698795928733e-01"), - convert(T, big"6.731844400389673824374042790213570079e-01"), - convert(T, big"2.803103804507635075215805236096803381e-01"), - convert(T, big"5.521508873507393276457754945308880998e-01")) - - γ32end = SVector(convert(T, big"0.000000000000000000000000000000000000e+00"), - convert(T, big"0.000000000000000000000000000000000000e+00"), - convert(T, big"2.752585813446636957256614568573008811e-01"), - convert(T, big"-8.950548709279785077579454232514633376e-01")) - - δ2end = SVector(convert(T, big"3.407687209321455242558804921815861422e-01"), - convert(T, big"3.414399280584625023244387687873774697e-01"), - convert(T, big"7.229302732875589702087936723400941329e-01"), - convert(T, big"0.000000000000000000000000000000000000e+00")) - - β1 = convert(T, big"2.300285062878154351930669430512780706e-01") - β2end = SVector(convert(T, big"3.021457892454169700189445968126242994e-01"), - convert(T, big"8.025601039472704213300183888573974531e-01"), - convert(T, big"4.362158997637629844305216319994356355e-01"), - convert(T, big"1.129268494470295369172265188216779157e-01")) - - c2end = SVector(convert(T, big"2.300285062878154351930669430512780706e-01"), - convert(T, big"4.050049049262914975700372321130661410e-01"), - convert(T, big"8.947823877926760224705450466361360720e-01"), - convert(T, big"7.235108137218888081489570284485201518e-01")) - - # difference of the usual bhat coefficients and the main b coefficients - bhat1 = convert(T, - big"1.046363371354093758897668305991705199e-01" - - - big"1.147931563369900682037379182772608287e-01") - bhat2end = SVector( - convert(T, - big"9.520431574956758809511173383346476348e-02" - - - big"8.933559295232859013880114997436974196e-02"), - convert(T, - big"4.482446645568668405072421350300379357e-01" - - - big"4.355858717379231779899161991033964256e-01"), - convert(T, - big"2.449030295461310135957132640369862245e-01" - - - big"2.473585295257286267503182138232950881e-01"), - convert(T, - big"1.070116530120251819121660365003405564e-01" - - - big"1.129268494470295369172265188216779157e-01")) - - LowStorageRK3SpConstantCache{4, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end, - bhat1, bhat2end) -end - -function alg_cache(alg::RDPK3Sp35, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - k = zero(rate_prototype) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - utilde = zero(u) - tmp = zero(u) - if eltype(u) === uEltypeNoUnits - atmp = utilde # alias the vectors to save memory - else - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - end - tab = RDPK3Sp35ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - LowStorageRK3SpCache( - u, uprev, fsalfirst, k, utilde, tmp, atmp, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::RDPK3Sp35, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - RDPK3Sp35ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function RDPK3Sp49ConstantCache(T, T2) - γ12end = SVector(convert(T, big"-4.655641301259180308677051498071354582e+00"), - convert(T, big"-7.720264924836063859141482018013692338e-01"), - convert(T, big"-4.024423213419724605695005429153112050e+00"), - convert(T, big"-2.129685246739018613087466942802498152e-02"), - convert(T, big"-2.435022519234470128602335652131234586e+00"), - convert(T, big"1.985627480986167686791439120784668251e-02"), - convert(T, big"-2.810790112885283952929218377438668784e-01"), - convert(T, big"1.689434895835535695524003319503844110e-01")) - - γ22end = SVector(convert(T, big"2.499262752607825957145627300817258023e+00"), - convert(T, big"5.866820365436136799319929406678132638e-01"), - convert(T, big"1.205141365412670762568835277881144391e+00"), - convert(T, big"3.474793796700868848597960521248007941e-01"), - convert(T, big"1.321346140128723105871355808477092220e+00"), - convert(T, big"3.119636324379370564023292317172847140e-01"), - convert(T, big"4.351419055894087609560896967082486864e-01"), - convert(T, big"2.359698299440788299161958168555704234e-01")) - - γ32end = SVector(convert(T, big"0.000000000000000000000000000000000000e+00"), - convert(T, big"0.000000000000000000000000000000000000e+00"), - convert(T, big"7.621037111138170045618771082985664430e-01"), - convert(T, big"-1.981182159087218433914909510116664154e-01"), - convert(T, big"-6.228960706317566993192689455719570179e-01"), - convert(T, big"-3.752246993432626328289874575355102038e-01"), - convert(T, big"-3.355436539000946543242869676125143358e-01"), - convert(T, big"-4.560963110717484359015342341157302403e-02")) - - δ2end = SVector(convert(T, big"1.262923854387806460989545005598562667e+00"), - convert(T, big"7.574967177560872438940839460448329992e-01"), - convert(T, big"5.163591158111222863455531895152351544e-01"), - convert(T, big"-2.746333792042827389548936599648122146e-02"), - convert(T, big"-4.382674653941770848797864513655752318e-01"), - convert(T, big"1.273587103668392811985704533534301656e+00"), - convert(T, big"-6.294740045442794829622796613103492913e-01"), - convert(T, big"0.000000000000000000000000000000000000e+00")) - - β1 = convert(T, big"2.836343531977826022543660465926414772e-01") - β2end = SVector(convert(T, big"9.736497978646965372894268287659773644e-01"), - convert(T, big"3.382358566377620380505126936670933370e-01"), - convert(T, big"-3.584937820217850715182820651063453804e-01"), - convert(T, big"-4.113955814725134294322006403954822487e-03"), - convert(T, big"1.427968962196019024010757034274849198e+00"), - convert(T, big"1.808467712038743032991177525728915926e-02"), - convert(T, big"1.605771316794521018947553625079465692e-01"), - convert(T, big"2.952226811394310028003810072027839487e-01")) - - c2end = SVector(convert(T, big"2.836343531977826022543660465926414772e-01"), - convert(T, big"5.484073767552486705240014599676811834e-01"), - convert(T, big"3.687229456675706936558667052479014150e-01"), - convert(T, big"-6.806119916032093175251948474173648331e-01"), - convert(T, big"3.518526451892056368706593492732753284e-01"), - convert(T, big"1.665941920204672094647868254892387293e+00"), - convert(T, big"9.715276989307335935187466054546761665e-01"), - convert(T, big"9.051569554420045339601721625247585643e-01")) - - # difference of the usual bhat coefficients and the main b coefficients - bhat1 = convert(T, - big"4.550655927970944948340364817140593012e-02" - - - big"4.503731969165884304041981629148469971e-02") - bhat2end = SVector( - convert(T, - big"1.175968310492638562142460384341959193e-01" - - - big"1.859217322011968812563859888433403777e-01"), - convert(T, - big"3.658257330515213200375475084421083608e-02" - - - big"3.329727509207630932171676116314110008e-02"), - convert(T, - big"-5.311555834355629559010061596928357525e-03" - - - big"-4.784222621050198909820741390895649698e-03"), - convert(T, - big"5.178250012713127329531367677410650996e-03" - - - big"4.055848062637567925908043629915811671e-03"), - convert(T, - big"4.954639022118682638697706200022961443e-01" - - - big"4.185027999682794463309031355073933444e-01"), - convert(T, - big"-5.999303132737865921441409466809521699e-03" - - - big"-4.381894507474277848407591859322000026e-03"), - convert(T, - big"9.405093434568315929035250835218733824e-02" - - - big"2.712846097324442608251358061215836749e-02"), - convert(T, - big"2.169318087627035072893925375820310602e-01" - - - big"2.952226811394310028003810072027839487e-01")) - - LowStorageRK3SpConstantCache{8, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end, - bhat1, bhat2end) -end - -function alg_cache(alg::RDPK3Sp49, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - k = zero(rate_prototype) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - utilde = zero(u) - tmp = zero(u) - if eltype(u) === uEltypeNoUnits - atmp = utilde # alias the vectors to save memory - else - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - end - tab = RDPK3Sp49ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - LowStorageRK3SpCache( - u, uprev, fsalfirst, k, utilde, tmp, atmp, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::RDPK3Sp49, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - RDPK3Sp49ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function RDPK3Sp510ConstantCache(T, T2) - γ12end = SVector(convert(T, big"4.043660078504695837542588769963326988e-01"), - convert(T, big"-8.503427464263185087039788184485627962e-01"), - convert(T, big"-6.950894167072419998080989313353063399e+00"), - convert(T, big"9.238765225328278557805080247596562995e-01"), - convert(T, big"-2.563178039957404359875124580586147888e+00"), - convert(T, big"2.545744869966347362604059848503340890e-01"), - convert(T, big"3.125831733863168874151935287174374515e-01"), - convert(T, big"-7.007114800567584871263283872289072079e-01"), - convert(T, big"4.839620970980726631935174740648996010e-01")) - - γ22end = SVector(convert(T, big"6.871467069752345566001768382316915820e-01"), - convert(T, big"1.093024760468898686510433898645775908e+00"), - convert(T, big"3.225975382330161123625348062949430509e+00"), - convert(T, big"1.041153700841396427100436517666787823e+00"), - convert(T, big"1.292821488864702752767390075072674807e+00"), - convert(T, big"7.391462769297006312785029455392854586e-01"), - convert(T, big"1.239129257039300081860496157739352186e-01"), - convert(T, big"1.842753479366766790220633908793933781e-01"), - convert(T, big"5.712788942697077644959290025755003720e-02")) - - γ32end = SVector(convert(T, big"0.000000000000000000000000000000000000e+00"), - convert(T, big"0.000000000000000000000000000000000000e+00"), - convert(T, big"-2.393405159342139386425044844626597490e+00"), - convert(T, big"-1.902854422095986544338294743445530533e+00"), - convert(T, big"-2.820042210583207174321941694153843259e+00"), - convert(T, big"-1.832698464130564949123807896975136336e+00"), - convert(T, big"-2.199094510750697865007677774395365522e-01"), - convert(T, big"-4.082430660384876496971887725512427800e-01"), - convert(T, big"-1.377669791121207993339861855818881150e-01")) - - δ2end = SVector(convert(T, big"-1.331778409133849616712007380176762548e-01"), - convert(T, big"8.260422785246030254485064732649153253e-01"), - convert(T, big"1.513700430513332405798616943654007796e+00"), - convert(T, big"-1.305810063177048110528482211982726539e+00"), - convert(T, big"3.036678789342507704281817524408221954e+00"), - convert(T, big"-1.449458267074592489788800461540171106e+00"), - convert(T, big"3.834313873320957483471400258279635203e+00"), - convert(T, big"4.122293971923324492772059928094971199e+00"), - convert(T, big"0.000000000000000000000000000000000000e+00")) - - β1 = convert(T, big"2.597883575710995826783320802193635406e-01") - β2end = SVector(convert(T, big"1.777008800169541694837687556103565007e-02"), - convert(T, big"2.481636637328140606807905234325691851e-01"), - convert(T, big"7.941736827560429420202759490815682546e-01"), - convert(T, big"3.885391296871822541486945325814526190e-01"), - convert(T, big"1.455051664264339366757555740296587660e-01"), - convert(T, big"1.587517379462528932413419955691782412e-01"), - convert(T, big"1.650605631567659573994022720500446501e-01"), - convert(T, big"2.118093299943235065178000892467421832e-01"), - convert(T, big"1.559392340339606299335442956580114440e-01")) - - c2end = SVector(convert(T, big"2.597883575710995826783320802193635406e-01"), - convert(T, big"9.904573115730917688557891428202061598e-02"), - convert(T, big"2.155511882303785204133426661931565216e-01"), - convert(T, big"5.007950078421880417512789524851012021e-01"), - convert(T, big"5.592251914858131230054392022144328176e-01"), - convert(T, big"5.449986973408778242805929551952000165e-01"), - convert(T, big"7.615224662599497796472095353126697300e-01"), - convert(T, big"8.427062083059167761623893618875787414e-01"), - convert(T, big"9.152209807185253394871325258038753352e-01")) - - # difference of the usual bhat coefficients and the main b coefficients - bhat1 = convert(T, - big"5.734588484676193812418453938089759359e-02" - - - big"-2.280102305596364773323878383881954511e-03") - bhat2end = SVector( - convert(T, - big"1.971447518039733870541652912891291496e-02" - - - big"1.407393020823230537861040991952849386e-02"), - convert(T, - big"7.215296605683716720707226840456658773e-02" - - - big"2.332691794172822486743039657924919496e-01"), - convert(T, - big"1.739659489807939956977075317768151880e-01" - - - big"4.808266700465181307162297999657715930e-02"), - convert(T, - big"3.703693600445487815015171515640585668e-01" - - - big"4.119003221139622842134291677033040683e-01"), - convert(T, - big"-1.215599039055065009827765147821222534e-01" - - - big"-1.291461071364752805327361051196128312e-01"), - convert(T, - big"1.180372945491121604465067725859678821e-01" - - - big"1.220746011038579789984601943748468541e-01"), - convert(T, - big"4.155688823364870056536983972605056553e-02" - - - big"4.357858803113387764356338334851554715e-02"), - convert(T, - big"1.227886627910379901351569893551486490e-01" - - - big"1.025076875289905073925255867102192694e-01"), - convert(T, - big"1.456284232223684285998448928597043056e-01" - - - big"1.559392340339606299335442956580114440e-01")) - - LowStorageRK3SpConstantCache{9, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end, - bhat1, bhat2end) -end - -function alg_cache(alg::RDPK3Sp510, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - k = zero(rate_prototype) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - utilde = zero(u) - tmp = zero(u) - if eltype(u) === uEltypeNoUnits - atmp = utilde # alias the vectors to save memory - else - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - end - tab = RDPK3Sp510ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK3SpCache( - u, uprev, fsalfirst, k, utilde, tmp, atmp, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::RDPK3Sp510, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - RDPK3Sp510ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -# 3S+ FSAL low storage methods: 3S methods adding another memory location for the embedded method (FSAL version) -# ## References -# - Ranocha, Dalcin, Parsani, Ketcheson (2021) -# Optimized Runge-Kutta Methods with Automatic Step Size Control for -# Compressible Computational Fluid Dynamics -# [arXiv:2104.06836](https://arxiv.org/abs/2104.06836) -@cache struct LowStorageRK3SpFSALCache{ - uType, rateType, uNoUnitsType, TabType, StageLimiter, - StepLimiter, Thread} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - k::rateType - utilde::uType - tmp::uType - atmp::uNoUnitsType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct LowStorageRK3SpFSALConstantCache{N, T, T2} <: OrdinaryDiffEqConstantCache - γ12end::SVector{N, T} # γ11 is always zero - γ22end::SVector{N, T} # γ21 is always one - γ32end::SVector{N, T} # γ31 is always zero - # TODO: γ302 == γ303 == 0 in all emthods implemented below -> possible optimization? - δ2end::SVector{N, T} # δ1 is always one - β1::T - β2end::SVector{N, T} - c2end::SVector{N, T2} # c1 is always zero - bhat1::T - bhat2end::SVector{N, T} - bhatfsal::T -end - -function RDPK3SpFSAL35ConstantCache(T, T2) - γ12end = SVector(convert(T, big"2.587771979725733308135192812685323706e-01"), - convert(T, big"-1.324380360140723382965420909764953437e-01"), - convert(T, big"5.056033948190826045833606441415585735e-02"), - convert(T, big"5.670532000739313812633197158607642990e-01")) - - γ22end = SVector(convert(T, big"5.528354909301389892439698870483746541e-01"), - convert(T, big"6.731871608203061824849561782794643600e-01"), - convert(T, big"2.803103963297672407841316576323901761e-01"), - convert(T, big"5.521525447020610386070346724931300367e-01")) - - γ32end = SVector(convert(T, big"0.000000000000000000000000000000000000e+00"), - convert(T, big"0.000000000000000000000000000000000000e+00"), - convert(T, big"2.752563273304676380891217287572780582e-01"), - convert(T, big"-8.950526174674033822276061734289327568e-01")) - - δ2end = SVector(convert(T, big"3.407655879334525365094815965895763636e-01"), - convert(T, big"3.414382655003386206551709871126405331e-01"), - convert(T, big"7.229275366787987419692007421895451953e-01"), - convert(T, big"0.000000000000000000000000000000000000e+00")) - - β1 = convert(T, big"2.300298624518076223899418286314123354e-01") - β2end = SVector(convert(T, big"3.021434166948288809034402119555380003e-01"), - convert(T, big"8.025606185416310937583009085873554681e-01"), - convert(T, big"4.362158943603440930655148245148766471e-01"), - convert(T, big"1.129272530455059129782111662594436580e-01")) - - c2end = SVector(convert(T, big"2.300298624518076223899418286314123354e-01"), - convert(T, big"4.050046072094990912268498160116125481e-01"), - convert(T, big"8.947822893693433545220710894560512805e-01"), - convert(T, big"7.235136928826589010272834603680114769e-01")) - - # difference of the usual bhat coefficients and the main b coefficients - bhat1 = convert(T, - big"9.484166705035703392326247283838082847e-02" - - - big"1.147935971023541171733601324486904546e-01") - bhat2end = SVector( - convert(T, - big"1.726371339430353766966762629176676070e-01" - - - big"8.933442853113315592708384523126474636e-02"), - convert(T, - big"3.998243189084371024483169698618455770e-01" - - - big"4.355871025008616992483722693795608738e-01"), - convert(T, - big"1.718016807580178450618829007973835152e-01" - - - big"2.473576188201451146729725866810402672e-01"), - convert(T, - big"5.881914422155740300718268359027168467e-02" - - - big"1.129272530455059129782111662594436580e-01")) - bhatfsal = convert(T, big"1.020760551185952388626787099944507877e-01") - - LowStorageRK3SpFSALConstantCache{4, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, - c2end, bhat1, bhat2end, bhatfsal) -end - -function alg_cache(alg::RDPK3SpFSAL35, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - k = zero(rate_prototype) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - utilde = zero(u) - tmp = zero(u) - if eltype(u) === uEltypeNoUnits - atmp = utilde # alias the vectors to save memory - else - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - end - tab = RDPK3SpFSAL35ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK3SpFSALCache(u, uprev, fsalfirst, k, utilde, tmp, atmp, tab, - alg.stage_limiter!, alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::RDPK3SpFSAL35, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - RDPK3SpFSAL35ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function RDPK3SpFSAL49ConstantCache(T, T2) - γ12end = SVector(convert(T, big"-4.655641447335068552684422206224169103e+00"), - convert(T, big"-7.720265099645871829248487209517314217e-01"), - convert(T, big"-4.024436690519806086742256154738379161e+00"), - convert(T, big"-2.129676284018530966221583708648634733e-02"), - convert(T, big"-2.435022509790109546199372365866450709e+00"), - convert(T, big"1.985627297131987000579523283542615256e-02"), - convert(T, big"-2.810791146791038566946663374735713961e-01"), - convert(T, big"1.689434168754859644351230590422137972e-01")) - - γ22end = SVector(convert(T, big"2.499262792574495009336242992898153462e+00"), - convert(T, big"5.866820377718875577451517985847920081e-01"), - convert(T, big"1.205146086523094569925592464380295241e+00"), - convert(T, big"3.474793722186732780030762737753849272e-01"), - convert(T, big"1.321346060965113109321230804210670518e+00"), - convert(T, big"3.119636464694193615946633676950358444e-01"), - convert(T, big"4.351419539684379261368971206040518552e-01"), - convert(T, big"2.359698130028753572503744518147537768e-01")) - - γ32end = SVector(convert(T, big"0.000000000000000000000000000000000000e+00"), - convert(T, big"0.000000000000000000000000000000000000e+00"), - convert(T, big"7.621006678721315291614677352949377871e-01"), - convert(T, big"-1.981182504339400567765766904309673119e-01"), - convert(T, big"-6.228959218699007450469629366684127462e-01"), - convert(T, big"-3.752248380775956442989480369774937099e-01"), - convert(T, big"-3.355438309135169811915662336248989661e-01"), - convert(T, big"-4.560955005031121479972862973705108039e-02")) - - δ2end = SVector(convert(T, big"1.262923876648114432874834923838556100e+00"), - convert(T, big"7.574967189685911558308119415539596711e-01"), - convert(T, big"5.163589453140728104667573195005629833e-01"), - convert(T, big"-2.746327421802609557034437892013640319e-02"), - convert(T, big"-4.382673178127944142238606608356542890e-01"), - convert(T, big"1.273587294602656522645691372699677063e+00"), - convert(T, big"-6.294740283927400326554066998751383342e-01"), - convert(T, big"0.000000000000000000000000000000000000e+00")) - - β1 = convert(T, big"2.836343005184365275160654678626695428e-01") - β2end = SVector(convert(T, big"9.736500104654741223716056170419660217e-01"), - convert(T, big"3.382359225242515288768487569778320563e-01"), - convert(T, big"-3.584943611106183357043212309791897386e-01"), - convert(T, big"-4.113944068471528211627210454497620358e-03"), - convert(T, big"1.427968894048586363415504654313371031e+00"), - convert(T, big"1.808470948394314017665968411915568633e-02"), - convert(T, big"1.605770645946802213926893453819236685e-01"), - convert(T, big"2.952227015964591648775833803635147962e-01")) - - c2end = SVector(convert(T, big"2.836343005184365275160654678626695428e-01"), - convert(T, big"5.484076570002894365286665352032296535e-01"), - convert(T, big"3.687228761669438493478872632332010073e-01"), - convert(T, big"-6.806126440140844191258463830024463902e-01"), - convert(T, big"3.518526124230705801739919476290327750e-01"), - convert(T, big"1.665941994879593315477304663913129942e+00"), - convert(T, big"9.715279295934715835299192116436237065e-01"), - convert(T, big"9.051569840159589594903399929316959062e-01")) - - # difference of the usual bhat coefficients and the main b coefficients - bhat1 = convert(T, - big"2.483675912451591196775756814283216443e-02" - - - big"4.503732627263753698356970706617404465e-02") - bhat2end = SVector( - convert(T, - big"1.866327774562103796990092260942180726e-01" - - - big"1.859217303699847950262276860012454333e-01"), - convert(T, - big"5.671080795936984495604436622517631183e-02" - - - big"3.329729672569717599759560403851202805e-02"), - convert(T, - big"-3.447695439149287702616943808570747099e-03" - - - big"-4.784204180958975587114459316829942677e-03"), - convert(T, - big"3.602245056516636472203469198006404016e-03" - - - big"4.055835961031310727671557609188874328e-03"), - convert(T, - big"4.545570622145088936800484247980581766e-01" - - - big"4.185027772596074197662616795629003544e-01"), - convert(T, - big"-2.434665289427612407531544765622888855e-04" - - - big"-4.381901968919326084347037216500072323e-03 "), - convert(T, - big"6.642755361103549971517945063138312147e-02" - - - big"2.712843796446089829255188189179448399e-02"), - convert(T, - big"1.613697079523505006226025497715177578e-01" - - - big"2.952227015964591648775833803635147962e-01")) - bhatfsal = convert(T, big"4.955424859358438183052504342394102722e-02") - - LowStorageRK3SpFSALConstantCache{8, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, - c2end, bhat1, bhat2end, bhatfsal) -end - -function alg_cache(alg::RDPK3SpFSAL49, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - k = zero(rate_prototype) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - utilde = zero(u) - tmp = zero(u) - if eltype(u) === uEltypeNoUnits - atmp = utilde # alias the vectors to save memory - else - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - end - tab = RDPK3SpFSAL49ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK3SpFSALCache(u, uprev, fsalfirst, k, utilde, tmp, atmp, tab, - alg.stage_limiter!, alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::RDPK3SpFSAL49, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - RDPK3SpFSAL49ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function RDPK3SpFSAL510ConstantCache(T, T2) - γ12end = SVector(convert(T, big"4.043660121685749695640462197806189975e-01"), - convert(T, big"-8.503427289575839690883191973980814832e-01"), - convert(T, big"-6.950894175262117526410215315179482885e+00"), - convert(T, big"9.238765192731084931855438934978371889e-01"), - convert(T, big"-2.563178056509891340215942413817786020e+00"), - convert(T, big"2.545744879365226143946122067064118430e-01"), - convert(T, big"3.125831707411998258746812355492206137e-01"), - convert(T, big"-7.007114414440507927791249989236719346e-01"), - convert(T, big"4.839621016023833375810172323297465039e-01")) - - γ22end = SVector(convert(T, big"6.871467028161416909922221357014564412e-01"), - convert(T, big"1.093024748914750833700799552463885117e+00"), - convert(T, big"3.225975379607193001678365742708874597e+00"), - convert(T, big"1.041153702510101386914019859778740444e+00"), - convert(T, big"1.292821487912164945157744726076279306e+00"), - convert(T, big"7.391462755788122847651304143259254381e-01"), - convert(T, big"1.239129251371800313941948224441873274e-01"), - convert(T, big"1.842753472370123193132193302369345580e-01"), - convert(T, big"5.712788998796583446479387686662738843e-02")) - - γ32end = SVector(convert(T, big"0.000000000000000000000000000000000000e+00"), - convert(T, big"0.000000000000000000000000000000000000e+00"), - convert(T, big"-2.393405133244194727221124311276648940e+00"), - convert(T, big"-1.902854422421760920850597670305403139e+00"), - convert(T, big"-2.820042207399977261483046412236557428e+00"), - convert(T, big"-1.832698465277380999601896111079977378e+00"), - convert(T, big"-2.199094483084671192328083958346519535e-01"), - convert(T, big"-4.082430635847870963724591602173546218e-01"), - convert(T, big"-1.377669797880289713535665985132703979e-01")) - - δ2end = SVector(convert(T, big"-1.331778419508803397033287009506932673e-01"), - convert(T, big"8.260422814750207498262063505871077303e-01"), - convert(T, big"1.513700425755728332485300719652378197e+00"), - convert(T, big"-1.305810059935023735972298885749903694e+00"), - convert(T, big"3.036678802924163246003321318996156380e+00"), - convert(T, big"-1.449458274398895177922690618003584514e+00"), - convert(T, big"3.834313899176362315089976408899373409e+00"), - convert(T, big"4.122293760012985409330881631526514714e+00"), - convert(T, big"0.000000000000000000000000000000000000e+00")) - - β1 = convert(T, big"2.597883554788674084039539165398464630e-01") - β2end = SVector(convert(T, big"1.777008889438867858759149597539211023e-02"), - convert(T, big"2.481636629715501931294746189266601496e-01"), - convert(T, big"7.941736871152005775821844297293296135e-01"), - convert(T, big"3.885391285642019129575902994397298066e-01"), - convert(T, big"1.455051657916305055730603387469193768e-01"), - convert(T, big"1.587517385964749337690916959584348979e-01"), - convert(T, big"1.650605617880053419242434594242509601e-01"), - convert(T, big"2.118093284937153836908655490906875007e-01"), - convert(T, big"1.559392342362059886106995325687547506e-01")) - - c2end = SVector(convert(T, big"2.597883554788674084039539165398464630e-01"), - convert(T, big"9.904573247592460887087003212056568980e-02"), - convert(T, big"2.155511890524058691860390281856497503e-01"), - convert(T, big"5.007950088969676776844289399972611534e-01"), - convert(T, big"5.592251911688643533787800688765883636e-01"), - convert(T, big"5.449986978853637084972622392134732553e-01"), - convert(T, big"7.615224694532590139829150720490417596e-01"), - convert(T, big"8.427062083267360939805493320684741215e-01"), - convert(T, big"9.152209805057669959657927210873423883e-01")) - - # difference of the usual bhat coefficients and the main b coefficients - bhat1 = convert(T, - big"-2.019255440012066080909442770590267512e-02" - - - big"-2.280100321836980811830528665041532799e-03") - bhat2end = SVector( - convert(T, - big"2.737903480959184339932730854141598275e-02" - - - big"1.407393115790186300730580636032878435e-02"), - convert(T, - big"3.028818636145965534365173822296811090e-01" - - - big"2.332691775508456597719992034291118324e-01"), - convert(T, - big"-3.656843880622222190071445247906780540e-02" - - - big"4.808266741353862546318531020856621860e-02"), - convert(T, - big"3.982664774676767729863101188528827405e-01" - - - big"4.119003217706951892385733111000873172e-01"), - convert(T, - big"-5.715959421140685436681459970502471634e-02" - - - big"-1.291461067807736321056740833501596735e-01"), - convert(T, - big"9.849855103848558320961101178888983150e-02" - - - big"1.220746013848710098878384114422516148e-01"), - convert(T, - big"6.654601552456084978615342374581437947e-02" - - - big"4.357858583174420432201228508067333299e-02"), - convert(T, - big"9.073479542748112726465375642050504556e-02" - - - big"1.025076877568080726158907518254273554e-01"), - convert(T, - big"8.432289325330803924891866923939606351e-02" - - - big"1.559392342362059886106995325687547506e-01")) - bhatfsal = convert(T, big"4.529095628204896774513180907141004447e-02") - - LowStorageRK3SpFSALConstantCache{9, T, T2}(γ12end, γ22end, γ32end, δ2end, β1, β2end, - c2end, bhat1, bhat2end, bhatfsal) -end - -function alg_cache(alg::RDPK3SpFSAL510, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - k = zero(rate_prototype) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - utilde = zero(u) - tmp = zero(u) - if eltype(u) === uEltypeNoUnits - atmp = utilde # alias the vectors to save memory - else - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - end - tab = RDPK3SpFSAL510ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK3SpFSALCache(u, uprev, fsalfirst, k, utilde, tmp, atmp, tab, - alg.stage_limiter!, alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::RDPK3SpFSAL510, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - RDPK3SpFSAL510ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -# 2R+ low storage methods introduced by van der Houwen -@cache struct LowStorageRK2RPCache{uType, rateType, uNoUnitsType, TabType, StageLimiter, - StepLimiter, Thread} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - gprev::uType - fsalfirst::rateType - tmp::uType - atmp::uNoUnitsType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct LowStorageRK2RPConstantCache{N, T, T2} <: OrdinaryDiffEqConstantCache - Aᵢ::SVector{N, T} - Bₗ::T - B̂ₗ::T - Bᵢ::SVector{N, T} - B̂ᵢ::SVector{N, T} - Cᵢ::SVector{N, T2} -end - -function CKLLSRK43_2ConstantCache(T, T2) - A1 = convert(T, Int128(11847461282814) // Int128(36547543011857)) - A2 = convert(T, Int128(3943225443063) // Int128(7078155732230)) - A3 = convert(T, Int128(-346793006927) // Int128(4029903576067)) - Aᵢ = SVector(A1, A2, A3) - - B1 = convert(T, Int128(1017324711453) // Int128(9774461848756)) - B2 = convert(T, Int128(8237718856693) // Int128(13685301971492)) - B3 = convert(T, Int128(57731312506979) // Int128(19404895981398)) - Bᵢ = SVector(B1, B2, B3) - - B̂1 = convert(T, Int128(15763415370699) // Int128(46270243929542)) - B̂2 = convert(T, Int128(514528521746) // Int128(5659431552419)) - B̂3 = convert(T, Int128(27030193851939) // Int128(9429696342944)) - B̂ᵢ = SVector(B̂1, B̂2, B̂3) - - Bₗ = convert(T, Int128(-101169746363290) // Int128(37734290219643)) - B̂ₗ = convert(T, Int128(-69544964788955) // Int128(30262026368149)) - - C1 = convert(T2, Int128(11847461282814) // Int128(36547543011857)) # A1 - C2 = convert(T2, Int128(2079258608735161403527719) // Int128(3144780143828896577027540)) # A2 + B1 - C3 = convert(T2, - Int128(41775191021672206476512620310545281003) // - Int128(67383242951014563804622635478530729598)) # A3 + B1 + B2 - Cᵢ = SVector(C1, C2, C3) - - LowStorageRK2RPConstantCache{3, T, T2}(Aᵢ, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) -end - -function alg_cache(alg::CKLLSRK43_2, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - k = zero(rate_prototype) - gprev = zero(u) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = CKLLSRK43_2ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK2RPCache(u, uprev, k, gprev, fsalfirst, tmp, atmp, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::CKLLSRK43_2, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - CKLLSRK43_2ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function CKLLSRK54_3CConstantCache(T, T2) - A1 = convert(T, BigInt(970286171893) // BigInt(4311952581923)) - A2 = convert(T, BigInt(6584761158862) // BigInt(12103376702013)) - A3 = convert(T, BigInt(2251764453980) // BigInt(15575788980749)) - A4 = convert(T, BigInt(26877169314380) // BigInt(34165994151039)) - Aᵢ = SVector(A1, A2, A3, A4) - - B1 = convert(T, BigInt(1153189308089) // BigInt(22510343858157)) - B2 = convert(T, BigInt(1772645290293) // BigInt(4653164025191)) - B3 = convert(T, BigInt(-1672844663538) // BigInt(4480602732383)) - B4 = convert(T, BigInt(2114624349019) // BigInt(3568978502595)) - Bᵢ = SVector(B1, B2, B3, B4) - - B̂1 = convert(T, BigInt(1016888040809) // BigInt(7410784769900)) - B̂2 = convert(T, BigInt(11231460423587) // BigInt(58533540763752)) - B̂3 = convert(T, BigInt(-1563879915014) // BigInt(6823010717585)) - B̂4 = convert(T, BigInt(606302364029) // BigInt(971179775848)) - B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4) - - Bₗ = convert(T, BigInt(5198255086312) // BigInt(14908931495163)) - B̂ₗ = convert(T, BigInt(1097981568119) // BigInt(3980877426909)) - - C1 = convert(T2, BigInt(970286171893) // BigInt(4311952581923)) # A1 - C2 = convert(T2, - BigInt(18020302501594987297224499) // BigInt(30272352378568762325374449)) # A2 + B1 - C3 = convert(T2, - BigInt(940957347754451928235896289983310398260) // - BigInt(1631475460071027605339136597003329167263)) # A3 + B1 + B2 - C4 = convert(T2, - BigInt(8054848232572758807908657851968985615984276476412066) // - BigInt(8139155613487734148190408375391604039319069461908135)) # A4 + B1 + B2 + B3 - Cᵢ = SVector(C1, C2, C3, C4) - - LowStorageRK2RPConstantCache{4, T, T2}(Aᵢ, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) -end - -function alg_cache(alg::CKLLSRK54_3C, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - k = zero(rate_prototype) - gprev = zero(u) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = CKLLSRK54_3CConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK2RPCache(u, uprev, k, gprev, fsalfirst, tmp, atmp, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::CKLLSRK54_3C, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - CKLLSRK54_3CConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function CKLLSRK95_4SConstantCache(T, T2) - A1 = convert(T, BigInt(1107026461565) // BigInt(5417078080134)) - A2 = convert(T, BigInt(38141181049399) // BigInt(41724347789894)) - A3 = convert(T, BigInt(493273079041) // BigInt(11940823631197)) - A4 = convert(T, BigInt(1851571280403) // BigInt(6147804934346)) - A5 = convert(T, BigInt(11782306865191) // BigInt(62590030070788)) - A6 = convert(T, BigInt(9452544825720) // BigInt(13648368537481)) - A7 = convert(T, BigInt(4435885630781) // BigInt(26285702406235)) - A8 = convert(T, BigInt(2357909744247) // BigInt(11371140753790)) - Aᵢ = SVector(A1, A2, A3, A4, A5, A6, A7, A8) - - B1 = convert(T, BigInt(2274579626619) // BigInt(23610510767302)) - B2 = convert(T, BigInt(693987741272) // BigInt(12394497460941)) - B3 = convert(T, BigInt(-347131529483) // BigInt(15096185902911)) - B4 = convert(T, BigInt(1144057200723) // BigInt(32081666971178)) - B5 = convert(T, BigInt(1562491064753) // BigInt(11797114684756)) - B6 = convert(T, BigInt(13113619727965) // BigInt(44346030145118)) - B7 = convert(T, BigInt(393957816125) // BigInt(7825732611452)) - B8 = convert(T, BigInt(720647959663) // BigInt(6565743875477)) - Bᵢ = SVector(B1, B2, B3, B4, B5, B6, B7, B8) - - B̂1 = convert(T, BigInt(266888888871) // BigInt(3040372307578)) - B̂2 = convert(T, BigInt(34125631160) // BigInt(2973680843661)) - B̂3 = convert(T, BigInt(-653811289250) // BigInt(9267220972999)) - B̂4 = convert(T, BigInt(323544662297) // BigInt(2461529853637)) - B̂5 = convert(T, BigInt(1105885670474) // BigInt(4964345317203)) - B̂6 = convert(T, BigInt(1408484642121) // BigInt(8758221613943)) - B̂7 = convert(T, BigInt(1454774750537) // BigInt(11112645198328)) - B̂8 = convert(T, BigInt(772137014323) // BigInt(4386814405182)) - B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4, B̂5, B̂6, B̂7, B̂8) - - Bₗ = convert(T, BigInt(3559252274877) // BigInt(14424734981077)) - B̂ₗ = convert(T, BigInt(277420604269) // BigInt(1857595682219)) - - C1 = convert(T2, BigInt(1107026461565) // BigInt(5417078080134)) # A1 - C2 = convert(T2, - BigInt(248859529315327119359384971) // BigInt(246283290687986423455311497)) # A2 + B1 - C3 = convert(T2, - BigInt(676645811244741430568548054467096184193) // - BigInt(3494367591912647069105975861901917224854)) # A3 + B1 + B2 - C4 = convert(T2, - BigInt(974370561662349106845723178377944301517533305964589) // - BigInt(2263290880944514209862892217007179742168288737673791)) # A4 + B1 + B2 + B3 - C5 = convert(T2, - BigInt(23738915426186839814576142955255044211724736499516359049188590711) // - BigInt(67203160149331519751012175988216621571869262839903428488408759604)) # A5 + B1 + B2 + B3 + B4 - C6 = convert(T2, - BigInt(1882683585832901544671586749377753597775777511029847145277760106172106584376955) // - BigInt(1901663903553486696887572033100456166564493852721284994300276200102719954709068)) # A6 + B1 + B2 + B3 + B4 + B5 - C7 = convert(T2, - BigInt(61872982955093233917984290421186995265732234396821660871734841970091372539489172106504162637) // - BigInt(81207728164913218881758751120099941603350662788460257311895072645631357391473675997419584220)) # A7 + B1 + B2 + B3 + B4 + B5 + B6 - C8 = convert(T2, - BigInt(197565042693102647130189450792520184956129841555961940530192020871289515369046683661585184411130637357) // - BigInt(232196202198018941876505157326935602816917261769279531369710269478309137067357703513986211472070374865)) # A8 + B1 + B2 + B3 + B4 + B5 + B6 + B7 - Cᵢ = SVector(C1, C2, C3, C4, C5, C6, C7, C8) - - LowStorageRK2RPConstantCache{8, T, T2}(Aᵢ, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) -end - -function alg_cache(alg::CKLLSRK95_4S, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - k = zero(rate_prototype) - gprev = zero(u) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = CKLLSRK95_4SConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK2RPCache(u, uprev, k, gprev, fsalfirst, tmp, atmp, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::CKLLSRK95_4S, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - CKLLSRK95_4SConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function CKLLSRK95_4CConstantCache(T, T2) - A1 = convert(T, BigInt(2756167973529) // BigInt(16886029417639)) - A2 = convert(T, BigInt(11436141375279) // BigInt(13592993952163)) - A3 = convert(T, BigInt(88551658327) // BigInt(2352971381260)) - A4 = convert(T, BigInt(1882111988787) // BigInt(5590444193957)) - A5 = convert(T, BigInt(846820081679) // BigInt(4754706910573)) - A6 = convert(T, BigInt(4475289710031) // BigInt(6420120086209)) - A7 = convert(T, BigInt(118394748311) // BigInt(9144450320350)) - A8 = convert(T, BigInt(3307377157135) // BigInt(13111544596386)) - Aᵢ = SVector(A1, A2, A3, A4, A5, A6, A7, A8) - - B1 = convert(T, BigInt(1051460336009) // BigInt(14326298067773)) - B2 = convert(T, BigInt(930517604889) // BigInt(7067438519321)) - B3 = convert(T, BigInt(-311910530565) // BigInt(11769786407153)) - B4 = convert(T, BigInt(-410144036239) // BigInt(7045999268647)) - B5 = convert(T, BigInt(16692278975653) // BigInt(83604524739127)) - B6 = convert(T, BigInt(3777666801280) // BigInt(13181243438959)) - B7 = convert(T, BigInt(286682614203) // BigInt(12966190094317)) - B8 = convert(T, BigInt(3296161604512) // BigInt(22629905347183)) - Bᵢ = SVector(B1, B2, B3, B4, B5, B6, B7, B8) - - B̂1 = convert(T, BigInt(3189770262221) // BigInt(35077884776239)) - B̂2 = convert(T, BigInt(780043871774) // BigInt(11919681558467)) - B̂3 = convert(T, BigInt(-483824475979) // BigInt(5387739450692)) - B̂4 = convert(T, BigInt(1306553327038) // BigInt(9528955984871)) - B̂5 = convert(T, BigInt(6521106697498) // BigInt(22565577506855)) - B̂6 = convert(T, BigInt(1400555694605) // BigInt(19784728594468)) - B̂7 = convert(T, BigInt(1183541508418) // BigInt(13436305181271)) - B̂8 = convert(T, BigInt(3036254792728) // BigInt(15493572606329)) - B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4, B̂5, B̂6, B̂7, B̂8) - - Bₗ = convert(T, BigInt(2993490409874) // BigInt(13266828321767)) - B̂ₗ = convert(T, BigInt(638483435745) // BigInt(4187244659458)) - - C1 = convert(T2, BigInt(2756167973529) // BigInt(16886029417639)) # A1 - C2 = convert(T2, - BigInt(178130064075748009421121134) // BigInt(194737282992122861693942999)) # A2 + B1 - C3 = convert(T2, - BigInt(57818276708998807530478158133449099851) // - BigInt(238238895426494403638887583424360627580)) # A3 + B1 + B2 - C4 = convert(T2, - BigInt(3432454166457135667348375590572529790194124848059104) // - BigInt(6662096512485931545803670383440459769502981926779993)) # A4 + B1 + B2 + B3 - C5 = convert(T2, - BigInt(11915126765643872062053118401193741919814944004335534493046474237) // - BigInt(39923715169802034300462756237193519081954994679332637422466438119)) # A5 + B1 + B2 + B3 + B4 - C6 = convert(T2, - BigInt(4583883621300589683158355859163890943947800555246686854224916208836514024614442) // - BigInt(4506922925096139856045533451931734406235454975594364558624038359246205017801029)) # A6 + B1 + B2 + B3 + B4 + B5 - C7 = convert(T2, - BigInt(52423219056629312880725209686636192777075511202228566787042655312097949192300218484424118619) // - BigInt(84615702680158836756876794083943762639542619835321175569533203672153042594634924742431352650)) # A7 + B1 + B2 + B3 + B4 + B5 + B6 - C8 = convert(T2, - BigInt(1385843715228499555828057735261132084759031703937678116167963792224108372724503731226480538087331079769069) // - BigInt(1573111845759510782008384284066606688388217112071821912231287750254246452350240904652428530379336814559998)) # A8 + B1 + B2 + B3 + B4 + B5 + B6 + B7 - Cᵢ = SVector(C1, C2, C3, C4, C5, C6, C7, C8) - - LowStorageRK2RPConstantCache{8, T, T2}(Aᵢ, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) -end - -function alg_cache(alg::CKLLSRK95_4C, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - k = zero(rate_prototype) - gprev = zero(u) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = CKLLSRK95_4CConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK2RPCache(u, uprev, k, gprev, fsalfirst, tmp, atmp, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::CKLLSRK95_4C, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - CKLLSRK95_4CConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function CKLLSRK95_4MConstantCache(T, T2) - A1 = convert(T, BigInt(5573095071601) // BigInt(11304125995793)) - A2 = convert(T, BigInt(315581365608) // BigInt(4729744040249)) - A3 = convert(T, BigInt(8734064225157) // BigInt(30508564569118)) - A4 = convert(T, BigInt(6457785058448) // BigInt(14982850401353)) - A5 = convert(T, BigInt(5771559441664) // BigInt(18187997215013)) - A6 = convert(T, BigInt(1906712129266) // BigInt(6681214991155)) - A7 = convert(T, BigInt(311585568784) // BigInt(2369973437185)) - A8 = convert(T, BigInt(-4840285693886) // BigInt(7758383361725)) - Aᵢ = SVector(A1, A2, A3, A4, A5, A6, A7, A8) - - B1 = convert(T, BigInt(549666665015) // BigInt(5899839355879)) - B2 = convert(T, BigInt(-548816778320) // BigInt(9402908589133)) - B3 = convert(T, BigInt(1672704946363) // BigInt(13015471661974)) - B4 = convert(T, BigInt(1025420337373) // BigInt(5970204766762)) - B5 = convert(T, BigInt(1524419752016) // BigInt(6755273790179)) - B6 = convert(T, BigInt(-10259399787359) // BigInt(43440802207630)) - B7 = convert(T, BigInt(4242280279850) // BigInt(10722460893763)) - B8 = convert(T, BigInt(1887552771913) // BigInt(6099058196803)) - Bᵢ = SVector(B1, B2, B3, B4, B5, B6, B7, B8) - - B̂1 = convert(T, BigInt(330911065672) // BigInt(9937126492277)) - B̂2 = convert(T, BigInt(-872991930418) // BigInt(11147305689291)) - B̂3 = convert(T, BigInt(2575378033706) // BigInt(14439313202205)) - B̂4 = convert(T, BigInt(3046892121673) // BigInt(11013392356255)) - B̂5 = convert(T, BigInt(1780184658016) // BigInt(8929499316295)) - B̂6 = convert(T, BigInt(10265149063) // BigInt(2098741126425)) - B̂7 = convert(T, BigInt(1643090076625) // BigInt(4891294770654)) - B̂8 = convert(T, BigInt(116106750067) // BigInt(3955800826265)) - B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4, B̂5, B̂6, B̂7, B̂8) - - Bₗ = convert(T, BigInt(-453873186647) // BigInt(15285235680030)) - B̂ₗ = convert(T, BigInt(866868642257) // BigInt(42331321870877)) - - C1 = convert(T2, BigInt(5573095071601) // BigInt(11304125995793)) - C2 = convert(T2, - BigInt(4461661993774357683398167) // BigInt(27904730031895199210773871)) - C3 = convert(T2, - BigInt(543425730194107827015264404954831354769) // - BigInt(1692482454734045499140692116457071506026)) - C4 = convert(T2, - BigInt(6429586327013850295560537918723231687699697140756067) // - BigInt(10818243561353065593628044468492745774799533452459554)) - C5 = convert(T2, - BigInt(555984804780268998022260997164198311752115182012221553157164786) // - BigInt(852213854337283773231630192518719827415190771786411558523853399)) - C6 = convert(T2, - BigInt(1789345671284476461332539715762783748132668223013904373945129499237446392572) // - BigInt(2114764997945705573761804541148983827155257005191540481884326639410208291635)) - C7 = convert(T2, - BigInt(2972211964132922642906704796208250552795647483819924111704054115070043529037601892705217) // - BigInt(6517454043294174770082798998332814729652497865130816822916618330047242844192616374937270)) - C8 = convert(T2, - BigInt(22038106775746116973750004935225594022265950105933360206617843987546593773108577078867914238620973639) // - BigInt(228770596964454885481304478061363897900267080665965044117230250287302271092811814450282133504194141850)) - Cᵢ = SVector(C1, C2, C3, C4, C5, C6, C7, C8) - - LowStorageRK2RPConstantCache{8, T, T2}(Aᵢ, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) -end - -function alg_cache(alg::CKLLSRK95_4M, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - k = zero(rate_prototype) - gprev = zero(u) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = CKLLSRK95_4MConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK2RPCache(u, uprev, k, gprev, fsalfirst, tmp, atmp, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::CKLLSRK95_4M, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - CKLLSRK95_4MConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -# 3R+ low storage methods introduced by van der Houwen -@cache struct LowStorageRK3RPCache{uType, rateType, uNoUnitsType, TabType, StageLimiter, - StepLimiter, Thread} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - uᵢ₋₁::uType - uᵢ₋₂::uType - fᵢ₋₂::rateType - gprev::uType - fsalfirst::rateType - tmp::uType - atmp::uNoUnitsType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct LowStorageRK3RPConstantCache{N, T, T2} <: OrdinaryDiffEqConstantCache - Aᵢ₁::SVector{N, T} - Aᵢ₂::SVector{N, T} - Bₗ::T - B̂ₗ::T - Bᵢ::SVector{N, T} - B̂ᵢ::SVector{N, T} - Cᵢ::SVector{N, T2} -end - -function CKLLSRK54_3C_3RConstantCache(T, T2) - A₁1 = convert(T, BigInt(2365592473904) // BigInt(8146167614645)) - A₁2 = convert(T, BigInt(4278267785271) // BigInt(6823155464066)) - A₁3 = convert(T, BigInt(2789585899612) // BigInt(8986505720531)) - A₁4 = convert(T, BigInt(15310836689591) // BigInt(24358012670437)) - Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4) - - A₂1 = convert(T, BigInt(0) // BigInt(1)) - A₂2 = convert(T, BigInt(-722262345248) // BigInt(10870640012513)) - A₂3 = convert(T, BigInt(1365858020701) // BigInt(8494387045469)) - A₂4 = convert(T, BigInt(3819021186) // BigInt(2763618202291)) - Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4) - - B1 = convert(T, BigInt(846876320697) // BigInt(6523801458457)) - B2 = convert(T, BigInt(3032295699695) // BigInt(12397907741132)) - B3 = convert(T, BigInt(612618101729) // BigInt(6534652265123)) - B4 = convert(T, BigInt(1155491934595) // BigInt(2954287928812)) - Bᵢ = SVector(B1, B2, B3, B4) - - B̂1 = convert(T, BigInt(1296459667021) // BigInt(9516889378644)) - B̂2 = convert(T, BigInt(2599004989233) // BigInt(11990680747819)) - B̂3 = convert(T, BigInt(1882083615375) // BigInt(8481715831096)) - B̂4 = convert(T, BigInt(1577862909606) // BigInt(5567358792761)) - B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4) - - Bₗ = convert(T, BigInt(707644755468) // BigInt(5028292464395)) - B̂ₗ = convert(T, BigInt(328334985361) // BigInt(2316973589007)) - - C1 = convert(T2, BigInt(2365592473904) // BigInt(8146167614645)) - C2 = convert(T2, - BigInt(41579400703344293287237655) // BigInt(74172066799272566561857858)) - C3 = convert(T2, - BigInt(299308060739053880467044545349561265546) // - BigInt(497993456493513966629488516767096447823)) - C4 = convert(T2, - BigInt(5468330126750791548369684419304733938034170906513585) // - BigInt(5444638279732761024893610553331663911104849888809108)) - Cᵢ = SVector(C1, C2, C3, C4) - - LowStorageRK3RPConstantCache{4, T, T2}(Aᵢ₁, Aᵢ₂, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) -end - -function alg_cache(alg::CKLLSRK54_3C_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - k = zero(rate_prototype) - uᵢ₋₁ = zero(u) - uᵢ₋₂ = zero(u) - fᵢ₋₂ = zero(rate_prototype) - gprev = zero(u) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = CKLLSRK54_3C_3RConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK3RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, fᵢ₋₂, gprev, fsalfirst, tmp, atmp, tab, - alg.stage_limiter!, alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::CKLLSRK54_3C_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - CKLLSRK54_3C_3RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function CKLLSRK54_3M_3RConstantCache(T, T2) - A₁1 = convert(T, BigInt(17396840518954) // BigInt(49788467287365)) - A₁2 = convert(T, BigInt(21253110367599) // BigInt(14558944785238)) - A₁3 = convert(T, BigInt(4293647616769) // BigInt(14519312872408)) - A₁4 = convert(T, BigInt(-8941886866937) // BigInt(7464816931160)) - Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4) - - A₂1 = convert(T, BigInt(0) // BigInt(1)) - A₂2 = convert(T, BigInt(-12587430488023) // BigInt(11977319897242)) - A₂3 = convert(T, BigInt(6191878339181) // BigInt(13848262311063)) - A₂4 = convert(T, BigInt(19121624165801) // BigInt(12321025968027)) - Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4) - - B1 = convert(T, BigInt(1977388745448) // BigInt(17714523675943)) - B2 = convert(T, BigInt(6528140725453) // BigInt(14879534818174)) - B3 = convert(T, BigInt(4395900531415) // BigInt(55649460397719)) - B4 = convert(T, BigInt(6567440254656) // BigInt(15757960182571)) - Bᵢ = SVector(B1, B2, B3, B4) - - B̂1 = convert(T, BigInt(390601394181) // BigInt(3503051559916)) - B̂2 = convert(T, BigInt(31150720071161) // BigInt(68604711794052)) - B̂3 = convert(T, BigInt(416927665232) // BigInt(6953044279741)) - B̂4 = convert(T, BigInt(3879867616328) // BigInt(8869216637007)) - B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4) - - Bₗ = convert(T, BigInt(-436008689643) // BigInt(9453681332953)) - B̂ₗ = convert(T, BigInt(-163749046041) // BigInt(2599987820560)) - - C1 = convert(T2, BigInt(17396840518954) // BigInt(49788467287365)) - C2 = convert(T2, BigInt(2546271293606266795002053) // BigInt(6227754966395669782804057)) - C3 = convert(T2, - BigInt(3043453778831534771251734214272440269577) // - BigInt(3561810617861654942925591050154818470872)) - C4 = convert(T2, - BigInt(10963106193663894855575270257133723083246622141340761) // - BigInt(12121458300971454511596914396147459030814063072954120)) - Cᵢ = SVector(C1, C2, C3, C4) - - LowStorageRK3RPConstantCache{4, T, T2}(Aᵢ₁, Aᵢ₂, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) -end - -function alg_cache(alg::CKLLSRK54_3M_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - k = zero(rate_prototype) - uᵢ₋₁ = zero(u) - uᵢ₋₂ = zero(u) - fᵢ₋₂ = zero(rate_prototype) - gprev = zero(u) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = CKLLSRK54_3M_3RConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK3RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, fᵢ₋₂, gprev, fsalfirst, tmp, atmp, tab, - alg.stage_limiter!, alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::CKLLSRK54_3M_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - CKLLSRK54_3M_3RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function CKLLSRK54_3N_3RConstantCache(T, T2) - A₁1 = convert(T, BigInt(4745337637855) // BigInt(22386579876409)) - A₁2 = convert(T, BigInt(6808157035527) // BigInt(13197844641179)) - A₁3 = convert(T, BigInt(4367509502613) // BigInt(10454198590847)) - A₁4 = convert(T, BigInt(1236962429870) // BigInt(3429868089329)) - Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4) - - A₂1 = convert(T, BigInt(0) // BigInt(1)) - A₂2 = convert(T, BigInt(546509042554) // BigInt(9152262712923)) - A₂3 = convert(T, BigInt(625707605167) // BigInt(5316659119056)) - A₂4 = convert(T, BigInt(582400652113) // BigInt(7078426004906)) - Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4) - - B1 = convert(T, BigInt(314199625218) // BigInt(7198350928319)) - B2 = convert(T, BigInt(6410344372641) // BigInt(17000082738695)) - B3 = convert(T, BigInt(292278564125) // BigInt(5593752632744)) - B4 = convert(T, BigInt(5010207514426) // BigInt(21876007855139)) - Bᵢ = SVector(B1, B2, B3, B4) - - B̂1 = convert(T, BigInt(1276689330531) // BigInt(10575835502045)) - B̂2 = convert(T, BigInt(267542835879) // BigInt(1241767155676)) - B̂3 = convert(T, BigInt(1564039648689) // BigInt(9024646069760)) - B̂4 = convert(T, BigInt(3243722451631) // BigInt(13364844673806)) - B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4) - - Bₗ = convert(T, BigInt(5597675544274) // BigInt(18784428342765)) - B̂ₗ = convert(T, BigInt(606464709716) // BigInt(2447238536635)) - - C1 = convert(T2, BigInt(4745337637855) // BigInt(22386579876409)) - C2 = convert(T2, - BigInt(6320253019873211389522417) // BigInt(10980921945492108365568747)) - C3 = convert(T2, - BigInt(231699760563456147635097088564862719039) // - BigInt(400094496217566390613617613962197753808)) - C4 = convert(T2, - BigInt(2565873674791335200443549967376635530873909687156071) // - BigInt(2970969302106648098855751120425897741072516011514170)) - Cᵢ = SVector(C1, C2, C3, C4) - - LowStorageRK3RPConstantCache{4, T, T2}(Aᵢ₁, Aᵢ₂, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) -end - -function alg_cache(alg::CKLLSRK54_3N_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - k = zero(rate_prototype) - uᵢ₋₁ = zero(u) - uᵢ₋₂ = zero(u) - fᵢ₋₂ = zero(rate_prototype) - gprev = zero(u) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = CKLLSRK54_3N_3RConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK3RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, fᵢ₋₂, gprev, fsalfirst, tmp, atmp, tab, - alg.stage_limiter!, alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::CKLLSRK54_3N_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - CKLLSRK54_3N_3RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function CKLLSRK85_4C_3RConstantCache(T, T2) - A₁1 = convert(T, BigInt(141236061735) // BigInt(3636543850841)) - A₁2 = convert(T, BigInt(7367658691349) // BigInt(25881828075080)) - A₁3 = convert(T, BigInt(6185269491390) // BigInt(13597512850793)) - A₁4 = convert(T, BigInt(2669739616339) // BigInt(18583622645114)) - A₁5 = convert(T, BigInt(42158992267337) // BigInt(9664249073111)) - A₁6 = convert(T, BigInt(970532350048) // BigInt(4459675494195)) - A₁7 = convert(T, BigInt(1415616989537) // BigInt(7108576874996)) - Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4, A₁5, A₁6, A₁7) - - A₂1 = convert(T, BigInt(0) // BigInt(1)) - A₂2 = convert(T, BigInt(-343061178215) // BigInt(2523150225462)) - A₂3 = convert(T, BigInt(-4057757969325) // BigInt(18246604264081)) - A₂4 = convert(T, BigInt(1415180642415) // BigInt(13311741862438)) - A₂5 = convert(T, BigInt(-93461894168145) // BigInt(25333855312294)) - A₂6 = convert(T, BigInt(7285104933991) // BigInt(14106269434317)) - A₂7 = convert(T, BigInt(-4825949463597) // BigInt(16828400578907)) - Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4, A₂5, A₂6, A₂7) - - B1 = convert(T, BigInt(514862045033) // BigInt(4637360145389)) - B2 = convert(T, BigInt(0) // BigInt(1)) - B3 = convert(T, BigInt(0) // BigInt(1)) - B4 = convert(T, BigInt(0) // BigInt(1)) - B5 = convert(T, BigInt(2561084526938) // BigInt(7959061818733)) - B6 = convert(T, BigInt(4857652849) // BigInt(7350455163355)) - B7 = convert(T, BigInt(1059943012790) // BigInt(2822036905401)) - Bᵢ = SVector(B1, B2, B3, B4, B5, B6, B7) - - B̂1 = convert(T, BigInt(1269299456316) // BigInt(16631323494719)) - B̂2 = convert(T, BigInt(0) // BigInt(1)) - B̂3 = convert(T, BigInt(2153976949307) // BigInt(22364028786708)) - B̂4 = convert(T, BigInt(2303038467735) // BigInt(18680122447354)) - B̂5 = convert(T, BigInt(7354111305649) // BigInt(15643939971922)) - B̂6 = convert(T, BigInt(768474111281) // BigInt(10081205039574)) - B̂7 = convert(T, BigInt(3439095334143) // BigInt(10786306938509)) - B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4, B̂5, B̂6, B̂7) - - Bₗ = convert(T, BigInt(2987336121747) // BigInt(15645656703944)) - B̂ₗ = convert(T, BigInt(-3808726110015) // BigInt(23644487528593)) - - C1 = convert(T2, BigInt(141236061735) // BigInt(3636543850841)) - C2 = convert(T2, - BigInt(4855329627204641469273019) // BigInt(32651870171503411731843480)) - C3 = convert(T2, - BigInt(395246570619540395679764439681768625174) // - BigInt(1150568172675067443707820382013045349637)) - C4 = convert(T2, - BigInt(103533040647279909858308372897770021461) // - BigInt(286797987459862321650077169609703051387)) - C5 = convert(T2, - BigInt(890342029406775514852349518244920625309) // - BigInt(1135377348321966192554675673174478190626)) - C6 = convert(T2, - BigInt(82180664649829640456237722943611531408) // - BigInt(97244490215364259564723087293866304345)) - C7 = convert(T2, - BigInt(1524044277359326675923410465291452002169116939509651) // - BigInt(4415279581486844959297591640758696961331751174567964)) - Cᵢ = SVector(C1, C2, C3, C4, C5, C6, C7) - - LowStorageRK3RPConstantCache{7, T, T2}(Aᵢ₁, Aᵢ₂, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) -end - -function alg_cache(alg::CKLLSRK85_4C_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - k = zero(rate_prototype) - uᵢ₋₁ = zero(u) - uᵢ₋₂ = zero(u) - fᵢ₋₂ = zero(rate_prototype) - gprev = zero(u) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = CKLLSRK85_4C_3RConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK3RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, fᵢ₋₂, gprev, fsalfirst, tmp, atmp, tab, - alg.stage_limiter!, alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::CKLLSRK85_4C_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - CKLLSRK85_4C_3RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function CKLLSRK85_4M_3RConstantCache(T, T2) - A₁1 = convert(T, BigInt(967290102210) // BigInt(6283494269639)) - A₁2 = convert(T, BigInt(852959821520) // BigInt(5603806251467)) - A₁3 = convert(T, BigInt(8043261511347) // BigInt(8583649637008)) - A₁4 = convert(T, BigInt(-115941139189) // BigInt(8015933834062)) - A₁5 = convert(T, BigInt(2151445634296) // BigInt(7749920058933)) - A₁6 = convert(T, BigInt(15619711431787) // BigInt(74684159414562)) - A₁7 = convert(T, BigInt(12444295717883) // BigInt(11188327299274)) - Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4, A₁5, A₁6, A₁7) - - A₂1 = convert(T, BigInt(0) // BigInt(1)) - A₂2 = convert(T, BigInt(475331134681) // BigInt(7396070923784)) - A₂3 = convert(T, BigInt(-8677837986029) // BigInt(16519245648862)) - A₂4 = convert(T, BigInt(2224500752467) // BigInt(10812521810777)) - A₂5 = convert(T, BigInt(1245361422071) // BigInt(3717287139065)) - A₂6 = convert(T, BigInt(1652079198131) // BigInt(3788458824028)) - A₂7 = convert(T, BigInt(-5225103653628) // BigInt(8584162722535)) - Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4, A₂5, A₂6, A₂7) - - B1 = convert(T, BigInt(83759458317) // BigInt(1018970565139)) - B2 = convert(T, BigInt(0) // BigInt(1)) - B3 = convert(T, BigInt(0) // BigInt(1)) - B4 = convert(T, BigInt(0) // BigInt(1)) - B5 = convert(T, BigInt(6968891091250) // BigInt(16855527649349)) - B6 = convert(T, BigInt(783521911849) // BigInt(8570887289572)) - B7 = convert(T, BigInt(3686104854613) // BigInt(11232032898210)) - Bᵢ = SVector(B1, B2, B3, B4, B5, B6, B7) - - B̂1 = convert(T, BigInt(-2632078767757) // BigInt(9365288548818)) - B̂2 = convert(T, BigInt(0) // BigInt(1)) - B̂3 = convert(T, BigInt(138832778584802) // BigInt(30360463697573)) - B̂4 = convert(T, BigInt(7424139574315) // BigInt(5603229049946)) - B̂5 = convert(T, BigInt(-32993229351515) // BigInt(6883415042289)) - B̂6 = convert(T, BigInt(-3927384735361) // BigInt(7982454543710)) - B̂7 = convert(T, BigInt(9224293159931) // BigInt(15708162311543)) - B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4, B̂5, B̂6, B̂7) - - Bₗ = convert(T, BigInt(517396786175) // BigInt(6104475356879)) - B̂ₗ = convert(T, BigInt(624338737541) // BigInt(7691046757191)) - - C1 = convert(T2, BigInt(967290102210) // BigInt(6283494269639)) - C2 = convert(T2, - BigInt(8972214919142352493858707) // BigInt(41446148478994088895191128)) - C3 = convert(T2, - BigInt(35682660731882055122214991891899678815) // - BigInt(72242678055272695781813348615158920272)) - C4 = convert(T2, - BigInt(24151963894889409757443700144610337197) // - BigInt(88316684951621554188239538678367088186)) - C5 = convert(T2, - BigInt(20396803294876689925555603189127802602) // - BigInt(29355195069529377650856010387665377655)) - C6 = convert(T2, - BigInt(104860372573190455963699691732496938387) // - BigInt(144152676952392296448858925279884773652)) - C7 = convert(T2, - BigInt(1648260218501227913212294426176971326433416596592133) // - BigInt(1649556119556299790473636959153132604082083356090490)) - Cᵢ = SVector(C1, C2, C3, C4, C5, C6, C7) - - LowStorageRK3RPConstantCache{7, T, T2}(Aᵢ₁, Aᵢ₂, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) -end - -function alg_cache(alg::CKLLSRK85_4M_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - k = zero(rate_prototype) - uᵢ₋₁ = zero(u) - uᵢ₋₂ = zero(u) - fᵢ₋₂ = zero(rate_prototype) - gprev = zero(u) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = CKLLSRK85_4M_3RConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK3RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, fᵢ₋₂, gprev, fsalfirst, tmp, atmp, tab, - alg.stage_limiter!, alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::CKLLSRK85_4M_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - CKLLSRK85_4M_3RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function CKLLSRK85_4P_3RConstantCache(T, T2) - A₁1 = convert(T, BigInt(1298271176151) // BigInt(60748409385661)) - A₁2 = convert(T, BigInt(14078610000243) // BigInt(41877490110127)) - A₁3 = convert(T, BigInt(553998884433) // BigInt(1150223130613)) - A₁4 = convert(T, BigInt(15658478150918) // BigInt(92423611770207)) - A₁5 = convert(T, BigInt(18843935397718) // BigInt(7227975568851)) - A₁6 = convert(T, BigInt(6206560082614) // BigInt(27846110321329)) - A₁7 = convert(T, BigInt(2841125392315) // BigInt(14844217636077)) - Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4, A₁5, A₁6, A₁7) - - A₂1 = convert(T, BigInt(0) // BigInt(1)) - A₂2 = convert(T, BigInt(-2491873887327) // BigInt(11519757507826)) - A₂3 = convert(T, BigInt(-3833614938189) // BigInt(14183712281236)) - A₂4 = convert(T, BigInt(628609886693) // BigInt(8177399110319)) - A₂5 = convert(T, BigInt(-4943723744483) // BigInt(2558074780976)) - A₂6 = convert(T, BigInt(1024000837540) // BigInt(1998038638351)) - A₂7 = convert(T, BigInt(-2492809296391) // BigInt(9064568868273)) - Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4, A₂5, A₂6, A₂7) - - B1 = convert(T, BigInt(346820227625) // BigInt(3124407780749)) - B2 = convert(T, BigInt(0) // BigInt(1)) - B3 = convert(T, BigInt(0) // BigInt(1)) - B4 = convert(T, BigInt(0) // BigInt(1)) - B5 = convert(T, BigInt(814249513470) // BigInt(2521483007009)) - B6 = convert(T, BigInt(195246859987) // BigInt(15831935944600)) - B7 = convert(T, BigInt(3570596951509) // BigInt(9788921605312)) - Bᵢ = SVector(B1, B2, B3, B4, B5, B6, B7) - - B̂1 = convert(T, BigInt(679447319381) // BigInt(8240332772531)) - B̂2 = convert(T, BigInt(0) // BigInt(1)) - B̂3 = convert(T, BigInt(798472430005) // BigInt(13882421602211)) - B̂4 = convert(T, BigInt(972791992243) // BigInt(13597677393897)) - B̂5 = convert(T, BigInt(2994516937385) // BigInt(6097853295694)) - B̂6 = convert(T, BigInt(1424705874463) // BigInt(19211220871144)) - B̂7 = convert(T, BigInt(11199564863291) // BigInt(35136367926059)) - B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4, B̂5, B̂6, B̂7) - - Bₗ = convert(T, BigInt(1886338382073) // BigInt(9981671730680)) - B̂ₗ = convert(T, BigInt(-1307718103703) // BigInt(13694144003901)) - - C1 = convert(T2, BigInt(1298271176151) // BigInt(60748409385661)) - C2 = convert(T2, - BigInt(57828749177833338114741189) // BigInt(482418531105044571804353902)) - C3 = convert(T2, - BigInt(16431909216114342992530887716659137419) // - BigInt(50972944352640941110022041298448213332)) - C4 = convert(T2, - BigInt(843711271601954807241466442429582743082) // - BigInt(2361379786784371499429045948205315798717)) - C5 = convert(T2, - BigInt(45377346645618697840609101263059649515) // - BigInt(57769368855607143441437855651622233424)) - C6 = convert(T2, - BigInt(147132600561369761792017800077859262701) // - BigInt(173834563932749284125206995856250290771)) - C7 = convert(T2, - BigInt(123785620236259768586332555932209432529705897037921) // - BigInt(353351523019265026737831367789312912172448045683187)) - Cᵢ = SVector(C1, C2, C3, C4, C5, C6, C7) - - LowStorageRK3RPConstantCache{7, T, T2}(Aᵢ₁, Aᵢ₂, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) -end - -function alg_cache(alg::CKLLSRK85_4P_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - k = zero(rate_prototype) - uᵢ₋₁ = zero(u) - uᵢ₋₂ = zero(u) - fᵢ₋₂ = zero(rate_prototype) - gprev = zero(u) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = CKLLSRK85_4P_3RConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK3RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, fᵢ₋₂, gprev, fsalfirst, tmp, atmp, tab, - alg.stage_limiter!, alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::CKLLSRK85_4P_3R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - CKLLSRK85_4P_3RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -# 4R+ low storage methods introduced by van der Houwen -@cache struct LowStorageRK4RPCache{uType, rateType, uNoUnitsType, TabType, StageLimiter, - StepLimiter, Thread} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - uᵢ₋₁::uType - uᵢ₋₂::uType - uᵢ₋₃::uType - fᵢ₋₂::rateType - fᵢ₋₃::rateType - gprev::uType - fsalfirst::rateType - tmp::uType - atmp::uNoUnitsType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct LowStorageRK4RPConstantCache{N, T, T2} <: OrdinaryDiffEqConstantCache - Aᵢ₁::SVector{N, T} - Aᵢ₂::SVector{N, T} - Aᵢ₃::SVector{N, T} - Bₗ::T - B̂ₗ::T - Bᵢ::SVector{N, T} - B̂ᵢ::SVector{N, T} - Cᵢ::SVector{N, T2} -end - -function CKLLSRK54_3N_4RConstantCache(T, T2) - A₁1 = convert(T, BigInt(9435338793489) // BigInt(32856462503258)) - A₁2 = convert(T, BigInt(6195609865473) // BigInt(14441396468602)) - A₁3 = convert(T, BigInt(7502925572378) // BigInt(28098850972003)) - A₁4 = convert(T, BigInt(4527781290407) // BigInt(9280887680514)) - Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4) - - A₂1 = convert(T, BigInt(0) // BigInt(1)) - A₂2 = convert(T, BigInt(2934593324920) // BigInt(16923654741811)) - A₂3 = convert(T, BigInt(16352725096886) // BigInt(101421723321009)) - A₂4 = convert(T, BigInt(3004243580591) // BigInt(16385320447374)) - Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4) - - A₃1 = convert(T, BigInt(0) // BigInt(1)) - A₃2 = convert(T, BigInt(0) // BigInt(1)) - A₃3 = convert(T, BigInt(390352446067) // BigInt(5989890148791)) - A₃4 = convert(T, BigInt(902830387041) // BigInt(8154716972155)) - Aᵢ₃ = SVector(A₃1, A₃2, A₃3, A₃4) - - B1 = convert(T, BigInt(929310922418) // BigInt(8329727308495)) - B2 = convert(T, BigInt(4343420149496) // BigInt(15735497610667)) - B3 = convert(T, BigInt(885252399220) // BigInt(9490460854667)) - B4 = convert(T, BigInt(3341719902227) // BigInt(13464012733180)) - Bᵢ = SVector(B1, B2, B3, B4) - - B̂1 = convert(T, BigInt(2929323122013) // BigInt(17725327880387)) - B̂2 = convert(T, BigInt(4379799101587) // BigInt(35838171763617)) - B̂3 = convert(T, BigInt(2267325134734) // BigInt(9725002913543)) - B̂4 = convert(T, BigInt(1519467056643) // BigInt(5852430786130)) - B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4) - - Bₗ = convert(T, BigInt(2131913067577) // BigInt(7868783702050)) - B̂ₗ = convert(T, BigInt(3636375423974) // BigInt(16547514622827)) - - C1 = convert(T2, BigInt(9435338793489) // BigInt(32856462503258)) - C2 = convert(T2, - BigInt(147231987957505837822553443) // BigInt(244401207824228867478118222)) - C3 = convert(T2, - BigInt(401086457089554669663078760253749450489) // - BigInt(812866282711293513804077001645679258017)) - C4 = convert(T2, - BigInt(153823244836258719400905156342054669945035476219421) // - BigInt(172160249040778711548900853819650745575758693592285)) - Cᵢ = SVector(C1, C2, C3, C4) - - LowStorageRK4RPConstantCache{4, T, T2}(Aᵢ₁, Aᵢ₂, Aᵢ₃, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) -end - -function alg_cache(alg::CKLLSRK54_3N_4R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - k = zero(rate_prototype) - uᵢ₋₁ = zero(u) - uᵢ₋₂ = zero(u) - uᵢ₋₃ = zero(u) - fᵢ₋₂ = zero(rate_prototype) - fᵢ₋₃ = zero(rate_prototype) - gprev = zero(u) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = CKLLSRK54_3N_4RConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK4RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, uᵢ₋₃, fᵢ₋₂, fᵢ₋₃, gprev, fsalfirst, tmp, - atmp, tab, alg.stage_limiter!, alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::CKLLSRK54_3N_4R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - CKLLSRK54_3N_4RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function CKLLSRK54_3M_4RConstantCache(T, T2) - A₁1 = convert(T, BigInt(7142524119) // BigInt(20567653057)) - A₁2 = convert(T, BigInt(20567653057) // BigInt(89550000000)) - A₁3 = convert(T, BigInt(7407775) // BigInt(2008982)) - A₁4 = convert(T, BigInt(-4577300) // BigInt(867302297)) - Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4) - - A₂1 = convert(T, BigInt(0) // BigInt(1)) - A₂2 = convert(T, BigInt(15198616943) // BigInt(89550000000)) - A₂3 = convert(T, BigInt(-226244183627) // BigInt(80359280000)) - A₂4 = convert(T, BigInt(33311687500) // BigInt(8703531091)) - Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4) - - A₃1 = convert(T, BigInt(0) // BigInt(1)) - A₃2 = convert(T, BigInt(0) // BigInt(1)) - A₃3 = convert(T, BigInt(9890667227) // BigInt(80359280000)) - A₃4 = convert(T, BigInt(-20567653057) // BigInt(6979191486)) - Aᵢ₃ = SVector(A₃1, A₃2, A₃3, A₃4) - - B1 = convert(T, BigInt(297809) // BigInt(2384418)) - B2 = convert(T, BigInt(0) // BigInt(1)) - B3 = convert(T, BigInt(156250000) // BigInt(270591503)) - B4 = convert(T, BigInt(5030000) // BigInt(888933)) - Bᵢ = SVector(B1, B2, B3, B4) - - B̂1 = convert(T, BigInt(121286694859) // BigInt(931793198518)) - B̂2 = convert(T, BigInt(0) // BigInt(1)) - B̂3 = convert(T, BigInt(9680751416357) // BigInt(17201392077364)) - B̂4 = convert(T, BigInt(6633076090000) // BigInt(1042143269349)) - B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4) - - Bₗ = convert(T, BigInt(-2927) // BigInt(546)) - B̂ₗ = convert(T, BigInt(-127961558623) // BigInt(21123456354)) - - C1 = convert(T2, BigInt(7142524119) // BigInt(20567653057)) - C2 = convert(T2, BigInt(1997) // BigInt(5000)) - C3 = convert(T2, BigInt(199) // BigInt(200)) - C4 = convert(T2, BigInt(1) // BigInt(1)) - Cᵢ = SVector(C1, C2, C3, C4) - - LowStorageRK4RPConstantCache{4, T, T2}(Aᵢ₁, Aᵢ₂, Aᵢ₃, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) -end - -function alg_cache(alg::CKLLSRK54_3M_4R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - k = zero(rate_prototype) - uᵢ₋₁ = zero(u) - uᵢ₋₂ = zero(u) - uᵢ₋₃ = zero(u) - fᵢ₋₂ = zero(rate_prototype) - fᵢ₋₃ = zero(rate_prototype) - gprev = zero(u) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = CKLLSRK54_3M_4RConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK4RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, uᵢ₋₃, fᵢ₋₂, fᵢ₋₃, gprev, fsalfirst, tmp, - atmp, tab, alg.stage_limiter!, alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::CKLLSRK54_3M_4R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - CKLLSRK54_3M_4RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function CKLLSRK65_4M_4RConstantCache(T, T2) - A₁1 = convert(T, BigInt(1811061732419) // BigInt(6538712036350)) - A₁2 = convert(T, BigInt(936386506953) // BigInt(6510757757683)) - A₁3 = convert(T, BigInt(8253430823511) // BigInt(9903985211908)) - A₁4 = convert(T, BigInt(4157325866175) // BigInt(11306150349782)) - A₁5 = convert(T, BigInt(3299942024581) // BigInt(13404534943033)) - Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4, A₁5) - - A₂1 = convert(T, BigInt(0) // BigInt(1)) - A₂2 = convert(T, BigInt(968127049827) // BigInt(6993254963231)) - A₂3 = convert(T, BigInt(-4242729801665) // BigInt(12001587034923)) - A₂4 = convert(T, BigInt(1960956671631) // BigInt(3017447659538)) - A₂5 = convert(T, BigInt(2088737530132) // BigInt(14638867961951)) - Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4, A₂5) - - A₃1 = convert(T, BigInt(0) // BigInt(1)) - A₃2 = convert(T, BigInt(0) // BigInt(1)) - A₃3 = convert(T, BigInt(332803037697) // BigInt(7529436905221)) - A₃4 = convert(T, BigInt(-19590089343957) // BigInt(51581831082203)) - A₃5 = convert(T, BigInt(3811366828049) // BigInt(10653298326636)) - Aᵢ₃ = SVector(A₃1, A₃2, A₃3, A₃4, A₃5) - - B1 = convert(T, BigInt(1437717300581) // BigInt(14622899446031)) - B2 = convert(T, BigInt(0) // BigInt(1)) - B3 = convert(T, BigInt(3070006287879) // BigInt(9321175678070)) - B4 = convert(T, BigInt(2276970273632) // BigInt(7940670647385)) - B5 = convert(T, BigInt(-1056149936631) // BigInt(7427907425983)) - Bᵢ = SVector(B1, B2, B3, B4, B5) - - B̂1 = convert(T, BigInt(399352205828) // BigInt(2843676810815)) - B̂2 = convert(T, BigInt(0) // BigInt(1)) - B̂3 = convert(T, BigInt(460449895996) // BigInt(4301836608005)) - B̂4 = convert(T, BigInt(15965746118666) // BigInt(21690343195681)) - B̂5 = convert(T, BigInt(-19281717001664) // BigInt(29911607353389)) - B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4, B̂5) - - Bₗ = convert(T, BigInt(2571845656138) // BigInt(6012342010435)) - B̂ₗ = convert(T, BigInt(5058427127221) // BigInt(7651806618075)) - - C1 = convert(T2, BigInt(1811061732419) // BigInt(6538712036350)) - C2 = convert(T2, - BigInt(12851630287335503073915984) // BigInt(45531389003311376172753773)) - C3 = convert(T2, - BigInt(468994575306978457607500930904657513641) // - BigInt(894975528626103930282351283769588361564)) - C4 = convert(T2, - BigInt(4735520442856752193881763097298943558246492547269018) // - BigInt(6433166018040288425494806218280078848936316641536447)) - C5 = convert(T2, - BigInt(25828983228256103590265182981008154883102570637999497) // - BigInt(30568689961801519095090666149791133914967119469889228)) - Cᵢ = SVector(C1, C2, C3, C4, C5) - - LowStorageRK4RPConstantCache{5, T, T2}(Aᵢ₁, Aᵢ₂, Aᵢ₃, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) -end - -function alg_cache(alg::CKLLSRK65_4M_4R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - k = zero(rate_prototype) - uᵢ₋₁ = zero(u) - uᵢ₋₂ = zero(u) - uᵢ₋₃ = zero(u) - fᵢ₋₂ = zero(rate_prototype) - fᵢ₋₃ = zero(rate_prototype) - gprev = zero(u) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = CKLLSRK65_4M_4RConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK4RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, uᵢ₋₃, fᵢ₋₂, fᵢ₋₃, gprev, fsalfirst, tmp, - atmp, tab, alg.stage_limiter!, alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::CKLLSRK65_4M_4R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - CKLLSRK65_4M_4RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function CKLLSRK85_4FM_4RConstantCache(T, T2) - A₁1 = convert(T, BigInt(319960152914) // BigInt(39034091721739)) - A₁2 = convert(T, BigInt(16440040368765) // BigInt(7252463661539)) - A₁3 = convert(T, BigInt(1381950791880) // BigInt(6599155371617)) - A₁4 = convert(T, BigInt(18466735994895) // BigInt(7394178462407)) - A₁5 = convert(T, BigInt(2786140924985) // BigInt(14262827431161)) - A₁6 = convert(T, BigInt(28327099865656) // BigInt(21470840267743)) - A₁7 = convert(T, BigInt(0) // BigInt(1)) - Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4, A₁5, A₁6, A₁7) - - A₂1 = convert(T, BigInt(0) // BigInt(1)) - A₂2 = convert(T, BigInt(-16195115415565) // BigInt(7808461210678)) - A₂3 = convert(T, BigInt(-1316066362688) // BigInt(10261382634081)) - A₂4 = convert(T, BigInt(-23893000145797) // BigInt(9614512377075)) - A₂5 = convert(T, BigInt(6556893593075) // BigInt(12530787773541)) - A₂6 = convert(T, BigInt(-5015572218207) // BigInt(5719938983072)) - A₂7 = convert(T, BigInt(0) // BigInt(1)) - Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4, A₂5, A₂6, A₂7) - - A₃1 = convert(T, BigInt(0) // BigInt(1)) - A₃2 = convert(T, BigInt(0) // BigInt(1)) - A₃3 = convert(T, BigInt(334167490531) // BigInt(1677017272502)) - A₃4 = convert(T, BigInt(4579492417936) // BigInt(7930641522963)) - A₃5 = convert(T, BigInt(-2255846922213) // BigInt(30066310003000)) - A₃6 = convert(T, BigInt(3212719728776) // BigInt(7037340048693)) - A₃7 = convert(T, BigInt(0) // BigInt(1)) - Aᵢ₃ = SVector(A₃1, A₃2, A₃3, A₃4, A₃5, A₃6, A₃7) - - B1 = convert(T, BigInt(1147876221211) // BigInt(13910763665259)) - B2 = convert(T, BigInt(0) // BigInt(1)) - B3 = convert(T, BigInt(182134362610) // BigInt(9852075053293)) - B4 = convert(T, BigInt(3396705055007) // BigInt(8495597747463)) - B5 = convert(T, BigInt(363006049056) // BigInt(22366003978609)) - B6 = convert(T, BigInt(6078825123673) // BigInt(15200143133108)) - B7 = convert(T, BigInt(583593328277) // BigInt(7028929464160)) - Bᵢ = SVector(B1, B2, B3, B4, B5, B6, B7) - - B̂1 = convert(T, BigInt(2023383632057) // BigInt(26525303340911)) - B̂2 = convert(T, BigInt(0) // BigInt(1)) - B̂3 = convert(T, BigInt(480990062147) // BigInt(12694528747923)) - B̂4 = convert(T, BigInt(14502014597821) // BigInt(36979005529861)) - B̂5 = convert(T, BigInt(-3883966523914) // BigInt(63014133260123)) - B̂6 = convert(T, BigInt(1643296191892) // BigInt(3432451463915)) - B̂7 = convert(T, BigInt(2576984903812) // BigInt(11692468803935)) - B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4, B̂5, B̂6, B̂7) - - Bₗ = convert(T, BigInt(0) // BigInt(1)) - B̂ₗ = convert(T, BigInt(-2393889703871) // BigInt(16641202878460)) - - C1 = convert(T2, BigInt(319960152914) // BigInt(39034091721739)) - C2 = convert(T2, - BigInt(10916931475666701983218135) // BigInt(56630581182979020764713442)) - C3 = convert(T2, - BigInt(31845189551971545944223680050155078355) // - BigInt(113561670251926090809438891701398790454)) - C4 = convert(T2, - BigInt(585892393366635581491792016142825500310911249371223) // - BigInt(871432942801472160798333604371480303171919616321325)) - C5 = convert(T2, - BigInt(6030664727234996630401450278844701818157369618311237) // - BigInt(8305630304762506786823923305099106403075216590053000)) - C6 = convert(T2, - BigInt(190737487565451971541550207118478711767748834018874068552898297) // - BigInt(190737487565451971541550204260359567420033302718711745345318816)) - C7 = convert(T2, - BigInt(194373043039840208108258122050794558876) // - BigInt(388106905684556737922360607016380520227)) - Cᵢ = SVector(C1, C2, C3, C4, C5, C6, C7) - - LowStorageRK4RPConstantCache{7, T, T2}(Aᵢ₁, Aᵢ₂, Aᵢ₃, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) -end - -function alg_cache(alg::CKLLSRK85_4FM_4R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - k = zero(rate_prototype) - uᵢ₋₁ = zero(u) - uᵢ₋₂ = zero(u) - uᵢ₋₃ = zero(u) - fᵢ₋₂ = zero(rate_prototype) - fᵢ₋₃ = zero(rate_prototype) - gprev = zero(u) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = CKLLSRK85_4FM_4RConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK4RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, uᵢ₋₃, fᵢ₋₂, fᵢ₋₃, gprev, fsalfirst, tmp, - atmp, tab, alg.stage_limiter!, alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::CKLLSRK85_4FM_4R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - CKLLSRK85_4FM_4RConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) -end - -# 5R+ low storage methods introduced by van der Houwen -@cache struct LowStorageRK5RPCache{uType, rateType, uNoUnitsType, TabType, StageLimiter, - StepLimiter, Thread} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - uᵢ₋₁::uType - uᵢ₋₂::uType - uᵢ₋₃::uType - uᵢ₋₄::uType - fᵢ₋₂::rateType - fᵢ₋₃::rateType - fᵢ₋₄::rateType - gprev::uType - fsalfirst::rateType - tmp::uType - atmp::uNoUnitsType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct LowStorageRK5RPConstantCache{N, T, T2} <: OrdinaryDiffEqConstantCache - Aᵢ₁::SVector{N, T} - Aᵢ₂::SVector{N, T} - Aᵢ₃::SVector{N, T} - Aᵢ₄::SVector{N, T} - Bₗ::T - B̂ₗ::T - Bᵢ::SVector{N, T} - B̂ᵢ::SVector{N, T} - Cᵢ::SVector{N, T2} -end - -function CKLLSRK75_4M_5RConstantCache(T, T2) - A₁1 = convert(T, BigInt(984894634849) // BigInt(6216792334776)) - A₁2 = convert(T, BigInt(984894634849) // BigInt(5526037630912)) - A₁3 = convert(T, BigInt(13256335809797) // BigInt(10977774807827)) - A₁4 = convert(T, BigInt(5386479425293) // BigInt(11045691190948)) - A₁5 = convert(T, BigInt(-1717767168952) // BigInt(11602237717369)) - A₁6 = convert(T, BigInt(-10054679524430) // BigInt(10306851287569)) - Aᵢ₁ = SVector(A₁1, A₁2, A₁3, A₁4, A₁5, A₁6) - - A₂1 = convert(T, BigInt(0) // BigInt(1)) - A₂2 = convert(T, BigInt(890852251480) // BigInt(14995156510369)) - A₂3 = convert(T, BigInt(-18544705752398) // BigInt(18426539884027)) - A₂4 = convert(T, BigInt(1115398761892) // BigInt(28058504699217)) - A₂5 = convert(T, BigInt(5538441135605) // BigInt(13014942352969)) - A₂6 = convert(T, BigInt(23855853001162) // BigInt(20968156556405)) - Aᵢ₂ = SVector(A₂1, A₂2, A₂3, A₂4, A₂5, A₂6) - - A₃1 = convert(T, BigInt(0) // BigInt(1)) - A₃2 = convert(T, BigInt(0) // BigInt(1)) - A₃3 = convert(T, BigInt(1722683259617) // BigInt(5669183367476)) - A₃4 = convert(T, BigInt(342961171087) // BigInt(6505721096888)) - A₃5 = convert(T, BigInt(-14472869285404) // BigInt(19736045536601)) - A₃6 = convert(T, BigInt(-8169744035288) // BigInt(5424738459363)) - Aᵢ₃ = SVector(A₃1, A₃2, A₃3, A₃4, A₃5, A₃6) - - A₄1 = convert(T, BigInt(0) // BigInt(1)) - A₄2 = convert(T, BigInt(0) // BigInt(1)) - A₄3 = convert(T, BigInt(0) // BigInt(1)) - A₄4 = convert(T, BigInt(762111618422) // BigInt(5198184381557)) - A₄5 = convert(T, BigInt(2896263505307) // BigInt(6364015805096)) - A₄6 = convert(T, BigInt(60049403517654) // BigInt(26787923986853)) - Aᵢ₄ = SVector(A₄1, A₄2, A₄3, A₄4, A₄5, A₄6) - - B1 = convert(T, BigInt(1008141064049) // BigInt(9867084721348)) - B2 = convert(T, BigInt(0) // BigInt(1)) - B3 = convert(T, BigInt(8222186491841) // BigInt(18352662300888)) - B4 = convert(T, BigInt(514621697208) // BigInt(8712119383831)) - B5 = convert(T, BigInt(1808964136873) // BigInt(4546032443428)) - B6 = convert(T, BigInt(-362754645297) // BigInt(3989911846061)) - Bᵢ = SVector(B1, B2, B3, B4, B5, B6) - - B̂1 = convert(T, BigInt(1633918545125) // BigInt(12016465907206)) - B̂2 = convert(T, BigInt(0) // BigInt(1)) - B̂3 = convert(T, BigInt(5614864639673) // BigInt(10804025076427)) - B̂4 = convert(T, BigInt(229286380958) // BigInt(6920724258831)) - B̂5 = convert(T, BigInt(5960415897193) // BigInt(14726168927560)) - B̂6 = convert(T, BigInt(-4042532386559) // BigInt(22820216867423)) - B̂ᵢ = SVector(B̂1, B̂2, B̂3, B̂4, B̂5, B̂6) - - Bₗ = convert(T, BigInt(599706619333) // BigInt(7161178965783)) - B̂ₗ = convert(T, BigInt(930770261899) // BigInt(11134660916874)) - - C1 = convert(T2, BigInt(984894634849) // BigInt(6216792334776)) - C2 = convert(T2, - BigInt(19691532261044641782999041) // BigInt(82863799157714161922926528)) - C3 = convert(T2, - BigInt(579140763944732527715749105230082493541) // - BigInt(1146776047854201324825397010814855303604)) - C4 = convert(T2, - BigInt(1904235205010770769196995566618512437342488019008993) // - BigInt(2620260981179174237577004881164696841381017975634264)) - C5 = convert(T2, - BigInt(4745866356039511505795256436748010529615723318082554645080208661) // - BigInt(46784744516176933667763632070461960177241008032286254911869725672)) - C6 = convert(T2, - BigInt(309879595293732553069368807532997606922999693101104106883289601491) // - BigInt(309879595293732553069368804305686805880909932549908997963514738540)) - Cᵢ = SVector(C1, C2, C3, C4, C5, C6) - - LowStorageRK5RPConstantCache{6, T, T2}(Aᵢ₁, Aᵢ₂, Aᵢ₃, Aᵢ₄, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ) -end - -function alg_cache(alg::CKLLSRK75_4M_5R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - k = zero(rate_prototype) - uᵢ₋₁ = zero(u) - uᵢ₋₂ = zero(u) - uᵢ₋₃ = zero(u) - uᵢ₋₄ = zero(u) - fᵢ₋₂ = zero(rate_prototype) - fᵢ₋₃ = zero(rate_prototype) - fᵢ₋₄ = zero(rate_prototype) - gprev = zero(u) - if calck - fsalfirst = zero(rate_prototype) - else - fsalfirst = k - end - tab = CKLLSRK75_4M_5RConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - LowStorageRK5RPCache(u, uprev, k, uᵢ₋₁, uᵢ₋₂, uᵢ₋₃, uᵢ₋₄, fᵢ₋₂, fᵢ₋₃, fᵢ₋₄, gprev, - fsalfirst, tmp, atmp, tab, alg.stage_limiter!, alg.step_limiter!, - alg.thread) -end - -function alg_cache(alg::CKLLSRK75_4M_5R, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - CKLLSRK75_4M_5RConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end From b011f36f94ab251565da435bc57dcf20617a2faf Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:54:05 -0400 Subject: [PATCH 06/71] Delete src/caches/rkc_caches.jl --- src/caches/rkc_caches.jl | 348 --------------------------------------- 1 file changed, 348 deletions(-) delete mode 100644 src/caches/rkc_caches.jl diff --git a/src/caches/rkc_caches.jl b/src/caches/rkc_caches.jl deleted file mode 100644 index 2594804d1d..0000000000 --- a/src/caches/rkc_caches.jl +++ /dev/null @@ -1,348 +0,0 @@ -mutable struct ROCK2ConstantCache{T, T2, zType} <: OrdinaryDiffEqConstantCache - ms::SVector{46, Int} - fp1::SVector{46, T} - fp2::SVector{46, T} - recf::Vector{T2} - zprev::zType - mdeg::Int - deg_index::Int - start::Int - min_stage::Int - max_stage::Int -end -@cache struct ROCK2Cache{uType, rateType, uNoUnitsType, C <: ROCK2ConstantCache} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - uᵢ₋₁::uType - uᵢ₋₂::uType - tmp::uType - atmp::uNoUnitsType - fsalfirst::rateType - k::rateType - constantcache::C -end - -function alg_cache(alg::ROCK2, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - constantcache = ROCK2ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits), - u) - uᵢ₋₁ = zero(u) - uᵢ₋₂ = zero(u) - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - fsalfirst = zero(rate_prototype) - k = zero(rate_prototype) - ROCK2Cache(u, uprev, uᵢ₋₁, uᵢ₋₂, tmp, atmp, fsalfirst, k, constantcache) -end - -function alg_cache(alg::ROCK2, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - ROCK2ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits), u) -end - -mutable struct ROCK4ConstantCache{T, T2, T3, T4, zType} <: OrdinaryDiffEqConstantCache - ms::SVector{50, Int} - fpa::Vector{T} - fpb::Vector{T2} - fpbe::Vector{T3} - recf::Vector{T4} - zprev::zType - mdeg::Int - deg_index::Int - start::Int - min_stage::Int - max_stage::Int -end - -@cache struct ROCK4Cache{uType, rateType, uNoUnitsType, C <: ROCK4ConstantCache} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - uᵢ₋₁::uType - uᵢ₋₂::uType - uᵢ₋₃::uType - tmp::uType - atmp::uNoUnitsType - fsalfirst::rateType - k::rateType - constantcache::C -end - -function alg_cache(alg::ROCK4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - constantcache = ROCK4ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits), - u) - uᵢ₋₁ = zero(u) - uᵢ₋₂ = zero(u) - uᵢ₋₃ = zero(u) - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - fsalfirst = zero(rate_prototype) - k = zero(rate_prototype) - ROCK4Cache(u, uprev, uᵢ₋₁, uᵢ₋₂, uᵢ₋₃, tmp, atmp, fsalfirst, k, constantcache) -end - -function alg_cache(alg::ROCK4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - ROCK4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits), u) -end - -mutable struct RKCConstantCache{zType} <: OrdinaryDiffEqConstantCache - #to match the types to call maxeig! - zprev::zType -end -@cache struct RKCCache{uType, rateType, uNoUnitsType, C <: RKCConstantCache} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - gprev::uType - gprev2::uType - tmp::uType - atmp::uNoUnitsType - fsalfirst::rateType - k::rateType - constantcache::C -end - -function alg_cache(alg::RKC, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - constantcache = RKCConstantCache(u) - gprev = zero(u) - gprev2 = zero(u) - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - fsalfirst = zero(rate_prototype) - k = zero(rate_prototype) - RKCCache(u, uprev, gprev, gprev2, tmp, atmp, fsalfirst, k, constantcache) -end - -function alg_cache(alg::RKC, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - RKCConstantCache(u) -end - -@cache mutable struct IRKCConstantCache{uType, rateType, N} <: OrdinaryDiffEqConstantCache - minm::Int - zprev::uType - nlsolver::N - du₁::rateType - du₂::rateType -end - -@cache mutable struct IRKCCache{uType, rateType, uNoUnitsType, N, C <: IRKCConstantCache} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - gprev::uType - gprev2::uType - fsalfirst::rateType - f1ⱼ₋₁::rateType - f1ⱼ₋₂::rateType - f2ⱼ₋₁::rateType - atmp::uNoUnitsType - nlsolver::N - du₁::rateType - du₂::rateType - constantcache::C -end - -function alg_cache(alg::IRKC, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - γ, c = 1.0, 1.0 - nlsolver = build_nlsolver(alg, u, uprev, p, t, dt, f, rate_prototype, uEltypeNoUnits, - uBottomEltypeNoUnits, tTypeNoUnits, γ, c, Val(false)) - zprev = u - du₁ = rate_prototype - du₂ = rate_prototype - IRKCConstantCache(50, zprev, nlsolver, du₁, du₂) -end - -function alg_cache(alg::IRKC, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - γ, c = 1.0, 1.0 - nlsolver = build_nlsolver(alg, u, uprev, p, t, dt, f, rate_prototype, uEltypeNoUnits, - uBottomEltypeNoUnits, tTypeNoUnits, γ, c, Val(true)) - - gprev = zero(u) - gprev2 = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - fsalfirst = zero(rate_prototype) - zprev = zero(u) - f1ⱼ₋₁ = zero(rate_prototype) - f1ⱼ₋₂ = zero(rate_prototype) - f2ⱼ₋₁ = zero(rate_prototype) - du₁ = zero(rate_prototype) - du₂ = zero(rate_prototype) - constantcache = IRKCConstantCache(50, zprev, nlsolver, du₁, du₂) - IRKCCache(u, uprev, gprev, gprev2, fsalfirst, f1ⱼ₋₁, f1ⱼ₋₂, f2ⱼ₋₁, atmp, nlsolver, du₁, - du₂, constantcache) -end - -mutable struct ESERK4ConstantCache{T, zType} <: OrdinaryDiffEqConstantCache - ms::SVector{46, Int} - Cᵤ::SVector{4, Int} - Cₑ::SVector{4, Int} - zprev::zType - Bᵢ::Vector{T} - mdeg::Int - start::Int - internal_deg::Int -end - -@cache struct ESERK4Cache{uType, rateType, uNoUnitsType, C <: ESERK4ConstantCache} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - uᵢ::uType - uᵢ₋₁::uType - uᵢ₋₂::uType - Sᵢ::uType - tmp::uType - atmp::uNoUnitsType - fsalfirst::rateType - k::rateType - constantcache::C -end - -function alg_cache(alg::ESERK4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - constantcache = ESERK4ConstantCache(u) - uᵢ = zero(u) - uᵢ₋₁ = zero(u) - uᵢ₋₂ = zero(u) - Sᵢ = zero(u) - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - fsalfirst = zero(rate_prototype) - k = zero(rate_prototype) - ESERK4Cache(u, uprev, uᵢ, uᵢ₋₁, uᵢ₋₂, Sᵢ, tmp, atmp, fsalfirst, k, constantcache) -end - -function alg_cache(alg::ESERK4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - ESERK4ConstantCache(u) -end - -mutable struct ESERK5ConstantCache{T, zType} <: OrdinaryDiffEqConstantCache - ms::SVector{49, Int} - Cᵤ::SVector{5, Int} - Cₑ::SVector{5, Int} - zprev::zType - Bᵢ::Vector{T} - mdeg::Int - start::Int - internal_deg::Int -end - -@cache struct ESERK5Cache{uType, rateType, uNoUnitsType, C <: ESERK5ConstantCache} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - uᵢ::uType - uᵢ₋₁::uType - uᵢ₋₂::uType - Sᵢ::uType - tmp::uType - atmp::uNoUnitsType - fsalfirst::rateType - k::rateType - constantcache::C -end - -function alg_cache(alg::ESERK5, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - constantcache = ESERK5ConstantCache(u) - uᵢ = zero(u) - uᵢ₋₁ = zero(u) - uᵢ₋₂ = zero(u) - Sᵢ = zero(u) - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - fsalfirst = zero(rate_prototype) - k = zero(rate_prototype) - ESERK5Cache(u, uprev, uᵢ, uᵢ₋₁, uᵢ₋₂, Sᵢ, tmp, atmp, fsalfirst, k, constantcache) -end - -function alg_cache(alg::ESERK5, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - ESERK5ConstantCache(u) -end - -mutable struct SERK2ConstantCache{T, zType} <: OrdinaryDiffEqConstantCache - ms::SVector{11, Int} - zprev::zType - Bᵢ::Vector{T} - mdeg::Int - start::Int - internal_deg::Int -end - -@cache struct SERK2Cache{uType, rateType, uNoUnitsType, C <: SERK2ConstantCache} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - uᵢ₋₁::uType - uᵢ₋₂::uType - Sᵢ::uType - tmp::uType - atmp::uNoUnitsType - fsalfirst::rateType - k::rateType - constantcache::C -end - -function alg_cache(alg::SERK2, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - constantcache = SERK2ConstantCache(u) - uᵢ₋₁ = zero(u) - uᵢ₋₂ = zero(u) - Sᵢ = zero(u) - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - fsalfirst = zero(rate_prototype) - k = zero(rate_prototype) - SERK2Cache(u, uprev, uᵢ₋₁, uᵢ₋₂, Sᵢ, tmp, atmp, fsalfirst, k, constantcache) -end - -function alg_cache(alg::SERK2, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SERK2ConstantCache(u) -end From 075885b76e884d0708aa02c01678ee5b8148f51d Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:54:58 -0400 Subject: [PATCH 07/71] Delete src/caches/rkn_caches.jl --- src/caches/rkn_caches.jl | 683 --------------------------------------- 1 file changed, 683 deletions(-) delete mode 100644 src/caches/rkn_caches.jl diff --git a/src/caches/rkn_caches.jl b/src/caches/rkn_caches.jl deleted file mode 100644 index 7582e1f498..0000000000 --- a/src/caches/rkn_caches.jl +++ /dev/null @@ -1,683 +0,0 @@ -@cache struct Nystrom4Cache{uType, rateType, reducedRateType} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - k₂::reducedRateType - k₃::reducedRateType - k₄::reducedRateType - k::rateType - tmp::uType -end - -# struct Nystrom4ConstantCache <: OrdinaryDiffEqConstantCache end - -function alg_cache(alg::Nystrom4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - reduced_rate_prototype = rate_prototype.x[2] - k₁ = zero(rate_prototype) - k₂ = zero(reduced_rate_prototype) - k₃ = zero(reduced_rate_prototype) - k₄ = zero(reduced_rate_prototype) - k = zero(rate_prototype) - tmp = zero(u) - Nystrom4Cache(u, uprev, k₁, k₂, k₃, k₄, k, tmp) -end - -struct Nystrom4ConstantCache <: OrdinaryDiffEqConstantCache end - -function alg_cache(alg::Nystrom4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - Nystrom4ConstantCache() -end - -# alg_cache(alg::Nystrom4,u,rate_prototype,::Type{uEltypeNoUnits},::Type{uBottomEltypeNoUnits},::Type{tTypeNoUnits},uprev,uprev2,f,t,dt,reltol,p,calck,::Val{false}) where {uEltypeNoUnits,uBottomEltypeNoUnits,tTypeNoUnits} = Nystrom4ConstantCache(constvalue(uBottomEltypeNoUnits),constvalue(tTypeNoUnits)) - -@cache struct FineRKN4Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - k2::reducedRateType - k3::reducedRateType - k4::reducedRateType - k5::reducedRateType - k::rateType - utilde::uType - tmp::uType - atmp::uNoUnitsType - tab::TabType -end - -function alg_cache(alg::FineRKN4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - reduced_rate_prototype = rate_prototype.x[2] - tab = FineRKN4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - k1 = zero(rate_prototype) - k2 = zero(reduced_rate_prototype) - k3 = zero(reduced_rate_prototype) - k4 = zero(reduced_rate_prototype) - k5 = zero(reduced_rate_prototype) - k = zero(rate_prototype) - utilde = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - tmp = zero(u) - FineRKN4Cache(u, uprev, k1, k2, k3, k4, k5, k, utilde, tmp, atmp, tab) -end - -function alg_cache(alg::FineRKN4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - FineRKN4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct FineRKN5Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - k2::reducedRateType - k3::reducedRateType - k4::reducedRateType - k5::reducedRateType - k6::reducedRateType - k7::reducedRateType - k::rateType - utilde::uType - tmp::uType - atmp::uNoUnitsType - tab::TabType -end - -function alg_cache(alg::FineRKN5, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - reduced_rate_prototype = rate_prototype.x[2] - tab = FineRKN5ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - k1 = zero(rate_prototype) - k2 = zero(reduced_rate_prototype) - k3 = zero(reduced_rate_prototype) - k4 = zero(reduced_rate_prototype) - k5 = zero(reduced_rate_prototype) - k6 = zero(reduced_rate_prototype) - k7 = zero(reduced_rate_prototype) - k = zero(rate_prototype) - utilde = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - tmp = zero(u) - FineRKN5Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k, utilde, tmp, atmp, tab) -end - -function alg_cache(alg::FineRKN5, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - FineRKN5ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct Nystrom4VelocityIndependentCache{uType, rateType, reducedRateType} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - k₂::reducedRateType - k₃::reducedRateType - k::rateType - tmp::uType -end - -function alg_cache(alg::Nystrom4VelocityIndependent, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - reduced_rate_prototype = rate_prototype.x[2] - k₁ = zero(rate_prototype) - k₂ = zero(reduced_rate_prototype) - k₃ = zero(reduced_rate_prototype) - k = zero(rate_prototype) - tmp = zero(u) - Nystrom4VelocityIndependentCache(u, uprev, k₁, k₂, k₃, k, tmp) -end - -struct Nystrom4VelocityIndependentConstantCache <: OrdinaryDiffEqConstantCache end - -function alg_cache(alg::Nystrom4VelocityIndependent, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - Nystrom4VelocityIndependentConstantCache() -end - -@cache struct IRKN3Cache{uType, rateType, TabType} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - uprev2::uType - fsalfirst::rateType - k₂::rateType - k::rateType - tmp::uType - tmp2::rateType - onestep_cache::Nystrom4VelocityIndependentCache - tab::TabType -end - -function alg_cache(alg::IRKN3, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - k₁ = zero(rate_prototype) - k₂ = zero(rate_prototype) - k₃ = zero(rate_prototype) - k = zero(rate_prototype) - tmp = zero(u) - tab = IRKN3ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - IRKN3Cache(u, uprev, uprev2, k₁, k₂, k, tmp, k₃, - Nystrom4VelocityIndependentCache(u, uprev, k₁, k₂.x[2], k₃.x[2], k, tmp), - tab) -end - -function alg_cache(alg::IRKN3, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - IRKN3ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct IRKN4Cache{uType, rateType, TabType} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - uprev2::uType - fsalfirst::rateType - k₂::rateType - k₃::rateType - k::rateType - tmp::uType - tmp2::rateType - onestep_cache::Nystrom4VelocityIndependentCache - tab::TabType -end - -function alg_cache(alg::IRKN4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - k₁ = zero(rate_prototype) - k₂ = zero(rate_prototype) - k₃ = zero(rate_prototype) - k = zero(rate_prototype) - tmp = zero(u) - tmp2 = zero(rate_prototype) - tab = IRKN4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - IRKN4Cache(u, uprev, uprev2, k₁, k₂, k₃, k, tmp, tmp2, - Nystrom4VelocityIndependentCache(u, uprev, k₁, k₂.x[2], k₃.x[2], k, tmp), - tab) -end - -function alg_cache(alg::IRKN4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - IRKN4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct Nystrom5VelocityIndependentCache{uType, rateType, reducedRateType, TabType} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - k₂::reducedRateType - k₃::reducedRateType - k₄::reducedRateType - k::rateType - tmp::uType - tab::TabType -end - -function alg_cache(alg::Nystrom5VelocityIndependent, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - reduced_rate_prototype = rate_prototype.x[2] - k₁ = zero(rate_prototype) - k₂ = zero(reduced_rate_prototype) - k₃ = zero(reduced_rate_prototype) - k₄ = zero(reduced_rate_prototype) - k = zero(rate_prototype) - tmp = zero(u) - tab = Nystrom5VelocityIndependentConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - Nystrom5VelocityIndependentCache(u, uprev, k₁, k₂, k₃, k₄, k, tmp, tab) -end - -function alg_cache(alg::Nystrom5VelocityIndependent, u, rate_prototype, - ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - Nystrom5VelocityIndependentConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) -end - -struct DPRKN4Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - k2::reducedRateType - k3::reducedRateType - k4::reducedRateType - k::rateType - utilde::uType - tmp::uType - atmp::uNoUnitsType - tab::TabType -end - -function alg_cache(alg::DPRKN4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - reduced_rate_prototype = rate_prototype.x[2] - tab = DPRKN4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - k1 = zero(rate_prototype) - k2 = zero(reduced_rate_prototype) - k3 = zero(reduced_rate_prototype) - k4 = zero(reduced_rate_prototype) - k = zero(rate_prototype) - utilde = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - tmp = zero(u) - DPRKN4Cache(u, uprev, k1, k2, k3, k4, k, utilde, tmp, atmp, tab) -end - -function alg_cache(alg::DPRKN4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - DPRKN4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct DPRKN5Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - k2::reducedRateType - k3::reducedRateType - k4::reducedRateType - k5::reducedRateType - k6::reducedRateType - k::rateType - utilde::uType - tmp::uType - atmp::uNoUnitsType - tab::TabType -end - -function alg_cache(alg::DPRKN5, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - reduced_rate_prototype = rate_prototype.x[2] - tab = DPRKN5ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - k1 = zero(rate_prototype) - k2 = zero(reduced_rate_prototype) - k3 = zero(reduced_rate_prototype) - k4 = zero(reduced_rate_prototype) - k5 = zero(reduced_rate_prototype) - k6 = zero(reduced_rate_prototype) - k = zero(rate_prototype) - utilde = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - tmp = zero(u) - DPRKN5Cache(u, uprev, k1, k2, k3, k4, k5, k6, k, utilde, tmp, atmp, tab) -end - -function alg_cache(alg::DPRKN5, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - DPRKN5ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct DPRKN6Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - k2::reducedRateType - k3::reducedRateType - k4::reducedRateType - k5::reducedRateType - k6::reducedRateType - k::rateType - utilde::uType - tmp::uType - atmp::uNoUnitsType - tab::TabType -end - -function alg_cache(alg::DPRKN6, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - reduced_rate_prototype = rate_prototype.x[2] - tab = DPRKN6ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - k1 = zero(rate_prototype) - k2 = zero(reduced_rate_prototype) - k3 = zero(reduced_rate_prototype) - k4 = zero(reduced_rate_prototype) - k5 = zero(reduced_rate_prototype) - k6 = zero(reduced_rate_prototype) - k = zero(rate_prototype) - utilde = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - tmp = zero(u) - DPRKN6Cache(u, uprev, k1, k2, k3, k4, k5, k6, k, utilde, tmp, atmp, tab) -end - -function alg_cache(alg::DPRKN6, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - DPRKN6ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct DPRKN6FMCache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - k2::reducedRateType - k3::reducedRateType - k4::reducedRateType - k5::reducedRateType - k6::reducedRateType - k::rateType - utilde::uType - tmp::uType - atmp::uNoUnitsType - tab::TabType -end - -function alg_cache(alg::DPRKN6FM, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - reduced_rate_prototype = rate_prototype.x[2] - tab = DPRKN6FMConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - k1 = zero(rate_prototype) - k2 = zero(reduced_rate_prototype) - k3 = zero(reduced_rate_prototype) - k4 = zero(reduced_rate_prototype) - k5 = zero(reduced_rate_prototype) - k6 = zero(reduced_rate_prototype) - k = zero(rate_prototype) - utilde = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - tmp = zero(u) - DPRKN6FMCache(u, uprev, k1, k2, k3, k4, k5, k6, k, utilde, tmp, atmp, tab) -end - -function alg_cache(alg::DPRKN6FM, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - DPRKN6FMConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct DPRKN8Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - k2::reducedRateType - k3::reducedRateType - k4::reducedRateType - k5::reducedRateType - k6::reducedRateType - k7::reducedRateType - k8::reducedRateType - k9::reducedRateType - k::rateType - utilde::uType - tmp::uType - atmp::uNoUnitsType - tab::TabType -end - -function alg_cache(alg::DPRKN8, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - reduced_rate_prototype = rate_prototype.x[2] - tab = DPRKN8ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - k1 = zero(rate_prototype) - k2 = zero(reduced_rate_prototype) - k3 = zero(reduced_rate_prototype) - k4 = zero(reduced_rate_prototype) - k5 = zero(reduced_rate_prototype) - k6 = zero(reduced_rate_prototype) - k7 = zero(reduced_rate_prototype) - k8 = zero(reduced_rate_prototype) - k9 = zero(reduced_rate_prototype) - k = zero(rate_prototype) - utilde = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - tmp = zero(u) - DPRKN8Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8, k9, k, utilde, tmp, atmp, tab) -end - -function alg_cache(alg::DPRKN8, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - DPRKN8ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct DPRKN12Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - k2::reducedRateType - k3::reducedRateType - k4::reducedRateType - k5::reducedRateType - k6::reducedRateType - k7::reducedRateType - k8::reducedRateType - k9::reducedRateType - k10::reducedRateType - k11::reducedRateType - k12::reducedRateType - k13::reducedRateType - k14::reducedRateType - k15::reducedRateType - k16::reducedRateType - k17::reducedRateType - k::rateType - utilde::uType - tmp::uType - atmp::uNoUnitsType - tab::TabType -end - -function alg_cache(alg::DPRKN12, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - reduced_rate_prototype = rate_prototype.x[2] - tab = DPRKN12ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - k1 = zero(rate_prototype) - k2 = zero(reduced_rate_prototype) - k3 = zero(reduced_rate_prototype) - k4 = zero(reduced_rate_prototype) - k5 = zero(reduced_rate_prototype) - k6 = zero(reduced_rate_prototype) - k7 = zero(reduced_rate_prototype) - k8 = zero(reduced_rate_prototype) - k9 = zero(reduced_rate_prototype) - k10 = zero(reduced_rate_prototype) - k11 = zero(reduced_rate_prototype) - k12 = zero(reduced_rate_prototype) - k13 = zero(reduced_rate_prototype) - k14 = zero(reduced_rate_prototype) - k15 = zero(reduced_rate_prototype) - k16 = zero(reduced_rate_prototype) - k17 = zero(reduced_rate_prototype) - k = zero(rate_prototype) - utilde = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - tmp = zero(u) - DPRKN12Cache( - u, uprev, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, - k16, k17, k, utilde, tmp, atmp, tab) -end - -function alg_cache(alg::DPRKN12, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - DPRKN12ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct ERKN4Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - k2::reducedRateType - k3::reducedRateType - k4::reducedRateType - k::rateType - utilde::uType - tmp::uType - atmp::uNoUnitsType - tab::TabType -end - -function alg_cache(alg::ERKN4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - reduced_rate_prototype = rate_prototype.x[2] - tab = ERKN4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - k1 = zero(rate_prototype) - k2 = zero(reduced_rate_prototype) - k3 = zero(reduced_rate_prototype) - k4 = zero(reduced_rate_prototype) - k = zero(rate_prototype) - utilde = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - tmp = zero(u) - ERKN4Cache(u, uprev, k1, k2, k3, k4, k, utilde, tmp, atmp, tab) -end - -function alg_cache(alg::ERKN4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - ERKN4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct ERKN5Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - k2::reducedRateType - k3::reducedRateType - k4::reducedRateType - k::rateType - utilde::uType - tmp::uType - atmp::uNoUnitsType - tab::TabType -end - -function alg_cache(alg::ERKN5, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - reduced_rate_prototype = rate_prototype.x[2] - tab = ERKN5ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - k1 = zero(rate_prototype) - k2 = zero(reduced_rate_prototype) - k3 = zero(reduced_rate_prototype) - k4 = zero(reduced_rate_prototype) - k = zero(rate_prototype) - utilde = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - tmp = zero(u) - ERKN5Cache(u, uprev, k1, k2, k3, k4, k, utilde, tmp, atmp, tab) -end - -function alg_cache(alg::ERKN5, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - ERKN5ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct ERKN7Cache{uType, rateType, reducedRateType, uNoUnitsType, TabType} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - k2::reducedRateType - k3::reducedRateType - k4::reducedRateType - k5::reducedRateType - k6::reducedRateType - k7::reducedRateType - k::rateType - utilde::uType - tmp::uType - atmp::uNoUnitsType - tab::TabType -end - -function alg_cache(alg::ERKN7, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - reduced_rate_prototype = rate_prototype.x[2] - tab = ERKN7ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - k1 = zero(rate_prototype) - k2 = zero(reduced_rate_prototype) - k3 = zero(reduced_rate_prototype) - k4 = zero(reduced_rate_prototype) - k5 = zero(reduced_rate_prototype) - k6 = zero(reduced_rate_prototype) - k7 = zero(reduced_rate_prototype) - k = zero(rate_prototype) - utilde = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - tmp = zero(u) - ERKN7Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k, utilde, tmp, atmp, tab) -end - -function alg_cache(alg::ERKN7, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - ERKN7ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end From ec9c8b377f4d2e7ded95397a3d75ea958b754d94 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:55:33 -0400 Subject: [PATCH 08/71] Delete src/caches/ssprk_caches.jl --- src/caches/ssprk_caches.jl | 1265 ------------------------------------ 1 file changed, 1265 deletions(-) delete mode 100644 src/caches/ssprk_caches.jl diff --git a/src/caches/ssprk_caches.jl b/src/caches/ssprk_caches.jl deleted file mode 100644 index b2c8833c69..0000000000 --- a/src/caches/ssprk_caches.jl +++ /dev/null @@ -1,1265 +0,0 @@ -@cache struct SSPRK22Cache{uType, rateType, StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - fsalfirst::rateType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct SSPRK22ConstantCache <: OrdinaryDiffEqConstantCache end - -function alg_cache(alg::SSPRK22, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - k = zero(rate_prototype) - if calck - fsalfirst = zero(k) - else - fsalfirst = k - end - SSPRK22Cache(u, uprev, k, fsalfirst, alg.stage_limiter!, alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::SSPRK22, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SSPRK22ConstantCache() -end - -@cache struct SSPRK33Cache{uType, rateType, StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - fsalfirst::rateType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct SSPRK33ConstantCache <: OrdinaryDiffEqConstantCache end - -function alg_cache(alg::SSPRK33, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - k = zero(rate_prototype) - if calck - fsalfirst = zero(k) - else - fsalfirst = k - end - SSPRK33Cache(u, uprev, k, fsalfirst, alg.stage_limiter!, alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::SSPRK33, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SSPRK33ConstantCache() -end - -@cache struct KYKSSPRK42Cache{ - uType, - rateType, - TabType, - StageLimiter, - StepLimiter, - Thread -} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - tmp::uType - fsalfirst::rateType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct KYKSSPRK42ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - α20::T - α21::T - α30::T - α32::T - α40::T - α43::T - β10::T - β21::T - β30::T - β32::T - β40::T - β43::T - c1::T2 - c2::T2 - c3::T2 -end - -function KYKSSPRK42ConstantCache(T, T2) - α20 = T(0.394806441339829) - α21 = T(0.605193558660171) - α30 = T(0.002797307087390) - α32 = T(0.997202692912610) - α40 = T(0.252860909354373) - α43 = T(0.747139090645627) - β10 = T(0.406584463657504) - β21 = T(0.246062298456822) - β30 = T(0.013637216641451) - β32 = T(0.405447122055692) - β40 = T(0.016453567333598) - β43 = T(0.303775146447707) - c1 = T2(0.406584463657504) - c2 = T2(0.4921245969136438) - c3 = T2(0.9098323119879613) - KYKSSPRK42ConstantCache(α20, α21, α30, α32, α40, α43, β10, β21, β30, β32, β40, β43, c1, - c2, c3) -end - -function alg_cache(alg::KYKSSPRK42, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - tab = KYKSSPRK42ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - KYKSSPRK42Cache( - u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, alg.step_limiter!, - alg.thread) -end - -function alg_cache(alg::KYKSSPRK42, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - KYKSSPRK42ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct SSPRK53Cache{uType, rateType, TabType, StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - fsalfirst::rateType - tmp::uType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct SSPRK53ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - α30::T - α32::T - α40::T - α43::T - α52::T - α54::T - β10::T - β21::T - β32::T - β43::T - β54::T - c1::T2 - c2::T2 - c3::T2 - c4::T2 - - function SSPRK53ConstantCache(T, T2) - α30 = T(0.355909775063327) - α32 = T(0.644090224936674) - α40 = T(0.367933791638137) - α43 = T(0.632066208361863) - α52 = T(0.237593836598569) - α54 = T(0.762406163401431) - β10 = T(0.377268915331368) - β21 = T(0.377268915331368) - β32 = T(0.242995220537396) - β43 = T(0.238458932846290) - β54 = T(0.287632146308408) - c1 = T2(0.377268915331368) - c2 = T2(0.754537830662736) - c3 = T2(0.728985661612188) - c4 = T2(0.699226135931670) - - new{T, T2}(α30, α32, α40, α43, α52, α54, β10, β21, β32, β43, β54, c1, c2, c3, c4) - end -end - -function alg_cache(alg::SSPRK53, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - if calck - fsalfirst = zero(k) - else - fsalfirst = k - end - tab = SSPRK53ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - SSPRK53Cache(u, uprev, k, fsalfirst, tmp, tab, alg.stage_limiter!, alg.step_limiter!, - alg.thread) -end - -function alg_cache(alg::SSPRK53, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SSPRK53ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct SHLDDRK52Cache{uType, rateType, TabType, StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - tmp::uType - fsalfirst::rateType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct SHLDDRK52ConstantCache{T1, T2} <: OrdinaryDiffEqConstantCache - α2::T1 - α3::T1 - α4::T1 - α5::T1 - β1::T1 - β2::T1 - β3::T1 - β4::T1 - β5::T1 - c2::T2 - c3::T2 - c4::T2 - c5::T2 -end - -function SHLDDRK52ConstantCache(T1, T2) - α2 = T1(-0.6913065) - α3 = T1(-2.655155) - α4 = T1(-0.8147688) - α5 = T1(-0.6686587) - β1 = T1(0.1) - β2 = T1(0.75) - β3 = T1(0.7) - β4 = T1(0.479313) - β5 = T1(0.310392) - c2 = T2(0.1) - c3 = T2(0.3315201) - c4 = T2(0.4577796) - c5 = T2(0.8666528) - SHLDDRK52ConstantCache(α2, α3, α4, α5, β1, β2, β3, β4, β5, c2, c3, c4, c5) -end - -function alg_cache(alg::SHLDDRK52, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SHLDDRK52ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function alg_cache(alg::SHLDDRK52, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - tab = SHLDDRK52ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - SHLDDRK52Cache(u, uprev, k, tmp, fsalfirst, tab, alg.stage_limiter!, alg.step_limiter!, - alg.thread) -end - -@cache mutable struct SHLDDRK_2NCache{uType, rateType, TabType, StageLimiter, StepLimiter, - Thread} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - tmp::uType - fsalfirst::rateType - tab::TabType - step::Int - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -mutable struct SHLDDRK_2NConstantCache{T1, T2} <: OrdinaryDiffEqConstantCache - α21::T1 - α31::T1 - α41::T1 - α51::T1 - β11::T1 - β21::T1 - β31::T1 - β41::T1 - β51::T1 - c21::T2 - c31::T2 - c41::T2 - c51::T2 - - α22::T1 - α32::T1 - α42::T1 - α52::T1 - α62::T1 - β12::T1 - β22::T1 - β32::T1 - β42::T1 - β52::T1 - β62::T1 - c22::T2 - c32::T2 - c42::T2 - c52::T2 - c62::T2 - - step::Int -end - -function SHLDDRK_2NConstantCache(T1, T2) - α21 = T1(-0.6051226) - α31 = T1(-2.0437564) - α41 = T1(-0.7406999) - α51 = T1(-4.4231765) - β11 = T1(0.2687454) - β21 = T1(0.8014706) - β31 = T1(0.5051570) - β41 = T1(0.5623568) - β51 = T1(0.0590065) - c21 = T2(0.2687454) - c31 = T2(0.5852280) - c41 = T2(0.6827066) - c51 = T2(1.1646854) - - α22 = T1(-0.4412737) - α32 = T1(-1.0739820) - α42 = T1(-1.7063570) - α52 = T1(-2.7979293) - α62 = T1(-4.0913537) - β12 = T1(0.1158488) - β22 = T1(0.3728769) - β32 = T1(0.7379536) - β42 = T1(0.5798110) - β52 = T1(1.0312849) - β62 = T1(0.15) - c22 = T2(0.1158485) - c32 = T2(0.3241850) - c42 = T2(0.6193208) - c52 = T2(0.8034472) - c62 = T2(0.9184166) - SHLDDRK_2NConstantCache( - α21, α31, α41, α51, β11, β21, β31, β41, β51, c21, c31, c41, c51, - α22, α32, α42, α52, α62, β12, β22, β32, β42, β52, β62, c22, c32, - c42, c52, c62, 1) -end - -function alg_cache(alg::SHLDDRK_2N, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SHLDDRK_2NConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function alg_cache(alg::SHLDDRK_2N, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - tab = SHLDDRK_2NConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - SHLDDRK_2NCache(u, uprev, k, tmp, fsalfirst, tab, 1, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -@cache struct SSPRK53_2N1Cache{ - uType, - rateType, - TabType, - StageLimiter, - StepLimiter, - Thread -} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - fsalfirst::rateType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct SSPRK53_2N1ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - α40::T - α43::T - β10::T - β21::T - β32::T - β43::T - β54::T - c1::T2 - c2::T2 - c3::T2 - c4::T2 - - function SSPRK53_2N1ConstantCache(T, T2) - α40 = T(0.571403511494104) - α43 = T(0.428596488505896) - β10 = T(0.443568244942995) - β21 = T(0.291111420073766) - β32 = T(0.270612601278217) - β43 = T(0.110577759392786) - β54 = T(0.458557505351052) - c1 = T2(0.443568244942995) - c2 = T2(0.734679665016762) - c3 = T2(1.005292266294979) - c4 = T2(0.541442494648948) - - new{T, T2}(α40, α43, β10, β21, β32, β43, β54, c1, c2, c3, c4) - end -end - -function alg_cache(alg::SSPRK53_2N1, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - k = zero(rate_prototype) - if calck - fsalfirst = zero(k) - else - fsalfirst = k - end - tab = SSPRK53_2N1ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - SSPRK53_2N1Cache(u, uprev, k, fsalfirst, tab, alg.stage_limiter!, alg.step_limiter!, - alg.thread) -end - -function alg_cache(alg::SSPRK53_2N1, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SSPRK53_2N1ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct SSPRK53_2N2Cache{ - uType, - rateType, - TabType, - StageLimiter, - StepLimiter, - Thread -} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - fsalfirst::rateType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct SSPRK53_2N2ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - α30::T - α32::T - α50::T - α54::T - β10::T - β21::T - β32::T - β43::T - β54::T - c1::T2 - c2::T2 - c3::T2 - c4::T2 - - function SSPRK53_2N2ConstantCache(T, T2) - α30 = T(0.682342861037239) - α32 = T(0.317657138962761) - α50 = T(0.045230974482400) - α54 = T(0.954769025517600) - β10 = T(0.465388589249323) - β21 = T(0.465388589249323) - β32 = T(0.124745797313998) - β43 = T(0.465388589249323) - β54 = T(0.154263303748666) - c1 = T2(0.465388589249323) - c2 = T2(0.930777178498646) - c3 = T2(0.420413812847710) - c4 = T2(0.885802402097033) - - new{T, T2}(α30, α32, α50, α54, β10, β21, β32, β43, β54, c1, c2, c3, c4) - end -end - -function alg_cache(alg::SSPRK53_2N2, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - k = zero(rate_prototype) - if calck - fsalfirst = zero(k) - else - fsalfirst = k - end - tab = SSPRK53_2N2ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - SSPRK53_2N2Cache(u, uprev, k, fsalfirst, tab, alg.stage_limiter!, alg.step_limiter!, - alg.thread) -end - -function alg_cache(alg::SSPRK53_2N2, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SSPRK53_2N2ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct SSPRK53_HCache{uType, rateType, TabType, StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - fsalfirst::rateType - tmp::uType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct SSPRK53_HConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - α30::T - α32::T - α40::T - α41::T - α43::T - β10::T - β21::T - β32::T - β43::T - β54::T - c1::T2 - c2::T2 - c3::T2 - c4::T2 - - function SSPRK53_HConstantCache(T, T2) - α30 = T(0.308684154602513) - α32 = T(0.691315845397487) - α40 = T(0.280514990468574) - α41 = T(0.270513101776498) - α43 = T(0.448971907754928) - β10 = T(0.377268915331368) - β21 = T(0.377268915331368) - β32 = T(0.260811979144498) - β43 = T(0.169383144652957) - β54 = T(0.377268915331368) - c1 = T2(0.377268915331368) - c2 = T2(0.754537830662737) - c3 = T2(0.782435937433493) - c4 = T2(0.622731084668631) - - new{T, T2}(α30, α32, α40, α41, α43, β10, β21, β32, β43, β54, c1, c2, c3, c4) - end -end - -function alg_cache(alg::SSPRK53_H, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - if calck - fsalfirst = zero(k) - else - fsalfirst = k - end - tab = SSPRK53_HConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - SSPRK53_HCache(u, uprev, k, fsalfirst, tmp, tab, alg.stage_limiter!, alg.step_limiter!, - alg.thread) -end - -function alg_cache(alg::SSPRK53_H, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SSPRK53_HConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct SSPRK63Cache{uType, rateType, TabType, StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - fsalfirst::rateType - tmp::uType - u₂::uType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct SSPRK63ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - α40::T - α41::T - α43::T - α62::T - α65::T - β10::T - β21::T - β32::T - β43::T - β54::T - β65::T - c1::T2 - c2::T2 - c3::T2 - c4::T2 - c5::T2 - - function SSPRK63ConstantCache(T, T2) - α40 = T(0.476769811285196) - α41 = T(0.098511733286064) - α43 = T(0.424718455428740) - α62 = T(0.155221702560091) - α65 = T(0.844778297439909) - β10 = T(0.284220721334261) - β21 = T(0.284220721334261) - β32 = T(0.284220721334261) - β43 = T(0.120713785765930) - β54 = T(0.284220721334261) - β65 = T(0.240103497065900) - c1 = T2(0.284220721334261) - c2 = T2(0.568441442668522) - c3 = T2(0.852662164002783) - c4 = T2(0.510854218958172) - c5 = T2(0.795074940292433) - - new{T, T2}(α40, α41, α43, α62, α65, β10, β21, β32, β43, β54, β65, c1, c2, c3, c4, - c5) - end -end - -function alg_cache(alg::SSPRK63, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - u₂ = zero(u) - k = zero(rate_prototype) - if calck - fsalfirst = zero(k) - else - fsalfirst = k - end - tab = SSPRK63ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - SSPRK63Cache(u, uprev, k, fsalfirst, tmp, u₂, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::SSPRK63, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SSPRK63ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct SSPRK73Cache{uType, rateType, TabType, StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - fsalfirst::rateType - tmp::uType - u₁::uType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct SSPRK73ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - α40::T - α43::T - α50::T - α51::T - α54::T - α73::T - α76::T - β10::T - β21::T - β32::T - β43::T - β54::T - β65::T - β76::T - c1::T2 - c2::T2 - c3::T2 - c4::T2 - c5::T2 - c6::T2 - - function SSPRK73ConstantCache(T, T2) - α40 = T(0.184962588071072) - α43 = T(0.815037411928928) - α50 = T(0.180718656570380) - α51 = T(0.314831034403793) - α54 = T(0.504450309025826) - α73 = T(0.120199000000000) - α76 = T(0.879801000000000) - β10 = T(0.233213863663009) - β21 = T(0.233213863663009) - β32 = T(0.233213863663009) - β43 = T(0.190078023865845) - β54 = T(0.117644805593912) - β65 = T(0.233213863663009) - β76 = T(0.205181790464579) - c1 = T2(0.233213863663009) - c2 = T2(0.466427727326018) - c3 = T2(0.699641590989027) - c4 = T2(0.760312095463379) - c5 = T2(0.574607439040817) - c6 = T2(0.807821302703826) - - new{T, T2}( - α40, α43, α50, α51, α54, α73, α76, β10, β21, β32, β43, β54, β65, β76, c1, - c2, c3, c4, c5, c6) - end -end - -function alg_cache(alg::SSPRK73, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - u₁ = zero(u) - k = zero(rate_prototype) - if calck - fsalfirst = zero(k) - else - fsalfirst = k - end - tab = SSPRK73ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - SSPRK73Cache(u, uprev, k, fsalfirst, tmp, u₁, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::SSPRK73, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SSPRK73ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct SSPRK83Cache{uType, rateType, TabType, StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - fsalfirst::rateType - tmp::uType - u₂::uType - u₃::uType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct SSPRK83ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - α50::T - α51::T - α54::T - α61::T - α65::T - α72::T - α73::T - α76::T - β10::T - β21::T - β32::T - β43::T - β54::T - β65::T - β76::T - β87::T - c1::T2 - c2::T2 - c3::T2 - c4::T2 - c5::T2 - c6::T2 - c7::T2 - - function SSPRK83ConstantCache(T, T2) - α50 = T(0.421366967085359) - α51 = T(0.005949401107575) - α54 = T(0.572683631807067) - α61 = T(0.004254010666365) - α65 = T(0.995745989333635) - α72 = T(0.104380143093325) - α73 = T(0.243265240906726) - α76 = T(0.652354615999950) - β10 = T(0.195804015330143) - β21 = T(0.195804015330143) - β32 = T(0.195804015330143) - β43 = T(0.195804015330143) - β54 = T(0.112133754621673) - β65 = T(0.194971062960412) - β76 = T(0.127733653231944) - β87 = T(0.195804015330143) - c1 = T2(0.195804015330143) - c2 = T2(0.391608030660286) - c3 = T2(0.587412045990429) - c4 = T2(0.783216061320572) - c5 = T2(0.561833689734037) - c6 = T2(0.755247658555329) - c7 = T2(0.804195984669857) - - new{T, T2}(α50, α51, α54, α61, α65, α72, α73, α76, β10, β21, β32, β43, β54, β65, - β76, β87, c1, c2, c3, c4, c5, c6, c7) - end -end - -function alg_cache(alg::SSPRK83, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - u₂ = zero(u) - u₃ = zero(u) - k = zero(rate_prototype) - if calck - fsalfirst = zero(k) - else - fsalfirst = k - end - tab = SSPRK83ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - SSPRK83Cache(u, uprev, k, fsalfirst, tmp, u₂, u₃, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::SSPRK83, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SSPRK83ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct SSPRK43Cache{uType, rateType, uNoUnitsType, TabType, StageLimiter, - StepLimiter, Thread} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - fsalfirst::rateType - utilde::uType - atmp::uNoUnitsType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct SSPRK43ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - one_third_u::T - two_thirds_u::T - half_u::T - half_t::T2 - - function SSPRK43ConstantCache(T, T2) - one_third_u = inv(T(3)) - two_thirds_u = 2 * one_third_u - half_u = T(0.5) - half_t = T2(0.5) - - new{T, T2}(one_third_u, two_thirds_u, half_u, half_t) - end -end - -function alg_cache(alg::SSPRK43, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - k = zero(rate_prototype) - if calck - fsalfirst = zero(k) - else - fsalfirst = k - end - utilde = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - tab = SSPRK43ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - SSPRK43Cache(u, uprev, k, fsalfirst, utilde, atmp, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::SSPRK43, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SSPRK43ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct SSPRK432Cache{ - uType, - rateType, - uNoUnitsType, - StageLimiter, - StepLimiter, - Thread -} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - fsalfirst::rateType - utilde::uType - atmp::uNoUnitsType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct SSPRK432ConstantCache <: OrdinaryDiffEqConstantCache end - -function alg_cache(alg::SSPRK432, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - k = zero(rate_prototype) - if calck - fsalfirst = zero(k) - else - fsalfirst = k - end - utilde = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - SSPRK432Cache(u, uprev, k, fsalfirst, utilde, atmp, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::SSPRK432, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SSPRK432ConstantCache() -end - -@cache mutable struct SSPRKMSVS32Cache{uType, rateType, dtArrayType, dtType, StageLimiter, - StepLimiter, Thread} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - u_2::uType - u_1::uType - k::rateType - tmp::uType - dts::dtArrayType - dtf::dtArrayType - μ::dtType - v_n::Float64 - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread - step::Int -end - -@cache mutable struct SSPRKMSVS32ConstantCache{uType, dtArrayType, dtType} <: - OrdinaryDiffEqConstantCache - u_2::uType - u_1::uType - dts::dtArrayType - dtf::dtArrayType - μ::dtType - v_n::Float64 - step::Int -end - -function alg_cache(alg::SSPRKMSVS32, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - fsalfirst = zero(rate_prototype) - dts = fill(zero(dt), 3) - dtf = fill(zero(dt), 2) - μ = zero(dt) - u_2 = zero(u) - u_1 = zero(u) - k = zero(rate_prototype) - tmp = zero(u) - SSPRKMSVS32Cache(u, uprev, fsalfirst, u_2, u_1, k, tmp, dts, dtf, μ, 0.5, - alg.stage_limiter!, alg.step_limiter!, alg.thread, 1) -end - -function alg_cache(alg::SSPRKMSVS32, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - dts = fill(zero(dt), 3) - dtf = fill(zero(dt), 2) - μ = zero(dt) - u_2 = u - u_1 = u - SSPRKMSVS32ConstantCache(u_2, u_1, dts, dtf, μ, 0.5, 1) -end - -@cache mutable struct SSPRKMSVS43Cache{ - uType, - rateType, - StageLimiter, - StepLimiter, - Thread -} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - fsalfirst::rateType - u_3::uType - u_2::uType - u_1::uType - k::rateType - k1::rateType - k2::rateType - k3::rateType - tmp::uType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread - step::Int -end - -@cache mutable struct SSPRKMSVS43ConstantCache{uType, rateType} <: - OrdinaryDiffEqConstantCache - u_3::uType - u_2::uType - u_1::uType - k1::rateType - k2::rateType - k3::rateType - step::Int -end - -function alg_cache(alg::SSPRKMSVS43, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - fsalfirst = zero(rate_prototype) - u_3 = zero(u) - u_2 = zero(u) - u_1 = zero(u) - k = zero(rate_prototype) - k1 = zero(rate_prototype) - k2 = zero(rate_prototype) - k3 = zero(rate_prototype) - tmp = zero(u) - SSPRKMSVS43Cache(u, uprev, fsalfirst, u_3, u_2, u_1, k, k1, k2, k3, tmp, - alg.stage_limiter!, alg.step_limiter!, alg.thread, 1) -end - -function alg_cache(alg::SSPRKMSVS43, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - u_3 = u - u_2 = u - u_1 = u - k1 = rate_prototype - k2 = rate_prototype - k3 = rate_prototype - SSPRKMSVS43ConstantCache(u_3, u_2, u_1, k1, k2, k3, 1) -end - -@cache struct SSPRK932Cache{ - uType, - rateType, - uNoUnitsType, - StageLimiter, - StepLimiter, - Thread -} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - fsalfirst::rateType - utilde::uType - atmp::uNoUnitsType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct SSPRK932ConstantCache <: OrdinaryDiffEqConstantCache end - -function alg_cache(alg::SSPRK932, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - k = zero(rate_prototype) - if calck - fsalfirst = zero(k) - else - fsalfirst = k - end - utilde = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - SSPRK932Cache(u, uprev, k, fsalfirst, utilde, atmp, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::SSPRK932, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SSPRK932ConstantCache() -end - -@cache struct SSPRK54Cache{uType, rateType, TabType, StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - fsalfirst::rateType - k₃::rateType - u₂::uType - u₃::uType - tmp::uType # should be u₄, but tmp is needed for callbacks - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct SSPRK54ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - β10::T - α20::T - α21::T - β21::T - α30::T - α32::T - β32::T - α40::T - α43::T - β43::T - α52::T - α53::T - β53::T - α54::T - β54::T - c1::T2 - c2::T2 - c3::T2 - c4::T2 - - function SSPRK54ConstantCache(T, T2) - β10 = T(0.391752226571890) - α20 = T(0.444370493651235) - α21 = T(0.555629506348765) - β21 = T(0.368410593050371) - α30 = T(0.620101851488403) - α32 = T(0.379898148511597) - β32 = T(0.251891774271694) - α40 = T(0.178079954393132) - α43 = T(0.821920045606868) - β43 = T(0.544974750228521) - α52 = T(0.517231671970585) - α53 = T(0.096059710526147) - β53 = T(0.063692468666290) - α54 = T(0.386708617503269) - β54 = T(0.226007483236906) - c1 = T2(0.391752226571890) - c2 = T2(0.586079689311540) - c3 = T2(0.474542363121400) - c4 = T2(0.935010630967653) - - new{T, T2}(β10, α20, α21, β21, α30, α32, β32, α40, α43, β43, α52, α53, β53, α54, - β54, c1, c2, c3, c4) - end -end - -function alg_cache(alg::SSPRK54, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - u₂ = zero(u) - u₃ = zero(u) - tmp = zero(u) - k = zero(rate_prototype) - if calck - fsalfirst = zero(k) - else - fsalfirst = k - end - k₃ = zero(rate_prototype) - tab = SSPRK54ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - SSPRK54Cache(u, uprev, k, fsalfirst, k₃, u₂, u₃, tmp, tab, alg.stage_limiter!, - alg.step_limiter!, alg.thread) -end - -function alg_cache(alg::SSPRK54, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SSPRK54ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct SSPRK104Cache{uType, rateType, StageLimiter, StepLimiter, Thread} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k::rateType - fsalfirst::rateType - k₄::rateType - tmp::uType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -struct SSPRK104ConstantCache <: OrdinaryDiffEqConstantCache end - -function alg_cache(alg::SSPRK104, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - if calck - fsalfirst = zero(k) - else - fsalfirst = k - end - k₄ = zero(rate_prototype) - SSPRK104Cache(u, uprev, k, fsalfirst, k₄, tmp, alg.stage_limiter!, alg.step_limiter!, - alg.thread) -end - -function alg_cache(alg::SSPRK104, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SSPRK104ConstantCache() -end From 2222a9c41573fa86b61c9ebb9837848a55ec8fcf Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:55:44 -0400 Subject: [PATCH 09/71] Delete src/caches/symplectic_caches.jl --- src/caches/symplectic_caches.jl | 419 -------------------------------- 1 file changed, 419 deletions(-) delete mode 100644 src/caches/symplectic_caches.jl diff --git a/src/caches/symplectic_caches.jl b/src/caches/symplectic_caches.jl deleted file mode 100644 index 71c55340dc..0000000000 --- a/src/caches/symplectic_caches.jl +++ /dev/null @@ -1,419 +0,0 @@ -@cache struct SymplecticEulerCache{uType, rateType} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - tmp::uType - k::rateType - fsalfirst::rateType -end - -function alg_cache(alg::SymplecticEuler, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SymplecticEulerCache(u, uprev, zero(u), zero(rate_prototype), zero(rate_prototype)) -end - -struct SymplecticEulerConstantCache <: OrdinaryDiffEqConstantCache end - -function alg_cache(alg::SymplecticEuler, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SymplecticEulerConstantCache() -end - -@cache struct VelocityVerletCache{uType, rateType, uEltypeNoUnits} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - tmp::uType - k::rateType - fsalfirst::rateType - half::uEltypeNoUnits -end - -struct VelocityVerletConstantCache{uEltypeNoUnits} <: OrdinaryDiffEqConstantCache - half::uEltypeNoUnits -end - -function alg_cache(alg::VelocityVerlet, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(rate_prototype) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - half = uEltypeNoUnits(1 // 2) - VelocityVerletCache(u, uprev, k, tmp, fsalfirst, half) -end - -function alg_cache(alg::VelocityVerlet, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - VelocityVerletConstantCache(uEltypeNoUnits(1 // 2)) -end - -@cache struct Symplectic2Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - tmp::uType - k::rateType - fsalfirst::rateType - tab::tableauType -end - -function alg_cache(alg::VerletLeapfrog, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - tab = VerletLeapfrogConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - Symplectic2Cache(u, uprev, k, tmp, fsalfirst, tab) -end - -function alg_cache(alg::VerletLeapfrog, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - VerletLeapfrogConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function alg_cache(alg::PseudoVerletLeapfrog, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - tab = PseudoVerletLeapfrogConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - Symplectic2Cache(u, uprev, k, tmp, fsalfirst, tab) -end - -function alg_cache(alg::PseudoVerletLeapfrog, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - PseudoVerletLeapfrogConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) -end - -function alg_cache(alg::McAte2, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - tab = McAte2ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - Symplectic2Cache(u, uprev, k, tmp, fsalfirst, tab) -end - -function alg_cache(alg::McAte2, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - McAte2ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct Symplectic3Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - tmp::uType - k::rateType - fsalfirst::rateType - tab::tableauType -end - -function alg_cache(alg::Ruth3, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - tab = Ruth3ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - Symplectic3Cache(u, uprev, k, tmp, fsalfirst, tab) -end - -function alg_cache(alg::Ruth3, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - Ruth3ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function alg_cache(alg::McAte3, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - tab = McAte3ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - Symplectic3Cache(u, uprev, k, tmp, fsalfirst, tab) -end - -function alg_cache(alg::McAte3, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - McAte3ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct Symplectic4Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - tmp::uType - k::rateType - fsalfirst::rateType - tab::tableauType -end - -function alg_cache(alg::McAte4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - tab = McAte4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - Symplectic4Cache(u, uprev, k, tmp, fsalfirst, tab) -end - -function alg_cache(alg::McAte4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - McAte4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function alg_cache(alg::CandyRoz4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - tab = CandyRoz4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - Symplectic4Cache(u, uprev, k, tmp, fsalfirst, tab) -end - -function alg_cache(alg::CandyRoz4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - McAte4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct Symplectic45Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - tmp::uType - k::rateType - fsalfirst::rateType - tab::tableauType -end - -function alg_cache(alg::CalvoSanz4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - tab = CalvoSanz4ConstantCache(constvalue(uBottomEltypeNoUnits), - constvalue(tTypeNoUnits)) - Symplectic45Cache(u, uprev, k, tmp, fsalfirst, tab) -end - -function alg_cache(alg::CalvoSanz4, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - CalvoSanz4ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -function alg_cache(alg::McAte42, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - tab = McAte42ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - Symplectic45Cache(u, uprev, k, tmp, fsalfirst, tab) -end - -function alg_cache(alg::McAte42, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - McAte42ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct Symplectic5Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - tmp::uType - k::rateType - fsalfirst::rateType - tab::tableauType -end - -function alg_cache(alg::McAte5, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - tab = McAte5ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - Symplectic5Cache(u, uprev, k, tmp, fsalfirst, tab) -end - -function alg_cache(alg::McAte5, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - McAte5ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct Symplectic6Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - tmp::uType - k::rateType - fsalfirst::rateType - tab::tableauType -end - -function alg_cache(alg::Yoshida6, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - tab = Yoshida6ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - Symplectic6Cache(u, uprev, k, tmp, fsalfirst, tab) -end - -function alg_cache(alg::Yoshida6, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - Yoshida6ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct Symplectic62Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - tmp::uType - k::rateType - fsalfirst::rateType - tab::tableauType -end - -function alg_cache(alg::KahanLi6, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - tab = KahanLi6ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - Symplectic62Cache(u, uprev, k, tmp, fsalfirst, tab) -end - -function alg_cache(alg::KahanLi6, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - KahanLi6ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct McAte8Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - tmp::uType - k::rateType - fsalfirst::rateType - tab::tableauType -end - -function alg_cache(alg::McAte8, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - tab = McAte8ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - McAte8Cache(u, uprev, k, tmp, fsalfirst, tab) -end - -function alg_cache(alg::McAte8, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - McAte8ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct KahanLi8Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - tmp::uType - k::rateType - fsalfirst::rateType - tab::tableauType -end - -function alg_cache(alg::KahanLi8, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - tab = KahanLi8ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - KahanLi8Cache(u, uprev, k, tmp, fsalfirst, tab) -end - -function alg_cache(alg::KahanLi8, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - KahanLi8ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end - -@cache struct SofSpa10Cache{uType, rateType, tableauType} <: OrdinaryDiffEqMutableCache - u::uType - uprev::uType - tmp::uType - k::rateType - fsalfirst::rateType - tab::tableauType -end - -function alg_cache(alg::SofSpa10, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tmp = zero(u) - k = zero(rate_prototype) - fsalfirst = zero(rate_prototype) - tab = SofSpa10ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - SofSpa10Cache(u, uprev, k, tmp, fsalfirst, tab) -end - -function alg_cache(alg::SofSpa10, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - SofSpa10ConstantCache(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) -end From e9421a9d9b012d83ff364239d3c78746959c13b6 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:56:02 -0400 Subject: [PATCH 10/71] Delete src/caches/verner_caches.jl --- src/caches/verner_caches.jl | 258 ------------------------------------ 1 file changed, 258 deletions(-) delete mode 100644 src/caches/verner_caches.jl diff --git a/src/caches/verner_caches.jl b/src/caches/verner_caches.jl deleted file mode 100644 index 08b1de0919..0000000000 --- a/src/caches/verner_caches.jl +++ /dev/null @@ -1,258 +0,0 @@ -@cache struct Vern6Cache{uType, rateType, uNoUnitsType, TabType, StageLimiter, StepLimiter, - Thread} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k1::rateType - k2::rateType - k3::rateType - k4::rateType - k5::rateType - k6::rateType - k7::rateType - k8::rateType - k9::rateType - utilde::uType - tmp::uType - rtmp::rateType - atmp::uNoUnitsType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -TruncatedStacktraces.@truncate_stacktrace Vern6Cache 1 - -function alg_cache(alg::Vern6, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tab = Vern6Tableau(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - k1 = zero(rate_prototype) - k2 = zero(rate_prototype) - k3 = k2 - k4 = zero(rate_prototype) - k5 = zero(rate_prototype) - k6 = zero(rate_prototype) - k7 = zero(rate_prototype) - k8 = k3 - k9 = zero(rate_prototype) - utilde = zero(u) - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - rtmp = uEltypeNoUnits === eltype(u) ? utilde : zero(rate_prototype) - Vern6Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8, k9, utilde, tmp, rtmp, atmp, tab, - alg.stage_limiter!, alg.step_limiter!, alg.thread) -end - -struct Vern6ConstantCache{TabType} <: OrdinaryDiffEqConstantCache - tab::TabType -end - -function alg_cache(alg::Vern6, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tab = Vern6Tableau(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - Vern6ConstantCache(tab) -end - -@cache struct Vern7Cache{uType, rateType, uNoUnitsType, StageLimiter, StepLimiter, - Thread} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k1::rateType - k2::rateType - k3::rateType - k4::rateType - k5::rateType - k6::rateType - k7::rateType - k8::rateType - k9::rateType - k10::rateType - utilde::uType - tmp::uType - rtmp::rateType - atmp::uNoUnitsType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -TruncatedStacktraces.@truncate_stacktrace Vern7Cache 1 - -function alg_cache(alg::Vern7, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - k1 = zero(rate_prototype) - k2 = zero(rate_prototype) - k3 = k2 - k4 = zero(rate_prototype) - k5 = zero(rate_prototype) - k6 = zero(rate_prototype) - k7 = zero(rate_prototype) - k8 = zero(rate_prototype) - k9 = zero(rate_prototype) - k10 = k2 - utilde = zero(u) - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - rtmp = uEltypeNoUnits === eltype(u) ? utilde : zero(rate_prototype) - Vern7Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, utilde, tmp, rtmp, atmp, - alg.stage_limiter!, alg.step_limiter!, alg.thread) -end - -struct Vern7ConstantCache <: OrdinaryDiffEqConstantCache end - -function alg_cache(alg::Vern7, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - Vern7ConstantCache() -end - -@cache struct Vern8Cache{uType, rateType, uNoUnitsType, TabType, StageLimiter, StepLimiter, - Thread} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k1::rateType - k2::rateType - k3::rateType - k4::rateType - k5::rateType - k6::rateType - k7::rateType - k8::rateType - k9::rateType - k10::rateType - k11::rateType - k12::rateType - k13::rateType - utilde::uType - tmp::uType - rtmp::rateType - atmp::uNoUnitsType - tab::TabType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -TruncatedStacktraces.@truncate_stacktrace Vern8Cache 1 - -function alg_cache(alg::Vern8, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tab = Vern8Tableau(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - k1 = zero(rate_prototype) - k2 = zero(rate_prototype) - k3 = k2 - k4 = zero(rate_prototype) - k5 = k2 - k6 = zero(rate_prototype) - k7 = zero(rate_prototype) - k8 = zero(rate_prototype) - tmp = zero(u) - k9 = zero(rate_prototype) - k10 = zero(rate_prototype) - k11 = zero(rate_prototype) - k12 = zero(rate_prototype) - k13 = k4 - utilde = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - rtmp = uEltypeNoUnits === eltype(u) ? utilde : zero(rate_prototype) - Vern8Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, utilde, - tmp, rtmp, atmp, tab, alg.stage_limiter!, alg.step_limiter!, alg.thread) -end - -struct Vern8ConstantCache{TabType} <: OrdinaryDiffEqConstantCache - tab::TabType -end - -function alg_cache(alg::Vern8, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - tab = Vern8Tableau(constvalue(uBottomEltypeNoUnits), constvalue(tTypeNoUnits)) - Vern8ConstantCache(tab) -end - -@cache struct Vern9Cache{uType, rateType, uNoUnitsType, StageLimiter, StepLimiter, - Thread} <: - OrdinaryDiffEqMutableCache - u::uType - uprev::uType - k1::rateType - k2::rateType - k3::rateType - k4::rateType - k5::rateType - k6::rateType - k7::rateType - k8::rateType - k9::rateType - k10::rateType - k11::rateType - k12::rateType - k13::rateType - k14::rateType - k15::rateType - k16::rateType - utilde::uType - tmp::uType - rtmp::rateType - atmp::uNoUnitsType - stage_limiter!::StageLimiter - step_limiter!::StepLimiter - thread::Thread -end - -TruncatedStacktraces.@truncate_stacktrace Vern9Cache 1 - -function alg_cache(alg::Vern9, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - k1 = zero(rate_prototype) - k2 = zero(rate_prototype) - k3 = k2 - k4 = zero(rate_prototype) - k5 = k3 - k6 = zero(rate_prototype) - k7 = k4 - k8 = k5 - k9 = zero(rate_prototype) - k10 = zero(rate_prototype) - k11 = zero(rate_prototype) - k12 = zero(rate_prototype) - k13 = zero(rate_prototype) - k14 = zero(rate_prototype) - k15 = zero(rate_prototype) - k16 = k6 - utilde = zero(u) - tmp = zero(u) - atmp = similar(u, uEltypeNoUnits) - recursivefill!(atmp, false) - rtmp = uEltypeNoUnits === eltype(u) ? utilde : zero(rate_prototype) - Vern9Cache(u, uprev, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, - k16, utilde, tmp, rtmp, atmp, alg.stage_limiter!, alg.step_limiter!, - alg.thread) -end - -struct Vern9ConstantCache <: OrdinaryDiffEqConstantCache end - -function alg_cache(alg::Vern9, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, - dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} - Vern9ConstantCache() -end From 19e524e578bad315dfe232d4e6e3fe9778f8aef9 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:56:15 -0400 Subject: [PATCH 11/71] Delete src/dense/verner_addsteps.jl --- src/dense/verner_addsteps.jl | 1323 ---------------------------------- 1 file changed, 1323 deletions(-) delete mode 100644 src/dense/verner_addsteps.jl diff --git a/src/dense/verner_addsteps.jl b/src/dense/verner_addsteps.jl deleted file mode 100644 index 9395b42cda..0000000000 --- a/src/dense/verner_addsteps.jl +++ /dev/null @@ -1,1323 +0,0 @@ -@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern6Cache, - always_calc_begin = false, allow_calc_end = true, - force_calc_end = false) - if length(k) < 9 || always_calc_begin - @unpack c1, c2, c3, c4, c5, c6, a21, a31, a32, a41, a43, a51, a53, a54, a61, a63, a64, a65, a71, a73, a74, a75, a76, a81, a83, a84, a85, a86, a87, a91, a94, a95, a96, a97, a98 = cache.tab - @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, tmp = cache - @.. broadcast=false tmp=uprev + dt * (a21 * k1) - f(k2, tmp, p, t + c1 * dt) - @.. broadcast=false tmp=uprev + dt * (a31 * k1 + a32 * k2) - f(k3, tmp, p, t + c2 * dt) - @.. broadcast=false tmp=uprev + dt * (a41 * k1 + a43 * k3) - f(k4, tmp, p, t + c3 * dt) - @.. broadcast=false tmp=uprev + dt * (a51 * k1 + a53 * k3 + a54 * k4) - f(k5, tmp, p, t + c4 * dt) - @.. broadcast=false tmp=uprev + dt * (a61 * k1 + a63 * k3 + a64 * k4 + a65 * k5) - f(k6, tmp, p, t + c5 * dt) - @.. broadcast=false tmp=uprev + - dt * (a71 * k1 + a73 * k3 + a74 * k4 + a75 * k5 + a76 * k6) - f(k7, tmp, p, t + c6 * dt) - @.. broadcast=false tmp=uprev + - dt * - (a81 * k1 + a83 * k3 + a84 * k4 + a85 * k5 + a86 * k6 + - a87 * k7) - f(k8, tmp, p, t + dt) - @.. broadcast=false tmp=uprev + - dt * - (a91 * k1 + a94 * k4 + a95 * k5 + a96 * k6 + a97 * k7 + - a98 * k8) - f(k9, tmp, p, t + dt) - copyat_or_push!(k, 1, k1) - copyat_or_push!(k, 2, k2) - copyat_or_push!(k, 3, k3) - copyat_or_push!(k, 4, k4) - copyat_or_push!(k, 5, k5) - copyat_or_push!(k, 6, k6) - copyat_or_push!(k, 7, k7) - copyat_or_push!(k, 8, k8) - copyat_or_push!(k, 9, k9) - end - if (allow_calc_end && length(k) < 12) || force_calc_end # Have not added the extra stages yet - @unpack c10, a1001, a1004, a1005, a1006, a1007, a1008, a1009, c11, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, c12, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211 = cache.tab.extra - @unpack tmp = cache - rtmp = similar(cache.k1) - uidx = eachindex(uprev) - @.. broadcast=false tmp=uprev + - dt * - (a1001 * k[1] + a1004 * k[4] + a1005 * k[5] + a1006 * k[6] + - a1007 * k[7] + a1008 * k[8] + a1009 * k[9]) - f(rtmp, tmp, p, t + c10 * dt) - copyat_or_push!(k, 10, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a1101 * k[1] + a1104 * k[4] + a1105 * k[5] + a1106 * k[6] + - a1107 * k[7] + a1108 * k[8] + a1109 * k[9] + a1110 * k[10]) - f(rtmp, tmp, p, t + c11 * dt) - copyat_or_push!(k, 11, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a1201 * k[1] + a1204 * k[4] + a1205 * k[5] + a1206 * k[6] + - a1207 * k[7] + a1208 * k[8] + a1209 * k[9] + - a1210 * k[10] + a1211 * k[11]) - f(rtmp, tmp, p, t + c12 * dt) - copyat_or_push!(k, 12, rtmp) - end - nothing -end - -@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern7Cache, - always_calc_begin = false, allow_calc_end = true, - force_calc_end = false) - T = constvalue(recursive_unitless_bottom_eltype(u)) - T2 = constvalue(typeof(one(t))) - if length(k) < 10 || always_calc_begin - @OnDemandTableauExtract Vern7Tableau T T2 - @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, tmp = cache - f(k1, uprev, p, t) - @.. broadcast=false tmp=uprev + dt * (a021 * k1) - f(k2, tmp, p, t + c2 * dt) - @.. broadcast=false tmp=uprev + dt * (a031 * k1 + a032 * k2) - f(k3, tmp, p, t + c3 * dt) - @.. broadcast=false tmp=uprev + dt * (a041 * k1 + a043 * k3) - f(k4, tmp, p, t + c4 * dt) - @.. broadcast=false tmp=uprev + dt * (a051 * k1 + a053 * k3 + a054 * k4) - f(k5, tmp, p, t + c5 * dt) - @.. broadcast=false tmp=uprev + dt * (a061 * k1 + a063 * k3 + a064 * k4 + a065 * k5) - f(k6, tmp, p, t + c6 * dt) - @.. broadcast=false tmp=uprev + - dt * - (a071 * k1 + a073 * k3 + a074 * k4 + a075 * k5 + a076 * k6) - f(k7, tmp, p, t + c7 * dt) - @.. broadcast=false tmp=uprev + - dt * - (a081 * k1 + a083 * k3 + a084 * k4 + a085 * k5 + a086 * k6 + - a087 * k7) - f(k8, tmp, p, t + c8 * dt) - @.. broadcast=false tmp=uprev + - dt * - (a091 * k1 + a093 * k3 + a094 * k4 + a095 * k5 + a096 * k6 + - a097 * k7 + a098 * k8) - f(k9, tmp, p, t + dt) - @.. broadcast=false tmp=uprev + - dt * - (a101 * k1 + a103 * k3 + a104 * k4 + a105 * k5 + a106 * k6 + - a107 * k7) - f(k10, tmp, p, t + dt) - copyat_or_push!(k, 1, k1) - copyat_or_push!(k, 2, k2) - copyat_or_push!(k, 3, k3) - copyat_or_push!(k, 4, k4) - copyat_or_push!(k, 5, k5) - copyat_or_push!(k, 6, k6) - copyat_or_push!(k, 7, k7) - copyat_or_push!(k, 8, k8) - copyat_or_push!(k, 9, k9) - copyat_or_push!(k, 10, k10) - end - if (allow_calc_end && length(k) < 16) || force_calc_end # Have not added the extra stages yet - @unpack tmp = cache - rtmp = similar(cache.k1) - @OnDemandTableauExtract Vern7ExtraStages T T2 - @.. broadcast=false tmp=uprev + - dt * - (a1101 * k[1] + a1104 * k[4] + a1105 * k[5] + a1106 * k[6] + - a1107 * k[7] + a1108 * k[8] + a1109 * k[9]) - f(rtmp, tmp, p, t + c11 * dt) - copyat_or_push!(k, 11, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a1201 * k[1] + a1204 * k[4] + a1205 * k[5] + a1206 * k[6] + - a1207 * k[7] + a1208 * k[8] + a1209 * k[9] + a1211 * k[11]) - f(rtmp, tmp, p, t + c12 * dt) - copyat_or_push!(k, 12, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a1301 * k[1] + a1304 * k[4] + a1305 * k[5] + a1306 * k[6] + - a1307 * k[7] + a1308 * k[8] + a1309 * k[9] + - a1311 * k[11] + a1312 * k[12]) - f(rtmp, tmp, p, t + c13 * dt) - copyat_or_push!(k, 13, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a1401 * k[1] + a1404 * k[4] + a1405 * k[5] + a1406 * k[6] + - a1407 * k[7] + a1408 * k[8] + a1409 * k[9] + - a1411 * k[11] + a1412 * k[12] + a1413 * k[13]) - f(rtmp, tmp, p, t + c14 * dt) - copyat_or_push!(k, 14, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a1501 * k[1] + a1504 * k[4] + a1505 * k[5] + a1506 * k[6] + - a1507 * k[7] + a1508 * k[8] + a1509 * k[9] + - a1511 * k[11] + a1512 * k[12] + a1513 * k[13]) - f(rtmp, tmp, p, t + c15 * dt) - copyat_or_push!(k, 15, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a1601 * k[1] + a1604 * k[4] + a1605 * k[5] + a1606 * k[6] + - a1607 * k[7] + a1608 * k[8] + a1609 * k[9] + - a1611 * k[11] + a1612 * k[12] + a1613 * k[13]) - f(rtmp, tmp, p, t + c16 * dt) - copyat_or_push!(k, 16, rtmp) - end - nothing -end - -@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern7Cache{<:Array}, - always_calc_begin = false, allow_calc_end = true, - force_calc_end = false) - T = constvalue(recursive_unitless_bottom_eltype(u)) - T2 = constvalue(typeof(one(t))) - if length(k) < 10 || always_calc_begin - @OnDemandTableauExtract Vern7Tableau T T2 - - @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, tmp = cache - f(k1, uprev, p, t) - - @inbounds @simd ivdep for i in eachindex(u) - tmp[i] = uprev[i] + dt * (a021 * k1[i]) - end - f(k2, tmp, p, t + c2 * dt) - - @inbounds @simd ivdep for i in eachindex(u) - tmp[i] = uprev[i] + dt * (a031 * k1[i] + a032 * k2[i]) - end - f(k3, tmp, p, t + c3 * dt) - - @inbounds @simd ivdep for i in eachindex(u) - tmp[i] = uprev[i] + dt * (a041 * k1[i] + a043 * k3[i]) - end - f(k4, tmp, p, t + c4 * dt) - - @inbounds @simd ivdep for i in eachindex(u) - tmp[i] = uprev[i] + dt * (a051 * k1[i] + a053 * k3[i] + a054 * k4[i]) - end - f(k5, tmp, p, t + c5 * dt) - - @inbounds @simd ivdep for i in eachindex(u) - tmp[i] = uprev[i] + - dt * (a061 * k1[i] + a063 * k3[i] + a064 * k4[i] + a065 * k5[i]) - end - f(k6, tmp, p, t + c6 * dt) - - @inbounds @simd ivdep for i in eachindex(u) - tmp[i] = uprev[i] + - dt * (a071 * k1[i] + a073 * k3[i] + a074 * k4[i] + a075 * k5[i] + - a076 * k6[i]) - end - f(k7, tmp, p, t + c7 * dt) - - @inbounds @simd ivdep for i in eachindex(u) - tmp[i] = uprev[i] + - dt * (a081 * k1[i] + a083 * k3[i] + a084 * k4[i] + a085 * k5[i] + - a086 * k6[i] + a087 * k7[i]) - end - f(k8, tmp, p, t + c8 * dt) - - @inbounds @simd ivdep for i in eachindex(u) - tmp[i] = uprev[i] + - dt * (a091 * k1[i] + a093 * k3[i] + a094 * k4[i] + a095 * k5[i] + - a096 * k6[i] + a097 * k7[i] + a098 * k8[i]) - end - f(k9, tmp, p, t + dt) - - @inbounds @simd ivdep for i in eachindex(u) - tmp[i] = uprev[i] + - dt * (a101 * k1[i] + a103 * k3[i] + a104 * k4[i] + a105 * k5[i] + - a106 * k6[i] + a107 * k7[i]) - end - f(k10, tmp, p, t + dt) - - copyat_or_push!(k, 1, k1) - copyat_or_push!(k, 2, k2) - copyat_or_push!(k, 3, k3) - copyat_or_push!(k, 4, k4) - copyat_or_push!(k, 5, k5) - copyat_or_push!(k, 6, k6) - copyat_or_push!(k, 7, k7) - copyat_or_push!(k, 8, k8) - copyat_or_push!(k, 9, k9) - copyat_or_push!(k, 10, k10) - end - if (allow_calc_end && length(k) < 16) || force_calc_end # Have not added the extra stages yet - @unpack tmp = cache - rtmp = similar(cache.k1) - @OnDemandTableauExtract Vern7ExtraStages T T2 - - @inbounds @simd ivdep for i in eachindex(u) - tmp[i] = uprev[i] + - dt * (a1101 * k[1][i] + a1104 * k[4][i] + a1105 * k[5][i] + - a1106 * k[6][i] + a1107 * k[7][i] + a1108 * k[8][i] + a1109 * k[9][i]) - end - f(rtmp, tmp, p, t + c11 * dt) - copyat_or_push!(k, 11, rtmp) - - @inbounds @simd ivdep for i in eachindex(u) - tmp[i] = uprev[i] + - dt * (a1201 * k[1][i] + a1204 * k[4][i] + a1205 * k[5][i] + - a1206 * k[6][i] + a1207 * k[7][i] + a1208 * k[8][i] + - a1209 * k[9][i] + a1211 * k[11][i]) - end - f(rtmp, tmp, p, t + c12 * dt) - copyat_or_push!(k, 12, rtmp) - - @inbounds @simd ivdep for i in eachindex(u) - tmp[i] = uprev[i] + - dt * (a1301 * k[1][i] + a1304 * k[4][i] + a1305 * k[5][i] + - a1306 * k[6][i] + a1307 * k[7][i] + a1308 * k[8][i] + - a1309 * k[9][i] + a1311 * k[11][i] + a1312 * k[12][i]) - end - f(rtmp, tmp, p, t + c13 * dt) - copyat_or_push!(k, 13, rtmp) - - @inbounds @simd ivdep for i in eachindex(u) - tmp[i] = uprev[i] + - dt * (a1401 * k[1][i] + a1404 * k[4][i] + a1405 * k[5][i] + - a1406 * k[6][i] + a1407 * k[7][i] + a1408 * k[8][i] + - a1409 * k[9][i] + a1411 * k[11][i] + a1412 * k[12][i] + - a1413 * k[13][i]) - end - f(rtmp, tmp, p, t + c14 * dt) - copyat_or_push!(k, 14, rtmp) - - @inbounds @simd ivdep for i in eachindex(u) - tmp[i] = uprev[i] + - dt * (a1501 * k[1][i] + a1504 * k[4][i] + a1505 * k[5][i] + - a1506 * k[6][i] + a1507 * k[7][i] + a1508 * k[8][i] + - a1509 * k[9][i] + a1511 * k[11][i] + a1512 * k[12][i] + - a1513 * k[13][i]) - end - f(rtmp, tmp, p, t + c15 * dt) - copyat_or_push!(k, 15, rtmp) - - @inbounds @simd ivdep for i in eachindex(u) - tmp[i] = uprev[i] + - dt * (a1601 * k[1][i] + a1604 * k[4][i] + a1605 * k[5][i] + - a1606 * k[6][i] + a1607 * k[7][i] + a1608 * k[8][i] + - a1609 * k[9][i] + a1611 * k[11][i] + a1612 * k[12][i] + - a1613 * k[13][i]) - end - f(rtmp, tmp, p, t + c16 * dt) - copyat_or_push!(k, 16, rtmp) - end - nothing -end - -@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern8Cache, - always_calc_begin = false, allow_calc_end = true, - force_calc_end = false) - if length(k) < 13 || always_calc_begin - @unpack c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, a0201, a0301, a0302, a0401, a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, a0704, a0705, a0706, a0801, a0804, a0805, a0806, a0807, a0901, a0904, a0905, a0906, a0907, a0908, a1001, a1004, a1005, a1006, a1007, a1008, a1009, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211, a1301, a1304, a1305, a1306, a1307, a1308, a1309, a1310 = cache.tab - @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, tmp = cache - f(k1, uprev, p, t) - @.. broadcast=false tmp=uprev + dt * (a0201 * k1) - f(k2, tmp, p, t + c2 * dt) - @.. broadcast=false tmp=uprev + dt * (a0301 * k1 + a0302 * k2) - f(k3, tmp, p, t + c3 * dt) - @.. broadcast=false tmp=uprev + dt * (a0401 * k1 + a0403 * k3) - f(k4, tmp, p, t + c4 * dt) - @.. broadcast=false tmp=uprev + dt * (a0501 * k1 + a0503 * k3 + a0504 * k4) - f(k5, tmp, p, t + c5 * dt) - @.. broadcast=false tmp=uprev + dt * (a0601 * k1 + a0604 * k4 + a0605 * k5) - f(k6, tmp, p, t + c6 * dt) - @.. broadcast=false tmp=uprev + - dt * (a0701 * k1 + a0704 * k4 + a0705 * k5 + a0706 * k6) - f(k7, tmp, p, t + c7 * dt) - @.. broadcast=false tmp=uprev + - dt * (a0801 * k1 + a0804 * k4 + a0805 * k5 + a0806 * k6 + - a0807 * k7) - f(k8, tmp, p, t + c8 * dt) - @.. broadcast=false tmp=uprev + - dt * (a0901 * k1 + a0904 * k4 + a0905 * k5 + a0906 * k6 + - a0907 * k7 + a0908 * k8) - f(k9, tmp, p, t + c9 * dt) - @.. broadcast=false tmp=uprev + - dt * (a1001 * k1 + a1004 * k4 + a1005 * k5 + a1006 * k6 + - a1007 * k7 + a1008 * k8 + a1009 * k9) - f(k10, tmp, p, t + c10 * dt) - @.. broadcast=false tmp=uprev + - dt * (a1101 * k1 + a1104 * k4 + a1105 * k5 + a1106 * k6 + - a1107 * k7 + a1108 * k8 + a1109 * k9 + a1110 * k10) - f(k11, tmp, p, t + c11 * dt) - @.. broadcast=false tmp=uprev + - dt * (a1201 * k1 + a1204 * k4 + a1205 * k5 + a1206 * k6 + - a1207 * k7 + a1208 * k8 + a1209 * k9 + a1210 * k10 + - a1211 * k11) - f(k12, tmp, p, t + dt) - @.. broadcast=false tmp=uprev + - dt * (a1301 * k1 + a1304 * k4 + a1305 * k5 + a1306 * k6 + - a1307 * k7 + a1308 * k8 + a1309 * k9 + a1310 * k10) - f(k13, tmp, p, t + dt) - copyat_or_push!(k, 1, k1) - copyat_or_push!(k, 2, k2) - copyat_or_push!(k, 3, k3) - copyat_or_push!(k, 4, k4) - copyat_or_push!(k, 5, k5) - copyat_or_push!(k, 6, k6) - copyat_or_push!(k, 7, k7) - copyat_or_push!(k, 8, k8) - copyat_or_push!(k, 9, k9) - copyat_or_push!(k, 10, k10) - copyat_or_push!(k, 11, k11) - copyat_or_push!(k, 12, k12) - copyat_or_push!(k, 13, k13) - end - if (allow_calc_end && length(k) < 21) || force_calc_end # Have not added the extra stages yet - rtmp = similar(cache.k1) - @unpack c14, a1401, a1406, a1407, a1408, a1409, a1410, a1411, a1412, c15, a1501, a1506, a1507, a1508, a1509, a1510, a1511, a1512, a1514, c16, a1601, a1606, a1607, a1608, a1609, a1610, a1611, a1612, a1614, a1615, c17, a1701, a1706, a1707, a1708, a1709, a1710, a1711, a1712, a1714, a1715, a1716, c18, a1801, a1806, a1807, a1808, a1809, a1810, a1811, a1812, a1814, a1815, a1816, a1817, c19, a1901, a1906, a1907, a1908, a1909, a1910, a1911, a1912, a1914, a1915, a1916, a1917, c20, a2001, a2006, a2007, a2008, a2009, a2010, a2011, a2012, a2014, a2015, a2016, a2017, c21, a2101, a2106, a2107, a2108, a2109, a2110, a2111, a2112, a2114, a2115, a2116, a2117 = cache.tab.extra - @unpack tmp = cache - @.. broadcast=false tmp=uprev + - dt * - (a1401 * k[1] + a1406 * k[6] + a1407 * k[7] + a1408 * k[8] + - a1409 * k[9] + a1410 * k[10] + a1411 * k[11] + - a1412 * k[12]) - f(rtmp, tmp, p, t + c14 * dt) - copyat_or_push!(k, 14, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a1501 * k[1] + a1506 * k[6] + a1507 * k[7] + a1508 * k[8] + - a1509 * k[9] + a1510 * k[10] + a1511 * k[11] + - a1512 * k[12] + a1514 * k[14]) - f(rtmp, tmp, p, t + c15 * dt) - copyat_or_push!(k, 15, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a1601 * k[1] + a1606 * k[6] + a1607 * k[7] + a1608 * k[8] + - a1609 * k[9] + a1610 * k[10] + a1611 * k[11] + - a1612 * k[12] + a1614 * k[14] + a1615 * k[15]) - f(rtmp, tmp, p, t + c16 * dt) - copyat_or_push!(k, 16, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a1701 * k[1] + a1706 * k[6] + a1707 * k[7] + a1708 * k[8] + - a1709 * k[9] + a1710 * k[10] + a1711 * k[11] + - a1712 * k[12] + a1714 * k[14] + a1715 * k[15] + - a1716 * k[16]) - f(rtmp, tmp, p, t + c17 * dt) - copyat_or_push!(k, 17, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a1801 * k[1] + a1806 * k[6] + a1807 * k[7] + a1808 * k[8] + - a1809 * k[9] + a1810 * k[10] + a1811 * k[11] + - a1812 * k[12] + a1814 * k[14] + a1815 * k[15] + - a1816 * k[16] + a1817 * k[17]) - f(rtmp, tmp, p, t + c18 * dt) - copyat_or_push!(k, 18, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a1901 * k[1] + a1906 * k[6] + a1907 * k[7] + a1908 * k[8] + - a1909 * k[9] + a1910 * k[10] + a1911 * k[11] + - a1912 * k[12] + a1914 * k[14] + a1915 * k[15] + - a1916 * k[16] + a1917 * k[17]) - f(rtmp, tmp, p, t + c19 * dt) - copyat_or_push!(k, 19, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a2001 * k[1] + a2006 * k[6] + a2007 * k[7] + a2008 * k[8] + - a2009 * k[9] + a2010 * k[10] + a2011 * k[11] + - a2012 * k[12] + a2014 * k[14] + a2015 * k[15] + - a2016 * k[16] + a2017 * k[17]) - f(rtmp, tmp, p, t + c20 * dt) - copyat_or_push!(k, 20, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a2101 * k[1] + a2106 * k[6] + a2107 * k[7] + a2108 * k[8] + - a2109 * k[9] + a2110 * k[10] + a2111 * k[11] + - a2112 * k[12] + a2114 * k[14] + a2115 * k[15] + - a2116 * k[16] + a2117 * k[17]) - f(rtmp, tmp, p, t + c21 * dt) - copyat_or_push!(k, 21, rtmp) - end - nothing -end - -@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern9Cache, - always_calc_begin = false, allow_calc_end = true, - force_calc_end = false) - T = constvalue(recursive_unitless_bottom_eltype(u)) - T2 = constvalue(typeof(one(t))) - if length(k) < 10 || always_calc_begin - @OnDemandTableauExtract Vern9Tableau T T2 - @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, tmp = cache - uidx = eachindex(uprev) - f(k1, uprev, p, t) - @.. broadcast=false tmp=uprev + dt * (a0201 * k1) - f(k2, tmp, p, t + c1 * dt) - @.. broadcast=false tmp=uprev + dt * (a0301 * k1 + a0302 * k2) - f(k3, tmp, p, t + c2 * dt) - @.. broadcast=false tmp=uprev + dt * (a0401 * k1 + a0403 * k3) - f(k4, tmp, p, t + c3 * dt) - @.. broadcast=false tmp=uprev + dt * (a0501 * k1 + a0503 * k3 + a0504 * k4) - f(k5, tmp, p, t + c4 * dt) - @.. broadcast=false tmp=uprev + dt * (a0601 * k1 + a0604 * k4 + a0605 * k5) - f(k6, tmp, p, t + c5 * dt) - @.. broadcast=false tmp=uprev + - dt * (a0701 * k1 + a0704 * k4 + a0705 * k5 + a0706 * k6) - f(k7, tmp, p, t + c6 * dt) - @.. broadcast=false tmp=uprev + dt * (a0801 * k1 + a0806 * k6 + a0807 * k7) - f(k8, tmp, p, t + c7 * dt) - @.. broadcast=false tmp=uprev + - dt * (a0901 * k1 + a0906 * k6 + a0907 * k7 + a0908 * k8) - f(k9, tmp, p, t + c8 * dt) - @.. broadcast=false tmp=uprev + - dt * (a1001 * k1 + a1006 * k6 + a1007 * k7 + a1008 * k8 + - a1009 * k9) - f(k10, tmp, p, t + c9 * dt) - @.. broadcast=false tmp=uprev + - dt * (a1101 * k1 + a1106 * k6 + a1107 * k7 + a1108 * k8 + - a1109 * k9 + a1110 * k10) - f(k11, tmp, p, t + c10 * dt) - @.. broadcast=false tmp=uprev + - dt * (a1201 * k1 + a1206 * k6 + a1207 * k7 + a1208 * k8 + - a1209 * k9 + a1210 * k10 + a1211 * k11) - f(k12, tmp, p, t + c11 * dt) - @.. broadcast=false tmp=uprev + - dt * (a1301 * k1 + a1306 * k6 + a1307 * k7 + a1308 * k8 + - a1309 * k9 + a1310 * k10 + a1311 * k11 + a1312 * k12) - f(k13, tmp, p, t + c12 * dt) - @.. broadcast=false tmp=uprev + - dt * (a1401 * k1 + a1406 * k6 + a1407 * k7 + a1408 * k8 + - a1409 * k9 + a1410 * k10 + a1411 * k11 + a1412 * k12 + - a1413 * k13) - f(k14, tmp, p, t + c13 * dt) - @.. broadcast=false tmp=uprev + - dt * (a1501 * k1 + a1506 * k6 + a1507 * k7 + a1508 * k8 + - a1509 * k9 + a1510 * k10 + a1511 * k11 + a1512 * k12 + - a1513 * k13 + a1514 * k14) - f(k15, tmp, p, t + dt) - @.. broadcast=false tmp=uprev + - dt * (a1601 * k1 + a1606 * k6 + a1607 * k7 + a1608 * k8 + - a1609 * k9 + a1610 * k10 + a1611 * k11 + a1612 * k12 + - a1613 * k13) - f(k16, tmp, p, t + dt) - copyat_or_push!(k, 1, k1) - copyat_or_push!(k, 2, k8) - copyat_or_push!(k, 3, k9) - copyat_or_push!(k, 4, k10) - copyat_or_push!(k, 5, k11) - copyat_or_push!(k, 6, k12) - copyat_or_push!(k, 7, k13) - copyat_or_push!(k, 8, k14) - copyat_or_push!(k, 9, k15) - copyat_or_push!(k, 10, k16) - end - if (allow_calc_end && length(k) < 20) || force_calc_end # Have not added the extra stages yet - rtmp = similar(cache.k1) - uidx = eachindex(uprev) - @unpack tmp = cache - @OnDemandTableauExtract Vern9ExtraStages T T2 - @.. broadcast=false tmp=uprev + - dt * - (a1701 * k[1] + a1708 * k[2] + a1709 * k[3] + a1710 * k[4] + - a1711 * k[5] + a1712 * k[6] + a1713 * k[7] + a1714 * k[8] + - a1715 * k[9]) - f(rtmp, tmp, p, t + c17 * dt) - copyat_or_push!(k, 11, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a1801 * k[1] + a1808 * k[2] + a1809 * k[3] + a1810 * k[4] + - a1811 * k[5] + a1812 * k[6] + a1813 * k[7] + a1814 * k[8] + - a1815 * k[9] + a1817 * k[11]) - f(rtmp, tmp, p, t + c18 * dt) - copyat_or_push!(k, 12, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a1901 * k[1] + a1908 * k[2] + a1909 * k[3] + a1910 * k[4] + - a1911 * k[5] + a1912 * k[6] + a1913 * k[7] + a1914 * k[8] + - a1915 * k[9] + a1917 * k[11] + a1918 * k[12]) - f(rtmp, tmp, p, t + c19 * dt) - copyat_or_push!(k, 13, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a2001 * k[1] + a2008 * k[2] + a2009 * k[3] + a2010 * k[4] + - a2011 * k[5] + a2012 * k[6] + a2013 * k[7] + a2014 * k[8] + - a2015 * k[9] + a2017 * k[11] + a2018 * k[12] + - a2019 * k[13]) - f(rtmp, tmp, p, t + c20 * dt) - copyat_or_push!(k, 14, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a2101 * k[1] + a2108 * k[2] + a2109 * k[3] + a2110 * k[4] + - a2111 * k[5] + a2112 * k[6] + a2113 * k[7] + a2114 * k[8] + - a2115 * k[9] + a2117 * k[11] + a2118 * k[12] + - a2119 * k[13] + a2120 * k[14]) - f(rtmp, tmp, p, t + c21 * dt) - copyat_or_push!(k, 15, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a2201 * k[1] + a2208 * k[2] + a2209 * k[3] + a2210 * k[4] + - a2211 * k[5] + a2212 * k[6] + a2213 * k[7] + a2214 * k[8] + - a2215 * k[9] + a2217 * k[11] + a2218 * k[12] + - a2219 * k[13] + a2220 * k[14] + a2221 * k[15]) - f(rtmp, tmp, p, t + c22 * dt) - copyat_or_push!(k, 16, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a2301 * k[1] + a2308 * k[2] + a2309 * k[3] + a2310 * k[4] + - a2311 * k[5] + a2312 * k[6] + a2313 * k[7] + a2314 * k[8] + - a2315 * k[9] + a2317 * k[11] + a2318 * k[12] + - a2319 * k[13] + a2320 * k[14] + a2321 * k[15]) - f(rtmp, tmp, p, t + c23 * dt) - copyat_or_push!(k, 17, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a2401 * k[1] + a2408 * k[2] + a2409 * k[3] + a2410 * k[4] + - a2411 * k[5] + a2412 * k[6] + a2413 * k[7] + a2414 * k[8] + - a2415 * k[9] + a2417 * k[11] + a2418 * k[12] + - a2419 * k[13] + a2420 * k[14] + a2421 * k[15]) - f(rtmp, tmp, p, t + c24 * dt) - copyat_or_push!(k, 18, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a2501 * k[1] + a2508 * k[2] + a2509 * k[3] + a2510 * k[4] + - a2511 * k[5] + a2512 * k[6] + a2513 * k[7] + a2514 * k[8] + - a2515 * k[9] + a2517 * k[11] + a2518 * k[12] + - a2519 * k[13] + a2520 * k[14] + a2521 * k[15]) - f(rtmp, tmp, p, t + c25 * dt) - copyat_or_push!(k, 19, rtmp) - @.. broadcast=false tmp=uprev + - dt * - (a2601 * k[1] + a2608 * k[2] + a2609 * k[3] + a2610 * k[4] + - a2611 * k[5] + a2612 * k[6] + a2613 * k[7] + a2614 * k[8] + - a2615 * k[9] + a2617 * k[11] + a2618 * k[12] + - a2619 * k[13] + a2620 * k[14] + a2621 * k[15]) - f(rtmp, tmp, p, t + c26 * dt) - copyat_or_push!(k, 20, rtmp) - end - nothing -end -@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern9Cache{<:Array}, - always_calc_begin = false, allow_calc_end = true, - force_calc_end = false) - T = constvalue(recursive_unitless_bottom_eltype(u)) - T2 = constvalue(typeof(one(t))) - if length(k) < 10 || always_calc_begin - @OnDemandTableauExtract Vern9Tableau T T2 - @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, tmp = cache - uidx = eachindex(uprev) - f(k1, uprev, p, t) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + dt * (a0201 * k1[i]) - end - f(k2, tmp, p, t + c1 * dt) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + dt * (a0301 * k1[i] + a0302 * k2[i]) - end - f(k3, tmp, p, t + c2 * dt) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + dt * (a0401 * k1[i] + a0403 * k3[i]) - end - f(k4, tmp, p, t + c3 * dt) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + dt * (a0501 * k1[i] + a0503 * k3[i] + a0504 * k4[i]) - end - f(k5, tmp, p, t + c4 * dt) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + dt * (a0601 * k1[i] + a0604 * k4[i] + a0605 * k5[i]) - end - f(k6, tmp, p, t + c5 * dt) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + - dt * (a0701 * k1[i] + a0704 * k4[i] + a0705 * k5[i] + a0706 * k6[i]) - end - f(k7, tmp, p, t + c6 * dt) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + dt * (a0801 * k1[i] + a0806 * k6[i] + a0807 * k7[i]) - end - f(k8, tmp, p, t + c7 * dt) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + - dt * (a0901 * k1[i] + a0906 * k6[i] + a0907 * k7[i] + a0908 * k8[i]) - end - f(k9, tmp, p, t + c8 * dt) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + - dt * (a1001 * k1[i] + a1006 * k6[i] + a1007 * k7[i] + a1008 * k8[i] + - a1009 * k9[i]) - end - f(k10, tmp, p, t + c9 * dt) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + - dt * (a1101 * k1[i] + a1106 * k6[i] + a1107 * k7[i] + a1108 * k8[i] + - a1109 * k9[i] + a1110 * k10[i]) - end - f(k11, tmp, p, t + c10 * dt) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + - dt * (a1201 * k1[i] + a1206 * k6[i] + a1207 * k7[i] + a1208 * k8[i] + - a1209 * k9[i] + a1210 * k10[i] + a1211 * k11[i]) - end - f(k12, tmp, p, t + c11 * dt) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + - dt * (a1301 * k1[i] + a1306 * k6[i] + a1307 * k7[i] + a1308 * k8[i] + - a1309 * k9[i] + a1310 * k10[i] + a1311 * k11[i] + a1312 * k12[i]) - end - f(k13, tmp, p, t + c12 * dt) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + - dt * (a1401 * k1[i] + a1406 * k6[i] + a1407 * k7[i] + a1408 * k8[i] + - a1409 * k9[i] + a1410 * k10[i] + a1411 * k11[i] + a1412 * k12[i] + - a1413 * k13[i]) - end - f(k14, tmp, p, t + c13 * dt) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + - dt * (a1501 * k1[i] + a1506 * k6[i] + a1507 * k7[i] + a1508 * k8[i] + - a1509 * k9[i] + a1510 * k10[i] + a1511 * k11[i] + a1512 * k12[i] + - a1513 * k13[i] + a1514 * k14[i]) - end - f(k15, tmp, p, t + dt) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + - dt * (a1601 * k1[i] + a1606 * k6[i] + a1607 * k7[i] + a1608 * k8[i] + - a1609 * k9[i] + a1610 * k10[i] + a1611 * k11[i] + a1612 * k12[i] + - a1613 * k13[i]) - end - f(k16, tmp, p, t + dt) - copyat_or_push!(k, 1, k1) - copyat_or_push!(k, 2, k8) - copyat_or_push!(k, 3, k9) - copyat_or_push!(k, 4, k10) - copyat_or_push!(k, 5, k11) - copyat_or_push!(k, 6, k12) - copyat_or_push!(k, 7, k13) - copyat_or_push!(k, 8, k14) - copyat_or_push!(k, 9, k15) - copyat_or_push!(k, 10, k16) - end - if (allow_calc_end && length(k) < 20) || force_calc_end # Have not added the extra stages yet - rtmp = similar(cache.k1) - uidx = eachindex(uprev) - @unpack tmp = cache - @OnDemandTableauExtract Vern9ExtraStages T T2 - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + - dt * (a1701 * k[1][i] + a1708 * k[2][i] + a1709 * k[3][i] + - a1710 * k[4][i] + a1711 * k[5][i] + a1712 * k[6][i] + - a1713 * k[7][i] + a1714 * k[8][i] + a1715 * k[9][i]) - end - f(rtmp, tmp, p, t + c17 * dt) - copyat_or_push!(k, 11, rtmp) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + - dt * (a1801 * k[1][i] + a1808 * k[2][i] + a1809 * k[3][i] + - a1810 * k[4][i] + a1811 * k[5][i] + a1812 * k[6][i] + - a1813 * k[7][i] + a1814 * k[8][i] + a1815 * k[9][i] + - a1817 * k[11][i]) - end - f(rtmp, tmp, p, t + c18 * dt) - copyat_or_push!(k, 12, rtmp) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + - dt * (a1901 * k[1][i] + a1908 * k[2][i] + a1909 * k[3][i] + - a1910 * k[4][i] + a1911 * k[5][i] + a1912 * k[6][i] + - a1913 * k[7][i] + a1914 * k[8][i] + a1915 * k[9][i] + - a1917 * k[11][i] + a1918 * k[12][i]) - end - f(rtmp, tmp, p, t + c19 * dt) - copyat_or_push!(k, 13, rtmp) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + - dt * (a2001 * k[1][i] + a2008 * k[2][i] + a2009 * k[3][i] + - a2010 * k[4][i] + a2011 * k[5][i] + a2012 * k[6][i] + - a2013 * k[7][i] + a2014 * k[8][i] + a2015 * k[9][i] + - a2017 * k[11][i] + a2018 * k[12][i] + a2019 * k[13][i]) - end - f(rtmp, tmp, p, t + c20 * dt) - copyat_or_push!(k, 14, rtmp) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + - dt * (a2101 * k[1][i] + a2108 * k[2][i] + a2109 * k[3][i] + - a2110 * k[4][i] + a2111 * k[5][i] + a2112 * k[6][i] + - a2113 * k[7][i] + a2114 * k[8][i] + a2115 * k[9][i] + - a2117 * k[11][i] + a2118 * k[12][i] + a2119 * k[13][i] + - a2120 * k[14][i]) - end - f(rtmp, tmp, p, t + c21 * dt) - copyat_or_push!(k, 15, rtmp) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + - dt * (a2201 * k[1][i] + a2208 * k[2][i] + a2209 * k[3][i] + - a2210 * k[4][i] + a2211 * k[5][i] + a2212 * k[6][i] + - a2213 * k[7][i] + a2214 * k[8][i] + a2215 * k[9][i] + - a2217 * k[11][i] + a2218 * k[12][i] + a2219 * k[13][i] + - a2220 * k[14][i] + a2221 * k[15][i]) - end - f(rtmp, tmp, p, t + c22 * dt) - copyat_or_push!(k, 16, rtmp) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + - dt * (a2301 * k[1][i] + a2308 * k[2][i] + a2309 * k[3][i] + - a2310 * k[4][i] + a2311 * k[5][i] + a2312 * k[6][i] + - a2313 * k[7][i] + a2314 * k[8][i] + a2315 * k[9][i] + - a2317 * k[11][i] + a2318 * k[12][i] + a2319 * k[13][i] + - a2320 * k[14][i] + a2321 * k[15][i]) - end - f(rtmp, tmp, p, t + c23 * dt) - copyat_or_push!(k, 17, rtmp) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + - dt * (a2401 * k[1][i] + a2408 * k[2][i] + a2409 * k[3][i] + - a2410 * k[4][i] + a2411 * k[5][i] + a2412 * k[6][i] + - a2413 * k[7][i] + a2414 * k[8][i] + a2415 * k[9][i] + - a2417 * k[11][i] + a2418 * k[12][i] + a2419 * k[13][i] + - a2420 * k[14][i] + a2421 * k[15][i]) - end - f(rtmp, tmp, p, t + c24 * dt) - copyat_or_push!(k, 18, rtmp) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + - dt * (a2501 * k[1][i] + a2508 * k[2][i] + a2509 * k[3][i] + - a2510 * k[4][i] + a2511 * k[5][i] + a2512 * k[6][i] + - a2513 * k[7][i] + a2514 * k[8][i] + a2515 * k[9][i] + - a2517 * k[11][i] + a2518 * k[12][i] + a2519 * k[13][i] + - a2520 * k[14][i] + a2521 * k[15][i]) - end - f(rtmp, tmp, p, t + c25 * dt) - copyat_or_push!(k, 19, rtmp) - - @inbounds @simd ivdep for i in uidx - tmp[i] = uprev[i] + - dt * (a2601 * k[1][i] + a2608 * k[2][i] + a2609 * k[3][i] + - a2610 * k[4][i] + a2611 * k[5][i] + a2612 * k[6][i] + - a2613 * k[7][i] + a2614 * k[8][i] + a2615 * k[9][i] + - a2617 * k[11][i] + a2618 * k[12][i] + a2619 * k[13][i] + - a2620 * k[14][i] + a2621 * k[15][i]) - end - f(rtmp, tmp, p, t + c26 * dt) - copyat_or_push!(k, 20, rtmp) - end - nothing -end - -@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern6ConstantCache, - always_calc_begin = false, allow_calc_end = true, - force_calc_end = false) - if length(k) < 9 || always_calc_begin - @unpack c1, c2, c3, c4, c5, c6, a21, a31, a32, a41, a43, a51, a53, a54, a61, a63, a64, a65, a71, a73, a74, a75, a76, a81, a83, a84, a85, a86, a87, a91, a94, a95, a96, a97, a98 = cache.tab - copyat_or_push!(k, 1, f(uprev, p, t)) - copyat_or_push!(k, 2, f(uprev + dt * (a21 * k[1]), p, t + c1 * dt)) - copyat_or_push!(k, 3, f(uprev + dt * (a31 * k[1] + a32 * k[2]), p, t + c2 * dt)) - copyat_or_push!(k, 4, f(uprev + dt * (a41 * k[1] + a43 * k[3]), p, t + c3 * dt)) - copyat_or_push!(k, 5, - f(uprev + dt * (a51 * k[1] + a53 * k[3] + a54 * k[4]), p, - t + c4 * dt)) - copyat_or_push!(k, 6, - f(uprev + dt * (a61 * k[1] + a63 * k[3] + a64 * k[4] + a65 * k[5]), - p, t + c5 * dt)) - copyat_or_push!(k, 7, - f( - uprev + - dt * - (a71 * k[1] + a73 * k[3] + a74 * k[4] + a75 * k[5] + a76 * k[6]), - p, t + c6 * dt)) - copyat_or_push!(k, 8, - f( - uprev + - dt * - (a81 * k[1] + a83 * k[3] + a84 * k[4] + a85 * k[5] + a86 * k[6] + - a87 * k[7]), - p, - t + dt)) - copyat_or_push!(k, 9, - f( - uprev + - dt * - (a91 * k[1] + a94 * k[4] + a95 * k[5] + a96 * k[6] + a97 * k[7] + - a98 * k[8]), - p, - t + dt)) - end - if (allow_calc_end && length(k) < 12) || force_calc_end # Have not added the extra stages yet - @unpack c10, a1001, a1004, a1005, a1006, a1007, a1008, a1009, c11, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, c12, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211 = cache.tab.extra - copyat_or_push!(k, 10, - f( - uprev + - dt * - (a1001 * k[1] + a1004 * k[4] + a1005 * k[5] + a1006 * k[6] + - a1007 * k[7] + a1008 * k[8] + a1009 * k[9]), - p, - t + c10 * dt)) - copyat_or_push!(k, 11, - f( - uprev + - dt * - (a1101 * k[1] + a1104 * k[4] + a1105 * k[5] + a1106 * k[6] + - a1107 * k[7] + a1108 * k[8] + a1109 * k[9] + a1110 * k[10]), - p, - t + c11 * dt)) - copyat_or_push!(k, 12, - f( - uprev + - dt * - (a1201 * k[1] + a1204 * k[4] + a1205 * k[5] + a1206 * k[6] + - a1207 * k[7] + a1208 * k[8] + a1209 * k[9] + a1210 * k[10] + - a1211 * k[11]), - p, - t + c12 * dt)) - end - nothing -end - -@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern7ConstantCache, - always_calc_begin = false, allow_calc_end = true, - force_calc_end = false) - T = constvalue(recursive_unitless_bottom_eltype(u)) - T2 = constvalue(typeof(one(t))) - if length(k) < 10 || always_calc_begin - @OnDemandTableauExtract Vern7Tableau T T2 - copyat_or_push!(k, 1, f(uprev, p, t)) - copyat_or_push!(k, 2, f(uprev + dt * (a021 * k[1]), p, t + c2 * dt)) - copyat_or_push!(k, 3, f(uprev + dt * (a031 * k[1] + a032 * k[2]), p, t + c3 * dt)) - copyat_or_push!(k, 4, f(uprev + dt * (a041 * k[1] + a043 * k[3]), p, t + c4 * dt)) - copyat_or_push!(k, 5, - f(uprev + dt * (a051 * k[1] + a053 * k[3] + a054 * k[4]), p, - t + c5 * dt)) - copyat_or_push!(k, 6, - f(uprev + - dt * (a061 * k[1] + a063 * k[3] + a064 * k[4] + a065 * k[5]), p, - t + c6 * dt)) - copyat_or_push!(k, 7, - f( - uprev + - dt * (a071 * k[1] + a073 * k[3] + a074 * k[4] + a075 * k[5] + - a076 * k[6]), - p, - t + c7 * dt)) - copyat_or_push!(k, 8, - f( - uprev + - dt * (a081 * k[1] + a083 * k[3] + a084 * k[4] + a085 * k[5] + - a086 * k[6] + a087 * k[7]), - p, - t + c8 * dt)) - copyat_or_push!(k, 9, - f( - uprev + - dt * (a091 * k[1] + a093 * k[3] + a094 * k[4] + a095 * k[5] + - a096 * k[6] + a097 * k[7] + a098 * k[8]), - p, - t + dt)) - copyat_or_push!(k, 10, - f( - uprev + - dt * (a101 * k[1] + a103 * k[3] + a104 * k[4] + a105 * k[5] + - a106 * k[6] + a107 * k[7]), - p, - t + dt)) - end - if (allow_calc_end && length(k) < 16) || force_calc_end # Have not added the extra stages yet - @OnDemandTableauExtract Vern7ExtraStages T T2 - copyat_or_push!(k, 11, - f( - uprev + - dt * - (a1101 * k[1] + a1104 * k[4] + a1105 * k[5] + a1106 * k[6] + - a1107 * k[7] + a1108 * k[8] + a1109 * k[9]), - p, - t + c11 * dt)) - copyat_or_push!(k, 12, - f( - uprev + - dt * - (a1201 * k[1] + a1204 * k[4] + a1205 * k[5] + a1206 * k[6] + - a1207 * k[7] + a1208 * k[8] + a1209 * k[9] + a1211 * k[11]), - p, - t + c12 * dt)) - copyat_or_push!(k, 13, - f( - uprev + - dt * - (a1301 * k[1] + a1304 * k[4] + a1305 * k[5] + a1306 * k[6] + - a1307 * k[7] + a1308 * k[8] + a1309 * k[9] + a1311 * k[11] + - a1312 * k[12]), - p, - t + c13 * dt)) - copyat_or_push!(k, 14, - f( - uprev + - dt * - (a1401 * k[1] + a1404 * k[4] + a1405 * k[5] + a1406 * k[6] + - a1407 * k[7] + a1408 * k[8] + a1409 * k[9] + a1411 * k[11] + - a1412 * k[12] + a1413 * k[13]), - p, - t + c14 * dt)) - copyat_or_push!(k, 15, - f( - uprev + - dt * - (a1501 * k[1] + a1504 * k[4] + a1505 * k[5] + a1506 * k[6] + - a1507 * k[7] + a1508 * k[8] + a1509 * k[9] + a1511 * k[11] + - a1512 * k[12] + a1513 * k[13]), - p, - t + c15 * dt)) - copyat_or_push!(k, 16, - f( - uprev + - dt * - (a1601 * k[1] + a1604 * k[4] + a1605 * k[5] + a1606 * k[6] + - a1607 * k[7] + a1608 * k[8] + a1609 * k[9] + a1611 * k[11] + - a1612 * k[12] + a1613 * k[13]), - p, - t + c16 * dt)) - end - nothing -end - -@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern8ConstantCache, - always_calc_begin = false, allow_calc_end = true, - force_calc_end = false) - if length(k) < 13 || always_calc_begin - @unpack c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, a0201, a0301, a0302, a0401, a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, a0704, a0705, a0706, a0801, a0804, a0805, a0806, a0807, a0901, a0904, a0905, a0906, a0907, a0908, a1001, a1004, a1005, a1006, a1007, a1008, a1009, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211, a1301, a1304, a1305, a1306, a1307, a1308, a1309, a1310 = cache.tab - copyat_or_push!(k, 1, f(uprev, p, t)) - copyat_or_push!(k, 2, f(uprev + dt * (a0201 * k[1]), p, t + c2 * dt)) - copyat_or_push!(k, 3, f(uprev + dt * (a0301 * k[1] + a0302 * k[2]), p, t + c3 * dt)) - copyat_or_push!(k, 4, f(uprev + dt * (a0401 * k[1] + a0403 * k[3]), p, t + c4 * dt)) - copyat_or_push!(k, 5, - f(uprev + dt * (a0501 * k[1] + a0503 * k[3] + a0504 * k[4]), p, - t + c5 * dt)) - copyat_or_push!(k, 6, - f(uprev + dt * (a0601 * k[1] + a0604 * k[4] + a0605 * k[5]), p, - t + c6 * dt)) - copyat_or_push!(k, 7, - f(uprev + - dt * (a0701 * k[1] + a0704 * k[4] + a0705 * k[5] + a0706 * k[6]), - p, t + c7 * dt)) - copyat_or_push!(k, 8, - f( - uprev + - dt * - (a0801 * k[1] + a0804 * k[4] + a0805 * k[5] + a0806 * k[6] + - a0807 * k[7]), - p, - t + c8 * dt)) - copyat_or_push!(k, 9, - f( - uprev + - dt * - (a0901 * k[1] + a0904 * k[4] + a0905 * k[5] + a0906 * k[6] + - a0907 * k[7] + a0908 * k[8]), - p, - t + c9 * dt)) - copyat_or_push!(k, 10, - f( - uprev + - dt * - (a1001 * k[1] + a1004 * k[4] + a1005 * k[5] + a1006 * k[6] + - a1007 * k[7] + a1008 * k[8] + a1009 * k[9]), - p, - t + c10 * dt)) - copyat_or_push!(k, 11, - f( - uprev + - dt * - (a1101 * k[1] + a1104 * k[4] + a1105 * k[5] + a1106 * k[6] + - a1107 * k[7] + a1108 * k[8] + a1109 * k[9] + a1110 * k[10]), - p, - t + c11 * dt)) - copyat_or_push!(k, 12, - f( - uprev + - dt * - (a1201 * k[1] + a1204 * k[4] + a1205 * k[5] + a1206 * k[6] + - a1207 * k[7] + a1208 * k[8] + a1209 * k[9] + a1210 * k[10] + - a1211 * k[11]), - p, - t + dt)) - copyat_or_push!(k, 13, - f( - uprev + - dt * - (a1301 * k[1] + a1304 * k[4] + a1305 * k[5] + a1306 * k[6] + - a1307 * k[7] + a1308 * k[8] + a1309 * k[9] + a1310 * k[10]), - p, - t + dt)) - end - if (allow_calc_end && length(k) < 21) || force_calc_end # Have not added the extra stages yet - @unpack c14, a1401, a1406, a1407, a1408, a1409, a1410, a1411, a1412, c15, a1501, a1506, a1507, a1508, a1509, a1510, a1511, a1512, a1514, c16, a1601, a1606, a1607, a1608, a1609, a1610, a1611, a1612, a1614, a1615, c17, a1701, a1706, a1707, a1708, a1709, a1710, a1711, a1712, a1714, a1715, a1716, c18, a1801, a1806, a1807, a1808, a1809, a1810, a1811, a1812, a1814, a1815, a1816, a1817, c19, a1901, a1906, a1907, a1908, a1909, a1910, a1911, a1912, a1914, a1915, a1916, a1917, c20, a2001, a2006, a2007, a2008, a2009, a2010, a2011, a2012, a2014, a2015, a2016, a2017, c21, a2101, a2106, a2107, a2108, a2109, a2110, a2111, a2112, a2114, a2115, a2116, a2117 = cache.tab.extra - copyat_or_push!(k, 14, - f( - uprev + - dt * - (a1401 * k[1] + a1406 * k[6] + a1407 * k[7] + a1408 * k[8] + - a1409 * k[9] + a1410 * k[10] + a1411 * k[11] + a1412 * k[12]), - p, - t + c14 * dt)) - copyat_or_push!(k, 15, - f( - uprev + - dt * - (a1501 * k[1] + a1506 * k[6] + a1507 * k[7] + a1508 * k[8] + - a1509 * k[9] + a1510 * k[10] + a1511 * k[11] + a1512 * k[12] + - a1514 * k[14]), - p, - t + c15 * dt)) - copyat_or_push!(k, 16, - f( - uprev + - dt * - (a1601 * k[1] + a1606 * k[6] + a1607 * k[7] + a1608 * k[8] + - a1609 * k[9] + a1610 * k[10] + a1611 * k[11] + a1612 * k[12] + - a1614 * k[14] + a1615 * k[15]), - p, - t + c16 * dt)) - copyat_or_push!(k, 17, - f( - uprev + - dt * - (a1701 * k[1] + a1706 * k[6] + a1707 * k[7] + a1708 * k[8] + - a1709 * k[9] + a1710 * k[10] + a1711 * k[11] + a1712 * k[12] + - a1714 * k[14] + a1715 * k[15] + a1716 * k[16]), - p, - t + c17 * dt)) - copyat_or_push!(k, 18, - f( - uprev + - dt * - (a1801 * k[1] + a1806 * k[6] + a1807 * k[7] + a1808 * k[8] + - a1809 * k[9] + a1810 * k[10] + a1811 * k[11] + a1812 * k[12] + - a1814 * k[14] + a1815 * k[15] + a1816 * k[16] + a1817 * k[17]), - p, t + c18 * dt)) - copyat_or_push!(k, 19, - f( - uprev + - dt * - (a1901 * k[1] + a1906 * k[6] + a1907 * k[7] + a1908 * k[8] + - a1909 * k[9] + a1910 * k[10] + a1911 * k[11] + a1912 * k[12] + - a1914 * k[14] + a1915 * k[15] + a1916 * k[16] + a1917 * k[17]), - p, t + c19 * dt)) - copyat_or_push!(k, 20, - f( - uprev + - dt * - (a2001 * k[1] + a2006 * k[6] + a2007 * k[7] + a2008 * k[8] + - a2009 * k[9] + a2010 * k[10] + a2011 * k[11] + a2012 * k[12] + - a2014 * k[14] + a2015 * k[15] + a2016 * k[16] + a2017 * k[17]), - p, t + c20 * dt)) - copyat_or_push!(k, 21, - f( - uprev + - dt * - (a2101 * k[1] + a2106 * k[6] + a2107 * k[7] + a2108 * k[8] + - a2109 * k[9] + a2110 * k[10] + a2111 * k[11] + a2112 * k[12] + - a2114 * k[14] + a2115 * k[15] + a2116 * k[16] + a2117 * k[17]), - p, t + c21 * dt)) - end - nothing -end - -@muladd function _ode_addsteps!(k, t, uprev, u, dt, f, p, cache::Vern9ConstantCache, - always_calc_begin = false, allow_calc_end = true, - force_calc_end = false) - T = constvalue(recursive_unitless_bottom_eltype(u)) - T2 = constvalue(typeof(one(t))) - if length(k) < 10 || always_calc_begin - @OnDemandTableauExtract Vern9Tableau T T2 - copyat_or_push!(k, 1, f(uprev, p, t)) - copyat_or_push!(k, 2, f(uprev + dt * (a0201 * k[1]), p, t + c1 * dt)) - copyat_or_push!(k, 3, f(uprev + dt * (a0301 * k[1] + a0302 * k[2]), p, t + c2 * dt)) - copyat_or_push!(k, 4, f(uprev + dt * (a0401 * k[1] + a0403 * k[3]), p, t + c3 * dt)) - copyat_or_push!(k, 5, - f(uprev + dt * (a0501 * k[1] + a0503 * k[3] + a0504 * k[4]), p, - t + c4 * dt)) - copyat_or_push!(k, 6, - f(uprev + dt * (a0601 * k[1] + a0604 * k[4] + a0605 * k[5]), p, - t + c5 * dt)) - copyat_or_push!(k, 7, - f(uprev + - dt * (a0701 * k[1] + a0704 * k[4] + a0705 * k[5] + a0706 * k[6]), - p, t + c6 * dt)) - copyat_or_push!(k, 2, - f(uprev + dt * (a0801 * k[1] + a0806 * k[6] + a0807 * k[7]), p, - t + c7 * dt)) - copyat_or_push!(k, 3, - f(uprev + - dt * (a0901 * k[1] + a0906 * k[6] + a0907 * k[7] + a0908 * k[2]), - p, t + c8 * dt)) - copyat_or_push!(k, 4, - f( - uprev + - dt * - (a1001 * k[1] + a1006 * k[6] + a1007 * k[7] + a1008 * k[2] + - a1009 * k[3]), - p, - t + c9 * dt)) - copyat_or_push!(k, 5, - f( - uprev + - dt * - (a1101 * k[1] + a1106 * k[6] + a1107 * k[7] + a1108 * k[2] + - a1109 * k[3] + a1110 * k[4]), - p, - t + c10 * dt)) - temp6 = recursivecopy(k[6]) - temp7 = recursivecopy(k[7]) - copyat_or_push!(k, 6, - f( - uprev + - dt * - (a1201 * k[1] + a1206 * temp6 + a1207 * temp7 + a1208 * k[2] + - a1209 * k[3] + a1210 * k[4] + a1211 * k[5]), - p, - t + c11 * dt)) - copyat_or_push!(k, 7, - f( - uprev + - dt * - (a1301 * k[1] + a1306 * temp6 + a1307 * temp7 + a1308 * k[2] + - a1309 * k[3] + a1310 * k[4] + a1311 * k[5] + a1312 * k[6]), - p, - t + c12 * dt)) - copyat_or_push!(k, 8, - f( - uprev + - dt * - (a1401 * k[1] + a1406 * temp6 + a1407 * temp7 + a1408 * k[2] + - a1409 * k[3] + a1410 * k[4] + a1411 * k[5] + a1412 * k[6] + - a1413 * k[7]), - p, - t + c13 * dt)) - copyat_or_push!(k, 9, - f( - uprev + - dt * - (a1501 * k[1] + a1506 * temp6 + a1507 * temp7 + a1508 * k[2] + - a1509 * k[3] + a1510 * k[4] + a1511 * k[5] + a1512 * k[6] + - a1513 * k[7] + a1514 * k[8]), - p, - t + dt)) - copyat_or_push!(k, 10, - f( - uprev + - dt * - (a1601 * k[1] + a1606 * temp6 + a1607 * temp7 + a1608 * k[2] + - a1609 * k[3] + a1610 * k[4] + a1611 * k[5] + a1612 * k[6] + - a1613 * k[7]), - p, - t + dt)) - end - if (allow_calc_end && length(k) < 20) || force_calc_end # Have not added the extra stages yet - @OnDemandTableauExtract Vern9ExtraStages T T2 - copyat_or_push!(k, 11, - f( - uprev + - dt * - (a1701 * k[1] + a1708 * k[2] + a1709 * k[3] + a1710 * k[4] + - a1711 * k[5] + a1712 * k[6] + a1713 * k[7] + a1714 * k[8] + - a1715 * k[9]), - p, - t + c17 * dt)) - copyat_or_push!(k, 12, - f( - uprev + - dt * - (a1801 * k[1] + a1808 * k[2] + a1809 * k[3] + a1810 * k[4] + - a1811 * k[5] + a1812 * k[6] + a1813 * k[7] + a1814 * k[8] + - a1815 * k[9] + a1817 * k[11]), - p, - t + c18 * dt)) - copyat_or_push!(k, 13, - f( - uprev + - dt * - (a1901 * k[1] + a1908 * k[2] + a1909 * k[3] + a1910 * k[4] + - a1911 * k[5] + a1912 * k[6] + a1913 * k[7] + a1914 * k[8] + - a1915 * k[9] + a1917 * k[11] + a1918 * k[12]), - p, - t + c19 * dt)) - copyat_or_push!(k, 14, - f( - uprev + - dt * - (a2001 * k[1] + a2008 * k[2] + a2009 * k[3] + a2010 * k[4] + - a2011 * k[5] + a2012 * k[6] + a2013 * k[7] + a2014 * k[8] + - a2015 * k[9] + a2017 * k[11] + a2018 * k[12] + a2019 * k[13]), - p, - t + c20 * dt)) - copyat_or_push!(k, 15, - f( - uprev + - dt * - (a2101 * k[1] + a2108 * k[2] + a2109 * k[3] + a2110 * k[4] + - a2111 * k[5] + a2112 * k[6] + a2113 * k[7] + a2114 * k[8] + - a2115 * k[9] + a2117 * k[11] + a2118 * k[12] + a2119 * k[13] + - a2120 * k[14]), - p, - t + c21 * dt)) - copyat_or_push!(k, 16, - f( - uprev + - dt * - (a2201 * k[1] + a2208 * k[2] + a2209 * k[3] + a2210 * k[4] + - a2211 * k[5] + a2212 * k[6] + a2213 * k[7] + a2214 * k[8] + - a2215 * k[9] + a2217 * k[11] + a2218 * k[12] + a2219 * k[13] + - a2220 * k[14] + a2221 * k[15]), - p, - t + c22 * dt)) - copyat_or_push!(k, 17, - f( - uprev + - dt * - (a2301 * k[1] + a2308 * k[2] + a2309 * k[3] + a2310 * k[4] + - a2311 * k[5] + a2312 * k[6] + a2313 * k[7] + a2314 * k[8] + - a2315 * k[9] + a2317 * k[11] + a2318 * k[12] + a2319 * k[13] + - a2320 * k[14] + a2321 * k[15]), - p, - t + c23 * dt)) - copyat_or_push!(k, 18, - f( - uprev + - dt * - (a2401 * k[1] + a2408 * k[2] + a2409 * k[3] + a2410 * k[4] + - a2411 * k[5] + a2412 * k[6] + a2413 * k[7] + a2414 * k[8] + - a2415 * k[9] + a2417 * k[11] + a2418 * k[12] + a2419 * k[13] + - a2420 * k[14] + a2421 * k[15]), - p, - t + c24 * dt)) - copyat_or_push!(k, 19, - f( - uprev + - dt * - (a2501 * k[1] + a2508 * k[2] + a2509 * k[3] + a2510 * k[4] + - a2511 * k[5] + a2512 * k[6] + a2513 * k[7] + a2514 * k[8] + - a2515 * k[9] + a2517 * k[11] + a2518 * k[12] + a2519 * k[13] + - a2520 * k[14] + a2521 * k[15]), - p, - t + c25 * dt)) - copyat_or_push!(k, 20, - f( - uprev + - dt * - (a2601 * k[1] + a2608 * k[2] + a2609 * k[3] + a2610 * k[4] + - a2611 * k[5] + a2612 * k[6] + a2613 * k[7] + a2614 * k[8] + - a2615 * k[9] + a2617 * k[11] + a2618 * k[12] + a2619 * k[13] + - a2620 * k[14] + a2621 * k[15]), - p, - t + c26 * dt)) - end - nothing -end From 7f8de0bfd26c1c36ca77767c9a8098782648f542 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:56:57 -0400 Subject: [PATCH 12/71] Delete src/perform_step/extrapolation_perform_step.jl --- .../extrapolation_perform_step.jl | 3639 ----------------- 1 file changed, 3639 deletions(-) delete mode 100644 src/perform_step/extrapolation_perform_step.jl diff --git a/src/perform_step/extrapolation_perform_step.jl b/src/perform_step/extrapolation_perform_step.jl deleted file mode 100644 index 48fec8c66d..0000000000 --- a/src/perform_step/extrapolation_perform_step.jl +++ /dev/null @@ -1,3639 +0,0 @@ -function initialize!(integrator, cache::AitkenNevilleCache) - integrator.kshortsize = 2 - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # For the interpolation, needs k at the updated point - integrator.stats.nf += 1 - - cache.step_no = 1 - alg = unwrap_alg(integrator, false) - cache.cur_order = max(alg.init_order, alg.min_order) -end - -function perform_step!(integrator, cache::AitkenNevilleCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - alg = unwrap_alg(integrator, false) - @unpack k, fsalfirst, T, utilde, atmp, dtpropose, cur_order, A = cache - @unpack u_tmps, k_tmps = cache - - max_order = min(size(T, 1), cur_order + 1) - - if !isthreaded(alg.threading) - for i in 1:max_order - dt_temp = dt / (2^(i - 1)) - # Solve using Euler method - @muladd @.. broadcast=false u=uprev + dt_temp * fsalfirst - f(k, u, p, t + dt_temp) - integrator.stats.nf += 1 - for j in 2:(2^(i - 1)) - @muladd @.. broadcast=false u=u + dt_temp * k - f(k, u, p, t + j * dt_temp) - integrator.stats.nf += 1 - end - @.. broadcast=false T[i, 1]=u - end - else - let max_order = max_order, uprev = uprev, dt = dt, fsalfirst = fsalfirst, p = p, - t = t, - u_tmps = u_tmps, k_tmps = k_tmps, T = T - # Balance workload of threads by computing T[1,1] with T[max_order,1] on - # same thread, T[2,1] with T[max_order-1,1] on same thread. Similarly fill - # first column of T matrix - @threaded alg.threading for i in 1:2 - startIndex = (i == 1) ? 1 : max_order - endIndex = (i == 1) ? max_order - 1 : max_order - for index in startIndex:endIndex - dt_temp = dt / (2^(index - 1)) - # Solve using Euler method - @muladd @.. broadcast=false u_tmps[Threads.threadid()]=uprev + - dt_temp * - fsalfirst - f(k_tmps[Threads.threadid()], u_tmps[Threads.threadid()], p, - t + dt_temp) - for j in 2:(2^(index - 1)) - @muladd @.. broadcast=false u_tmps[Threads.threadid()]=u_tmps[Threads.threadid()] + - dt_temp * - k_tmps[Threads.threadid()] - f(k_tmps[Threads.threadid()], u_tmps[Threads.threadid()], p, - t + j * dt_temp) - end - @.. broadcast=false T[index, 1]=u_tmps[Threads.threadid()] - end - end - end - integrator.stats.nf += 2^max_order - 1 - end - - # Richardson extrapolation - tmp = 1 - for j in 2:max_order - tmp *= 2 - for i in j:max_order - @.. broadcast=false T[i, j]=(tmp * T[i, j - 1] - T[i - 1, j - 1]) / (tmp - 1) - end - end - - if integrator.opts.adaptive - minimum_work = Inf - if isone(cache.step_no) - range_start = 2 - else - range_start = max(2, cur_order - 1) - end - - for i in range_start:max_order - A = 2^(i - 1) - @.. broadcast=false utilde=T[i, i] - T[i, i - 1] - atmp = calculate_residuals(utilde, uprev, T[i, i], integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, - t) - EEst = integrator.opts.internalnorm(atmp, t) - - beta1 = integrator.opts.controller.beta1 - e = integrator.EEst - qold = integrator.qold - - integrator.opts.controller.beta1 = 1 / (i + 1) - integrator.EEst = EEst - dtpropose = step_accept_controller!(integrator, alg, - stepsize_controller!(integrator, alg)) - integrator.EEst = e - integrator.opts.controller.beta1 = beta1 - integrator.qold = qold - - work = A / dtpropose - - if work < minimum_work - integrator.opts.controller.beta1 = 1 / (i + 1) - cache.dtpropose = dtpropose - cache.cur_order = i - minimum_work = work - integrator.EEst = EEst - end - end - end - - # using extrapolated value of u - @.. broadcast=false u=T[cache.cur_order, cache.cur_order] - cache.step_no = cache.step_no + 1 - f(k, u, p, t + dt) - integrator.stats.nf += 1 -end - -function initialize!(integrator, cache::AitkenNevilleConstantCache) - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - cache.step_no = 1 - alg = unwrap_alg(integrator, false) - cache.cur_order = max(alg.init_order, alg.min_order) -end - -function perform_step!(integrator, cache::AitkenNevilleConstantCache, repeat_step = false) - @unpack t, dt, uprev, f, p = integrator - alg = unwrap_alg(integrator, false) - @unpack dtpropose, T, cur_order, work, A = cache - - max_order = min(size(T, 1), cur_order + 1) - - if !isthreaded(alg.threading) - for i in 1:max_order - dt_temp = dt / (2^(i - 1)) # Romberg sequence - - # Solve using Euler method with dt_temp = dt/n_{i} - @muladd u = @.. broadcast=false uprev+dt_temp * integrator.fsalfirst - k = f(u, p, t + dt_temp) - integrator.stats.nf += 1 - - for j in 2:(2^(i - 1)) - @muladd u = @.. broadcast=false u+dt_temp * k - k = f(u, p, t + j * dt_temp) - integrator.stats.nf += 1 - end - T[i, 1] = u - end - else - let max_order = max_order, dt = dt, uprev = uprev, integrator = integrator, p = p, - t = t, T = T - # Balance workload of threads by computing T[1,1] with T[max_order,1] on - # same thread, T[2,1] with T[max_order-1,1] on same thread. Similarly fill - # first column of T matrix - @threaded alg.threading for i in 1:2 - startIndex = (i == 1) ? 1 : max_order - endIndex = (i == 1) ? max_order - 1 : max_order - - for index in startIndex:endIndex - dt_temp = dt / 2^(index - 1) - @muladd u = @.. broadcast=false uprev+dt_temp * integrator.fsalfirst - k_temp = f(u, p, t + dt_temp) - for j in 2:(2^(index - 1)) - @muladd u = @.. broadcast=false u+dt_temp * k_temp - k_temp = f(u, p, t + j * dt_temp) - end - T[index, 1] = u - end - end - end - - integrator.stats.nf += 2^max_order - 1 - end - - # Richardson extrapolation - tmp = 1 - for j in 2:max_order - tmp *= 2 - for i in j:max_order - T[i, j] = (tmp * T[i, j - 1] - T[i - 1, j - 1]) / (tmp - 1) - end - end - - if integrator.opts.adaptive - minimum_work = Inf - if isone(cache.step_no) - range_start = 2 - else - range_start = max(2, cur_order - 1) - end - - for i in range_start:max_order - A = 2^(i - 1) - utilde = T[i, i] - T[i, i - 1] - atmp = calculate_residuals(utilde, uprev, T[i, i], integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, - t) - EEst = integrator.opts.internalnorm(atmp, t) - - beta1 = integrator.opts.controller.beta1 - e = integrator.EEst - qold = integrator.qold - - integrator.opts.controller.beta1 = 1 / (i + 1) - integrator.EEst = EEst - dtpropose = step_accept_controller!(integrator, alg, - stepsize_controller!(integrator, alg)) - integrator.EEst = e - integrator.opts.controller.beta1 = beta1 - integrator.qold = qold - - work = A / dtpropose - - if work < minimum_work - integrator.opts.controller.beta1 = 1 / (i + 1) - cache.dtpropose = dtpropose - cache.cur_order = i - minimum_work = work - integrator.EEst = EEst - end - end - end - - cache.step_no = cache.step_no + 1 - - # Use extrapolated value of u - integrator.u = T[cache.cur_order, cache.cur_order] - - k = f(integrator.u, p, t + dt) - integrator.stats.nf += 1 - integrator.fsallast = k - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -function initialize!(integrator, cache::ImplicitEulerExtrapolationCache) - integrator.kshortsize = 2 - - integrator.fsalfirst = zero(first(cache.k_tmps)) - integrator.f(integrator.fsalfirst, integrator.u, integrator.p, integrator.t) - integrator.fsallast = zero(integrator.fsalfirst) - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.stats.nf += 1 - - cache.step_no = 1 - #alg = unwrap_alg(integrator, true) - #cache.cur_order = max(alg.init_order, alg.min_order) -end - -function perform_step!(integrator, cache::ImplicitEulerExtrapolationCache, - repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - alg = unwrap_alg(integrator, true) - @unpack T, utilde, atmp, dtpropose, n_curr, A, stage_number, diff1, diff2 = cache - @unpack J, W, uf, tf, jac_config = cache - @unpack u_tmps, k_tmps, linsolve_tmps, u_tmps2 = cache - - @unpack sequence = cache - - if integrator.opts.adaptive - # Set up the order window - # alg.min_order + 1 ≦ n_curr ≦ alg.max_order - 1 is enforced by step_*_controller! - if !(alg.min_order + 1 <= n_curr <= alg.max_order - 1) - error("Something went wrong while setting up the order window: $n_curr ∉ [$(alg.min_order+1),$(alg.max_order-1)]. - Please report this error ") - end - win_min = n_curr - 1 - win_max = n_curr + 1 - - # Set up the current extrapolation order - cache.n_old = n_curr # Save the suggested order for step_*_controller! - n_curr = win_min # Start with smallest order in the order window - end - - if !isthreaded(alg.threading) - calc_J!(J, integrator, cache) # Store the calculated jac as it won't change in internal discretisation - for index in 1:(n_curr + 1) - dt_temp = dt / sequence[index] - jacobian2W!(W[1], integrator.f.mass_matrix, dt_temp, J, false) - integrator.stats.nw += 1 - @.. broadcast=false k_tmps[1]=integrator.fsalfirst - @.. broadcast=false u_tmps[1]=uprev - - for j in 1:sequence[index] - @.. broadcast=false linsolve_tmps[1]=dt_temp * k_tmps[1] - - linsolve = cache.linsolve[1] - - if !repeat_step && j == 1 - linres = dolinsolve(integrator, linsolve; A = W[1], - b = _vec(linsolve_tmps[1]), linu = _vec(k_tmps[1])) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[1]), linu = _vec(k_tmps[1])) - end - - cache.linsolve[1] = linres.cache - - integrator.stats.nsolve += 1 - @.. broadcast=false k_tmps[1]=-k_tmps[1] - @.. broadcast=false u_tmps2[1]=u_tmps[1] - @.. broadcast=false u_tmps[1]=u_tmps[1] + k_tmps[1] - if index <= 2 && j >= 2 - # Deuflhard Stability check for initial two sequences - @.. broadcast=false diff2[1]=u_tmps[1] - u_tmps2[1] - @.. broadcast=false diff2[1]=0.5 * (diff2[1] - diff1[1]) - if integrator.opts.internalnorm(diff1[1], t) < - integrator.opts.internalnorm(diff2[1], t) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - @.. broadcast=false diff1[1]=u_tmps[1] - u_tmps2[1] - - f(k_tmps[1], u_tmps[1], p, t + j * dt_temp) - integrator.stats.nf += 1 - end - - @.. broadcast=false T[index, 1]=u_tmps[1] - end - else - calc_J!(J, integrator, cache) # Store the calculated jac as it won't change in internal discretisation - let n_curr = n_curr, uprev = uprev, dt = dt, p = p, t = t, T = T, W = W, - integrator = integrator, cache = cache, repeat_step = repeat_step, - k_tmps = k_tmps, u_tmps = u_tmps, u_tmps2 = u_tmps2, diff1 = diff1, - diff2 = diff2 - - @threaded alg.threading for i in 1:2 - startIndex = (i == 1) ? 1 : n_curr + 1 - endIndex = (i == 1) ? n_curr : n_curr + 1 - for index in startIndex:endIndex - dt_temp = dt / sequence[index] - jacobian2W!( - W[Threads.threadid()], integrator.f.mass_matrix, dt_temp, J, - false) - @.. broadcast=false k_tmps[Threads.threadid()]=integrator.fsalfirst - @.. broadcast=false u_tmps[Threads.threadid()]=uprev - for j in 1:sequence[index] - @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_temp * - k_tmps[Threads.threadid()] - - linsolve = cache.linsolve[Threads.threadid()] - - if !repeat_step && j == 1 - linres = dolinsolve(integrator, linsolve; - A = W[Threads.threadid()], - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - end - - cache.linsolve[Threads.threadid()] = linres.cache - - @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] - @.. broadcast=false u_tmps2[Threads.threadid()]=u_tmps[Threads.threadid()] - @.. broadcast=false u_tmps[Threads.threadid()]=u_tmps[Threads.threadid()] + - k_tmps[Threads.threadid()] - if index <= 2 && j >= 2 - # Deuflhard Stability check for initial two sequences - @.. broadcast=false diff2[Threads.threadid()]=u_tmps[Threads.threadid()] - - u_tmps2[Threads.threadid()] - @.. broadcast=false diff2[Threads.threadid()]=0.5 * - (diff2[Threads.threadid()] - - diff1[Threads.threadid()]) - if integrator.opts.internalnorm(diff1[Threads.threadid()], t) < - integrator.opts.internalnorm(diff2[Threads.threadid()], t) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - @.. broadcast=false diff1[Threads.threadid()]=u_tmps[Threads.threadid()] - - u_tmps2[Threads.threadid()] - f(k_tmps[Threads.threadid()], u_tmps[Threads.threadid()], p, - t + j * dt_temp) - end - - @.. broadcast=false T[index, 1]=u_tmps[Threads.threadid()] - end - integrator.force_stepfail ? break : continue - end - end - - nevals = sum(sequence[1:(n_curr + 1)]) - 1 - integrator.stats.nw += n_curr + 1 - integrator.stats.nf += nevals - integrator.stats.nsolve += nevals - end - - if integrator.force_stepfail - return - end - - # Polynomial extrapolation - for j in 2:(n_curr + 1) - for i in j:(n_curr + 1) - @.. broadcast=false T[i, j]=((sequence[i] / sequence[i - j + 1]) * T[i, j - 1] - - T[i - 1, j - 1]) / - ((sequence[i] / sequence[i - j + 1]) - 1) - end - end - - if integrator.opts.adaptive - # Compute all information relating to an extrapolation order ≦ win_min - for i in (win_min - 1):win_min - @.. broadcast=false integrator.u=T[i + 1, i + 1] - @.. broadcast=false cache.utilde=T[i + 1, i] - - calculate_residuals!(cache.res, integrator.u, cache.utilde, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(cache.res, t) - cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! - stepsize_controller_internal!(integrator, alg) # Update cache.Q - end - - # Check if an approximation of some order in the order window can be accepted - # Make sure a stepsize scaling factor of order (alg.min_order + 1) is provided for the step_*_controller! - while n_curr <= win_max - if accept_step_controller(integrator, integrator.opts.controller) - # Accept current approximation u of order n_curr - break - elseif (n_curr < alg.min_order + 1) || - integrator.EEst <= - typeof(integrator.EEst)(prod(sequence[(n_curr + 2):(win_max + 1)] .// - sequence[1]^2)) - # Reject current approximation order but pass convergence monitor - # Compute approximation of order (n_curr + 1) - n_curr = n_curr + 1 - cache.n_curr = n_curr - - dt_temp = dt / sequence[n_curr + 1] - jacobian2W!(W[1], integrator.f.mass_matrix, dt_temp, J, false) - integrator.stats.nw += 1 - @.. broadcast=false k_tmps[1]=integrator.fsalfirst - @.. broadcast=false u_tmps[1]=uprev - - for j in 1:sequence[n_curr + 1] - @.. broadcast=false linsolve_tmps[1]=dt_temp * k_tmps[1] - - linsolve = cache.linsolve[1] - - if !repeat_step && j == 1 - linres = dolinsolve(integrator, linsolve; A = W[1], - b = _vec(linsolve_tmps[1]), - linu = _vec(k_tmps[1])) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[1]), - linu = _vec(k_tmps[1])) - end - - cache.linsolve[1] = linres.cache - - integrator.stats.nsolve += 1 - @.. broadcast=false k_tmps[1]=-k_tmps[1] - @.. broadcast=false u_tmps[1]=u_tmps[1] + k_tmps[1] - f(k_tmps[1], u_tmps[1], p, t + j * dt_temp) - integrator.stats.nf += 1 - end - - @.. broadcast=false T[n_curr + 1, 1]=u_tmps[1] - - for j in 2:(n_curr + 1) - for i in j:(n_curr + 1) - @.. broadcast=false T[i, j]=((sequence[i] / sequence[i - j + 1]) * - T[i, j - 1] - T[i - 1, j - 1]) / - ((sequence[i] / sequence[i - j + 1]) - - 1) - end - end - - @.. broadcast=false integrator.u=T[n_curr + 1, n_curr + 1] - @.. broadcast=false cache.utilde=T[n_curr + 1, n_curr] - - calculate_residuals!(cache.res, integrator.u, cache.utilde, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(cache.res, t) - stepsize_controller_internal!(integrator, alg) # Update cache.Q - else - # Reject the current approximation and not pass convergence monitor - break - end - end - else - @.. broadcast=false integrator.u=T[n_curr + 1, n_curr + 1] - end - - cache.step_no = cache.step_no + 1 - f(integrator.fsallast, integrator.u, p, t + dt) - integrator.stats.nf += 1 -end - -function initialize!(integrator, cache::ImplicitEulerExtrapolationConstantCache) - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -function perform_step!(integrator, cache::ImplicitEulerExtrapolationConstantCache, - repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - alg = unwrap_alg(integrator, true) - @unpack dtpropose, T, n_curr, work, A, tf, uf = cache - @unpack sequence, stage_number = cache - - if integrator.opts.adaptive - # Set up the order window - # alg.min_order + 1 ≦ n_curr ≦ alg.max_order - 1 is enforced by step_*_controller! - if !(alg.min_order + 1 <= n_curr <= alg.max_order - 1) - error("Something went wrong while setting up the order window: $n_curr ∉ [$(alg.min_order+1),$(alg.max_order-1)]. - Please report this error ") - end - win_min = n_curr - 1 - win_max = n_curr + 1 - - # Set up the current extrapolation order - cache.n_old = n_curr # Save the suggested order for step_*_controller! - n_curr = win_min # Start with smallest order in the order window - end - - J = calc_J(integrator, cache) # Store the calculated jac as it won't change in internal discretisation - if !isthreaded(alg.threading) - for index in 1:(n_curr + 1) - dt_temp = dt / sequence[index] - W = dt_temp * J - integrator.f.mass_matrix - integrator.stats.nw += 1 - k_copy = integrator.fsalfirst - u_tmp = uprev - diff1 = zero(u_tmp) - for j in 1:sequence[index] - k = _reshape(W \ -_vec(dt_temp * k_copy), axes(uprev)) - integrator.stats.nsolve += 1 - u_tmp2 = u_tmp - u_tmp = u_tmp + k - if index <= 2 && j >= 2 - # Deuflhard Stability check for initial two sequences - diff2 = u_tmp - u_tmp2 - diff2 = 0.5 * (diff2 - diff1) - if integrator.opts.internalnorm(diff1, t) < - integrator.opts.internalnorm(diff2, t) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - diff1 = u_tmp - u_tmp2 - k_copy = f(u_tmp, p, t + j * dt_temp) - integrator.stats.nf += 1 - end - - T[index, 1] = u_tmp - end - else - J = calc_J(integrator, cache) # Store the calculated jac as it won't change in internal discretisation - let n_curr = n_curr, dt = dt, integrator = integrator, cache = cache, - repeat_step = repeat_step, - uprev = uprev, T = T - - @threaded alg.threading for i in 1:2 - startIndex = (i == 1) ? 1 : n_curr + 1 - endIndex = (i == 1) ? n_curr : n_curr + 1 - for index in startIndex:endIndex - dt_temp = dt / sequence[index] - W = dt_temp * J - integrator.f.mass_matrix - k_copy = integrator.fsalfirst - u_tmp = uprev - diff1 = zero(u_tmp) - for j in 1:sequence[index] - k = _reshape(W \ -_vec(dt_temp * k_copy), axes(uprev)) - u_tmp2 = u_tmp - u_tmp = u_tmp + k - if index <= 2 && j >= 2 - # Deuflhard Stability check for initial two sequences - diff2 = u_tmp - u_tmp2 - diff2 = 0.5 * (diff2 - diff1) - if integrator.opts.internalnorm(diff1, t) < - integrator.opts.internalnorm(diff2, t) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - diff1 = u_tmp - u_tmp2 - k_copy = f(u_tmp, p, t + j * dt_temp) - end - T[index, 1] = u_tmp - end - integrator.force_stepfail ? break : continue - end - end - - if integrator.force_stepfail - return - end - - nevals = sum(sequence[1:(n_curr + 1)]) - 1 - integrator.stats.nw += n_curr + 1 - integrator.stats.nf += nevals - integrator.stats.nsolve += nevals - end - - # Richardson extrapolation - tmp = 1 - for j in 2:(n_curr + 1) - tmp *= 2 - for i in j:(n_curr + 1) - T[i, j] = ((sequence[i] / sequence[i - j + 1]) * T[i, j - 1] - - T[i - 1, j - 1]) / - ((sequence[i] / sequence[i - j + 1]) - 1) - end - end - - integrator.dt = dt - - if integrator.opts.adaptive - # Compute all information relating to an extrapolation order ≦ win_min - for i in (win_min - 1):win_min - u = T[i + 1, i + 1] - utilde = T[i + 1, i] - res = calculate_residuals(u, utilde, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, - t) - integrator.EEst = integrator.opts.internalnorm(res, t) - cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! - stepsize_controller_internal!(integrator, alg) # Update cache.Q - end - - # Check if an approximation of some order in the order window can be accepted - # Make sure a stepsize scaling factor of order (alg.min_order + 1) is provided for the step_*_controller! - while n_curr <= win_max - if accept_step_controller(integrator, integrator.opts.controller) - # Accept current approximation u of order n_curr - break - elseif (n_curr < alg.min_order + 1) || - integrator.EEst <= - typeof(integrator.EEst)(prod(sequence[(n_curr + 2):(win_max + 1)] .// - sequence[1]^2)) - # Reject current approximation order but pass convergence monitor - # Always compute approximation of order (n_curr + 1) - n_curr = n_curr + 1 - cache.n_curr = n_curr - - # Update T - dt_temp = dt / sequence[n_curr + 1] - W = dt_temp * J - integrator.f.mass_matrix - integrator.stats.nw += 1 - k_copy = integrator.fsalfirst - u_tmp = uprev - - for j in 1:sequence[n_curr + 1] - k = _reshape(W \ -_vec(dt_temp * k_copy), axes(uprev)) - integrator.stats.nsolve += 1 - u_tmp = u_tmp + k - k_copy = f(u_tmp, p, t + j * dt_temp) - integrator.stats.nf += 1 - end - - T[n_curr + 1, 1] = u_tmp - - #Extrapolate to new order - for j in 2:(n_curr + 1) - for i in j:(n_curr + 1) - T[i, j] = ((sequence[i] / sequence[i - j + 1]) * T[i, j - 1] - - T[i - 1, j - 1]) / - ((sequence[i] / sequence[i - j + 1]) - 1) - end - end - # Update u, integrator.EEst and cache.Q - u = T[n_curr + 1, n_curr + 1] - utilde = T[n_curr + 1, n_curr] - res = calculate_residuals(u, utilde, integrator.opts.abstol, - integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(res, t) - stepsize_controller_internal!(integrator, alg) # Update cache.Q - else - # Reject the current approximation and not pass convergence monitor - break - end - end - else - integrator.u = T[n_curr + 1, n_curr + 1] - end - - # Use extrapolated value of u - integrator.u = T[n_curr + 1, n_curr + 1] - k_temp = f(integrator.u, p, t + dt) - integrator.stats.nf += 1 - integrator.fsallast = k_temp - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -function initialize!(integrator, cache::ExtrapolationMidpointDeuflhardCache) - # cf. initialize! of MidpointCache - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 2 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation -end - -function perform_step!(integrator, cache::ExtrapolationMidpointDeuflhardCache, - repeat_step = false) - # Unpack all information needed - @unpack t, uprev, dt, f, p = integrator - alg = unwrap_alg(integrator, false) - @unpack n_curr, u_temp1, u_temp2, utilde, res, T, fsalfirst, k = cache - @unpack u_temp3, u_temp4, k_tmps = cache - - # Coefficients for obtaining u - @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients - # Coefficients for obtaining utilde - @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients - # Additional constant information - @unpack subdividing_sequence = cache.coefficients - @unpack stage_number = cache - @unpack sequence_factor = alg - - fill!(cache.Q, zero(eltype(cache.Q))) - tol = integrator.opts.internalnorm(integrator.opts.reltol, t) # Used by the convergence monitor - - if integrator.opts.adaptive - # Set up the order window - win_min = max(alg.min_order, n_curr - 1) - win_max = min(alg.max_order, n_curr + 1) - - # Set up the current extrapolation order - cache.n_old = n_curr # Save the suggested order for step_*_controller! - n_curr = win_min # Start with smallest order in the order window - end - - #Compute the internal discretisations - if !isthreaded(alg.threading) - for i in 0:n_curr - j_int = sequence_factor * subdividing_sequence[i + 1] - dt_int = dt / j_int # Stepsize of the ith internal discretisation - @.. broadcast=false u_temp2=uprev - @.. broadcast=false u_temp1=u_temp2 + dt_int * fsalfirst # Euler starting step - for j in 2:j_int - f(k, cache.u_temp1, p, t + (j - 1) * dt_int) - integrator.stats.nf += 1 - @.. broadcast=false T[i + 1]=u_temp2 + 2 * dt_int * k # Explicit Midpoint rule - @.. broadcast=false u_temp2=u_temp1 - @.. broadcast=false u_temp1=T[i + 1] - end - end - else - if alg.sequence == :romberg - # Compute solution by using maximum two threads for romberg sequence - # One thread will fill T matrix till second last element and another thread will - # fill last element of T matrix. - # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) - # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, - dt = dt, u_temp3 = u_temp3, - u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T - - @threaded alg.threading for i in 1:2 - startIndex = (i == 1) ? 0 : n_curr - endIndex = (i == 1) ? n_curr - 1 : n_curr - for index in startIndex:endIndex - j_int_temp = sequence_factor * subdividing_sequence[index + 1] - dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation - @.. broadcast=false u_temp4[Threads.threadid()]=uprev - @.. broadcast=false u_temp3[Threads.threadid()]=u_temp4[Threads.threadid()] + - dt_int_temp * - fsalfirst # Euler starting step - for j in 2:j_int_temp - f(k_tmps[Threads.threadid()], - cache.u_temp3[Threads.threadid()], - p, t + (j - 1) * dt_int_temp) - @.. broadcast=false T[index + 1]=u_temp4[Threads.threadid()] + - 2 * dt_int_temp * - k_tmps[Threads.threadid()] # Explicit Midpoint rule - @.. broadcast=false u_temp4[Threads.threadid()]=u_temp3[Threads.threadid()] - @.. broadcast=false u_temp3[Threads.threadid()]=T[index + 1] - end - end - end - end - else - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, - dt = dt, u_temp3 = u_temp3, - u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T - - @threaded alg.threading for i in 0:(n_curr ÷ 2) - indices = (i, n_curr - i) - for index in indices - j_int_temp = sequence_factor * subdividing_sequence[index + 1] - dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation - @.. broadcast=false u_temp4[Threads.threadid()]=uprev - @.. broadcast=false u_temp3[Threads.threadid()]=u_temp4[Threads.threadid()] + - dt_int_temp * - fsalfirst # Euler starting step - for j in 2:j_int_temp - f(k_tmps[Threads.threadid()], u_temp3[Threads.threadid()], p, - t + (j - 1) * dt_int_temp) - @.. broadcast=false T[index + 1]=u_temp4[Threads.threadid()] + - 2 * dt_int_temp * - k_tmps[Threads.threadid()] # Explicit Midpoint rule - @.. broadcast=false u_temp4[Threads.threadid()]=u_temp3[Threads.threadid()] - @.. broadcast=false u_temp3[Threads.threadid()]=T[index + 1] - end - if indices[2] <= indices[1] - break - end - end - end - end - end - nevals = cache.stage_number[n_curr - alg.min_order + 1] - 1 - integrator.stats.nf += nevals - end - - if integrator.opts.adaptive - # Compute all information relating to an extrapolation order ≦ win_min - for i in (alg.min_order):n_curr - - #integrator.u .= extrapolation_scalars[i+1] * sum( broadcast(*, cache.T[1:(i+1)], extrapolation_weights[1:(i+1), (i+1)]) ) # Approximation of extrapolation order i - #cache.utilde .= extrapolation_scalars_2[i] * sum( broadcast(*, cache.T[2:(i+1)], extrapolation_weights_2[1:i, i]) ) # and its internal counterpart - - u_temp1 .= false - u_temp2 .= false - for j in 1:(i + 1) - @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (i + 1)] - end - for j in 2:(i + 1) - @.. broadcast=false u_temp2+=cache.T[j] * extrapolation_weights_2[j - 1, i] - end - @.. broadcast=false integrator.u=extrapolation_scalars[i + 1] * u_temp1 - @.. broadcast=false cache.utilde=extrapolation_scalars_2[i] * u_temp2 - - calculate_residuals!(cache.res, integrator.u, cache.utilde, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(cache.res, t) - cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! - stepsize_controller_internal!(integrator, alg) # Update cache.Q - end - - # Check if an approximation of some order in the order window can be accepted - while n_curr <= win_max - if accept_step_controller(integrator, integrator.opts.controller) - # Accept current approximation u of order n_curr - break - elseif integrator.EEst <= - tol^(stage_number[n_curr - alg.min_order + 1] / - stage_number[win_max - alg.min_order + 1] - 1) - # Reject current approximation order but pass convergence monitor - # Compute approximation of order (n_curr + 1) - n_curr = n_curr + 1 - cache.n_curr = n_curr - - # Update cache.T - j_int = sequence_factor * subdividing_sequence[n_curr + 1] - dt_int = dt / j_int # Stepsize of the new internal discretisation - @.. broadcast=false u_temp2=uprev - @.. broadcast=false u_temp1=u_temp2 + dt_int * fsalfirst # Euler starting step - for j in 2:j_int - f(k, cache.u_temp1, p, t + (j - 1) * dt_int) - integrator.stats.nf += 1 - @.. broadcast=false T[n_curr + 1]=u_temp2 + 2 * dt_int * k - @.. broadcast=false u_temp2=u_temp1 - @.. broadcast=false u_temp1=T[n_curr + 1] - end - - # Update u, integrator.EEst and cache.Q - #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr - #cache.utilde .= extrapolation_scalars_2[n_curr] * sum( broadcast(*, cache.T[2:(n_curr+1)], extrapolation_weights_2[1:n_curr, n_curr]) ) # and its internal counterpart - - u_temp1 .= false - u_temp2 .= false - for j in 1:(n_curr + 1) - @.. broadcast=false u_temp1+=cache.T[j] * - extrapolation_weights[j, (n_curr + 1)] - end - for j in 2:(n_curr + 1) - @.. broadcast=false u_temp2+=cache.T[j] * - extrapolation_weights_2[j - 1, n_curr] - end - @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 - @.. broadcast=false cache.utilde=extrapolation_scalars_2[n_curr] * u_temp2 - - calculate_residuals!(cache.res, integrator.u, cache.utilde, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(cache.res, t) - stepsize_controller_internal!(integrator, alg) # Update cache.Q - else - # Reject the current approximation and not pass convergence monitor - break - end - end - else - - #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr - u_temp1 .= false - for j in 1:(n_curr + 1) - @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (n_curr + 1)] - end - @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 - end - - f(cache.k, integrator.u, p, t + dt) # Update FSAL - integrator.stats.nf += 1 -end - -function initialize!(integrator, cache::ExtrapolationMidpointDeuflhardConstantCache) - # cf. initialize! of MidpointConstantCache - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -function perform_step!(integrator, cache::ExtrapolationMidpointDeuflhardConstantCache, - repeat_step = false) - # Unpack all information needed - @unpack t, uprev, dt, f, p = integrator - alg = unwrap_alg(integrator, false) - @unpack n_curr = cache - # Coefficients for obtaining u - @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients - # Coefficients for obtaining utilde - @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients - # Additional constant information - @unpack subdividing_sequence = cache.coefficients - @unpack stage_number = cache - @unpack sequence_factor = alg - - # Create auxiliary variables - u_temp1, u_temp2 = copy(uprev), copy(uprev) # Auxiliary variables for computing the internal discretisations - u, utilde = copy(uprev), copy(uprev) # Storage for the latest approximation and its internal counterpart - tol = integrator.opts.internalnorm(integrator.opts.reltol, t) # Used by the convergence monitor - T = fill(zero(uprev), alg.max_order + 1) # Storage for the internal discretisations obtained by the explicit midpoint rule - fill!(cache.Q, zero(eltype(cache.Q))) - - # Start computation - if integrator.opts.adaptive - # Set up the order window - win_min = max(alg.min_order, n_curr - 1) - win_max = min(alg.max_order, n_curr + 1) - - # Set up the current extrapolation order - cache.n_old = n_curr # Save the suggested order for step_*_controller! - n_curr = win_min # Start with smallest order in the order window - end - - # Compute the internal discretisations - if !isthreaded(alg.threading) - for i in 0:n_curr - j_int = sequence_factor * subdividing_sequence[i + 1] - dt_int = dt / j_int # Stepsize of the ith internal discretisation - u_temp2 = uprev - u_temp1 = u_temp2 + dt_int * integrator.fsalfirst # Euler starting step - for j in 2:j_int - T[i + 1] = u_temp2 + 2 * dt_int * f(u_temp1, p, t + (j - 1) * dt_int) # Explicit Midpoint rule - integrator.stats.nf += 1 - u_temp2 = u_temp1 - u_temp1 = T[i + 1] - end - end - else - if alg.sequence == :romberg - # Compute solution by using maximum two threads for romberg sequence - # One thread will fill T matrix till second last element and another thread will - # fill last element of T matrix. - # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) - # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, - dt = dt, - integrator = integrator, p = p, t = t, T = T - - @threaded alg.threading for i in 1:2 - startIndex = (i == 1) ? 0 : n_curr - endIndex = (i == 1) ? n_curr - 1 : n_curr - for index in startIndex:endIndex - j_int_temp = sequence_factor * subdividing_sequence[index + 1] - dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation - u_temp4 = uprev - u_temp3 = u_temp4 + dt_int_temp * integrator.fsalfirst # Euler starting step - for j in 2:j_int_temp - T[index + 1] = u_temp4 + - 2 * dt_int_temp * - f(u_temp3, p, t + (j - 1) * dt_int_temp) # Explicit Midpoint rule - u_temp4 = u_temp3 - u_temp3 = T[index + 1] - end - end - end - end - else - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, dt = dt, - uprev = uprev, - p = p, t = t, T = T - - @threaded alg.threading for i in 0:(n_curr ÷ 2) - indices = (i, n_curr - i) - for index in indices - j_int_temp = sequence_factor * subdividing_sequence[index + 1] - dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation - u_temp4 = uprev - u_temp3 = u_temp4 + dt_int_temp * integrator.fsalfirst # Euler starting step - for j in 2:j_int_temp - T[index + 1] = u_temp4 + - 2 * dt_int_temp * - f(u_temp3, p, t + (j - 1) * dt_int_temp) # Explicit Midpoint rule - u_temp4 = u_temp3 - u_temp3 = T[index + 1] - end - if indices[2] <= indices[1] - break - end - end - end - end - end - nevals = cache.stage_number[n_curr - alg.min_order + 1] - 1 - integrator.stats.nf += nevals - end - - if integrator.opts.adaptive - # Compute all information relating to an extrapolation order ≦ win_min - for i in (alg.min_order):n_curr - u = eltype(uprev).(extrapolation_scalars[i + 1]) * - sum(broadcast(*, T[1:(i + 1)], - eltype(uprev).(extrapolation_weights[1:(i + 1), (i + 1)]))) # Approximation of extrapolation order i - utilde = eltype(uprev).(extrapolation_scalars_2[i]) * - sum(broadcast(*, T[2:(i + 1)], - eltype(uprev).(extrapolation_weights_2[1:i, i]))) # and its internal counterpart - res = calculate_residuals(u, utilde, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, - t) - integrator.EEst = integrator.opts.internalnorm(res, t) - cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! - stepsize_controller_internal!(integrator, alg) # Update cache.Q - end - - # Check if an approximation of some order in the order window can be accepted - while n_curr <= win_max - if accept_step_controller(integrator, integrator.opts.controller) - # Accept current approximation u of order n_curr - break - elseif integrator.EEst <= - tol^(stage_number[n_curr - alg.min_order + 1] / - stage_number[win_max - alg.min_order + 1] - 1) - # Reject current approximation order but pass convergence monitor - # Compute approximation of order (n_curr + 1) - n_curr = n_curr + 1 - cache.n_curr = n_curr - - # Update T - j_int = sequence_factor * subdividing_sequence[n_curr + 1] - dt_int = dt / j_int # Stepsize of the new internal discretisation - u_temp2 = uprev - u_temp1 = u_temp2 + dt_int * integrator.fsalfirst # Euler starting step - for j in 2:j_int - T[n_curr + 1] = u_temp2 + - 2 * dt_int * f(u_temp1, p, t + (j - 1) * dt_int) - integrator.stats.nf += 1 - u_temp2 = u_temp1 - u_temp1 = T[n_curr + 1] - end - - # Update u, integrator.EEst and cache.Q - u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * - sum(broadcast(*, T[1:(n_curr + 1)], - eltype(uprev).(extrapolation_weights[1:(n_curr + 1), - (n_curr + 1)]))) # Approximation of extrapolation order n_curr - utilde = eltype(uprev).(extrapolation_scalars_2[n_curr]) * - sum(broadcast(*, T[2:(n_curr + 1)], - eltype(uprev).(extrapolation_weights_2[1:n_curr, - n_curr]))) # and its internal counterpart - res = calculate_residuals(u, utilde, integrator.opts.abstol, - integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(res, t) - stepsize_controller_internal!(integrator, alg) # Update cache.Q - else - # Reject the current approximation and not pass convergence monitor - break - end - end - else - u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * - sum(broadcast(*, T[1:(n_curr + 1)], - eltype(uprev).(extrapolation_weights[1:(n_curr + 1), - (n_curr + 1)]))) # Approximation of extrapolation order n_curr - end - - # Save the latest approximation and update FSAL - integrator.u = u - integrator.fsallast = f(u, p, t + dt) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -function initialize!(integrator, cache::ImplicitDeuflhardExtrapolationCache) - # cf. initialize! of MidpointCache - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 2 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation -end - -function perform_step!(integrator, cache::ImplicitDeuflhardExtrapolationCache, - repeat_step = false) - # Unpack all information needed - @unpack t, uprev, dt, f, p = integrator - alg = unwrap_alg(integrator, true) - @unpack n_curr, u_temp1, u_temp2, utilde, res, T, fsalfirst, k, diff1, diff2 = cache - @unpack u_temp3, u_temp4, k_tmps = cache - - # Coefficients for obtaining u - @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients - # Coefficients for obtaining utilde - @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients - # Additional constant information - @unpack subdividing_sequence = cache.coefficients - @unpack stage_number = cache - - @unpack J, W, uf, tf, linsolve_tmps, jac_config = cache - - fill!(cache.Q, zero(eltype(cache.Q))) - - if integrator.opts.adaptive - # Set up the order window - win_min = max(alg.min_order, n_curr - 1) - win_max = min(alg.max_order, n_curr + 1) - - # Set up the current extrapolation order - cache.n_old = n_curr # Save the suggested order for step_*_controller! - n_curr = win_min # Start with smallest order in the order window - end - - #Compute the internal discretisations - calc_J!(J, integrator, cache) # Store the calculated jac as it won't change in internal discretisation - if !isthreaded(alg.threading) - for i in 0:n_curr - j_int = 4 * subdividing_sequence[i + 1] - dt_int = dt / j_int # Stepsize of the ith internal discretisation - jacobian2W!(W[1], integrator.f.mass_matrix, dt_int, J, false) - integrator.stats.nw += 1 - @.. broadcast=false u_temp2=uprev - @.. broadcast=false linsolve_tmps[1]=dt_int * fsalfirst - - linsolve = cache.linsolve[1] - - if !repeat_step - linres = dolinsolve(integrator, linsolve; A = W[1], - b = _vec(linsolve_tmps[1]), linu = _vec(k)) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[1]), linu = _vec(k)) - end - - cache.linsolve[1] = linres.cache - - integrator.stats.nsolve += 1 - @.. broadcast=false k=-k - @.. broadcast=false u_temp1=u_temp2 + k # Euler starting step - @.. broadcast=false diff1[1]=u_temp1 - u_temp2 - for j in 2:j_int - f(k, cache.u_temp1, p, t + (j - 1) * dt_int) - integrator.stats.nf += 1 - @.. broadcast=false linsolve_tmps[1]=dt_int * k - (u_temp1 - u_temp2) - - linsolve = cache.linsolve[1] - - if !repeat_step && j == 1 - linres = dolinsolve(integrator, linsolve; A = W[1], - b = _vec(linsolve_tmps[1]), linu = _vec(k)) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[1]), linu = _vec(k)) - end - cache.linsolve[1] = linres.cache - - integrator.stats.nsolve += 1 - @.. broadcast=false k=-k - @.. broadcast=false T[i + 1]=2 * u_temp1 - u_temp2 + 2 * k # Explicit Midpoint rule - @.. broadcast=false u_temp2=u_temp1 - @.. broadcast=false u_temp1=T[i + 1] - if (i <= 1) - # Deuflhard Stability check for initial two sequences - @.. broadcast=false diff2[1]=u_temp1 - u_temp2 - if (integrator.opts.internalnorm(diff1[1], t) < - integrator.opts.internalnorm(0.5 * (diff2[1] - diff1[1]), t)) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - end - end - else - if alg.sequence == :romberg - # Compute solution by using maximum two threads for romberg sequence - # One thread will fill T matrix till second last element and another thread will - # fill last element of T matrix. - # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) - # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, - dt = dt, u_temp3 = u_temp3, - u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T - - @threaded alg.threading for i in 1:2 - startIndex = (i == 1) ? 0 : n_curr - endIndex = (i == 1) ? n_curr - 1 : n_curr - - for index in startIndex:endIndex - j_int_temp = 4 * subdividing_sequence[index + 1] - dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation - jacobian2W!(W[Threads.threadid()], integrator.f.mass_matrix, - dt_int_temp, J, false) - @.. broadcast=false u_temp4[Threads.threadid()]=uprev - @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * - fsalfirst - - linsolve = cache.linsolve[Threads.threadid()] - - if !repeat_step - linres = dolinsolve(integrator, linsolve; - A = W[Threads.threadid()], - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - end - cache.linsolve[Threads.threadid()] = linres.cache - - @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] - @.. broadcast=false u_temp3[Threads.threadid()]=u_temp4[Threads.threadid()] + - k_tmps[Threads.threadid()] # Euler starting step - @.. broadcast=false diff1[Threads.threadid()]=u_temp3[Threads.threadid()] - - u_temp4[Threads.threadid()] - for j in 2:j_int_temp - f(k_tmps[Threads.threadid()], - cache.u_temp3[Threads.threadid()], - p, t + (j - 1) * dt_int_temp) - @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * - k_tmps[Threads.threadid()] - - (u_temp3[Threads.threadid()] - - u_temp4[Threads.threadid()]) - - linsolve = cache.linsolve[Threads.threadid()] - - if !repeat_step && j == 1 - linres = dolinsolve(integrator, linsolve; - A = W[Threads.threadid()], - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - end - cache.linsolve[Threads.threadid()] = linres.cache - - @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] - @.. broadcast=false T[index + 1]=2 * - u_temp3[Threads.threadid()] - - u_temp4[Threads.threadid()] + - 2 * k_tmps[Threads.threadid()] # Explicit Midpoint rule - @.. broadcast=false u_temp4[Threads.threadid()]=u_temp3[Threads.threadid()] - @.. broadcast=false u_temp3[Threads.threadid()]=T[index + 1] - if (index <= 1) - # Deuflhard Stability check for initial two sequences - @.. broadcast=false diff2[Threads.threadid()]=u_temp3[Threads.threadid()] - - u_temp4[Threads.threadid()] - @.. broadcast=false diff2[Threads.threadid()]=0.5 * - (diff2[Threads.threadid()] - - diff1[Threads.threadid()]) - if (integrator.opts.internalnorm(diff1[Threads.threadid()], - t) < - integrator.opts.internalnorm(diff2[Threads.threadid()], - t)) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - end - end - integrator.force_stepfail ? break : continue - end - end - else - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, - dt = dt, u_temp3 = u_temp3, - u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T - - @threaded alg.threading for i in 0:(n_curr ÷ 2) - indices = i != n_curr - i ? (i, n_curr - i) : (-1, n_curr - i) #Use flag to avoid union - for index in indices - index == -1 && continue - j_int_temp = 4 * subdividing_sequence[index + 1] - dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation - jacobian2W!(W[Threads.threadid()], integrator.f.mass_matrix, - dt_int_temp, J, false) - @.. broadcast=false u_temp4[Threads.threadid()]=uprev - @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * - fsalfirst - - linsolve = cache.linsolve[Threads.threadid()] - - if !repeat_step - linres = dolinsolve(integrator, linsolve; - A = W[Threads.threadid()], - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - end - cache.linsolve[Threads.threadid()] = linres.cache - - @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] - @.. broadcast=false u_temp3[Threads.threadid()]=u_temp4[Threads.threadid()] + - k_tmps[Threads.threadid()] # Euler starting step - @.. broadcast=false diff1[Threads.threadid()]=u_temp3[Threads.threadid()] - - u_temp4[Threads.threadid()] - for j in 2:j_int_temp - f(k_tmps[Threads.threadid()], - cache.u_temp3[Threads.threadid()], - p, t + (j - 1) * dt_int_temp) - @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * - k_tmps[Threads.threadid()] - - (u_temp3[Threads.threadid()] - - u_temp4[Threads.threadid()]) - - linsolve = cache.linsolve[Threads.threadid()] - - if !repeat_step && j == 1 - linres = dolinsolve(integrator, linsolve; - A = W[Threads.threadid()], - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - end - cache.linsolve[Threads.threadid()] = linres.cache - - @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] - @.. broadcast=false T[index + 1]=2 * - u_temp3[Threads.threadid()] - - u_temp4[Threads.threadid()] + - 2 * k_tmps[Threads.threadid()] # Explicit Midpoint rule - @.. broadcast=false u_temp4[Threads.threadid()]=u_temp3[Threads.threadid()] - @.. broadcast=false u_temp3[Threads.threadid()]=T[index + 1] - if (index <= 1) - # Deuflhard Stability check for initial two sequences - @.. broadcast=false diff2[Threads.threadid()]=u_temp3[Threads.threadid()] - - u_temp4[Threads.threadid()] - @.. broadcast=false diff2[Threads.threadid()]=0.5 * - (diff2[Threads.threadid()] - - diff1[Threads.threadid()]) - if (integrator.opts.internalnorm(diff1[Threads.threadid()], - t) < - integrator.opts.internalnorm(diff2[Threads.threadid()], - t)) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - end - end - integrator.force_stepfail ? break : continue - end - end - end - end - - if integrator.force_stepfail - return - end - - if integrator.opts.adaptive - # Compute all information relating to an extrapolation order ≦ win_min - for i in (alg.min_order):n_curr - - #integrator.u .= extrapolation_scalars[i+1] * sum( broadcast(*, cache.T[1:(i+1)], extrapolation_weights[1:(i+1), (i+1)]) ) # Approximation of extrapolation order i - #cache.utilde .= extrapolation_scalars_2[i] * sum( broadcast(*, cache.T[2:(i+1)], extrapolation_weights_2[1:i, i]) ) # and its internal counterpart - - u_temp1 .= false - u_temp2 .= false - for j in 1:(i + 1) - @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (i + 1)] - end - for j in 2:(i + 1) - @.. broadcast=false u_temp2+=cache.T[j] * extrapolation_weights_2[j - 1, i] - end - @.. broadcast=false integrator.u=extrapolation_scalars[i + 1] * u_temp1 - @.. broadcast=false cache.utilde=extrapolation_scalars_2[i] * u_temp2 - - calculate_residuals!(cache.res, integrator.u, cache.utilde, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(cache.res, t) - cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! - stepsize_controller_internal!(integrator, alg) # Update cache.Q - end - - # Check if an approximation of some order in the order window can be accepted - while n_curr <= win_max - tol = integrator.opts.internalnorm(cache.utilde - integrator.u, t) / - integrator.EEst # Used by the convergence monitor - if accept_step_controller(integrator, integrator.opts.controller) - # Accept current approximation u of order n_curr - break - elseif integrator.EEst <= - tol^(stage_number[n_curr - alg.min_order + 1] / - stage_number[win_max - alg.min_order + 1] - 1) - # Reject current approximation order but pass convergence monitor - # Compute approximation of order (n_curr + 1) - n_curr = n_curr + 1 - cache.n_curr = n_curr - - # Update cache.T - j_int = 4 * subdividing_sequence[n_curr + 1] - dt_int = dt / j_int # Stepsize of the new internal discretisation - jacobian2W!(W[1], integrator.f.mass_matrix, dt_int, J, false) - integrator.stats.nw += 1 - @.. broadcast=false u_temp2=uprev - @.. broadcast=false linsolve_tmps[1]=dt_int * fsalfirst - - linsolve = cache.linsolve[1] - linres = dolinsolve(integrator, linsolve; b = _vec(linsolve_tmps[1]), - linu = _vec(k)) - cache.linsolve[1] = linres.cache - - integrator.stats.nsolve += 1 - @.. broadcast=false k=-k - @.. broadcast=false u_temp1=u_temp2 + k # Euler starting step - for j in 2:j_int - f(k, cache.u_temp1, p, t + (j - 1) * dt_int) - integrator.stats.nf += 1 - @.. broadcast=false linsolve_tmps[1]=dt_int * k - (u_temp1 - u_temp2) - - linsolve = cache.linsolve[1] - linres = dolinsolve(integrator, linsolve; b = _vec(linsolve_tmps[1]), - linu = _vec(k)) - cache.linsolve[1] = linres.cache - - integrator.stats.nsolve += 1 - @.. broadcast=false k=-k - @.. broadcast=false T[n_curr + 1]=2 * u_temp1 - u_temp2 + 2 * k # Explicit Midpoint rule - @.. broadcast=false u_temp2=u_temp1 - @.. broadcast=false u_temp1=T[n_curr + 1] - end - - # Update u, integrator.EEst and cache.Q - #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr - #cache.utilde .= extrapolation_scalars_2[n_curr] * sum( broadcast(*, cache.T[2:(n_curr+1)], extrapolation_weights_2[1:n_curr, n_curr]) ) # and its internal counterpart - - u_temp1 .= false - u_temp2 .= false - for j in 1:(n_curr + 1) - @.. broadcast=false u_temp1+=cache.T[j] * - extrapolation_weights[j, (n_curr + 1)] - end - for j in 2:(n_curr + 1) - @.. broadcast=false u_temp2+=cache.T[j] * - extrapolation_weights_2[j - 1, n_curr] - end - @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 - @.. broadcast=false cache.utilde=extrapolation_scalars_2[n_curr] * u_temp2 - - calculate_residuals!(cache.res, integrator.u, cache.utilde, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(cache.res, t) - stepsize_controller_internal!(integrator, alg) # Update cache.Q - else - # Reject the current approximation and not pass convergence monitor - break - end - end - else - - #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr - u_temp1 .= false - for j in 1:(n_curr + 1) - @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (n_curr + 1)] - end - @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 - end - - f(cache.k, integrator.u, p, t + dt) # Update FSAL - integrator.stats.nf += 1 -end - -function initialize!(integrator, cache::ImplicitDeuflhardExtrapolationConstantCache) - # cf. initialize! of MidpointConstantCache - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -function perform_step!(integrator, cache::ImplicitDeuflhardExtrapolationConstantCache, - repeat_step = false) - # Unpack all information needed - @unpack t, uprev, dt, f, p = integrator - alg = unwrap_alg(integrator, true) - @unpack n_curr = cache - # Coefficients for obtaining u - @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients - # Coefficients for obtaining utilde - @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients - # Additional constant information - @unpack subdividing_sequence = cache.coefficients - @unpack stage_number = cache - - # Create auxiliary variables - u_temp1, u_temp2 = copy(uprev), copy(uprev) # Auxiliary variables for computing the internal discretisations - u, utilde = copy(uprev), copy(uprev) # Storage for the latest approximation and its internal counterpart - T = fill(zero(uprev), alg.max_order + 1) # Storage for the internal discretisations obtained by the explicit midpoint rule - fill!(cache.Q, zero(eltype(cache.Q))) - - # Start computation - if integrator.opts.adaptive - # Set up the order window - win_min = max(alg.min_order, n_curr - 1) - win_max = min(alg.max_order, n_curr + 1) - - # Set up the current extrapolation order - cache.n_old = n_curr # Save the suggested order for step_*_controller! - n_curr = win_min # Start with smallest order in the order window - end - - # Compute the internal discretisations - J = calc_J(integrator, cache) # Store the calculated jac as it won't change in internal discretisation - if !isthreaded(alg.threading) - for i in 0:n_curr - j_int = 4 * subdividing_sequence[i + 1] - dt_int = dt / j_int # Stepsize of the ith internal discretisation - W = dt_int * J - integrator.f.mass_matrix - integrator.stats.nw += 1 - u_temp2 = uprev - u_temp1 = u_temp2 + - _reshape(W \ -_vec(dt_int * integrator.fsalfirst), axes(uprev)) # Euler starting step - diff1 = u_temp1 - u_temp2 - for j in 2:j_int - T[i + 1] = 2 * u_temp1 - u_temp2 + - 2 * _reshape( - W \ - -_vec(dt_int * f(u_temp1, p, t + (j - 1) * dt_int) - - (u_temp1 - u_temp2)), - axes(uprev)) - integrator.stats.nf += 1 - u_temp2 = u_temp1 - u_temp1 = T[i + 1] - if (i <= 1) - # Deuflhard Stability check for initial two sequences - diff2 = u_temp1 - u_temp2 - if (integrator.opts.internalnorm(diff1, t) < - integrator.opts.internalnorm(0.5 * (diff2 - diff1), t)) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - end - end - else - if alg.sequence == :romberg - # Compute solution by using maximum two threads for romberg sequence - # One thread will fill T matrix till second last element and another thread will - # fill last element of T matrix. - # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) - # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, - dt = dt, u_temp2 = u_temp2, - u_temp2 = u_temp2, p = p, t = t, T = T - - @threaded alg.threading for i in 1:2 - startIndex = (i == 1) ? 0 : n_curr - endIndex = (i == 1) ? n_curr - 1 : n_curr - - for index in startIndex:endIndex - j_int = 4 * subdividing_sequence[index + 1] - dt_int = dt / j_int # Stepsize of the ith internal discretisation - W = dt_int * J - integrator.f.mass_matrix - integrator.stats.nw += 1 - u_temp4 = uprev - u_temp3 = u_temp4 + - _reshape(W \ -_vec(dt_int * integrator.fsalfirst), - axes(uprev)) # Euler starting step - diff1 = u_temp3 - u_temp4 - for j in 2:j_int - T[index + 1] = 2 * u_temp3 - u_temp4 + - 2 * _reshape( - W \ - -_vec(dt_int * f(u_temp3, p, - t + (j - 1) * dt_int) - - (u_temp3 - u_temp4)), - axes(uprev)) - integrator.stats.nf += 1 - u_temp4 = u_temp3 - u_temp3 = T[index + 1] - if (index <= 1) - # Deuflhard Stability check for initial two sequences - diff2 = u_temp3 - u_temp4 - if (integrator.opts.internalnorm(diff1[1], t) < - integrator.opts.internalnorm( - 0.5 * - (diff2[1] - diff1[1]), t)) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - end - end - integrator.force_stepfail ? break : continue - end - end - else - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, - dt = dt, - integrator = integrator, p = p, t = t, T = T - - @threaded alg.threading for i in 0:(n_curr ÷ 2) - indices = i != n_curr - i ? (i, n_curr - i) : (-1, n_curr - i) - for index in indices - index == -1 && continue - j_int = 4 * subdividing_sequence[index + 1] - dt_int = dt / j_int # Stepsize of the ith internal discretisation - W = dt_int * J - integrator.f.mass_matrix - integrator.stats.nw += 1 - u_temp4 = uprev - u_temp3 = u_temp4 + - _reshape(W \ -_vec(dt_int * integrator.fsalfirst), - axes(uprev)) # Euler starting step - diff1 = u_temp3 - u_temp4 - for j in 2:j_int - T[index + 1] = 2 * u_temp3 - u_temp4 + - 2 * _reshape( - W \ - -_vec(dt_int * f(u_temp3, p, - t + (j - 1) * dt_int) - - (u_temp3 - u_temp4)), - axes(uprev)) - integrator.stats.nf += 1 - u_temp4 = u_temp3 - u_temp3 = T[index + 1] - if (index <= 1) - # Deuflhard Stability check for initial two sequences - diff2 = u_temp3 - u_temp4 - if (integrator.opts.internalnorm(diff1, t) < - integrator.opts.internalnorm(0.5 * (diff2 - diff1), t)) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - end - end - integrator.force_stepfail ? break : continue - end - end - end - end - - if integrator.force_stepfail - return - end - - if integrator.opts.adaptive - # Compute all information relating to an extrapolation order ≦ win_min - for i in (alg.min_order):n_curr - u = eltype(uprev).(extrapolation_scalars[i + 1]) * - sum(broadcast(*, T[1:(i + 1)], - eltype(uprev).(extrapolation_weights[1:(i + 1), (i + 1)]))) # Approximation of extrapolation order i - utilde = eltype(uprev).(extrapolation_scalars_2[i]) * - sum(broadcast(*, T[2:(i + 1)], - eltype(uprev).(extrapolation_weights_2[1:i, i]))) # and its internal counterpart - res = calculate_residuals(u, utilde, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, - t) - integrator.EEst = integrator.opts.internalnorm(res, t) - cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! - stepsize_controller_internal!(integrator, alg) # Update cache.Q - end - - # Check if an approximation of some order in the order window can be accepted - while n_curr <= win_max - tol = integrator.opts.internalnorm(utilde - u, t) / integrator.EEst # Used by the convergence monitor - if accept_step_controller(integrator, integrator.opts.controller) - # Accept current approximation u of order n_curr - break - elseif integrator.EEst <= - tol^(stage_number[n_curr - alg.min_order + 1] / - stage_number[win_max - alg.min_order + 1] - 1) - # Reject current approximation order but pass convergence monitor - # Compute approximation of order (n_curr + 1) - n_curr = n_curr + 1 - cache.n_curr = n_curr - - # Update T - j_int = 4 * subdividing_sequence[n_curr + 1] - dt_int = dt / j_int # Stepsize of the new internal discretisation - W = dt_int * J - integrator.f.mass_matrix - integrator.stats.nw += 1 - u_temp2 = uprev - u_temp1 = u_temp2 + - _reshape(W \ -_vec(dt_int * integrator.fsalfirst), axes(uprev)) # Euler starting step - for j in 2:j_int - T[n_curr + 1] = 2 * u_temp1 - u_temp2 + - 2 * _reshape( - W \ - -_vec(dt_int * - f(u_temp1, p, t + (j - 1) * dt_int) - - (u_temp1 - u_temp2)), - axes(uprev)) - integrator.stats.nf += 1 - u_temp2 = u_temp1 - u_temp1 = T[n_curr + 1] - end - - # Update u, integrator.EEst and cache.Q - u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * - sum(broadcast(*, T[1:(n_curr + 1)], - eltype(uprev).(extrapolation_weights[1:(n_curr + 1), - (n_curr + 1)]))) # Approximation of extrapolation order n_curr - utilde = eltype(uprev).(extrapolation_scalars_2[n_curr]) * - sum(broadcast(*, T[2:(n_curr + 1)], - eltype(uprev).(extrapolation_weights_2[1:n_curr, - n_curr]))) # and its internal counterpart - res = calculate_residuals(u, utilde, integrator.opts.abstol, - integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(res, t) - stepsize_controller_internal!(integrator, alg) # Update cache.Q - else - # Reject the current approximation and not pass convergence monitor - break - end - end - else - u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * - sum(broadcast(*, T[1:(n_curr + 1)], - eltype(uprev).(extrapolation_weights[1:(n_curr + 1), - (n_curr + 1)]))) # Approximation of extrapolation order n_curr - end - - # Save the latest approximation and update FSAL - integrator.u = u - integrator.fsallast = f(u, p, t + dt) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.stats.nf += 1 -end - -function initialize!(integrator, cache::ExtrapolationMidpointHairerWannerCache) - # cf. initialize! of MidpointCache - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 2 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation -end - -function perform_step!(integrator, cache::ExtrapolationMidpointHairerWannerCache, - repeat_step = false) - # Unpack all information needed - @unpack t, uprev, dt, f, p = integrator - alg = unwrap_alg(integrator, false) - @unpack n_curr, u_temp1, u_temp2, utilde, res, T, fsalfirst, k = cache - @unpack u_temp3, u_temp4, k_tmps = cache - # Coefficients for obtaining u - @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients - # Coefficients for obtaining utilde - @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients - # Additional constant information - @unpack subdividing_sequence = cache.coefficients - @unpack sequence_factor = alg - - fill!(cache.Q, zero(eltype(cache.Q))) - - if integrator.opts.adaptive - # Set up the order window - # alg.min_order + 1 ≦ n_curr ≦ alg.max_order - 1 is enforced by step_*_controller! - if !(alg.min_order + 1 <= n_curr <= alg.max_order - 1) - error("Something went wrong while setting up the order window: $n_curr ∉ [$(alg.min_order+1),$(alg.max_order-1)]. - Please report this error ") - end - win_min = n_curr - 1 - win_max = n_curr + 1 - - # Set up the current extrapolation order - cache.n_old = n_curr # Save the suggested order for step_*_controller! - n_curr = win_min # Start with smallest order in the order window - end - - #Compute the internal discretisations - if !isthreaded(alg.threading) - for i in 0:n_curr - j_int = sequence_factor * subdividing_sequence[i + 1] - dt_int = dt / j_int # Stepsize of the ith internal discretisation - @.. broadcast=false u_temp2=uprev - @.. broadcast=false u_temp1=u_temp2 + dt_int * fsalfirst # Euler starting step - for j in 2:j_int - f(k, cache.u_temp1, p, t + (j - 1) * dt_int) - integrator.stats.nf += 1 - @.. broadcast=false T[i + 1]=u_temp2 + 2 * dt_int * k # Explicit Midpoint rule - @.. broadcast=false u_temp2=u_temp1 - @.. broadcast=false u_temp1=T[i + 1] - end - end - else - if alg.sequence == :romberg - # Compute solution by using maximum two threads for romberg sequence - # One thread will fill T matrix till second last element and another thread will - # fill last element of T matrix. - # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) - # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, - dt = dt, u_temp3 = u_temp3, - u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T - - @threaded alg.threading for i in 1:2 - startIndex = (i == 1) ? 0 : n_curr - endIndex = (i == 1) ? n_curr - 1 : n_curr - - for index in startIndex:endIndex - j_int_temp = sequence_factor * subdividing_sequence[index + 1] - dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation - @.. broadcast=false u_temp4[Threads.threadid()]=uprev - @.. broadcast=false u_temp3[Threads.threadid()]=u_temp4[Threads.threadid()] + - dt_int_temp * - fsalfirst # Euler starting step - for j in 2:j_int_temp - f(k_tmps[Threads.threadid()], - cache.u_temp3[Threads.threadid()], - p, t + (j - 1) * dt_int_temp) - @.. broadcast=false T[index + 1]=u_temp4[Threads.threadid()] + - 2 * dt_int_temp * - k_tmps[Threads.threadid()] # Explicit Midpoint rule - @.. broadcast=false u_temp4[Threads.threadid()]=u_temp3[Threads.threadid()] - @.. broadcast=false u_temp3[Threads.threadid()]=T[index + 1] - end - end - end - end - else - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, - dt = dt, u_temp3 = u_temp3, - u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T - - @threaded alg.threading for i in 0:(n_curr ÷ 2) - indices = i != n_curr - i ? (i, n_curr - i) : (-1, n_curr - i) - for index in indices - index == -1 && continue - j_int_temp = sequence_factor * subdividing_sequence[index + 1] - dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation - @.. broadcast=false u_temp4[Threads.threadid()]=uprev - @.. broadcast=false u_temp3[Threads.threadid()]=u_temp4[Threads.threadid()] + - dt_int_temp * - fsalfirst # Euler starting step - for j in 2:j_int_temp - f(k_tmps[Threads.threadid()], - cache.u_temp3[Threads.threadid()], - p, t + (j - 1) * dt_int_temp) - @.. broadcast=false T[index + 1]=u_temp4[Threads.threadid()] + - 2 * dt_int_temp * - k_tmps[Threads.threadid()] # Explicit Midpoint rule - @.. broadcast=false u_temp4[Threads.threadid()]=u_temp3[Threads.threadid()] - @.. broadcast=false u_temp3[Threads.threadid()]=T[index + 1] - end - end - end - end - end - nevals = cache.stage_number[n_curr + 1] - 1 - integrator.stats.nf += nevals - end - - if integrator.opts.adaptive - # Compute all information relating to an extrapolation order ≦ win_min - for i in (win_min - 1):win_min - - #integrator.u .= extrapolation_scalars[i+1] * sum( broadcast(*, cache.T[1:(i+1)], extrapolation_weights[1:(i+1), (i+1)]) ) # Approximation of extrapolation order i - #cache.utilde .= extrapolation_scalars_2[i] * sum( broadcast(*, cache.T[2:(i+1)], extrapolation_weights_2[1:i, i]) ) # and its internal counterpart - - u_temp1 .= false - u_temp2 .= false - for j in 1:(i + 1) - @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (i + 1)] - end - for j in 2:(i + 1) - @.. broadcast=false u_temp2+=cache.T[j] * extrapolation_weights_2[j - 1, i] - end - @.. broadcast=false integrator.u=extrapolation_scalars[i + 1] * u_temp1 - @.. broadcast=false cache.utilde=extrapolation_scalars_2[i] * u_temp2 - - calculate_residuals!(cache.res, integrator.u, cache.utilde, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(cache.res, t) - cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! - stepsize_controller_internal!(integrator, alg) # Update cache.Q - end - - # Check if an approximation of some order in the order window can be accepted - # Make sure a stepsize scaling factor of order (alg.min_order + 1) is provided for the step_*_controller! - while n_curr <= win_max - if accept_step_controller(integrator, integrator.opts.controller) - # Accept current approximation u of order n_curr - break - elseif (n_curr < alg.min_order + 1) || - integrator.EEst <= - typeof(integrator.EEst)(prod(subdividing_sequence[(n_curr + 2):(win_max + 1)] .// - subdividing_sequence[1]^2)) - # Reject current approximation order but pass convergence monitor - # Compute approximation of order (n_curr + 1) - n_curr = n_curr + 1 - cache.n_curr = n_curr - - # Update cache.T - j_int = sequence_factor * subdividing_sequence[n_curr + 1] - dt_int = dt / j_int # Stepsize of the new internal discretisation - @.. broadcast=false u_temp2=uprev - @.. broadcast=false u_temp1=u_temp2 + dt_int * fsalfirst # Euler starting step - for j in 2:j_int - f(k, cache.u_temp1, p, t + (j - 1) * dt_int) - integrator.stats.nf += 1 - @.. broadcast=false T[n_curr + 1]=u_temp2 + 2 * dt_int * k - @.. broadcast=false u_temp2=u_temp1 - @.. broadcast=false u_temp1=T[n_curr + 1] - end - - # Update u, integrator.EEst and cache.Q - #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr - #cache.utilde .= extrapolation_scalars_2[n_curr] * sum( broadcast(*, cache.T[2:(n_curr+1)], extrapolation_weights_2[1:n_curr, n_curr]) ) # and its internal counterpart - - u_temp1 .= false - u_temp2 .= false - for j in 1:(n_curr + 1) - @.. broadcast=false u_temp1+=cache.T[j] * - extrapolation_weights[j, (n_curr + 1)] - end - for j in 2:(n_curr + 1) - @.. broadcast=false u_temp2+=cache.T[j] * - extrapolation_weights_2[j - 1, n_curr] - end - @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 - @.. broadcast=false cache.utilde=extrapolation_scalars_2[n_curr] * u_temp2 - - calculate_residuals!(cache.res, integrator.u, cache.utilde, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(cache.res, t) - stepsize_controller_internal!(integrator, alg) # Update cache.Q - else - # Reject the current approximation and not pass convergence monitor - break - end - end - else - - #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr - u_temp1 .= false - for j in 1:(n_curr + 1) - @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (n_curr + 1)] - end - @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 - end - - f(cache.k, integrator.u, p, t + dt) # Update FSAL - integrator.stats.nf += 1 -end - -function initialize!(integrator, cache::ExtrapolationMidpointHairerWannerConstantCache) - # cf. initialize! of MidpointConstantCache - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -function perform_step!(integrator, cache::ExtrapolationMidpointHairerWannerConstantCache, - repeat_step = false) - # Unpack all information needed - @unpack t, uprev, dt, f, p = integrator - alg = unwrap_alg(integrator, false) - @unpack n_curr = cache - # Coefficients for obtaining u - @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients - # Coefficients for obtaining utilde - @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients - # Additional constant information - @unpack subdividing_sequence = cache.coefficients - @unpack sequence_factor = alg - - # Create auxiliary variables - u_temp1, u_temp2 = copy(uprev), copy(uprev) # Auxiliary variables for computing the internal discretisations - u, utilde = copy(uprev), copy(uprev) # Storage for the latest approximation and its internal counterpart - T = fill(zero(uprev), alg.max_order + 1) # Storage for the internal discretisations obtained by the explicit midpoint rule - fill!(cache.Q, zero(eltype(cache.Q))) - - if integrator.opts.adaptive - # Set up the order window - # alg.min_order + 1 ≦ n_curr ≦ alg.max_order - 1 is enforced by step_*_controller! - if !(alg.min_order + 1 <= n_curr <= alg.max_order - 1) - error("Something went wrong while setting up the order window: $n_curr ∉ [$(alg.min_order+1),$(alg.max_order-1)]. - Please report this error ") - end - win_min = n_curr - 1 - win_max = n_curr + 1 - - # Set up the current extrapolation order - cache.n_old = n_curr # Save the suggested order for step_*_controller! - n_curr = win_min # Start with smallest order in the order window - end - - #Compute the internal discretisations - if !isthreaded(alg.threading) - for i in 0:n_curr - j_int = sequence_factor * subdividing_sequence[i + 1] - dt_int = dt / j_int # Stepsize of the ith internal discretisation - u_temp2 = uprev - u_temp1 = u_temp2 + dt_int * integrator.fsalfirst # Euler starting step - for j in 2:j_int - T[i + 1] = u_temp2 + 2 * dt_int * f(u_temp1, p, t + (j - 1) * dt_int) # Explicit Midpoint rule - integrator.stats.nf += 1 - u_temp2 = u_temp1 - u_temp1 = T[i + 1] - end - end - else - if alg.sequence == :romberg - # Compute solution by using maximum two threads for romberg sequence - # One thread will fill T matrix till second last element and another thread will - # fill last element of T matrix. - # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) - # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, dt = dt, - uprev = uprev, - integrator = integrator, T = T, p = p, t = t - - @threaded alg.threading for i in 1:2 - startIndex = (i == 1) ? 0 : n_curr - endIndex = (i == 1) ? n_curr - 1 : n_curr - for index in startIndex:endIndex - j_int_temp = sequence_factor * subdividing_sequence[index + 1] - dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation - u_temp4 = uprev - u_temp3 = u_temp4 + dt_int_temp * integrator.fsalfirst # Euler starting step - for j in 2:j_int_temp - T[index + 1] = u_temp4 + - 2 * dt_int_temp * - f(u_temp3, p, t + (j - 1) * dt_int_temp) # Explicit Midpoint rule - u_temp4 = u_temp3 - u_temp3 = T[index + 1] - end - end - end - end - else - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, dt = dt, - uprev = uprev, - integrator = integrator, T = T, p = p, t = t - - @threaded alg.threading for i in 0:(n_curr ÷ 2) - indices = i != n_curr - i ? (i, n_curr - i) : (-1, n_curr - i) - for index in indices - index == -1 && continue - j_int_temp = sequence_factor * subdividing_sequence[index + 1] - dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation - u_temp4 = uprev - u_temp3 = u_temp4 + dt_int_temp * integrator.fsalfirst # Euler starting step - for j in 2:j_int_temp - T[index + 1] = u_temp4 + - 2 * dt_int_temp * - f(u_temp3, p, t + (j - 1) * dt_int_temp) # Explicit Midpoint rule - u_temp4 = u_temp3 - u_temp3 = T[index + 1] - end - end - end - end - end - nevals = cache.stage_number[n_curr + 1] - 1 - integrator.stats.nf += nevals - end - if integrator.opts.adaptive - # Compute all information relating to an extrapolation order ≦ win_min - for i in (win_min - 1):win_min - u = eltype(uprev).(extrapolation_scalars[i + 1]) * - sum(broadcast(*, T[1:(i + 1)], - eltype(uprev).(extrapolation_weights[1:(i + 1), (i + 1)]))) # Approximation of extrapolation order i - utilde = eltype(uprev).(extrapolation_scalars_2[i]) * - sum(broadcast(*, T[2:(i + 1)], - eltype(uprev).(extrapolation_weights_2[1:i, i]))) # and its internal counterpart - res = calculate_residuals(u, utilde, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, - t) - integrator.EEst = integrator.opts.internalnorm(res, t) - cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! - stepsize_controller_internal!(integrator, alg) # Update cache.Q - end - - # Check if an approximation of some order in the order window can be accepted - # Make sure a stepsize scaling factor of order (alg.min_order + 1) is provided for the step_*_controller! - while n_curr <= win_max - if accept_step_controller(integrator, integrator.opts.controller) - # Accept current approximation u of order n_curr - break - elseif (n_curr < alg.min_order + 1) || - integrator.EEst <= - typeof(integrator.EEst)(prod(subdividing_sequence[(n_curr + 2):(win_max + 1)] .// - subdividing_sequence[1]^2)) - # Reject current approximation order but pass convergence monitor - # Always compute approximation of order (n_curr + 1) - n_curr = n_curr + 1 - cache.n_curr = n_curr - - # Update T - j_int = sequence_factor * subdividing_sequence[n_curr + 1] - dt_int = dt / j_int # Stepsize of the new internal discretisation - u_temp2 = uprev - u_temp1 = u_temp2 + dt_int * integrator.fsalfirst # Euler starting step - for j in 2:j_int - T[n_curr + 1] = u_temp2 + - 2 * dt_int * f(u_temp1, p, t + (j - 1) * dt_int) - integrator.stats.nf += 1 - u_temp2 = u_temp1 - u_temp1 = T[n_curr + 1] - end - - # Update u, integrator.EEst and cache.Q - u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * - sum(broadcast(*, T[1:(n_curr + 1)], - eltype(uprev).(extrapolation_weights[1:(n_curr + 1), - (n_curr + 1)]))) # Approximation of extrapolation order n_curr - utilde = eltype(uprev).(extrapolation_scalars_2[n_curr]) * - sum(broadcast(*, T[2:(n_curr + 1)], - eltype(uprev).(extrapolation_weights_2[1:n_curr, - n_curr]))) # and its internal counterpart - res = calculate_residuals(u, utilde, integrator.opts.abstol, - integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(res, t) - stepsize_controller_internal!(integrator, alg) # Update cache.Q - else - # Reject the current approximation and not pass convergence monitor - break - end - end - else - u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * - sum(broadcast(*, T[1:(n_curr + 1)], - eltype(uprev).(extrapolation_weights[1:(n_curr + 1), - (n_curr + 1)]))) # Approximation of extrapolation order n_curr - end - - # Save the latest approximation and update FSAL - integrator.u = u - integrator.fsallast = f(u, p, t + dt) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.stats.nf += 1 -end - -function initialize!(integrator, cache::ImplicitHairerWannerExtrapolationConstantCache) - # cf. initialize! of MidpointConstantCache - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -function perform_step!(integrator, cache::ImplicitHairerWannerExtrapolationConstantCache, - repeat_step = false) - # Unpack all information needed - @unpack t, uprev, dt, f, p = integrator - alg = unwrap_alg(integrator, true) - @unpack n_curr = cache - # Coefficients for obtaining u - @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients - # Coefficients for obtaining utilde - @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients - # Additional constant information - @unpack subdividing_sequence = cache.coefficients - - # Create auxiliary variables - u_temp1, u_temp2 = copy(uprev), copy(uprev) # Auxiliary variables for computing the internal discretisations - u, utilde = copy(uprev), copy(uprev) # Storage for the latest approximation and its internal counterpart - T = fill(zero(uprev), alg.max_order + 1) # Storage for the internal discretisations obtained by the explicit midpoint rule - fill!(cache.Q, zero(eltype(cache.Q))) - - if integrator.opts.adaptive - # Set up the order window - # alg.min_order + 1 ≦ n_curr ≦ alg.max_order - 1 is enforced by step_*_controller! - if !(alg.min_order + 1 <= n_curr <= alg.max_order - 1) - error("Something went wrong while setting up the order window: $n_curr ∉ [$(alg.min_order+1),$(alg.max_order-1)]. - Please report this error ") - end - win_min = n_curr - 1 - win_max = n_curr + 1 - - # Set up the current extrapolation order - cache.n_old = n_curr # Save the suggested order for step_*_controller! - n_curr = win_min # Start with smallest order in the order window - end - - #Compute the internal discretisations - J = calc_J(integrator, cache) # Store the calculated jac as it won't change in internal discretisation - if !isthreaded(alg.threading) - for i in 0:n_curr - j_int = 4 * subdividing_sequence[i + 1] - dt_int = dt / j_int # Stepsize of the ith internal discretisation - W = dt_int * J - integrator.f.mass_matrix - integrator.stats.nw += 1 - u_temp2 = uprev - u_temp1 = u_temp2 + - _reshape(W \ -_vec(dt_int * integrator.fsalfirst), axes(uprev)) # Euler starting step - diff1 = u_temp1 - u_temp2 - for j in 2:(j_int + 1) - T[i + 1] = 2 * u_temp1 - u_temp2 + - 2 * _reshape( - W \ - -_vec(dt_int * f(u_temp1, p, t + (j - 1) * dt_int) - - (u_temp1 - u_temp2)), - axes(uprev)) - integrator.stats.nf += 1 - if (j == j_int + 1) - T[i + 1] = 0.5(T[i + 1] + u_temp2) - end - u_temp2 = u_temp1 - u_temp1 = T[i + 1] - if (i <= 1) - # Deuflhard Stability check for initial two sequences - diff2 = u_temp1 - u_temp2 - if (integrator.opts.internalnorm(diff1, t) < - integrator.opts.internalnorm(0.5 * (diff2 - diff1), t)) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - diff1 = u_temp1 - u_temp2 - end - end - else - if alg.sequence == :romberg - # Compute solution by using maximum two threads for romberg sequence - # One thread will fill T matrix till second last element and another thread will - # fill last element of T matrix. - # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) - # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, - dt = dt, u_temp2 = u_temp2, - u_temp2 = u_temp2, p = p, t = t, T = T - - @threaded alg.threading for i in 1:2 - startIndex = (i == 1) ? 0 : n_curr - endIndex = (i == 1) ? n_curr - 1 : n_curr - - for index in startIndex:endIndex - j_int = 4 * subdividing_sequence[index + 1] - dt_int = dt / j_int # Stepsize of the ith internal discretisation - W = dt_int * J - integrator.f.mass_matrix - integrator.stats.nw += 1 - u_temp4 = uprev - u_temp3 = u_temp4 + - _reshape(W \ -_vec(dt_int * integrator.fsalfirst), - axes(uprev)) # Euler starting step - diff1 = u_temp3 - u_temp4 - for j in 2:(j_int + 1) - T[index + 1] = 2 * u_temp3 - u_temp4 + - 2 * _reshape( - W \ - -_vec(dt_int * f(u_temp3, p, - t + (j - 1) * dt_int) - - (u_temp3 - u_temp4)), - axes(uprev)) - integrator.stats.nf += 1 - if (j == j_int + 1) - T[index + 1] = 0.5(T[index + 1] + u_temp4) - end - u_temp4 = u_temp3 - u_temp3 = T[index + 1] - if (index <= 1) - # Deuflhard Stability check for initial two sequences - diff2 = u_temp3 - u_temp4 - if (integrator.opts.internalnorm(diff1, t) < - integrator.opts.internalnorm(0.5 * (diff2 - diff1), t)) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - diff1 = u_temp3 - u_temp4 - end - end - integrator.force_stepfail ? break : continue - end - end - else - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, - dt = dt, - integrator = integrator, p = p, t = t, T = T - - @threaded alg.threading for i in 0:(n_curr ÷ 2) - indices = i != n_curr - i ? (i, n_curr - i) : (-1, n_curr - i) - for index in indices - index == -1 && continue - j_int = 4 * subdividing_sequence[index + 1] - dt_int = dt / j_int # Stepsize of the ith internal discretisation - W = dt_int * J - integrator.f.mass_matrix - integrator.stats.nw += 1 - u_temp4 = uprev - u_temp3 = u_temp4 + - _reshape(W \ -_vec(dt_int * integrator.fsalfirst), - axes(uprev)) # Euler starting step - diff1 = u_temp3 - u_temp4 - for j in 2:(j_int + 1) - T[index + 1] = 2 * u_temp3 - u_temp4 + - 2 * _reshape( - W \ - -_vec(dt_int * f(u_temp3, p, - t + (j - 1) * dt_int) - - (u_temp3 - u_temp4)), - axes(uprev)) - integrator.stats.nf += 1 - if (j == j_int + 1) - T[index + 1] = 0.5(T[index + 1] + u_temp4) - end - u_temp4 = u_temp3 - u_temp3 = T[index + 1] - if (index <= 1) - # Deuflhard Stability check for initial two sequences - diff2 = u_temp3 - u_temp4 - if (integrator.opts.internalnorm(diff1, t) < - integrator.opts.internalnorm(0.5 * (diff2 - diff1), t)) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - diff1 = u_temp3 - u_temp4 - end - end - integrator.force_stepfail ? break : continue - end - end - end - end - - if integrator.force_stepfail - return - end - - if integrator.opts.adaptive - # Compute all information relating to an extrapolation order ≦ win_min - for i in (win_min - 1):win_min - u = eltype(uprev).(extrapolation_scalars[i + 1]) * - sum(broadcast(*, T[1:(i + 1)], - eltype(uprev).(extrapolation_weights[1:(i + 1), (i + 1)]))) # Approximation of extrapolation order i - utilde = eltype(uprev).(extrapolation_scalars_2[i]) * - sum(broadcast(*, T[2:(i + 1)], - eltype(uprev).(extrapolation_weights_2[1:i, i]))) # and its internal counterpart - res = calculate_residuals(u, utilde, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, - t) - integrator.EEst = integrator.opts.internalnorm(res, t) - cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! - stepsize_controller_internal!(integrator, alg) # Update cache.Q - end - - # Check if an approximation of some order in the order window can be accepted - # Make sure a stepsize scaling factor of order (alg.min_order + 1) is provided for the step_*_controller! - while n_curr <= win_max - if accept_step_controller(integrator, integrator.opts.controller) - # Accept current approximation u of order n_curr - break - elseif (n_curr < alg.min_order + 1) || - integrator.EEst <= - typeof(integrator.EEst)(prod(subdividing_sequence[(n_curr + 2):(win_max + 1)] .// - subdividing_sequence[1]^2)) - # Reject current approximation order but pass convergence monitor - # Always compute approximation of order (n_curr + 1) - n_curr = n_curr + 1 - cache.n_curr = n_curr - - # Update T - j_int = 4 * subdividing_sequence[n_curr + 1] - dt_int = dt / j_int # Stepsize of the new internal discretisation - W = dt_int * J - integrator.f.mass_matrix - integrator.stats.nw += 1 - u_temp2 = uprev - u_temp1 = u_temp2 + - _reshape(W \ -_vec(dt_int * integrator.fsalfirst), axes(uprev)) # Euler starting step - for j in 2:(j_int + 1) - T[n_curr + 1] = 2 * u_temp1 - u_temp2 + - 2 * _reshape( - W \ - -_vec(dt_int * - f(u_temp1, p, t + (j - 1) * dt_int) - - (u_temp1 - u_temp2)), - axes(uprev)) - integrator.stats.nf += 1 - if (j == j_int + 1) - T[n_curr + 1] = 0.5(T[n_curr + 1] + u_temp2) - end - u_temp2 = u_temp1 - u_temp1 = T[n_curr + 1] - end - - # Update u, integrator.EEst and cache.Q - u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * - sum(broadcast(*, T[1:(n_curr + 1)], - eltype(uprev).(extrapolation_weights[1:(n_curr + 1), - (n_curr + 1)]))) # Approximation of extrapolation order n_curr - utilde = eltype(uprev).(extrapolation_scalars_2[n_curr]) * - sum(broadcast(*, T[2:(n_curr + 1)], - eltype(uprev).(extrapolation_weights_2[1:n_curr, - n_curr]))) # and its internal counterpart - res = calculate_residuals(u, utilde, integrator.opts.abstol, - integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(res, t) - stepsize_controller_internal!(integrator, alg) # Update cache.Q - else - # Reject the current approximation and not pass convergence monitor - break - end - end - else - u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * - sum(broadcast(*, T[1:(n_curr + 1)], - eltype(uprev).(extrapolation_weights[1:(n_curr + 1), - (n_curr + 1)]))) # Approximation of extrapolation order n_curr - end - - # Save the latest approximation and update FSAL - integrator.u = u - integrator.fsallast = f(u, p, t + dt) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -function initialize!(integrator, cache::ImplicitHairerWannerExtrapolationCache) - # cf. initialize! of MidpointCache - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 2 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation -end - -function perform_step!(integrator, cache::ImplicitHairerWannerExtrapolationCache, - repeat_step = false) - # Unpack all information needed - @unpack t, uprev, dt, f, p = integrator - alg = unwrap_alg(integrator, true) - @unpack n_curr, u_temp1, u_temp2, utilde, res, T, fsalfirst, k, diff1, diff2 = cache - @unpack u_temp3, u_temp4, k_tmps = cache - # Coefficients for obtaining u - @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients - # Coefficients for obtaining utilde - @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients - # Additional constant information - @unpack subdividing_sequence = cache.coefficients - - @unpack J, W, uf, tf, linsolve_tmps, jac_config = cache - - fill!(cache.Q, zero(eltype(cache.Q))) - - if integrator.opts.adaptive - # Set up the order window - # alg.min_order + 1 ≦ n_curr ≦ alg.max_order - 1 is enforced by step_*_controller! - if !(alg.min_order + 1 <= n_curr <= alg.max_order - 1) - error("Something went wrong while setting up the order window: $n_curr ∉ [$(alg.min_order+1),$(alg.max_order-1)]. - Please report this error ") - end - win_min = n_curr - 1 - win_max = n_curr + 1 - - # Set up the current extrapolation order - cache.n_old = n_curr # Save the suggested order for step_*_controller! - n_curr = win_min # Start with smallest order in the order window - end - - #Compute the internal discretisations - calc_J!(J, integrator, cache) # Store the calculated jac as it won't change in internal discretisation - if !isthreaded(alg.threading) - for i in 0:n_curr - j_int = 4 * subdividing_sequence[i + 1] - dt_int = dt / j_int # Stepsize of the ith internal discretisation - jacobian2W!(W[1], integrator.f.mass_matrix, dt_int, J, false) - integrator.stats.nw += 1 - @.. broadcast=false u_temp2=uprev - @.. broadcast=false linsolve_tmps[1]=dt_int * fsalfirst - - linsolve = cache.linsolve[1] - if !repeat_step - linres = dolinsolve(integrator, linsolve; A = W[1], - b = _vec(linsolve_tmps[1]), linu = _vec(k)) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[1]), linu = _vec(k)) - end - cache.linsolve[1] = linres.cache - - integrator.stats.nsolve += 1 - @.. broadcast=false k=-k - @.. broadcast=false u_temp1=u_temp2 + k # Euler starting step - @.. broadcast=false diff1[1]=u_temp1 - u_temp2 - for j in 2:(j_int + 1) - f(k, cache.u_temp1, p, t + (j - 1) * dt_int) - integrator.stats.nf += 1 - @.. broadcast=false linsolve_tmps[1]=dt_int * k - (u_temp1 - u_temp2) - - linsolve = cache.linsolve[1] - - if !repeat_step && j == 1 - linres = dolinsolve(integrator, linsolve; A = W[1], - b = _vec(linsolve_tmps[1]), linu = _vec(k)) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[1]), linu = _vec(k)) - end - cache.linsolve[1] = linres.cache - - integrator.stats.nsolve += 1 - @.. broadcast=false k=-k - @.. broadcast=false T[i + 1]=2 * u_temp1 - u_temp2 + 2 * k # Explicit Midpoint rule - if (j == j_int + 1) - @.. broadcast=false T[i + 1]=0.5(T[i + 1] + u_temp2) - end - @.. broadcast=false u_temp2=u_temp1 - @.. broadcast=false u_temp1=T[i + 1] - if (i <= 1) - # Deuflhard Stability check for initial two sequences - @.. broadcast=false diff2[1]=u_temp1 - u_temp2 - @.. broadcast=false diff2[1]=0.5 * (diff2[1] - diff1[1]) - if (integrator.opts.internalnorm(diff1[1], t) < - integrator.opts.internalnorm(diff2[1], t)) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - @.. broadcast=false diff1[1]=u_temp1 - u_temp2 - end - end - else - if alg.sequence == :romberg - # Compute solution by using maximum two threads for romberg sequence - # One thread will fill T matrix till second last element and another thread will - # fill last element of T matrix. - # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) - # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, - dt = dt, u_temp3 = u_temp3, - u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T - - @threaded alg.threading for i in 1:2 - startIndex = (i == 1) ? 0 : n_curr - endIndex = (i == 1) ? n_curr - 1 : n_curr - - for index in startIndex:endIndex - j_int_temp = 4 * subdividing_sequence[index + 1] - dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation - jacobian2W!(W[Threads.threadid()], integrator.f.mass_matrix, - dt_int_temp, J, false) - @.. broadcast=false u_temp4[Threads.threadid()]=uprev - @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * - fsalfirst - - linsolve = cache.linsolve[Threads.threadid()] - - if !repeat_step - linres = dolinsolve(integrator, linsolve; - A = W[Threads.threadid()], - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - end - cache.linsolve[Threads.threadid()] = linres.cache - - @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] - @.. broadcast=false u_temp3[Threads.threadid()]=u_temp4[Threads.threadid()] + - k_tmps[Threads.threadid()] # Euler starting step - @.. broadcast=false diff1[Threads.threadid()]=u_temp3[Threads.threadid()] - - u_temp4[Threads.threadid()] - for j in 2:(j_int_temp + 1) - f(k_tmps[Threads.threadid()], - cache.u_temp3[Threads.threadid()], - p, t + (j - 1) * dt_int_temp) - @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * - k_tmps[Threads.threadid()] - - (u_temp3[Threads.threadid()] - - u_temp4[Threads.threadid()]) - - linsolve = cache.linsolve[Threads.threadid()] - if !repeat_step && j == 1 - linres = dolinsolve(integrator, linsolve; - A = W[Threads.threadid()], - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - end - cache.linsolve[Threads.threadid()] = linres.cache - - @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] - @.. broadcast=false T[index + 1]=2 * - u_temp3[Threads.threadid()] - - u_temp4[Threads.threadid()] + - 2 * k_tmps[Threads.threadid()] # Explicit Midpoint rule - if (j == j_int_temp + 1) - @.. broadcast=false T[index + 1]=0.5(T[index + 1] + - u_temp4[Threads.threadid()]) - end - @.. broadcast=false u_temp4[Threads.threadid()]=u_temp3[Threads.threadid()] - @.. broadcast=false u_temp3[Threads.threadid()]=T[index + 1] - if (index <= 1) - # Deuflhard Stability check for initial two sequences - @.. broadcast=false diff2[Threads.threadid()]=u_temp3[Threads.threadid()] - - u_temp4[Threads.threadid()] - @.. broadcast=false diff2[Threads.threadid()]=0.5 * - (diff2[Threads.threadid()] - - diff1[Threads.threadid()]) - if (integrator.opts.internalnorm(diff1[Threads.threadid()], - t) < - integrator.opts.internalnorm(diff2[Threads.threadid()], - t)) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - @.. broadcast=false diff1[Threads.threadid()]=u_temp3[Threads.threadid()] - - u_temp4[Threads.threadid()] - end - end - integrator.force_stepfail ? break : continue - end - end - else - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, - dt = dt, u_temp3 = u_temp3, - u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T - - @threaded alg.threading for i in 0:(n_curr ÷ 2) - tid = Threads.threadid() - linsolvetmp = linsolve_tmps[tid] - ktmp = k_tmps[tid] - indices = i != n_curr - i ? (i, n_curr - i) : (-1, n_curr - i) #Use flag to avoid type union/branch - for index in indices - index == -1 && continue - j_int_temp = 4 * subdividing_sequence[index + 1] - dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation - jacobian2W!(W[tid], integrator.f.mass_matrix, dt_int_temp, J, false) - @.. broadcast=false u_temp4[tid]=uprev - @.. broadcast=false linsolvetmp=dt_int_temp * fsalfirst - - linsolve = cache.linsolve[tid] - if !repeat_step - linres = dolinsolve(integrator, linsolve; A = W[tid], - b = _vec(linsolvetmp), linu = _vec(ktmp)) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolvetmp), linu = _vec(ktmp)) - end - cache.linsolve[tid] = linres.cache - - @.. broadcast=false ktmp=-ktmp - @.. broadcast=false u_temp3[tid]=u_temp4[tid] + ktmp # Euler starting step - @.. broadcast=false diff1[tid]=u_temp3[tid] - u_temp4[tid] - for j in 2:(j_int_temp + 1) - f(ktmp, cache.u_temp3[tid], p, t + (j - 1) * dt_int_temp) - @.. broadcast=false linsolvetmp=dt_int_temp * ktmp - - (u_temp3[tid] - u_temp4[tid]) - - linsolve = cache.linsolve[tid] - - if (!repeat_step && j == 1) - linres = dolinsolve(integrator, linsolve; A = W[tid], - b = _vec(linsolvetmp), - linu = _vec(ktmp)) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolvetmp), - linu = _vec(ktmp)) - end - cache.linsolve[tid] = linres.cache - - @.. broadcast=false ktmp=-ktmp - @.. broadcast=false T[index + 1]=2 * u_temp3[tid] - - u_temp4[tid] + 2 * ktmp # Explicit Midpoint rule - if (j == j_int_temp + 1) - @.. broadcast=false T[index + 1]=0.5(T[index + 1] + - u_temp4[tid]) - end - @.. broadcast=false u_temp4[tid]=u_temp3[tid] - @.. broadcast=false u_temp3[tid]=T[index + 1] - if (index <= 1) - # Deuflhard Stability check for initial two sequences - @.. broadcast=false diff2[tid]=u_temp3[tid] - u_temp4[tid] - @.. broadcast=false diff2[tid]=0.5 * - (diff2[tid] - diff1[tid]) - if (integrator.opts.internalnorm(diff1[tid], t) < - integrator.opts.internalnorm(diff2[tid], t)) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - @.. broadcast=false diff1[tid]=u_temp3[tid] - u_temp4[tid] - end - end - integrator.force_stepfail ? break : continue - end - end - end - end - - if integrator.force_stepfail - return - end - - if integrator.opts.adaptive - # Compute all information relating to an extrapolation order ≦ win_min - for i in (win_min - 1):win_min - - #integrator.u .= extrapolation_scalars[i+1] * sum( broadcast(*, cache.T[1:(i+1)], extrapolation_weights[1:(i+1), (i+1)]) ) # Approximation of extrapolation order i - #cache.utilde .= extrapolation_scalars_2[i] * sum( broadcast(*, cache.T[2:(i+1)], extrapolation_weights_2[1:i, i]) ) # and its internal counterpart - - u_temp1 .= false - u_temp2 .= false - for j in 1:(i + 1) - @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (i + 1)] - end - for j in 2:(i + 1) - @.. broadcast=false u_temp2+=cache.T[j] * extrapolation_weights_2[j - 1, i] - end - @.. broadcast=false integrator.u=extrapolation_scalars[i + 1] * u_temp1 - @.. broadcast=false cache.utilde=extrapolation_scalars_2[i] * u_temp2 - - calculate_residuals!(cache.res, integrator.u, cache.utilde, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(cache.res, t) - cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! - stepsize_controller_internal!(integrator, alg) # Update cache.Q - end - - # Check if an approximation of some order in the order window can be accepted - # Make sure a stepsize scaling factor of order (alg.min_order + 1) is provided for the step_*_controller! - while n_curr <= win_max - EEst1 = one(integrator.EEst) - for i in (n_curr + 2):(win_max + 1) - EEst1 *= subdividing_sequence[i] / subdividing_sequence[1] - end - EEst1 *= EEst1 - if accept_step_controller(integrator, integrator.opts.controller) - # Accept current approximation u of order n_curr - break - elseif (n_curr < alg.min_order + 1) || integrator.EEst <= EEst1 - # Reject current approximation order but pass convergence monitor - # Compute approximation of order (n_curr + 1) - n_curr = n_curr + 1 - cache.n_curr = n_curr - - # Update cache.T - j_int = 4 * subdividing_sequence[n_curr + 1] - dt_int = dt / j_int # Stepsize of the new internal discretisation - jacobian2W!(W[1], integrator.f.mass_matrix, dt_int, J, false) - integrator.stats.nw += 1 - @.. broadcast=false u_temp2=uprev - @.. broadcast=false linsolve_tmps[1]=dt_int * fsalfirst - - linsolve = cache.linsolve[1] - - if !repeat_step - linres = dolinsolve(integrator, linsolve; A = W[1], - b = _vec(linsolve_tmps[1]), linu = _vec(k)) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[1]), linu = _vec(k)) - end - cache.linsolve[1] = linres.cache - - integrator.stats.nsolve += 1 - @.. broadcast=false k=-k - @.. broadcast=false u_temp1=u_temp2 + k # Euler starting step - for j in 2:(j_int + 1) - f(k, cache.u_temp1, p, t + (j - 1) * dt_int) - integrator.stats.nf += 1 - @.. broadcast=false linsolve_tmps[1]=dt_int * k - (u_temp1 - u_temp2) - - linsolve = cache.linsolve[1] - - if !repeat_step && j == 1 - linres = dolinsolve(integrator, linsolve; A = W[1], - b = _vec(linsolve_tmps[1]), linu = _vec(k)) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[1]), linu = _vec(k)) - end - cache.linsolve[1] = linres.cache - - integrator.stats.nsolve += 1 - @.. broadcast=false k=-k - @.. broadcast=false T[n_curr + 1]=2 * u_temp1 - u_temp2 + 2 * k # Explicit Midpoint rule - if (j == j_int + 1) - @.. broadcast=false T[n_curr + 1]=0.5(T[n_curr + 1] + u_temp2) - end - @.. broadcast=false u_temp2=u_temp1 - @.. broadcast=false u_temp1=T[n_curr + 1] - end - - # Update u, integrator.EEst and cache.Q - #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr - #cache.utilde .= extrapolation_scalars_2[n_curr] * sum( broadcast(*, cache.T[2:(n_curr+1)], extrapolation_weights_2[1:n_curr, n_curr]) ) # and its internal counterpart - - u_temp1 .= false - u_temp2 .= false - for j in 1:(n_curr + 1) - @.. broadcast=false u_temp1+=cache.T[j] * - extrapolation_weights[j, (n_curr + 1)] - end - for j in 2:(n_curr + 1) - @.. broadcast=false u_temp2+=cache.T[j] * - extrapolation_weights_2[j - 1, n_curr] - end - @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 - @.. broadcast=false cache.utilde=extrapolation_scalars_2[n_curr] * u_temp2 - - calculate_residuals!(cache.res, integrator.u, cache.utilde, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(cache.res, t) - stepsize_controller_internal!(integrator, alg) # Update cache.Q - else - # Reject the current approximation and not pass convergence monitor - break - end - end - else - - #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr - u_temp1 .= false - for j in 1:(n_curr + 1) - @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (n_curr + 1)] - end - @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 - end - - f(cache.k, integrator.u, p, t + dt) # Update FSAL - integrator.stats.nf += 1 -end - -function initialize!(integrator, cache::ImplicitEulerBarycentricExtrapolationConstantCache) - # cf. initialize! of MidpointConstantCache - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -function perform_step!(integrator, - cache::ImplicitEulerBarycentricExtrapolationConstantCache, - repeat_step = false) - # Unpack all information needed - @unpack t, uprev, dt, f, p = integrator - alg = unwrap_alg(integrator, true) - @unpack n_curr = cache - # Coefficients for obtaining u - @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients - # Coefficients for obtaining utilde - @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients - # Additional constant information - @unpack subdividing_sequence = cache.coefficients - @unpack sequence_factor = alg - - # Create auxiliary variables - u_temp1, u_temp2 = copy(uprev), copy(uprev) # Auxiliary variables for computing the internal discretisations - u, utilde = copy(uprev), copy(uprev) # Storage for the latest approximation and its internal counterpart - T = fill(zero(uprev), alg.max_order + 1) # Storage for the internal discretisations obtained by the explicit midpoint rule - fill!(cache.Q, zero(eltype(cache.Q))) - - if integrator.opts.adaptive - # Set up the order window - # alg.min_order + 1 ≦ n_curr ≦ alg.max_order - 1 is enforced by step_*_controller! - if !(alg.min_order + 1 <= n_curr <= alg.max_order - 1) - error("Something went wrong while setting up the order window: $n_curr ∉ [$(alg.min_order+1),$(alg.max_order-1)]. - Please report this error ") - end - win_min = n_curr - 1 - win_max = n_curr + 1 - - # Set up the current extrapolation order - cache.n_old = n_curr # Save the suggested order for step_*_controller! - n_curr = win_min # Start with smallest order in the order window - end - - #Compute the internal discretisations - J = calc_J(integrator, cache) # Store the calculated jac as it won't change in internal discretisation - if !isthreaded(alg.threading) - for i in 0:n_curr - j_int = sequence_factor * subdividing_sequence[i + 1] - dt_int = dt / j_int # Stepsize of the ith internal discretisation - W = dt_int * J - integrator.f.mass_matrix - integrator.stats.nw += 1 - u_temp2 = uprev - u_temp1 = u_temp2 + - _reshape(W \ -_vec(dt_int * integrator.fsalfirst), axes(uprev)) # Euler starting step - diff1 = u_temp1 - u_temp2 - for j in 2:(j_int + 1) - T[i + 1] = u_temp1 + - _reshape( - W \ -_vec(dt_int * f(u_temp1, p, t + (j - 1) * dt_int)), - axes(uprev)) - integrator.stats.nf += 1 - if (j == j_int + 1) - T[i + 1] = 0.25(T[i + 1] + 2 * u_temp1 + u_temp2) - end - u_temp2 = u_temp1 - u_temp1 = T[i + 1] - if (i <= 1) - # Deuflhard Stability check for initial two sequences - diff2 = u_temp1 - u_temp2 - if (integrator.opts.internalnorm(diff1, t) < - integrator.opts.internalnorm(0.5 * (diff2 - diff1), t)) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - diff1 = u_temp1 - u_temp2 - end - end - else - if alg.sequence == :romberg - # Compute solution by using maximum two threads for romberg sequence - # One thread will fill T matrix till second last element and another thread will - # fill last element of T matrix. - # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) - # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, - dt = dt, u_temp2 = u_temp2, - u_temp2 = u_temp2, p = p, t = t, T = T - - @threaded alg.threading for i in 1:2 - startIndex = (i == 1) ? 0 : n_curr - endIndex = (i == 1) ? n_curr - 1 : n_curr - - for index in startIndex:endIndex - j_int = sequence_factor * subdividing_sequence[index + 1] - dt_int = dt / j_int # Stepsize of the ith internal discretisation - W = dt_int * J - integrator.f.mass_matrix - integrator.stats.nw += 1 - u_temp4 = uprev - u_temp3 = u_temp4 + - _reshape(W \ -_vec(dt_int * integrator.fsalfirst), - axes(uprev)) # Euler starting step - diff1 = u_temp3 - u_temp4 - for j in 2:(j_int + 1) - T[index + 1] = u_temp3 + _reshape( - W \ - -_vec(dt_int * f(u_temp3, p, - t + (j - 1) * dt_int)), - axes(uprev)) - integrator.stats.nf += 1 - if (j == j_int + 1) - T[index + 1] = 0.25(T[index + 1] + 2 * u_temp3 + u_temp4) - end - u_temp4 = u_temp3 - u_temp3 = T[index + 1] - if (index <= 1) - # Deuflhard Stability check for initial two sequences - diff2 = u_temp3 - u_temp4 - if (integrator.opts.internalnorm(diff1, t) < - integrator.opts.internalnorm(0.5 * (diff2 - diff1), t)) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - diff1 = u_temp3 - u_temp4 - end - end - integrator.force_stepfail ? break : continue - end - end - else - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, - dt = dt, - integrator = integrator, p = p, t = t, T = T - - @threaded alg.threading for i in 0:(n_curr ÷ 2) - indices = i != n_curr - i ? (i, n_curr - i) : (-1, n_curr - i) - for index in indices - index == -1 && continue - j_int = sequence_factor * subdividing_sequence[index + 1] - dt_int = dt / j_int # Stepsize of the ith internal discretisation - W = dt_int * J - integrator.f.mass_matrix - integrator.stats.nw += 1 - u_temp4 = uprev - u_temp3 = u_temp4 + - _reshape(W \ -_vec(dt_int * integrator.fsalfirst), - axes(uprev)) # Euler starting step - diff1 = u_temp3 - u_temp4 - for j in 2:(j_int + 1) - T[index + 1] = u_temp3 + _reshape( - W \ - -_vec(dt_int * f(u_temp3, p, - t + (j - 1) * dt_int)), - axes(uprev)) - integrator.stats.nf += 1 - if (j == j_int + 1) - T[index + 1] = 0.25(T[index + 1] + 2 * u_temp3 + u_temp4) - end - u_temp4 = u_temp3 - u_temp3 = T[index + 1] - if (index <= 1) - # Deuflhard Stability check for initial two sequences - diff2 = u_temp3 - u_temp4 - if (integrator.opts.internalnorm(diff1, t) < - integrator.opts.internalnorm(0.5 * (diff2 - diff1), t)) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - diff1 = u_temp3 - u_temp4 - end - end - integrator.force_stepfail ? break : continue - end - end - end - end - - if integrator.force_stepfail - return - end - - if integrator.opts.adaptive - # Compute all information relating to an extrapolation order ≦ win_min - for i in (win_min - 1):win_min - u = eltype(uprev).(extrapolation_scalars[i + 1]) * - sum(broadcast(*, T[1:(i + 1)], - eltype(uprev).(extrapolation_weights[1:(i + 1), (i + 1)]))) # Approximation of extrapolation order i - utilde = eltype(uprev).(extrapolation_scalars_2[i]) * - sum(broadcast(*, T[2:(i + 1)], - eltype(uprev).(extrapolation_weights_2[1:i, i]))) # and its internal counterpart - res = calculate_residuals(u, utilde, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, - t) - integrator.EEst = integrator.opts.internalnorm(res, t) - cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! - stepsize_controller_internal!(integrator, alg) # Update cache.Q - end - - # Check if an approximation of some order in the order window can be accepted - # Make sure a stepsize scaling factor of order (alg.min_order + 1) is provided for the step_*_controller! - while n_curr <= win_max - if accept_step_controller(integrator, integrator.opts.controller) - # Accept current approximation u of order n_curr - break - elseif (n_curr < alg.min_order + 1) || - integrator.EEst <= - typeof(integrator.EEst)(prod(subdividing_sequence[(n_curr + 2):(win_max + 1)] .// - subdividing_sequence[1]^2)) - # Reject current approximation order but pass convergence monitor - # Always compute approximation of order (n_curr + 1) - n_curr = n_curr + 1 - cache.n_curr = n_curr - - # Update T - j_int = sequence_factor * subdividing_sequence[n_curr + 1] - dt_int = dt / j_int # Stepsize of the new internal discretisation - W = dt_int * J - integrator.f.mass_matrix - integrator.stats.nw += 1 - u_temp2 = uprev - u_temp1 = u_temp2 + - _reshape(W \ -_vec(dt_int * integrator.fsalfirst), axes(uprev)) # Euler starting step - for j in 2:(j_int + 1) - T[n_curr + 1] = u_temp1 + _reshape( - W \ - -_vec(dt_int * - f(u_temp1, p, t + (j - 1) * dt_int)), - axes(uprev)) - integrator.stats.nf += 1 - if (j == j_int + 1) - T[n_curr + 1] = 0.25(T[n_curr + 1] + 2 * u_temp1 + u_temp2) - end - u_temp2 = u_temp1 - u_temp1 = T[n_curr + 1] - end - - # Update u, integrator.EEst and cache.Q - u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * - sum(broadcast(*, T[1:(n_curr + 1)], - eltype(uprev).(extrapolation_weights[1:(n_curr + 1), - (n_curr + 1)]))) # Approximation of extrapolation order n_curr - utilde = eltype(uprev).(extrapolation_scalars_2[n_curr]) * - sum(broadcast(*, T[2:(n_curr + 1)], - eltype(uprev).(extrapolation_weights_2[1:n_curr, - n_curr]))) # and its internal counterpart - res = calculate_residuals(u, utilde, integrator.opts.abstol, - integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(res, t) - stepsize_controller_internal!(integrator, alg) # Update cache.Q - else - # Reject the current approximation and not pass convergence monitor - break - end - end - else - u = eltype(uprev).(extrapolation_scalars[n_curr + 1]) * - sum(broadcast(*, T[1:(n_curr + 1)], - eltype(uprev).(extrapolation_weights[1:(n_curr + 1), - (n_curr + 1)]))) # Approximation of extrapolation order n_curr - end - - # Save the latest approximation and update FSAL - integrator.u = u - integrator.fsallast = f(u, p, t + dt) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -function initialize!(integrator, cache::ImplicitEulerBarycentricExtrapolationCache) - # cf. initialize! of MidpointCache - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 2 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation -end - -function perform_step!(integrator, cache::ImplicitEulerBarycentricExtrapolationCache, - repeat_step = false) - # Unpack all information needed - @unpack t, uprev, dt, f, p = integrator - alg = unwrap_alg(integrator, true) - @unpack n_curr, u_temp1, u_temp2, utilde, res, T, fsalfirst, k, diff1, diff2 = cache - @unpack u_temp3, u_temp4, k_tmps = cache - # Coefficients for obtaining u - @unpack extrapolation_weights, extrapolation_scalars = cache.coefficients - # Coefficients for obtaining utilde - @unpack extrapolation_weights_2, extrapolation_scalars_2 = cache.coefficients - # Additional constant information - @unpack subdividing_sequence = cache.coefficients - @unpack sequence_factor = alg - - @unpack J, W, uf, tf, linsolve_tmps, jac_config = cache - - fill!(cache.Q, zero(eltype(cache.Q))) - - if integrator.opts.adaptive - # Set up the order window - # alg.min_order + 1 ≦ n_curr ≦ alg.max_order - 1 is enforced by step_*_controller! - if !(alg.min_order + 1 <= n_curr <= alg.max_order - 1) - error("Something went wrong while setting up the order window: $n_curr ∉ [$(alg.min_order+1),$(alg.max_order-1)]. - Please report this error ") - end - win_min = n_curr - 1 - win_max = n_curr + 1 - - # Set up the current extrapolation order - cache.n_old = n_curr # Save the suggested order for step_*_controller! - n_curr = win_min # Start with smallest order in the order window - end - - #Compute the internal discretisations - calc_J!(J, integrator, cache) # Store the calculated jac as it won't change in internal discretisation - if !isthreaded(alg.threading) - for i in 0:n_curr - j_int = sequence_factor * subdividing_sequence[i + 1] - dt_int = dt / j_int # Stepsize of the ith internal discretisation - jacobian2W!(W[1], integrator.f.mass_matrix, dt_int, J, false) - integrator.stats.nw += 1 - @.. broadcast=false u_temp2=uprev - @.. broadcast=false linsolve_tmps[1]=dt_int * fsalfirst - - linsolve = cache.linsolve[1] - - if !repeat_step - linres = dolinsolve(integrator, linsolve; A = W[1], - b = _vec(linsolve_tmps[1]), linu = _vec(k)) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[1]), linu = _vec(k)) - end - cache.linsolve[1] = linres.cache - - integrator.stats.nsolve += 1 - @.. broadcast=false k=-k - @.. broadcast=false u_temp1=u_temp2 + k # Euler starting step - @.. broadcast=false diff1[1]=u_temp1 - u_temp2 - for j in 2:(j_int + 1) - f(k, cache.u_temp1, p, t + (j - 1) * dt_int) - integrator.stats.nf += 1 - @.. broadcast=false linsolve_tmps[1]=dt_int * k - - linsolve = cache.linsolve[1] - if !repeat_step && j == 1 - linres = dolinsolve(integrator, linsolve; A = W[1], - b = _vec(linsolve_tmps[1]), linu = _vec(k)) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[1]), linu = _vec(k)) - end - cache.linsolve[1] = linres.cache - - integrator.stats.nsolve += 1 - @.. broadcast=false k=-k - @.. broadcast=false T[i + 1]=u_temp1 + k - if (j == j_int + 1) - @.. broadcast=false T[i + 1]=0.25(T[i + 1] + 2 * u_temp1 + u_temp2) - end - @.. broadcast=false u_temp2=u_temp1 - @.. broadcast=false u_temp1=T[i + 1] - if (i <= 1) - # Deuflhard Stability check for initial two sequences - @.. broadcast=false diff2[1]=u_temp1 - u_temp2 - @.. broadcast=false diff2[1]=0.5 * (diff2[1] - diff1[1]) - if (integrator.opts.internalnorm(diff1[1], t) < - integrator.opts.internalnorm(diff2[1], t)) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - @.. broadcast=false diff1[1]=u_temp1 - u_temp2 - end - end - else - if alg.sequence == :romberg - # Compute solution by using maximum two threads for romberg sequence - # One thread will fill T matrix till second last element and another thread will - # fill last element of T matrix. - # Romberg sequence --> 1, 2, 4, 8, ..., 2^(i) - # 1 + 2 + 4 + ... + 2^(i-1) = 2^(i) - 1 - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, - dt = dt, u_temp3 = u_temp3, - u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T - - @threaded alg.threading for i in 1:2 - startIndex = (i == 1) ? 0 : n_curr - endIndex = (i == 1) ? n_curr - 1 : n_curr - - for index in startIndex:endIndex - j_int_temp = sequence_factor * subdividing_sequence[index + 1] - dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation - jacobian2W!(W[Threads.threadid()], integrator.f.mass_matrix, - dt_int_temp, J, false) - @.. broadcast=false u_temp4[Threads.threadid()]=uprev - @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * - fsalfirst - - linsolve = cache.linsolve[Threads.threadid()] - - if !repeat_step - linres = dolinsolve(integrator, linsolve; - A = W[Threads.threadid()], - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - end - cache.linsolve[Threads.threadid()] = linres.cache - - @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] - @.. broadcast=false u_temp3[Threads.threadid()]=u_temp4[Threads.threadid()] + - k_tmps[Threads.threadid()] # Euler starting step - @.. broadcast=false diff1[Threads.threadid()]=u_temp3[Threads.threadid()] - - u_temp4[Threads.threadid()] - for j in 2:(j_int_temp + 1) - f(k_tmps[Threads.threadid()], - cache.u_temp3[Threads.threadid()], - p, t + (j - 1) * dt_int_temp) - @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * - k_tmps[Threads.threadid()] - - linsolve = cache.linsolve[Threads.threadid()] - - if !repeat_step && j == 1 - linres = dolinsolve(integrator, linsolve; - A = W[Threads.threadid()], - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - end - cache.linsolve[Threads.threadid()] = linres.cache - - @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] - @.. broadcast=false T[index + 1]=u_temp3[Threads.threadid()] + - k_tmps[Threads.threadid()] # Explicit Midpoint rule - if (j == j_int_temp + 1) - @.. broadcast=false T[index + 1]=0.25(T[index + 1] + - 2 * - u_temp3[Threads.threadid()] + - u_temp4[Threads.threadid()]) - end - @.. broadcast=false u_temp4[Threads.threadid()]=u_temp3[Threads.threadid()] - @.. broadcast=false u_temp3[Threads.threadid()]=T[index + 1] - if (index <= 1) - # Deuflhard Stability check for initial two sequences - @.. broadcast=false diff2[Threads.threadid()]=u_temp3[Threads.threadid()] - - u_temp4[Threads.threadid()] - @.. broadcast=false diff2[Threads.threadid()]=0.5 * - (diff2[Threads.threadid()] - - diff1[Threads.threadid()]) - if (integrator.opts.internalnorm(diff1[Threads.threadid()], - t) < - integrator.opts.internalnorm(diff2[Threads.threadid()], - t)) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - @.. broadcast=false diff1[Threads.threadid()]=u_temp3[Threads.threadid()] - - u_temp4[Threads.threadid()] - end - end - integrator.force_stepfail ? break : continue - end - end - else - let n_curr = n_curr, subdividing_sequence = subdividing_sequence, uprev = uprev, - dt = dt, u_temp3 = u_temp3, - u_temp4 = u_temp4, k_tmps = k_tmps, p = p, t = t, T = T - - @threaded alg.threading for i in 0:(n_curr ÷ 2) - indices = i != n_curr - i ? (i, n_curr - i) : (-1, n_curr - i) - for index in indices - index == -1 && continue - j_int_temp = sequence_factor * subdividing_sequence[index + 1] - dt_int_temp = dt / j_int_temp # Stepsize of the ith internal discretisation - jacobian2W!(W[Threads.threadid()], integrator.f.mass_matrix, - dt_int_temp, J, false) - @.. broadcast=false u_temp4[Threads.threadid()]=uprev - @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * - fsalfirst - - linsolve = cache.linsolve[Threads.threadid()] - - if !repeat_step - linres = dolinsolve(integrator, linsolve; - A = W[Threads.threadid()], - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - end - cache.linsolve[Threads.threadid()] = linres.cache - - @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] - @.. broadcast=false u_temp3[Threads.threadid()]=u_temp4[Threads.threadid()] + - k_tmps[Threads.threadid()] # Euler starting step - @.. broadcast=false diff1[Threads.threadid()]=u_temp3[Threads.threadid()] - - u_temp4[Threads.threadid()] - for j in 2:(j_int_temp + 1) - f(k_tmps[Threads.threadid()], - cache.u_temp3[Threads.threadid()], - p, t + (j - 1) * dt_int_temp) - @.. broadcast=false linsolve_tmps[Threads.threadid()]=dt_int_temp * - k_tmps[Threads.threadid()] - - linsolve = cache.linsolve[Threads.threadid()] - - if (!repeat_step && j == 1) - linres = dolinsolve(integrator, linsolve; - A = W[Threads.threadid()], - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[Threads.threadid()]), - linu = _vec(k_tmps[Threads.threadid()])) - end - cache.linsolve[Threads.threadid()] = linres.cache - - @.. broadcast=false k_tmps[Threads.threadid()]=-k_tmps[Threads.threadid()] - @.. broadcast=false T[index + 1]=u_temp3[Threads.threadid()] + - k_tmps[Threads.threadid()] # Explicit Midpoint rule - if (j == j_int_temp + 1) - @.. broadcast=false T[index + 1]=0.25(T[index + 1] + - 2 * - u_temp3[Threads.threadid()] + - u_temp4[Threads.threadid()]) - end - @.. broadcast=false u_temp4[Threads.threadid()]=u_temp3[Threads.threadid()] - @.. broadcast=false u_temp3[Threads.threadid()]=T[index + 1] - if (index <= 1) - # Deuflhard Stability check for initial two sequences - @.. broadcast=false diff2[Threads.threadid()]=u_temp3[Threads.threadid()] - - u_temp4[Threads.threadid()] - @.. broadcast=false diff2[Threads.threadid()]=0.5 * - (diff2[Threads.threadid()] - - diff1[Threads.threadid()]) - if (integrator.opts.internalnorm(diff1[Threads.threadid()], - t) < - integrator.opts.internalnorm(diff2[Threads.threadid()], - t)) - # Divergence of iteration, overflow is possible. Force fail and start with smaller step - integrator.force_stepfail = true - return - end - end - @.. broadcast=false diff1[Threads.threadid()]=u_temp3[Threads.threadid()] - - u_temp4[Threads.threadid()] - end - end - integrator.force_stepfail ? break : continue - end - end - end - end - - if integrator.force_stepfail - return - end - - if integrator.opts.adaptive - # Compute all information relating to an extrapolation order ≦ win_min - for i in (win_min - 1):win_min - - #integrator.u .= extrapolation_scalars[i+1] * sum( broadcast(*, cache.T[1:(i+1)], extrapolation_weights[1:(i+1), (i+1)]) ) # Approximation of extrapolation order i - #cache.utilde .= extrapolation_scalars_2[i] * sum( broadcast(*, cache.T[2:(i+1)], extrapolation_weights_2[1:i, i]) ) # and its internal counterpart - - u_temp1 .= false - u_temp2 .= false - for j in 1:(i + 1) - @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (i + 1)] - end - for j in 2:(i + 1) - @.. broadcast=false u_temp2+=cache.T[j] * extrapolation_weights_2[j - 1, i] - end - @.. broadcast=false integrator.u=extrapolation_scalars[i + 1] * u_temp1 - @.. broadcast=false cache.utilde=extrapolation_scalars_2[i] * u_temp2 - - calculate_residuals!(cache.res, integrator.u, cache.utilde, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(cache.res, t) - cache.n_curr = i # Update cache's n_curr for stepsize_controller_internal! - stepsize_controller_internal!(integrator, alg) # Update cache.Q - end - - # Check if an approximation of some order in the order window can be accepted - # Make sure a stepsize scaling factor of order (alg.min_order + 1) is provided for the step_*_controller! - while n_curr <= win_max - EEst1 = one(integrator.EEst) - for i in (n_curr + 2):(win_max + 1) - EEst1 *= subdividing_sequence[i] / subdividing_sequence[1] - end - EEst1 *= EEst1 - - #@show integrator.opts.internalnorm(integrator.u - cache.utilde,t) - if accept_step_controller(integrator, integrator.opts.controller) - # Accept current approximation u of order n_curr - break - elseif (n_curr < alg.min_order + 1) || integrator.EEst <= EEst1 - # Reject current approximation order but pass convergence monitor - # Compute approximation of order (n_curr + 1) - n_curr = n_curr + 1 - cache.n_curr = n_curr - - # Update cache.T - j_int = sequence_factor * subdividing_sequence[n_curr + 1] - dt_int = dt / j_int # Stepsize of the new internal discretisation - jacobian2W!(W[1], integrator.f.mass_matrix, dt_int, J, false) - integrator.stats.nw += 1 - @.. broadcast=false u_temp2=uprev - @.. broadcast=false linsolve_tmps[1]=dt_int * fsalfirst - - linsolve = cache.linsolve[1] - - if !repeat_step - linres = dolinsolve(integrator, linsolve; A = W[1], - b = _vec(linsolve_tmps[1]), linu = _vec(k)) - else - linres = dolinsolve(integrator, linsolve; A = nothing, - b = _vec(linsolve_tmps[1]), linu = _vec(k)) - end - cache.linsolve[1] = linres.cache - - integrator.stats.nsolve += 1 - @.. broadcast=false k=-k - @.. broadcast=false u_temp1=u_temp2 + k # Euler starting step - for j in 2:(j_int + 1) - f(k, cache.u_temp1, p, t + (j - 1) * dt_int) - integrator.stats.nf += 1 - @.. broadcast=false linsolve_tmps[1]=dt_int * k - - linsolve = cache.linsolve[1] - linres = dolinsolve(integrator, linsolve; b = _vec(linsolve_tmps[1]), - linu = _vec(k)) - cache.linsolve[1] = linres.cache - - integrator.stats.nsolve += 1 - @.. broadcast=false k=-k - @.. broadcast=false T[n_curr + 1]=u_temp1 + k # Explicit Midpoint rule - if (j == j_int + 1) - @.. broadcast=false T[n_curr + 1]=0.25(T[n_curr + 1] + 2 * u_temp1 + - u_temp2) - end - @.. broadcast=false u_temp2=u_temp1 - @.. broadcast=false u_temp1=T[n_curr + 1] - end - - # Update u, integrator.EEst and cache.Q - #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr - #cache.utilde .= extrapolation_scalars_2[n_curr] * sum( broadcast(*, cache.T[2:(n_curr+1)], extrapolation_weights_2[1:n_curr, n_curr]) ) # and its internal counterpart - - u_temp1 .= false - u_temp2 .= false - for j in 1:(n_curr + 1) - @.. broadcast=false u_temp1+=cache.T[j] * - extrapolation_weights[j, (n_curr + 1)] - end - for j in 2:(n_curr + 1) - @.. broadcast=false u_temp2+=cache.T[j] * - extrapolation_weights_2[j - 1, n_curr] - end - @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 - @.. broadcast=false cache.utilde=extrapolation_scalars_2[n_curr] * u_temp2 - - calculate_residuals!(cache.res, integrator.u, cache.utilde, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(cache.res, t) - stepsize_controller_internal!(integrator, alg) # Update cache.Q - else - # Reject the current approximation and not pass convergence monitor - break - end - end - else - - #integrator.u .= extrapolation_scalars[n_curr+1] * sum( broadcast(*, cache.T[1:(n_curr+1)], extrapolation_weights[1:(n_curr+1), (n_curr+1)]) ) # Approximation of extrapolation order n_curr - u_temp1 .= false - for j in 1:(n_curr + 1) - @.. broadcast=false u_temp1+=cache.T[j] * extrapolation_weights[j, (n_curr + 1)] - end - @.. broadcast=false integrator.u=extrapolation_scalars[n_curr + 1] * u_temp1 - end - - f(cache.k, integrator.u, p, t + dt) # Update FSAL - integrator.stats.nf += 1 -end From 2eb16b6c3c9aa4114ca55acef6a8f343847ee356 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:57:12 -0400 Subject: [PATCH 13/71] Delete src/perform_step/feagin_rk_perform_step.jl --- src/perform_step/feagin_rk_perform_step.jl | 1288 -------------------- 1 file changed, 1288 deletions(-) delete mode 100644 src/perform_step/feagin_rk_perform_step.jl diff --git a/src/perform_step/feagin_rk_perform_step.jl b/src/perform_step/feagin_rk_perform_step.jl deleted file mode 100644 index a0ded6fa0b..0000000000 --- a/src/perform_step/feagin_rk_perform_step.jl +++ /dev/null @@ -1,1288 +0,0 @@ -function initialize!(integrator, cache::Feagin10ConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -@muladd function perform_step!(integrator, cache::Feagin10ConstantCache, - repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1203, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211, a1300, a1302, a1303, a1305, a1306, a1307, a1308, a1309, a1310, a1311, a1312, a1400, a1401, a1404, a1406, a1412, a1413, a1500, a1502, a1514, a1600, a1601, a1602, a1604, a1605, a1606, a1607, a1608, a1609, a1610, a1611, a1612, a1613, a1614, a1615, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16 = cache - k1 = integrator.fsalfirst - a = dt * a0100 - k2 = f(uprev + a * k1, p, t + c1 * dt) - k3 = f(uprev + dt * (a0200 * k1 + a0201 * k2), p, t + c2 * dt) - k4 = f(uprev + dt * (a0300 * k1 + a0302 * k3), p, t + c3 * dt) - k5 = f(uprev + dt * (a0400 * k1 + a0402 * k3 + a0403 * k4), p, t + c4 * dt) - k6 = f(uprev + dt * (a0500 * k1 + a0503 * k4 + a0504 * k5), p, t + c5 * dt) - k7 = f(uprev + dt * (a0600 * k1 + a0603 * k4 + a0604 * k5 + a0605 * k6), p, t + c6 * dt) - k8 = f(uprev + dt * (a0700 * k1 + a0704 * k5 + a0705 * k6 + a0706 * k7), p, t + c7 * dt) - k9 = f(uprev + dt * (a0800 * k1 + a0805 * k6 + a0806 * k7 + a0807 * k8), p, t + c8 * dt) - k10 = f(uprev + dt * (a0900 * k1 + a0905 * k6 + a0906 * k7 + a0907 * k8 + a0908 * k9), - p, t + c9 * dt) - k11 = f( - uprev + - dt * - (a1000 * k1 + a1005 * k6 + a1006 * k7 + a1007 * k8 + a1008 * k9 + a1009 * k10), - p, t + c10 * dt) - k12 = f( - uprev + - dt * - (a1100 * k1 + a1105 * k6 + a1106 * k7 + a1107 * k8 + a1108 * k9 + a1109 * k10 + - a1110 * k11), - p, - t + c11 * dt) - k13 = f( - uprev + - dt * - (a1200 * k1 + a1203 * k4 + a1204 * k5 + a1205 * k6 + a1206 * k7 + a1207 * k8 + - a1208 * k9 + a1209 * k10 + a1210 * k11 + a1211 * k12), - p, - t + c12 * dt) - k14 = f( - uprev + - dt * - (a1300 * k1 + a1302 * k3 + a1303 * k4 + a1305 * k6 + a1306 * k7 + a1307 * k8 + - a1308 * k9 + a1309 * k10 + a1310 * k11 + a1311 * k12 + a1312 * k13), - p, - t + c13 * dt) - k15 = f( - uprev + - dt * - (a1400 * k1 + a1401 * k2 + a1404 * k5 + a1406 * k7 + a1412 * k13 + a1413 * k14), - p, t + c14 * dt) - k16 = f(uprev + dt * (a1500 * k1 + a1502 * k3 + a1514 * k15), p, t + c15 * dt) - k17 = f( - uprev + - dt * - (a1600 * k1 + a1601 * k2 + a1602 * k3 + a1604 * k5 + a1605 * k6 + a1606 * k7 + - a1607 * k8 + a1608 * k9 + a1609 * k10 + a1610 * k11 + a1611 * k12 + - a1612 * k13 + a1613 * k14 + a1614 * k15 + a1615 * k16), - p, - t + c16 * dt) - integrator.stats.nf += 16 - u = uprev + - dt * - (b1 * k1 + b2 * k2 + b3 * k3 + b5 * k5 + b7 * k7 + b9 * k9 + b10 * k10 + b11 * k11 + - b12 * k12 + b13 * k13 + b14 * k14 + b15 * k15 + b16 * k16 + b17 * k17) - if integrator.opts.adaptive - utilde = @.. broadcast=false dt*(k2-k16)*adaptiveConst - atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - k = f(u, p, t + dt) # For the interpolation, needs k at the updated point - integrator.stats.nf += 1 - integrator.fsallast = k - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.u = u -end - -function initialize!(integrator, cache::Feagin10Cache) - integrator.fsalfirst = cache.fsalfirst - integrator.fsallast = cache.k - integrator.kshortsize = 2 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 -end - -#= -@muladd function perform_step!(integrator, cache::Feagin10Cache, repeat_step=false) - @unpack t,dt,uprev,u,f,p = integrator - @unpack adaptiveConst,a0100,a0200,a0201,a0300,a0302,a0400,a0402,a0403,a0500,a0503,a0504,a0600,a0603,a0604,a0605,a0700,a0704,a0705,a0706,a0800,a0805,a0806,a0807,a0900,a0905,a0906,a0907,a0908,a1000,a1005,a1006,a1007,a1008,a1009,a1100,a1105,a1106,a1107,a1108,a1109,a1110,a1200,a1203,a1204,a1205,a1206,a1207,a1208,a1209,a1210,a1211,a1300,a1302,a1303,a1305,a1306,a1307,a1308,a1309,a1310,a1311,a1312,a1400,a1401,a1404,a1406,a1412,a1413,a1500,a1502,a1514,a1600,a1601,a1602,a1604,a1605,a1606,a1607,a1608,a1609,a1610,a1611,a1612,a1613,a1614,a1615,b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,c11,c12,c13,c14,c15,c16 = cache.tab - @unpack k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12,k13,k14,k15,k16,k17,tmp,atmp,uprev,k = cache - k1 = cache.fsalfirst - a = dt*a0100 - @.. broadcast=false tmp = uprev + a*k1 - f(k2, tmp, p, t + c1*dt) - @.. broadcast=false tmp = uprev + dt*(a0200*k1 + a0201*k2) - f(k3, tmp, p, t + c2*dt ) - @.. broadcast=false tmp = uprev + dt*(a0300*k1 + a0302*k3) - f(k4, tmp, p, t + c3*dt) - @.. broadcast=false tmp = uprev + dt*(a0400*k1 + a0402*k3 + a0403*k4) - f(k5, tmp, p, t + c4*dt) - @.. broadcast=false tmp = uprev + dt*(a0500*k1 + a0503*k4 + a0504*k5) - f(k6, tmp, p, t + c5*dt) - @.. broadcast=false tmp = uprev + dt*(a0600*k1 + a0603*k4 + a0604*k5 + a0605*k6) - f(k7, tmp, p, t + c6*dt) - @.. broadcast=false tmp = uprev + dt*(a0700*k1 + a0704*k5 + a0705*k6 + a0706*k7) - f(k8, tmp, p, t + c7*dt) - @.. broadcast=false tmp = uprev + dt*(a0800*k1 + a0805*k6 + a0806*k7 + a0807*k8) - f(k9, tmp, p, t + c8*dt) - @.. broadcast=false tmp = uprev + dt*(a0900*k1 + a0905*k6 + a0906*k7 + a0907*k8 + a0908*k9) - f(k10, tmp, p, t + c9*dt) - @.. broadcast=false tmp = uprev + dt*(a1000*k1 + a1005*k6 + a1006*k7 + a1007*k8 + a1008*k9 + a1009*k10) - f(k11, tmp, p, t + c10*dt) - @.. broadcast=false tmp = uprev + dt*(a1100*k1 + a1105*k6 + a1106*k7 + a1107*k8 + a1108*k9 + a1109*k10 + a1110*k11) - f(k12, tmp, p, t + c11*dt) - @.. broadcast=false tmp = uprev + dt*(a1200*k1 + a1203*k4 + a1204*k5 + a1205*k6 + a1206*k7 + a1207*k8 + a1208*k9 + a1209*k10 + a1210*k11 + a1211*k12) - f(k13, tmp, p, t + c12*dt) - @.. broadcast=false tmp = uprev + dt*(a1300*k1 + a1302*k3 + a1303*k4 + a1305*k6 + a1306*k7 + a1307*k8 + a1308*k9 + a1309*k10 + a1310*k11 + a1311*k12 + a1312*k13) - f(k14, tmp, p, t + c13*dt) - @.. broadcast=false tmp = uprev + dt*(a1400*k1 + a1401*k2 + a1404*k5 + a1406*k7 + a1412*k13 + a1413*k14) - f(k15, tmp, p, t + c14*dt) - @.. broadcast=false tmp = uprev + dt*(a1500*k1 + a1502*k3 + a1514*k15) - f(k16, tmp, p, t + c15*dt) - @.. broadcast=false tmp = uprev + dt*(a1600*k1 + a1601*k2 + a1602*k3 + a1604*k5 + a1605*k6 + a1606*k7 + a1607*k8 + a1608*k9 + a1609*k10 + a1610*k11 + a1611*k12 + a1612*k13 + a1613*k14 + a1614*k15 + a1615*k16) - f(k17, tmp, p, t + c16*dt) - @.. broadcast=false u = uprev + dt*(b1*k1 + b2*k2 + b3*k3 + b5*k5 + b7*k7 + b9*k9 + b10*k10 + b11*k11 + b12*k12 + b13*k13 + b14*k14 + b15*k15 + b16*k16 + b17*k17) - if integrator.opts.adaptive - @.. broadcast=false tmp = dt*(k2 - k16) * adaptiveConst - calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, integrator.opts.reltol,integrator.opts.internalnorm,t) - integrator.EEst = integrator.opts.internalnorm(atmp,t) - end - f(integrator.fsallast,u,p,t+dt) # For the interpolation, needs k at the updated point -end -=# - -@muladd function perform_step!(integrator, cache::Feagin10Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - uidx = eachindex(integrator.uprev) - @unpack adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1203, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211, a1300, a1302, a1303, a1305, a1306, a1307, a1308, a1309, a1310, a1311, a1312, a1400, a1401, a1404, a1406, a1412, a1413, a1500, a1502, a1514, a1600, a1601, a1602, a1604, a1605, a1606, a1607, a1608, a1609, a1610, a1611, a1612, a1613, a1614, a1615, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16 = cache.tab - @unpack k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, k17, tmp, atmp, uprev, k = cache - k1 = cache.fsalfirst - a = dt * a0100 - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + a * k1[i] - end - f(k2, tmp, p, t + c1 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + dt * (a0200 * k1[i] + a0201 * k2[i]) - end - f(k3, tmp, p, t + c2 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + dt * (a0300 * k1[i] + a0302 * k3[i]) - end - f(k4, tmp, p, t + c3 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + dt * (a0400 * k1[i] + a0402 * k3[i] + a0403 * k4[i]) - end - f(k5, tmp, p, t + c4 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + dt * (a0500 * k1[i] + a0503 * k4[i] + a0504 * k5[i]) - end - f(k6, tmp, p, t + c5 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a0600 * k1[i] + a0603 * k4[i] + a0604 * k5[i] + a0605 * k6[i]) - end - f(k7, tmp, p, t + c6 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a0700 * k1[i] + a0704 * k5[i] + a0705 * k6[i] + a0706 * k7[i]) - end - f(k8, tmp, p, t + c7 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a0800 * k1[i] + a0805 * k6[i] + a0806 * k7[i] + a0807 * k8[i]) - end - f(k9, tmp, p, t + c8 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a0900 * k1[i] + a0905 * k6[i] + a0906 * k7[i] + a0907 * k8[i] + - a0908 * k9[i]) - end - f(k10, tmp, p, t + c9 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a1000 * k1[i] + a1005 * k6[i] + a1006 * k7[i] + a1007 * k8[i] + - a1008 * k9[i] + a1009 * k10[i]) - end - f(k11, tmp, p, t + c10 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a1100 * k1[i] + a1105 * k6[i] + a1106 * k7[i] + a1107 * k8[i] + - a1108 * k9[i] + a1109 * k10[i] + a1110 * k11[i]) - end - f(k12, tmp, p, t + c11 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a1200 * k1[i] + a1203 * k4[i] + a1204 * k5[i] + a1205 * k6[i] + - a1206 * k7[i] + a1207 * k8[i] + a1208 * k9[i] + a1209 * k10[i] + - a1210 * k11[i] + a1211 * k12[i]) - end - f(k13, tmp, p, t + c12 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a1300 * k1[i] + a1302 * k3[i] + a1303 * k4[i] + a1305 * k6[i] + - a1306 * k7[i] + a1307 * k8[i] + a1308 * k9[i] + a1309 * k10[i] + - a1310 * k11[i] + a1311 * k12[i] + a1312 * k13[i]) - end - f(k14, tmp, p, t + c13 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a1400 * k1[i] + a1401 * k2[i] + a1404 * k5[i] + a1406 * k7[i] + - a1412 * k13[i] + a1413 * k14[i]) - end - f(k15, tmp, p, t + c14 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + dt * (a1500 * k1[i] + a1502 * k3[i] + a1514 * k15[i]) - end - f(k16, tmp, p, t + c15 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a1600 * k1[i] + a1601 * k2[i] + a1602 * k3[i] + a1604 * k5[i] + - a1605 * k6[i] + a1606 * k7[i] + a1607 * k8[i] + a1608 * k9[i] + - a1609 * k10[i] + a1610 * k11[i] + a1611 * k12[i] + - a1612 * k13[i] + a1613 * k14[i] + a1614 * k15[i] + - a1615 * k16[i]) - end - f(k17, tmp, p, t + c16 * dt) - @tight_loop_macros for i in uidx - @inbounds u[i] = uprev[i] + - dt * - (b1 * k1[i] + b2 * k2[i] + b3 * k3[i] + b5 * k5[i] + b7 * k7[i] + - b9 * k9[i] + b10 * k10[i] + b11 * k11[i] + b12 * k12[i] + - b13 * k13[i] + b14 * k14[i] + b15 * k15[i] + b16 * k16[i] + - b17 * k17[i]) - end - integrator.stats.nf += 16 - if integrator.opts.adaptive - @tight_loop_macros for i in uidx - @inbounds tmp[i] = dt * (k2[i] - k16[i]) * adaptiveConst - end - calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - f(integrator.fsallast, u, p, t + dt) # For the interpolation, needs k at the updated point - integrator.stats.nf += 1 -end - -function initialize!(integrator, cache::Feagin12ConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -@muladd function perform_step!(integrator, cache::Feagin12ConstantCache, - repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1208, a1209, a1210, a1211, a1300, a1308, a1309, a1310, a1311, a1312, a1400, a1408, a1409, a1410, a1411, a1412, a1413, a1500, a1508, a1509, a1510, a1511, a1512, a1513, a1514, a1600, a1608, a1609, a1610, a1611, a1612, a1613, a1614, a1615, a1700, a1705, a1706, a1707, a1708, a1709, a1710, a1711, a1712, a1713, a1714, a1715, a1716, a1800, a1805, a1806, a1807, a1808, a1809, a1810, a1811, a1812, a1813, a1814, a1815, a1816, a1817, a1900, a1904, a1905, a1906, a1908, a1909, a1910, a1911, a1912, a1913, a1914, a1915, a1916, a1917, a1918, a2000, a2003, a2004, a2005, a2007, a2009, a2010, a2017, a2018, a2019, a2100, a2102, a2103, a2106, a2107, a2109, a2110, a2117, a2118, a2119, a2120, a2200, a2201, a2204, a2206, a2220, a2221, a2300, a2302, a2322, a2400, a2401, a2402, a2404, a2406, a2407, a2408, a2409, a2410, a2411, a2412, a2413, a2414, a2415, a2416, a2417, a2418, a2419, a2420, a2421, a2422, a2423, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, b19, b20, b21, b22, b23, b24, b25 = cache - k1 = integrator.fsalfirst - a = dt * a0100 - k2 = f(uprev + a * k1, p, t + c1 * dt) - k3 = f(uprev + dt * (a0200 * k1 + a0201 * k2), p, t + c2 * dt) - k4 = f(uprev + dt * (a0300 * k1 + a0302 * k3), p, t + c3 * dt) - k5 = f(uprev + dt * (a0400 * k1 + a0402 * k3 + a0403 * k4), p, t + c4 * dt) - k6 = f(uprev + dt * (a0500 * k1 + a0503 * k4 + a0504 * k5), p, t + c5 * dt) - k7 = f(uprev + dt * (a0600 * k1 + a0603 * k4 + a0604 * k5 + a0605 * k6), p, t + c6 * dt) - k8 = f(uprev + dt * (a0700 * k1 + a0704 * k5 + a0705 * k6 + a0706 * k7), p, t + c7 * dt) - k9 = f(uprev + dt * (a0800 * k1 + a0805 * k6 + a0806 * k7 + a0807 * k8), p, t + c8 * dt) - k10 = f(uprev + dt * (a0900 * k1 + a0905 * k6 + a0906 * k7 + a0907 * k8 + a0908 * k9), - p, t + c9 * dt) - k11 = f( - uprev + - dt * - (a1000 * k1 + a1005 * k6 + a1006 * k7 + a1007 * k8 + a1008 * k9 + a1009 * k10), - p, t + c10 * dt) - k12 = f( - uprev + - dt * - (a1100 * k1 + a1105 * k6 + a1106 * k7 + a1107 * k8 + a1108 * k9 + a1109 * k10 + - a1110 * k11), - p, - t + c11 * dt) - k13 = f( - uprev + - dt * (a1200 * k1 + a1208 * k9 + a1209 * k10 + a1210 * k11 + a1211 * k12), p, - t + c12 * dt) - k14 = f( - uprev + - dt * (a1300 * k1 + a1308 * k9 + a1309 * k10 + a1310 * k11 + a1311 * k12 + - a1312 * k13), - p, - t + c13 * dt) - k15 = f( - uprev + - dt * (a1400 * k1 + a1408 * k9 + a1409 * k10 + a1410 * k11 + a1411 * k12 + - a1412 * k13 + a1413 * k14), - p, - t + c14 * dt) - k16 = f( - uprev + - dt * (a1500 * k1 + a1508 * k9 + a1509 * k10 + a1510 * k11 + a1511 * k12 + - a1512 * k13 + a1513 * k14 + a1514 * k15), - p, - t + c15 * dt) - k17 = f( - uprev + - dt * ((a1600 * k1 + a1608 * k9 + a1609 * k10) + - (a1610 * k11 + a1611 * k12 + a1612 * k13 + a1613 * k14) + - (a1614 * k15 + a1615 * k16)), - p, - t + c16 * dt) - k18 = f( - uprev + - dt * ((a1700 * k1 + a1705 * k6 + a1706 * k7) + - (a1707 * k8 + a1708 * k9 + a1709 * k10 + a1710 * k11) + - (a1711 * k12 + a1712 * k13 + a1713 * k14 + a1714 * k15) + - (a1715 * k16 + a1716 * k17)), - p, - t + c17 * dt) - k19 = f( - uprev + - dt * ((a1800 * k1 + a1805 * k6 + a1806 * k7) + - (a1807 * k8 + a1808 * k9 + a1809 * k10 + a1810 * k11) + - (a1811 * k12 + a1812 * k13 + a1813 * k14 + a1814 * k15) + - (a1815 * k16 + a1816 * k17 + a1817 * k18)), - p, - t + c18 * dt) - k20 = f( - uprev + - dt * ((a1900 * k1 + a1904 * k5 + a1905 * k6) + - (a1906 * k7 + a1908 * k9 + a1909 * k10 + a1910 * k11) + - (a1911 * k12 + a1912 * k13 + a1913 * k14 + a1914 * k15) + - (a1915 * k16 + a1916 * k17 + a1917 * k18 + a1918 * k19)), - p, - t + c19 * dt) - k21 = f( - uprev + - dt * ((a2000 * k1 + a2003 * k4 + a2004 * k5) + - (a2005 * k6 + a2007 * k8 + a2009 * k10 + a2010 * k11) + - (a2017 * k18 + a2018 * k19 + a2019 * k20)), - p, - t + c20 * dt) - k22 = f( - uprev + - dt * ((a2100 * k1 + a2102 * k3 + a2103 * k4) + - (a2106 * k7 + a2107 * k8 + a2109 * k10 + a2110 * k11) + - (a2117 * k18 + a2118 * k19 + a2119 * k20 + a2120 * k21)), - p, - t + c21 * dt) - k23 = f( - uprev + - dt * ((a2200 * k1 + a2201 * k2 + a2204 * k5) + - (a2206 * k7 + a2220 * k21 + a2221 * k22)), - p, - t + c22 * dt) - k24 = f(uprev + dt * (a2300 * k1 + a2302 * k3 + a2322 * k23), p, t + c23 * dt) - k25 = f( - uprev + - dt * ((a2400 * k1 + a2401 * k2 + a2402 * k3) + - (a2404 * k5 + a2406 * k7 + a2407 * k8 + a2408 * k9) + - (a2409 * k10 + a2410 * k11 + a2411 * k12 + a2412 * k13) + - (a2413 * k14 + a2414 * k15 + a2415 * k16 + a2416 * k17) + - (a2417 * k18 + a2418 * k19 + a2419 * k20 + a2420 * k21) + - (a2421 * k22 + a2422 * k23 + a2423 * k24)), - p, - t + c24 * dt) - integrator.stats.nf += 24 - u = uprev + - dt * ((b1 * k1 + b2 * k2 + b3 * k3 + b5 * k5) + - (b7 * k7 + b8 * k8 + b10 * k10 + b11 * k11) + - (b13 * k13 + b14 * k14 + b15 * k15 + b16 * k16) + - (b17 * k17 + b18 * k18 + b19 * k19 + b20 * k20) + - (b21 * k21 + b22 * k22 + b23 * k23) + (b24 * k24 + b25 * k25)) - k = f(u, p, t + dt) - integrator.stats.nf += 1 - integrator.fsallast = k - if integrator.opts.adaptive - utilde = @.. broadcast=false dt*(k2-k24)*adaptiveConst - atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.u = u -end - -function initialize!(integrator, cache::Feagin12Cache) - integrator.fsalfirst = cache.fsalfirst - integrator.fsallast = cache.k - integrator.kshortsize = 2 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 -end - -#= -@muladd function perform_step!(integrator, cache::Feagin12Cache, repeat_step=false) - @unpack t,dt,uprev,u,f,p = integrator - @unpack adaptiveConst,a0100,a0200,a0201,a0300,a0302,a0400,a0402,a0403,a0500,a0503,a0504,a0600,a0603,a0604,a0605,a0700,a0704,a0705,a0706,a0800,a0805,a0806,a0807,a0900,a0905,a0906,a0907,a0908,a1000,a1005,a1006,a1007,a1008,a1009,a1100,a1105,a1106,a1107,a1108,a1109,a1110,a1200,a1208,a1209,a1210,a1211,a1300,a1308,a1309,a1310,a1311,a1312,a1400,a1408,a1409,a1410,a1411,a1412,a1413,a1500,a1508,a1509,a1510,a1511,a1512,a1513,a1514,a1600,a1608,a1609,a1610,a1611,a1612,a1613,a1614,a1615,a1700,a1705,a1706,a1707,a1708,a1709,a1710,a1711,a1712,a1713,a1714,a1715,a1716,a1800,a1805,a1806,a1807,a1808,a1809,a1810,a1811,a1812,a1813,a1814,a1815,a1816,a1817,a1900,a1904,a1905,a1906,a1908,a1909,a1910,a1911,a1912,a1913,a1914,a1915,a1916,a1917,a1918,a2000,a2003,a2004,a2005,a2007,a2009,a2010,a2017,a2018,a2019,a2100,a2102,a2103,a2106,a2107,a2109,a2110,a2117,a2118,a2119,a2120,a2200,a2201,a2204,a2206,a2220,a2221,a2300,a2302,a2322,a2400,a2401,a2402,a2404,a2406,a2407,a2408,a2409,a2410,a2411,a2412,a2413,a2414,a2415,a2416,a2417,a2418,a2419,a2420,a2421,a2422,a2423,c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,c11,c12,c13,c14,c15,c16,c17,c18,c19,c20,c21,c22,c23,c24,b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19,b20,b21,b22,b23,b24,b25 = cache.tab - @unpack k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12,k13,k14,k15,k16,k17,k18,k19,k20,k21,k22,k23,k24,k25,tmp,atmp,uprev,k = cache - k1 = cache.fsalfirst - a = dt*a0100 - @.. broadcast=false tmp = uprev + a*k1 - f(k2, tmp, p, t + c1*dt) - @.. broadcast=false tmp = uprev + dt*(a0200*k1 + a0201*k2) - f(k3, tmp, p, t + c2*dt ) - @.. broadcast=false tmp = uprev + dt*(a0300*k1 + a0302*k3) - f(k4, tmp, p, t + c3*dt) - @.. broadcast=false tmp = uprev + dt*(a0400*k1 + a0402*k3 + a0403*k4) - f(k5, tmp, p, t + c4*dt) - @.. broadcast=false tmp = uprev + dt*(a0500*k1 + a0503*k4 + a0504*k5) - f(k6, tmp, p, t + c5*dt) - @.. broadcast=false tmp = uprev + dt*(a0600*k1 + a0603*k4 + a0604*k5 + a0605*k6) - f(k7, tmp, p, t + c6*dt) - @.. broadcast=false tmp = uprev + dt*(a0700*k1 + a0704*k5 + a0705*k6 + a0706*k7) - f(k8, tmp, p, t + c7*dt) - @.. broadcast=false tmp = uprev + dt*(a0800*k1 + a0805*k6 + a0806*k7 + a0807*k8) - f(k9, tmp, p, t + c8*dt) - @.. broadcast=false tmp = uprev + dt*(a0900*k1 + a0905*k6 + a0906*k7 + a0907*k8 + a0908*k9) - f(k10, tmp, p, t + c9*dt) - @.. broadcast=false tmp = uprev + dt*(a1000*k1 + a1005*k6 + a1006*k7 + a1007*k8 + a1008*k9 + a1009*k10) - f(k11, tmp, p, t + c10*dt) - @.. broadcast=false tmp = uprev + dt*(a1100*k1 + a1105*k6 + a1106*k7 + a1107*k8 + a1108*k9 + a1109*k10 + a1110*k11) - f(k12, tmp, p, t + c11*dt) - @.. broadcast=false tmp = uprev + dt*(a1200*k1 + a1208*k9 + a1209*k10 + a1210*k11 + a1211*k12) - f(k13, tmp, p, t + c12*dt) - @.. broadcast=false tmp = uprev + dt*(a1300*k1 + a1308*k9 + a1309*k10 + a1310*k11 + a1311*k12 + a1312*k13) - f(k14, tmp, p, t + c13*dt) - @.. broadcast=false tmp = uprev + dt*(a1400*k1 + a1408*k9 + a1409*k10 + a1410*k11 + a1411*k12 + a1412*k13 + a1413*k14) - f(k15, tmp, p, t + c14*dt) - @.. broadcast=false tmp = uprev + dt*(a1500*k1 + a1508*k9 + a1509*k10 + a1510*k11 + a1511*k12 + a1512*k13 + a1513*k14 + a1514*k15) - f(k16, tmp, p, t + c15*dt) - @.. broadcast=false tmp = uprev + dt*((a1600*k1 + a1608*k9 + a1609*k10) + (a1610*k11 + a1611*k12 + a1612*k13 + a1613*k14) + (a1614*k15 + a1615*k16)) - f(k17, tmp, p, t + c16*dt) - @.. broadcast=false tmp = uprev + dt*((a1700*k1 + a1705*k6 + a1706*k7) + (a1707*k8 + a1708*k9 + a1709*k10 + a1710*k11) + (a1711*k12 + a1712*k13 + a1713*k14 + a1714*k15) + (a1715*k16 + a1716*k17)) - f(k18, tmp, p, t + c17*dt) - @.. broadcast=false tmp = uprev + dt*((a1800*k1 + a1805*k6 + a1806*k7) + (a1807*k8 + a1808*k9 + a1809*k10 + a1810*k11) + (a1811*k12 + a1812*k13 + a1813*k14 + a1814*k15) + (a1815*k16 + a1816*k17 + a1817*k18)) - f(k19, tmp, p, t + c18*dt) - @.. broadcast=false tmp = uprev + dt*((a1900*k1 + a1904*k5 + a1905*k6) + (a1906*k7 + a1908*k9 + a1909*k10 + a1910*k11) + (a1911*k12 + a1912*k13 + a1913*k14 + a1914*k15) + (a1915*k16 + a1916*k17 + a1917*k18 + a1918*k19)) - f(k20, tmp, p, t + c19*dt) - @.. broadcast=false tmp = uprev + dt*((a2000*k1 + a2003*k4 + a2004*k5) + (a2005*k6 + a2007*k8 + a2009*k10 + a2010*k11) + (a2017*k18 + a2018*k19 + a2019*k20)) - f(k21, tmp, p, t + c20*dt) - @.. broadcast=false tmp = uprev + dt*((a2100*k1 + a2102*k3 + a2103*k4) + (a2106*k7 + a2107*k8 + a2109*k10 + a2110*k11) + (a2117*k18 + a2118*k19 + a2119*k20 + a2120*k21)) - f(k22, tmp, p, t + c21*dt) - @.. broadcast=false tmp = uprev + dt*((a2200*k1 + a2201*k2 + a2204*k5) + (a2206*k7 + a2220*k21 + a2221*k22)) - f(k23, tmp, p, t + c22*dt) - @.. broadcast=false tmp = uprev + dt*(a2300*k1 + a2302*k3 + a2322*k23) - f(k24, tmp, p, t + c23*dt) - @.. broadcast=false tmp = uprev + dt*((a2400*k1 + a2401*k2 + a2402*k3) + (a2404*k5 + a2406*k7 + a2407*k8 + a2408*k9) + (a2409*k10 + a2410*k11 + a2411*k12 + a2412*k13) + (a2413*k14 + a2414*k15 + a2415*k16 + a2416*k17) + (a2417*k18 + a2418*k19 + a2419*k20 + a2420*k21) + (a2421*k22 + a2422*k23 + a2423*k24)) - f(k25, tmp, p, t + c24*dt) - @.. broadcast=false u = uprev + dt*((b1*k1 + b2*k2 + b3*k3 + b5*k5) + (b7*k7 + b8*k8 + b10*k10 + b11*k11) + (b13*k13 + b14*k14 + b15*k15 + b16*k16) + (b17*k17 + b18*k18 + b19*k19 + b20*k20) + (b21*k21 + b22*k22 + b23*k23) + (b24*k24 + b25*k25)) - if integrator.opts.adaptive - @.. broadcast=false tmp = dt*(k2 - k24) * adaptiveConst - calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, integrator.opts.reltol,integrator.opts.internalnorm,t) - integrator.EEst = integrator.opts.internalnorm(atmp,t) - end - f(k, u, p, t+dt) -end -=# - -@muladd function perform_step!(integrator, cache::Feagin12Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - uidx = eachindex(integrator.uprev) - @unpack adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1208, a1209, a1210, a1211, a1300, a1308, a1309, a1310, a1311, a1312, a1400, a1408, a1409, a1410, a1411, a1412, a1413, a1500, a1508, a1509, a1510, a1511, a1512, a1513, a1514, a1600, a1608, a1609, a1610, a1611, a1612, a1613, a1614, a1615, a1700, a1705, a1706, a1707, a1708, a1709, a1710, a1711, a1712, a1713, a1714, a1715, a1716, a1800, a1805, a1806, a1807, a1808, a1809, a1810, a1811, a1812, a1813, a1814, a1815, a1816, a1817, a1900, a1904, a1905, a1906, a1908, a1909, a1910, a1911, a1912, a1913, a1914, a1915, a1916, a1917, a1918, a2000, a2003, a2004, a2005, a2007, a2009, a2010, a2017, a2018, a2019, a2100, a2102, a2103, a2106, a2107, a2109, a2110, a2117, a2118, a2119, a2120, a2200, a2201, a2204, a2206, a2220, a2221, a2300, a2302, a2322, a2400, a2401, a2402, a2404, a2406, a2407, a2408, a2409, a2410, a2411, a2412, a2413, a2414, a2415, a2416, a2417, a2418, a2419, a2420, a2421, a2422, a2423, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, b19, b20, b21, b22, b23, b24, b25 = cache.tab - @unpack k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, k17, k18, k19, k20, k21, k22, k23, k24, k25, tmp, atmp, uprev, k = cache - k1 = cache.fsalfirst - a = dt * a0100 - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + a * k1[i] - end - f(k2, tmp, p, t + c1 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + dt * (a0200 * k1[i] + a0201 * k2[i]) - end - f(k3, tmp, p, t + c2 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + dt * (a0300 * k1[i] + a0302 * k3[i]) - end - f(k4, tmp, p, t + c3 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + dt * (a0400 * k1[i] + a0402 * k3[i] + a0403 * k4[i]) - end - f(k5, tmp, p, t + c4 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + dt * (a0500 * k1[i] + a0503 * k4[i] + a0504 * k5[i]) - end - f(k6, tmp, p, t + c5 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a0600 * k1[i] + a0603 * k4[i] + a0604 * k5[i] + a0605 * k6[i]) - end - f(k7, tmp, p, t + c6 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a0700 * k1[i] + a0704 * k5[i] + a0705 * k6[i] + a0706 * k7[i]) - end - f(k8, tmp, p, t + c7 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a0800 * k1[i] + a0805 * k6[i] + a0806 * k7[i] + a0807 * k8[i]) - end - f(k9, tmp, p, t + c8 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a0900 * k1[i] + a0905 * k6[i] + a0906 * k7[i] + a0907 * k8[i] + - a0908 * k9[i]) - end - f(k10, tmp, p, t + c9 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a1000 * k1[i] + a1005 * k6[i] + a1006 * k7[i] + a1007 * k8[i] + - a1008 * k9[i] + a1009 * k10[i]) - end - f(k11, tmp, p, t + c10 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a1100 * k1[i] + a1105 * k6[i] + a1106 * k7[i] + a1107 * k8[i] + - a1108 * k9[i] + a1109 * k10[i] + a1110 * k11[i]) - end - f(k12, tmp, p, t + c11 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * (a1200 * k1[i] + a1208 * k9[i] + a1209 * k10[i] + - a1210 * k11[i] + a1211 * k12[i]) - end - f(k13, tmp, p, t + c12 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * (a1300 * k1[i] + a1308 * k9[i] + a1309 * k10[i] + - a1310 * k11[i] + a1311 * k12[i] + a1312 * k13[i]) - end - f(k14, tmp, p, t + c13 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * (a1400 * k1[i] + a1408 * k9[i] + a1409 * k10[i] + - a1410 * k11[i] + a1411 * k12[i] + a1412 * k13[i] + - a1413 * k14[i]) - end - f(k15, tmp, p, t + c14 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * (a1500 * k1[i] + a1508 * k9[i] + a1509 * k10[i] + - a1510 * k11[i] + a1511 * k12[i] + a1512 * k13[i] + - a1513 * k14[i] + a1514 * k15[i]) - end - f(k16, tmp, p, t + c15 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * ((a1600 * k1[i] + a1608 * k9[i] + a1609 * k10[i]) + - (a1610 * k11[i] + a1611 * k12[i] + a1612 * k13[i] + - a1613 * k14[i]) + (a1614 * k15[i] + a1615 * k16[i])) - end - f(k17, tmp, p, t + c16 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * ((a1700 * k1[i] + a1705 * k6[i] + a1706 * k7[i]) + - (a1707 * k8[i] + a1708 * k9[i] + a1709 * k10[i] + - a1710 * k11[i]) + - (a1711 * k12[i] + a1712 * k13[i] + a1713 * k14[i] + - a1714 * k15[i]) + (a1715 * k16[i] + a1716 * k17[i])) - end - f(k18, tmp, p, t + c17 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * ((a1800 * k1[i] + a1805 * k6[i] + a1806 * k7[i]) + - (a1807 * k8[i] + a1808 * k9[i] + a1809 * k10[i] + - a1810 * k11[i]) + - (a1811 * k12[i] + a1812 * k13[i] + a1813 * k14[i] + - a1814 * k15[i]) + - (a1815 * k16[i] + a1816 * k17[i] + a1817 * k18[i])) - end - f(k19, tmp, p, t + c18 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * ((a1900 * k1[i] + a1904 * k5[i] + a1905 * k6[i]) + - (a1906 * k7[i] + a1908 * k9[i] + a1909 * k10[i] + - a1910 * k11[i]) + - (a1911 * k12[i] + a1912 * k13[i] + a1913 * k14[i] + - a1914 * k15[i]) + - (a1915 * k16[i] + a1916 * k17[i] + a1917 * k18[i] + - a1918 * k19[i])) - end - f(k20, tmp, p, t + c19 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * ((a2000 * k1[i] + a2003 * k4[i] + a2004 * k5[i]) + - (a2005 * k6[i] + a2007 * k8[i] + a2009 * k10[i] + - a2010 * k11[i]) + - (a2017 * k18[i] + a2018 * k19[i] + a2019 * k20[i])) - end - f(k21, tmp, p, t + c20 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * ((a2100 * k1[i] + a2102 * k3[i] + a2103 * k4[i]) + - (a2106 * k7[i] + a2107 * k8[i] + a2109 * k10[i] + - a2110 * k11[i]) + - (a2117 * k18[i] + a2118 * k19[i] + a2119 * k20[i] + - a2120 * k21[i])) - end - f(k22, tmp, p, t + c21 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * ((a2200 * k1[i] + a2201 * k2[i] + a2204 * k5[i]) + - (a2206 * k7[i] + a2220 * k21[i] + a2221 * k22[i])) - end - f(k23, tmp, p, t + c22 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + dt * (a2300 * k1[i] + a2302 * k3[i] + a2322 * k23[i]) - end - f(k24, tmp, p, t + c23 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * ((a2400 * k1[i] + a2401 * k2[i] + a2402 * k3[i]) + - (a2404 * k5[i] + a2406 * k7[i] + a2407 * k8[i] + - a2408 * k9[i]) + - (a2409 * k10[i] + a2410 * k11[i] + a2411 * k12[i] + - a2412 * k13[i]) + - (a2413 * k14[i] + a2414 * k15[i] + a2415 * k16[i] + - a2416 * k17[i]) + - (a2417 * k18[i] + a2418 * k19[i] + a2419 * k20[i] + - a2420 * k21[i]) + - (a2421 * k22[i] + a2422 * k23[i] + a2423 * k24[i])) - end - f(k25, tmp, p, t + c24 * dt) - @tight_loop_macros for i in uidx - @inbounds u[i] = uprev[i] + - dt * ((b1 * k1[i] + b2 * k2[i] + b3 * k3[i] + b5 * k5[i]) + - (b7 * k7[i] + b8 * k8[i] + b10 * k10[i] + b11 * k11[i]) + - (b13 * k13[i] + b14 * k14[i] + b15 * k15[i] + b16 * k16[i]) + - (b17 * k17[i] + b18 * k18[i] + b19 * k19[i] + b20 * k20[i]) + - (b21 * k21[i] + b22 * k22[i] + b23 * k23[i]) + - (b24 * k24[i] + b25 * k25[i])) - end - integrator.stats.nf += 24 - if integrator.opts.adaptive - @tight_loop_macros for i in uidx - @inbounds tmp[i] = dt * (k2[i] - k24[i]) * adaptiveConst - end - calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - f(k, u, p, t + dt) - integrator.stats.nf += 1 -end - -function initialize!(integrator, cache::Feagin14ConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -@muladd function perform_step!(integrator, cache::Feagin14ConstantCache, - repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1208, a1209, a1210, a1211, a1300, a1308, a1309, a1310, a1311, a1312, a1400, a1408, a1409, a1410, a1411, a1412, a1413, a1500, a1508, a1509, a1510, a1511, a1512, a1513, a1514, a1600, a1608, a1609, a1610, a1611, a1612, a1613, a1614, a1615, a1700, a1712, a1713, a1714, a1715, a1716, a1800, a1812, a1813, a1814, a1815, a1816, a1817, a1900, a1912, a1913, a1914, a1915, a1916, a1917, a1918, a2000, a2012, a2013, a2014, a2015, a2016, a2017, a2018, a2019, a2100, a2112, a2113, a2114, a2115, a2116, a2117, a2118, a2119, a2120, a2200, a2212, a2213, a2214, a2215, a2216, a2217, a2218, a2219, a2220, a2221, a2300, a2308, a2309, a2310, a2311, a2312, a2313, a2314, a2315, a2316, a2317, a2318, a2319, a2320, a2321, a2322, a2400, a2408, a2409, a2410, a2411, a2412, a2413, a2414, a2415, a2416, a2417, a2418, a2419, a2420, a2421, a2422, a2423, a2500, a2508, a2509, a2510, a2511, a2512, a2513, a2514, a2515, a2516, a2517, a2518, a2519, a2520, a2521, a2522, a2523, a2524, a2600, a2605, a2606, a2607, a2608, a2609, a2610, a2612, a2613, a2614, a2615, a2616, a2617, a2618, a2619, a2620, a2621, a2622, a2623, a2624, a2625, a2700, a2705, a2706, a2707, a2708, a2709, a2711, a2712, a2713, a2714, a2715, a2716, a2717, a2718, a2719, a2720, a2721, a2722, a2723, a2724, a2725, a2726, a2800, a2805, a2806, a2807, a2808, a2810, a2811, a2813, a2814, a2815, a2823, a2824, a2825, a2826, a2827, a2900, a2904, a2905, a2906, a2909, a2910, a2911, a2913, a2914, a2915, a2923, a2924, a2925, a2926, a2927, a2928, a3000, a3003, a3004, a3005, a3007, a3009, a3010, a3013, a3014, a3015, a3023, a3024, a3025, a3027, a3028, a3029, a3100, a3102, a3103, a3106, a3107, a3109, a3110, a3113, a3114, a3115, a3123, a3124, a3125, a3127, a3128, a3129, a3130, a3200, a3201, a3204, a3206, a3230, a3231, a3300, a3302, a3332, a3400, a3401, a3402, a3404, a3406, a3407, a3409, a3410, a3411, a3412, a3413, a3414, a3415, a3416, a3417, a3418, a3419, a3420, a3421, a3422, a3423, a3424, a3425, a3426, a3427, a3428, a3429, a3430, a3431, a3432, a3433, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31, b32, b33, b34, b35 = cache - k1 = integrator.fsalfirst - a = dt * a0100 - k2 = f(uprev + a * k1, p, t + c1 * dt) - k3 = f(uprev + dt * (a0200 * k1 + a0201 * k2), p, t + c2 * dt) - k4 = f(uprev + dt * (a0300 * k1 + a0302 * k3), p, t + c3 * dt) - k5 = f(uprev + dt * (a0400 * k1 + a0402 * k3 + a0403 * k4), p, t + c4 * dt) - k6 = f(uprev + dt * (a0500 * k1 + a0503 * k4 + a0504 * k5), p, t + c5 * dt) - k7 = f(uprev + dt * (a0600 * k1 + a0603 * k4 + a0604 * k5 + a0605 * k6), p, t + c6 * dt) - k8 = f(uprev + dt * (a0700 * k1 + a0704 * k5 + a0705 * k6 + a0706 * k7), p, t + c7 * dt) - k9 = f(uprev + dt * (a0800 * k1 + a0805 * k6 + a0806 * k7 + a0807 * k8), p, t + c8 * dt) - k10 = f(uprev + dt * (a0900 * k1 + a0905 * k6 + a0906 * k7 + a0907 * k8 + a0908 * k9), - p, t + c9 * dt) - k11 = f( - uprev + - dt * - (a1000 * k1 + a1005 * k6 + a1006 * k7 + a1007 * k8 + a1008 * k9 + a1009 * k10), - p, t + c10 * dt) - k12 = f( - uprev + - dt * - (a1100 * k1 + a1105 * k6 + a1106 * k7 + a1107 * k8 + a1108 * k9 + a1109 * k10 + - a1110 * k11), - p, - t + c11 * dt) - k13 = f( - uprev + - dt * (a1200 * k1 + a1208 * k9 + a1209 * k10 + a1210 * k11 + a1211 * k12), p, - t + c12 * dt) - k14 = f( - uprev + - dt * (a1300 * k1 + a1308 * k9 + a1309 * k10 + a1310 * k11 + a1311 * k12 + - a1312 * k13), - p, - t + c13 * dt) - k15 = f( - uprev + - dt * (a1400 * k1 + a1408 * k9 + a1409 * k10 + a1410 * k11 + a1411 * k12 + - a1412 * k13 + a1413 * k14), - p, - t + c14 * dt) - k16 = f( - uprev + - dt * (a1500 * k1 + a1508 * k9 + a1509 * k10 + a1510 * k11 + a1511 * k12 + - a1512 * k13 + a1513 * k14 + a1514 * k15), - p, - t + c15 * dt) - k17 = f( - uprev + - dt * (a1600 * k1 + a1608 * k9 + a1609 * k10 + a1610 * k11 + a1611 * k12 + - a1612 * k13 + a1613 * k14 + a1614 * k15 + a1615 * k16), - p, - t + c16 * dt) - k18 = f( - uprev + - dt * (a1700 * k1 + a1712 * k13 + a1713 * k14 + a1714 * k15 + a1715 * k16 + - a1716 * k17), - p, - t + c17 * dt) - k19 = f( - uprev + - dt * (a1800 * k1 + a1812 * k13 + a1813 * k14 + a1814 * k15 + a1815 * k16 + - a1816 * k17 + a1817 * k18), - p, - t + c18 * dt) - k20 = f( - uprev + - dt * (a1900 * k1 + a1912 * k13 + a1913 * k14 + a1914 * k15 + a1915 * k16 + - a1916 * k17 + a1917 * k18 + a1918 * k19), - p, - t + c19 * dt) - k21 = f( - uprev + - dt * (a2000 * k1 + a2012 * k13 + a2013 * k14 + a2014 * k15 + a2015 * k16 + - a2016 * k17 + a2017 * k18 + a2018 * k19 + a2019 * k20), - p, - t + c20 * dt) - k22 = f( - uprev + - dt * (a2100 * k1 + a2112 * k13 + a2113 * k14 + a2114 * k15 + a2115 * k16 + - a2116 * k17 + a2117 * k18 + a2118 * k19 + a2119 * k20 + a2120 * k21), - p, - t + c21 * dt) - k23 = f( - uprev + - dt * (a2200 * k1 + a2212 * k13 + a2213 * k14 + a2214 * k15 + a2215 * k16 + - a2216 * k17 + a2217 * k18 + a2218 * k19 + a2219 * k20 + a2220 * k21 + - a2221 * k22), - p, - t + c22 * dt) - k24 = f( - uprev + - dt * (a2300 * k1 + a2308 * k9 + a2309 * k10 + a2310 * k11 + a2311 * k12 + - a2312 * k13 + a2313 * k14 + a2314 * k15 + a2315 * k16 + a2316 * k17 + - a2317 * k18 + a2318 * k19 + a2319 * k20 + a2320 * k21 + a2321 * k22 + - a2322 * k23), - p, - t + c23 * dt) - k25 = f( - uprev + - dt * (a2400 * k1 + a2408 * k9 + a2409 * k10 + a2410 * k11 + a2411 * k12 + - a2412 * k13 + a2413 * k14 + a2414 * k15 + a2415 * k16 + a2416 * k17 + - a2417 * k18 + a2418 * k19 + a2419 * k20 + a2420 * k21 + a2421 * k22 + - a2422 * k23 + a2423 * k24), - p, - t + c24 * dt) - k26 = f( - uprev + - dt * (a2500 * k1 + a2508 * k9 + a2509 * k10 + a2510 * k11 + a2511 * k12 + - a2512 * k13 + a2513 * k14 + a2514 * k15 + a2515 * k16 + a2516 * k17 + - a2517 * k18 + a2518 * k19 + a2519 * k20 + a2520 * k21 + a2521 * k22 + - a2522 * k23 + a2523 * k24 + a2524 * k25), - p, - t + c25 * dt) - k27 = f( - uprev + - dt * - (a2600 * k1 + a2605 * k6 + a2606 * k7 + a2607 * k8 + a2608 * k9 + a2609 * k10 + - a2610 * k11 + a2612 * k13 + a2613 * k14 + a2614 * k15 + a2615 * k16 + - a2616 * k17 + a2617 * k18 + a2618 * k19 + a2619 * k20 + a2620 * k21 + - a2621 * k22 + a2622 * k23 + a2623 * k24 + a2624 * k25 + a2625 * k26), - p, - t + c26 * dt) - k28 = f( - uprev + - dt * - (a2700 * k1 + a2705 * k6 + a2706 * k7 + a2707 * k8 + a2708 * k9 + a2709 * k10 + - a2711 * k12 + a2712 * k13 + a2713 * k14 + a2714 * k15 + a2715 * k16 + - a2716 * k17 + a2717 * k18 + a2718 * k19 + a2719 * k20 + a2720 * k21 + - a2721 * k22 + a2722 * k23 + a2723 * k24 + a2724 * k25 + a2725 * k26 + - a2726 * k27), - p, - t + c27 * dt) - k29 = f( - uprev + - dt * - (a2800 * k1 + a2805 * k6 + a2806 * k7 + a2807 * k8 + a2808 * k9 + a2810 * k11 + - a2811 * k12 + a2813 * k14 + a2814 * k15 + a2815 * k16 + a2823 * k24 + - a2824 * k25 + a2825 * k26 + a2826 * k27 + a2827 * k28), - p, - t + c28 * dt) - k30 = f( - uprev + - dt * - (a2900 * k1 + a2904 * k5 + a2905 * k6 + a2906 * k7 + a2909 * k10 + a2910 * k11 + - a2911 * k12 + a2913 * k14 + a2914 * k15 + a2915 * k16 + a2923 * k24 + - a2924 * k25 + a2925 * k26 + a2926 * k27 + a2927 * k28 + a2928 * k29), - p, - t + c29 * dt) - k31 = f( - uprev + - dt * - (a3000 * k1 + a3003 * k4 + a3004 * k5 + a3005 * k6 + a3007 * k8 + a3009 * k10 + - a3010 * k11 + a3013 * k14 + a3014 * k15 + a3015 * k16 + a3023 * k24 + - a3024 * k25 + a3025 * k26 + a3027 * k28 + a3028 * k29 + a3029 * k30), - p, - t + c30 * dt) - k32 = f( - uprev + - dt * - (a3100 * k1 + a3102 * k3 + a3103 * k4 + a3106 * k7 + a3107 * k8 + a3109 * k10 + - a3110 * k11 + a3113 * k14 + a3114 * k15 + a3115 * k16 + a3123 * k24 + - a3124 * k25 + a3125 * k26 + a3127 * k28 + a3128 * k29 + a3129 * k30 + - a3130 * k31), - p, - t + c31 * dt) - k33 = f( - uprev + - dt * - (a3200 * k1 + a3201 * k2 + a3204 * k5 + a3206 * k7 + a3230 * k31 + a3231 * k32), - p, t + c32 * dt) - k34 = f(uprev + dt * (a3300 * k1 + a3302 * k3 + a3332 * k33), p, t + c33 * dt) - k35 = f( - uprev + - dt * - (a3400 * k1 + a3401 * k2 + a3402 * k3 + a3404 * k5 + a3406 * k7 + a3407 * k8 + - a3409 * k10 + a3410 * k11 + a3411 * k12 + a3412 * k13 + a3413 * k14 + - a3414 * k15 + a3415 * k16 + a3416 * k17 + a3417 * k18 + a3418 * k19 + - a3419 * k20 + a3420 * k21 + a3421 * k22 + a3422 * k23 + a3423 * k24 + - a3424 * k25 + a3425 * k26 + a3426 * k27 + a3427 * k28 + a3428 * k29 + - a3429 * k30 + a3430 * k31 + a3431 * k32 + a3432 * k33 + a3433 * k34), - p, - t + c34 * dt) - integrator.stats.nf += 34 - u = uprev + - dt * - (b1 * k1 + b2 * k2 + b3 * k3 + b5 * k5 + b7 * k7 + b8 * k8 + b10 * k10 + b11 * k11 + - b12 * k12 + b14 * k14 + b15 * k15 + b16 * k16 + b18 * k18 + b19 * k19 + b20 * k20 + - b21 * k21 + b22 * k22 + b23 * k23 + b24 * k24 + b25 * k25 + b26 * k26 + b27 * k27 + - b28 * k28 + b29 * k29 + b30 * k30 + b31 * k31 + b32 * k32 + b33 * k33 + b34 * k34 + - b35 * k35) - if integrator.opts.adaptive - utilde = @.. broadcast=false dt*(k2-k34)*adaptiveConst - atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - k = f(u, p, t + dt) # For the interpolation, needs k at the updated point - integrator.stats.nf += 1 - integrator.fsallast = k - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.u = u -end - -function initialize!(integrator, cache::Feagin14Cache) - integrator.fsalfirst = cache.fsalfirst - integrator.fsallast = cache.k - integrator.kshortsize = 2 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 -end - -#= -@muladd function perform_step!(integrator, cache::Feagin14Cache, repeat_step=false) - @unpack t,dt,uprev,u,f,p = integrator - @unpack adaptiveConst,a0100,a0200,a0201,a0300,a0302,a0400,a0402,a0403,a0500,a0503,a0504,a0600,a0603,a0604,a0605,a0700,a0704,a0705,a0706,a0800,a0805,a0806,a0807,a0900,a0905,a0906,a0907,a0908,a1000,a1005,a1006,a1007,a1008,a1009,a1100,a1105,a1106,a1107,a1108,a1109,a1110,a1200,a1208,a1209,a1210,a1211,a1300,a1308,a1309,a1310,a1311,a1312,a1400,a1408,a1409,a1410,a1411,a1412,a1413,a1500,a1508,a1509,a1510,a1511,a1512,a1513,a1514,a1600,a1608,a1609,a1610,a1611,a1612,a1613,a1614,a1615,a1700,a1712,a1713,a1714,a1715,a1716,a1800,a1812,a1813,a1814,a1815,a1816,a1817,a1900,a1912,a1913,a1914,a1915,a1916,a1917,a1918,a2000,a2012,a2013,a2014,a2015,a2016,a2017,a2018,a2019,a2100,a2112,a2113,a2114,a2115,a2116,a2117,a2118,a2119,a2120,a2200,a2212,a2213,a2214,a2215,a2216,a2217,a2218,a2219,a2220,a2221,a2300,a2308,a2309,a2310,a2311,a2312,a2313,a2314,a2315,a2316,a2317,a2318,a2319,a2320,a2321,a2322,a2400,a2408,a2409,a2410,a2411,a2412,a2413,a2414,a2415,a2416,a2417,a2418,a2419,a2420,a2421,a2422,a2423,a2500,a2508,a2509,a2510,a2511,a2512,a2513,a2514,a2515,a2516,a2517,a2518,a2519,a2520,a2521,a2522,a2523,a2524,a2600,a2605,a2606,a2607,a2608,a2609,a2610,a2612,a2613,a2614,a2615,a2616,a2617,a2618,a2619,a2620,a2621,a2622,a2623,a2624,a2625,a2700,a2705,a2706,a2707,a2708,a2709,a2711,a2712,a2713,a2714,a2715,a2716,a2717,a2718,a2719,a2720,a2721,a2722,a2723,a2724,a2725,a2726,a2800,a2805,a2806,a2807,a2808,a2810,a2811,a2813,a2814,a2815,a2823,a2824,a2825,a2826,a2827,a2900,a2904,a2905,a2906,a2909,a2910,a2911,a2913,a2914,a2915,a2923,a2924,a2925,a2926,a2927,a2928,a3000,a3003,a3004,a3005,a3007,a3009,a3010,a3013,a3014,a3015,a3023,a3024,a3025,a3027,a3028,a3029,a3100,a3102,a3103,a3106,a3107,a3109,a3110,a3113,a3114,a3115,a3123,a3124,a3125,a3127,a3128,a3129,a3130,a3200,a3201,a3204,a3206,a3230,a3231,a3300,a3302,a3332,a3400,a3401,a3402,a3404,a3406,a3407,a3409,a3410,a3411,a3412,a3413,a3414,a3415,a3416,a3417,a3418,a3419,a3420,a3421,a3422,a3423,a3424,a3425,a3426,a3427,a3428,a3429,a3430,a3431,a3432,a3433,c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,c11,c12,c13,c14,c15,c16,c17,c18,c19,c20,c21,c22,c23,c24,c25,c26,c27,c28,c29,c30,c31,c32,c33,c34,b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35 = cache.tab - @unpack k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12,k13,k14,k15,k16,k17,k18,k19,k20,k21,k22,k23,k24,k25,k26,k27,k28,k29,k30,k31,k32,k33,k34,k35,tmp,atmp,uprev,k = cache - k1 = cache.fsalfirst - f(k1, uprev, p, t) - a = dt*a0100 - @.. broadcast=false tmp = uprev + a*k1 - f(k2, tmp, p, t + c1*dt) - @.. broadcast=false tmp = uprev + dt*(a0200*k1 + a0201*k2) - f(k3, tmp, p, t + c2*dt ) - @.. broadcast=false tmp = uprev + dt*(a0300*k1 + a0302*k3) - f(k4, tmp, p, t + c3*dt) - @.. broadcast=false tmp = uprev + dt*(a0400*k1 + a0402*k3 + a0403*k4) - f(k5, tmp, p, t + c4*dt) - @.. broadcast=false tmp = uprev + dt*(a0500*k1 + a0503*k4 + a0504*k5) - f(k6, tmp, p, t + c5*dt) - @.. broadcast=false tmp = uprev + dt*(a0600*k1 + a0603*k4 + a0604*k5 + a0605*k6) - f(k7, tmp, p, t + c6*dt) - @.. broadcast=false tmp = uprev + dt*(a0700*k1 + a0704*k5 + a0705*k6 + a0706*k7) - f(k8, tmp, p, t + c7*dt) - @.. broadcast=false tmp = uprev + dt*(a0800*k1 + a0805*k6 + a0806*k7 + a0807*k8) - f(k9, tmp, p, t + c8*dt) - @.. broadcast=false tmp = uprev + dt*(a0900*k1 + a0905*k6 + a0906*k7 + a0907*k8 + a0908*k9) - f(k10, tmp, p, t + c9*dt) - @.. broadcast=false tmp = uprev + dt*(a1000*k1 + a1005*k6 + a1006*k7 + a1007*k8 + a1008*k9 + a1009*k10) - f(k11, tmp, p, t + c10*dt) - @.. broadcast=false tmp = uprev + dt*(a1100*k1 + a1105*k6 + a1106*k7 + a1107*k8 + a1108*k9 + a1109*k10 + a1110*k11) - f(k12, tmp, p, t + c11*dt) - @.. broadcast=false tmp = uprev + dt*(a1200*k1 + a1208*k9 + a1209*k10 + a1210*k11 + a1211*k12) - f(k13, tmp, p, t + c12*dt) - @.. broadcast=false tmp = uprev + dt*(a1300*k1 + a1308*k9 + a1309*k10 + a1310*k11 + a1311*k12 + a1312*k13) - f(k14, tmp, p, t + c13*dt) - @.. broadcast=false tmp = uprev + dt*(a1400*k1 + a1408*k9 + a1409*k10 + a1410*k11 + a1411*k12 + a1412*k13 + a1413*k14) - f(k15, tmp, p, t + c14*dt) - @.. broadcast=false tmp = uprev + dt*(a1500*k1 + a1508*k9 + a1509*k10 + a1510*k11 + a1511*k12 + a1512*k13 + a1513*k14 + a1514*k15) - f(k16, tmp, p, t + c15*dt) - @.. broadcast=false tmp = uprev + dt*(a1600*k1 + a1608*k9 + a1609*k10 + a1610*k11 + a1611*k12 + a1612*k13 + a1613*k14 + a1614*k15 + a1615*k16) - f(k17, tmp, p, t + c16*dt) - @.. broadcast=false tmp = uprev + dt*(a1700*k1 + a1712*k13 + a1713*k14 + a1714*k15 + a1715*k16 + a1716*k17) - f(k18, tmp, p, t + c17*dt) - @.. broadcast=false tmp = uprev + dt*(a1800*k1 + a1812*k13 + a1813*k14 + a1814*k15 + a1815*k16 + a1816*k17 + a1817*k18) - f(k19, tmp, p, t + c18*dt) - @.. broadcast=false tmp = uprev + dt*(a1900*k1 + a1912*k13 + a1913*k14 + a1914*k15 + a1915*k16 + a1916*k17 + a1917*k18 + a1918*k19) - f(k20, tmp, p, t + c19*dt) - @.. broadcast=false tmp = uprev + dt*(a2000*k1 + a2012*k13 + a2013*k14 + a2014*k15 + a2015*k16 + a2016*k17 + a2017*k18 + a2018*k19 + a2019*k20) - f(k21, tmp, p, t + c20*dt) - @.. broadcast=false tmp = uprev + dt*(a2100*k1 + a2112*k13 + a2113*k14 + a2114*k15 + a2115*k16 + a2116*k17 + a2117*k18 + a2118*k19 + a2119*k20 + a2120*k21) - f(k22, tmp, p, t + c21*dt) - @.. broadcast=false tmp = uprev + dt*(a2200*k1 + a2212*k13 + a2213*k14 + a2214*k15 + a2215*k16 + a2216*k17 + a2217*k18 + a2218*k19 + a2219*k20 + a2220*k21 + a2221*k22) - f(k23, tmp, p, t + c22*dt) - @.. broadcast=false tmp = uprev + dt*(a2300*k1 + a2308*k9 + a2309*k10 + a2310*k11 + a2311*k12 + a2312*k13 + a2313*k14 + a2314*k15 + a2315*k16 + a2316*k17 + a2317*k18 + a2318*k19 + a2319*k20 + a2320*k21 + a2321*k22 + a2322*k23) - f(k24, tmp, p, t + c23*dt) - @.. broadcast=false tmp = uprev + dt*(a2400*k1 + a2408*k9 + a2409*k10 + a2410*k11 + a2411*k12 + a2412*k13 + a2413*k14 + a2414*k15 + a2415*k16 + a2416*k17 + a2417*k18 + a2418*k19 + a2419*k20 + a2420*k21 + a2421*k22 + a2422*k23 + a2423*k24) - f(k25, tmp, p, t + c24*dt) - @.. broadcast=false tmp = uprev + dt*(a2500*k1 + a2508*k9 + a2509*k10 + a2510*k11 + a2511*k12 + a2512*k13 + a2513*k14 + a2514*k15 + a2515*k16 + a2516*k17 + a2517*k18 + a2518*k19 + a2519*k20 + a2520*k21 + a2521*k22 + a2522*k23 + a2523*k24 + a2524*k25) - f(k26, tmp, p, t + c25*dt) - @.. broadcast=false tmp = uprev + dt*(a2600*k1 + a2605*k6 + a2606*k7 + a2607*k8 + a2608*k9 + a2609*k10 + a2610*k11 + a2612*k13 + a2613*k14 + a2614*k15 + a2615*k16 + a2616*k17 + a2617*k18 + a2618*k19 + a2619*k20 + a2620*k21 + a2621*k22 + a2622*k23 + a2623*k24 + a2624*k25 + a2625*k26) - f(k27, tmp, p, t + c26*dt) - @.. broadcast=false tmp = uprev + dt*(a2700*k1 + a2705*k6 + a2706*k7 + a2707*k8 + a2708*k9 + a2709*k10 + a2711*k12 + a2712*k13 + a2713*k14 + a2714*k15 + a2715*k16 + a2716*k17 + a2717*k18 + a2718*k19 + a2719*k20 + a2720*k21 + a2721*k22 + a2722*k23 + a2723*k24 + a2724*k25 + a2725*k26 + a2726*k27) - f(k28, tmp, p, t + c27*dt) - @.. broadcast=false tmp = uprev + dt*(a2800*k1 + a2805*k6 + a2806*k7 + a2807*k8 + a2808*k9 + a2810*k11 + a2811*k12 + a2813*k14 + a2814*k15 + a2815*k16 + a2823*k24 + a2824*k25 + a2825*k26 + a2826*k27 + a2827*k28) - f(k29, tmp, p, t + c28*dt) - @.. broadcast=false tmp = uprev + dt*(a2900*k1 + a2904*k5 + a2905*k6 + a2906*k7 + a2909*k10 + a2910*k11 + a2911*k12 + a2913*k14 + a2914*k15 + a2915*k16 + a2923*k24 + a2924*k25 + a2925*k26 + a2926*k27 + a2927*k28 + a2928*k29) - f(k30, tmp, p, t + c29*dt) - @.. broadcast=false tmp = uprev + dt*(a3000*k1 + a3003*k4 + a3004*k5 + a3005*k6 + a3007*k8 + a3009*k10 + a3010*k11 + a3013*k14 + a3014*k15 + a3015*k16 + a3023*k24 + a3024*k25 + a3025*k26 + a3027*k28 + a3028*k29 + a3029*k30) - f(k31, tmp, p, t + c30*dt) - @.. broadcast=false tmp = uprev + dt*(a3100*k1 + a3102*k3 + a3103*k4 + a3106*k7 + a3107*k8 + a3109*k10 + a3110*k11 + a3113*k14 + a3114*k15 + a3115*k16 + a3123*k24 + a3124*k25 + a3125*k26 + a3127*k28 + a3128*k29 + a3129*k30 + a3130*k31) - f(k32, tmp, p, t + c31*dt) - @.. broadcast=false tmp = uprev + dt*(a3200*k1 + a3201*k2 + a3204*k5 + a3206*k7 + a3230*k31 + a3231*k32) - f(k33, tmp, p, t + c32*dt) - @.. broadcast=false tmp = uprev + dt*(a3300*k1 + a3302*k3 + a3332*k33) - f(k34, tmp, p, t + c33*dt) - @.. broadcast=false tmp = uprev + dt*(a3400*k1 + a3401*k2 + a3402*k3 + a3404*k5 + a3406*k7 + a3407*k8 + a3409*k10 + a3410*k11 + a3411*k12 + a3412*k13 + a3413*k14 + a3414*k15 + a3415*k16 + a3416*k17 + a3417*k18 + a3418*k19 + a3419*k20 + a3420*k21 + a3421*k22 + a3422*k23 + a3423*k24 + a3424*k25 + a3425*k26 + a3426*k27 + a3427*k28 + a3428*k29 + a3429*k30 + a3430*k31 + a3431*k32 + a3432*k33 + a3433*k34) - f(k35, tmp, p, t + c34*dt) - @.. broadcast=false u = uprev + dt*(b1*k1 + b2*k2 + b3*k3 + b5*k5 + b7*k7 + b8*k8 + b10*k10 + b11*k11 + b12*k12 + b14*k14 + b15*k15 + b16*k16 + b18*k18 + b19*k19 + b20*k20 + b21*k21 + b22*k22 + b23*k23 + b24*k24 + b25*k25 + b26*k26 + b27*k27 + b28*k28 + b29*k29 + b30*k30 + b31*k31 + b32*k32 + b33*k33 + b34*k34 + b35*k35) - if integrator.opts.adaptive - @.. broadcast=false tmp = dt*(k2 - k34) * adaptiveConst - calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, integrator.opts.reltol,integrator.opts.internalnorm,t) - integrator.EEst = integrator.opts.internalnorm(atmp,t) - end - f(integrator.fsallast,u,p,t+dt) # For the interpolation, needs k at the updated point -end -=# - -@muladd function perform_step!(integrator, cache::Feagin14Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - uidx = eachindex(integrator.uprev) - @unpack adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1208, a1209, a1210, a1211, a1300, a1308, a1309, a1310, a1311, a1312, a1400, a1408, a1409, a1410, a1411, a1412, a1413, a1500, a1508, a1509, a1510, a1511, a1512, a1513, a1514, a1600, a1608, a1609, a1610, a1611, a1612, a1613, a1614, a1615, a1700, a1712, a1713, a1714, a1715, a1716, a1800, a1812, a1813, a1814, a1815, a1816, a1817, a1900, a1912, a1913, a1914, a1915, a1916, a1917, a1918, a2000, a2012, a2013, a2014, a2015, a2016, a2017, a2018, a2019, a2100, a2112, a2113, a2114, a2115, a2116, a2117, a2118, a2119, a2120, a2200, a2212, a2213, a2214, a2215, a2216, a2217, a2218, a2219, a2220, a2221, a2300, a2308, a2309, a2310, a2311, a2312, a2313, a2314, a2315, a2316, a2317, a2318, a2319, a2320, a2321, a2322, a2400, a2408, a2409, a2410, a2411, a2412, a2413, a2414, a2415, a2416, a2417, a2418, a2419, a2420, a2421, a2422, a2423, a2500, a2508, a2509, a2510, a2511, a2512, a2513, a2514, a2515, a2516, a2517, a2518, a2519, a2520, a2521, a2522, a2523, a2524, a2600, a2605, a2606, a2607, a2608, a2609, a2610, a2612, a2613, a2614, a2615, a2616, a2617, a2618, a2619, a2620, a2621, a2622, a2623, a2624, a2625, a2700, a2705, a2706, a2707, a2708, a2709, a2711, a2712, a2713, a2714, a2715, a2716, a2717, a2718, a2719, a2720, a2721, a2722, a2723, a2724, a2725, a2726, a2800, a2805, a2806, a2807, a2808, a2810, a2811, a2813, a2814, a2815, a2823, a2824, a2825, a2826, a2827, a2900, a2904, a2905, a2906, a2909, a2910, a2911, a2913, a2914, a2915, a2923, a2924, a2925, a2926, a2927, a2928, a3000, a3003, a3004, a3005, a3007, a3009, a3010, a3013, a3014, a3015, a3023, a3024, a3025, a3027, a3028, a3029, a3100, a3102, a3103, a3106, a3107, a3109, a3110, a3113, a3114, a3115, a3123, a3124, a3125, a3127, a3128, a3129, a3130, a3200, a3201, a3204, a3206, a3230, a3231, a3300, a3302, a3332, a3400, a3401, a3402, a3404, a3406, a3407, a3409, a3410, a3411, a3412, a3413, a3414, a3415, a3416, a3417, a3418, a3419, a3420, a3421, a3422, a3423, a3424, a3425, a3426, a3427, a3428, a3429, a3430, a3431, a3432, a3433, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31, b32, b33, b34, b35 = cache.tab - @unpack k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, k17, k18, k19, k20, k21, k22, k23, k24, k25, k26, k27, k28, k29, k30, k31, k32, k33, k34, k35, tmp, atmp, uprev, k = cache - k1 = cache.fsalfirst - a = dt * a0100 - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + a * k1[i] - end - f(k2, tmp, p, t + c1 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + dt * (a0200 * k1[i] + a0201 * k2[i]) - end - f(k3, tmp, p, t + c2 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + dt * (a0300 * k1[i] + a0302 * k3[i]) - end - f(k4, tmp, p, t + c3 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + dt * (a0400 * k1[i] + a0402 * k3[i] + a0403 * k4[i]) - end - f(k5, tmp, p, t + c4 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + dt * (a0500 * k1[i] + a0503 * k4[i] + a0504 * k5[i]) - end - f(k6, tmp, p, t + c5 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a0600 * k1[i] + a0603 * k4[i] + a0604 * k5[i] + a0605 * k6[i]) - end - f(k7, tmp, p, t + c6 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a0700 * k1[i] + a0704 * k5[i] + a0705 * k6[i] + a0706 * k7[i]) - end - f(k8, tmp, p, t + c7 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a0800 * k1[i] + a0805 * k6[i] + a0806 * k7[i] + a0807 * k8[i]) - end - f(k9, tmp, p, t + c8 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a0900 * k1[i] + a0905 * k6[i] + a0906 * k7[i] + a0907 * k8[i] + - a0908 * k9[i]) - end - f(k10, tmp, p, t + c9 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a1000 * k1[i] + a1005 * k6[i] + a1006 * k7[i] + a1007 * k8[i] + - a1008 * k9[i] + a1009 * k10[i]) - end - f(k11, tmp, p, t + c10 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a1100 * k1[i] + a1105 * k6[i] + a1106 * k7[i] + a1107 * k8[i] + - a1108 * k9[i] + a1109 * k10[i] + a1110 * k11[i]) - end - f(k12, tmp, p, t + c11 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * (a1200 * k1[i] + a1208 * k9[i] + a1209 * k10[i] + - a1210 * k11[i] + a1211 * k12[i]) - end - f(k13, tmp, p, t + c12 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * (a1300 * k1[i] + a1308 * k9[i] + a1309 * k10[i] + - a1310 * k11[i] + a1311 * k12[i] + a1312 * k13[i]) - end - f(k14, tmp, p, t + c13 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * (a1400 * k1[i] + a1408 * k9[i] + a1409 * k10[i] + - a1410 * k11[i] + a1411 * k12[i] + a1412 * k13[i] + - a1413 * k14[i]) - end - f(k15, tmp, p, t + c14 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * (a1500 * k1[i] + a1508 * k9[i] + a1509 * k10[i] + - a1510 * k11[i] + a1511 * k12[i] + a1512 * k13[i] + - a1513 * k14[i] + a1514 * k15[i]) - end - f(k16, tmp, p, t + c15 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * (a1600 * k1[i] + a1608 * k9[i] + a1609 * k10[i] + - a1610 * k11[i] + a1611 * k12[i] + a1612 * k13[i] + - a1613 * k14[i] + a1614 * k15[i] + a1615 * k16[i]) - end - f(k17, tmp, p, t + c16 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * (a1700 * k1[i] + a1712 * k13[i] + a1713 * k14[i] + - a1714 * k15[i] + a1715 * k16[i] + a1716 * k17[i]) - end - f(k18, tmp, p, t + c17 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * (a1800 * k1[i] + a1812 * k13[i] + a1813 * k14[i] + - a1814 * k15[i] + a1815 * k16[i] + a1816 * k17[i] + - a1817 * k18[i]) - end - f(k19, tmp, p, t + c18 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * (a1900 * k1[i] + a1912 * k13[i] + a1913 * k14[i] + - a1914 * k15[i] + a1915 * k16[i] + a1916 * k17[i] + - a1917 * k18[i] + a1918 * k19[i]) - end - f(k20, tmp, p, t + c19 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * (a2000 * k1[i] + a2012 * k13[i] + a2013 * k14[i] + - a2014 * k15[i] + a2015 * k16[i] + a2016 * k17[i] + - a2017 * k18[i] + a2018 * k19[i] + a2019 * k20[i]) - end - f(k21, tmp, p, t + c20 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * (a2100 * k1[i] + a2112 * k13[i] + a2113 * k14[i] + - a2114 * k15[i] + a2115 * k16[i] + a2116 * k17[i] + - a2117 * k18[i] + a2118 * k19[i] + a2119 * k20[i] + - a2120 * k21[i]) - end - f(k22, tmp, p, t + c21 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * (a2200 * k1[i] + a2212 * k13[i] + a2213 * k14[i] + - a2214 * k15[i] + a2215 * k16[i] + a2216 * k17[i] + - a2217 * k18[i] + a2218 * k19[i] + a2219 * k20[i] + - a2220 * k21[i] + a2221 * k22[i]) - end - f(k23, tmp, p, t + c22 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * (a2300 * k1[i] + a2308 * k9[i] + a2309 * k10[i] + - a2310 * k11[i] + a2311 * k12[i] + a2312 * k13[i] + - a2313 * k14[i] + a2314 * k15[i] + a2315 * k16[i] + - a2316 * k17[i] + a2317 * k18[i] + a2318 * k19[i] + - a2319 * k20[i] + a2320 * k21[i] + a2321 * k22[i] + - a2322 * k23[i]) - end - f(k24, tmp, p, t + c23 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * (a2400 * k1[i] + a2408 * k9[i] + a2409 * k10[i] + - a2410 * k11[i] + a2411 * k12[i] + a2412 * k13[i] + - a2413 * k14[i] + a2414 * k15[i] + a2415 * k16[i] + - a2416 * k17[i] + a2417 * k18[i] + a2418 * k19[i] + - a2419 * k20[i] + a2420 * k21[i] + a2421 * k22[i] + - a2422 * k23[i] + a2423 * k24[i]) - end - f(k25, tmp, p, t + c24 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * (a2500 * k1[i] + a2508 * k9[i] + a2509 * k10[i] + - a2510 * k11[i] + a2511 * k12[i] + a2512 * k13[i] + - a2513 * k14[i] + a2514 * k15[i] + a2515 * k16[i] + - a2516 * k17[i] + a2517 * k18[i] + a2518 * k19[i] + - a2519 * k20[i] + a2520 * k21[i] + a2521 * k22[i] + - a2522 * k23[i] + a2523 * k24[i] + a2524 * k25[i]) - end - f(k26, tmp, p, t + c25 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a2600 * k1[i] + a2605 * k6[i] + a2606 * k7[i] + a2607 * k8[i] + - a2608 * k9[i] + a2609 * k10[i] + a2610 * k11[i] + - a2612 * k13[i] + a2613 * k14[i] + a2614 * k15[i] + - a2615 * k16[i] + a2616 * k17[i] + a2617 * k18[i] + - a2618 * k19[i] + a2619 * k20[i] + a2620 * k21[i] + - a2621 * k22[i] + a2622 * k23[i] + a2623 * k24[i] + - a2624 * k25[i] + a2625 * k26[i]) - end - f(k27, tmp, p, t + c26 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a2700 * k1[i] + a2705 * k6[i] + a2706 * k7[i] + a2707 * k8[i] + - a2708 * k9[i] + a2709 * k10[i] + a2711 * k12[i] + - a2712 * k13[i] + a2713 * k14[i] + a2714 * k15[i] + - a2715 * k16[i] + a2716 * k17[i] + a2717 * k18[i] + - a2718 * k19[i] + a2719 * k20[i] + a2720 * k21[i] + - a2721 * k22[i] + a2722 * k23[i] + a2723 * k24[i] + - a2724 * k25[i] + a2725 * k26[i] + a2726 * k27[i]) - end - f(k28, tmp, p, t + c27 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a2800 * k1[i] + a2805 * k6[i] + a2806 * k7[i] + a2807 * k8[i] + - a2808 * k9[i] + a2810 * k11[i] + a2811 * k12[i] + - a2813 * k14[i] + a2814 * k15[i] + a2815 * k16[i] + - a2823 * k24[i] + a2824 * k25[i] + a2825 * k26[i] + - a2826 * k27[i] + a2827 * k28[i]) - end - f(k29, tmp, p, t + c28 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a2900 * k1[i] + a2904 * k5[i] + a2905 * k6[i] + a2906 * k7[i] + - a2909 * k10[i] + a2910 * k11[i] + a2911 * k12[i] + - a2913 * k14[i] + a2914 * k15[i] + a2915 * k16[i] + - a2923 * k24[i] + a2924 * k25[i] + a2925 * k26[i] + - a2926 * k27[i] + a2927 * k28[i] + a2928 * k29[i]) - end - f(k30, tmp, p, t + c29 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a3000 * k1[i] + a3003 * k4[i] + a3004 * k5[i] + a3005 * k6[i] + - a3007 * k8[i] + a3009 * k10[i] + a3010 * k11[i] + - a3013 * k14[i] + a3014 * k15[i] + a3015 * k16[i] + - a3023 * k24[i] + a3024 * k25[i] + a3025 * k26[i] + - a3027 * k28[i] + a3028 * k29[i] + a3029 * k30[i]) - end - f(k31, tmp, p, t + c30 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a3100 * k1[i] + a3102 * k3[i] + a3103 * k4[i] + a3106 * k7[i] + - a3107 * k8[i] + a3109 * k10[i] + a3110 * k11[i] + - a3113 * k14[i] + a3114 * k15[i] + a3115 * k16[i] + - a3123 * k24[i] + a3124 * k25[i] + a3125 * k26[i] + - a3127 * k28[i] + a3128 * k29[i] + a3129 * k30[i] + - a3130 * k31[i]) - end - f(k32, tmp, p, t + c31 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a3200 * k1[i] + a3201 * k2[i] + a3204 * k5[i] + a3206 * k7[i] + - a3230 * k31[i] + a3231 * k32[i]) - end - f(k33, tmp, p, t + c32 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + dt * (a3300 * k1[i] + a3302 * k3[i] + a3332 * k33[i]) - end - f(k34, tmp, p, t + c33 * dt) - @tight_loop_macros for i in uidx - @inbounds tmp[i] = uprev[i] + - dt * - (a3400 * k1[i] + a3401 * k2[i] + a3402 * k3[i] + a3404 * k5[i] + - a3406 * k7[i] + a3407 * k8[i] + a3409 * k10[i] + - a3410 * k11[i] + a3411 * k12[i] + a3412 * k13[i] + - a3413 * k14[i] + a3414 * k15[i] + a3415 * k16[i] + - a3416 * k17[i] + a3417 * k18[i] + a3418 * k19[i] + - a3419 * k20[i] + a3420 * k21[i] + a3421 * k22[i] + - a3422 * k23[i] + a3423 * k24[i] + a3424 * k25[i] + - a3425 * k26[i] + a3426 * k27[i] + a3427 * k28[i] + - a3428 * k29[i] + a3429 * k30[i] + a3430 * k31[i] + - a3431 * k32[i] + a3432 * k33[i] + a3433 * k34[i]) - end - f(k35, tmp, p, t + c34 * dt) - @tight_loop_macros for i in uidx - @inbounds u[i] = uprev[i] + - dt * - (b1 * k1[i] + b2 * k2[i] + b3 * k3[i] + b5 * k5[i] + b7 * k7[i] + - b8 * k8[i] + b10 * k10[i] + b11 * k11[i] + b12 * k12[i] + - b14 * k14[i] + b15 * k15[i] + b16 * k16[i] + b18 * k18[i] + - b19 * k19[i] + b20 * k20[i] + b21 * k21[i] + b22 * k22[i] + - b23 * k23[i] + b24 * k24[i] + b25 * k25[i] + b26 * k26[i] + - b27 * k27[i] + b28 * k28[i] + b29 * k29[i] + b30 * k30[i] + - b31 * k31[i] + b32 * k32[i] + b33 * k33[i] + b34 * k34[i] + - b35 * k35[i]) - end - integrator.stats.nf += 35 - if integrator.opts.adaptive - @tight_loop_macros for i in uidx - @inbounds tmp[i] = dt * (k2[i] - k34[i]) * adaptiveConst - end - calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - f(integrator.fsallast, u, p, t + dt) # For the interpolation, needs k at the updated point - integrator.stats.nf += 1 -end From 82cc87232e47217a3fa38569f510c65e7ed949bc Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:58:08 -0400 Subject: [PATCH 14/71] Delete src/perform_step/low_storage_rk_perform_step.jl --- .../low_storage_rk_perform_step.jl | 842 ------------------ 1 file changed, 842 deletions(-) delete mode 100644 src/perform_step/low_storage_rk_perform_step.jl diff --git a/src/perform_step/low_storage_rk_perform_step.jl b/src/perform_step/low_storage_rk_perform_step.jl deleted file mode 100644 index 4ee07826a7..0000000000 --- a/src/perform_step/low_storage_rk_perform_step.jl +++ /dev/null @@ -1,842 +0,0 @@ - -# 2N low storage methods -function initialize!(integrator, cache::LowStorageRK2NConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::LowStorageRK2NConstantCache, - repeat_step = false) - @unpack t, dt, u, f, p = integrator - @unpack A2end, B1, B2end, c2end = cache - - # u1 - tmp = dt * integrator.fsalfirst - u = u + B1 * tmp - - # other stages - for i in eachindex(A2end) - k = f(u, p, t + c2end[i] * dt) - integrator.stats.nf += 1 - tmp = A2end[i] * tmp + dt * k - u = u + B2end[i] * tmp - end - - integrator.stats.nf += 1 - integrator.k[1] = integrator.fsalfirst - integrator.fsalfirst = f(u, p, t + dt) # For interpolation, then FSAL'd - integrator.u = u -end - -function initialize!(integrator, cache::LowStorageRK2NCache) - @unpack k, tmp, williamson_condition = cache - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = k - integrator.fsalfirst = k # used for get_du - integrator.fsallast = k - integrator.f(k, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation - integrator.stats.nf += 1 -end - -@muladd function perform_step!(integrator, cache::LowStorageRK2NCache, repeat_step = false) - @unpack t, dt, u, f, p = integrator - @unpack k, tmp, williamson_condition, stage_limiter!, step_limiter!, thread = cache - @unpack A2end, B1, B2end, c2end = cache.tab - - # u1 - f(k, u, p, t) - integrator.stats.nf += 1 - @.. broadcast=false thread=thread tmp=dt * k - @.. broadcast=false thread=thread u=u + B1 * tmp - # other stages - for i in eachindex(A2end) - if williamson_condition - f(ArrayFuse(tmp, u, (A2end[i], dt, B2end[i])), u, p, t + c2end[i] * dt) - else - @.. broadcast=false thread=thread tmp=A2end[i] * tmp - stage_limiter!(u, integrator, p, t + c2end[i] * dt) - f(k, u, p, t + c2end[i] * dt) - @.. broadcast=false thread=thread tmp=tmp + dt * k - @.. broadcast=false thread=thread u=u + B2end[i] * tmp - end - integrator.stats.nf += 1 - end - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) -end - -# 2C low storage methods -function initialize!(integrator, cache::LowStorageRK2CConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::LowStorageRK2CConstantCache, - repeat_step = false) - @unpack t, dt, u, f, p = integrator - @unpack A2end, B1, B2end, c2end = cache - - # u1 - k = integrator.fsalfirst = f(u, p, t) - integrator.k[1] = integrator.fsalfirst - integrator.stats.nf += 1 - u = u + B1 * dt * k - - # other stages - for i in eachindex(A2end) - tmp = u + A2end[i] * dt * k - k = f(tmp, p, t + c2end[i] * dt) - integrator.stats.nf += 1 - u = u + B2end[i] * dt * k - end - - integrator.u = u -end - -function initialize!(integrator, cache::LowStorageRK2CCache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation - integrator.stats.nf += 1 -end - -@muladd function perform_step!(integrator, cache::LowStorageRK2CCache, repeat_step = false) - @unpack t, dt, u, f, p = integrator - @unpack k, fsalfirst, tmp, stage_limiter!, step_limiter!, thread = cache - @unpack A2end, B1, B2end, c2end = cache.tab - - # u1 - @.. broadcast=false thread=thread k=integrator.fsalfirst - @.. broadcast=false thread=thread u=u + B1 * dt * k - - # other stages - for i in eachindex(A2end) - @.. broadcast=false thread=thread tmp=u + A2end[i] * dt * k - f(k, tmp, p, t + c2end[i] * dt) - integrator.stats.nf += 1 - @.. broadcast=false thread=thread u=u + B2end[i] * dt * k - end - - f(k, u, p, t + dt) - integrator.stats.nf += 1 -end - -# 3S low storage methods -function initialize!(integrator, cache::LowStorageRK3SConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::LowStorageRK3SConstantCache, - repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end = cache - - # u1 - tmp = u - u = tmp + β1 * dt * integrator.fsalfirst - - # other stages - for i in eachindex(γ12end) - k = f(u, p, t + c2end[i] * dt) - integrator.stats.nf += 1 - tmp = tmp + δ2end[i] * u - u = γ12end[i] * u + γ22end[i] * tmp + γ32end[i] * uprev + β2end[i] * dt * k - end - - integrator.fsallast = f(u, p, t + dt) # For interpolation, then FSAL'd - integrator.stats.nf += 1 - integrator.k[1] = integrator.fsalfirst - integrator.u = u -end - -function initialize!(integrator, cache::LowStorageRK3SCache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation - integrator.stats.nf += 1 -end - -@muladd function perform_step!(integrator, cache::LowStorageRK3SCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, fsalfirst, tmp, stage_limiter!, step_limiter!, thread = cache - @unpack γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end = cache.tab - - # u1 - @.. broadcast=false thread=thread tmp=u - @.. broadcast=false thread=thread u=tmp + β1 * dt * integrator.fsalfirst - - # other stages - for i in eachindex(γ12end) - f(k, u, p, t + c2end[i] * dt) - integrator.stats.nf += 1 - @.. broadcast=false thread=thread tmp=tmp + δ2end[i] * u - @.. broadcast=false thread=thread u=γ12end[i] * u + γ22end[i] * tmp + - γ32end[i] * uprev + - β2end[i] * dt * k - end - - f(k, u, p, t + dt) - integrator.stats.nf += 1 -end - -# 3S+ low storage methods: 3S methods adding another memory location for the embedded method (non-FSAL version) -function initialize!(integrator, cache::LowStorageRK3SpConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::LowStorageRK3SpConstantCache, - repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end, bhat1, bhat2end = cache - - # u1 - integrator.fsalfirst = f(uprev, p, t) - integrator.stats.nf += 1 - integrator.k[1] = integrator.fsalfirst - tmp = uprev - u = tmp + β1 * dt * integrator.fsalfirst - if integrator.opts.adaptive - utilde = bhat1 * dt * integrator.fsalfirst - end - - # other stages - for i in eachindex(γ12end) - k = f(u, p, t + c2end[i] * dt) - integrator.stats.nf += 1 - tmp = tmp + δ2end[i] * u - u = γ12end[i] * u + γ22end[i] * tmp + γ32end[i] * uprev + β2end[i] * dt * k - if integrator.opts.adaptive - utilde = utilde + bhat2end[i] * dt * k - end - end - - if integrator.opts.adaptive - atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - - integrator.u = u -end - -function initialize!(integrator, cache::LowStorageRK3SpCache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::LowStorageRK3SpCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, tmp, utilde, atmp, stage_limiter!, step_limiter!, thread = cache - @unpack γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end, bhat1, bhat2end = cache.tab - - # u1 - f(integrator.fsalfirst, uprev, p, t) - integrator.stats.nf += 1 - @.. broadcast=false thread=thread tmp=uprev - @.. broadcast=false thread=thread u=tmp + β1 * dt * integrator.fsalfirst - if integrator.opts.adaptive - @.. broadcast=false thread=thread utilde=bhat1 * dt * integrator.fsalfirst - end - - # other stages - for i in eachindex(γ12end) - stage_limiter!(u, integrator, p, t + c2end[i] * dt) - f(k, u, p, t + c2end[i] * dt) - integrator.stats.nf += 1 - @.. broadcast=false thread=thread tmp=tmp + δ2end[i] * u - @.. broadcast=false thread=thread u=γ12end[i] * u + γ22end[i] * tmp + - γ32end[i] * uprev + β2end[i] * dt * k - if integrator.opts.adaptive - @.. broadcast=false thread=thread utilde=utilde + bhat2end[i] * dt * k - end - end - - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - - if integrator.opts.adaptive - calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t, - thread) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -# 3S+ FSAL low storage methods: 3S methods adding another memory location for the embedded method (FSAL version) -function initialize!(integrator, cache::LowStorageRK3SpFSALConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -@muladd function perform_step!(integrator, cache::LowStorageRK3SpFSALConstantCache, - repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end, bhat1, bhat2end, bhatfsal = cache - - # u1 - tmp = uprev - u = tmp + β1 * dt * integrator.fsalfirst - if integrator.opts.adaptive - utilde = bhat1 * dt * integrator.fsalfirst - end - - # other stages - for i in eachindex(γ12end) - k = f(u, p, t + c2end[i] * dt) - integrator.stats.nf += 1 - tmp = tmp + δ2end[i] * u - u = γ12end[i] * u + γ22end[i] * tmp + γ32end[i] * uprev + β2end[i] * dt * k - if integrator.opts.adaptive - utilde = utilde + bhat2end[i] * dt * k - end - end - - # FSAL - integrator.fsallast = f(u, p, t + dt) - integrator.stats.nf += 1 - - if integrator.opts.adaptive - utilde = utilde + bhatfsal * dt * integrator.fsallast - atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.u = u -end - -function initialize!(integrator, cache::LowStorageRK3SpFSALCache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 2 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation - integrator.stats.nf += 1 -end - -@muladd function perform_step!(integrator, cache::LowStorageRK3SpFSALCache, - repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, tmp, utilde, atmp, stage_limiter!, step_limiter!, thread = cache - @unpack γ12end, γ22end, γ32end, δ2end, β1, β2end, c2end, bhat1, bhat2end, bhatfsal = cache.tab - - # u1 - @.. broadcast=false thread=thread tmp=uprev - @.. broadcast=false thread=thread u=tmp + β1 * dt * integrator.fsalfirst - if integrator.opts.adaptive - @.. broadcast=false thread=thread utilde=bhat1 * dt * integrator.fsalfirst - end - - # other stages - for i in eachindex(γ12end) - stage_limiter!(u, integrator, p, t + c2end[i] * dt) - f(k, u, p, t + c2end[i] * dt) - integrator.stats.nf += 1 - @.. broadcast=false thread=thread tmp=tmp + δ2end[i] * u - @.. broadcast=false thread=thread u=γ12end[i] * u + γ22end[i] * tmp + - γ32end[i] * uprev + β2end[i] * dt * k - if integrator.opts.adaptive - @.. broadcast=false thread=thread utilde=utilde + bhat2end[i] * dt * k - end - end - - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - - # FSAL - f(k, u, p, t + dt) - integrator.stats.nf += 1 - - if integrator.opts.adaptive - @.. broadcast=false thread=thread utilde=utilde + bhatfsal * dt * k - calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t, - thread) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -# 2R+ low storage methods -function initialize!(integrator, cache::LowStorageRK2RPConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::LowStorageRK2RPConstantCache, - repeat_step = false) - @unpack t, dt, u, uprev, f, fsalfirst, p = integrator - @unpack Aᵢ, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ = cache - - k = fsalfirst - integrator.opts.adaptive && (tmp = zero(uprev)) - - #stages 1 to s-1 - for i in eachindex(Aᵢ) - integrator.opts.adaptive && (tmp = tmp + (Bᵢ[i] - B̂ᵢ[i]) * dt * k) - gprev = u + Aᵢ[i] * dt * k - u = u + Bᵢ[i] * dt * k - k = f(gprev, p, t + Cᵢ[i] * dt) - integrator.stats.nf += 1 - end - - #last stage - integrator.opts.adaptive && (tmp = tmp + (Bₗ - B̂ₗ) * dt * k) - u = u + Bₗ * dt * k - - #Error estimate - if integrator.opts.adaptive - atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - - integrator.k[1] = integrator.fsalfirst - integrator.fsallast = f(u, p, t + dt) # For interpolation, then FSAL'd - integrator.stats.nf += 1 - integrator.u = u -end - -function initialize!(integrator, cache::LowStorageRK2RPCache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) - integrator.stats.nf += 1 -end - -@muladd function perform_step!(integrator, cache::LowStorageRK2RPCache, repeat_step = false) - @unpack t, dt, u, uprev, f, fsalfirst, p = integrator - @unpack k, gprev, tmp, atmp, stage_limiter!, step_limiter!, thread = cache - @unpack Aᵢ, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ = cache.tab - - @.. broadcast=false thread=thread k=fsalfirst - integrator.opts.adaptive && (@.. broadcast=false tmp=zero(uprev)) - - #stages 1 to s-1 - for i in eachindex(Aᵢ) - integrator.opts.adaptive && - (@.. broadcast=false thread=thread tmp=tmp + (Bᵢ[i] - B̂ᵢ[i]) * dt * k) - @.. broadcast=false thread=thread gprev=u + Aᵢ[i] * dt * k - @.. broadcast=false thread=thread u=u + Bᵢ[i] * dt * k - f(k, gprev, p, t + Cᵢ[i] * dt) - integrator.stats.nf += 1 - end - - #last stage - integrator.opts.adaptive && - (@.. broadcast=false thread=thread tmp=tmp + (Bₗ - B̂ₗ) * dt * k) - @.. broadcast=false thread=thread u=u + Bₗ * dt * k - - #Error estimate - if integrator.opts.adaptive - calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t, - thread) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - - f(k, u, p, t + dt) - integrator.stats.nf += 1 -end - -# 3R+ low storage methods -function initialize!(integrator, cache::LowStorageRK3RPConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::LowStorageRK3RPConstantCache, - repeat_step = false) - @unpack t, dt, u, uprev, f, fsalfirst, p = integrator - @unpack Aᵢ₁, Aᵢ₂, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ = cache - - fᵢ₋₂ = zero(fsalfirst) - k = fsalfirst - uᵢ₋₁ = uprev - uᵢ₋₂ = uprev - integrator.opts.adaptive && (tmp = zero(uprev)) - - #stages 1 to s-1 - for i in eachindex(Aᵢ₁) - integrator.opts.adaptive && (tmp = tmp + (Bᵢ[i] - B̂ᵢ[i]) * dt * k) - gprev = uᵢ₋₂ + (Aᵢ₁[i] * k + Aᵢ₂[i] * fᵢ₋₂) * dt - u = u + Bᵢ[i] * dt * k - fᵢ₋₂ = k - uᵢ₋₂ = uᵢ₋₁ - uᵢ₋₁ = u - k = f(gprev, p, t + Cᵢ[i] * dt) - integrator.stats.nf += 1 - end - - #last stage - integrator.opts.adaptive && (tmp = tmp + (Bₗ - B̂ₗ) * dt * k) - u = u + Bₗ * dt * k - - #Error estimate - if integrator.opts.adaptive - atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - - integrator.k[1] = integrator.fsalfirst - integrator.fsallast = f(u, p, t + dt) # For interpolation, then FSAL'd - integrator.stats.nf += 1 - integrator.u = u -end - -function initialize!(integrator, cache::LowStorageRK3RPCache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) - integrator.stats.nf += 1 -end - -@muladd function perform_step!(integrator, cache::LowStorageRK3RPCache, repeat_step = false) - @unpack t, dt, u, uprev, f, fsalfirst, p = integrator - @unpack k, uᵢ₋₁, uᵢ₋₂, gprev, fᵢ₋₂, tmp, atmp, stage_limiter!, step_limiter!, thread = cache - @unpack Aᵢ₁, Aᵢ₂, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ = cache.tab - - @.. broadcast=false thread=thread fᵢ₋₂=zero(fsalfirst) - @.. broadcast=false thread=thread k=fsalfirst - integrator.opts.adaptive && (@.. broadcast=false thread=thread tmp=zero(uprev)) - @.. broadcast=false thread=thread uᵢ₋₁=uprev - @.. broadcast=false thread=thread uᵢ₋₂=uprev - - #stages 1 to s-1 - for i in eachindex(Aᵢ₁) - integrator.opts.adaptive && - (@.. broadcast=false thread=thread tmp=tmp + (Bᵢ[i] - B̂ᵢ[i]) * dt * k) - @.. broadcast=false thread=thread gprev=uᵢ₋₂ + (Aᵢ₁[i] * k + Aᵢ₂[i] * fᵢ₋₂) * dt - @.. broadcast=false thread=thread u=u + Bᵢ[i] * dt * k - @.. broadcast=false thread=thread fᵢ₋₂=k - @.. broadcast=false thread=thread uᵢ₋₂=uᵢ₋₁ - @.. broadcast=false thread=thread uᵢ₋₁=u - f(k, gprev, p, t + Cᵢ[i] * dt) - integrator.stats.nf += 1 - end - - #last stage - integrator.opts.adaptive && - (@.. broadcast=false thread=thread tmp=tmp + (Bₗ - B̂ₗ) * dt * k) - @.. broadcast=false thread=thread u=u + Bₗ * dt * k - - #Error estimate - if integrator.opts.adaptive - calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t, - thread) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - - f(k, u, p, t + dt) - integrator.stats.nf += 1 -end - -# 4R+ low storage methods -function initialize!(integrator, cache::LowStorageRK4RPConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::LowStorageRK4RPConstantCache, - repeat_step = false) - @unpack t, dt, u, uprev, f, fsalfirst, p = integrator - @unpack Aᵢ₁, Aᵢ₂, Aᵢ₃, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ = cache - - fᵢ₋₂ = zero(fsalfirst) - fᵢ₋₃ = zero(fsalfirst) - k = fsalfirst - uᵢ₋₁ = uprev - uᵢ₋₂ = uprev - uᵢ₋₃ = uprev - integrator.opts.adaptive && (tmp = zero(uprev)) - - #stages 1 to s-1 - for i in eachindex(Aᵢ₁) - integrator.opts.adaptive && (tmp = tmp + (Bᵢ[i] - B̂ᵢ[i]) * dt * k) - gprev = uᵢ₋₃ + (Aᵢ₁[i] * k + Aᵢ₂[i] * fᵢ₋₂ + Aᵢ₃[i] * fᵢ₋₃) * dt - u = u + Bᵢ[i] * dt * k - fᵢ₋₃ = fᵢ₋₂ - fᵢ₋₂ = k - uᵢ₋₃ = uᵢ₋₂ - uᵢ₋₂ = uᵢ₋₁ - uᵢ₋₁ = u - k = f(gprev, p, t + Cᵢ[i] * dt) - integrator.stats.nf += 1 - end - - #last stage - integrator.opts.adaptive && (tmp = tmp + (Bₗ - B̂ₗ) * dt * k) - u = u + Bₗ * dt * k - - #Error estimate - if integrator.opts.adaptive - atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - - integrator.k[1] = integrator.fsalfirst - integrator.fsallast = f(u, p, t + dt) # For interpolation, then FSAL'd - integrator.stats.nf += 1 - integrator.u = u -end - -function initialize!(integrator, cache::LowStorageRK4RPCache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) - integrator.stats.nf += 1 -end - -@muladd function perform_step!(integrator, cache::LowStorageRK4RPCache, repeat_step = false) - @unpack t, dt, u, uprev, f, fsalfirst, p = integrator - @unpack k, uᵢ₋₁, uᵢ₋₂, uᵢ₋₃, gprev, fᵢ₋₂, fᵢ₋₃, tmp, atmp, stage_limiter!, step_limiter!, thread = cache - @unpack Aᵢ₁, Aᵢ₂, Aᵢ₃, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ = cache.tab - - @.. broadcast=false thread=thread fᵢ₋₂=zero(fsalfirst) - @.. broadcast=false thread=thread fᵢ₋₃=zero(fsalfirst) - @.. broadcast=false thread=thread k=fsalfirst - integrator.opts.adaptive && (@.. broadcast=false thread=thread tmp=zero(uprev)) - @.. broadcast=false thread=thread uᵢ₋₁=uprev - @.. broadcast=false thread=thread uᵢ₋₂=uprev - @.. broadcast=false thread=thread uᵢ₋₃=uprev - - #stages 1 to s-1 - for i in eachindex(Aᵢ₁) - integrator.opts.adaptive && - (@.. broadcast=false thread=thread tmp=tmp + (Bᵢ[i] - B̂ᵢ[i]) * dt * k) - @.. broadcast=false thread=thread gprev=uᵢ₋₃ + - (Aᵢ₁[i] * k + Aᵢ₂[i] * fᵢ₋₂ + - Aᵢ₃[i] * fᵢ₋₃) * - dt - @.. broadcast=false thread=thread u=u + Bᵢ[i] * dt * k - @.. broadcast=false thread=thread fᵢ₋₃=fᵢ₋₂ - @.. broadcast=false thread=thread fᵢ₋₂=k - @.. broadcast=false thread=thread uᵢ₋₃=uᵢ₋₂ - @.. broadcast=false thread=thread uᵢ₋₂=uᵢ₋₁ - @.. broadcast=false thread=thread uᵢ₋₁=u - f(k, gprev, p, t + Cᵢ[i] * dt) - integrator.stats.nf += 1 - end - - #last stage - integrator.opts.adaptive && - (@.. broadcast=false thread=thread tmp=tmp + (Bₗ - B̂ₗ) * dt * k) - @.. broadcast=false thread=thread u=u + Bₗ * dt * k - - #Error estimate - if integrator.opts.adaptive - calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t, - thread) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - - f(k, u, p, t + dt) - integrator.stats.nf += 1 -end - -# 5R+ low storage methods -function initialize!(integrator, cache::LowStorageRK5RPConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::LowStorageRK5RPConstantCache, - repeat_step = false) - @unpack t, dt, u, uprev, f, fsalfirst, p = integrator - @unpack Aᵢ₁, Aᵢ₂, Aᵢ₃, Aᵢ₄, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ = cache - - fᵢ₋₂ = zero(fsalfirst) - fᵢ₋₃ = zero(fsalfirst) - fᵢ₋₄ = zero(fsalfirst) - k = fsalfirst - uᵢ₋₁ = uprev - uᵢ₋₂ = uprev - uᵢ₋₃ = uprev - uᵢ₋₄ = uprev - integrator.opts.adaptive && (tmp = zero(uprev)) - - #stages 1 to s-1 - for i in eachindex(Aᵢ₁) - integrator.opts.adaptive && (tmp = tmp + (Bᵢ[i] - B̂ᵢ[i]) * dt * k) - gprev = uᵢ₋₄ + (Aᵢ₁[i] * k + Aᵢ₂[i] * fᵢ₋₂ + Aᵢ₃[i] * fᵢ₋₃ + Aᵢ₄[i] * fᵢ₋₄) * dt - u = u + Bᵢ[i] * dt * k - fᵢ₋₄ = fᵢ₋₃ - fᵢ₋₃ = fᵢ₋₂ - fᵢ₋₂ = k - uᵢ₋₄ = uᵢ₋₃ - uᵢ₋₃ = uᵢ₋₂ - uᵢ₋₂ = uᵢ₋₁ - uᵢ₋₁ = u - k = f(gprev, p, t + Cᵢ[i] * dt) - integrator.stats.nf += 1 - end - - #last stage - integrator.opts.adaptive && (tmp = tmp + (Bₗ - B̂ₗ) * dt * k) - u = u + Bₗ * dt * k - - #Error estimate - if integrator.opts.adaptive - atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - - integrator.k[1] = integrator.fsalfirst - integrator.fsallast = f(u, p, t + dt) # For interpolation, then FSAL'd - integrator.stats.nf += 1 - integrator.u = u -end - -function initialize!(integrator, cache::LowStorageRK5RPCache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) - integrator.stats.nf += 1 -end - -@muladd function perform_step!(integrator, cache::LowStorageRK5RPCache, repeat_step = false) - @unpack t, dt, u, uprev, f, fsalfirst, p = integrator - @unpack k, uᵢ₋₁, uᵢ₋₂, uᵢ₋₃, uᵢ₋₄, gprev, fᵢ₋₂, fᵢ₋₃, fᵢ₋₄, tmp, atmp, stage_limiter!, step_limiter!, thread = cache - @unpack Aᵢ₁, Aᵢ₂, Aᵢ₃, Aᵢ₄, Bₗ, B̂ₗ, Bᵢ, B̂ᵢ, Cᵢ = cache.tab - - @.. broadcast=false thread=thread fᵢ₋₂=zero(fsalfirst) - @.. broadcast=false thread=thread fᵢ₋₃=zero(fsalfirst) - @.. broadcast=false thread=thread fᵢ₋₄=zero(fsalfirst) - @.. broadcast=false thread=thread k=fsalfirst - integrator.opts.adaptive && (@.. broadcast=false thread=thread tmp=zero(uprev)) - @.. broadcast=false thread=thread uᵢ₋₁=uprev - @.. broadcast=false thread=thread uᵢ₋₂=uprev - @.. broadcast=false thread=thread uᵢ₋₃=uprev - @.. broadcast=false thread=thread uᵢ₋₄=uprev - - #stages 1 to s-1 - for i in eachindex(Aᵢ₁) - integrator.opts.adaptive && - (@.. broadcast=false thread=thread tmp=tmp + (Bᵢ[i] - B̂ᵢ[i]) * dt * k) - @.. broadcast=false thread=thread gprev=uᵢ₋₄ + - (Aᵢ₁[i] * k + Aᵢ₂[i] * fᵢ₋₂ + - Aᵢ₃[i] * fᵢ₋₃ + - Aᵢ₄[i] * fᵢ₋₄) * dt - @.. broadcast=false thread=thread u=u + Bᵢ[i] * dt * k - @.. broadcast=false thread=thread fᵢ₋₄=fᵢ₋₃ - @.. broadcast=false thread=thread fᵢ₋₃=fᵢ₋₂ - @.. broadcast=false thread=thread fᵢ₋₂=k - @.. broadcast=false thread=thread uᵢ₋₄=uᵢ₋₃ - @.. broadcast=false thread=thread uᵢ₋₃=uᵢ₋₂ - @.. broadcast=false thread=thread uᵢ₋₂=uᵢ₋₁ - @.. broadcast=false thread=thread uᵢ₋₁=u - f(k, gprev, p, t + Cᵢ[i] * dt) - integrator.stats.nf += 1 - end - - #last stage - integrator.opts.adaptive && - (@.. broadcast=false thread=thread tmp=tmp + (Bₗ - B̂ₗ) * dt * k) - @.. broadcast=false thread=thread u=u + Bₗ * dt * k - - #Error estimate - if integrator.opts.adaptive - calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t, - thread) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - - f(k, u, p, t + dt) - integrator.stats.nf += 1 -end From 7d751641053f5df5afd7d61a569d03b97e41ae14 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:58:23 -0400 Subject: [PATCH 15/71] Delete src/perform_step/rkc_perform_step.jl --- src/perform_step/rkc_perform_step.jl | 1296 -------------------------- 1 file changed, 1296 deletions(-) delete mode 100644 src/perform_step/rkc_perform_step.jl diff --git a/src/perform_step/rkc_perform_step.jl b/src/perform_step/rkc_perform_step.jl deleted file mode 100644 index d96ce34b59..0000000000 --- a/src/perform_step/rkc_perform_step.jl +++ /dev/null @@ -1,1296 +0,0 @@ -function initialize!(integrator, cache::ROCK2ConstantCache) - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - alg = unwrap_alg(integrator, true) - cache.max_stage = (alg.max_stages < 1 || alg.max_stages > 200) ? 200 : alg.max_stages - cache.min_stage = (alg.min_stages > cache.max_stage) ? cache.max_stage : alg.min_stages - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -@muladd function perform_step!(integrator, cache::ROCK2ConstantCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p, fsalfirst = integrator - @unpack ms, fp1, fp2, recf = cache - alg = unwrap_alg(integrator, true) - alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) - # The the number of degree for Chebyshev polynomial - mdeg = Int(floor(sqrt((1.5 + abs(dt) * integrator.eigen_est) / 0.811) + 1)) - mdeg = min(max(mdeg, cache.min_stage), cache.max_stage) - cache.mdeg = max(mdeg, 3) - 2 - choosedeg!(cache) - # recurrence - # for the first stage - tᵢ₋₁ = t + dt * recf[cache.start] - tᵢ₋₂ = t + dt * recf[cache.start] - tᵢ₋₃ = t - uᵢ₋₂ = copy(uprev) - uᵢ₋₁ = uprev + (dt * recf[cache.start]) * fsalfirst - cache.mdeg < 2 && (u = uᵢ₋₁) - # for the second to the ms[cache.mdeg] th stages - for i in 2:(cache.mdeg) - μ, κ = recf[cache.start + (i - 2) * 2 + 1], recf[cache.start + (i - 2) * 2 + 2] - ν = -1 - κ - u = f(uᵢ₋₁, p, tᵢ₋₁) - tᵢ₋₁ = dt * μ - ν * tᵢ₋₂ - κ * tᵢ₋₃ - u = (dt * μ) * u - ν * uᵢ₋₁ - κ * uᵢ₋₂ - i < cache.mdeg && (uᵢ₋₂ = uᵢ₋₁; - uᵢ₋₁ = u) - tᵢ₋₃ = tᵢ₋₂ - tᵢ₋₂ = tᵢ₋₁ - end # end if - # two-stage finishing procedure. - δt₁ = dt * fp1[cache.deg_index] - δt₂ = dt * fp2[cache.deg_index] - uᵢ₋₂ = f(u, p, tᵢ₋₁) - integrator.stats.nf += 1 - uᵢ₋₁ = u + δt₁ * uᵢ₋₂ - tᵢ₋₁ += δt₁ - u = f(uᵢ₋₁, p, tᵢ₋₁) - integrator.stats.nf += 1 - - if integrator.opts.adaptive - tmp = δt₂ * (u - uᵢ₋₂) - u = uᵢ₋₁ + δt₁ * u + tmp - else - u = uᵢ₋₁ + δt₁ * u + δt₂ * (u - uᵢ₋₂) - end - # error estimate - if integrator.opts.adaptive - atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast = f(u, p, t + dt) - integrator.stats.nf += 1 - integrator.u = u -end - -function initialize!(integrator, cache::ROCK2Cache) - integrator.kshortsize = 2 - resize!(integrator.k, integrator.kshortsize) - integrator.fsalfirst = cache.fsalfirst # done by pointers, no copying - integrator.fsallast = cache.k - alg = unwrap_alg(integrator, true) - cache.constantcache.max_stage = (alg.max_stages < 1 || alg.max_stages > 200) ? 200 : - alg.max_stages - cache.constantcache.min_stage = (alg.min_stages > cache.constantcache.max_stage) ? - cache.constantcache.max_stage : alg.min_stages - - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 -end - -@muladd function perform_step!(integrator, cache::ROCK2Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p, fsalfirst = integrator - @unpack k, tmp, uᵢ₋₂, uᵢ₋₁, atmp = cache - @unpack ms, fp1, fp2, recf = cache.constantcache - ccache = cache.constantcache - alg = unwrap_alg(integrator, true) - alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) - # The the number of degree for Chebyshev polynomial - mdeg = Int(floor(sqrt((1.5 + abs(dt) * integrator.eigen_est) / 0.811) + 1)) - mdeg = min(max(mdeg, ccache.min_stage), ccache.max_stage) - ccache.mdeg = max(mdeg, 3) - 2 - choosedeg!(cache) - # recurrence - # for the first stage - tᵢ₋₁ = t + dt * recf[ccache.start] - tᵢ₋₂ = t + dt * recf[ccache.start] - tᵢ₋₃ = t - @.. broadcast=false uᵢ₋₂=uprev - @.. broadcast=false uᵢ₋₁=uprev + (dt * recf[ccache.start]) * fsalfirst - ccache.mdeg < 2 && (@.. broadcast=false u=uᵢ₋₁) - # for the second to the ms[ccache.mdeg] th stages - for i in 2:(ccache.mdeg) - μ, κ = recf[ccache.start + (i - 2) * 2 + 1], recf[ccache.start + (i - 2) * 2 + 2] - ν = -1 - κ - f(k, uᵢ₋₁, p, tᵢ₋₁) - tᵢ₋₁ = dt * μ - ν * tᵢ₋₂ - κ * tᵢ₋₃ - @.. broadcast=false u=(dt * μ) * k - ν * uᵢ₋₁ - κ * uᵢ₋₂ - if i < ccache.mdeg - @.. broadcast=false uᵢ₋₂=uᵢ₋₁ - @.. broadcast=false uᵢ₋₁=u - end - tᵢ₋₃ = tᵢ₋₂ - tᵢ₋₂ = tᵢ₋₁ - end # end if - # two-stage finishing procedure. - δt₁ = dt * fp1[ccache.deg_index] - δt₂ = dt * fp2[ccache.deg_index] - f(k, u, p, tᵢ₋₁) - integrator.stats.nf += 1 - @.. broadcast=false uᵢ₋₁=u + δt₁ * k - if integrator.opts.adaptive - @.. broadcast=false tmp=-δt₂ * k - else - @.. broadcast=false u=-δt₂ * k - end - c = DiffEqBase.value(sign(δt₁)) * integrator.opts.internalnorm(δt₁, t) - tᵢ₋₁ += c - f(k, uᵢ₋₁, p, tᵢ₋₁) - integrator.stats.nf += 1 - - if integrator.opts.adaptive - @.. broadcast=false tmp+=δt₂ * k - @.. broadcast=false u=uᵢ₋₁ + δt₁ * k + tmp - else - @.. broadcast=false u+=uᵢ₋₁ + (δt₁ + δt₂) * k - end - - # error estimate - if integrator.opts.adaptive - calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.k[1] = integrator.fsalfirst - f(integrator.fsallast, u, p, t + dt) - integrator.stats.nf += 1 - integrator.k[2] = integrator.fsallast - integrator.u = u -end - -function initialize!(integrator, cache::ROCK4ConstantCache) - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - alg = unwrap_alg(integrator, true) - cache.max_stage = (alg.max_stages < 1 || alg.max_stages > 152) ? 152 : alg.max_stages - cache.min_stage = (alg.min_stages > cache.max_stage) ? cache.max_stage : alg.min_stages - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -@muladd function perform_step!(integrator, cache::ROCK4ConstantCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p, fsalfirst = integrator - @unpack ms, fpa, fpb, fpbe, recf = cache - alg = unwrap_alg(integrator, true) - alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) - # The the number of degree for Chebyshev polynomial - mdeg = Int(floor(sqrt((3 + abs(dt) * integrator.eigen_est) / 0.353) + 1)) - mdeg = min(max(mdeg, cache.min_stage), cache.max_stage) - cache.mdeg = max(mdeg, 5) - 4 - choosedeg!(cache) - # recurrence - # for the first stage - tᵢ₋₁ = t + dt * recf[cache.start] - tᵢ₋₂ = t + dt * recf[cache.start] - tᵢ₋₃ = t - uᵢ₋₂ = copy(uprev) - uᵢ₋₁ = uprev + (dt * recf[cache.start]) * fsalfirst - cache.mdeg < 2 && (u = uᵢ₋₁) - # for the second to the cache.mdeg th stages - for i in 2:(cache.mdeg) - μ, κ = recf[cache.start + (i - 2) * 2 + 1], recf[cache.start + (i - 2) * 2 + 2] - ν = -1 - κ - u = f(uᵢ₋₁, p, tᵢ₋₁) - tᵢ₋₁ = dt * μ - ν * tᵢ₋₂ - κ * tᵢ₋₃ - u = (dt * μ) * u - ν * uᵢ₋₁ - κ * uᵢ₋₂ - i < cache.mdeg && (uᵢ₋₂ = uᵢ₋₁; - uᵢ₋₁ = u) - tᵢ₋₃ = tᵢ₋₂ - tᵢ₋₂ = tᵢ₋₁ - end - - # These constants correspond to the Buther Tableau coefficients of explicit RK methods - a₂₁ = dt * fpa[cache.deg_index][1] - a₃₁ = dt * fpa[cache.deg_index][2] - a₃₂ = dt * fpa[cache.deg_index][3] - a₄₁ = dt * fpa[cache.deg_index][4] - a₄₂ = dt * fpa[cache.deg_index][5] - a₄₃ = dt * fpa[cache.deg_index][6] - B₁ = dt * fpb[cache.deg_index][1] - B₂ = dt * fpb[cache.deg_index][2] - B₃ = dt * fpb[cache.deg_index][3] - B₄ = dt * fpb[cache.deg_index][4] - # coefficients of embedded method for error estimation - B̂₁ = dt * (fpbe[cache.deg_index][1] - fpb[cache.deg_index][1]) - B̂₂ = dt * (fpbe[cache.deg_index][2] - fpb[cache.deg_index][2]) - B̂₃ = dt * (fpbe[cache.deg_index][3] - fpb[cache.deg_index][3]) - B̂₄ = dt * (fpbe[cache.deg_index][4] - fpb[cache.deg_index][4]) - B̂₅ = dt * fpbe[cache.deg_index][5] - - # 4-stage finishing procedure. - # Stage-1 - uᵢ₋₁ = f(u, p, tᵢ₋₁) - integrator.stats.nf += 1 - uᵢ₋₂ = u + a₃₁ * uᵢ₋₁ - uᵢ₋₃ = u + a₄₁ * uᵢ₋₁ - u += B₁ * uᵢ₋₁ - integrator.opts.adaptive && (tmp = B̂₁ * uᵢ₋₁) - uᵢ₋₁ = u + (a₂₁ - B₁) * uᵢ₋₁ - - # Stage-2 - c₂ = a₂₁ - _c₂ = DiffEqBase.value(sign(c₂)) * integrator.opts.internalnorm(c₂, t) - tᵢ₋₂ = tᵢ₋₁ + _c₂ - uᵢ₋₁ = f(uᵢ₋₁, p, tᵢ₋₂) - integrator.stats.nf += 1 - uᵢ₋₂ += a₃₂ * uᵢ₋₁ - uᵢ₋₃ += a₄₂ * uᵢ₋₁ - u += B₂ * uᵢ₋₁ - integrator.opts.adaptive && (tmp += B̂₂ * uᵢ₋₁) - - # Stage-3 - c₃ = a₃₁ + a₃₂ - _c₃ = DiffEqBase.value(sign(c₃)) * integrator.opts.internalnorm(c₃, t) - tᵢ₋₂ = tᵢ₋₁ + _c₃ - uᵢ₋₂ = f(uᵢ₋₂, p, tᵢ₋₂) - integrator.stats.nf += 1 - uᵢ₋₃ += a₄₃ * uᵢ₋₂ - u += B₃ * uᵢ₋₂ - integrator.opts.adaptive && (tmp += B̂₃ * uᵢ₋₂) - - #Stage-4 - c₄ = a₄₁ + a₄₂ + a₄₃ - _c₄ = DiffEqBase.value(sign(c₄)) * integrator.opts.internalnorm(c₄, t) - tᵢ₋₂ = tᵢ₋₁ + _c₄ - uᵢ₋₃ = f(uᵢ₋₃, p, tᵢ₋₂) - integrator.stats.nf += 1 - u += B₄ * uᵢ₋₃ - integrator.opts.adaptive && (tmp += B̂₄ * uᵢ₋₃) - - uᵢ₋₁ = f(u, p, t + dt) - integrator.stats.nf += 1 - - #Error estimate (embedded method of order 3) - if integrator.opts.adaptive - tmp += B̂₅ * uᵢ₋₁ - atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast = uᵢ₋₁ - integrator.u = u -end - -function initialize!(integrator, cache::ROCK4Cache) - integrator.kshortsize = 2 - resize!(integrator.k, integrator.kshortsize) - integrator.fsalfirst = cache.fsalfirst - integrator.fsallast = cache.k - alg = unwrap_alg(integrator, true) - cache.constantcache.max_stage = (alg.max_stages < 1 || alg.max_stages > 152) ? 152 : - alg.max_stages - cache.constantcache.min_stage = (alg.min_stages > cache.constantcache.max_stage) ? - cache.constantcache.max_stage : alg.min_stages - - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) - integrator.stats.nf += 1 -end - -@muladd function perform_step!(integrator, cache::ROCK4Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p, fsalfirst = integrator - @unpack uᵢ₋₁, uᵢ₋₂, uᵢ₋₃, tmp, atmp, k = cache - @unpack ms, fpa, fpb, fpbe, recf = cache.constantcache - ccache = cache.constantcache - alg = unwrap_alg(integrator, true) - alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) - # The the number of degree for Chebyshev polynomial - mdeg = Int(floor(sqrt((3 + abs(dt) * integrator.eigen_est) / 0.353) + 1)) - mdeg = min(max(mdeg, ccache.min_stage), ccache.max_stage) - ccache.mdeg = max(mdeg, 5) - 4 - choosedeg!(cache) - # recurrence - # for the first stage - tᵢ₋₁ = t + dt * recf[ccache.start] - tᵢ₋₂ = t + dt * recf[ccache.start] - tᵢ₋₃ = t - @.. broadcast=false uᵢ₋₂=uprev - @.. broadcast=false uᵢ₋₁=uprev + (dt * recf[ccache.start]) * fsalfirst - ccache.mdeg < 2 && (@.. broadcast=false u=uᵢ₋₁) - # for the second to the ccache.mdeg th stages - for i in 2:(ccache.mdeg) - μ, κ = recf[ccache.start + (i - 2) * 2 + 1], recf[ccache.start + (i - 2) * 2 + 2] - ν = -1 - κ - f(k, uᵢ₋₁, p, tᵢ₋₁) - tᵢ₋₁ = (dt * μ) - ν * tᵢ₋₂ - κ * tᵢ₋₃ - @.. broadcast=false u=(dt * μ) * k - ν * uᵢ₋₁ - κ * uᵢ₋₂ - if i < ccache.mdeg - @.. broadcast=false uᵢ₋₂=uᵢ₋₁ - @.. broadcast=false uᵢ₋₁=u - end - tᵢ₋₃ = tᵢ₋₂ - tᵢ₋₂ = tᵢ₋₁ - end - - # These constants correspond to the Buther Tableau coefficients of explicit RK methods - a₂₁ = dt * fpa[ccache.deg_index][1] - a₃₁ = dt * fpa[ccache.deg_index][2] - a₃₂ = dt * fpa[ccache.deg_index][3] - a₄₁ = dt * fpa[ccache.deg_index][4] - a₄₂ = dt * fpa[ccache.deg_index][5] - a₄₃ = dt * fpa[ccache.deg_index][6] - B₁ = dt * fpb[ccache.deg_index][1] - B₂ = dt * fpb[ccache.deg_index][2] - B₃ = dt * fpb[ccache.deg_index][3] - B₄ = dt * fpb[ccache.deg_index][4] - # coefficients of embedded method for error estimation - B̂₁ = dt * (fpbe[ccache.deg_index][1] - fpb[ccache.deg_index][1]) - B̂₂ = dt * (fpbe[ccache.deg_index][2] - fpb[ccache.deg_index][2]) - B̂₃ = dt * (fpbe[ccache.deg_index][3] - fpb[ccache.deg_index][3]) - B̂₄ = dt * (fpbe[ccache.deg_index][4] - fpb[ccache.deg_index][4]) - B̂₅ = dt * fpbe[ccache.deg_index][5] - - # 4-stage finishing procedure. - # Stage-1 - - f(k, u, p, tᵢ₋₁) - integrator.stats.nf += 1 - @.. broadcast=false uᵢ₋₂=u + a₃₁ * k - @.. broadcast=false uᵢ₋₃=u + a₄₁ * k - @.. broadcast=false uᵢ₋₁=u + a₂₁ * k - @.. broadcast=false u+=B₁ * k - integrator.opts.adaptive && (@.. broadcast=false tmp=B̂₁ * k) - - # Stage-2 - c₂ = a₂₁ - _c₂ = DiffEqBase.value(sign(c₂)) * integrator.opts.internalnorm(c₂, t) - tᵢ₋₂ = tᵢ₋₁ + _c₂ - f(k, uᵢ₋₁, p, tᵢ₋₂) - integrator.stats.nf += 1 - @.. broadcast=false uᵢ₋₂+=a₃₂ * k - @.. broadcast=false uᵢ₋₃+=a₄₂ * k - @.. broadcast=false u+=B₂ * k - integrator.opts.adaptive && (@.. broadcast=false tmp+=B̂₂ * k) - - # Stage-3 - c₃ = a₃₁ + a₃₂ - _c₃ = DiffEqBase.value(sign(c₃)) * integrator.opts.internalnorm(c₃, t) - tᵢ₋₂ = tᵢ₋₁ + _c₃ - f(k, uᵢ₋₂, p, tᵢ₋₂) - integrator.stats.nf += 1 - @.. broadcast=false uᵢ₋₃+=a₄₃ * k - @.. broadcast=false u+=B₃ * k - integrator.opts.adaptive && (@.. broadcast=false tmp+=B̂₃ * k) - - #Stage-4 - c₄ = a₄₁ + a₄₂ + a₄₃ - _c₄ = DiffEqBase.value(sign(c₄)) * integrator.opts.internalnorm(c₄, t) - tᵢ₋₂ = tᵢ₋₁ + _c₄ - f(k, uᵢ₋₃, p, tᵢ₋₂) - integrator.stats.nf += 1 - @.. broadcast=false u+=B₄ * k - integrator.opts.adaptive && (tmp += B̂₄ * k) - - f(k, u, p, t + dt) - integrator.stats.nf += 1 - - #Error estimate (embedded method of order 3) - if integrator.opts.adaptive - tmp += B̂₅ * k - calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - @.. broadcast=false integrator.fsallast=k - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.u = u -end - -function initialize!(integrator, cache::RKCConstantCache) - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -@muladd function perform_step!(integrator, cache::RKCConstantCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p, fsalfirst = integrator - alg = unwrap_alg(integrator, true) - alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) - # The the number of degree for Chebyshev polynomial - #maxm = max(2,Int(floor(sqrt(integrator.opts.internalnorm(integrator.opts.reltol,t)/(10*eps(integrator.opts.internalnorm(uprev,t))))))) - maxm = 50 - mdeg = 1 + Int(floor(sqrt(1.54 * abs(dt) * integrator.eigen_est + 1))) - mdeg = (mdeg > maxm) ? maxm : mdeg - - w0 = 1 + 2 / (13 * (mdeg^2)) - temp1 = w0^2 - 1 - temp2 = sqrt(temp1) - arg = mdeg * log(w0 + temp2) - w1 = (sinh(arg) * temp1) / (cosh(arg) * mdeg * temp2 - w0 * sinh(arg)) - b1 = 1 / ((2 * w0)^2) - b2 = b1 - - # stage-1 - gprev2 = copy(uprev) - μs = w1 * b1 - gprev = uprev + dt * μs * fsalfirst - th2 = zero(eltype(u)) - th1 = μs - z1 = w0 - z2 = one(eltype(u)) - dz1 = one(eltype(u)) - dz2 = zero(eltype(u)) - d2z1 = zero(eltype(u)) - d2z2 = zero(eltype(u)) - - # stage 2 - mdeg - for iter in 2:mdeg - z = 2 * w0 * z1 - z2 - dz = 2 * w0 * dz1 - dz2 + 2 * z1 - d2z = 2 * w0 * d2z1 - d2z2 + 4 * dz1 - b = d2z / (dz^2) - νs = 1 - z1 * b1 - μ = (2 * w0 * b) / b1 - ν = -b / b2 - μs = μ * w1 / w0 - #using u as temporary storage - u = f(gprev, p, t + dt * th1) - integrator.stats.nf += 1 - u = μ * gprev + ν * gprev2 + (1 - μ - ν) * uprev + dt * μs * (u - νs * fsalfirst) - th = μ * th1 + ν * th2 + μs * (1 - νs) - if (iter < mdeg) - gprev2 = gprev - gprev = u - th2 = th1 - th1 = th - b2 = b1 - b1 = b - z2 = z1 - z1 = z - dz2 = dz1 - dz1 = dz - d2z2 = d2z1 - d2z1 = d2z - end - end - # error estimate - if integrator.opts.adaptive - tmp = 0.8 * (uprev - u) + 0.4 * dt * (fsalfirst + gprev) - atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast = f(u, p, t + dt) - integrator.stats.nf += 1 - integrator.u = u -end - -function initialize!(integrator, cache::RKCCache) - integrator.kshortsize = 2 - resize!(integrator.k, integrator.kshortsize) - integrator.fsalfirst = cache.fsalfirst # done by pointers, no copying - integrator.fsallast = cache.k - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 -end - -@muladd function perform_step!(integrator, cache::RKCCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p, fsalfirst = integrator - @unpack k, tmp, gprev2, gprev, atmp = cache - alg = unwrap_alg(integrator, true) - alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) - # The the number of degree for Chebyshev polynomial - #maxm = max(2,Int(floor(sqrt(integrator.opts.internalnorm(integrator.opts.reltol,t)/10eps(t))))) - maxm = 50 - mdeg = 1 + Int(floor(sqrt(1.54 * abs(dt) * integrator.eigen_est + 1))) - mdeg = (mdeg > maxm) ? maxm : mdeg - - w0 = 1 + 2 / (13 * (mdeg^2)) - temp1 = w0^2 - 1 - temp2 = sqrt(temp1) - arg = mdeg * log(w0 + temp2) - w1 = (sinh(arg) * temp1) / (cosh(arg) * mdeg * temp2 - w0 * sinh(arg)) - b1 = 1 / ((2 * w0)^2) - b2 = b1 - - # stage-1 - @.. broadcast=false gprev2=uprev - μs = w1 * b1 - @.. broadcast=false gprev=uprev + dt * μs * fsalfirst - th2 = zero(eltype(u)) - th1 = μs - z1 = w0 - z2 = one(eltype(u)) - dz1 = one(eltype(u)) - dz2 = zero(eltype(u)) - d2z1 = zero(eltype(u)) - d2z2 = zero(eltype(u)) - - # stage 2 - mdeg - for iter in 2:mdeg - z = 2 * w0 * z1 - z2 - dz = 2 * w0 * dz1 - dz2 + 2 * z1 - d2z = 2 * w0 * d2z1 - d2z2 + 4 * dz1 - b = d2z / (dz^2) - νs = 1 - z1 * b1 - μ = (2 * w0 * b) / b1 - ν = -b / b2 - μs = μ * w1 / w0 - f(k, gprev, p, t + dt * th1) - integrator.stats.nf += 1 - @.. broadcast=false u=μ * gprev + ν * gprev2 + (1 - μ - ν) * uprev + - dt * μs * (k - νs * fsalfirst) - th = μ * th1 + ν * th2 + μs * (1 - νs) - if (iter < mdeg) - gprev2 = gprev - gprev = u - th2 = th1 - th1 = th - b2 = b1 - b1 = b - z2 = z1 - z1 = z - dz2 = dz1 - dz1 = dz - d2z2 = d2z1 - d2z1 = d2z - end - end - # error estimate - if integrator.opts.adaptive - @.. broadcast=false tmp=0.8 * (uprev - u) + 0.4 * dt * (fsalfirst + gprev) - calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.k[1] = integrator.fsalfirst - f(integrator.fsallast, u, p, t + dt) - integrator.stats.nf += 1 - integrator.k[2] = integrator.fsallast - integrator.u = u -end - -function initialize!(integrator, cache::IRKCConstantCache) - @unpack uprev, p, t = integrator - @unpack f1, f2 = integrator.f - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - cache.du₁ = f1(uprev, p, t) - cache.du₂ = f2(uprev, p, t) - integrator.stats.nf += 1 - integrator.stats.nf2 += 1 - integrator.fsalfirst = cache.du₁ + cache.du₂ - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -function perform_step!(integrator, cache::IRKCConstantCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p, fsalfirst = integrator - @unpack minm, du₁, du₂, nlsolver = cache - @unpack f1, f2 = integrator.f - alg = unwrap_alg(integrator, true) - alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) - - # The the number of degree for Chebyshev polynomial - #maxm = max(2,Int(floor(sqrt(integrator.opts.internalnorm(integrator.opts.reltol,t)/(10 *eps(integrator.opts.internalnorm(uprev,t))))))) - maxm = 50 - mdeg = 1 + floor(Int, sqrt(1.54 * abs(dt) * integrator.eigen_est + 1)) - mdeg = min(maxm, max(minm, mdeg)) - - ω₀ = 1 + 2 / (13 * (mdeg^2)) - temp₁ = ω₀^2 - 1 - temp₂ = sqrt(temp₁) - θ = mdeg * log(ω₀ + temp₂) - ω₁ = (sinh(θ) * temp₁) / (cosh(θ) * mdeg * temp₂ - ω₀ * sinh(θ)) - Bⱼ₋₂ = 1 / (4 * ω₀^2) - Bⱼ₋₁ = 1 / ω₀ - - #stage-1 - f1ⱼ₋₂ = du₁ - gprev2 = copy(uprev) - μs = ω₁ * Bⱼ₋₁ - μs₁ = μs - - # initial guess for implicit part - # if alg.extrapolant == :linear - # nlsolver.z = dt*du₁ - # else # :constant - # nlsolver.z = zero(u) - # end - - nlsolver.z = dt * du₁ - - nlsolver.tmp = uprev + dt * μs₁ * du₂ - nlsolver.γ = μs₁ - nlsolver.c = μs - markfirststage!(nlsolver) - z = nlsolve!(nlsolver, integrator, cache, false) - # nlsolvefail(nlsolver) && return - gprev = nlsolver.tmp + μs₁ * z - - Cⱼ₋₂ = zero(eltype(u)) - Cⱼ₋₁ = μs - Tⱼ₋₁ = ω₀ - Tⱼ₋₂ = one(eltype(u)) - Tⱼ₋₁′ = one(eltype(u)) - Tⱼ₋₂′ = zero(eltype(u)) - Tⱼ₋₁″ = zero(eltype(u)) - Tⱼ₋₂″ = zero(eltype(u)) - - #stage- 2...mdeg - for iter in 2:mdeg - Tⱼ = 2 * ω₀ * Tⱼ₋₁ - Tⱼ₋₂ - Tⱼ′ = 2 * ω₀ * Tⱼ₋₁′ + 2 * Tⱼ₋₁ - Tⱼ₋₂′ - Tⱼ″ = 2 * ω₀ * Tⱼ₋₁″ + 4 * Tⱼ₋₁′ - Tⱼ₋₂″ - Bⱼ = Tⱼ″ / (Tⱼ′^2) - μ = (2 * ω₀ * Bⱼ) / Bⱼ₋₁ - ν = -Bⱼ / Bⱼ₋₂ - μs = (μ * ω₁) / ω₀ - νs = -(1 - Tⱼ₋₁ * Bⱼ₋₁) * μs - Cⱼ = μ * Cⱼ₋₁ + ν * Cⱼ₋₂ + μs + νs - - f1ⱼ₋₁ = f1(gprev, p, t + Cⱼ₋₁ * dt) - f2ⱼ₋₁ = f2(gprev, p, t + Cⱼ₋₁ * dt) - integrator.stats.nf += 1 - integrator.stats.nf2 += 1 - nlsolver.tmp = (1 - μ - ν) * uprev + μ * gprev + ν * gprev2 + dt * μs * f2ⱼ₋₁ + - dt * νs * du₂ + (νs - (1 - μ - ν) * μs₁) * dt * du₁ - - ν * μs₁ * dt * f1ⱼ₋₂ - nlsolver.z = dt * f1ⱼ₋₁ - nlsolver.c = Cⱼ - z = nlsolve!(nlsolver, integrator, cache, false) - # ignoring newton method's convergence failure - # nlsolvefail(nlsolver) && return - u = nlsolver.tmp + μs₁ * z - if (iter < mdeg) - f1ⱼ₋₂ = f1ⱼ₋₁ - gprev2 = gprev - gprev = u - Cⱼ₋₂ = Cⱼ₋₁ - Cⱼ₋₁ = Cⱼ - Bⱼ₋₂ = Bⱼ₋₁ - Bⱼ₋₁ = Bⱼ - Tⱼ₋₂ = Tⱼ₋₁ - Tⱼ₋₁ = Tⱼ - Tⱼ₋₂′ = Tⱼ₋₁′ - Tⱼ₋₁′ = Tⱼ′ - Tⱼ₋₂″ = Tⱼ₋₁″ - Tⱼ₋₁″ = Tⱼ″ - end - end - - cache.du₁ = f1(u, p, t + dt) - cache.du₂ = f2(u, p, t + dt) - integrator.stats.nf += 1 - integrator.stats.nf2 += 1 - # error estimate - if isnewton(nlsolver) && integrator.opts.adaptive - update_W!(integrator, cache, dt, false) - tmp = dt * (0.5 * (cache.du₂ - du₂) + (0.5 - μs₁) * (cache.du₁ - du₁)) - tmp = _reshape(get_W(nlsolver) \ _vec(tmp), axes(tmp)) - atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - - integrator.fsallast = cache.du₁ + cache.du₂ - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.u = u -end - -function initialize!(integrator, cache::IRKCCache) - @unpack uprev, p, t = integrator - @unpack f1, f2 = integrator.f - integrator.kshortsize = 2 - integrator.fsalfirst = cache.fsalfirst - integrator.fsallast = du_alias_or_new(cache.nlsolver, integrator.fsalfirst) - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - f1(cache.du₁, uprev, p, t) - f2(cache.du₂, uprev, p, t) - integrator.stats.nf += 1 - integrator.stats.nf2 += 1 - @.. broadcast=false integrator.fsalfirst=cache.du₁ + cache.du₂ -end - -function perform_step!(integrator, cache::IRKCCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack gprev, gprev2, f1ⱼ₋₁, f1ⱼ₋₂, f2ⱼ₋₁, du₁, du₂, atmp, nlsolver = cache - @unpack tmp, z = nlsolver - @unpack minm = cache.constantcache - @unpack f1, f2 = integrator.f - - alg = unwrap_alg(integrator, true) - alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) - # The the number of degree for Chebyshev polynomial - #maxm = max(2,int(floor(sqrt(integrator.opts.internalnorm(integrator.opts.reltol,t)/(10 *eps(integrator.opts.internalnorm(uprev,t))))))) - maxm = 50 - mdeg = 1 + Int(floor(sqrt(1.54 * abs(dt) * integrator.eigen_est + 1))) - mdeg = (mdeg < minm) ? minm : mdeg - mdeg = (mdeg >= maxm) ? maxm : mdeg - - ω₀ = 1 + 2 / (13 * (mdeg^2)) - temp₁ = ω₀^2 - 1 - temp₂ = sqrt(temp₁) - θ = mdeg * log(ω₀ + temp₂) - ω₁ = (sinh(θ) * temp₁) / (cosh(θ) * mdeg * temp₂ - ω₀ * sinh(θ)) - Bⱼ₋₂ = 1 / (4 * ω₀^2) - Bⱼ₋₁ = 1 / ω₀ - - #stage-1 - f1ⱼ₋₂ = du₁ - @.. broadcast=false gprev2=uprev - μs = ω₁ * Bⱼ₋₁ - μs₁ = μs - - # initial guess - # if alg.extrapolant == :linear - # @.. broadcast=false z = dt*du₁ - # else # :constant - # @.. broadcast=false z = zero(eltype(u)) - # end - @.. broadcast=false nlsolver.z=dt * du₁ - - @.. broadcast=false nlsolver.tmp=uprev + dt * μs₁ * du₂ - nlsolver.γ = μs₁ - nlsolver.c = μs - markfirststage!(nlsolver) - z = nlsolve!(nlsolver, integrator, cache, false) - # ignoring newton method's convergence failure - # nlsolvefail(nlsolver) && return - @.. broadcast=false gprev=nlsolver.tmp + μs₁ * nlsolver.z - - Cⱼ₋₂ = zero(eltype(u)) - Cⱼ₋₁ = μs - Tⱼ₋₁ = ω₀ - Tⱼ₋₂ = one(eltype(u)) - Tⱼ₋₁′ = one(eltype(u)) - Tⱼ₋₂′ = zero(eltype(u)) - Tⱼ₋₁″ = zero(eltype(u)) - Tⱼ₋₂″ = zero(eltype(u)) - - #stage- 2...mdeg - for iter in 2:mdeg - Tⱼ = 2 * ω₀ * Tⱼ₋₁ - Tⱼ₋₂ - Tⱼ′ = 2 * ω₀ * Tⱼ₋₁′ + 2 * Tⱼ₋₁ - Tⱼ₋₂′ - Tⱼ″ = 2 * ω₀ * Tⱼ₋₁″ + 4 * Tⱼ₋₁′ - Tⱼ₋₂″ - Bⱼ = Tⱼ″ / (Tⱼ′^2) - μ = (2 * ω₀ * Bⱼ) / Bⱼ₋₁ - ν = -Bⱼ / Bⱼ₋₂ - μs = (μ * ω₁) / ω₀ - νs = -(1 - Tⱼ₋₁ * Bⱼ₋₁) * μs - Cⱼ = μ * Cⱼ₋₁ + ν * Cⱼ₋₂ + μs + νs - - f1(f1ⱼ₋₁, gprev, p, t + Cⱼ₋₁ * dt) - f2(f2ⱼ₋₁, gprev, p, t + Cⱼ₋₁ * dt) - integrator.stats.nf += 1 - integrator.stats.nf2 += 1 - @.. broadcast=false nlsolver.tmp=(1 - μ - ν) * uprev + μ * gprev + ν * gprev2 + - dt * μs * f2ⱼ₋₁ + dt * νs * du₂ + - (νs - (1 - μ - ν) * μs₁) * dt * du₁ - - ν * μs₁ * dt * f1ⱼ₋₂ - @.. broadcast=false nlsolver.z=dt * f1ⱼ₋₁ - nlsolver.c = Cⱼ - - z = nlsolve!(nlsolver, integrator, cache, false) - # nlsolvefail(nlsolver) && return - @.. broadcast=false u=nlsolver.tmp + μs₁ * nlsolver.z - if (iter < mdeg) - @.. broadcast=false f1ⱼ₋₂=f1ⱼ₋₁ - @.. broadcast=false gprev2=gprev - @.. broadcast=false gprev=u - Cⱼ₋₂ = Cⱼ₋₁ - Cⱼ₋₁ = Cⱼ - Bⱼ₋₂ = Bⱼ₋₁ - Bⱼ₋₁ = Bⱼ - Tⱼ₋₂ = Tⱼ₋₁ - Tⱼ₋₁ = Tⱼ - Tⱼ₋₂′ = Tⱼ₋₁′ - Tⱼ₋₁′ = Tⱼ′ - Tⱼ₋₂″ = Tⱼ₋₁″ - Tⱼ₋₁″ = Tⱼ″ - end - end - - @.. broadcast=false f1ⱼ₋₁=du₁ - @.. broadcast=false f2ⱼ₋₁=du₂ - f1(du₁, u, p, t + dt) - f2(du₂, u, p, t + dt) - integrator.stats.nf += 1 - integrator.stats.nf2 += 1 - # error estimate - if isnewton(nlsolver) && integrator.opts.adaptive - update_W!(integrator, cache, dt, false) - @.. broadcast=false gprev=dt * 0.5 * (du₂ - f2ⱼ₋₁) + - dt * (0.5 - μs₁) * (du₁ - f1ⱼ₋₁) - - linsolve = nlsolver.cache.linsolve - linres = dolinsolve(integrator, linsolve; b = _vec(gprev), linu = _vec(tmp)) - - calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - - @.. broadcast=false integrator.fsallast=du₁ + du₂ - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.u = u -end - -function initialize!(integrator, cache::ESERK4ConstantCache) - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -@muladd function perform_step!(integrator, cache::ESERK4ConstantCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p, fsalfirst = integrator - @unpack ms, Cᵤ, Cₑ = cache - alg = unwrap_alg(integrator, true) - alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) - - mdeg = Int(floor(sqrt(abs(dt) * integrator.eigen_est)) + 1) - mdeg = (mdeg > 4000) ? 4000 : mdeg - cache.mdeg = mdeg - choosedeg_SERK!(integrator, cache) - mdeg = cache.mdeg - start = cache.start - internal_deg = cache.internal_deg - α = 2.0 / (mdeg^2) - - u = zero(uprev) - tmp = zero(uprev) - - for i in 1:4 - hᵢ = dt / i - tᵢ = t - Sᵢ = zero(u) - uᵢ₋₁ = uprev - uᵢ₋₂ = zero(u) - for j in 1:i - r = tᵢ - Sᵢ = (cache.Bᵢ[start]) * uᵢ₋₁ - for st in 1:mdeg - k = f(uᵢ₋₁, p, r) - integrator.stats.nf += 1 - - if st % internal_deg == 1 - uᵢ = uᵢ₋₁ + α * hᵢ * k - else - uᵢ = 2 * uᵢ₋₁ - uᵢ₋₂ + 2 * α * hᵢ * k - end - q = convert(Int, floor(st / internal_deg)) - r = tᵢ + α * (st^2 + q * internal_deg^2) * hᵢ - Sᵢ = Sᵢ + (cache.Bᵢ[start + st]) * uᵢ - if st < mdeg - uᵢ₋₂ = uᵢ₋₁ - uᵢ₋₁ = uᵢ - end - end - - if j < i - tᵢ = tᵢ + hᵢ - uᵢ₋₁ = Sᵢ - end - end - - u = u + Cᵤ[i] * Sᵢ - integrator.opts.adaptive && (tmp = tmp + Cₑ[i] * Sᵢ) - end - - u = u / 6 - if integrator.opts.adaptive - tmp = tmp / 6 - atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast = f(u, p, t + dt) - integrator.stats.nf += 1 - integrator.u = u -end - -function initialize!(integrator, cache::ESERK4Cache) - integrator.kshortsize = 2 - resize!(integrator.k, integrator.kshortsize) - integrator.fsalfirst = cache.fsalfirst - integrator.fsallast = cache.k - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) - integrator.stats.nf += 1 -end - -@muladd function perform_step!(integrator, cache::ESERK4Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p, fsalfirst = integrator - @unpack uᵢ, uᵢ₋₁, uᵢ₋₂, Sᵢ, tmp, atmp, k = cache - @unpack ms, Cᵤ, Cₑ = cache.constantcache - ccache = cache.constantcache - alg = unwrap_alg(integrator, true) - alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) - - mdeg = Int(floor(sqrt(abs(dt) * integrator.eigen_est)) + 1) - mdeg = (mdeg > 4000) ? 4000 : mdeg - ccache.mdeg = mdeg - choosedeg_SERK!(integrator, cache) - mdeg = ccache.mdeg - start = ccache.start - internal_deg = ccache.internal_deg - α = 2.0 / (mdeg^2) - - @.. broadcast=false u=zero(uprev) - @.. broadcast=false tmp=zero(uprev) - for i in 1:4 - hᵢ = dt / i - tᵢ = t - @.. broadcast=false Sᵢ=zero(u) - @.. broadcast=false uᵢ₋₁=uprev - @.. broadcast=false uᵢ₋₂=zero(u) - for j in 1:i - r = tᵢ - @.. broadcast=false Sᵢ=(cache.constantcache.Bᵢ[start]) * uᵢ₋₁ - for st in 1:mdeg - f(k, uᵢ₋₁, p, r) - integrator.stats.nf += 1 - - if st % internal_deg == 1 - @.. broadcast=false uᵢ=uᵢ₋₁ + α * hᵢ * k - else - @.. broadcast=false uᵢ=2 * uᵢ₋₁ - uᵢ₋₂ + 2 * α * hᵢ * k - end - q = convert(Int, floor(st / internal_deg)) - r = tᵢ + α * (st^2 + q * internal_deg^2) * hᵢ - @.. broadcast=false Sᵢ=Sᵢ + (cache.constantcache.Bᵢ[start + st]) * uᵢ - if st < mdeg - @.. broadcast=false uᵢ₋₂=uᵢ₋₁ - @.. broadcast=false uᵢ₋₁=uᵢ - end - end - - if j < i - tᵢ = tᵢ + hᵢ - @.. broadcast=false uᵢ₋₁=Sᵢ - end - end - - @.. broadcast=false u=u + Cᵤ[i] * Sᵢ - integrator.opts.adaptive && (@.. broadcast=false tmp=tmp + Cₑ[i] * Sᵢ) - end - - @.. broadcast=false u=u / 6 - - if integrator.opts.adaptive - @.. broadcast=false tmp=tmp / 6 - calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.k[1] = integrator.fsalfirst - f(integrator.fsallast, u, p, t + dt) - integrator.stats.nf += 1 - integrator.k[2] = integrator.fsallast - integrator.u = u -end - -function initialize!(integrator, cache::ESERK5ConstantCache) - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -@muladd function perform_step!(integrator, cache::ESERK5ConstantCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p, fsalfirst = integrator - @unpack ms, Cᵤ, Cₑ, Bᵢ = cache - alg = unwrap_alg(integrator, true) - alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) - - mdeg = Int(floor(sqrt(abs(dt) * integrator.eigen_est / 0.98)) + 1) - mdeg = (mdeg > 2000) ? 2000 : mdeg - cache.mdeg = mdeg - choosedeg_SERK!(integrator, cache) - mdeg = cache.mdeg - start = cache.start - internal_deg = cache.internal_deg - α = 100.0 / (49.0 * mdeg^2) - - u = zero(uprev) - tmp = zero(uprev) - for i in 1:5 - hᵢ = dt / i - tᵢ = t - Sᵢ = zero(u) - uᵢ₋₁ = uprev - uᵢ₋₂ = zero(u) - for j in 1:i - r = tᵢ - Sᵢ = (Bᵢ[start]) * uᵢ₋₁ - for st in 1:mdeg - k = f(uᵢ₋₁, p, r) - integrator.stats.nf += 1 - - if st % internal_deg == 1 - uᵢ = uᵢ₋₁ + α * hᵢ * k - else - uᵢ = 2 * uᵢ₋₁ - uᵢ₋₂ + 2 * α * hᵢ * k - end - q = convert(Int, floor(st / internal_deg)) - r = tᵢ + α * (st^2 + q * internal_deg^2) * hᵢ - Sᵢ = Sᵢ + (Bᵢ[start + st]) * uᵢ - if st < mdeg - uᵢ₋₂ = uᵢ₋₁ - uᵢ₋₁ = uᵢ - end - end - - if j < i - tᵢ = tᵢ + hᵢ - uᵢ₋₁ = Sᵢ - end - end - - u = u + Cᵤ[i] * Sᵢ - integrator.opts.adaptive && (tmp = tmp + Cₑ[i] * Sᵢ) - end - - u = u / 24 - if integrator.opts.adaptive - tmp = tmp / 24 - atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast = f(u, p, t + dt) - integrator.stats.nf += 1 - integrator.u = u -end - -function initialize!(integrator, cache::ESERK5Cache) - integrator.kshortsize = 2 - resize!(integrator.k, integrator.kshortsize) - integrator.fsalfirst = cache.fsalfirst - integrator.fsallast = cache.k - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) - integrator.stats.nf += 1 -end - -@muladd function perform_step!(integrator, cache::ESERK5Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p, fsalfirst = integrator - @unpack uᵢ, uᵢ₋₁, uᵢ₋₂, Sᵢ, tmp, atmp, k = cache - @unpack ms, Cᵤ, Cₑ, Bᵢ = cache.constantcache - ccache = cache.constantcache - alg = unwrap_alg(integrator, true) - alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) - - mdeg = Int(floor(sqrt(abs(dt) * integrator.eigen_est / 0.98)) + 1) - mdeg = (mdeg > 2000) ? 2000 : mdeg - ccache.mdeg = mdeg - choosedeg_SERK!(integrator, cache) - mdeg = ccache.mdeg - start = ccache.start - internal_deg = ccache.internal_deg - α = 100.0 / (49.0 * mdeg^2) - - @.. broadcast=false u=zero(uprev) - @.. broadcast=false tmp=zero(uprev) - for i in 1:5 - hᵢ = dt / i - tᵢ = t - @.. broadcast=false Sᵢ=zero(u) - @.. broadcast=false uᵢ₋₁=uprev - @.. broadcast=false uᵢ₋₂=zero(u) - for j in 1:i - r = tᵢ - @.. broadcast=false Sᵢ=(Bᵢ[start]) * uᵢ₋₁ - for st in 1:mdeg - f(k, uᵢ₋₁, p, r) - integrator.stats.nf += 1 - - if st % internal_deg == 1 - @.. broadcast=false uᵢ=uᵢ₋₁ + α * hᵢ * k - else - @.. broadcast=false uᵢ=2 * uᵢ₋₁ - uᵢ₋₂ + 2 * α * hᵢ * k - end - q = convert(Int, floor(st / internal_deg)) - r = tᵢ + α * (st^2 + q * internal_deg^2) * hᵢ - @.. broadcast=false Sᵢ=Sᵢ + (Bᵢ[start + st]) * uᵢ - if st < mdeg - @.. broadcast=false uᵢ₋₂=uᵢ₋₁ - @.. broadcast=false uᵢ₋₁=uᵢ - end - end - - if j < i - tᵢ = tᵢ + hᵢ - @.. broadcast=false uᵢ₋₁=Sᵢ - end - end - - @.. broadcast=false u=u + Cᵤ[i] * Sᵢ - integrator.opts.adaptive && (@.. broadcast=false tmp=tmp + Cₑ[i] * Sᵢ) - end - - @.. broadcast=false u=u / 24 - - if integrator.opts.adaptive - @.. broadcast=false tmp=tmp / 24 - calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.k[1] = integrator.fsalfirst - f(integrator.fsallast, u, p, t + dt) - integrator.stats.nf += 1 - integrator.k[2] = integrator.fsallast - integrator.u = u -end - -function initialize!(integrator, cache::SERK2ConstantCache) - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -@muladd function perform_step!(integrator, cache::SERK2ConstantCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p, fsalfirst = integrator - @unpack ms, Bᵢ = cache - alg = unwrap_alg(integrator, true) - alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) - - mdeg = Int(floor(sqrt(abs(dt) * integrator.eigen_est / 0.8)) + 1) - mdeg = (mdeg > 250) ? 250 : mdeg - cache.mdeg = mdeg - choosedeg_SERK!(integrator, cache) - mdeg = cache.mdeg - start = cache.start - internal_deg = cache.internal_deg - α = 1.0 / (0.4 * mdeg^2) - - uᵢ₋₁ = uprev - uᵢ₋₂ = uprev - Sᵢ = Bᵢ[start] * uprev - for i in 1:10 - k = f(uᵢ₋₁, p, t + (1 + (i - 1) * internal_deg^2) * α * dt) - integrator.stats.nf += 1 - u = uᵢ₋₁ + α * dt * k - Sᵢ = Sᵢ + Bᵢ[start + (i - 1) * internal_deg + 1] * u - uᵢ₋₂ = uᵢ₋₁ - uᵢ₋₁ = u - for j in 2:internal_deg - k = f(uᵢ₋₁, p, t + (j^2 + (i - 1) * internal_deg^2) * α * dt) - integrator.stats.nf += 1 - u = 2 * uᵢ₋₁ - uᵢ₋₂ + 2 * α * dt * k - Sᵢ = Sᵢ + Bᵢ[start + j + (i - 1) * internal_deg] * u - if j * i < mdeg - uᵢ₋₂ = uᵢ₋₁ - uᵢ₋₁ = u - end - end - end - u = Sᵢ - k = f(u, p, t + dt) - integrator.stats.nf += 1 - - if integrator.opts.adaptive - tmp = u - uprev - dt * k - atmp = calculate_residuals(tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast = k - integrator.u = u -end - -function initialize!(integrator, cache::SERK2Cache) - integrator.kshortsize = 2 - resize!(integrator.k, integrator.kshortsize) - integrator.fsalfirst = cache.fsalfirst - integrator.fsallast = cache.k - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) - integrator.stats.nf += 1 -end - -@muladd function perform_step!(integrator, cache::SERK2Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p, fsalfirst = integrator - @unpack uᵢ₋₁, uᵢ₋₂, Sᵢ, tmp, atmp, k = cache - @unpack ms, Bᵢ = cache.constantcache - ccache = cache.constantcache - alg = unwrap_alg(integrator, true) - alg.eigen_est === nothing ? maxeig!(integrator, cache) : alg.eigen_est(integrator) - - mdeg = Int(floor(sqrt(abs(dt) * integrator.eigen_est / 0.8)) + 1) - mdeg = (mdeg > 250) ? 250 : mdeg - ccache.mdeg = mdeg - choosedeg_SERK!(integrator, cache) - mdeg = ccache.mdeg - start = ccache.start - internal_deg = ccache.internal_deg - α = 1.0 / (0.4 * mdeg^2) - - @.. broadcast=false uᵢ₋₁=uprev - @.. broadcast=false uᵢ₋₂=uprev - @.. broadcast=false Sᵢ=Bᵢ[start] * uprev - for i in 1:10 - f(k, uᵢ₋₁, p, t + (1 + (i - 1) * internal_deg^2) * α * dt) - integrator.stats.nf += 1 - @.. broadcast=false u=uᵢ₋₁ + α * dt * k - @.. broadcast=false Sᵢ=Sᵢ + Bᵢ[start + (i - 1) * internal_deg + 1] * u - @.. broadcast=false uᵢ₋₂=uᵢ₋₁ - @.. broadcast=false uᵢ₋₁=u - for j in 2:internal_deg - f(k, uᵢ₋₂, p, t + (j^2 + (i - 1) * internal_deg^2) * α * dt) - integrator.stats.nf += 1 - @.. broadcast=false u=2 * uᵢ₋₁ - uᵢ₋₂ + 2 * α * dt * k - @.. broadcast=false Sᵢ=Sᵢ + Bᵢ[start + j + (i - 1) * internal_deg] * u - if j < mdeg - @.. broadcast=false uᵢ₋₂=uᵢ₋₁ - @.. broadcast=false uᵢ₋₁=u - end - end - end - @.. broadcast=false u=Sᵢ - f(k, u, p, t + dt) - integrator.stats.nf += 1 - - if integrator.opts.adaptive - @.. broadcast=false tmp=u - uprev - dt * k - calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast = k - integrator.u = u -end From 4112f61da939ada603cfab3ec74721034ec74f72 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:58:34 -0400 Subject: [PATCH 16/71] Delete src/perform_step/rkn_perform_step.jl --- src/perform_step/rkn_perform_step.jl | 1821 -------------------------- 1 file changed, 1821 deletions(-) delete mode 100644 src/perform_step/rkn_perform_step.jl diff --git a/src/perform_step/rkn_perform_step.jl b/src/perform_step/rkn_perform_step.jl deleted file mode 100644 index 1c29dc53e4..0000000000 --- a/src/perform_step/rkn_perform_step.jl +++ /dev/null @@ -1,1821 +0,0 @@ -## y'' = f(t, y, y') -## y(t₀) = y₀; y'(t₀) = y'₀ -## kᵢ' = f(t₀+cᵢh, y₀+cᵢhy'₀+h²∑āᵢⱼk'ⱼ, y'₀+h∑aᵢⱼk'ⱼ) -## y₁ = y₀ + hy'₀ + h²∑b̄ᵢk'ᵢ -## y'₁ = y'₀ + h∑bᵢk'ᵢ - -const NystromCCDefaultInitialization = Union{Nystrom4ConstantCache, FineRKN4ConstantCache, - FineRKN5ConstantCache, - Nystrom4VelocityIndependentConstantCache, - Nystrom5VelocityIndependentConstantCache, - IRKN3ConstantCache, IRKN4ConstantCache, - DPRKN4ConstantCache, DPRKN5ConstantCache, - DPRKN6FMConstantCache, DPRKN8ConstantCache, - DPRKN12ConstantCache, ERKN4ConstantCache, - ERKN5ConstantCache, ERKN7ConstantCache} - -function initialize!(integrator, cache::NystromCCDefaultInitialization) - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - duprev, uprev = integrator.uprev.x - kdu = integrator.f.f1(duprev, uprev, integrator.p, integrator.t) - ku = integrator.f.f2(duprev, uprev, integrator.p, integrator.t) - integrator.stats.nf += 1 - integrator.stats.nf2 += 1 - integrator.fsalfirst = ArrayPartition((kdu, ku)) -end - -const NystromDefaultInitialization = Union{Nystrom4Cache, FineRKN4Cache, FineRKN5Cache, - Nystrom4VelocityIndependentCache, - Nystrom5VelocityIndependentCache, - IRKN3Cache, IRKN4Cache, - DPRKN4Cache, DPRKN5Cache, - DPRKN6FMCache, DPRKN8Cache, - DPRKN12Cache, ERKN4Cache, - ERKN5Cache, ERKN7Cache} - -function initialize!(integrator, cache::NystromDefaultInitialization) - @unpack fsalfirst, k = cache - duprev, uprev = integrator.uprev.x - - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 2 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f.f1(integrator.k[1].x[1], duprev, uprev, integrator.p, integrator.t) - integrator.f.f2(integrator.k[1].x[2], duprev, uprev, integrator.p, integrator.t) - integrator.stats.nf += 1 - integrator.stats.nf2 += 1 -end - -@muladd function perform_step!(integrator, cache::Nystrom4ConstantCache, - repeat_step = false) - @unpack t, dt, f, p = integrator - duprev, uprev = integrator.uprev.x - k₁ = integrator.fsalfirst.x[1] - halfdt = dt / 2 - dtsq = dt^2 - eighth_dtsq = dtsq / 8 - half_dtsq = dtsq / 2 - ttmp = t + halfdt - - ## y₁ = y₀ + hy'₀ + h²∑b̄ᵢk'ᵢ - ku = uprev + halfdt * duprev + eighth_dtsq * k₁ - ## y'₁ = y'₀ + h∑bᵢk'ᵢ - kdu = duprev + halfdt * k₁ - - k₂ = f.f1(kdu, ku, p, ttmp) - ku = uprev + halfdt * duprev + eighth_dtsq * k₁ - kdu = duprev + halfdt * k₂ - - k₃ = f.f1(kdu, ku, p, ttmp) - ku = uprev + dt * duprev + half_dtsq * k₃ - kdu = duprev + dt * k₃ - - k₄ = f.f1(kdu, ku, p, t + dt) - u = uprev + (dtsq / 6) * (k₁ + k₂ + k₃) + dt * duprev - du = duprev + (dt / 6) * (k₁ + k₄ + 2 * (k₂ + k₃)) - - integrator.u = ArrayPartition((du, u)) - integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) - integrator.stats.nf += 4 - integrator.stats.nf2 += 1 - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -@muladd function perform_step!(integrator, cache::Nystrom4Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - du, u = integrator.u.x - duprev, uprev = integrator.uprev.x - @unpack tmp, fsalfirst, k₂, k₃, k₄, k = cache - kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] - k₁ = integrator.fsalfirst.x[1] - halfdt = dt / 2 - dtsq = dt^2 - eighth_dtsq = dtsq / 8 - half_dtsq = dtsq / 2 - ttmp = t + halfdt - - ## y₁ = y₀ + hy'₀ + h²∑b̄ᵢk'ᵢ - @.. broadcast=false ku=uprev + halfdt * duprev + eighth_dtsq * k₁ - ## y'₁ = y'₀ + h∑bᵢk'ᵢ - @.. broadcast=false kdu=duprev + halfdt * k₁ - - f.f1(k₂, kdu, ku, p, ttmp) - @.. broadcast=false ku=uprev + halfdt * duprev + eighth_dtsq * k₁ - @.. broadcast=false kdu=duprev + halfdt * k₂ - - f.f1(k₃, kdu, ku, p, ttmp) - @.. broadcast=false ku=uprev + dt * duprev + half_dtsq * k₃ - @.. broadcast=false kdu=duprev + dt * k₃ - - f.f1(k₄, kdu, ku, p, t + dt) - @.. broadcast=false u=uprev + (dtsq / 6) * (k₁ + k₂ + k₃) + dt * duprev - @.. broadcast=false du=duprev + (dt / 6) * (k₁ + k₄ + 2 * (k₂ + k₃)) - - f.f1(k.x[1], du, u, p, t + dt) - f.f2(k.x[2], du, u, p, t + dt) - integrator.stats.nf += 4 - integrator.stats.nf2 += 1 -end - -@muladd function perform_step!(integrator, cache::FineRKN4ConstantCache, - repeat_step = false) - @unpack t, dt, f, p = integrator - duprev, uprev = integrator.uprev.x - @unpack c2, c3, c4, c5, a21, a31, a32, a41, a43, a51, - a52, a53, a54, abar21, abar31, abar32, abar41, abar42, abar43, abar51, - abar52, abar53, abar54, b1, b3, b4, b5, bbar1, bbar3, bbar4, bbar5, btilde1, btilde3, btilde4, btilde5, bptilde1, - bptilde3, bptilde4, bptilde5 = cache - k1 = integrator.fsalfirst.x[1] - - ku = uprev + dt * (c2 * duprev + dt * (a21 * k1)) - kdu = duprev + dt * (abar21 * k1) - - k2 = f.f1(kdu, ku, p, t + dt * c2) - ku = uprev + dt * (c3 * duprev + dt * (a31 * k1 + a32 * k2)) - kdu = duprev + dt * (abar31 * k1 + abar32 * k2) - - k3 = f.f1(kdu, ku, p, t + dt * c3) - ku = uprev + dt * (c4 * duprev + dt * (a41 * k1 + a43 * k3)) # a42 = 0 - kdu = duprev + dt * (abar41 * k1 + abar42 * k2 + abar43 * k3) - - k4 = f.f1(kdu, ku, p, t + dt * c4) - ku = uprev + dt * (c5 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) - kdu = duprev + dt * (abar51 * k1 + abar52 * k2 + abar53 * k3 + abar54 * k4) - - k5 = f.f1(kdu, ku, p, t + dt * c5) - - u = uprev + dt * (duprev + dt * (b1 * k1 + b3 * k3 + b4 * k4 + b5 * k5)) # b2 = 0 - du = duprev + dt * (bbar1 * k1 + bbar3 * k3 + bbar4 * k4 + bbar5 * k5) # bbar2 = 0 - - integrator.u = ArrayPartition((du, u)) - integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) - integrator.stats.nf += 5 - integrator.stats.nf2 += 1 - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - - if integrator.opts.adaptive - dtsq = dt^2 - uhat = dtsq * (btilde1 * k1 + btilde3 * k3 + btilde4 * k4 + btilde5 * k5) # btilde2 = 0 - duhat = dt * (bptilde1 * k1 + bptilde3 * k3 + bptilde4 * k4 + bptilde5 * k5) # bptilde2 = 0 - utilde = ArrayPartition((duhat, uhat)) - atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -@muladd function perform_step!(integrator, cache::FineRKN4Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - du, u = integrator.u.x - duprev, uprev = integrator.uprev.x - @unpack tmp, atmp, fsalfirst, k2, k3, k4, k5, k, utilde = cache - @unpack c2, c3, c4, c5, a21, a31, a32, a41, a43, a51, - a52, a53, a54, abar21, abar31, abar32, abar41, abar42, abar43, abar51, - abar52, abar53, abar54, b1, b3, b4, b5, bbar1, bbar3, bbar4, bbar5, btilde1, btilde3, btilde4, btilde5, bptilde1, - bptilde3, bptilde4, bptilde5 = cache.tab - kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] - uidx = eachindex(integrator.uprev.x[2]) - k1 = integrator.fsalfirst.x[1] - - @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a21 * k1)) - @.. broadcast=false kdu=duprev + dt * (abar21 * k1) - - f.f1(k2, kdu, ku, p, t + dt * c2) - @.. broadcast=false ku=uprev + dt * (c3 * duprev + dt * (a31 * k1 + a32 * k2)) - @.. broadcast=false kdu=duprev + dt * (abar31 * k1 + abar32 * k2) - - f.f1(k3, kdu, ku, p, t + dt * c3) - @.. broadcast=false ku=uprev + - dt * (c4 * duprev + dt * (a41 * k1 + a43 * k3)) # a42 = 0 - @.. broadcast=false kdu=duprev + dt * (abar41 * k1 + abar42 * k2 + abar43 * k3) - - f.f1(k4, kdu, ku, p, t + dt * c4) - @.. broadcast=false ku=uprev + - dt * - (c5 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) - @.. broadcast=false kdu=duprev + - dt * (abar51 * k1 + abar52 * k2 + abar53 * k3 + abar54 * k4) - - f.f1(k5, kdu, ku, p, t + dt * c5) - @.. broadcast=false u=uprev + - dt * (duprev + dt * (b1 * k1 + b3 * k3 + b4 * k4 + b5 * k5)) # b2 = 0 - @.. broadcast=false du=duprev + - dt * - (bbar1 * k1 + bbar3 * k3 + bbar4 * k4 + bbar5 * k5) # bbar2 = 0 - - f.f1(k.x[1], du, u, p, t + dt) - f.f2(k.x[2], du, u, p, t + dt) - integrator.stats.nf += 5 - integrator.stats.nf2 += 1 - if integrator.opts.adaptive - duhat, uhat = utilde.x - dtsq = dt^2 - @.. broadcast=false uhat=dtsq * - (btilde1 * k1 + btilde3 * k3 + btilde4 * k4 + - btilde5 * k5) # btilde2 = 0 - @.. broadcast=false duhat=dt * - (bptilde1 * k1 + bptilde3 * k3 + bptilde4 * k4 + - bptilde5 * k5) # bptilde2 = 0 - - calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -@muladd function perform_step!(integrator, cache::FineRKN5ConstantCache, - repeat_step = false) - @unpack t, dt, f, p = integrator - duprev, uprev = integrator.uprev.x - @unpack c2, c3, c4, c5, c6, c7, a21, a31, a32, a41, a43, a51, a52, a53, a54, a61, a62, a63, a64, a71, a73, a74, a75, abar21, abar31, abar32, abar41, abar42, abar43, abar51, abar52, abar53, abar54, abar61, abar62, abar63, abar64, abar65, abar71, abar73, abar74, abar75, abar76, b1, b3, b4, b5, bbar1, bbar3, bbar4, bbar5, bbar6, btilde1, btilde3, btilde4, btilde5, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6, bptilde7 = cache - k1 = integrator.fsalfirst.x[1] - - ku = uprev + dt * (c2 * duprev + dt * (a21 * k1)) - kdu = duprev + dt * (abar21 * k1) - - k2 = f.f1(kdu, ku, p, t + dt * c2) - ku = uprev + dt * (c3 * duprev + dt * (a31 * k1 + a32 * k2)) - kdu = duprev + dt * (abar31 * k1 + abar32 * k2) - - k3 = f.f1(kdu, ku, p, t + dt * c3) - ku = uprev + dt * (c4 * duprev + dt * (a41 * k1 + a43 * k3)) # a42 = 0 - kdu = duprev + dt * (abar41 * k1 + abar42 * k2 + abar43 * k3) - - k4 = f.f1(kdu, ku, p, t + dt * c4) - ku = uprev + dt * (c5 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) - kdu = duprev + dt * (abar51 * k1 + abar52 * k2 + abar53 * k3 + abar54 * k4) - - k5 = f.f1(kdu, ku, p, t + dt * c5) - ku = uprev + - dt * (c6 * duprev + dt * (a61 * k1 + a62 * k2 + a63 * k3 + a64 * k4)) # a65 = 0 - kdu = duprev + - dt * (abar61 * k1 + abar62 * k2 + abar63 * k3 + abar64 * k4 + abar65 * k5) - - k6 = f.f1(kdu, ku, p, t + dt * c6) - ku = uprev + - dt * (c7 * duprev + - dt * (a71 * k1 + a73 * k3 + a74 * k4 + a75 * k5)) # a72 = a76 = 0 - kdu = duprev + - dt * (abar71 * k1 + abar73 * k3 + abar74 * k4 + abar75 * k5 + - abar76 * k6) # abar72 = 0 - - k7 = f.f1(kdu, ku, p, t + dt * c7) - u = uprev + dt * (duprev + dt * (b1 * k1 + b3 * k3 + b4 * k4 + b5 * k5)) # no b6, b7 - du = duprev + dt * (bbar1 * k1 + bbar3 * k3 + bbar4 * k4 + bbar5 * k5 + bbar6 * k6) # no b2, b7 - - integrator.u = ArrayPartition((du, u)) - integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) - integrator.stats.nf += 7 - integrator.stats.nf2 += 1 - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - - if integrator.opts.adaptive - dtsq = dt^2 - uhat = dtsq * (btilde1 * k1 + btilde3 * k3 + btilde4 * k4 + btilde5 * k5) - duhat = dt * (bptilde1 * k1 + bptilde3 * k3 + bptilde4 * k4 + bptilde5 * k5 + - bptilde6 * k6 + bptilde7 * k7) - utilde = ArrayPartition((duhat, uhat)) - atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -@muladd function perform_step!(integrator, cache::FineRKN5Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - du, u = integrator.u.x - duprev, uprev = integrator.uprev.x - @unpack tmp, atmp, fsalfirst, k2, k3, k4, k5, k6, k7, k, utilde = cache - @unpack c1, c2, c3, c4, c5, c6, c7, a21, a31, a32, a41, a43, a51, a52, a53, a54, a61, a62, a63, a64, a71, a73, a74, a75, abar21, abar31, abar32, abar41, abar42, abar43, abar51, abar52, abar53, abar54, abar61, abar62, abar63, abar64, abar65, abar71, abar73, abar74, abar75, abar76, b1, b3, b4, b5, bbar1, bbar3, bbar4, bbar5, bbar6, btilde1, btilde3, btilde4, btilde5, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6, bptilde7 = cache.tab - kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] - uidx = eachindex(integrator.uprev.x[2]) - k1 = integrator.fsalfirst.x[1] - - @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a21 * k1)) - @.. broadcast=false kdu=duprev + dt * (abar21 * k1) - - f.f1(k2, kdu, ku, p, t + dt * c2) - @.. broadcast=false ku=uprev + dt * (c3 * duprev + dt * (a31 * k1 + a32 * k2)) - @.. broadcast=false kdu=duprev + dt * (abar31 * k1 + abar32 * k2) - - f.f1(k3, kdu, ku, p, t + dt * c3) - @.. broadcast=false ku=uprev + - dt * (c4 * duprev + dt * (a41 * k1 + a43 * k3)) # a42 = 0 - @.. broadcast=false kdu=duprev + dt * (abar41 * k1 + abar42 * k2 + abar43 * k3) - - f.f1(k4, kdu, ku, p, t + dt * c4) - @.. broadcast=false ku=uprev + - dt * - (c5 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) - @.. broadcast=false kdu=duprev + - dt * (abar51 * k1 + abar52 * k2 + abar53 * k3 + abar54 * k4) - - f.f1(k5, kdu, ku, p, t + dt * c5) - @.. broadcast=false ku=uprev + - dt * (c6 * duprev + - dt * (a61 * k1 + a62 * k2 + a63 * k3 + a64 * k4)) # a65 = 0 - @.. broadcast=false kdu=duprev + - dt * (abar61 * k1 + abar62 * k2 + abar63 * k3 + abar64 * k4 + - abar65 * k5) - - f.f1(k6, kdu, ku, p, t + dt * c6) - @.. broadcast=false ku=uprev + - dt * (c7 * duprev + - dt * (a71 * k1 + a73 * k3 + a74 * k4 + a75 * k5)) # a72 = a76 = 0 - @.. broadcast=false kdu=duprev + - dt * (abar71 * k1 + abar73 * k3 + abar74 * k4 + - abar75 * k5 + abar76 * k6) # abar72 = 0 - - f.f1(k7, kdu, ku, p, t + dt * c7) - @.. broadcast=false u=uprev + - dt * (duprev + dt * (b1 * k1 + b3 * k3 + b4 * k4 + b5 * k5)) - @.. broadcast=false du=duprev + - dt * - (bbar1 * k1 + bbar3 * k3 + bbar4 * k4 + bbar5 * k5 + bbar6 * k6) - - f.f1(k.x[1], du, u, p, t + dt) - f.f2(k.x[2], du, u, p, t + dt) - integrator.stats.nf += 7 - integrator.stats.nf2 += 1 - if integrator.opts.adaptive - duhat, uhat = utilde.x - dtsq = dt^2 - @.. broadcast=false uhat=dtsq * - (btilde1 * k1 + btilde3 * k3 + btilde4 * k4 + - btilde5 * k5) - @.. broadcast=false duhat=dt * - (bptilde1 * k1 + bptilde3 * k3 + bptilde4 * k4 + - bptilde5 * k5 + bptilde6 * k6 + bptilde7 * k7) - - calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -@muladd function perform_step!(integrator, cache::Nystrom4VelocityIndependentConstantCache, - repeat_step = false) - @unpack t, dt, f, p = integrator - duprev, uprev = integrator.uprev.x - k₁ = integrator.fsalfirst.x[1] - halfdt = dt / 2 - dtsq = dt^2 - eighth_dtsq = dtsq / 8 - half_dtsq = dtsq / 2 - ttmp = t + halfdt - - ## y₁ = y₀ + hy'₀ + h²∑b̄ᵢk'ᵢ - ku = uprev + halfdt * duprev + eighth_dtsq * k₁ - - k₂ = f.f1(duprev, ku, p, ttmp) - ku = uprev + dt * duprev + half_dtsq * k₂ - - k₃ = f.f1(duprev, ku, p, t + dt) - u = uprev + (dtsq / 6) * (k₁ + 2 * k₂) + dt * duprev - du = duprev + (dt / 6) * (k₁ + k₃ + 4 * k₂) - - integrator.u = ArrayPartition((du, u)) - integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) - integrator.stats.nf += 3 - integrator.stats.nf2 += 1 - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -@muladd function perform_step!(integrator, cache::Nystrom4VelocityIndependentCache, - repeat_step = false) - @unpack t, dt, f, p = integrator - du, u = integrator.u.x - duprev, uprev = integrator.uprev.x - @unpack tmp, fsalfirst, k₂, k₃, k = cache - kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] - k₁ = integrator.fsalfirst.x[1] - halfdt = dt / 2 - dtsq = dt^2 - eighth_dtsq = dtsq / 8 - half_dtsq = dtsq / 2 - ttmp = t + halfdt - - ## y₁ = y₀ + hy'₀ + h²∑b̄ᵢk'ᵢ - @.. broadcast=false ku=uprev + halfdt * duprev + eighth_dtsq * k₁ - - f.f1(k₂, duprev, ku, p, ttmp) - @.. broadcast=false ku=uprev + dt * duprev + half_dtsq * k₂ - - f.f1(k₃, duprev, ku, p, t + dt) - @.. broadcast=false u=uprev + (dtsq / 6) * (k₁ + 2 * k₂) + dt * duprev - @.. broadcast=false du=duprev + (dt / 6) * (k₁ + k₃ + 4 * k₂) - - f.f1(k.x[1], du, u, p, t + dt) - f.f2(k.x[2], du, u, p, t + dt) - integrator.stats.nf += 3 - integrator.stats.nf2 += 1 -end - -@muladd function perform_step!(integrator, cache::IRKN3ConstantCache, repeat_step = false) - @unpack t, dt, k, tprev, f, p = integrator - duprev, uprev = integrator.uprev.x - duprev2, uprev2 = integrator.uprev2.x - @unpack bconst1, bconst2, c1, a21, b1, b2, bbar1, bbar2 = cache - k₁ = integrator.fsalfirst - # if there's a discontinuity or the solver is in the first step - if integrator.iter < 2 && !integrator.u_modified - perform_step!(integrator, Nystrom4VelocityIndependentConstantCache()) - k = integrator.fsallast - k1cache = ArrayPartition((k.x[1], f.f1(duprev, uprev, p, t + c1 * dt))) - kdu = uprev + dt * (c1 * duprev + dt * a21 * k1cache.x[1]) - k₂.x[1] = f.f1(duprev, kdu, p, t + c1 * dt) - integrator.stats.nf += 2 - else - kdu = uprev2 + dt * (c1 * duprev2 + dt * a21 * k1cache.x[1]) - ku = uprev + dt * (c1 * duprev + dt * a21 * k1cache.x[2]) - - k₂x1 = f.f1(duprev, ku, p, t + c1 * dt) - du = duprev + - dt * (b1 * k1cache.x[1] + bbar1 * k1cache.x[1] + b2 * (k₂x1 - k₂.x[1])) - u = uprev + bconst1 * dt * duprev + - dt * (bconst2 * duprev2 + dt * bbar2 * (k₂x1 - k₂.x[1])) - - integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), - f.f2(du, u, p, t + dt))) - integrator.stats.nf += 3 - integrator.stats.nf2 += 1 - copyto!(k₂.x[1], k₂.x[2]) - k1cache = ArrayPartition((k1cache.x[1], k.x[2])) - end # end if -end - -@muladd function perform_step!(integrator, cache::IRKN3Cache, repeat_step = false) - @unpack t, dt, k, tprev, f, p = integrator - du, u = integrator.u.x - duprev, uprev = integrator.uprev.x - duprev2, uprev2 = integrator.uprev2.x - uidx = eachindex(integrator.uprev.x[1]) - @unpack tmp, fsalfirst, k₂, k = cache - @unpack bconst1, bconst2, c1, a21, b1, b2, bbar1, bbar2 = cache.tab - kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] - k1cache = cache.tmp2 - k₁ = fsalfirst - # if there's a discontinuity or the solver is in the first step - if integrator.iter < 2 && !integrator.u_modified - perform_step!(integrator, integrator.cache.onestep_cache) - copyto!(k1cache.x[1], k.x[1]) - f.f1(k1cache.x[2], duprev, uprev, p, t + c1 * dt) - @.. broadcast=false kdu=uprev + dt * (c1 * duprev + dt * a21 * k1cache.x[2]) - f.f1(k₂.x[1], duprev, kdu, p, t + c1 * dt) - integrator.stats.nf += 2 - else - @.. broadcast=false kdu=uprev2 + dt * (c1 * duprev2 + dt * a21 * k1cache.x[1]) - @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1cache.x[2]) - - f.f1(k₂.x[2], duprev, ku, p, t + c1 * dt) - @tight_loop_macros for i in uidx - @inbounds u[i] = uprev[i] + bconst1 * dt * duprev[i] + - dt * - (bconst2 * duprev2[i] + dt * bbar2 * (k₂.x[2][i] - k₂.x[1][i])) - @inbounds du[i] = duprev[i] + - dt * (b1 * k1cache.x[1][i] + bbar1 * k1cache.x[2][i] + - b2 * (k₂.x[2][i] - k₂.x[1][i])) - end - f.f1(k.x[1], du, u, p, t + dt) - f.f2(k.x[2], du, u, p, t + dt) - integrator.stats.nf += 3 - integrator.stats.nf2 += 1 - copyto!(k₂.x[1], k₂.x[2]) - copyto!(k1cache.x[2], k1cache.x[1]) - copyto!(k1cache.x[1], k.x[1]) - end # end if -end - -@muladd function perform_step!(integrator, cache::IRKN4Cache, repeat_step = false) - @unpack t, dt, k, tprev, f, p = integrator - du, u = integrator.u.x - duprev, uprev = integrator.uprev.x - duprev2, uprev2 = integrator.uprev2.x - uidx = eachindex(integrator.uprev.x[1]) - @unpack tmp, tmp2, fsalfirst, k₂, k₃, k = cache - @unpack bconst1, bconst2, c1, c2, a21, a32, b1, b2, b3, bbar1, bbar2, bbar3 = cache.tab - kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] - k1cache = integrator.cache.tmp2 - k₁ = fsalfirst - # if there's a discontinuity or the solver is in the first step - if integrator.iter < 2 && !integrator.u_modified - perform_step!(integrator, integrator.cache.onestep_cache) - copyto!(k1cache.x[1], k.x[1]) - f.f1(k1cache.x[2], duprev, uprev, p, t + c1 * dt) - @.. broadcast=false kdu=uprev + dt * (c1 * duprev + dt * a21 * k1cache.x[1]) - f.f1(k₂.x[1], duprev, kdu, p, t + c1 * dt) - @.. broadcast=false kdu=uprev + dt * (c2 * duprev + dt * a32 * k1cache.x[2]) - f.f1(k₃.x[1], duprev, kdu, p, t + c1 * dt) - integrator.stats.nf += 3 - else - @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1cache.x[1]) - @.. broadcast=false kdu=uprev2 + dt * (c1 * duprev2 + dt * a21 * k1cache.x[2]) - - f.f1(k₂.x[2], duprev, ku, p, t + c1 * dt) - @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * a32 * k₂.x[2]) - @.. broadcast=false kdu=uprev2 + dt * (c2 * duprev2 + dt * a32 * k₂.x[1]) - - f.f1(k₃.x[2], duprev, ku, p, t + c2 * dt) - @tight_loop_macros for i in uidx - @inbounds u[i] = uprev[i] + dt * bconst1 * duprev[i] + - dt * (bconst2 * duprev2[i] + - dt * (bbar2 * (k₂.x[2][i] - k₂.x[1][i]) + - bbar3 * (k₃.x[2][i] - k₃.x[1][i]))) - @inbounds du[i] = duprev[i] + - dt * (b1 * k1cache.x[1][i] + bbar1 * k1cache.x[2][i] + - b2 * (k₂.x[2][i] - k₂.x[1][i]) + - b3 * (k₃.x[2][i] - k₃.x[1][i])) - end - f.f1(k.x[1], du, u, p, t + dt) - f.f2(k.x[2], du, u, p, t + dt) - integrator.stats.nf += 4 - integrator.stats.nf2 += 1 - copyto!(k₂.x[1], k₂.x[2]) - copyto!(k₃.x[1], k₃.x[2]) - copyto!(k1cache.x[2], k1cache.x[1]) - copyto!(k1cache.x[1], k.x[1]) - end # end if -end - -@muladd function perform_step!(integrator, cache::Nystrom5VelocityIndependentConstantCache, - repeat_step = false) - @unpack t, dt, f, p = integrator - duprev, uprev = integrator.uprev.x - @unpack c1, c2, a21, a31, a32, a41, a42, a43, bbar1, bbar2, bbar3, b1, b2, b3, b4 = cache - k₁ = integrator.fsalfirst.x[1] - - ku = uprev + dt * (c1 * duprev + dt * a21 * k₁) - - k₂ = f.f1(duprev, ku, p, t + c1 * dt) - ku = uprev + dt * (c2 * duprev + dt * (a31 * k₁ + a32 * k₂)) - - k₃ = f.f1(duprev, ku, p, t + c2 * dt) - ku = uprev + dt * (duprev + dt * (a41 * k₁ + a42 * k₂ + a43 * k₃)) - - k₄ = f.f1(duprev, ku, p, t + dt) - u = uprev + dt * (duprev + dt * (bbar1 * k₁ + bbar2 * k₂ + bbar3 * k₃)) - du = duprev + dt * (b1 * k₁ + b2 * k₂ + b3 * k₃ + b4 * k₄) - - integrator.u = ArrayPartition((du, u)) - integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) - integrator.stats.nf += 4 - integrator.stats.nf2 += 1 - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -@muladd function perform_step!(integrator, cache::Nystrom5VelocityIndependentCache, - repeat_step = false) - @unpack t, dt, f, p = integrator - du, u = integrator.u.x - duprev, uprev = integrator.uprev.x - uidx = eachindex(integrator.uprev.x[1]) - @unpack tmp, fsalfirst, k₂, k₃, k₄, k = cache - @unpack c1, c2, a21, a31, a32, a41, a42, a43, bbar1, bbar2, bbar3, b1, b2, b3, b4 = cache.tab - kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] - k₁ = integrator.fsalfirst.x[1] - - @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k₁) - - f.f1(k₂, du, ku, p, t + c1 * dt) - @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k₁ + a32 * k₂)) - - f.f1(k₃, du, ku, p, t + c2 * dt) - #@tight_loop_macros for i in uidx - # @inbounds ku[i] = uprev[i] + dt*(duprev[i] + dt*(a41*k₁[i] + a42*k₂[i] + a43*k₃[i])) - #end - @.. broadcast=false ku=uprev + dt * (duprev + dt * (a41 * k₁ + a42 * k₂ + a43 * k₃)) - - f.f1(k₄, duprev, ku, p, t + dt) - #@tight_loop_macros for i in uidx - # @inbounds u[i] = uprev[i] + dt*(duprev[i] + dt*(bbar1*k₁[i] + bbar2*k₂[i] + bbar3*k₃[i])) - # @inbounds du[i] = duprev[i] + dt*(b1*k₁[i] + b2*k₂[i] + b3*k₃[i] + b4*k₄[i]) - #end - @.. broadcast=false u=uprev + - dt * (duprev + dt * (bbar1 * k₁ + bbar2 * k₂ + bbar3 * k₃)) - @.. broadcast=false du=duprev + dt * (b1 * k₁ + b2 * k₂ + b3 * k₃ + b4 * k₄) - f.f1(k.x[1], du, u, p, t + dt) - f.f2(k.x[2], du, u, p, t + dt) - integrator.stats.nf += 4 - integrator.stats.nf2 += 1 - return nothing -end - -@muladd function perform_step!(integrator, cache::DPRKN4ConstantCache, repeat_step = false) - @unpack t, dt, f, p = integrator - duprev, uprev = integrator.uprev.x - @unpack c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, bp1, bp2, bp3, bp4, btilde1, btilde2, btilde3, btilde4, bptilde1, bptilde2, bptilde3, bptilde4 = cache - k1 = integrator.fsalfirst.x[1] - - ku = uprev + dt * (c1 * duprev + dt * a21 * k1) - - k2 = f.f1(duprev, ku, p, t + dt * c1) - ku = uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) - - k3 = f.f1(duprev, ku, p, t + dt * c2) - ku = uprev + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) - - k4 = f.f1(duprev, ku, p, t + dt * c3) - - u = uprev + dt * (duprev + dt * (b1 * k1 + b2 * k2 + b3 * k3)) - du = duprev + dt * (bp1 * k1 + bp2 * k2 + bp3 * k3 + bp4 * k4) - - integrator.u = ArrayPartition((du, u)) - integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) - integrator.stats.nf += 4 - integrator.stats.nf2 += 1 - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - - if integrator.opts.adaptive - dtsq = dt^2 - uhat = dtsq * (btilde1 * k1 + btilde2 * k2 + btilde3 * k3 + btilde4 * k4) - duhat = dt * (bptilde1 * k1 + bptilde2 * k2 + bptilde3 * k3 + bptilde4 * k4) - utilde = ArrayPartition((duhat, uhat)) - atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -@muladd function perform_step!(integrator, cache::DPRKN4Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - du, u = integrator.u.x - duprev, uprev = integrator.uprev.x - @unpack tmp, atmp, fsalfirst, k2, k3, k4, k, utilde = cache - @unpack c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, bp1, bp2, bp3, bp4, btilde1, btilde2, btilde3, btilde4, bptilde1, bptilde2, bptilde3, bptilde4 = cache.tab - kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] - uidx = eachindex(integrator.uprev.x[2]) - k1 = integrator.fsalfirst.x[1] - - @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1) - - f.f1(k2, duprev, ku, p, t + dt * c1) - @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) - - f.f1(k3, duprev, ku, p, t + dt * c2) - @.. broadcast=false ku=uprev + - dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) - - f.f1(k4, duprev, ku, p, t + dt * c3) - @tight_loop_macros for i in uidx - @inbounds u[i] = uprev[i] + - dt * (duprev[i] + - dt * (b1 * k1[i] + b2 * k2[i] + b3 * k3[i])) - @inbounds du[i] = duprev[i] + - dt * (bp1 * k1[i] + bp2 * k2[i] + bp3 * k3[i] + bp4 * k4[i]) - end - - f.f1(k.x[1], du, u, p, t + dt) - f.f2(k.x[2], du, u, p, t + dt) - integrator.stats.nf += 4 - integrator.stats.nf2 += 1 - if integrator.opts.adaptive - duhat, uhat = utilde.x - dtsq = dt^2 - @tight_loop_macros for i in uidx - @inbounds uhat[i] = dtsq * - (btilde1 * k1[i] + btilde2 * k2[i] + btilde3 * k3[i] + - btilde4 * k4[i]) - @inbounds duhat[i] = dt * - (bptilde1 * k1[i] + bptilde2 * k2[i] + bptilde3 * k3[i] + - bptilde4 * k4[i]) - end - calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -@muladd function perform_step!(integrator, cache::DPRKN5ConstantCache, repeat_step = false) - @unpack t, dt, f, p = integrator - duprev, uprev = integrator.uprev.x - @unpack c1, c2, c3, c4, c5, a21, a31, a32, a41, a43, a51, a53, a54, a61, a63, a64, a65, b1, b3, b4, b5, bp1, bp3, bp4, bp5, bp6, btilde1, btilde3, btilde4, btilde5, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6 = cache - k1 = integrator.fsalfirst.x[1] - - ku = uprev + dt * (c1 * duprev + dt * a21 * k1) - - k2 = f.f1(duprev, ku, p, t + dt * c1) - ku = uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) - - k3 = f.f1(duprev, ku, p, t + dt * c2) - ku = uprev + dt * (c3 * duprev + dt * (a41 * k1 + a43 * k3)) - - k4 = f.f1(duprev, ku, p, t + dt * c3) - ku = uprev + dt * (c4 * duprev + dt * (a51 * k1 + a53 * k3 + a54 * k4)) - - k5 = f.f1(duprev, ku, p, t + dt * c4) - ku = uprev + - dt * (c5 * duprev + dt * (a61 * k1 + a63 * k3 + a64 * k4 + a65 * k5)) - - k6 = f.f1(duprev, ku, p, t + dt * c5) - u = uprev + - dt * (duprev + dt * (b1 * k1 + b3 * k3 + b4 * k4 + b5 * k5)) - du = duprev + - dt * (bp1 * k1 + bp3 * k3 + bp4 * k4 + bp5 * k5 + bp6 * k6) - - integrator.u = ArrayPartition((du, u)) - integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) - integrator.stats.nf += 6 - integrator.stats.nf2 += 1 - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - - if integrator.opts.adaptive - dtsq = dt^2 - uhat = dtsq * (btilde1 * k1 + btilde3 * k3 + btilde4 * k4 + btilde5 * k5) - duhat = dt * (bptilde1 * k1 + bptilde3 * k3 + bptilde4 * k4 + bptilde5 * k5 + - bptilde6 * k6) - utilde = ArrayPartition((duhat, uhat)) - atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -@muladd function perform_step!(integrator, cache::DPRKN5Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - du, u = integrator.u.x - duprev, uprev = integrator.uprev.x - @unpack tmp, atmp, fsalfirst, k2, k3, k4, k5, k6, k, utilde = cache - @unpack c1, c2, c3, c4, c5, a21, a31, a32, a41, a43, a51, a53, a54, a61, a63, a64, a65, b1, b3, b4, b5, bp1, bp3, bp4, bp5, bp6, btilde1, btilde3, btilde4, btilde5, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6 = cache.tab - kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] - uidx = eachindex(integrator.uprev.x[2]) - k1 = integrator.fsalfirst.x[1] - - @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1) - - f.f1(k2, duprev, ku, p, t + dt * c1) - @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) - - f.f1(k3, duprev, ku, p, t + dt * c2) - @.. broadcast=false ku=uprev + - dt * (c3 * duprev + dt * (a41 * k1 + a43 * k3)) - - f.f1(k4, duprev, ku, p, t + dt * c3) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c4 * duprev[i] + - dt * (a51 * k1[i] + a53 * k3[i] + a54 * k4[i])) - end - - f.f1(k5, duprev, ku, p, t + dt * c4) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c5 * duprev[i] + - dt * (a61 * k1[i] + a63 * k3[i] + a64 * k4[i] + a65 * k5[i])) - end - - f.f1(k6, duprev, ku, p, t + dt * c5) - @tight_loop_macros for i in uidx - @inbounds u[i] = uprev[i] + - dt * (duprev[i] + - dt * (b1 * k1[i] + b3 * k3[i] + b4 * k4[i] + b5 * k5[i])) - @inbounds du[i] = duprev[i] + - dt * (bp1 * k1[i] + bp3 * k3[i] + bp4 * k4[i] + bp5 * k5[i] + - bp6 * k6[i]) - end - - f.f1(k.x[1], du, u, p, t + dt) - f.f2(k.x[2], du, u, p, t + dt) - integrator.stats.nf += 6 - integrator.stats.nf2 += 1 - if integrator.opts.adaptive - duhat, uhat = utilde.x - dtsq = dt^2 - @tight_loop_macros for i in uidx - @inbounds uhat[i] = dtsq * - (btilde1 * k1[i] + btilde3 * k3[i] + btilde4 * k4[i] + - btilde5 * k5[i]) - @inbounds duhat[i] = dt * - (bptilde1 * k1[i] + bptilde3 * k3[i] + bptilde4 * k4[i] + - bptilde5 * k5[i] + bptilde6 * k6[i]) - end - calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -function initialize!(integrator, cache::DPRKN6ConstantCache) - duprev, uprev = integrator.uprev.x - integrator.kshortsize = 3 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - kdu = integrator.f.f1(duprev, uprev, integrator.p, integrator.t) - ku = integrator.f.f2(duprev, uprev, integrator.p, integrator.t) - integrator.stats.nf += 1 - integrator.stats.nf2 += 1 - integrator.fsalfirst = ArrayPartition((kdu, ku)) - integrator.fsallast = zero(integrator.fsalfirst) - - integrator.k[1] = integrator.fsalfirst - @inbounds for i in 2:(integrator.kshortsize - 1) - integrator.k[i] = zero(integrator.fsalfirst) - end - integrator.k[integrator.kshortsize] = integrator.fsallast -end - -@muladd function perform_step!(integrator, cache::DPRKN6ConstantCache, repeat_step = false) - @unpack t, dt, f, p = integrator - duprev, uprev = integrator.uprev.x - @unpack c1, c2, c3, c4, c5, a21, a31, a32, a41, a42, a43, a51, a52, a53, a54, a61, a63, a64, a65, b1, b3, b4, b5, bp1, bp3, bp4, bp5, bp6, btilde1, btilde2, btilde3, btilde4, btilde5, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6 = cache - k1 = integrator.fsalfirst.x[1] - - ku = uprev + dt * (c1 * duprev + dt * a21 * k1) - - k2 = f.f1(duprev, ku, p, t + dt * c1) - ku = uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) - - k3 = f.f1(duprev, ku, p, t + dt * c2) - ku = uprev + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) - - k4 = f.f1(duprev, ku, p, t + dt * c3) - ku = uprev + dt * (c4 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) - - k5 = f.f1(duprev, ku, p, t + dt * c4) - ku = uprev + dt * (c5 * duprev + dt * (a61 * k1 + a63 * k3 + a64 * k4 + a65 * k5)) # no a62 - - k6 = f.f1(duprev, ku, p, t + dt * c5) - u = uprev + dt * (duprev + dt * (b1 * k1 + b3 * k3 + b4 * k4 + b5 * k5)) # b1 -- b5, no b2 - du = duprev + dt * (bp1 * k1 + bp3 * k3 + bp4 * k4 + bp5 * k5 + bp6 * k6) # bp1 -- bp6, no bp2 - - #= - @tight_loop_macros for i in uidx - @inbounds u[i] = uprev[i] + dt*(duprev[i] + dt*(bhat1*k1.x[2][i] + bhat2*k2.x[2][i] + bhat3*k3.x[2][i])) - @inbounds du[i] = duprev[i]+ dt*(bphat1*k1.x[2][i] + bphat3*k3.x[2][i] + bphat4*k4.x[2][i] + bphat5*k5.x[2][i] + bphat6*k6.x[2][i]) - end - =# - - integrator.u = ArrayPartition((du, u)) - integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) - integrator.k[1] = ArrayPartition(integrator.fsalfirst.x[1], k2) - integrator.k[2] = ArrayPartition(k3, k4) - integrator.k[3] = ArrayPartition(k5, k6) - integrator.stats.nf += 6 - integrator.stats.nf2 += 1 - - if integrator.opts.adaptive - dtsq = dt^2 - uhat = dtsq * - (btilde1 * k1 + btilde2 * k2 + btilde3 * k3 + btilde4 * k4 + btilde5 * k5) - duhat = dt * (bptilde1 * k1 + bptilde3 * k3 + bptilde4 * k4 + bptilde5 * k5 + - bptilde6 * k6) - utilde = ArrayPartition((duhat, uhat)) - atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -function initialize!(integrator, cache::DPRKN6Cache) - @unpack fsalfirst, k = cache - duprev, uprev = integrator.uprev.x - - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 3 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = ArrayPartition(cache.fsalfirst.x[1], cache.k2) - integrator.k[2] = ArrayPartition(cache.k3, cache.k4) - integrator.k[3] = ArrayPartition(cache.k5, cache.k6) - integrator.f.f1(integrator.fsallast.x[1], duprev, uprev, integrator.p, integrator.t) - integrator.f.f2(integrator.fsallast.x[2], duprev, uprev, integrator.p, integrator.t) - integrator.stats.nf += 1 - integrator.stats.nf2 += 1 -end - -@muladd function perform_step!(integrator, cache::DPRKN6Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - du, u = integrator.u.x - duprev, uprev = integrator.uprev.x - @unpack tmp, atmp, fsalfirst, k2, k3, k4, k5, k6, k, utilde = cache - @unpack c1, c2, c3, c4, c5, a21, a31, a32, a41, a42, a43, a51, a52, a53, a54, a61, a63, a64, a65, b1, b3, b4, b5, bp1, bp3, bp4, bp5, bp6, btilde1, btilde2, btilde3, btilde4, btilde5, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6 = cache.tab - kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] - uidx = eachindex(integrator.uprev.x[2]) - k1 = integrator.fsalfirst.x[1] - - @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1) - - f.f1(k2, du, ku, p, t + dt * c1) - @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) - - f.f1(k3, du, ku, p, t + dt * c2) - @.. broadcast=false ku=uprev + - dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) - - f.f1(k4, du, ku, p, t + dt * c3) - @.. broadcast=false ku=uprev + - dt * - (c4 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) - - f.f1(k5, du, ku, p, t + dt * c4) - @.. broadcast=false ku=uprev + - dt * - (c5 * duprev + dt * (a61 * k1 + a63 * k3 + a64 * k4 + a65 * k5)) # no a62 - - f.f1(k6, du, ku, p, t + dt * c5) - - @.. broadcast=false u=uprev + - dt * (duprev + dt * (b1 * k1 + b3 * k3 + b4 * k4 + b5 * k5)) # b1 -- b5, no b2 - @.. broadcast=false du=duprev + - dt * (bp1 * k1 + bp3 * k3 + bp4 * k4 + bp5 * k5 + bp6 * k6) # bp1 -- bp6, no bp2 - - #= - @tight_loop_macros for i in uidx - @inbounds u[i] = uprev[i] + dt*(duprev[i] + dt*(bhat1*k1.x[2][i] + bhat2*k2.x[2][i] + bhat3*k3.x[2][i])) - @inbounds du[i] = duprev[i]+ dt*(bphat1*k1.x[2][i] + bphat3*k3.x[2][i] + bphat4*k4.x[2][i] + bphat5*k5.x[2][i] + bphat6*k6.x[2][i]) - end - =# - - f.f1(k.x[1], du, u, p, t + dt) - f.f2(k.x[2], du, u, p, t + dt) - integrator.stats.nf += 6 - integrator.stats.nf2 += 1 - if integrator.opts.adaptive - duhat, uhat = utilde.x - dtsq = dt^2 - @.. broadcast=false uhat=dtsq * (btilde1 * k1 + btilde2 * k2 + btilde3 * k3 + - btilde4 * k4 + btilde5 * k5) - @.. broadcast=false duhat=dt * (bptilde1 * k1 + bptilde3 * k3 + bptilde4 * k4 + - bptilde5 * k5 + bptilde6 * k6) - calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -@muladd function perform_step!(integrator, cache::DPRKN6FMConstantCache, - repeat_step = false) - @unpack t, dt, f, p = integrator - duprev, uprev = integrator.uprev.x - @unpack c1, c2, c3, c4, c5, a21, a31, a32, a41, a42, a43, a51, a52, a53, a54, a61, a62, a63, a64, a65, b1, b2, b3, b4, b5, bp1, bp2, bp3, bp4, bp5, bp6, btilde1, btilde2, btilde3, btilde4, btilde5, bptilde1, bptilde2, bptilde3, bptilde4, bptilde5 = cache - k1 = integrator.fsalfirst.x[1] - - ku = uprev + dt * (c1 * duprev + dt * a21 * k1) - - k2 = f.f1(duprev, ku, p, t + dt * c1) - ku = uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) - - k3 = f.f1(duprev, ku, p, t + dt * c2) - ku = uprev + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) - - k4 = f.f1(duprev, ku, p, t + dt * c3) - ku = uprev + dt * (c4 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) - - k5 = f.f1(duprev, ku, p, t + dt * c4) - ku = uprev + - dt * (c5 * duprev + dt * (a61 * k1 + a62 * k2 + a63 * k3 + a64 * k4 + a65 * k5)) - - k6 = f.f1(duprev, ku, p, t + dt * c5) - u = uprev + - dt * (duprev + dt * (b1 * k1 + b2 * k2 + b3 * k3 + b4 * k4 + b5 * k5)) - du = duprev + - dt * (bp1 * k1 + bp2 * k2 + bp3 * k3 + bp4 * k4 + bp5 * k5 + bp6 * k6) - - integrator.u = ArrayPartition((du, u)) - integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) - integrator.stats.nf += 6 - integrator.stats.nf2 += 1 - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - - if integrator.opts.adaptive - dtsq = dt^2 - uhat = dtsq * - (btilde1 * k1 + btilde2 * k2 + btilde3 * k3 + btilde4 * k4 + btilde5 * k5) - duhat = dt * (bptilde1 * k1 + bptilde2 * k2 + bptilde3 * k3 + bptilde4 * k4 + - bptilde5 * k5) - utilde = ArrayPartition((duhat, uhat)) - atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -@muladd function perform_step!(integrator, cache::DPRKN6FMCache, repeat_step = false) - @unpack t, dt, f, p = integrator - du, u = integrator.u.x - duprev, uprev = integrator.uprev.x - @unpack tmp, atmp, fsalfirst, k2, k3, k4, k5, k6, k, utilde = cache - @unpack c1, c2, c3, c4, c5, a21, a31, a32, a41, a42, a43, a51, a52, a53, a54, a61, a62, a63, a64, a65, b1, b2, b3, b4, b5, bp1, bp2, bp3, bp4, bp5, bp6, btilde1, btilde2, btilde3, btilde4, btilde5, bptilde1, bptilde2, bptilde3, bptilde4, bptilde5 = cache.tab - kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] - uidx = eachindex(integrator.uprev.x[2]) - k1 = integrator.fsalfirst.x[1] - - @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1) - - f.f1(k2, duprev, ku, p, t + dt * c1) - @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) - - f.f1(k3, duprev, ku, p, t + dt * c2) - @.. broadcast=false ku=uprev + - dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) - - f.f1(k4, duprev, ku, p, t + dt * c3) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c4 * duprev[i] + - dt * (a51 * k1[i] + a52 * k2[i] + a53 * k3[i] + a54 * k4[i])) - end - - f.f1(k5, duprev, ku, p, t + dt * c4) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c5 * duprev[i] + - dt * (a61 * k1[i] + a62 * k2[i] + a63 * k3[i] + a64 * k4[i] + - a65 * k5[i])) - end - - f.f1(k6, duprev, ku, p, t + dt * c5) - @tight_loop_macros for i in uidx - @inbounds u[i] = uprev[i] + - dt * (duprev[i] + - dt * - (b1 * k1[i] + b2 * k2[i] + b3 * k3[i] + b4 * k4[i] + b5 * k5[i])) - @inbounds du[i] = duprev[i] + - dt * (bp1 * k1[i] + bp2 * k2[i] + bp3 * k3[i] + bp4 * k4[i] + - bp5 * k5[i] + bp6 * k6[i]) - end - - f.f1(k.x[1], du, u, p, t + dt) - f.f2(k.x[2], du, u, p, t + dt) - integrator.stats.nf += 6 - integrator.stats.nf2 += 1 - if integrator.opts.adaptive - duhat, uhat = utilde.x - dtsq = dt^2 - @tight_loop_macros for i in uidx - @inbounds uhat[i] = dtsq * - (btilde1 * k1[i] + btilde2 * k2[i] + btilde3 * k3[i] + - btilde4 * k4[i] + btilde5 * k5[i]) - @inbounds duhat[i] = dt * - (bptilde1 * k1[i] + bptilde2 * k2[i] + bptilde3 * k3[i] + - bptilde4 * k4[i] + bptilde5 * k5[i]) - end - calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -@muladd function perform_step!(integrator, cache::DPRKN8ConstantCache, repeat_step = false) - @unpack t, dt, f, p = integrator - duprev, uprev = integrator.uprev.x - @unpack c1, c2, c3, c4, c5, c6, c7, c8, a21, a31, a32, a41, a42, a43, a51, a52, a53, a54, a61, a62, a63, a64, a65, a71, a72, a73, a74, a75, a76, a81, a82, a83, a84, a85, a86, a87, a91, a93, a94, a95, a96, a97, b1, b3, b4, b5, b6, b7, bp1, bp3, bp4, bp5, bp6, bp7, bp8, btilde1, btilde3, btilde4, btilde5, btilde6, btilde7, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6, bptilde7, bptilde8, bptilde9 = cache - k1 = integrator.fsalfirst.x[1] - - ku = uprev + dt * (c1 * duprev + dt * a21 * k1) - - k2 = f.f1(duprev, ku, p, t + dt * c1) - ku = uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) - - k3 = f.f1(duprev, ku, p, t + dt * c2) - ku = uprev + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) - - k4 = f.f1(duprev, ku, p, t + dt * c3) - ku = uprev + dt * (c4 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) - - k5 = f.f1(duprev, ku, p, t + dt * c4) - ku = uprev + - dt * (c5 * duprev + dt * (a61 * k1 + a62 * k2 + a63 * k3 + a64 * k4 + a65 * k5)) - - k6 = f.f1(duprev, ku, p, t + dt * c5) - ku = uprev + - dt * (c6 * duprev + - dt * (a71 * k1 + a72 * k2 + a73 * k3 + a74 * k4 + a75 * k5 + a76 * k6)) - - k7 = f.f1(duprev, ku, p, t + dt * c6) - ku = uprev + - dt * (c7 * duprev + - dt * (a81 * k1 + a82 * k2 + a83 * k3 + a84 * k4 + a85 * k5 + a86 * k6 + a87 * k7)) - - k8 = f.f1(duprev, ku, p, t + dt * c7) - ku = uprev + - dt * (c8 * duprev + - dt * (a91 * k1 + a93 * k3 + a94 * k4 + a95 * k5 + a96 * k6 + a97 * k7)) # no a92 & a98 - - k9 = f.f1(duprev, ku, p, t + dt * c8) - u = uprev + - dt * (duprev + dt * (b1 * k1 + b3 * k3 + b4 * k4 + b5 * k5 + b6 * k6 + b7 * k7)) # b1 -- b7, no b2 - du = duprev + - dt * (bp1 * k1 + bp3 * k3 + bp4 * k4 + bp5 * k5 + bp6 * k6 + bp7 * k7 + bp8 * k8) # bp1 -- bp8, no bp2 - - integrator.u = ArrayPartition((du, u)) - integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) - integrator.stats.nf += 9 - integrator.stats.nf2 += 1 - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - - if integrator.opts.adaptive - dtsq = dt^2 - uhat = dtsq * - (btilde1 * k1 + btilde3 * k3 + btilde4 * k4 + btilde5 * k5 + btilde6 * k6 + - btilde7 * k7) - duhat = dt * (bptilde1 * k1 + bptilde3 * k3 + bptilde4 * k4 + bptilde5 * k5 + - bptilde6 * k6 + bptilde7 * k7 + bptilde8 * k8 + bptilde9 * k9) - utilde = ArrayPartition((duhat, uhat)) - atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -@muladd function perform_step!(integrator, cache::DPRKN8Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - du, u = integrator.u.x - duprev, uprev = integrator.uprev.x - @unpack tmp, atmp, fsalfirst, k2, k3, k4, k5, k6, k7, k8, k9, k, utilde = cache - @unpack c1, c2, c3, c4, c5, c6, c7, c8, a21, a31, a32, a41, a42, a43, a51, a52, a53, a54, a61, a62, a63, a64, a65, a71, a72, a73, a74, a75, a76, a81, a82, a83, a84, a85, a86, a87, a91, a93, a94, a95, a96, a97, b1, b3, b4, b5, b6, b7, bp1, bp3, bp4, bp5, bp6, bp7, bp8, btilde1, btilde3, btilde4, btilde5, btilde6, btilde7, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6, bptilde7, bptilde8, bptilde9 = cache.tab - kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] - uidx = eachindex(integrator.uprev.x[2]) - k1 = integrator.fsalfirst.x[1] - - @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1) - - f.f1(k2, duprev, ku, p, t + dt * c1) - @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) - - f.f1(k3, duprev, ku, p, t + dt * c2) - @.. broadcast=false ku=uprev + - dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) - - f.f1(k4, duprev, ku, p, t + dt * c3) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c4 * duprev[i] + - dt * (a51 * k1[i] + a52 * k2[i] + a53 * k3[i] + a54 * k4[i])) - end - - f.f1(k5, duprev, ku, p, t + dt * c4) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c5 * duprev[i] + - dt * (a61 * k1[i] + a62 * k2[i] + a63 * k3[i] + a64 * k4[i] + - a65 * k5[i])) - end - - f.f1(k6, duprev, ku, p, t + dt * c5) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c6 * duprev[i] + - dt * (a71 * k1[i] + a72 * k2[i] + a73 * k3[i] + a74 * k4[i] + - a75 * k5[i] + a76 * k6[i])) - end - - f.f1(k7, duprev, ku, p, t + dt * c6) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c7 * duprev[i] + - dt * (a81 * k1[i] + a82 * k2[i] + a83 * k3[i] + a84 * k4[i] + - a85 * k5[i] + a86 * k6[i] + a87 * k7[i])) - end - - f.f1(k8, duprev, ku, p, t + dt * c7) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c8 * duprev[i] + - dt * (a91 * k1[i] + a93 * k3[i] + a94 * k4[i] + a95 * k5[i] + - a96 * k6[i] + a97 * k7[i])) # no a92 & a98 - end - - f.f1(k9, duprev, ku, p, t + dt * c8) - @tight_loop_macros for i in uidx - @inbounds u[i] = uprev[i] + - dt * (duprev[i] + - dt * - (b1 * k1[i] + b3 * k3[i] + b4 * k4[i] + b5 * k5[i] + b6 * k6[i] + - b7 * k7[i])) # b1 -- b7, no b2 - @inbounds du[i] = duprev[i] + - dt * (bp1 * k1[i] + bp3 * k3[i] + bp4 * k4[i] + bp5 * k5[i] + - bp6 * k6[i] + bp7 * k7[i] + bp8 * k8[i]) # bp1 -- bp8, no bp2 - end - - f.f1(k.x[1], du, u, p, t + dt) - f.f2(k.x[2], du, u, p, t + dt) - integrator.stats.nf += 9 - integrator.stats.nf2 += 1 - if integrator.opts.adaptive - duhat, uhat = utilde.x - dtsq = dt^2 - @tight_loop_macros for i in uidx - @inbounds uhat[i] = dtsq * - (btilde1 * k1[i] + btilde3 * k3[i] + btilde4 * k4[i] + - btilde5 * k5[i] + btilde6 * k6[i] + btilde7 * k7[i]) - @inbounds duhat[i] = dt * - (bptilde1 * k1[i] + bptilde3 * k3[i] + bptilde4 * k4[i] + - bptilde5 * k5[i] + bptilde6 * k6[i] + bptilde7 * k7[i] + - bptilde8 * k8[i] + bptilde9 * k9[i]) - end - calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -@muladd function perform_step!(integrator, cache::DPRKN12ConstantCache, repeat_step = false) - @unpack t, dt, f, p = integrator - duprev, uprev = integrator.uprev.x - @unpack c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, a21, a31, a32, a41, a42, a43, a51, a53, a54, a61, a63, a64, a65, a71, a73, a74, a75, a76, a81, a84, a85, a86, a87, a91, a93, a94, a95, a96, a97, a98, a101, a103, a104, a105, a106, a107, a108, a109, a111, a113, a114, a115, a116, a117, a118, a119, a1110, a121, a123, a124, a125, a126, a127, a128, a129, a1210, a1211, a131, a133, a134, a135, a136, a137, a138, a139, a1310, a1311, a1312, a141, a143, a144, a145, a146, a147, a148, a149, a1410, a1411, a1412, a1413, a151, a153, a154, a155, a156, a157, a158, a159, a1510, a1511, a1512, a1513, a1514, a161, a163, a164, a165, a166, a167, a168, a169, a1610, a1611, a1612, a1613, a1614, a1615, a171, a173, a174, a175, a176, a177, a178, a179, a1710, a1711, a1712, a1713, a1714, a1715, b1, b7, b8, b9, b10, b11, b12, b13, b14, b15, bp1, bp7, bp8, bp9, bp10, bp11, bp12, bp13, bp14, bp15, bp16, bp17, btilde1, btilde7, btilde8, btilde9, btilde10, btilde11, btilde12, btilde13, btilde14, btilde15, bptilde1, bptilde7, bptilde8, bptilde9, bptilde10, bptilde11, bptilde12, bptilde13, bptilde14, bptilde15, bptilde16, bptilde17 = cache - k1 = integrator.fsalfirst.x[1] - - ku = uprev + dt * (c1 * duprev + dt * a21 * k1) - - k2 = f.f1(duprev, ku, p, t + dt * c1) - ku = uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) - - k3 = f.f1(duprev, ku, p, t + dt * c2) - ku = uprev + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) - - k4 = f.f1(duprev, ku, p, t + dt * c3) - ku = uprev + dt * (c4 * duprev + dt * (a51 * k1 + a53 * k3 + a54 * k4)) # no a52 - - k5 = f.f1(duprev, ku, p, t + dt * c4) - ku = uprev + dt * (c5 * duprev + dt * (a61 * k1 + a63 * k3 + a64 * k4 + a65 * k5)) # no a62 - - k6 = f.f1(duprev, ku, p, t + dt * c5) - ku = uprev + - dt * (c6 * duprev + dt * (a71 * k1 + a73 * k3 + a74 * k4 + a75 * k5 + a76 * k6)) # no a72 - - k7 = f.f1(duprev, ku, p, t + dt * c6) - ku = uprev + - dt * (c7 * duprev + dt * (a81 * k1 + a84 * k4 + a85 * k5 + a86 * k6 + a87 * k7)) # no a82, a83 - - k8 = f.f1(duprev, ku, p, t + dt * c7) - ku = uprev + - dt * (c8 * duprev + - dt * (a91 * k1 + a93 * k3 + a94 * k4 + a95 * k5 + a96 * k6 + a97 * k7 + a98 * k8)) # no a92 - - k9 = f.f1(duprev, ku, p, t + dt * c8) - ku = uprev + - dt * (c9 * duprev + - dt * (a101 * k1 + a103 * k3 + a104 * k4 + a105 * k5 + a106 * k6 + a107 * k7 + - a108 * k8 + a109 * k9)) # no a102 - - k10 = f.f1(duprev, ku, p, t + dt * c9) - ku = uprev + - dt * (c10 * duprev + - dt * (a111 * k1 + a113 * k3 + a114 * k4 + a115 * k5 + a116 * k6 + a117 * k7 + - a118 * k8 + a119 * k9 + a1110 * k10)) # no a112 - - k11 = f.f1(duprev, ku, p, t + dt * c10) - ku = uprev + - dt * (c11 * duprev + - dt * (a121 * k1 + a123 * k3 + a124 * k4 + a125 * k5 + a126 * k6 + a127 * k7 + - a128 * k8 + a129 * k9 + a1210 * k10 + a1211 * k11)) # no a122 - - k12 = f.f1(duprev, ku, p, t + dt * c11) - ku = uprev + - dt * (c12 * duprev + - dt * (a131 * k1 + a133 * k3 + a134 * k4 + a135 * k5 + a136 * k6 + a137 * k7 + - a138 * k8 + a139 * k9 + a1310 * k10 + a1311 * k11 + a1312 * k12)) # no a132 - - k13 = f.f1(duprev, ku, p, t + dt * c12) - ku = uprev + - dt * (c13 * duprev + - dt * (a141 * k1 + a143 * k3 + a144 * k4 + a145 * k5 + a146 * k6 + a147 * k7 + - a148 * k8 + a149 * k9 + a1410 * k10 + a1411 * k11 + a1412 * k12 + a1413 * k13)) # no a142 - - k14 = f.f1(duprev, ku, p, t + dt * c13) - ku = uprev + - dt * (c14 * duprev + - dt * (a151 * k1 + a153 * k3 + a154 * k4 + a155 * k5 + a156 * k6 + a157 * k7 + - a158 * k8 + a159 * k9 + a1510 * k10 + a1511 * k11 + a1512 * k12 + a1513 * k13 + - a1514 * k14)) # no a152 - - k15 = f.f1(duprev, ku, p, t + dt * c14) - ku = uprev + - dt * (c15 * duprev + - dt * (a161 * k1 + a163 * k3 + a164 * k4 + a165 * k5 + a166 * k6 + a167 * k7 + - a168 * k8 + a169 * k9 + a1610 * k10 + a1611 * k11 + a1612 * k12 + a1613 * k13 + - a1614 * k14 + a1615 * k15)) # no a162 - - k16 = f.f1(duprev, ku, p, t + dt * c15) - ku = uprev + - dt * (c16 * duprev + - dt * (a171 * k1 + a173 * k3 + a174 * k4 + a175 * k5 + a176 * k6 + a177 * k7 + - a178 * k8 + a179 * k9 + a1710 * k10 + a1711 * k11 + a1712 * k12 + a1713 * k13 + - a1714 * k14 + a1715 * k15)) # no a172, a1716 - - k17 = f.f1(duprev, ku, p, t + dt * c16) - u = uprev + - dt * (duprev + - dt * (b1 * k1 + b7 * k7 + b8 * k8 + b9 * k9 + b10 * k10 + b11 * k11 + b12 * k12 + - b13 * k13 + b14 * k14 + b15 * k15)) # b1 & b7 -- b15 - du = duprev + - dt * - (bp1 * k1 + bp7 * k7 + bp8 * k8 + bp9 * k9 + bp10 * k10 + bp11 * k11 + bp12 * k12 + - bp13 * k13 + bp14 * k14 + bp15 * k15 + bp16 * k16 + bp17 * k17) # bp1 & bp7 -- bp17 - - integrator.u = ArrayPartition((du, u)) - integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) - integrator.stats.nf += 17 - integrator.stats.nf2 += 1 - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - if integrator.opts.adaptive - dtsq = dt^2 - uhat = dtsq * - (btilde1 * k1 + btilde7 * k7 + btilde8 * k8 + btilde9 * k9 + btilde10 * k10 + - btilde11 * k11 + btilde12 * k12 + btilde13 * k13 + btilde14 * k14 + - btilde15 * k15) # btilde1 & btilde7 -- btilde15 - duhat = dt * (bptilde1 * k1 + bptilde7 * k7 + bptilde8 * k8 + bptilde9 * k9 + - bptilde10 * k10 + bptilde11 * k11 + bptilde12 * k12 + bptilde13 * k13 + - bptilde14 * k14 + bptilde15 * k15 + bptilde16 * k16 + bptilde17 * k17) # bptilde1 & bptilde7 -- bptilde17 - utilde = ArrayPartition((duhat, uhat)) - atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -@muladd function perform_step!(integrator, cache::DPRKN12Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - du, u = integrator.u.x - duprev, uprev = integrator.uprev.x - @unpack tmp, atmp, fsalfirst, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, k17, k, utilde = cache - @unpack c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, a21, a31, a32, a41, a42, a43, a51, a53, a54, a61, a63, a64, a65, a71, a73, a74, a75, a76, a81, a84, a85, a86, a87, a91, a93, a94, a95, a96, a97, a98, a101, a103, a104, a105, a106, a107, a108, a109, a111, a113, a114, a115, a116, a117, a118, a119, a1110, a121, a123, a124, a125, a126, a127, a128, a129, a1210, a1211, a131, a133, a134, a135, a136, a137, a138, a139, a1310, a1311, a1312, a141, a143, a144, a145, a146, a147, a148, a149, a1410, a1411, a1412, a1413, a151, a153, a154, a155, a156, a157, a158, a159, a1510, a1511, a1512, a1513, a1514, a161, a163, a164, a165, a166, a167, a168, a169, a1610, a1611, a1612, a1613, a1614, a1615, a171, a173, a174, a175, a176, a177, a178, a179, a1710, a1711, a1712, a1713, a1714, a1715, b1, b7, b8, b9, b10, b11, b12, b13, b14, b15, bp1, bp7, bp8, bp9, bp10, bp11, bp12, bp13, bp14, bp15, bp16, bp17, btilde1, btilde7, btilde8, btilde9, btilde10, btilde11, btilde12, btilde13, btilde14, btilde15, bptilde1, bptilde7, bptilde8, bptilde9, bptilde10, bptilde11, bptilde12, bptilde13, bptilde14, bptilde15, bptilde16, bptilde17 = cache.tab - kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] - uidx = eachindex(integrator.uprev.x[2]) - k1 = integrator.fsalfirst.x[1] - - @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1) - - f.f1(k2, duprev, ku, p, t + dt * c1) - @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) - - f.f1(k3, duprev, ku, p, t + dt * c2) - @.. broadcast=false ku=uprev + - dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) - - f.f1(k4, duprev, ku, p, t + dt * c3) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * - (c4 * duprev[i] + dt * (a51 * k1[i] + a53 * k3[i] + a54 * k4[i])) # no a52 - end - - f.f1(k5, duprev, ku, p, t + dt * c4) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c5 * duprev[i] + - dt * (a61 * k1[i] + a63 * k3[i] + a64 * k4[i] + a65 * k5[i])) # no a62 - end - - f.f1(k6, duprev, ku, p, t + dt * c5) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c6 * duprev[i] + - dt * (a71 * k1[i] + a73 * k3[i] + a74 * k4[i] + a75 * k5[i] + - a76 * k6[i])) # no a72 - end - - f.f1(k7, duprev, ku, p, t + dt * c6) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c7 * duprev[i] + - dt * (a81 * k1[i] + a84 * k4[i] + a85 * k5[i] + a86 * k6[i] + - a87 * k7[i])) # no a82, a83 - end - - f.f1(k8, duprev, ku, p, t + dt * c7) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c8 * duprev[i] + - dt * (a91 * k1[i] + a93 * k3[i] + a94 * k4[i] + a95 * k5[i] + - a96 * k6[i] + a97 * k7[i] + a98 * k8[i])) # no a92 - end - - f.f1(k9, duprev, ku, p, t + dt * c8) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c9 * duprev[i] + - dt * - (a101 * k1[i] + a103 * k3[i] + a104 * k4[i] + a105 * k5[i] + - a106 * k6[i] + a107 * k7[i] + a108 * k8[i] + a109 * k9[i])) # no a102 - end - - f.f1(k10, duprev, ku, p, t + dt * c9) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c10 * duprev[i] + - dt * - (a111 * k1[i] + a113 * k3[i] + a114 * k4[i] + a115 * k5[i] + - a116 * k6[i] + a117 * k7[i] + a118 * k8[i] + a119 * k9[i] + - a1110 * k10[i])) # no a112 - end - - f.f1(k11, duprev, ku, p, t + dt * c10) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c11 * duprev[i] + - dt * - (a121 * k1[i] + a123 * k3[i] + a124 * k4[i] + a125 * k5[i] + - a126 * k6[i] + a127 * k7[i] + a128 * k8[i] + a129 * k9[i] + - a1210 * k10[i] + a1211 * k11[i])) # no a122 - end - - f.f1(k12, duprev, ku, p, t + dt * c11) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c12 * duprev[i] + - dt * - (a131 * k1[i] + a133 * k3[i] + a134 * k4[i] + a135 * k5[i] + - a136 * k6[i] + a137 * k7[i] + a138 * k8[i] + a139 * k9[i] + - a1310 * k10[i] + a1311 * k11[i] + a1312 * k12[i])) # no a132 - end - - f.f1(k13, duprev, ku, p, t + dt * c12) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c13 * duprev[i] + - dt * - (a141 * k1[i] + a143 * k3[i] + a144 * k4[i] + a145 * k5[i] + - a146 * k6[i] + a147 * k7[i] + a148 * k8[i] + a149 * k9[i] + - a1410 * k10[i] + a1411 * k11[i] + a1412 * k12[i] + - a1413 * k13[i])) # no a142 - end - - f.f1(k14, duprev, ku, p, t + dt * c13) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c14 * duprev[i] + - dt * - (a151 * k1[i] + a153 * k3[i] + a154 * k4[i] + a155 * k5[i] + - a156 * k6[i] + a157 * k7[i] + a158 * k8[i] + a159 * k9[i] + - a1510 * k10[i] + a1511 * k11[i] + a1512 * k12[i] + - a1513 * k13[i] + a1514 * k14[i])) # no a152 - end - - f.f1(k15, duprev, ku, p, t + dt * c14) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c15 * duprev[i] + - dt * - (a161 * k1[i] + a163 * k3[i] + a164 * k4[i] + a165 * k5[i] + - a166 * k6[i] + a167 * k7[i] + a168 * k8[i] + a169 * k9[i] + - a1610 * k10[i] + a1611 * k11[i] + a1612 * k12[i] + - a1613 * k13[i] + a1614 * k14[i] + a1615 * k15[i])) # no a162 - end - - f.f1(k16, duprev, ku, p, t + dt * c15) - @tight_loop_macros for i in uidx - @inbounds ku[i] = uprev[i] + - dt * (c16 * duprev[i] + - dt * - (a171 * k1[i] + a173 * k3[i] + a174 * k4[i] + a175 * k5[i] + - a176 * k6[i] + a177 * k7[i] + a178 * k8[i] + a179 * k9[i] + - a1710 * k10[i] + a1711 * k11[i] + a1712 * k12[i] + - a1713 * k13[i] + a1714 * k14[i] + a1715 * k15[i])) # no a172, a1716 - end - - f.f1(k17, duprev, ku, p, t + dt * c16) - @tight_loop_macros for i in uidx - @inbounds u[i] = uprev[i] + - dt * (duprev[i] + - dt * (b1 * k1[i] + b7 * k7[i] + b8 * k8[i] + b9 * k9[i] + - b10 * k10[i] + b11 * k11[i] + b12 * k12[i] + b13 * k13[i] + - b14 * k14[i] + b15 * k15[i])) # b1 & b7 -- b15 - @inbounds du[i] = duprev[i] + - dt * (bp1 * k1[i] + bp7 * k7[i] + bp8 * k8[i] + bp9 * k9[i] + - bp10 * k10[i] + bp11 * k11[i] + bp12 * k12[i] + bp13 * k13[i] + - bp14 * k14[i] + bp15 * k15[i] + bp16 * k16[i] + bp17 * k17[i]) # bp1 & bp7 -- bp17 - end - - f.f1(k.x[1], du, u, p, t + dt) - f.f2(k.x[2], du, u, p, t + dt) - integrator.stats.nf += 17 - integrator.stats.nf2 += 1 - if integrator.opts.adaptive - duhat, uhat = utilde.x - dtsq = dt^2 - @tight_loop_macros for i in uidx - @inbounds uhat[i] = dtsq * - (btilde1 * k1[i] + btilde7 * k7[i] + btilde8 * k8[i] + - btilde9 * k9[i] + btilde10 * k10[i] + btilde11 * k11[i] + - btilde12 * k12[i] + btilde13 * k13[i] + btilde14 * k14[i] + - btilde15 * k15[i]) # btilde1 & btilde7 -- btilde15 - @inbounds duhat[i] = dt * - (bptilde1 * k1[i] + bptilde7 * k7[i] + bptilde8 * k8[i] + - bptilde9 * k9[i] + bptilde10 * k10[i] + - bptilde11 * k11[i] + bptilde12 * k12[i] + - bptilde13 * k13[i] + bptilde14 * k14[i] + - bptilde15 * k15[i] + bptilde16 * k16[i] + - bptilde17 * k17[i]) # bptilde1 & bptilde7 -- bptilde17 - end - calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -@muladd function perform_step!(integrator, cache::ERKN4ConstantCache, repeat_step = false) - @unpack t, dt, f, p = integrator - duprev, uprev = integrator.uprev.x - @unpack c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, b4, bp1, bp2, bp3, bp4, btilde1, btilde2, btilde3, btilde4, bptilde1, bptilde2, bptilde3, bptilde4 = cache - k1 = integrator.fsalfirst.x[1] - - ku = uprev + dt * (c1 * duprev + dt * a21 * k1) - - k2 = f.f1(duprev, ku, p, t + dt * c1) - ku = uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) - - k3 = f.f1(duprev, ku, p, t + dt * c2) - ku = uprev + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) - - k4 = f.f1(duprev, ku, p, t + dt * c3) - u = uprev + dt * (duprev + dt * (b1 * k1 + b2 * k2 + b3 * k3 + b4 * k4)) - du = duprev + dt * (bp1 * k1 + bp2 * k2 + bp3 * k3 + bp4 * k4) - - integrator.u = ArrayPartition((du, u)) - integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) - integrator.stats.nf += 4 - integrator.stats.nf2 += 1 - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - - if integrator.opts.adaptive - dtsq = dt^2 - uhat = dtsq * (btilde1 * k1 + btilde2 * k2 + btilde3 * k3 + btilde4 * k4) - duhat = dt * (bptilde1 * k1 + bptilde2 * k2 + bptilde3 * k3 + bptilde4 * k4) - utilde = ArrayPartition((duhat, uhat)) - atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -@muladd function perform_step!(integrator, cache::ERKN4Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - du, u = integrator.u.x - duprev, uprev = integrator.uprev.x - @unpack tmp, atmp, fsalfirst, k2, k3, k4, k, utilde = cache - @unpack c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, b4, bp1, bp2, bp3, bp4, btilde1, btilde2, btilde3, btilde4, bptilde1, bptilde2, bptilde3, bptilde4 = cache.tab - kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] - uidx = eachindex(integrator.uprev.x[2]) - k1 = integrator.fsalfirst.x[1] - - @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1) - - f.f1(k2, duprev, ku, p, t + dt * c1) - @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) - - f.f1(k3, duprev, ku, p, t + dt * c2) - @.. broadcast=false ku=uprev + - dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) - - f.f1(k4, duprev, ku, p, t + dt * c3) - @tight_loop_macros for i in uidx - @inbounds u[i] = uprev[i] + - dt * (duprev[i] + - dt * (b1 * k1[i] + b2 * k2[i] + b3 * k3[i] + b4 * k4[i])) - @inbounds du[i] = duprev[i] + - dt * (bp1 * k1[i] + bp2 * k2[i] + bp3 * k3[i] + bp4 * k4[i]) - end - - f.f1(k.x[1], du, u, p, t + dt) - f.f2(k.x[2], du, u, p, t + dt) - integrator.stats.nf += 4 - integrator.stats.nf2 += 1 - if integrator.opts.adaptive - duhat, uhat = utilde.x - dtsq = dt^2 - @tight_loop_macros for i in uidx - @inbounds uhat[i] = dtsq * - (btilde1 * k1[i] + btilde2 * k2[i] + btilde3 * k3[i] + - btilde4 * k4[i]) - @inbounds duhat[i] = dt * - (bptilde1 * k1[i] + bptilde2 * k2[i] + bptilde3 * k3[i] + - bptilde4 * k4[i]) - end - calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -@muladd function perform_step!(integrator, cache::ERKN5ConstantCache, repeat_step = false) - @unpack t, dt, f, p = integrator - duprev, uprev = integrator.uprev.x - @unpack c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, b4, bp1, bp2, bp3, bp4, btilde1, btilde2, btilde3, btilde4 = cache - k1 = integrator.fsalfirst.x[1] - - ku = uprev + dt * (c1 * duprev + dt * a21 * k1) - - k2 = f.f1(duprev, ku, p, t + dt * c1) - ku = uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) - - k3 = f.f1(duprev, ku, p, t + dt * c2) - ku = uprev + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) - - k4 = f.f1(duprev, ku, p, t + dt * c3) - u = uprev + dt * (duprev + dt * (b1 * k1 + b2 * k2 + b3 * k3 + b4 * k4)) - du = duprev + dt * (bp1 * k1 + bp2 * k2 + bp3 * k3 + bp4 * k4) - - integrator.u = ArrayPartition((du, u)) - integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) - integrator.stats.nf += 4 - integrator.stats.nf2 += 1 - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - if integrator.opts.adaptive - dtsq = dt^2 - uhat = dtsq * (btilde1 * k1 + btilde2 * k2 + btilde3 * k3 + btilde4 * k4) - atmp = calculate_residuals(uhat, integrator.uprev.x[2], integrator.u.x[2], - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -@muladd function perform_step!(integrator, cache::ERKN5Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - du, u = integrator.u.x - duprev, uprev = integrator.uprev.x - @unpack tmp, atmp, fsalfirst, k2, k3, k4, k, utilde = cache - @unpack c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, b4, bp1, bp2, bp3, bp4, btilde1, btilde2, btilde3, btilde4 = cache.tab - kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] - uidx = eachindex(integrator.uprev.x[2]) - k1 = integrator.fsalfirst.x[1] - - @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1) - - f.f1(k2, duprev, ku, p, t + dt * c1) - @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) - - f.f1(k3, duprev, ku, p, t + dt * c2) - @.. broadcast=false ku=uprev + - dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) - - f.f1(k4, duprev, ku, p, t + dt * c3) - @tight_loop_macros for i in uidx - @inbounds u[i] = uprev[i] + - dt * (duprev[i] + - dt * (b1 * k1[i] + b2 * k2[i] + b3 * k3[i] + b4 * k4[i])) - @inbounds du[i] = duprev[i] + - dt * (bp1 * k1[i] + bp2 * k2[i] + bp3 * k3[i] + bp4 * k4[i]) - end - - f.f1(k.x[1], du, u, p, t + dt) - f.f2(k.x[2], du, u, p, t + dt) - integrator.stats.nf += 4 - integrator.stats.nf2 += 1 - if integrator.opts.adaptive - duhat, uhat = utilde.x - dtsq = dt^2 - @tight_loop_macros for i in uidx - @inbounds uhat[i] = dtsq * - (btilde1 * k1[i] + btilde2 * k2[i] + btilde3 * k3[i] + - btilde4 * k4[i]) - end - calculate_residuals!(atmp.x[2], uhat, integrator.uprev.x[2], integrator.u.x[2], - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp.x[2], t) - end -end - -@muladd function perform_step!(integrator, cache::ERKN7ConstantCache, repeat_step = false) - @unpack t, dt, f, p = integrator - duprev, uprev = integrator.uprev.x - @unpack c1, c2, c3, c4, c5, c6, a21, a31, a32, a41, a42, a43, a51, a52, a53, a54, a61, a62, a63, a64, a65, a71, a73, a74, a75, a76, b1, b3, b4, b5, b6, bp1, bp3, bp4, bp5, bp6, bp7, btilde1, btilde3, btilde4, btilde5, btilde6, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6, bptilde7 = cache - k1 = integrator.fsalfirst.x[1] - - ku = uprev + dt * (c1 * duprev + dt * a21 * k1) - - k2 = f.f1(duprev, ku, p, t + dt * c1) - ku = uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) - - k3 = f.f1(duprev, ku, p, t + dt * c2) - ku = uprev + dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) - - k4 = f.f1(duprev, ku, p, t + dt * c3) - ku = uprev + dt * (c4 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) - - k5 = f.f1(duprev, ku, p, t + dt * c4) - ku = uprev + - dt * (c5 * duprev + dt * (a61 * k1 + a62 * k2 + a63 * k3 + a64 * k4 + a65 * k5)) - - k6 = f.f1(duprev, ku, p, t + dt * c5) - ku = uprev + - dt * (c6 * duprev + dt * (a71 * k1 + a73 * k3 + a74 * k4 + a75 * k5 + a76 * k6)) - - k7 = f.f1(duprev, ku, p, t + dt * c6) - u = uprev + dt * (duprev + dt * (b1 * k1 + b3 * k3 + b4 * k4 + b5 * k5 + b6 * k6)) - du = duprev + dt * (bp1 * k1 + bp3 * k3 + bp4 * k4 + bp5 * k5 + bp6 * k6 + bp7 * k7) - - integrator.u = ArrayPartition((du, u)) - integrator.fsallast = ArrayPartition((f.f1(du, u, p, t + dt), f.f2(du, u, p, t + dt))) - integrator.stats.nf += 4 - integrator.stats.nf2 += 1 - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - - if integrator.opts.adaptive - dtsq = dt^2 - uhat = dtsq * - (btilde1 * k1 + btilde3 * k3 + btilde4 * k4 + btilde5 * k5 + btilde6 * k6) - duhat = dt * (bptilde1 * k1 + bptilde3 * k3 + bptilde4 * k4 + bptilde5 * k5 + - bptilde6 * k6 + bptilde7 * k7) - utilde = ArrayPartition((duhat, uhat)) - atmp = calculate_residuals(utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -@muladd function perform_step!(integrator, cache::ERKN7Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - du, u = integrator.u.x - duprev, uprev = integrator.uprev.x - @unpack tmp, atmp, fsalfirst, k2, k3, k4, k5, k6, k7, k, utilde = cache - @unpack c1, c2, c3, c4, c5, c6, a21, a31, a32, a41, a42, a43, a51, a52, a53, a54, a61, a62, a63, a64, a65, a71, a73, a74, a75, a76, b1, b3, b4, b5, b6, bp1, bp3, bp4, bp5, bp6, bp7, btilde1, btilde3, btilde4, btilde5, btilde6, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6, bptilde7 = cache.tab - kdu, ku = integrator.cache.tmp.x[1], integrator.cache.tmp.x[2] - uidx = eachindex(integrator.uprev.x[2]) - k1 = integrator.fsalfirst.x[1] - - @.. broadcast=false ku=uprev + dt * (c1 * duprev + dt * a21 * k1) - - f.f1(k2, duprev, ku, p, t + dt * c1) - @.. broadcast=false ku=uprev + dt * (c2 * duprev + dt * (a31 * k1 + a32 * k2)) - - f.f1(k3, duprev, ku, p, t + dt * c2) - @.. broadcast=false ku=uprev + - dt * (c3 * duprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)) - - f.f1(k4, duprev, ku, p, t + dt * c3) - @.. broadcast=false ku=uprev + - dt * - (c4 * duprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)) - - f.f1(k5, duprev, ku, p, t + dt * c4) - @.. broadcast=false ku=uprev + - dt * (c5 * duprev + - dt * (a61 * k1 + a62 * k2 + a63 * k3 + a64 * k4 + a65 * k5)) - - f.f1(k6, duprev, ku, p, t + dt * c5) - @.. broadcast=false ku=uprev + - dt * (c6 * duprev + - dt * (a71 * k1 + a73 * k3 + a74 * k4 + a75 * k5 + a76 * k6)) - - f.f1(k7, duprev, ku, p, t + dt * c6) - @tight_loop_macros for i in uidx - @inbounds u[i] = uprev[i] + - dt * (duprev[i] + - dt * - (b1 * k1[i] + b3 * k3[i] + b4 * k4[i] + b5 * k5[i] + b6 * k6[i])) - @inbounds du[i] = duprev[i] + - dt * (bp1 * k1[i] + bp3 * k3[i] + bp4 * k4[i] + bp5 * k5[i] + - bp6 * k6[i] + bp7 * k7[i]) - end - - f.f1(k.x[1], du, u, p, t + dt) - f.f2(k.x[2], du, u, p, t + dt) - integrator.stats.nf += 4 - integrator.stats.nf2 += 1 - if integrator.opts.adaptive - duhat, uhat = utilde.x - dtsq = dt^2 - @tight_loop_macros for i in uidx - @inbounds uhat[i] = dtsq * - (btilde1 * k1[i] + btilde3 * k3[i] + btilde4 * k4[i] + - btilde5 * k5[i] + btilde6 * k6[i]) - @inbounds duhat[i] = dt * - (bptilde1 * k1[i] + bptilde3 * k3[i] + bptilde4 * k4[i] + - bptilde5 * k5[i] + bptilde6 * k6[i] + bptilde7 * k7[i]) - end - calculate_residuals!(atmp, utilde, integrator.uprev, integrator.u, - integrator.opts.abstol, integrator.opts.reltol, - integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end From 28759d034a70f183bfc3a535cee22cfdf75c6dc0 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:58:48 -0400 Subject: [PATCH 17/71] Delete src/perform_step/ssprk_perform_step.jl --- src/perform_step/ssprk_perform_step.jl | 1707 ------------------------ 1 file changed, 1707 deletions(-) delete mode 100644 src/perform_step/ssprk_perform_step.jl diff --git a/src/perform_step/ssprk_perform_step.jl b/src/perform_step/ssprk_perform_step.jl deleted file mode 100644 index 4f39c2e83c..0000000000 --- a/src/perform_step/ssprk_perform_step.jl +++ /dev/null @@ -1,1707 +0,0 @@ -function initialize!(integrator, cache::SSPRK22ConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK22ConstantCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - - # u1 -> stored as u - integrator.fsalfirst = f(uprev, p, t) - integrator.k[1] = integrator.fsalfirst - u = uprev + dt * integrator.fsalfirst - k = f(u, p, t + dt) - # u - u = (uprev + u + dt * k) / 2 - - integrator.stats.nf += 2 - integrator.u = u -end - -function initialize!(integrator, cache::SSPRK22Cache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK22Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, fsalfirst, stage_limiter!, step_limiter!, thread = cache - - # u1 -> stored as u - f(fsalfirst, uprev, p, t) - @.. broadcast=false thread=thread u=uprev + dt * fsalfirst - stage_limiter!(u, integrator, p, t + dt) - f(k, u, p, t + dt) - # u - @.. broadcast=false thread=thread u=(uprev + u + dt * k) / 2 - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - integrator.stats.nf += 2 -end - -function initialize!(integrator, cache::KYKSSPRK42Cache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation -end - -@muladd function perform_step!(integrator, cache::KYKSSPRK42Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, tmp, fsalfirst, stage_limiter!, step_limiter!, thread = cache - @unpack α20, α21, α30, α32, α40, α43, β10, β21, β30, β32, β40, β43, c1, c2, c3 = cache.tab - - δ = fsalfirst - # u1 -> stored as u - @.. broadcast=false thread=thread u=uprev + dt * β10 * δ - stage_limiter!(u, integrator, p, t + c1 * dt) - f(k, u, p, t + c1 * dt) - # u2 - @.. broadcast=false thread=thread tmp=α20 * uprev + α21 * u + dt * β21 * k - stage_limiter!(tmp, integrator, p, t + c2 * dt) - f(k, tmp, p, t + c2 * dt) - # u3 - @.. broadcast=false thread=thread tmp=α30 * uprev + α32 * tmp + dt * β30 * δ + - dt * β32 * k - stage_limiter!(tmp, integrator, p, t + c3 * dt) - f(k, tmp, p, t + c3 * dt) - # u - @.. broadcast=false thread=thread u=α40 * uprev + α43 * tmp + dt * β40 * δ + - dt * β43 * k - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - f(k, u, p, t + dt) -end - -function initialize!(integrator, cache::KYKSSPRK42ConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::KYKSSPRK42ConstantCache) - @unpack t, dt, uprev, u, f, p = integrator - @unpack α20, α21, α30, α32, α40, α43, β10, β21, β30, β32, β40, β43, c1, c2, c3 = cache - - #u1 - δ = integrator.fsalfirst - u = uprev + dt * β10 * δ - k = f(u, p, t + c1 * dt) - #u2 - tmp = α20 * uprev + α21 * u + dt * β21 * k - k = f(tmp, p, t + c2 * dt) - #u3 - tmp = α30 * uprev + α32 * tmp + dt * β30 * δ + dt * β32 * k - k = f(tmp, p, t + c3 * dt) - #u - u = α40 * uprev + α43 * tmp + dt * β40 * δ + dt * β43 * k - - integrator.fsallast = f(u, p, t + dt) # For interpolation, then FSAL'd - integrator.k[1] = integrator.fsalfirst - integrator.u = u -end - -function initialize!(integrator, cache::SHLDDRK52ConstantCache) - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -@muladd function perform_step!(integrator, cache::SHLDDRK52ConstantCache, - repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack α2, α3, α4, α5, β1, β2, β3, β4, β5, c2, c3, c4, c5 = cache - - # u1 - tmp = dt * integrator.fsalfirst - u = uprev + β1 * tmp - # u2 - tmp = α2 * tmp + dt * f(u, p, t + c2 * dt) - u = u + β2 * tmp - # u3 - tmp = α3 * tmp + dt * f(u, p, t + c3 * dt) - u = u + β3 * tmp - # u4 - tmp = α4 * tmp + dt * f(u, p, t + c4 * dt) - u = u + β4 * tmp - # u5 = u - tmp = α5 * tmp + dt * f(u, p, t + c5 * dt) - u = u + β5 * tmp - - integrator.fsallast = f(u, p, t + dt) # For interpolation, then FSAL'd - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.u = u -end - -function initialize!(integrator, cache::SHLDDRK52Cache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 2 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation -end - -@muladd function perform_step!(integrator, cache::SHLDDRK52Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, fsalfirst, tmp, stage_limiter!, step_limiter!, thread = cache - @unpack α2, α3, α4, α5, β1, β2, β3, β4, β5, c2, c3, c4, c5 = cache.tab - - # u1 - @.. thread=thread tmp=dt * fsalfirst - @.. thread=thread u=uprev + β1 * tmp - stage_limiter!(u, integrator, p, t + c2 * dt) - # u2 - f(k, u, p, t + c2 * dt) - @.. thread=thread tmp=α2 * tmp + dt * k - @.. thread=thread u=u + β2 * tmp - stage_limiter!(u, integrator, p, t + c3 * dt) - # u3 - f(k, u, p, t + c3 * dt) - @.. thread=thread tmp=α3 * tmp + dt * k - @.. thread=thread u=u + β3 * tmp - stage_limiter!(u, integrator, p, t + c4 * dt) - # u4 - f(k, u, p, t + c4 * dt) - @.. thread=thread tmp=α4 * tmp + dt * k - @.. thread=thread u=u + β4 * tmp - stage_limiter!(u, integrator, p, t + c5 * dt) - # u5 = u - f(k, u, p, t + c5 * dt) - @.. thread=thread tmp=α5 * tmp + dt * k - @.. thread=thread u=u + β5 * tmp - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - - f(k, u, p, t + dt) -end - -function initialize!(integrator, cache::SHLDDRK_2NConstantCache) - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -@muladd function perform_step!(integrator, cache::SHLDDRK_2NConstantCache, - repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack α21, α31, α41, α51, β11, β21, β31, β41, β51, c21, c31, c41, c51, α22, α32, α42, α52, α62, β12, β22, β32, β42, β52, β62, c22, c32, c42, c52, c62 = cache - - if integrator.u_modified - cache.step = 1 - end - # cnt = cache.step - - if cache.step % 2 == 1 - cache.step += 1 - # u1 - tmp = dt * integrator.fsalfirst - u = uprev + β11 * tmp - # u2 - tmp = α21 * tmp + dt * f(u, p, t + c21 * dt) - u = u + β21 * tmp - # u3 - tmp = α31 * tmp + dt * f(u, p, t + c31 * dt) - u = u + β31 * tmp - # u4 - tmp = α41 * tmp + dt * f(u, p, t + c41 * dt) - u = u + β41 * tmp - # u5 = u - tmp = α51 * tmp + dt * f(u, p, t + c51 * dt) - u = u + β51 * tmp - - else - cache.step += 1 - # u1 - tmp = dt * integrator.fsalfirst - u = uprev + β12 * tmp - # u2 - tmp = α22 * tmp + dt * f(u, p, t + c22 * dt) - u = u + β22 * tmp - # u3 - tmp = α32 * tmp + dt * f(u, p, t + c32 * dt) - u = u + β32 * tmp - # u4 - tmp = α42 * tmp + dt * f(u, p, t + c42 * dt) - u = u + β42 * tmp - # u5 = u - tmp = α52 * tmp + dt * f(u, p, t + c52 * dt) - u = u + β52 * tmp - tmp = α62 * tmp + dt * f(u, p, t + c62 * dt) - u = u + β62 * tmp - end - - integrator.fsallast = f(u, p, t + dt) # For interpolation, then FSAL'd - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.u = u -end - -function initialize!(integrator, cache::SHLDDRK_2NCache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 2 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # FSAL for interpolation -end - -@muladd function perform_step!(integrator, cache::SHLDDRK_2NCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, fsalfirst, tmp, stage_limiter!, step_limiter!, thread = cache - @unpack α21, α31, α41, α51, β11, β21, β31, β41, β51, c21, c31, c41, c51, α22, α32, α42, α52, α62, β12, β22, β32, β42, β52, β62, c22, c32, c42, c52, c62 = cache.tab - - if integrator.u_modified - cache.step = 1 - end - - if cache.step % 2 == 1 - # u1 - @.. thread=thread tmp=dt * fsalfirst - @.. thread=thread u=uprev + β11 * tmp - stage_limiter!(u, integrator, p, t + c21 * dt) - # u2 - f(k, u, p, t + c21 * dt) - @.. thread=thread tmp=α21 * tmp + dt * k - @.. thread=thread u=u + β21 * tmp - stage_limiter!(u, integrator, p, t + c31 * dt) - # u3 - f(k, u, p, t + c31 * dt) - @.. thread=thread tmp=α31 * tmp + dt * k - @.. thread=thread u=u + β31 * tmp - stage_limiter!(u, integrator, p, t + c41 * dt) - # u4 - f(k, u, p, t + c41 * dt) - @.. thread=thread tmp=α41 * tmp + dt * k - @.. thread=thread u=u + β41 * tmp - stage_limiter!(u, integrator, p, t + c51 * dt) - # u5 = u - f(k, u, p, t + c51 * dt) - @.. thread=thread tmp=α51 * tmp + dt * k - @.. thread=thread u=u + β51 * tmp - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - - f(k, u, p, t + dt) - else - # u1 - @.. thread=thread tmp=dt * fsalfirst - @.. thread=thread u=uprev + β12 * tmp - stage_limiter!(u, integrator, p, t + c22 * dt) - # u2 - f(k, u, p, t + c22 * dt) - @.. thread=thread tmp=α22 * tmp + dt * k - @.. thread=thread u=u + β22 * tmp - stage_limiter!(u, integrator, p, t + c32 * dt) - # u3 - f(k, u, p, t + c32 * dt) - @.. thread=thread tmp=α32 * tmp + dt * k - @.. thread=thread u=u + β32 * tmp - stage_limiter!(u, integrator, p, t + c42 * dt) - # u4 - f(k, u, p, t + c42 * dt) - @.. thread=thread tmp=α42 * tmp + dt * k - @.. thread=thread u=u + β42 * tmp - stage_limiter!(u, integrator, p, t + c52 * dt) - # u5 = u - f(k, u, p, t + c52 * dt) - @.. thread=thread tmp=α52 * tmp + dt * k - @.. thread=thread u=u + β52 * tmp - stage_limiter!(u, integrator, p, t + c62 * dt) - # u6 = u - f(k, u, p, t + c62 * dt) - @.. thread=thread tmp=α62 * tmp + dt * k - @.. thread=thread u=u + β62 * tmp - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - - f(k, u, p, t + dt) - end -end - -function initialize!(integrator, cache::SSPRK33ConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK33ConstantCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - - # u1 - integrator.fsalfirst = f(uprev, p, t) - integrator.k[1] = integrator.fsalfirst - u = uprev + dt * integrator.fsalfirst - k = f(u, p, t + dt) - # u2 - u = (3 * uprev + u + dt * k) / 4 - k = f(u, p, t + dt / 2) - # u - u = (uprev + 2 * u + 2 * dt * k) / 3 - - integrator.stats.nf += 3 - integrator.u = u -end - -function initialize!(integrator, cache::SSPRK33Cache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK33Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, fsalfirst, stage_limiter!, step_limiter!, thread = cache - - # u1 - f(fsalfirst, uprev, p, t) - @.. broadcast=false thread=thread u=uprev + dt * fsalfirst - stage_limiter!(u, integrator, p, t + dt) - f(k, u, p, t + dt) - # u2 - @.. broadcast=false thread=thread u=(3 * uprev + u + dt * k) / 4 - stage_limiter!(u, integrator, p, t + dt / 2) - f(k, u, p, t + dt / 2) - # u - @.. broadcast=false thread=thread u=(uprev + 2 * u + 2 * dt * k) / 3 - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - integrator.stats.nf += 3 -end - -function initialize!(integrator, cache::SSPRK53ConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK53ConstantCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack α30, α32, α40, α43, α52, α54, β10, β21, β32, β43, β54, c1, c2, c3, c4 = cache - - # u1 - integrator.fsalfirst = f(uprev, p, t) - integrator.k[1] = integrator.fsalfirst - tmp = uprev + β10 * dt * integrator.fsalfirst - k = f(tmp, p, t + c1 * dt) - # u2 -> stored as u - u = tmp + β21 * dt * k - k = f(u, p, t + c2 * dt) - # u3 - tmp = α30 * uprev + α32 * u + β32 * dt * k - k = f(tmp, p, t + c3 * dt) - # u4 - tmp = α40 * uprev + α43 * tmp + β43 * dt * k - k = f(tmp, p, t + c4 * dt) - # u - u = α52 * u + α54 * tmp + β54 * dt * k - - integrator.stats.nf += 5 - integrator.u = u -end - -function initialize!(integrator, cache::SSPRK53Cache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK53Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, fsalfirst, tmp, stage_limiter!, step_limiter!, thread = cache - @unpack α30, α32, α40, α43, α52, α54, β10, β21, β32, β43, β54, c1, c2, c3, c4 = cache.tab - - # u1 - f(fsalfirst, uprev, p, t) - @.. broadcast=false thread=thread tmp=uprev + β10 * dt * fsalfirst - stage_limiter!(tmp, integrator, p, t + c1 * dt) - f(k, tmp, p, t + c1 * dt) - # u2 -> stored as u - @.. broadcast=false thread=thread u=tmp + β21 * dt * k - stage_limiter!(u, integrator, p, t + c2 * dt) - f(k, u, p, t + c2 * dt) - # u3 - @.. broadcast=false thread=thread tmp=α30 * uprev + α32 * u + β32 * dt * k - stage_limiter!(tmp, integrator, p, t + c3 * dt) - f(k, tmp, p, t + c3 * dt) - # u4 - @.. broadcast=false thread=thread tmp=α40 * uprev + α43 * tmp + β43 * dt * k - stage_limiter!(tmp, integrator, p, t + c4 * dt) - f(k, tmp, p, t + c4 * dt) - # u - @.. broadcast=false thread=thread u=α52 * u + α54 * tmp + β54 * dt * k - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - integrator.stats.nf += 5 -end - -function initialize!(integrator, cache::SSPRK53_2N1ConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK53_2N1ConstantCache, - repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack α40, α43, β10, β21, β32, β43, β54, c1, c2, c3, c4 = cache - #stores in u for all intermediate stages - # u1 - integrator.fsalfirst = f(uprev, p, t) - integrator.k[1] = integrator.fsalfirst - u = uprev + β10 * dt * integrator.fsalfirst - k = f(u, p, t + c1 * dt) - # u2 - u = u + β21 * dt * k - k = f(u, p, t + c2 * dt) - # u3 - u = u + β32 * dt * k - k = f(u, p, t + c3 * dt) - # u4 - u = α40 * uprev + α43 * u + β43 * dt * k - k = f(u, p, t + c4 * dt) - # u - u = u + β54 * dt * k - - integrator.stats.nf += 1 - integrator.u = u -end - -function initialize!(integrator, cache::SSPRK53_2N1Cache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK53_2N1Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, fsalfirst, stage_limiter!, step_limiter!, thread = cache - @unpack α40, α43, β10, β21, β32, β43, β54, c1, c2, c3, c4 = cache.tab - - #stores in u for all intermediate stages - # u1 - f(fsalfirst, uprev, p, t) - @.. broadcast=false thread=thread u=uprev + β10 * dt * fsalfirst - stage_limiter!(u, integrator, p, t + c1 * dt) - f(k, u, p, t + c1 * dt) - # u2 - @.. broadcast=false thread=thread u=u + β21 * dt * k - stage_limiter!(u, integrator, p, t + c2 * dt) - f(k, u, p, t + c2 * dt) - # u3 - @.. broadcast=false thread=thread u=u + β32 * dt * k - stage_limiter!(u, integrator, p, t + c3 * dt) - f(k, u, p, t + c3 * dt) - # u4 - @.. broadcast=false thread=thread u=α40 * uprev + α43 * u + β43 * dt * k - stage_limiter!(u, integrator, p, t + c4 * dt) - f(k, u, p, t + c4 * dt) - # u - @.. broadcast=false thread=thread u=u + β54 * dt * k - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - integrator.stats.nf += 5 -end - -function initialize!(integrator, cache::SSPRK53_2N2ConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK53_2N2ConstantCache, - repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack α30, α32, α50, α54, β10, β21, β32, β43, β54, c1, c2, c3, c4 = cache - #stores in u for all intermediate stages - # u1 - integrator.fsalfirst = f(uprev, p, t) - integrator.k[1] = integrator.fsalfirst - u = uprev + β10 * dt * integrator.fsalfirst - k = f(u, p, t + c1 * dt) - # u2 -> stored as u - u = u + β21 * dt * k - k = f(u, p, t + c2 * dt) - # u3 - u = α30 * uprev + α32 * u + β32 * dt * k - k = f(u, p, t + c3 * dt) - # u4 - u = u + β43 * dt * k - k = f(u, p, t + c4 * dt) - # u - u = α50 * uprev + α54 * u + β54 * dt * k - - integrator.stats.nf += 5 - integrator.u = u -end - -function initialize!(integrator, cache::SSPRK53_2N2Cache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK53_2N2Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, fsalfirst, stage_limiter!, step_limiter!, thread = cache - @unpack α30, α32, α50, α54, β10, β21, β32, β43, β54, c1, c2, c3, c4 = cache.tab - - # u1 - f(fsalfirst, uprev, p, t) - @.. broadcast=false thread=thread u=uprev + β10 * dt * fsalfirst - stage_limiter!(u, integrator, p, t + c1 * dt) - f(k, u, p, t + c1 * dt) - # u2 -> stored as u - @.. broadcast=false thread=thread u=u + β21 * dt * k - stage_limiter!(u, integrator, p, t + c2 * dt) - f(k, u, p, t + c2 * dt) - # u3 - @.. broadcast=false thread=thread u=α30 * uprev + α32 * u + β32 * dt * k - stage_limiter!(u, integrator, p, t + c3 * dt) - f(k, u, p, t + c3 * dt) - # u4 - @.. broadcast=false thread=thread u=u + β43 * dt * k - stage_limiter!(u, integrator, p, t + c4 * dt) - f(k, u, p, t + c4 * dt) - # u - @.. broadcast=false thread=thread u=α50 * uprev + α54 * u + β54 * dt * k - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - integrator.stats.nf += 5 -end - -function initialize!(integrator, cache::SSPRK53_HConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK53_HConstantCache, - repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack α30, α32, α40, α41, α43, β10, β21, β32, β43, β54, c1, c2, c3, c4 = cache - #stores in u for all intermediate stages - # u1 - integrator.fsalfirst = f(uprev, p, t) - integrator.k[1] = integrator.fsalfirst - tmp = uprev + β10 * dt * integrator.fsalfirst - k = f(tmp, p, t + c1 * dt) - # u2 - u = tmp + β21 * dt * k - k = f(u, p, t + c2 * dt) - # u3 - u = α30 * uprev + α32 * u + β32 * dt * k - k = f(u, p, t + c3 * dt) - # u4 - u = α40 * uprev + α41 * tmp + α43 * u + β43 * dt * k - k = f(u, p, t + c4 * dt) - # u - u = u + β54 * dt * k - - integrator.stats.nf += 5 - integrator.u = u -end - -function initialize!(integrator, cache::SSPRK53_HCache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK53_HCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, fsalfirst, tmp, stage_limiter!, step_limiter!, thread = cache - @unpack α30, α32, α40, α41, α43, β10, β21, β32, β43, β54, c1, c2, c3, c4 = cache.tab - #stores in u for all intermediate stages - # u1 - f(fsalfirst, uprev, p, t) - @.. broadcast=false thread=thread tmp=uprev + β10 * dt * fsalfirst - stage_limiter!(tmp, integrator, p, t + c1 * dt) - f(k, tmp, p, t + c1 * dt) - # u2 - @.. broadcast=false thread=thread u=tmp + β21 * dt * k - stage_limiter!(u, integrator, p, t + c2 * dt) - f(k, u, p, t + c2 * dt) - # u3 - @.. broadcast=false thread=thread u=α30 * uprev + α32 * u + β32 * dt * k - stage_limiter!(u, integrator, p, t + c3 * dt) - f(k, u, p, t + c3 * dt) - # u4 - @.. broadcast=false thread=thread u=α40 * uprev + α41 * tmp + α43 * u + β43 * dt * k - stage_limiter!(u, integrator, p, t + c4 * dt) - f(k, u, p, t + c4 * dt) - # u - @.. broadcast=false thread=thread u=u + β54 * dt * k - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - integrator.stats.nf += 5 -end - -function initialize!(integrator, cache::SSPRK63ConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK63ConstantCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack α40, α41, α43, α62, α65, β10, β21, β32, β43, β54, β65, c1, c2, c3, c4, c5 = cache - - # u1 -> stored as u - integrator.fsalfirst = f(uprev, p, t) - integrator.k[1] = integrator.fsalfirst - u = uprev + β10 * dt * integrator.fsalfirst - k = f(u, p, t + c1 * dt) - # u2 - u₂ = u + β21 * dt * k - k = f(u₂, p, t + c2 * dt) - # u3 - tmp = u₂ + β32 * dt * k - k = f(tmp, p, t + c3 * dt) - # u4 - tmp = α40 * uprev + α41 * u + α43 * tmp + β43 * dt * k - k = f(tmp, p, t + c4 * dt) - # u5 - tmp = tmp + β54 * dt * k - k = f(tmp, p, t + c5 * dt) - # u - u = α62 * u₂ + α65 * tmp + β65 * dt * k - - integrator.stats.nf += 6 - integrator.u = u -end - -function initialize!(integrator, cache::SSPRK63Cache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK63Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, fsalfirst, tmp, u₂, stage_limiter!, step_limiter!, thread = cache - @unpack α40, α41, α43, α62, α65, β10, β21, β32, β43, β54, β65, c1, c2, c3, c4, c5 = cache.tab - - # u1 -> stored as u - f(fsalfirst, uprev, p, t) - @.. broadcast=false thread=thread u=uprev + β10 * dt * fsalfirst - stage_limiter!(u, integrator, p, t + c1 * dt) - f(k, u, p, t + c1 * dt) - # u2 - @.. broadcast=false thread=thread u₂=u + β21 * dt * k - stage_limiter!(u₂, integrator, p, t + c2 * dt) - f(k, u₂, p, t + c2 * dt) - # u3 - @.. broadcast=false thread=thread tmp=u₂ + β32 * dt * k - stage_limiter!(tmp, integrator, p, t + c3 * dt) - f(k, tmp, p, t + c3 * dt) - # u4 - @.. broadcast=false thread=thread tmp=α40 * uprev + α41 * u + α43 * tmp + β43 * dt * k - stage_limiter!(tmp, integrator, p, t + c4 * dt) - f(k, tmp, p, t + c4 * dt) - # u5 - @.. broadcast=false thread=thread tmp=tmp + β54 * dt * k - stage_limiter!(tmp, integrator, p, t + c5 * dt) - f(k, tmp, p, t + c5 * dt) - # u - @.. broadcast=false thread=thread u=α62 * u₂ + α65 * tmp + β65 * dt * k - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - integrator.stats.nf += 6 -end - -function initialize!(integrator, cache::SSPRK73ConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK73ConstantCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack α40, α43, α50, α51, α54, α73, α76, β10, β21, β32, β43, β54, β65, β76, c1, c2, c3, c4, c5, c6 = cache - - # u1 - integrator.fsalfirst = f(uprev, p, t) - integrator.k[1] = integrator.fsalfirst - u₁ = uprev + β10 * dt * integrator.fsalfirst - k = f(u₁, p, t + c1 * dt) - # u2 - tmp = u₁ + β21 * dt * k - k = f(tmp, p, t + c2 * dt) - # u3 -> stored as u - u = tmp + β32 * dt * k - k = f(u, p, t + c3 * dt) - # u4 - tmp = α40 * uprev + α43 * u + β43 * dt * k - k = f(tmp, p, t + c4 * dt) - # u5 - tmp = α50 * uprev + α51 * u₁ + α54 * tmp + β54 * dt * k - k = f(tmp, p, t + c5 * dt) - # u6 - tmp = tmp + β65 * dt * k - k = f(tmp, p, t + c6 * dt) - # u - u = α73 * u + α76 * tmp + β76 * dt * k - - integrator.stats.nf += 7 - integrator.u = u -end - -function initialize!(integrator, cache::SSPRK73Cache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK73Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, fsalfirst, tmp, u₁, stage_limiter!, step_limiter!, thread = cache - @unpack α40, α43, α50, α51, α54, α73, α76, β10, β21, β32, β43, β54, β65, β76, c1, c2, c3, c4, c5, c6 = cache.tab - - # u1 - f(fsalfirst, uprev, p, t) - @.. broadcast=false thread=thread u₁=uprev + β10 * dt * fsalfirst - stage_limiter!(u₁, integrator, p, t + c1 * dt) - f(k, u₁, p, t + c1 * dt) - # u2 - @.. broadcast=false thread=thread tmp=u₁ + β21 * dt * k - stage_limiter!(tmp, integrator, p, t + c2 * dt) - f(k, tmp, p, t + c2 * dt) - # u3 -> stored as u - @.. broadcast=false thread=thread u=tmp + β32 * dt * k - stage_limiter!(u, integrator, p, t + c3 * dt) - f(k, u, p, t + c3 * dt) - # u4 - @.. broadcast=false thread=thread tmp=α40 * uprev + α43 * u + β43 * dt * k - stage_limiter!(tmp, integrator, p, t + c4 * dt) - f(k, tmp, p, t + c4 * dt) - # u5 - @.. broadcast=false thread=thread tmp=α50 * uprev + α51 * u₁ + α54 * tmp + β54 * dt * k - stage_limiter!(tmp, integrator, p, t + c5 * dt) - f(k, tmp, p, t + c5 * dt) - # u6 - @.. broadcast=false thread=thread tmp=tmp + β65 * dt * k - stage_limiter!(tmp, integrator, p, t + c6 * dt) - f(k, tmp, p, t + c6 * dt) - # u - @.. broadcast=false thread=thread u=α73 * u + α76 * tmp + β76 * dt * k - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - integrator.stats.nf += 7 -end - -function initialize!(integrator, cache::SSPRK83ConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK83ConstantCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack α50, α51, α54, α61, α65, α72, α73, α76, β10, β21, β32, β43, β54, β65, β76, β87, c1, c2, c3, c4, c5, c6, c7 = cache - - # u1 -> save as u - integrator.fsalfirst = f(uprev, p, t) - integrator.k[1] = integrator.fsalfirst - u = uprev + β10 * dt * integrator.fsalfirst - k = f(u, p, t + c1 * dt) - # u2 - u₂ = u + β21 * dt * k - k = f(u₂, p, t + c2 * dt) - # u3 - u₃ = u₂ + β32 * dt * k - k = f(u₃, p, t + c3 * dt) - # u4 - tmp = u₃ + β43 * dt * k - k = f(tmp, p, t + c4 * dt) - # u5 - tmp = α50 * uprev + α51 * u + α54 * tmp + β54 * dt * k - k = f(tmp, p, t + c5 * dt) - # u6 - tmp = α61 * u + α65 * tmp + β65 * dt * k - k = f(tmp, p, t + c6 * dt) - # u7 - tmp = α72 * u₂ + α73 * u₃ + α76 * tmp + β76 * dt * k - k = f(tmp, p, t + c7 * dt) - # u - u = tmp + β87 * dt * k - - integrator.stats.nf += 8 - integrator.u = u -end - -function initialize!(integrator, cache::SSPRK83Cache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK83Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, fsalfirst, tmp, u₂, u₃, stage_limiter!, step_limiter!, thread = cache - @unpack α50, α51, α54, α61, α65, α72, α73, α76, β10, β21, β32, β43, β54, β65, β76, β87, c1, c2, c3, c4, c5, c6, c7 = cache.tab - - # u1 -> save as u - f(fsalfirst, uprev, p, t) - @.. broadcast=false thread=thread u=uprev + β10 * dt * fsalfirst - stage_limiter!(u, integrator, p, t + c1 * dt) - f(k, u, p, t + c1 * dt) - # u2 - @.. broadcast=false thread=thread u₂=u + β21 * dt * k - stage_limiter!(u₂, integrator, p, t + c2 * dt) - f(k, u₂, p, t + c2 * dt) - # u3 - @.. broadcast=false thread=thread u₃=u₂ + β32 * dt * k - stage_limiter!(u₃, integrator, p, t + c3 * dt) - f(k, u₃, p, t + c3 * dt) - # u4 - @.. broadcast=false thread=thread tmp=u₃ + β43 * dt * k - stage_limiter!(tmp, integrator, p, t + c4 * dt) - f(k, tmp, p, t + c4 * dt) - # u5 - @.. broadcast=false thread=thread tmp=α50 * uprev + α51 * u + α54 * tmp + β54 * dt * k - stage_limiter!(tmp, integrator, p, t + c5 * dt) - f(k, tmp, p, t + c5 * dt) - # u6 - @.. broadcast=false thread=thread tmp=α61 * u + α65 * tmp + β65 * dt * k - stage_limiter!(tmp, integrator, p, t + c6 * dt) - f(k, tmp, p, t + c6 * dt) - # u7 - @.. broadcast=false thread=thread tmp=α72 * u₂ + α73 * u₃ + α76 * tmp + β76 * dt * k - stage_limiter!(tmp, integrator, p, t + c7 * dt) - f(k, tmp, p, t + c7 * dt) - # u - @.. broadcast=false thread=thread u=tmp + β87 * dt * k - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - integrator.stats.nf += 8 -end - -function initialize!(integrator, cache::SSPRK43ConstantCache) - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK43ConstantCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack one_third_u, two_thirds_u, half_u, half_t = cache - dt_2 = half_t * dt - - # u1 - integrator.fsalfirst = f(uprev, p, t) - integrator.k[1] = integrator.fsalfirst - u = uprev + dt_2 * integrator.fsalfirst - k = f(u, p, t + dt_2) - # u2 - u = u + dt_2 * k - k = f(u, p, t + dt) - u = u + dt_2 * k - if integrator.opts.adaptive - utilde = one_third_u * uprev + two_thirds_u * u # corresponds to bhat = (1/3, 1/3, 1/3, 0) - end - # u3 - u = two_thirds_u * uprev + one_third_u * u - k = f(u, p, t + dt_2) - # u - u = u + dt_2 * k # corresponds to b = (1/6, 1/6, 1/6, 1/2) - - integrator.stats.nf += 4 - if integrator.opts.adaptive - utilde = half_u * (utilde - u) # corresponds to bhat = (1/4, 1/4, 1/4, 1/4) - atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.u = u -end - -function initialize!(integrator, cache::SSPRK43Cache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK43Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, fsalfirst, utilde, atmp, stage_limiter!, step_limiter!, thread = cache - @unpack one_third_u, two_thirds_u, half_u, half_t = cache.tab - dt_2 = half_t * dt - - # u1 - f(fsalfirst, uprev, p, t) - @.. broadcast=false thread=thread u=uprev + dt_2 * fsalfirst - stage_limiter!(u, integrator, p, t + dt_2) - f(k, u, p, t + dt_2) - # u2 - @.. broadcast=false thread=thread u=u + dt_2 * k - stage_limiter!(u, integrator, p, t + dt) - f(k, u, p, t + dt) - # - @.. broadcast=false thread=thread u=u + dt_2 * k - stage_limiter!(u, integrator, p, t + dt + dt_2) - if integrator.opts.adaptive - @.. broadcast=false utilde=one_third_u * uprev + two_thirds_u * u # corresponds to bhat = (1/3, 1/3, 1/3, 0) - end - # u3 - @.. broadcast=false thread=thread u=two_thirds_u * uprev + one_third_u * u - f(k, u, p, t + dt_2) - # - @.. broadcast=false thread=thread u=u + dt_2 * k # corresponds to b = (1/6, 1/6, 1/6, 1/2) - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - - if integrator.opts.adaptive - @.. broadcast=false thread=thread utilde=half_u * (utilde - u) # corresponds to bhat = (1/4, 1/4, 1/4, 1/4) - calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t, - thread) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.stats.nf += 4 -end - -function initialize!(integrator, cache::SSPRK432ConstantCache) - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK432ConstantCache, - repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - dt_2 = dt / 2 - - # u1 - integrator.fsalfirst = f(uprev, p, t) - integrator.k[1] = integrator.fsalfirst - u = uprev + dt_2 * integrator.fsalfirst - k = f(u, p, t + dt_2) - # u2 - u = u + dt_2 * k - k = f(u, p, t + dt) - u = u + dt_2 * k - if integrator.opts.adaptive - utilde = (uprev + 2 * u) / 3 - end - # u3 - u = (2 * uprev + u) / 3 - k = f(u, p, t + dt_2) - # u - u = u + dt_2 * k - - integrator.stats.nf += 4 - if integrator.opts.adaptive - utilde = utilde - u - atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.u = u -end - -function initialize!(integrator, cache::SSPRK432Cache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK432Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, fsalfirst, utilde, atmp, stage_limiter!, step_limiter!, thread = cache - dt_2 = dt / 2 - - # u1 - f(fsalfirst, uprev, p, t) - @.. broadcast=false thread=thread u=uprev + dt_2 * fsalfirst - stage_limiter!(u, integrator, p, t + dt_2) - f(k, u, p, t + dt_2) - # u2 - @.. broadcast=false thread=thread u=u + dt_2 * k - stage_limiter!(u, integrator, p, t + dt) - f(k, u, p, t + dt) - # - @.. broadcast=false thread=thread u=u + dt_2 * k - stage_limiter!(u, integrator, p, t + dt + dt_2) - if integrator.opts.adaptive - @.. broadcast=false utilde=(uprev + 2 * u) / 3 - end - # u3 - @.. broadcast=false thread=thread u=(2 * uprev + u) / 3 - f(k, u, p, t + dt_2) - # - @.. broadcast=false thread=thread u=u + dt_2 * k - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - - if integrator.opts.adaptive - @.. broadcast=false thread=thread utilde=utilde - u - calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t, - thread) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.stats.nf += 4 -end - -function initialize!(integrator, cache::SSPRKMSVS32ConstantCache) - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRKMSVS32ConstantCache, - repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack u_1, u_2, dts, dtf, μ, v_n = cache - - if integrator.iter == 1 - cache.dts[1] = dt - cache.dts[2] = dt - cache.dtf[1] = dt - end - accpt = true - dt = dts[1] - - if cache.step < 3 #starting Procedure - k = f(u, p, t + dt) - u = uprev + dt * k - k = f(u, p, t + dt) - integrator.stats.nf += 2 - u = (uprev + u + dt * k) / 2 - if cache.step == 1 - u_2 = uprev - else - u_1 = uprev - end - if integrator.opts.adaptive - v_n = dt / dts[2] * 0.5 - cache.dtf[2] = dtf[1] - cache.dtf[1] = dt / v_n * 0.5 - if v_n > 0.5 - cache.step -= 1 - accpt = false - end - cache.dts[3] = dts[2] - cache.dts[2] = dt - dt = 0.9 * dtf[1] - μ = min(dtf[1], dtf[2]) - end - else - if integrator.opts.adaptive - Ω = (dts[2] + dts[3]) / dt - else - Ω = 2 - end - u = (Ω * Ω - 1) / (Ω * Ω) * (uprev + Ω / (Ω - 1) * dt * integrator.fsalfirst) + - 1 / (Ω * Ω) * u_2 - u_2 = u_1 - u_1 = uprev - if integrator.opts.adaptive - v_n = (dts[2] + dts[3] - dt) / (dts[2] + dts[3]) * 0.5 - dt = (dts[2] + dts[3]) / (dts[2] + dts[3] + μ) * μ - cache.dtf[2] = dtf[1] - dtf[1] = dt / v_n * 0.5 - cache.dts[3] = dts[2] - cache.dts[2] = dt - μ = min(dtf[1], dtf[2]) - end - end - if accpt == true - integrator.fsallast = f(u, p, t + dt) - integrator.stats.nf += 1 - integrator.k[1] = integrator.fsalfirst - integrator.u = u - else - integrator.fsallast = f(uprev, p, t + dt) - integrator.stats.nf += 1 - integrator.k[1] = integrator.fsalfirst - integrator.u = uprev - end - cache.dts[1] = dt - cache.step += 1 - cache.u_1 = u_1 - cache.u_2 = u_2 - cache.μ = μ -end - -function initialize!(integrator, cache::SSPRKMSVS32Cache) - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.fsalfirst = cache.fsalfirst # done by pointers, no copying - integrator.fsallast = cache.k - integrator.k[1] = integrator.fsalfirst - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) - integrator.stats.nf += 1 -end - -@muladd function perform_step!(integrator, cache::SSPRKMSVS32Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, fsalfirst, u_1, u_2, stage_limiter!, step_limiter!, thread = cache - - if cache.step < 3 - @.. broadcast=false thread=thread u=uprev + dt * fsalfirst - stage_limiter!(u, integrator, p, t + dt) - f(k, u, p, t + dt) - integrator.stats.nf += 1 - @.. broadcast=false thread=thread u=(uprev + u + dt * k) / 2 - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - - if cache.step == 1 - cache.u_2 .= uprev - else - cache.u_1 .= uprev - end - else - Ω = 2 - @.. broadcast=false thread=thread u=((Ω * Ω - 1) / (Ω * Ω)) * - (uprev + (Ω / (Ω - 1)) * dt * fsalfirst) + - (1 / (Ω * Ω)) * cache.u_2 - cache.u_2 .= u_1 - cache.u_1 .= uprev - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - end - cache.step += 1 - integrator.stats.nf += 1 - f(k, u, p, t + dt) -end - -function initialize!(integrator, cache::SSPRKMSVS43ConstantCache) - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRKMSVS43ConstantCache, - repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack u_1, u_2, u_3, k1, k2, k3 = cache - - if cache.step < 4 - u = uprev + dt * integrator.fsalfirst - k = f(u, p, t + dt) - u = (uprev + u + dt * k) / 2 - if cache.step == 1 - u_3 = uprev - cache.k3 = f(u_3, p, t + dt) - integrator.stats.nf += 1 - end - if cache.step == 2 - u_2 = uprev - cache.k2 = f(u_2, p, t + dt) - integrator.stats.nf += 1 - end - if cache.step == 3 - u_1 = uprev - cache.k1 = f(u_1, p, t + dt) - integrator.stats.nf += 1 - end - # u - else - u = (16 / 27) * (uprev + 3 * dt * integrator.fsalfirst) + - (11 / 27) * (u_3 + (12 / 11) * dt * k3) - cache.k3 = k2 - cache.k2 = k1 - cache.k1 = integrator.fsalfirst - u_3 = u_2 - u_2 = u_1 - u_1 = uprev - end - integrator.fsallast = f(u, p, t + dt) # For interpolation, then FSAL'd - integrator.stats.nf += 1 - integrator.k[1] = integrator.fsalfirst - integrator.u = u - cache.step += 1 - cache.u_1 = u_1 - cache.u_2 = u_2 - cache.u_3 = u_3 -end - -function initialize!(integrator, cache::SSPRKMSVS43Cache) - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.fsalfirst = cache.fsalfirst # done by pointers, no copying - integrator.fsallast = cache.k - integrator.k[1] = integrator.fsalfirst - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 -end - -@muladd function perform_step!(integrator, cache::SSPRKMSVS43Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, fsalfirst, u_1, u_2, u_3, stage_limiter!, step_limiter!, thread, k1, k2, k3 = cache - - if cache.step < 4 - @.. broadcast=false thread=thread u=uprev + dt * fsalfirst - stage_limiter!(u, integrator, p, t + dt) - f(k, u, p, t + dt) - integrator.stats.nf += 1 - @.. broadcast=false thread=thread u=(uprev + u + dt * k) / 2 - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - if cache.step == 1 - cache.u_3 .= uprev - f(k3, u_3, p, t + dt) - integrator.stats.nf += 1 - end - if cache.step == 2 - cache.u_2 .= uprev - f(k2, u_2, p, t + dt) - integrator.stats.nf += 1 - end - if cache.step == 3 - cache.u_1 .= uprev - f(k1, u_1, p, t + dt) - integrator.stats.nf += 1 - end - # u - else - @.. broadcast=false thread=thread u=(16 / 27) * (uprev + 3 * dt * fsalfirst) + - (11 / 27) * (u_3 + (12 / 11) * dt * k3) - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - cache.k3 .= k2 - cache.k2 .= k1 - cache.k1 .= fsalfirst - cache.u_3 .= u_2 - cache.u_2 .= u_1 - cache.u_1 .= uprev - end - cache.step += 1 - integrator.stats.nf += 1 - f(k, u, p, t + dt) -end - -function initialize!(integrator, cache::SSPRK932ConstantCache) - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK932ConstantCache, - repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - dt_6 = dt / 6 - dt_3 = dt / 3 - dt_2 = dt / 2 - - # u1 - integrator.fsalfirst = f(uprev, p, t) - integrator.k[1] = integrator.fsalfirst - u = uprev + dt_6 * integrator.fsalfirst - k = f(u, p, t + dt_6) - # u2 - u = u + dt_6 * k - k = f(u, p, t + dt_3) - # u3 - u = u + dt_6 * k - k = f(u, p, t + dt_2) - # u4 - u = u + dt_6 * k - k = f(u, p, t + 2 * dt_3) - # u5 - u = u + dt_6 * k - k = f(u, p, t + 5 * dt_6) - integrator.stats.nf += 6 - # u6 - u = u + dt_6 * k - if integrator.opts.adaptive - k = f(u, p, t + dt) - integrator.stats.nf += 1 - utilde = (uprev + 6 * u + 6 * dt * k) / 7 - end - # u6* - u = (3 * uprev + dt_2 * integrator.fsalfirst + 2 * u) / 5 - k = f(u, p, t + dt_2) - # u7* - u = u + dt_6 * k - k = f(u, p, t + 2 * dt_3) - # u8* - u = u + dt_6 * k - k = f(u, p, t + 5 * dt_6) - # u - u = u + dt_6 * k - - integrator.stats.nf += 3 - if integrator.opts.adaptive - utilde = utilde - u - atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.u = u -end - -function initialize!(integrator, cache::SSPRK932Cache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK932Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, fsalfirst, utilde, atmp, stage_limiter!, step_limiter!, thread = cache - dt_6 = dt / 6 - dt_3 = dt / 3 - dt_2 = dt / 2 - - # u1 - f(fsalfirst, uprev, p, t) - @.. broadcast=false thread=thread u=uprev + dt_6 * fsalfirst - stage_limiter!(u, integrator, p, t + dt_6) - f(k, u, p, t + dt_6) - # u2 - @.. broadcast=false thread=thread u=u + dt_6 * k - stage_limiter!(u, integrator, p, t + dt_3) - f(k, u, p, t + dt_3) - # u3 - @.. broadcast=false thread=thread u=u + dt_6 * k - stage_limiter!(u, integrator, p, t + dt_2) - f(k, u, p, t + dt_2) - # u4 - @.. broadcast=false thread=thread u=u + dt_6 * k - stage_limiter!(u, integrator, p, t + 2 * dt_3) - f(k, u, p, t + 2 * dt_3) - # u5 - @.. broadcast=false thread=thread u=u + dt_6 * k - stage_limiter!(u, integrator, p, t + 5 * dt_6) - f(k, u, p, t + 5 * dt_6) - integrator.stats.nf += 6 - # u6 - @.. broadcast=false thread=thread u=u + dt_6 * k - if integrator.opts.adaptive - stage_limiter!(u, integrator, p, t + dt) - f(k, u, p, t + dt) - integrator.stats.nf += 1 - @.. broadcast=false thread=thread utilde=(uprev + 6 * u + 6 * dt * k) / 7 - end - # u6* - @.. broadcast=false thread=thread u=(3 * uprev + dt_2 * integrator.fsalfirst + 2 * u) / - 5 - stage_limiter!(u, integrator, p, t + dt_6) - f(k, u, p, t + dt_2) - # u7* - @.. broadcast=false thread=thread u=u + dt_6 * k - stage_limiter!(u, integrator, p, t + 2 * dt_3) - f(k, u, p, t + 2 * dt_3) - # u8* - @.. broadcast=false thread=thread u=u + dt_6 * k - stage_limiter!(u, integrator, p, t + 5 * dt_6) - f(k, u, p, t + 5 * dt_6) - # u9* - @.. broadcast=false thread=thread u=u + dt_6 * k - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - integrator.stats.nf += 3 - - if integrator.opts.adaptive - @.. broadcast=false thread=thread utilde=utilde - u - calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t, - thread) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end -end - -function initialize!(integrator, cache::SSPRK54ConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK54ConstantCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack β10, α20, α21, β21, α30, α32, β32, α40, α43, β43, α52, α53, β53, α54, β54, c1, c2, c3, c4 = cache - - # u₁ - integrator.fsalfirst = f(uprev, p, t) - integrator.k[1] = integrator.fsalfirst - u₂ = uprev + β10 * dt * integrator.fsalfirst - k = f(u₂, p, t + c1 * dt) - # u₂ - u₂ = α20 * uprev + α21 * u₂ + β21 * dt * k - k = f(u₂, p, t + c2 * dt) - # u₃ - u₃ = α30 * uprev + α32 * u₂ + β32 * dt * k - k₃ = f(u₃, p, t + c3 * dt) - # u₄ -> stored as tmp - tmp = α40 * uprev + α43 * u₃ + β43 * dt * k₃ - k = f(tmp, p, t + c4 * dt) - # u - u = α52 * u₂ + α53 * u₃ + β53 * dt * k₃ + α54 * tmp + β54 * dt * k - - integrator.stats.nf += 5 - integrator.u = u -end - -function initialize!(integrator, cache::SSPRK54Cache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK54Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, fsalfirst, k₃, u₂, u₃, tmp, stage_limiter!, step_limiter!, thread = cache - @unpack β10, α20, α21, β21, α30, α32, β32, α40, α43, β43, α52, α53, β53, α54, β54, c1, c2, c3, c4 = cache.tab - - # u₁ - f(fsalfirst, uprev, p, t) - @.. broadcast=false thread=thread u₂=uprev + β10 * dt * fsalfirst - stage_limiter!(u₂, integrator, p, t + c1 * dt) - f(k, u₂, p, t + c1 * dt) - # u₂ - @.. broadcast=false thread=thread u₂=α20 * uprev + α21 * u₂ + β21 * dt * k - stage_limiter!(u₂, integrator, p, t + c2 * dt) - f(k, u₂, p, t + c2 * dt) - # u₃ - @.. broadcast=false thread=thread u₃=α30 * uprev + α32 * u₂ + β32 * dt * k - stage_limiter!(u₃, integrator, p, t + c3 * dt) - f(k₃, u₃, p, t + c3 * dt) - # u₄ -> stored as tmp - @.. broadcast=false thread=thread tmp=α40 * uprev + α43 * u₃ + β43 * dt * k₃ - stage_limiter!(tmp, integrator, p, t + c4 * dt) - f(k, tmp, p, t + c4 * dt) - # u - @.. broadcast=false thread=thread u=α52 * u₂ + α53 * u₃ + β53 * dt * k₃ + α54 * tmp + - β54 * dt * k - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - integrator.stats.nf += 5 -end - -function initialize!(integrator, cache::SSPRK104ConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - integrator.kshortsize = 1 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK104ConstantCache, - repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - dt_6 = dt / 6 - dt_3 = dt / 3 - dt_2 = dt / 2 - - integrator.fsalfirst = f(uprev, p, t) - integrator.k[1] = integrator.fsalfirst - tmp = uprev + dt_6 * integrator.fsalfirst # u₁ - k = f(tmp, p, t + dt_6) - tmp = tmp + dt_6 * k # u₂ - k = f(tmp, p, t + dt_3) - tmp = tmp + dt_6 * k # u₃ - k = f(tmp, p, t + dt_2) - u = tmp + dt_6 * k # u₄ - k₄ = f(u, p, t + 2 * dt_3) - tmp = (3 * uprev + 2 * u + 2 * dt_6 * k₄) / 5 # u₅ - k = f(tmp, p, t + dt_3) - tmp = tmp + dt_6 * k # u₆ - k = f(tmp, p, t + dt_2) - tmp = tmp + dt_6 * k # u₇ - k = f(tmp, p, t + 2 * dt_3) - tmp = tmp + dt_6 * k # u₈ - k = f(tmp, p, t + 5 * dt_6) - tmp = tmp + dt_6 * k # u₉ - k = f(tmp, p, t + dt) - u = (uprev + 9 * (u + dt_6 * k₄) + 15 * (tmp + dt_6 * k)) / 25 - - integrator.stats.nf += 10 - integrator.u = u -end - -function initialize!(integrator, cache::SSPRK104Cache) - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - integrator.kshortsize = 1 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst -end - -@muladd function perform_step!(integrator, cache::SSPRK104Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack k, fsalfirst, k₄, tmp, stage_limiter!, step_limiter!, thread = cache - dt_6 = dt / 6 - dt_3 = dt / 3 - dt_2 = dt / 2 - - f(fsalfirst, uprev, p, t) - @.. broadcast=false thread=thread tmp=uprev + dt_6 * fsalfirst - stage_limiter!(tmp, integrator, p, t + dt_6) - f(k, tmp, p, t + dt_6) - @.. broadcast=false tmp=tmp + dt_6 * k - stage_limiter!(tmp, integrator, p, t + dt_3) - f(k, tmp, p, t + dt_3) - @.. broadcast=false thread=thread tmp=tmp + dt_6 * k - stage_limiter!(tmp, integrator, p, t + dt_2) - f(k, tmp, p, t + dt_2) - @.. broadcast=false thread=thread u=tmp + dt_6 * k - stage_limiter!(u, integrator, p, t + 2 * dt_3) - f(k₄, u, p, t + 2 * dt_3) - @.. broadcast=false thread=thread tmp=(3 * uprev + 2 * u + 2 * dt_6 * k₄) / 5 - stage_limiter!(tmp, integrator, p, t + dt_3) - f(k, tmp, p, t + dt_3) - @.. broadcast=false thread=thread tmp=tmp + dt_6 * k - stage_limiter!(tmp, integrator, p, t + dt_2) - f(k, tmp, p, t + dt_2) - @.. broadcast=false thread=thread tmp=tmp + dt_6 * k - stage_limiter!(tmp, integrator, p, t + 2 * dt_3) - f(k, tmp, p, t + 2 * dt_3) - @.. broadcast=false thread=thread tmp=tmp + dt_6 * k - stage_limiter!(tmp, integrator, p, t + 5 * dt_6) - f(k, tmp, p, t + 5 * dt_6) - @.. broadcast=false thread=thread tmp=tmp + dt_6 * k - stage_limiter!(tmp, integrator, p, t + dt) - f(k, tmp, p, t + dt) - @.. broadcast=false thread=thread u=(uprev + 9 * (u + dt_6 * k₄) + - 15 * (tmp + dt_6 * k)) / 25 - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - integrator.stats.nf += 10 -end From 8372fe097128a74b0bd7720aa4099f352880a4d8 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:58:59 -0400 Subject: [PATCH 18/71] Delete src/perform_step/symplectic_perform_step.jl --- src/perform_step/symplectic_perform_step.jl | 2025 ------------------- 1 file changed, 2025 deletions(-) delete mode 100644 src/perform_step/symplectic_perform_step.jl diff --git a/src/perform_step/symplectic_perform_step.jl b/src/perform_step/symplectic_perform_step.jl deleted file mode 100644 index 413f1882a2..0000000000 --- a/src/perform_step/symplectic_perform_step.jl +++ /dev/null @@ -1,2025 +0,0 @@ -# http://www.chimica.unipd.it/antonino.polimeno/pubblica/downloads/JChemPhys_101_4062.pdf - -function initialize!(integrator, cache::SymplecticEulerConstantCache) - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - # Do the calculation pre - # So that way FSAL interpolation - duprev, uprev = integrator.uprev.x - du, u = integrator.u.x - kdu = integrator.f.f1(duprev, uprev, integrator.p, integrator.t) - kuprev = integrator.f.f2(duprev, uprev, integrator.p, integrator.t) - @muladd du = duprev + integrator.dt * kdu - ku = integrator.f.f2(du, uprev, integrator.p, integrator.t) - integrator.stats.nf2 += 1 - integrator.stats.nf += 2 - integrator.fsalfirst = ArrayPartition((kdu, kuprev)) - integrator.fsallast = ArrayPartition((zero(kdu), ku)) -end - -@muladd function perform_step!(integrator, cache::SymplecticEulerConstantCache, - repeat_step = false) - @unpack t, dt, f, p = integrator - duprev, uprev = integrator.uprev.x - kuprev = integrator.fsalfirst.x[2] - u = uprev + dt * kuprev - # Now actually compute the step - # Do it at the end for interpolations! - kdu = f.f1(duprev, u, p, t) - du = duprev + dt * kdu - - ku = f.f2(du, u, p, t) - integrator.stats.nf2 += 1 - integrator.stats.nf += 1 - - integrator.u = ArrayPartition((du, u)) - integrator.fsallast = ArrayPartition((kdu, ku)) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast -end - -function initialize!(integrator, cache::SymplecticEulerCache) - integrator.kshortsize = 2 - @unpack k, fsalfirst = cache - integrator.fsalfirst = fsalfirst - integrator.fsallast = k - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - # Do the calculation pre - # So that way FSAL interpolation - duprev, uprev = integrator.uprev.x - du, u = integrator.u.x - kuprev = integrator.fsalfirst.x[2] - kdu, ku = integrator.fsallast.x - integrator.f.f1(kdu, duprev, uprev, integrator.p, integrator.t) - integrator.f.f2(kuprev, duprev, uprev, integrator.p, integrator.t) - @muladd @.. broadcast=false du=duprev + integrator.dt * kdu - integrator.f.f2(ku, du, uprev, integrator.p, integrator.t) - integrator.stats.nf += 1 - integrator.stats.nf2 += 2 -end - -@muladd function perform_step!(integrator, cache::SymplecticEulerCache, repeat_step = false) - @unpack t, dt, f, p = integrator - duprev, uprev = integrator.uprev.x - du, u = integrator.u.x - kuprev = integrator.fsalfirst.x[2] - kdu, ku = integrator.fsallast.x - @.. broadcast=false u=uprev + dt * kuprev - # Now actually compute the step - # Do it at the end for interpolations! - integrator.stats.nf2 += 1 - integrator.stats.nf += 1 - f.f1(kdu, duprev, u, p, t) - @.. broadcast=false du=duprev + dt * kdu - f.f2(ku, du, u, p, t) -end - -const MutableCachesHamilton = Union{Symplectic2Cache, Symplectic3Cache, - Symplectic4Cache, Symplectic45Cache, Symplectic5Cache, - Symplectic6Cache, Symplectic62Cache, - McAte8Cache, KahanLi8Cache, SofSpa10Cache} -const MutableCachesNewton = Union{VelocityVerletCache} - -const ConstantCachesHamilton = Union{Symplectic2ConstantCache, Symplectic3ConstantCache, - Symplectic4ConstantCache, Symplectic45ConstantCache, - Symplectic5ConstantCache, - Symplectic6ConstantCache, Symplectic62ConstantCache, - McAte8ConstantCache, KahanLi8ConstantCache, - SofSpa10ConstantCache} -const ConstantCachesNewton = Union{VelocityVerletConstantCache} - -# some of the algorithms are designed only for the case -# f.f2(p, q, pa, t) = p which is the Newton/Lagrange equations -# If called with different functions (which are possible in the Hamiltonian case) -# an exception is thrown to avoid silently calculate wrong results. -verify_f2(f, p, q, pa, t, ::Any, ::C) where {C <: ConstantCachesHamilton} = f(p, q, pa, t) -function verify_f2(f, res, p, q, pa, t, ::Any, ::C) where {C <: MutableCachesHamilton} - f(res, p, q, pa, t) -end - -function verify_f2(f, p, q, pa, t, integrator, ::C) where {C <: ConstantCachesNewton} - res = f(p, q, pa, t) - res == p ? p : throwex(integrator) -end -function verify_f2(f, res, p, q, pa, t, integrator, ::C) where {C <: MutableCachesNewton} - f(res, p, q, pa, t) - res == p ? res : throwex(integrator) -end -function throwex(integrator) - algn = typeof(integrator.alg) - throw(ArgumentError("Algorithm $algn is not applicable if f2(p, q, t) != p")) -end - -# provide the mutable uninitialized objects to keep state and derivative in case of mutable caches -# no such objects are required for constant caches -function alloc_symp_state(integrator) - (integrator.u.x..., integrator.cache.tmp.x...) -end - -# load state and derivatives at begin of symplectic iteration steps -function load_symp_state(integrator) - (integrator.uprev.x..., integrator.fsallast.x...) -end - -# store state and derivatives at the end of symplectic iteration steps -function store_symp_state!(integrator, ::OrdinaryDiffEqConstantCache, du, u, kdu, ku) - integrator.u = ArrayPartition((du, u)) - integrator.fsallast = ArrayPartition((kdu, ku)) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - nothing -end - -function store_symp_state!(integrator, ::OrdinaryDiffEqMutableCache, kdu, ku) - copyto!(integrator.k[1].x[1], integrator.k[2].x[1]) - copyto!(integrator.k[1].x[2], integrator.k[2].x[2]) - copyto!(integrator.k[2].x[2], ku) - copyto!(integrator.k[2].x[1], kdu) - nothing -end - -function initialize!(integrator, - cache::C) where {C <: - Union{MutableCachesHamilton, MutableCachesNewton}} - integrator.fsalfirst = cache.fsalfirst - integrator.fsallast = cache.k - - integrator.kshortsize = 2 - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - - duprev, uprev = integrator.uprev.x - integrator.f.f1(integrator.k[2].x[1], duprev, uprev, integrator.p, integrator.t) - verify_f2(integrator.f.f2, integrator.k[2].x[2], duprev, uprev, integrator.p, - integrator.t, integrator, cache) - integrator.stats.nf += 1 - integrator.stats.nf2 += 1 -end - -function initialize!(integrator, - cache::C) where { - C <: - Union{ConstantCachesHamilton, ConstantCachesNewton}} - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - duprev, uprev = integrator.uprev.x - kdu = integrator.f.f1(duprev, uprev, integrator.p, integrator.t) - ku = verify_f2(integrator.f.f2, duprev, uprev, integrator.p, integrator.t, integrator, - cache) - integrator.stats.nf += 1 - integrator.stats.nf2 += 1 - integrator.fsallast = ArrayPartition((kdu, ku)) - integrator.k[2] = integrator.fsallast - integrator.fsalfirst = integrator.fsallast -end - -@muladd function perform_step!(integrator, cache::VelocityVerletConstantCache, - repeat_step = false) - @unpack t, dt, f, p = integrator - duprev, uprev = load_symp_state(integrator) - - # x(t+Δt) = x(t) + v(t)*Δt + 1/2*a(t)*Δt^2 - ku = integrator.fsallast.x[1] - dtsq = dt^2 - half = cache.half - u = uprev + dt * duprev + dtsq * (half * ku) - kdu = f.f1(duprev, u, p, t + dt) - # v(t+Δt) = v(t) + 1/2*(a(t)+a(t+Δt))*Δt - du = duprev + dt * (half * ku + half * kdu) - - integrator.stats.nf += 2 - store_symp_state!(integrator, cache, du, u, kdu, du) -end - -@muladd function perform_step!(integrator, cache::VelocityVerletCache, repeat_step = false) - @unpack t, dt, f, p = integrator - duprev, uprev = load_symp_state(integrator) - du, u, kdu, ku = alloc_symp_state(integrator) - - # x(t+Δt) = x(t) + v(t)*Δt + 1/2*a(t)*Δt^2 - ku = integrator.fsallast.x[1] - dtsq = dt^2 - half = cache.half - @.. broadcast=false u=uprev + dt * duprev + dtsq * (half * ku) - f.f1(kdu, duprev, u, p, t + dt) - integrator.stats.nf += 2 - # v(t+Δt) = v(t) + 1/2*(a(t)+a(t+Δt))*Δt - @.. broadcast=false du=duprev + dt * (half * ku + half * kdu) - - store_symp_state!(integrator, cache, kdu, du) -end - -@muladd function perform_step!(integrator, cache::Symplectic2ConstantCache, - repeat_step = false) - @unpack t, dt, f, p = integrator - @unpack a1, a2, b1, b2 = cache - duprev, uprev, _, kuprev = load_symp_state(integrator) - - # update position - u = uprev + dt * b1 * kuprev - # update velocity - kdu = f.f1(duprev, u, p, t) - du = duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b2 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a2 * kdu - kdu = f.f1(du, u, p, tnew) - ku = f.f2(du, u, p, tnew) - - integrator.stats.nf += 3 - integrator.stats.nf2 += 2 - store_symp_state!(integrator, cache, du, u, kdu, ku) -end - -@muladd function perform_step!(integrator, cache::Symplectic2Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - @unpack a1, a2, b1, b2 = cache.tab - duprev, uprev, _, kuprev = load_symp_state(integrator) - du, u, kdu, ku = alloc_symp_state(integrator) - - # update position - @.. broadcast=false u=uprev + dt * b1 * kuprev - # update velocity - f.f1(kdu, duprev, u, p, t) - @.. broadcast=false du=duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b2 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a2 * kdu - f.f1(kdu, du, u, p, tnew) - f.f2(ku, du, u, p, tnew) - - integrator.stats.nf += 3 - integrator.stats.nf2 += 2 - store_symp_state!(integrator, cache, kdu, ku) -end - -@muladd function perform_step!(integrator, cache::Symplectic3ConstantCache, - repeat_step = false) - @unpack t, dt, f, p = integrator - @unpack a1, a2, a3, b1, b2, b3 = cache - duprev, uprev, _, kuprev = load_symp_state(integrator) - - # update position - u = uprev + dt * b1 * kuprev - # update velocity - kdu = f.f1(duprev, u, p, integrator.t) - du = duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b2 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a2 * kdu - - # update position & velocity - tnew = tnew + a2 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b3 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a3 * kdu - kdu = f.f1(du, u, p, tnew) - ku = f.f2(du, u, p, tnew) - - integrator.stats.nf += 4 - integrator.stats.nf2 += 3 - store_symp_state!(integrator, cache, du, u, kdu, ku) -end - -@muladd function perform_step!(integrator, cache::Symplectic3Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - @unpack a1, a2, a3, b1, b2, b3 = cache.tab - duprev, uprev, _, kuprev = load_symp_state(integrator) - du, u, kdu, ku = alloc_symp_state(integrator) - - # update position - @.. broadcast=false u=uprev + dt * b1 * kuprev - # update velocity - f.f1(kdu, duprev, u, p, integrator.t) - @.. broadcast=false du=duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b2 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a2 * kdu - - # update position & velocity - tnew = tnew + a2 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b3 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a3 * kdu - f.f1(kdu, du, u, p, tnew) - f.f2(ku, du, u, p, tnew) - - integrator.stats.nf += 4 - integrator.stats.nf2 += 3 - store_symp_state!(integrator, cache, kdu, ku) -end - -@muladd function perform_step!(integrator, cache::Symplectic4ConstantCache, - repeat_step = false) - @unpack t, dt, f, p = integrator - @unpack a1, a2, a3, a4, b1, b2, b3, b4 = cache - duprev, uprev, _, kuprev = load_symp_state(integrator) - - # update position - u = uprev + dt * b1 * kuprev - # update velocity - kdu = f.f1(duprev, u, p, t) - du = duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b2 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a2 * kdu - - # update position & velocity - tnew = tnew + a2 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b3 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a3 * kdu - - # update position & velocity - tnew = tnew + a3 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b4 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a4 * kdu - kdu = f.f1(du, u, p, tnew) - ku = f.f2(du, u, p, tnew) - - integrator.stats.nf += 5 - integrator.stats.nf2 += 4 - store_symp_state!(integrator, cache, du, u, kdu, ku) -end - -@muladd function perform_step!(integrator, cache::Symplectic4Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - @unpack a1, a2, a3, a4, b1, b2, b3, b4 = cache.tab - duprev, uprev, _, kuprev = load_symp_state(integrator) - du, u, kdu, ku = alloc_symp_state(integrator) - - # update position - @.. broadcast=false u=uprev + dt * b1 * kuprev - # update velocity - f.f1(kdu, duprev, u, p, t) - @.. broadcast=false du=duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b2 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a2 * kdu - - # update position & velocity - tnew = tnew + a2 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b3 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a3 * kdu - - # update position & velocity - tnew = tnew + a3 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b4 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a4 * kdu - f.f1(kdu, du, u, p, tnew) - f.f2(ku, du, u, p, tnew) - - integrator.stats.nf += 5 - integrator.stats.nf2 += 4 - store_symp_state!(integrator, cache, kdu, ku) -end - -@muladd function perform_step!(integrator, cache::Symplectic45ConstantCache, - repeat_step = false) - @unpack t, dt, f, p = integrator - alg = unwrap_alg(integrator, false) - @unpack a1, a2, a3, a4, a5, b1, b2, b3, b4, b5 = cache - duprev, uprev, _, kuprev = load_symp_state(integrator) - - # update position - u = uprev + dt * b1 * kuprev - # update velocity - kdu = f.f1(duprev, u, p, t) - du = duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b2 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a2 * kdu - - # update position & velocity - tnew = tnew + a2 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b3 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a3 * kdu - - # update position & velocity - tnew = tnew + a3 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b4 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a4 * kdu - - # update position & velocity - tnew = tnew + a4 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b5 * ku - - kdu = f.f1(du, u, p, tnew) - if alg isa McAte42 - du = du + dt * a5 * kdu - kdu = f.f1(du, u, p, tnew) - integrator.stats.nf += 1 - end - ku = f.f2(du, u, p, tnew) - - integrator.stats.nf += 5 - integrator.stats.nf2 += 5 - store_symp_state!(integrator, cache, du, u, kdu, ku) -end - -@muladd function perform_step!(integrator, cache::Symplectic45Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - alg = unwrap_alg(integrator, false) - @unpack a1, a2, a3, a4, a5, b1, b2, b3, b4, b5 = cache.tab - duprev, uprev, _, kuprev = load_symp_state(integrator) - du, u, kdu, ku = alloc_symp_state(integrator) - - # update position - @.. broadcast=false u=uprev + dt * b1 * kuprev - # update velocity - f.f1(kdu, duprev, u, p, t) - @.. broadcast=false du=duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b2 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a2 * kdu - - # update position & velocity - tnew = tnew + a2 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b3 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a3 * kdu - - # update position & velocity - tnew = tnew + a3 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b4 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a4 * kdu - - # update position & velocity - tnew = tnew + a4 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b5 * ku - - f.f1(kdu, du, u, p, tnew) - if alg isa McAte42 - @.. broadcast=false du=du + dt * a5 * kdu - f.f1(kdu, du, u, p, tnew) - integrator.stats.nf += 1 - end - f.f2(ku, du, u, p, tnew) - - integrator.stats.nf += 5 - integrator.stats.nf2 += 5 - store_symp_state!(integrator, cache, kdu, ku) -end - -@muladd function perform_step!(integrator, cache::Symplectic5ConstantCache, - repeat_step = false) - @unpack t, dt, f, p = integrator - @unpack a1, a2, a3, a4, a5, a6, b1, b2, b3, b4, b5, b6 = cache - duprev, uprev, _, kuprev = load_symp_state(integrator) - - # update position - u = uprev + dt * b1 * kuprev - # update velocity - kdu = f.f1(duprev, u, p, integrator.t) - du = duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b2 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a2 * kdu - - # update position & velocity - tnew = tnew + a2 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b3 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a3 * kdu - - # update position & velocity - tnew = tnew + a3 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b4 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a4 * kdu - - # update position & velocity - tnew = tnew + a4 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b5 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a5 * kdu - - tnew = tnew + a5 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b6 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a6 * kdu - kdu = f.f1(du, u, p, tnew) - ku = f.f2(du, u, p, tnew) - - integrator.stats.nf += 7 - integrator.stats.nf2 += 6 - store_symp_state!(integrator, cache, du, u, kdu, ku) -end - -@muladd function perform_step!(integrator, cache::Symplectic5Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - @unpack a1, a2, a3, a4, a5, a6, b1, b2, b3, b4, b5, b6 = cache.tab - duprev, uprev, _, kuprev = load_symp_state(integrator) - du, u, kdu, ku = alloc_symp_state(integrator) - - # update position - @.. broadcast=false u=uprev + dt * b1 * kuprev - # update velocity - f.f1(kdu, duprev, u, p, integrator.t) - @.. broadcast=false du=duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b2 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a2 * kdu - - # update position & velocity - tnew = tnew + a2 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b3 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a3 * kdu - - # update position & velocity - tnew = tnew + a3 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b4 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a4 * kdu - - # update position & velocity - tnew = tnew + a4 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b5 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a5 * kdu - - tnew = tnew + a5 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b6 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a6 * kdu - f.f1(kdu, du, u, p, tnew) - f.f2(ku, du, u, p, tnew) - - integrator.stats.nf += 7 - integrator.stats.nf2 += 6 - store_symp_state!(integrator, cache, kdu, ku) -end - -@muladd function perform_step!(integrator, cache::Symplectic6ConstantCache, - repeat_step = false) - @unpack t, dt, f, p = integrator - @unpack a1, a2, a3, a4, a5, a6, a7, a8, b1, b2, b3, b4, b5, b6, b7, b8 = cache - duprev, uprev, _, kuprev = load_symp_state(integrator) - - # update position - u = uprev + dt * b1 * kuprev - # update velocity - kdu = f.f1(duprev, u, p, integrator.t) - du = duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b2 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a2 * kdu - - # update position & velocity - tnew = tnew + a2 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b3 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a3 * kdu - - # update position & velocity - tnew = tnew + a3 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b4 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a4 * kdu - - # update position & velocity - tnew = tnew + a4 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b5 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a5 * kdu - - tnew = tnew + a5 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b6 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a6 * kdu - - tnew = tnew + a6 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b7 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a7 * kdu - - tnew = tnew + a7 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b8 * ku - - kdu = f.f1(du, u, p, tnew) - # @.. broadcast=false du = du + dt*a8*kdu - ku = f.f2(du, u, p, tnew) - - integrator.stats.nf += 8 - integrator.stats.nf2 += 8 - store_symp_state!(integrator, cache, du, u, kdu, ku) -end - -@muladd function perform_step!(integrator, cache::Symplectic6Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - @unpack a1, a2, a3, a4, a5, a6, a7, a8, b1, b2, b3, b4, b5, b6, b7, b8 = cache.tab - duprev, uprev, _, kuprev = load_symp_state(integrator) - du, u, kdu, ku = alloc_symp_state(integrator) - - # update position - @.. broadcast=false u=uprev + dt * b1 * kuprev - # update velocity - f.f1(kdu, duprev, u, p, integrator.t) - @.. broadcast=false du=duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b2 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a2 * kdu - - # update position & velocity - tnew = tnew + a2 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b3 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a3 * kdu - - # update position & velocity - tnew = tnew + a3 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b4 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a4 * kdu - - # update position & velocity - tnew = tnew + a4 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b5 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a5 * kdu - - tnew = tnew + a5 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b6 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a6 * kdu - - tnew = tnew + a6 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b7 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a7 * kdu - - tnew = tnew + a7 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b8 * ku - - f.f1(kdu, du, u, p, tnew) - # @.. broadcast=false du = du + dt*a8*kdu - f.f2(ku, du, u, p, tnew) - - integrator.stats.nf += 8 - integrator.stats.nf2 += 8 - store_symp_state!(integrator, cache, kdu, ku) -end - -@muladd function perform_step!(integrator, cache::Symplectic62ConstantCache, - repeat_step = false) - @unpack t, dt, f, p = integrator - @unpack a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10 = cache - duprev, uprev, _, kuprev = load_symp_state(integrator) - - # update position - u = uprev + dt * b1 * kuprev - # update velocity - kdu = f.f1(duprev, u, p, integrator.t) - du = duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b2 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a2 * kdu - - # update position & velocity - tnew = tnew + a2 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b3 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a3 * kdu - - # update position & velocity - tnew = tnew + a3 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b4 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a4 * kdu - - # update position & velocity - tnew = tnew + a4 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b5 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a5 * kdu - - tnew = tnew + a5 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b6 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a6 * kdu - - tnew = tnew + a6 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b7 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a7 * kdu - - tnew = tnew + a7 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b8 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a8 * kdu - - tnew = tnew + a8 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b9 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a9 * kdu - - tnew = tnew + a9 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b10 * ku - - kdu = f.f1(du, u, p, tnew) - # @.. broadcast=false du = du + dt*a10*kdu - ku = f.f2(du, u, p, tnew) - - integrator.stats.nf += 10 - integrator.stats.nf2 += 10 - store_symp_state!(integrator, cache, du, u, kdu, ku) -end - -@muladd function perform_step!(integrator, cache::Symplectic62Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - @unpack a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10 = cache.tab - duprev, uprev, _, kuprev = load_symp_state(integrator) - du, u, kdu, ku = alloc_symp_state(integrator) - - # update position - @.. broadcast=false u=uprev + dt * b1 * kuprev - # update velocity - f.f1(kdu, duprev, u, p, integrator.t) - @.. broadcast=false du=duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b2 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a2 * kdu - - # update position & velocity - tnew = tnew + a2 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b3 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a3 * kdu - - # update position & velocity - tnew = tnew + a3 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b4 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a4 * kdu - - # update position & velocity - tnew = tnew + a4 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b5 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a5 * kdu - - tnew = tnew + a5 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b6 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a6 * kdu - - tnew = tnew + a6 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b7 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a7 * kdu - - tnew = tnew + a7 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b8 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a8 * kdu - - tnew = tnew + a8 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b9 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a9 * kdu - - tnew = tnew + a9 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b10 * ku - - f.f1(kdu, du, u, p, tnew) - # @.. broadcast=false du = du + dt*a10*kdu - f.f2(ku, du, u, p, tnew) - - integrator.stats.nf += 10 - integrator.stats.nf2 += 10 - store_symp_state!(integrator, cache, kdu, ku) -end - -@muladd function perform_step!(integrator, cache::McAte8ConstantCache, repeat_step = false) - @unpack t, dt, f, p = integrator - @unpack a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, - b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16 = cache - duprev, uprev, _, kuprev = load_symp_state(integrator) - - # update position - u = uprev + dt * b1 * kuprev - # update velocity - kdu = f.f1(duprev, u, p, integrator.t) - du = duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b2 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a2 * kdu - - # update position & velocity - tnew = tnew + a2 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b3 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a3 * kdu - - # update position & velocity - tnew = tnew + a3 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b4 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a4 * kdu - - # update position & velocity - tnew = tnew + a4 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b5 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a5 * kdu - - tnew = tnew + a5 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b6 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a6 * kdu - - tnew = tnew + a6 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b7 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a7 * kdu - - tnew = tnew + a7 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b8 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a8 * kdu - - tnew = tnew + a8 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b9 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a9 * kdu - - tnew = tnew + a9 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b10 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a10 * kdu - - tnew = tnew + a10 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b11 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a11 * kdu - - tnew = tnew + a11 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b12 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a12 * kdu - - tnew = tnew + a12 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b13 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a13 * kdu - - tnew = tnew + a13 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b14 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a14 * kdu - - tnew = tnew + a14 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b15 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a15 * kdu - - tnew = tnew + a15 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b16 * ku - - kdu = f.f1(du, u, p, tnew) - # @.. broadcast=false du = du + dt*a16*kdu - ku = f.f2(du, u, p, tnew) - - integrator.stats.nf += 16 - integrator.stats.nf2 += 16 - store_symp_state!(integrator, cache, du, u, kdu, ku) -end - -@muladd function perform_step!(integrator, cache::McAte8Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - @unpack a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, - b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16 = cache.tab - duprev, uprev, _, kuprev = load_symp_state(integrator) - du, u, kdu, ku = alloc_symp_state(integrator) - - # update position - @.. broadcast=false u=uprev + dt * b1 * kuprev - # update velocity - f.f1(kdu, duprev, u, p, integrator.t) - @.. broadcast=false du=duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b2 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a2 * kdu - - # update position & velocity - tnew = tnew + a2 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b3 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a3 * kdu - - # update position & velocity - tnew = tnew + a3 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b4 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a4 * kdu - - # update position & velocity - tnew = tnew + a4 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b5 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a5 * kdu - - tnew = tnew + a5 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b6 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a6 * kdu - - tnew = tnew + a6 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b7 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a7 * kdu - - tnew = tnew + a7 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b8 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a8 * kdu - - tnew = tnew + a8 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b9 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a9 * kdu - - tnew = tnew + a9 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b10 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a10 * kdu - - tnew = tnew + a10 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b11 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a11 * kdu - - tnew = tnew + a11 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b12 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a12 * kdu - - tnew = tnew + a12 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b13 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a13 * kdu - - tnew = tnew + a13 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b14 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a14 * kdu - - tnew = tnew + a14 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b15 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a15 * kdu - - tnew = tnew + a15 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b16 * ku - - f.f1(kdu, du, u, p, tnew) - # @.. broadcast=false du = du + dt*a16*kdu - f.f2(ku, du, u, p, tnew) - - integrator.stats.nf += 16 - integrator.stats.nf2 += 16 - store_symp_state!(integrator, cache, kdu, ku) -end - -@muladd function perform_step!(integrator, cache::KahanLi8ConstantCache, - repeat_step = false) - @unpack t, dt, f, p = integrator - @unpack a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18, - b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18 = cache - duprev, uprev, _, kuprev = load_symp_state(integrator) - - # update position - u = uprev + dt * b1 * kuprev - # update velocity - kdu = f.f1(duprev, u, p, integrator.t) - du = duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b2 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a2 * kdu - - # update position & velocity - tnew = tnew + a2 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b3 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a3 * kdu - - # update position & velocity - tnew = tnew + a3 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b4 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a4 * kdu - - # update position & velocity - tnew = tnew + a4 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b5 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a5 * kdu - - tnew = tnew + a5 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b6 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a6 * kdu - - tnew = tnew + a6 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b7 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a7 * kdu - - tnew = tnew + a7 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b8 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a8 * kdu - - tnew = tnew + a8 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b9 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a9 * kdu - - tnew = tnew + a9 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b10 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a10 * kdu - - tnew = tnew + a10 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b11 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a11 * kdu - - tnew = tnew + a11 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b12 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a12 * kdu - - tnew = tnew + a12 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b13 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a13 * kdu - - tnew = tnew + a13 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b14 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a14 * kdu - - tnew = tnew + a14 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b15 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a15 * kdu - - tnew = tnew + a15 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b16 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a16 * kdu - - tnew = tnew + a16 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b17 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a17 * kdu - - tnew = tnew + a17 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b18 * ku - - kdu = f.f1(du, u, p, tnew) - # @.. broadcast=false du = du + dt*a18*kdu - ku = f.f2(du, u, p, tnew) - - integrator.stats.nf += 18 - integrator.stats.nf2 += 18 - store_symp_state!(integrator, cache, du, u, kdu, ku) -end - -@muladd function perform_step!(integrator, cache::KahanLi8Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - @unpack a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18, - b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18 = cache.tab - duprev, uprev, _, kuprev = load_symp_state(integrator) - du, u, kdu, ku = alloc_symp_state(integrator) - - # update position - @.. broadcast=false u=uprev + dt * b1 * kuprev - # update velocity - f.f1(kdu, duprev, u, p, integrator.t) - @.. broadcast=false du=duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b2 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a2 * kdu - - # update position & velocity - tnew = tnew + a2 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b3 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a3 * kdu - - # update position & velocity - tnew = tnew + a3 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b4 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a4 * kdu - - # update position & velocity - tnew = tnew + a4 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b5 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a5 * kdu - - tnew = tnew + a5 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b6 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a6 * kdu - - tnew = tnew + a6 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b7 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a7 * kdu - - tnew = tnew + a7 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b8 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a8 * kdu - - tnew = tnew + a8 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b9 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a9 * kdu - - tnew = tnew + a9 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b10 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a10 * kdu - - tnew = tnew + a10 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b11 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a11 * kdu - - tnew = tnew + a11 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b12 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a12 * kdu - - tnew = tnew + a12 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b13 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a13 * kdu - - tnew = tnew + a13 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b14 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a14 * kdu - - tnew = tnew + a14 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b15 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a15 * kdu - - tnew = tnew + a15 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b16 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a16 * kdu - - tnew = tnew + a16 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b17 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a17 * kdu - - tnew = tnew + a17 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b18 * ku - - f.f1(kdu, du, u, p, tnew) - # @.. broadcast=false du = du + dt*a18*kdu - f.f2(ku, du, u, p, tnew) - - integrator.stats.nf += 18 - integrator.stats.nf2 += 18 - store_symp_state!(integrator, cache, kdu, ku) -end - -@muladd function perform_step!(integrator, cache::SofSpa10ConstantCache, - repeat_step = false) - @unpack t, dt, f, p = integrator - @unpack a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18, - a19, a20, a21, a22, a23, a24, a25, a26, a27, a28, a29, a30, a31, a32, a33, a34, - a35, a36, - b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, - b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31, b32, b33, b34, - b35, b36 = cache - duprev, uprev, _, kuprev = load_symp_state(integrator) - - # update position - u = uprev + dt * b1 * kuprev - # update velocity - kdu = f.f1(duprev, u, p, integrator.t) - du = duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b2 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a2 * kdu - - # update position & velocity - tnew = tnew + a2 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b3 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a3 * kdu - - # update position & velocity - tnew = tnew + a3 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b4 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a4 * kdu - - # update position & velocity - tnew = tnew + a4 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b5 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a5 * kdu - - tnew = tnew + a5 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b6 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a6 * kdu - - tnew = tnew + a6 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b7 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a7 * kdu - - tnew = tnew + a7 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b8 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a8 * kdu - - tnew = tnew + a8 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b9 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a9 * kdu - - tnew = tnew + a9 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b10 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a10 * kdu - - tnew = tnew + a10 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b11 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a11 * kdu - - tnew = tnew + a11 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b12 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a12 * kdu - - tnew = tnew + a12 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b13 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a13 * kdu - - tnew = tnew + a13 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b14 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a14 * kdu - - tnew = tnew + a14 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b15 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a15 * kdu - - tnew = tnew + a15 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b16 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a16 * kdu - - tnew = tnew + a16 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b17 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a17 * kdu - - tnew = tnew + a17 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b18 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a18 * kdu - - tnew = tnew + a18 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b19 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a19 * kdu - - tnew = tnew + a19 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b20 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a20 * kdu - - tnew = tnew + a20 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b21 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a21 * kdu - - tnew = tnew + a21 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b22 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a22 * kdu - - tnew = tnew + a22 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b23 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a23 * kdu - - tnew = tnew + a23 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b24 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a24 * kdu - - tnew = tnew + a24 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b25 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a25 * kdu - - tnew = tnew + a25 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b26 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a26 * kdu - - tnew = tnew + a26 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b27 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a27 * kdu - - tnew = tnew + a27 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b28 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a28 * kdu - - tnew = tnew + a28 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b29 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a29 * kdu - - tnew = tnew + a29 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b30 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a30 * kdu - - tnew = tnew + a30 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b31 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a31 * kdu - - tnew = tnew + a31 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b32 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a32 * kdu - - tnew = tnew + a32 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b33 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a33 * kdu - - tnew = tnew + a33 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b34 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a34 * kdu - - tnew = tnew + a34 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b35 * ku - - kdu = f.f1(du, u, p, tnew) - du = du + dt * a35 * kdu - - tnew = tnew + a35 * dt - ku = f.f2(du, u, p, tnew) - u = u + dt * b36 * ku - - kdu = f.f1(du, u, p, tnew) - # @.. broadcast=false du = du + dt*a30*kdu - ku = f.f2(du, u, p, tnew) - - integrator.stats.nf += 36 - integrator.stats.nf2 += 36 - store_symp_state!(integrator, cache, du, u, kdu, ku) -end - -@muladd function perform_step!(integrator, cache::SofSpa10Cache, repeat_step = false) - @unpack t, dt, f, p = integrator - @unpack a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18, - a19, a20, a21, a22, a23, a24, a25, a26, a27, a28, a29, a30, a31, a32, a33, a34, - a35, a36, - b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, - b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31, b32, b33, b34, - b35, b36 = cache.tab - duprev, uprev, _, kuprev = load_symp_state(integrator) - du, u, kdu, ku = alloc_symp_state(integrator) - - # update position - @.. broadcast=false u=uprev + dt * b1 * kuprev - # update velocity - f.f1(kdu, duprev, u, p, integrator.t) - @.. broadcast=false du=duprev + dt * a1 * kdu - # update position & velocity - tnew = t + a1 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b2 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a2 * kdu - - # update position & velocity - tnew = tnew + a2 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b3 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a3 * kdu - - # update position & velocity - tnew = tnew + a3 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b4 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a4 * kdu - - # update position & velocity - tnew = tnew + a4 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b5 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a5 * kdu - - tnew = tnew + a5 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b6 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a6 * kdu - - tnew = tnew + a6 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b7 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a7 * kdu - - tnew = tnew + a7 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b8 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a8 * kdu - - tnew = tnew + a8 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b9 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a9 * kdu - - tnew = tnew + a9 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b10 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a10 * kdu - - tnew = tnew + a10 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b11 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a11 * kdu - - tnew = tnew + a11 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b12 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a12 * kdu - - tnew = tnew + a12 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b13 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a13 * kdu - - tnew = tnew + a13 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b14 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a14 * kdu - - tnew = tnew + a14 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b15 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a15 * kdu - - tnew = tnew + a15 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b16 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a16 * kdu - - tnew = tnew + a16 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b17 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a17 * kdu - - tnew = tnew + a17 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b18 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a18 * kdu - - tnew = tnew + a18 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b19 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a19 * kdu - - tnew = tnew + a19 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b20 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a20 * kdu - - tnew = tnew + a20 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b21 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a21 * kdu - - tnew = tnew + a21 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b22 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a22 * kdu - - tnew = tnew + a22 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b23 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a23 * kdu - - tnew = tnew + a23 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b24 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a24 * kdu - - tnew = tnew + a24 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b25 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a25 * kdu - - tnew = tnew + a25 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b26 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a26 * kdu - - tnew = tnew + a26 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b27 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a27 * kdu - - tnew = tnew + a27 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b28 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a28 * kdu - - tnew = tnew + a28 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b29 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a29 * kdu - - tnew = tnew + a29 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b30 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a30 * kdu - - tnew = tnew + a30 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b31 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a31 * kdu - - tnew = tnew + a31 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b32 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a32 * kdu - - tnew = tnew + a32 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b33 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a33 * kdu - - tnew = tnew + a33 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b34 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a34 * kdu - - tnew = tnew + a34 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b35 * ku - - f.f1(kdu, du, u, p, tnew) - @.. broadcast=false du=du + dt * a35 * kdu - - tnew = tnew + a35 * dt - f.f2(ku, du, u, p, tnew) - @.. broadcast=false u=u + dt * b36 * ku - - f.f1(kdu, du, u, p, tnew) - # @.. broadcast=false du = du + dt*a30*kdu - f.f2(ku, du, u, p, tnew) - - integrator.stats.nf += 36 - integrator.stats.nf2 += 36 - store_symp_state!(integrator, cache, kdu, ku) -end From 84158aba8a7ea5da1c181642f8fcca12d5e52c69 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:59:09 -0400 Subject: [PATCH 19/71] Delete src/perform_step/verner_rk_perform_step.jl --- src/perform_step/verner_rk_perform_step.jl | 1284 -------------------- 1 file changed, 1284 deletions(-) delete mode 100644 src/perform_step/verner_rk_perform_step.jl diff --git a/src/perform_step/verner_rk_perform_step.jl b/src/perform_step/verner_rk_perform_step.jl deleted file mode 100644 index 0a44e217da..0000000000 --- a/src/perform_step/verner_rk_perform_step.jl +++ /dev/null @@ -1,1284 +0,0 @@ -function initialize!(integrator, cache::Vern6ConstantCache) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - alg = unwrap_alg(integrator, false) - alg.lazy ? (integrator.kshortsize = 9) : (integrator.kshortsize = 12) - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - @inbounds for i in 2:8 - integrator.k[i] = zero(integrator.fsalfirst) - end - integrator.k[integrator.kshortsize] = integrator.fsallast - - if !alg.lazy - @inbounds for i in 10:12 - integrator.k[i] = zero(integrator.fsalfirst) - end - end -end - -@muladd function perform_step!(integrator, cache::Vern6ConstantCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack c1, c2, c3, c4, c5, c6, a21, a31, a32, a41, a43, a51, a53, a54, a61, a63, a64, a65, a71, a73, a74, a75, a76, a81, a83, a84, a85, a86, a87, a91, a94, a95, a96, a97, a98, btilde1, btilde4, btilde5, btilde6, btilde7, btilde8, btilde9 = cache.tab - k1 = integrator.fsalfirst - a = dt * a21 - k2 = f(uprev + a * k1, p, t + c1 * dt) - k3 = f(uprev + dt * (a31 * k1 + a32 * k2), p, t + c2 * dt) - k4 = f(uprev + dt * (a41 * k1 + a43 * k3), p, t + c3 * dt) - k5 = f(uprev + dt * (a51 * k1 + a53 * k3 + a54 * k4), p, t + c4 * dt) - k6 = f(uprev + dt * (a61 * k1 + a63 * k3 + a64 * k4 + a65 * k5), p, t + c5 * dt) - k7 = f(uprev + dt * (a71 * k1 + a73 * k3 + a74 * k4 + a75 * k5 + a76 * k6), p, - t + c6 * dt) - g8 = uprev + dt * (a81 * k1 + a83 * k3 + a84 * k4 + a85 * k5 + a86 * k6 + a87 * k7) - k8 = f(g8, p, t + dt) - u = uprev + dt * (a91 * k1 + a94 * k4 + a95 * k5 + a96 * k6 + a97 * k7 + a98 * k8) - integrator.fsallast = f(u, p, t + dt) - k9 = integrator.fsallast - integrator.stats.nf += 8 - if integrator.alg isa CompositeAlgorithm - g9 = u - ϱu = integrator.opts.internalnorm(k9 - k8, t) - ϱd = integrator.opts.internalnorm(g9 - g8, t) - integrator.eigen_est = ϱu / ϱd - end - if integrator.opts.adaptive - utilde = dt * - (btilde1 * k1 + btilde4 * k4 + btilde5 * k5 + btilde6 * k6 + btilde7 * k7 + - btilde8 * k8 + btilde9 * k9) - atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.k[1] = k1 - integrator.k[2] = k2 - integrator.k[3] = k3 - integrator.k[4] = k4 - integrator.k[5] = k5 - integrator.k[6] = k6 - integrator.k[7] = k7 - integrator.k[8] = k8 - integrator.k[9] = k9 - - alg = unwrap_alg(integrator, false) - if !alg.lazy && (integrator.opts.adaptive == false || - accept_step_controller(integrator, integrator.opts.controller)) - k = integrator.k - @unpack c10, a1001, a1004, a1005, a1006, a1007, a1008, a1009, c11, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, c12, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211 = cache.tab.extra - k[10] = f( - uprev + - dt * (a1001 * k[1] + a1004 * k[4] + a1005 * k[5] + a1006 * k[6] + - a1007 * k[7] + a1008 * k[8] + a1009 * k[9]), - p, - t + c10 * dt) - k[11] = f( - uprev + - dt * (a1101 * k[1] + a1104 * k[4] + a1105 * k[5] + a1106 * k[6] + - a1107 * k[7] + a1108 * k[8] + a1109 * k[9] + a1110 * k[10]), - p, - t + c11 * dt) - k[12] = f( - uprev + - dt * (a1201 * k[1] + a1204 * k[4] + a1205 * k[5] + a1206 * k[6] + - a1207 * k[7] + a1208 * k[8] + a1209 * k[9] + a1210 * k[10] + - a1211 * k[11]), - p, - t + c12 * dt) - integrator.stats.nf += 3 - end - - integrator.u = u -end - -function initialize!(integrator, cache::Vern6Cache) - alg = unwrap_alg(integrator, false) - alg.lazy ? (integrator.kshortsize = 9) : (integrator.kshortsize = 12) - integrator.fsalfirst = cache.k1 - integrator.fsallast = cache.k9 - @unpack k = integrator - resize!(k, integrator.kshortsize) - k[1] = cache.k1 - k[2] = cache.k2 - k[3] = cache.k3 - k[4] = cache.k4 - k[5] = cache.k5 - k[6] = cache.k6 - k[7] = cache.k7 - k[8] = cache.k8 - k[9] = cache.k9 # Set the pointers - - if !alg.lazy - k[10] = similar(cache.k1) - k[11] = similar(cache.k1) - k[12] = similar(cache.k1) - end - - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 -end - -@muladd function perform_step!(integrator, cache::Vern6Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - uidx = eachindex(integrator.uprev) - @unpack c1, c2, c3, c4, c5, c6, a21, a31, a32, a41, a43, a51, a53, a54, a61, a63, a64, a65, a71, a73, a74, a75, a76, a81, a83, a84, a85, a86, a87, a91, a94, a95, a96, a97, a98, btilde1, btilde4, btilde5, btilde6, btilde7, btilde8, btilde9 = cache.tab - @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, utilde, tmp, rtmp, atmp, stage_limiter!, step_limiter!, thread = cache - a = dt * a21 - @.. broadcast=false thread=thread tmp=uprev + a * k1 - stage_limiter!(tmp, integrator, p, t + c1 * dt) - f(k2, tmp, p, t + c1 * dt) - @.. broadcast=false thread=thread tmp=uprev + dt * (a31 * k1 + a32 * k2) - stage_limiter!(tmp, integrator, p, t + c2 * dt) - f(k3, tmp, p, t + c2 * dt) - @.. broadcast=false thread=thread tmp=uprev + dt * (a41 * k1 + a43 * k3) - stage_limiter!(tmp, integrator, p, t + c3 * dt) - f(k4, tmp, p, t + c3 * dt) - @.. broadcast=false thread=thread tmp=uprev + dt * (a51 * k1 + a53 * k3 + a54 * k4) - stage_limiter!(tmp, integrator, p, t + c4 * dt) - f(k5, tmp, p, t + c4 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a61 * k1 + a63 * k3 + a64 * k4 + a65 * k5) - stage_limiter!(tmp, integrator, p, t + c5 * dt) - f(k6, tmp, p, t + c5 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a71 * k1 + a73 * k3 + a74 * k4 + a75 * k5 + - a76 * k6) - stage_limiter!(tmp, integrator, p, t + c6 * dt) - f(k7, tmp, p, t + c6 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a81 * k1 + a83 * k3 + a84 * k4 + a85 * k5 + - a86 * k6 + - a87 * k7) - stage_limiter!(tmp, integrator, p, t + dt) - f(k8, tmp, p, t + dt) - @.. broadcast=false thread=thread u=uprev + - dt * - (a91 * k1 + a94 * k4 + a95 * k5 + a96 * k6 + - a97 * k7 + a98 * k8) - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - f(k9, u, p, t + dt) - integrator.stats.nf += 8 - if integrator.alg isa CompositeAlgorithm - g9 = u - g8 = tmp - @.. broadcast=false thread=thread rtmp=k9 - k8 - ϱu = integrator.opts.internalnorm(rtmp, t) - @.. broadcast=false thread=thread utilde=g9 - g8 - ϱd = integrator.opts.internalnorm(utilde, t) - integrator.eigen_est = ϱu / ϱd - end - if integrator.opts.adaptive - @.. broadcast=false thread=thread utilde=dt * (btilde1 * k1 + btilde4 * k4 + - btilde5 * k5 + - btilde6 * k6 + btilde7 * k7 + - btilde8 * k8 + - btilde9 * k9) - calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t, - thread) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - - alg = unwrap_alg(integrator, false) - if !alg.lazy && (integrator.opts.adaptive == false || - accept_step_controller(integrator, integrator.opts.controller)) - k = integrator.k - @unpack c10, a1001, a1004, a1005, a1006, a1007, a1008, a1009, c11, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, c12, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211 = cache.tab.extra - @unpack tmp = cache - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a1001 * k[1] + a1004 * k[4] + a1005 * k[5] + - a1006 * k[6] + - a1007 * k[7] + a1008 * k[8] + a1009 * k[9]) - f(k[10], tmp, p, t + c10 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a1101 * k[1] + a1104 * k[4] + a1105 * k[5] + - a1106 * k[6] + - a1107 * k[7] + a1108 * k[8] + a1109 * k[9] + - a1110 * k[10]) - f(k[11], tmp, p, t + c11 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a1201 * k[1] + a1204 * k[4] + a1205 * k[5] + - a1206 * k[6] + - a1207 * k[7] + a1208 * k[8] + a1209 * k[9] + - a1210 * k[10] + a1211 * k[11]) - integrator.stats.nf += 3 - f(k[12], tmp, p, t + c12 * dt) - end - return nothing -end - -function initialize!(integrator, cache::Vern7ConstantCache) - alg = unwrap_alg(integrator, false) - alg.lazy ? (integrator.kshortsize = 10) : (integrator.kshortsize = 16) - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - @inbounds for i in eachindex(integrator.k) - integrator.k[i] = zero(integrator.uprev) ./ oneunit(integrator.t) - end -end - -@muladd function perform_step!(integrator, cache::Vern7ConstantCache, repeat_step = false) - @unpack t, dt, uprev, u, k, f, p = integrator - T = constvalue(recursive_unitless_bottom_eltype(u)) - T2 = constvalue(typeof(one(t))) - @OnDemandTableauExtract Vern7Tableau T T2 - k1 = f(uprev, p, t) - a = dt * a021 - k2 = f(uprev + a * k1, p, t + c2 * dt) - k3 = f(uprev + dt * (a031 * k1 + a032 * k2), p, t + c3 * dt) - k4 = f(uprev + dt * (a041 * k1 + a043 * k3), p, t + c4 * dt) - k5 = f(uprev + dt * (a051 * k1 + a053 * k3 + a054 * k4), p, t + c5 * dt) - k6 = f(uprev + dt * (a061 * k1 + a063 * k3 + a064 * k4 + a065 * k5), p, t + c6 * dt) - k7 = f(uprev + dt * (a071 * k1 + a073 * k3 + a074 * k4 + a075 * k5 + a076 * k6), p, - t + c7 * dt) - k8 = f( - uprev + - dt * (a081 * k1 + a083 * k3 + a084 * k4 + a085 * k5 + a086 * k6 + a087 * k7), - p, - t + c8 * dt) - g9 = uprev + - dt * - (a091 * k1 + a093 * k3 + a094 * k4 + a095 * k5 + a096 * k6 + a097 * k7 + a098 * k8) - g10 = uprev + - dt * (a101 * k1 + a103 * k3 + a104 * k4 + a105 * k5 + a106 * k6 + a107 * k7) - k9 = f(g9, p, t + dt) - k10 = f(g10, p, t + dt) - integrator.stats.nf += 10 - u = uprev + dt * (b1 * k1 + b4 * k4 + b5 * k5 + b6 * k6 + b7 * k7 + b8 * k8 + b9 * k9) - if integrator.alg isa CompositeAlgorithm - ϱu = integrator.opts.internalnorm(k10 - k9, t) - ϱd = integrator.opts.internalnorm(g10 - g9, t) - integrator.eigen_est = ϱu / ϱd - end - if integrator.opts.adaptive - utilde = dt * - (btilde1 * k1 + btilde4 * k4 + btilde5 * k5 + btilde6 * k6 + btilde7 * k7 + - btilde8 * k8 + btilde9 * k9 + btilde10 * k10) - atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.k[1] = k1 - integrator.k[2] = k2 - integrator.k[3] = k3 - integrator.k[4] = k4 - integrator.k[5] = k5 - integrator.k[6] = k6 - integrator.k[7] = k7 - integrator.k[8] = k8 - integrator.k[9] = k9 - integrator.k[10] = k10 - integrator.u = u - - alg = unwrap_alg(integrator, false) - if !alg.lazy && (integrator.opts.adaptive == false || - accept_step_controller(integrator, integrator.opts.controller)) - k = integrator.k - @OnDemandTableauExtract Vern7ExtraStages T T2 - k[11] = f( - uprev + - dt * (a1101 * k[1] + a1104 * k[4] + a1105 * k[5] + a1106 * k[6] + - a1107 * k[7] + a1108 * k[8] + a1109 * k[9]), - p, - t + c11 * dt) - k[12] = f( - uprev + - dt * (a1201 * k[1] + a1204 * k[4] + a1205 * k[5] + a1206 * k[6] + - a1207 * k[7] + a1208 * k[8] + a1209 * k[9] + a1211 * k[11]), - p, - t + c12 * dt) - k[13] = f( - uprev + - dt * (a1301 * k[1] + a1304 * k[4] + a1305 * k[5] + a1306 * k[6] + - a1307 * k[7] + a1308 * k[8] + a1309 * k[9] + a1311 * k[11] + - a1312 * k[12]), - p, - t + c13 * dt) - k[14] = f( - uprev + - dt * (a1401 * k[1] + a1404 * k[4] + a1405 * k[5] + a1406 * k[6] + - a1407 * k[7] + a1408 * k[8] + a1409 * k[9] + a1411 * k[11] + - a1412 * k[12] + a1413 * k[13]), - p, - t + c14 * dt) - k[15] = f( - uprev + - dt * (a1501 * k[1] + a1504 * k[4] + a1505 * k[5] + a1506 * k[6] + - a1507 * k[7] + a1508 * k[8] + a1509 * k[9] + a1511 * k[11] + - a1512 * k[12] + a1513 * k[13]), - p, - t + c15 * dt) - k[16] = f( - uprev + - dt * (a1601 * k[1] + a1604 * k[4] + a1605 * k[5] + a1606 * k[6] + - a1607 * k[7] + a1608 * k[8] + a1609 * k[9] + a1611 * k[11] + - a1612 * k[12] + a1613 * k[13]), - p, - t + c16 * dt) - integrator.stats.nf += 6 - end -end - -function initialize!(integrator, cache::Vern7Cache) - @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10 = cache - @unpack k = integrator - alg = unwrap_alg(integrator, false) - alg.lazy ? (integrator.kshortsize = 10) : (integrator.kshortsize = 16) - resize!(k, integrator.kshortsize) - k[1] = k1 - k[2] = k2 - k[3] = k3 - k[4] = k4 - k[5] = k5 - k[6] = k6 - k[7] = k7 - k[8] = k8 - k[9] = k9 - k[10] = k10 # Setup pointers - - if !alg.lazy - k[11] = similar(cache.k1) - k[12] = similar(cache.k1) - k[13] = similar(cache.k1) - k[14] = similar(cache.k1) - k[15] = similar(cache.k1) - k[16] = similar(cache.k1) - end -end - -@muladd function perform_step!(integrator, cache::Vern7Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - T = constvalue(recursive_unitless_bottom_eltype(u)) - T2 = constvalue(typeof(one(t))) - @OnDemandTableauExtract Vern7Tableau T T2 - @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, utilde, tmp, rtmp, atmp, stage_limiter!, step_limiter!, thread = cache - f(k1, uprev, p, t) - a = dt * a021 - @.. broadcast=false thread=thread tmp=uprev + a * k1 - stage_limiter!(tmp, integrator, p, t + c2 * dt) - f(k2, tmp, p, t + c2 * dt) - @.. broadcast=false thread=thread tmp=uprev + dt * (a031 * k1 + a032 * k2) - stage_limiter!(tmp, integrator, p, t + c3 * dt) - f(k3, tmp, p, t + c3 * dt) - @.. broadcast=false thread=thread tmp=uprev + dt * (a041 * k1 + a043 * k3) - stage_limiter!(tmp, integrator, p, t + c4 * dt) - f(k4, tmp, p, t + c4 * dt) - @.. broadcast=false thread=thread tmp=uprev + dt * (a051 * k1 + a053 * k3 + a054 * k4) - stage_limiter!(tmp, integrator, p, t + c5 * dt) - f(k5, tmp, p, t + c5 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a061 * k1 + a063 * k3 + a064 * k4 + a065 * k5) - stage_limiter!(tmp, integrator, p, t + c6 * dt) - f(k6, tmp, p, t + c6 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a071 * k1 + a073 * k3 + a074 * k4 + a075 * k5 + - a076 * k6) - stage_limiter!(tmp, integrator, p, t + c7 * dt) - f(k7, tmp, p, t + c7 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a081 * k1 + a083 * k3 + a084 * k4 + a085 * k5 + - a086 * k6 + - a087 * k7) - stage_limiter!(tmp, integrator, p, t + c8 * dt) - f(k8, tmp, p, t + c8 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a091 * k1 + a093 * k3 + a094 * k4 + a095 * k5 + - a096 * k6 + - a097 * k7 + a098 * k8) - stage_limiter!(tmp, integrator, p, t + dt) - f(k9, tmp, p, t + dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a101 * k1 + a103 * k3 + a104 * k4 + a105 * k5 + - a106 * k6 + - a107 * k7) - stage_limiter!(tmp, integrator, p, t + dt) - f(k10, tmp, p, t + dt) - @.. broadcast=false thread=thread u=uprev + - dt * - (b1 * k1 + b4 * k4 + b5 * k5 + b6 * k6 + b7 * k7 + - b8 * k8 + - b9 * k9) - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - integrator.stats.nf += 10 - if integrator.alg isa CompositeAlgorithm - g10 = u - g9 = tmp - @.. broadcast=false thread=thread rtmp=k10 - k9 - ϱu = integrator.opts.internalnorm(rtmp, t) - @.. broadcast=false thread=thread utilde=g10 - g9 - ϱd = integrator.opts.internalnorm(utilde, t) - integrator.eigen_est = ϱu / ϱd - end - if integrator.opts.adaptive - @.. broadcast=false thread=thread utilde=dt * (btilde1 * k1 + btilde4 * k4 + - btilde5 * k5 + - btilde6 * k6 + btilde7 * k7 + - btilde8 * k8 + - btilde9 * k9 + btilde10 * k10) - calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t, - thread) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - alg = unwrap_alg(integrator, false) - if !alg.lazy && (integrator.opts.adaptive == false || - accept_step_controller(integrator, integrator.opts.controller)) - k = integrator.k - @unpack tmp = cache - @OnDemandTableauExtract Vern7ExtraStages T T2 - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a1101 * k[1] + a1104 * k[4] + a1105 * k[5] + - a1106 * k[6] + - a1107 * k[7] + a1108 * k[8] + a1109 * k[9]) - f(k[11], tmp, p, t + c11 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a1201 * k[1] + a1204 * k[4] + a1205 * k[5] + - a1206 * k[6] + - a1207 * k[7] + a1208 * k[8] + a1209 * k[9] + - a1211 * k[11]) - f(k[12], tmp, p, t + c12 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a1301 * k[1] + a1304 * k[4] + a1305 * k[5] + - a1306 * k[6] + - a1307 * k[7] + a1308 * k[8] + a1309 * k[9] + - a1311 * k[11] + a1312 * k[12]) - f(k[13], tmp, p, t + c13 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a1401 * k[1] + a1404 * k[4] + a1405 * k[5] + - a1406 * k[6] + - a1407 * k[7] + a1408 * k[8] + a1409 * k[9] + - a1411 * k[11] + a1412 * k[12] + - a1413 * k[13]) - f(k[14], tmp, p, t + c14 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a1501 * k[1] + a1504 * k[4] + a1505 * k[5] + - a1506 * k[6] + - a1507 * k[7] + a1508 * k[8] + a1509 * k[9] + - a1511 * k[11] + a1512 * k[12] + - a1513 * k[13]) - f(k[15], tmp, p, t + c15 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a1601 * k[1] + a1604 * k[4] + a1605 * k[5] + - a1606 * k[6] + - a1607 * k[7] + a1608 * k[8] + a1609 * k[9] + - a1611 * k[11] + a1612 * k[12] + - a1613 * k[13]) - f(k[16], tmp, p, t + c16 * dt) - integrator.stats.nf += 6 - end - return nothing -end - -function initialize!(integrator, cache::Vern8ConstantCache) - alg = unwrap_alg(integrator, false) - alg.lazy ? (integrator.kshortsize = 13) : (integrator.kshortsize = 21) - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - @inbounds for i in eachindex(integrator.k) - integrator.k[i] = zero(integrator.uprev) ./ oneunit(integrator.t) - end -end - -@muladd function perform_step!(integrator, cache::Vern8ConstantCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - @unpack c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, a0201, a0301, a0302, a0401, a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, a0704, a0705, a0706, a0801, a0804, a0805, a0806, a0807, a0901, a0904, a0905, a0906, a0907, a0908, a1001, a1004, a1005, a1006, a1007, a1008, a1009, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211, a1301, a1304, a1305, a1306, a1307, a1308, a1309, a1310, b1, b6, b7, b8, b9, b10, b11, b12, btilde1, btilde6, btilde7, btilde8, btilde9, btilde10, btilde11, btilde12, btilde13 = cache.tab - k1 = f(uprev, p, t) - a = dt * a0201 - k2 = f(uprev + a * k1, p, t + c2 * dt) - k3 = f(uprev + dt * (a0301 * k1 + a0302 * k2), p, t + c3 * dt) - k4 = f(uprev + dt * (a0401 * k1 + a0403 * k3), p, t + c4 * dt) - k5 = f(uprev + dt * (a0501 * k1 + a0503 * k3 + a0504 * k4), p, t + c5 * dt) - k6 = f(uprev + dt * (a0601 * k1 + a0604 * k4 + a0605 * k5), p, t + c6 * dt) - k7 = f(uprev + dt * (a0701 * k1 + a0704 * k4 + a0705 * k5 + a0706 * k6), p, t + c7 * dt) - k8 = f( - uprev + dt * (a0801 * k1 + a0804 * k4 + a0805 * k5 + a0806 * k6 + a0807 * k7), p, - t + c8 * dt) - k9 = f( - uprev + - dt * - (a0901 * k1 + a0904 * k4 + a0905 * k5 + a0906 * k6 + a0907 * k7 + a0908 * k8), - p, - t + c9 * dt) - k10 = f( - uprev + - dt * - (a1001 * k1 + a1004 * k4 + a1005 * k5 + a1006 * k6 + a1007 * k7 + a1008 * k8 + - a1009 * k9), - p, - t + c10 * dt) - k11 = f( - uprev + - dt * - (a1101 * k1 + a1104 * k4 + a1105 * k5 + a1106 * k6 + a1107 * k7 + a1108 * k8 + - a1109 * k9 + a1110 * k10), - p, - t + c11 * dt) - g12 = uprev + - dt * - (a1201 * k1 + a1204 * k4 + a1205 * k5 + a1206 * k6 + a1207 * k7 + a1208 * k8 + - a1209 * k9 + a1210 * k10 + a1211 * k11) - g13 = uprev + - dt * - (a1301 * k1 + a1304 * k4 + a1305 * k5 + a1306 * k6 + a1307 * k7 + a1308 * k8 + - a1309 * k9 + a1310 * k10) - k12 = f(g12, p, t + dt) - k13 = f(g13, p, t + dt) - integrator.stats.nf += 13 - u = uprev + - dt * (b1 * k1 + b6 * k6 + b7 * k7 + b8 * k8 + b9 * k9 + b10 * k10 + b11 * k11 + - b12 * k12) - if integrator.alg isa CompositeAlgorithm - ϱu = integrator.opts.internalnorm(k13 - k12, t) - ϱd = integrator.opts.internalnorm(g13 - g12, t) - integrator.eigen_est = ϱu / ϱd - end - if integrator.opts.adaptive - utilde = dt * - (btilde1 * k1 + btilde6 * k6 + btilde7 * k7 + btilde8 * k8 + btilde9 * k9 + - btilde10 * k10 + btilde11 * k11 + btilde12 * k12 + btilde13 * k13) - atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - integrator.k[1] = k1 - integrator.k[2] = k2 - integrator.k[3] = k3 - integrator.k[4] = k4 - integrator.k[5] = k5 - integrator.k[6] = k6 - integrator.k[7] = k7 - integrator.k[8] = k8 - integrator.k[9] = k9 - integrator.k[10] = k10 - integrator.k[11] = k11 - integrator.k[12] = k12 - integrator.k[13] = k13 - integrator.u = u - - alg = unwrap_alg(integrator, false) - if !alg.lazy && (integrator.opts.adaptive == false || - accept_step_controller(integrator, integrator.opts.controller)) - k = integrator.k - @unpack c14, a1401, a1406, a1407, a1408, a1409, a1410, a1411, a1412, c15, a1501, a1506, a1507, a1508, a1509, a1510, a1511, a1512, a1514, c16, a1601, a1606, a1607, a1608, a1609, a1610, a1611, a1612, a1614, a1615, c17, a1701, a1706, a1707, a1708, a1709, a1710, a1711, a1712, a1714, a1715, a1716, c18, a1801, a1806, a1807, a1808, a1809, a1810, a1811, a1812, a1814, a1815, a1816, a1817, c19, a1901, a1906, a1907, a1908, a1909, a1910, a1911, a1912, a1914, a1915, a1916, a1917, c20, a2001, a2006, a2007, a2008, a2009, a2010, a2011, a2012, a2014, a2015, a2016, a2017, c21, a2101, a2106, a2107, a2108, a2109, a2110, a2111, a2112, a2114, a2115, a2116, a2117 = cache.tab.extra - k[14] = f( - uprev + - dt * (a1401 * k[1] + a1406 * k[6] + a1407 * k[7] + a1408 * k[8] + - a1409 * k[9] + a1410 * k[10] + a1411 * k[11] + a1412 * k[12]), - p, - t + c14 * dt) - k[15] = f( - uprev + - dt * (a1501 * k[1] + a1506 * k[6] + a1507 * k[7] + a1508 * k[8] + - a1509 * k[9] + a1510 * k[10] + a1511 * k[11] + a1512 * k[12] + - a1514 * k[14]), - p, - t + c15 * dt) - k[16] = f( - uprev + - dt * (a1601 * k[1] + a1606 * k[6] + a1607 * k[7] + a1608 * k[8] + - a1609 * k[9] + a1610 * k[10] + a1611 * k[11] + a1612 * k[12] + - a1614 * k[14] + a1615 * k[15]), - p, - t + c16 * dt) - k[17] = f( - uprev + - dt * (a1701 * k[1] + a1706 * k[6] + a1707 * k[7] + a1708 * k[8] + - a1709 * k[9] + a1710 * k[10] + a1711 * k[11] + a1712 * k[12] + - a1714 * k[14] + a1715 * k[15] + a1716 * k[16]), - p, - t + c17 * dt) - k[18] = f( - uprev + - dt * (a1801 * k[1] + a1806 * k[6] + a1807 * k[7] + a1808 * k[8] + - a1809 * k[9] + a1810 * k[10] + a1811 * k[11] + a1812 * k[12] + - a1814 * k[14] + a1815 * k[15] + a1816 * k[16] + a1817 * k[17]), - p, - t + c18 * dt) - k[19] = f( - uprev + - dt * (a1901 * k[1] + a1906 * k[6] + a1907 * k[7] + a1908 * k[8] + - a1909 * k[9] + a1910 * k[10] + a1911 * k[11] + a1912 * k[12] + - a1914 * k[14] + a1915 * k[15] + a1916 * k[16] + a1917 * k[17]), - p, - t + c19 * dt) - k[20] = f( - uprev + - dt * (a2001 * k[1] + a2006 * k[6] + a2007 * k[7] + a2008 * k[8] + - a2009 * k[9] + a2010 * k[10] + a2011 * k[11] + a2012 * k[12] + - a2014 * k[14] + a2015 * k[15] + a2016 * k[16] + a2017 * k[17]), - p, - t + c20 * dt) - k[21] = f( - uprev + - dt * (a2101 * k[1] + a2106 * k[6] + a2107 * k[7] + a2108 * k[8] + - a2109 * k[9] + a2110 * k[10] + a2111 * k[11] + a2112 * k[12] + - a2114 * k[14] + a2115 * k[15] + a2116 * k[16] + a2117 * k[17]), - p, - t + c21 * dt) - integrator.stats.nf += 8 - end -end - -function initialize!(integrator, cache::Vern8Cache) - @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13 = cache - @unpack k = integrator - alg = unwrap_alg(integrator, false) - alg.lazy ? (integrator.kshortsize = 13) : (integrator.kshortsize = 21) - resize!(k, integrator.kshortsize) - k[1] = k1 - k[2] = k2 - k[3] = k3 - k[4] = k4 - k[5] = k5 - k[6] = k6 - k[7] = k7 - k[8] = k8 - k[9] = k9 - k[10] = k10 - k[11] = k11 - k[12] = k12 - k[13] = k13 # Setup pointers - - if !alg.lazy - for i in 14:21 - k[i] = similar(cache.k1) - end - end -end - -@muladd function perform_step!(integrator, cache::Vern8Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - uidx = eachindex(integrator.uprev) - @unpack c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, a0201, a0301, a0302, a0401, a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, a0704, a0705, a0706, a0801, a0804, a0805, a0806, a0807, a0901, a0904, a0905, a0906, a0907, a0908, a1001, a1004, a1005, a1006, a1007, a1008, a1009, a1101, a1104, a1105, a1106, a1107, a1108, a1109, a1110, a1201, a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211, a1301, a1304, a1305, a1306, a1307, a1308, a1309, a1310, b1, b6, b7, b8, b9, b10, b11, b12, btilde1, btilde6, btilde7, btilde8, btilde9, btilde10, btilde11, btilde12, btilde13 = cache.tab - @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, utilde, tmp, rtmp, atmp, stage_limiter!, step_limiter!, thread = cache - f(k1, uprev, p, t) - a = dt * a0201 - @.. broadcast=false thread=thread tmp=uprev + a * k1 - stage_limiter!(tmp, integrator, p, t + c2 * dt) - f(k2, tmp, p, t + c2 * dt) - @.. broadcast=false thread=thread tmp=uprev + dt * (a0301 * k1 + a0302 * k2) - stage_limiter!(tmp, integrator, p, t + c3 * dt) - f(k3, tmp, p, t + c3 * dt) - @.. broadcast=false thread=thread tmp=uprev + dt * (a0401 * k1 + a0403 * k3) - stage_limiter!(tmp, integrator, p, t + c4 * dt) - f(k4, tmp, p, t + c4 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a0501 * k1 + a0503 * k3 + a0504 * k4) - stage_limiter!(tmp, integrator, p, t + c5 * dt) - f(k5, tmp, p, t + c5 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a0601 * k1 + a0604 * k4 + a0605 * k5) - stage_limiter!(tmp, integrator, p, t + c6 * dt) - f(k6, tmp, p, t + c6 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a0701 * k1 + a0704 * k4 + a0705 * k5 + - a0706 * k6) - stage_limiter!(tmp, integrator, p, t + c7 * dt) - f(k7, tmp, p, t + c7 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a0801 * k1 + a0804 * k4 + a0805 * k5 + - a0806 * k6 + a0807 * k7) - stage_limiter!(tmp, integrator, p, t + c8 * dt) - f(k8, tmp, p, t + c8 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a0901 * k1 + a0904 * k4 + a0905 * k5 + - a0906 * k6 + - a0907 * k7 + a0908 * k8) - stage_limiter!(tmp, integrator, p, t + c9 * dt) - f(k9, tmp, p, t + c9 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a1001 * k1 + a1004 * k4 + a1005 * k5 + - a1006 * k6 + - a1007 * k7 + a1008 * k8 + a1009 * k9) - stage_limiter!(tmp, integrator, p, t + c10 * dt) - f(k10, tmp, p, t + c10 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a1101 * k1 + a1104 * k4 + a1105 * k5 + - a1106 * k6 + - a1107 * k7 + a1108 * k8 + a1109 * k9 + - a1110 * k10) - stage_limiter!(tmp, integrator, p, t + c11 * dt) - f(k11, tmp, p, t + c11 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a1201 * k1 + a1204 * k4 + a1205 * k5 + - a1206 * k6 + - a1207 * k7 + a1208 * k8 + a1209 * k9 + - a1210 * k10 + - a1211 * k11) - stage_limiter!(tmp, integrator, p, t + dt) - f(k12, tmp, p, t + dt) - @.. broadcast=false thread=thread u=uprev + - dt * - (a1301 * k1 + a1304 * k4 + a1305 * k5 + a1306 * k6 + - a1307 * k7 + - a1308 * k8 + a1309 * k9 + a1310 * k10) - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - f(k13, u, p, t + dt) - integrator.stats.nf += 13 - if integrator.alg isa CompositeAlgorithm - g13 = u - g12 = tmp - @.. broadcast=false thread=thread rtmp=k13 - k12 - ϱu = integrator.opts.internalnorm(rtmp, t) - @.. broadcast=false thread=thread utilde=g13 - g12 - ϱd = integrator.opts.internalnorm(utilde, t) - integrator.eigen_est = ϱu / ϱd - end - @.. broadcast=false thread=thread u=uprev + - dt * - (b1 * k1 + b6 * k6 + b7 * k7 + b8 * k8 + b9 * k9 + - b10 * k10 + - b11 * k11 + b12 * k12) - if integrator.opts.adaptive - @.. broadcast=false thread=thread utilde=dt * (btilde1 * k1 + btilde6 * k6 + - btilde7 * k7 + - btilde8 * k8 + btilde9 * k9 + - btilde10 * k10 + - btilde11 * k11 + btilde12 * k12 + - btilde13 * k13) - calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t, - thread) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - - alg = unwrap_alg(integrator, false) - if !alg.lazy && (integrator.opts.adaptive == false || - accept_step_controller(integrator, integrator.opts.controller)) - k = integrator.k - @unpack c14, a1401, a1406, a1407, a1408, a1409, a1410, a1411, a1412, c15, a1501, a1506, a1507, a1508, a1509, a1510, a1511, a1512, a1514, c16, a1601, a1606, a1607, a1608, a1609, a1610, a1611, a1612, a1614, a1615, c17, a1701, a1706, a1707, a1708, a1709, a1710, a1711, a1712, a1714, a1715, a1716, c18, a1801, a1806, a1807, a1808, a1809, a1810, a1811, a1812, a1814, a1815, a1816, a1817, c19, a1901, a1906, a1907, a1908, a1909, a1910, a1911, a1912, a1914, a1915, a1916, a1917, c20, a2001, a2006, a2007, a2008, a2009, a2010, a2011, a2012, a2014, a2015, a2016, a2017, c21, a2101, a2106, a2107, a2108, a2109, a2110, a2111, a2112, a2114, a2115, a2116, a2117 = cache.tab.extra - @unpack tmp = cache - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a1401 * k[1] + a1406 * k[6] + a1407 * k[7] + - a1408 * k[8] + - a1409 * k[9] + a1410 * k[10] + - a1411 * k[11] + - a1412 * k[12]) - f(k[14], tmp, p, t + c14 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a1501 * k[1] + a1506 * k[6] + a1507 * k[7] + - a1508 * k[8] + - a1509 * k[9] + a1510 * k[10] + - a1511 * k[11] + - a1512 * k[12] + a1514 * k[14]) - f(k[15], tmp, p, t + c15 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a1601 * k[1] + a1606 * k[6] + a1607 * k[7] + - a1608 * k[8] + - a1609 * k[9] + a1610 * k[10] + - a1611 * k[11] + - a1612 * k[12] + a1614 * k[14] + - a1615 * k[15]) - f(k[16], tmp, p, t + c16 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a1701 * k[1] + a1706 * k[6] + a1707 * k[7] + - a1708 * k[8] + - a1709 * k[9] + a1710 * k[10] + - a1711 * k[11] + - a1712 * k[12] + a1714 * k[14] + - a1715 * k[15] + - a1716 * k[16]) - f(k[17], tmp, p, t + c17 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a1801 * k[1] + a1806 * k[6] + a1807 * k[7] + - a1808 * k[8] + - a1809 * k[9] + a1810 * k[10] + - a1811 * k[11] + - a1812 * k[12] + a1814 * k[14] + - a1815 * k[15] + - a1816 * k[16] + a1817 * k[17]) - f(k[18], tmp, p, t + c18 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a1901 * k[1] + a1906 * k[6] + a1907 * k[7] + - a1908 * k[8] + - a1909 * k[9] + a1910 * k[10] + - a1911 * k[11] + - a1912 * k[12] + a1914 * k[14] + - a1915 * k[15] + - a1916 * k[16] + a1917 * k[17]) - f(k[19], tmp, p, t + c19 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a2001 * k[1] + a2006 * k[6] + a2007 * k[7] + - a2008 * k[8] + - a2009 * k[9] + a2010 * k[10] + - a2011 * k[11] + - a2012 * k[12] + a2014 * k[14] + - a2015 * k[15] + - a2016 * k[16] + a2017 * k[17]) - f(k[20], tmp, p, t + c20 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a2101 * k[1] + a2106 * k[6] + a2107 * k[7] + - a2108 * k[8] + - a2109 * k[9] + a2110 * k[10] + - a2111 * k[11] + - a2112 * k[12] + a2114 * k[14] + - a2115 * k[15] + - a2116 * k[16] + a2117 * k[17]) - integrator.stats.nf += 8 - f(k[21], tmp, p, t + c21 * dt) - end - return nothing -end - -function initialize!(integrator, cache::Vern9ConstantCache) - alg = unwrap_alg(integrator, false) - alg.lazy ? (integrator.kshortsize = 10) : (integrator.kshortsize = 20) - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - - # Avoid undefined entries if k is an array of arrays - @inbounds for i in eachindex(integrator.k) - integrator.k[i] = zero(integrator.uprev) ./ oneunit(integrator.t) - end -end - -@muladd function perform_step!(integrator, cache::Vern9ConstantCache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - T = constvalue(recursive_unitless_bottom_eltype(u)) - T2 = constvalue(typeof(one(t))) - @OnDemandTableauExtract Vern9Tableau T T2 - k1 = f(uprev, p, t) - a = dt * a0201 - k2 = f(uprev + a * k1, p, t + c1 * dt) - k3 = f(uprev + dt * (a0301 * k1 + a0302 * k2), p, t + c2 * dt) - k4 = f(uprev + dt * (a0401 * k1 + a0403 * k3), p, t + c3 * dt) - k5 = f(uprev + dt * (a0501 * k1 + a0503 * k3 + a0504 * k4), p, t + c4 * dt) - k6 = f(uprev + dt * (a0601 * k1 + a0604 * k4 + a0605 * k5), p, t + c5 * dt) - k7 = f(uprev + dt * (a0701 * k1 + a0704 * k4 + a0705 * k5 + a0706 * k6), p, t + c6 * dt) - k8 = f(uprev + dt * (a0801 * k1 + a0806 * k6 + a0807 * k7), p, t + c7 * dt) - k9 = f(uprev + dt * (a0901 * k1 + a0906 * k6 + a0907 * k7 + a0908 * k8), p, t + c8 * dt) - k10 = f(uprev + dt * (a1001 * k1 + a1006 * k6 + a1007 * k7 + a1008 * k8 + a1009 * k9), - p, t + c9 * dt) - k11 = f( - uprev + - dt * - (a1101 * k1 + a1106 * k6 + a1107 * k7 + a1108 * k8 + a1109 * k9 + a1110 * k10), - p, t + c10 * dt) - k12 = f( - uprev + - dt * - (a1201 * k1 + a1206 * k6 + a1207 * k7 + a1208 * k8 + a1209 * k9 + a1210 * k10 + - a1211 * k11), - p, - t + c11 * dt) - k13 = f( - uprev + - dt * - (a1301 * k1 + a1306 * k6 + a1307 * k7 + a1308 * k8 + a1309 * k9 + a1310 * k10 + - a1311 * k11 + a1312 * k12), - p, - t + c12 * dt) - k14 = f( - uprev + - dt * - (a1401 * k1 + a1406 * k6 + a1407 * k7 + a1408 * k8 + a1409 * k9 + a1410 * k10 + - a1411 * k11 + a1412 * k12 + a1413 * k13), - p, - t + c13 * dt) - g15 = uprev + - dt * - (a1501 * k1 + a1506 * k6 + a1507 * k7 + a1508 * k8 + a1509 * k9 + a1510 * k10 + - a1511 * k11 + a1512 * k12 + a1513 * k13 + a1514 * k14) - g16 = uprev + - dt * - (a1601 * k1 + a1606 * k6 + a1607 * k7 + a1608 * k8 + a1609 * k9 + a1610 * k10 + - a1611 * k11 + a1612 * k12 + a1613 * k13) - k15 = f(g15, p, t + dt) - k16 = f(g16, p, t + dt) - integrator.stats.nf += 16 - u = uprev + - dt * (b1 * k1 + b8 * k8 + b9 * k9 + b10 * k10 + b11 * k11 + b12 * k12 + b13 * k13 + - b14 * k14 + b15 * k15) - if integrator.alg isa CompositeAlgorithm - ϱu = integrator.opts.internalnorm(k16 - k15, t) - ϱd = integrator.opts.internalnorm(g16 - g15, t) - integrator.eigen_est = ϱu / ϱd - end - if integrator.opts.adaptive - utilde = dt * (btilde1 * k1 + btilde8 * k8 + btilde9 * k9 + btilde10 * k10 + - btilde11 * k11 + btilde12 * k12 + btilde13 * k13 + btilde14 * k14 + - btilde15 * k15 + btilde16 * k16) - atmp = calculate_residuals(utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - # k2, k3,k4,k5,k6,k7 are not used in the code (not even in interpolations), we dont need their pointers. - # So we mapped k[2] (from integrator) with k8 (from cache), k[3] with k9 and so on. - integrator.k[1] = k1 - integrator.k[2] = k8 - integrator.k[3] = k9 - integrator.k[4] = k10 - integrator.k[5] = k11 - integrator.k[6] = k12 - integrator.k[7] = k13 - integrator.k[8] = k14 - integrator.k[9] = k15 - integrator.k[10] = k16 - integrator.u = u - - alg = unwrap_alg(integrator, false) - if !alg.lazy && (integrator.opts.adaptive == false || - accept_step_controller(integrator, integrator.opts.controller)) - k = integrator.k - @OnDemandTableauExtract Vern9ExtraStages T T2 - k[11] = f( - uprev + - dt * (a1701 * k[1] + a1708 * k[2] + a1709 * k[3] + a1710 * k[4] + - a1711 * k[5] + a1712 * k[6] + a1713 * k[7] + a1714 * k[8] + - a1715 * k[9]), - p, t + c17 * dt) - k[12] = f( - uprev + - dt * (a1801 * k[1] + a1808 * k[2] + a1809 * k[3] + a1810 * k[4] + - a1811 * k[5] + a1812 * k[6] + a1813 * k[7] + a1814 * k[8] + - a1815 * k[9] + a1817 * k[11]), - p, - t + c18 * dt) - k[13] = f( - uprev + - dt * (a1901 * k[1] + a1908 * k[2] + a1909 * k[3] + a1910 * k[4] + - a1911 * k[5] + a1912 * k[6] + a1913 * k[7] + a1914 * k[8] + - a1915 * k[9] + a1917 * k[11] + a1918 * k[12]), - p, - t + c19 * dt) - k[14] = f( - uprev + - dt * (a2001 * k[1] + a2008 * k[2] + a2009 * k[3] + a2010 * k[4] + - a2011 * k[5] + a2012 * k[6] + a2013 * k[7] + a2014 * k[8] + - a2015 * k[9] + a2017 * k[11] + a2018 * k[12] + a2019 * k[13]), - p, - t + c20 * dt) - k[15] = f( - uprev + - dt * (a2101 * k[1] + a2108 * k[2] + a2109 * k[3] + a2110 * k[4] + - a2111 * k[5] + a2112 * k[6] + a2113 * k[7] + a2114 * k[8] + - a2115 * k[9] + a2117 * k[11] + a2118 * k[12] + a2119 * k[13] + - a2120 * k[14]), - p, - t + c21 * dt) - k[16] = f( - uprev + - dt * (a2201 * k[1] + a2208 * k[2] + a2209 * k[3] + a2210 * k[4] + - a2211 * k[5] + a2212 * k[6] + a2213 * k[7] + a2214 * k[8] + - a2215 * k[9] + a2217 * k[11] + a2218 * k[12] + a2219 * k[13] + - a2220 * k[14] + a2221 * k[15]), - p, - t + c22 * dt) - k[17] = f( - uprev + - dt * (a2301 * k[1] + a2308 * k[2] + a2309 * k[3] + a2310 * k[4] + - a2311 * k[5] + a2312 * k[6] + a2313 * k[7] + a2314 * k[8] + - a2315 * k[9] + a2317 * k[11] + a2318 * k[12] + a2319 * k[13] + - a2320 * k[14] + a2321 * k[15]), - p, - t + c23 * dt) - k[18] = f( - uprev + - dt * (a2401 * k[1] + a2408 * k[2] + a2409 * k[3] + a2410 * k[4] + - a2411 * k[5] + a2412 * k[6] + a2413 * k[7] + a2414 * k[8] + - a2415 * k[9] + a2417 * k[11] + a2418 * k[12] + a2419 * k[13] + - a2420 * k[14] + a2421 * k[15]), - p, - t + c24 * dt) - k[19] = f( - uprev + - dt * (a2501 * k[1] + a2508 * k[2] + a2509 * k[3] + a2510 * k[4] + - a2511 * k[5] + a2512 * k[6] + a2513 * k[7] + a2514 * k[8] + - a2515 * k[9] + a2517 * k[11] + a2518 * k[12] + a2519 * k[13] + - a2520 * k[14] + a2521 * k[15]), - p, - t + c25 * dt) - k[20] = f( - uprev + - dt * (a2601 * k[1] + a2608 * k[2] + a2609 * k[3] + a2610 * k[4] + - a2611 * k[5] + a2612 * k[6] + a2613 * k[7] + a2614 * k[8] + - a2615 * k[9] + a2617 * k[11] + a2618 * k[12] + a2619 * k[13] + - a2620 * k[14] + a2621 * k[15]), - p, - t + c26 * dt) - integrator.stats.nf += 10 - end -end - -function initialize!(integrator, cache::Vern9Cache) - @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16 = cache - @unpack k = integrator - alg = unwrap_alg(integrator, false) - alg.lazy ? (integrator.kshortsize = 10) : (integrator.kshortsize = 20) - resize!(k, integrator.kshortsize) - # k2, k3,k4,k5,k6,k7 are not used in the code (not even in interpolations), we dont need their pointers. - # So we mapped k[2] (from integrator) with k8 (from cache), k[3] with k9 and so on. - k[1] = k1 - k[2] = k8 - k[3] = k9 - k[4] = k10 - k[5] = k11 - k[6] = k12 - k[7] = k13 - k[8] = k14 - k[9] = k15 - k[10] = k16 # Setup pointers - - if !alg.lazy - for i in 11:20 - k[i] = similar(cache.k1) - end - end -end - -@muladd function perform_step!(integrator, cache::Vern9Cache, repeat_step = false) - @unpack t, dt, uprev, u, f, p = integrator - uidx = eachindex(integrator.uprev) - T = constvalue(recursive_unitless_bottom_eltype(u)) - T2 = constvalue(typeof(one(t))) - @OnDemandTableauExtract Vern9Tableau T T2 - @unpack k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, utilde, tmp, rtmp, atmp, stage_limiter!, step_limiter!, thread = cache - f(k1, uprev, p, t) - a = dt * a0201 - @.. broadcast=false thread=thread tmp=uprev + a * k1 - stage_limiter!(tmp, integrator, p, t + c1 * dt) - f(k2, tmp, p, t + c1 * dt) - @.. broadcast=false thread=thread tmp=uprev + dt * (a0301 * k1 + a0302 * k2) - stage_limiter!(tmp, integrator, p, t + c2 * dt) - f(k3, tmp, p, t + c2 * dt) - @.. broadcast=false thread=thread tmp=uprev + dt * (a0401 * k1 + a0403 * k3) - stage_limiter!(tmp, integrator, p, t + c3 * dt) - f(k4, tmp, p, t + c3 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a0501 * k1 + a0503 * k3 + a0504 * k4) - stage_limiter!(tmp, integrator, p, t + c4 * dt) - f(k5, tmp, p, t + c4 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a0601 * k1 + a0604 * k4 + a0605 * k5) - stage_limiter!(tmp, integrator, p, t + c5 * dt) - f(k6, tmp, p, t + c5 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a0701 * k1 + a0704 * k4 + a0705 * k5 + - a0706 * k6) - stage_limiter!(tmp, integrator, p, t + c6 * dt) - f(k7, tmp, p, t + c6 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a0801 * k1 + a0806 * k6 + a0807 * k7) - stage_limiter!(tmp, integrator, p, t + c7 * dt) - f(k8, tmp, p, t + c7 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a0901 * k1 + a0906 * k6 + a0907 * k7 + - a0908 * k8) - stage_limiter!(tmp, integrator, p, t + c8 * dt) - f(k9, tmp, p, t + c8 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a1001 * k1 + a1006 * k6 + a1007 * k7 + - a1008 * k8 + a1009 * k9) - stage_limiter!(tmp, integrator, p, t + c9 * dt) - f(k10, tmp, p, t + c9 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a1101 * k1 + a1106 * k6 + a1107 * k7 + - a1108 * k8 + - a1109 * k9 + a1110 * k10) - stage_limiter!(tmp, integrator, p, t + c10 * dt) - f(k11, tmp, p, t + c10 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a1201 * k1 + a1206 * k6 + a1207 * k7 + - a1208 * k8 + - a1209 * k9 + a1210 * k10 + a1211 * k11) - stage_limiter!(tmp, integrator, p, t + c11 * dt) - f(k12, tmp, p, t + c11 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a1301 * k1 + a1306 * k6 + a1307 * k7 + - a1308 * k8 + - a1309 * k9 + a1310 * k10 + a1311 * k11 + - a1312 * k12) - stage_limiter!(tmp, integrator, p, t + c12 * dt) - f(k13, tmp, p, t + c12 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a1401 * k1 + a1406 * k6 + a1407 * k7 + - a1408 * k8 + - a1409 * k9 + a1410 * k10 + a1411 * k11 + - a1412 * k12 + - a1413 * k13) - stage_limiter!(tmp, integrator, p, t + c13 * dt) - f(k14, tmp, p, t + c13 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * (a1501 * k1 + a1506 * k6 + a1507 * k7 + - a1508 * k8 + - a1509 * k9 + a1510 * k10 + a1511 * k11 + - a1512 * k12 + - a1513 * k13 + a1514 * k14) - stage_limiter!(tmp, integrator, p, t + dt) - f(k15, tmp, p, t + dt) - @.. broadcast=false thread=thread u=uprev + - dt * - (a1601 * k1 + a1606 * k6 + a1607 * k7 + a1608 * k8 + - a1609 * k9 + - a1610 * k10 + a1611 * k11 + a1612 * k12 + - a1613 * k13) - stage_limiter!(u, integrator, p, t + dt) - step_limiter!(u, integrator, p, t + dt) - f(k16, u, p, t + dt) - integrator.stats.nf += 16 - if integrator.alg isa CompositeAlgorithm - g16 = u - g15 = tmp - @.. broadcast=false thread=thread rtmp=k16 - k15 - ϱu = integrator.opts.internalnorm(rtmp, t) - @.. broadcast=false thread=thread utilde=g16 - g15 - ϱd = integrator.opts.internalnorm(utilde, t) - integrator.eigen_est = ϱu / ϱd - end - @.. broadcast=false thread=thread u=uprev + - dt * - (b1 * k1 + b8 * k8 + b9 * k9 + b10 * k10 + - b11 * k11 + b12 * k12 + - b13 * k13 + b14 * k14 + b15 * k15) - if integrator.opts.adaptive - @.. broadcast=false thread=thread utilde=dt * (btilde1 * k1 + btilde8 * k8 + - btilde9 * k9 + - btilde10 * k10 + btilde11 * k11 + - btilde12 * k12 + - btilde13 * k13 + btilde14 * k14 + - btilde15 * k15 + - btilde16 * k16) - calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, - integrator.opts.reltol, integrator.opts.internalnorm, t, - thread) - integrator.EEst = integrator.opts.internalnorm(atmp, t) - end - - alg = unwrap_alg(integrator, false) - if !alg.lazy && (integrator.opts.adaptive == false || - accept_step_controller(integrator, integrator.opts.controller)) - k = integrator.k - @unpack tmp = cache - @OnDemandTableauExtract Vern9ExtraStages T T2 - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a1701 * k[1] + a1708 * k[2] + a1709 * k[3] + - a1710 * k[4] + - a1711 * k[5] + a1712 * k[6] + a1713 * k[7] + - a1714 * k[8] + - a1715 * k[9]) - f(k[11], tmp, p, t + c17 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a1801 * k[1] + a1808 * k[2] + a1809 * k[3] + - a1810 * k[4] + - a1811 * k[5] + a1812 * k[6] + a1813 * k[7] + - a1814 * k[8] + - a1815 * k[9] + a1817 * k[11]) - f(k[12], tmp, p, t + c18 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a1901 * k[1] + a1908 * k[2] + a1909 * k[3] + - a1910 * k[4] + - a1911 * k[5] + a1912 * k[6] + a1913 * k[7] + - a1914 * k[8] + - a1915 * k[9] + a1917 * k[11] + a1918 * k[12]) - f(k[13], tmp, p, t + c19 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a2001 * k[1] + a2008 * k[2] + a2009 * k[3] + - a2010 * k[4] + - a2011 * k[5] + a2012 * k[6] + a2013 * k[7] + - a2014 * k[8] + - a2015 * k[9] + a2017 * k[11] + - a2018 * k[12] + - a2019 * k[13]) - f(k[14], tmp, p, t + c20 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a2101 * k[1] + a2108 * k[2] + a2109 * k[3] + - a2110 * k[4] + - a2111 * k[5] + a2112 * k[6] + a2113 * k[7] + - a2114 * k[8] + - a2115 * k[9] + a2117 * k[11] + - a2118 * k[12] + - a2119 * k[13] + a2120 * k[14]) - f(k[15], tmp, p, t + c21 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a2201 * k[1] + a2208 * k[2] + a2209 * k[3] + - a2210 * k[4] + - a2211 * k[5] + a2212 * k[6] + a2213 * k[7] + - a2214 * k[8] + - a2215 * k[9] + a2217 * k[11] + - a2218 * k[12] + - a2219 * k[13] + a2220 * k[14] + - a2221 * k[15]) - f(k[16], tmp, p, t + c22 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a2301 * k[1] + a2308 * k[2] + a2309 * k[3] + - a2310 * k[4] + - a2311 * k[5] + a2312 * k[6] + a2313 * k[7] + - a2314 * k[8] + - a2315 * k[9] + a2317 * k[11] + - a2318 * k[12] + - a2319 * k[13] + a2320 * k[14] + - a2321 * k[15]) - f(k[17], tmp, p, t + c23 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a2401 * k[1] + a2408 * k[2] + a2409 * k[3] + - a2410 * k[4] + - a2411 * k[5] + a2412 * k[6] + a2413 * k[7] + - a2414 * k[8] + - a2415 * k[9] + a2417 * k[11] + - a2418 * k[12] + - a2419 * k[13] + a2420 * k[14] + - a2421 * k[15]) - f(k[18], tmp, p, t + c24 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a2501 * k[1] + a2508 * k[2] + a2509 * k[3] + - a2510 * k[4] + - a2511 * k[5] + a2512 * k[6] + a2513 * k[7] + - a2514 * k[8] + - a2515 * k[9] + a2517 * k[11] + - a2518 * k[12] + - a2519 * k[13] + a2520 * k[14] + - a2521 * k[15]) - f(k[19], tmp, p, t + c25 * dt) - @.. broadcast=false thread=thread tmp=uprev + - dt * - (a2601 * k[1] + a2608 * k[2] + a2609 * k[3] + - a2610 * k[4] + - a2611 * k[5] + a2612 * k[6] + a2613 * k[7] + - a2614 * k[8] + - a2615 * k[9] + a2617 * k[11] + - a2618 * k[12] + - a2619 * k[13] + a2620 * k[14] + - a2621 * k[15]) - integrator.stats.nf += 10 - f(k[20], tmp, p, t + c26 * dt) - end - return nothing -end From 0baa146d097f56904b6dfa47a2d6662bf779e347 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:59:48 -0400 Subject: [PATCH 20/71] Delete src/rkc_utils.jl --- src/rkc_utils.jl | 276 ----------------------------------------------- 1 file changed, 276 deletions(-) delete mode 100644 src/rkc_utils.jl diff --git a/src/rkc_utils.jl b/src/rkc_utils.jl deleted file mode 100644 index 661197f5a7..0000000000 --- a/src/rkc_utils.jl +++ /dev/null @@ -1,276 +0,0 @@ -# This function calculates the largest eigenvalue -# (absolute value wise) by power iteration. -const RKCAlgs = Union{RKC, IRKC, ESERK4, ESERK5, SERK2} -function maxeig!(integrator, cache::OrdinaryDiffEqConstantCache) - isfirst = integrator.iter == 1 || integrator.u_modified - @unpack t, dt, uprev, u, f, p, fsalfirst = integrator - maxiter = (integrator.alg isa Union{ESERK4, ESERK5, SERK2}) ? 100 : 50 - - safe = (integrator.alg isa RKCAlgs) ? 1.0 : 1.2 - # Initial guess for eigenvector `z` - if isfirst - if integrator.alg isa RKCAlgs - if integrator.alg isa IRKC - z = cache.du₂ - else - z = fsalfirst - end - else - fz = fsalfirst - z = f(fz, p, t) - integrator.stats.nf += 1 - end - else - z = cache.zprev - end - # Perturbation - u_norm = integrator.opts.internalnorm(uprev, t) - z_norm = integrator.opts.internalnorm(z, t) - pert = eps(u_norm) - sqrt_pert = sqrt(pert) - is_u_zero = u_norm == zero(u_norm) - is_z_zero = z_norm == zero(z_norm) - # Normalize `z` such that z-u lie in a circle - if (!is_u_zero && !is_z_zero) - dz_u = u_norm * sqrt_pert - quot = dz_u / z_norm - z = uprev + quot * z - elseif !is_u_zero - dz_u = u_norm * sqrt_pert - z = uprev + uprev * dz_u - elseif !is_z_zero - dz_u = pert - quot = dz_u / z_norm - z *= quot - else - dz_u = pert - z = dz_u * ones(z) - end # endif - # Start power iteration - integrator.eigen_est = 0 - for iter in 1:maxiter - if integrator.alg isa IRKC - fz = f.f2(z, p, t) - integrator.stats.nf2 += 1 - tmp = fz - cache.du₂ - else - fz = f(z, p, t) - integrator.stats.nf += 1 - tmp = fz - fsalfirst - end - Δ = integrator.opts.internalnorm(tmp, t) - eig_prev = integrator.eigen_est - integrator.eigen_est = Δ / dz_u * safe - # Convergence - if integrator.alg isa RKCAlgs # To match the constants given in the paper - if iter >= 2 && - abs(eig_prev - integrator.eigen_est) < - max(integrator.eigen_est, 1.0 / integrator.opts.dtmax) * 0.01 - integrator.eigen_est *= 1.2 - # Store the eigenvector - cache.zprev = z - uprev - return true - end - else - if iter >= 2 && - abs(eig_prev - integrator.eigen_est) < integrator.eigen_est * 0.05 - # Store the eigenvector - cache.zprev = z - uprev - return true - end - end - - # Next `z` - if Δ != zero(Δ) - quot = dz_u / Δ - z = uprev + quot * tmp - else - # An arbitrary change on `z` - nind = length(z) - if (nind != 1) - ind = 1 + iter % nind - # val = (uprev[ind] - (z[ind] - uprev[ind]))*one(eltype(z))*2 - _vec(z) .= _vec(z) .* (1 .- 2 .* ((1:length(z)) .== ind)) - else - z = -z - end - end - end - return false -end - -function maxeig!(integrator, cache::OrdinaryDiffEqMutableCache) - isfirst = integrator.iter == 1 || integrator.u_modified - @unpack t, dt, uprev, u, f, p, fsalfirst = integrator - if cache isa IRKCCache - fz, z, atmp = integrator.fsallast, cache.nlsolver.tmp, cache.atmp - else - fz, z, atmp = cache.k, cache.tmp, cache.atmp - end - ccache = cache.constantcache - maxiter = (integrator.alg isa Union{ESERK4, ESERK5, SERK2}) ? 100 : 50 - safe = (integrator.alg isa RKCAlgs) ? 1.0 : 1.2 - # Initial guess for eigenvector `z` - if isfirst - if integrator.alg isa RKCAlgs - if integrator.alg isa IRKC - @.. broadcast=false z=cache.du₂ - else - @.. broadcast=false z=fsalfirst - end - else - @.. broadcast=false fz=fsalfirst - f(z, fz, p, t) - integrator.stats.nf += 1 - end - else - @.. broadcast=false z=ccache.zprev - end - # Perturbation - u_norm = integrator.opts.internalnorm(uprev, t) - z_norm = integrator.opts.internalnorm(z, t) - pert = eps(u_norm) - sqrt_pert = sqrt(pert) - is_u_zero = u_norm == zero(u_norm) - is_z_zero = z_norm == zero(z_norm) - # Normalize `z` such that z-u lie in a circle - if (!is_u_zero && !is_z_zero) - dz_u = u_norm * sqrt_pert - quot = dz_u / z_norm - @.. broadcast=false z=uprev + quot * z - elseif !is_u_zero - dz_u = u_norm * sqrt_pert - @.. broadcast=false z=uprev + uprev * dz_u - elseif !is_z_zero - dz_u = pert - quot = dz_u / z_norm - @.. broadcast=false z*=quot - else - dz_u = pert - @.. broadcast=false z=dz_u * one(eltype(z)) - end # endif - # Start power iteration - integrator.eigen_est = 0 - for iter in 1:maxiter - if integrator.alg isa IRKC - f.f2(fz, z, p, t) - integrator.stats.nf2 += 1 - @.. broadcast=false atmp=fz - cache.du₂ - else - f(fz, z, p, t) - integrator.stats.nf += 1 - @.. broadcast=false atmp=fz - fsalfirst - end - Δ = integrator.opts.internalnorm(atmp, t) - eig_prev = integrator.eigen_est - integrator.eigen_est = Δ / dz_u * safe - # Convergence - if integrator.alg isa RKCAlgs # To match the constants given in the paper - if iter >= 2 && - abs(eig_prev - integrator.eigen_est) < - max(integrator.eigen_est, 1.0 / integrator.opts.dtmax) * 0.01 - integrator.eigen_est *= 1.2 - # Store the eigenvector - @.. broadcast=false ccache.zprev=z - uprev - return true - end - else - if iter >= 2 && - abs(eig_prev - integrator.eigen_est) < integrator.eigen_est * 0.05 - # Store the eigenvector - @.. broadcast=false ccache.zprev=z - uprev - return true - end - end - # Next `z` - if Δ != zero(Δ) - quot = dz_u / Δ - @.. broadcast=false z=uprev + quot * atmp - else - # An arbitrary change on `z` - nind = length(uprev) - if (nind != 1) - ind = 1 + iter % nind - # val = (uprev[ind] - (z[ind] - uprev[ind]))*one(eltype(z)) - _vec(z) .= _vec(z) .* (1 .- 2 .* ((1:length(z)) .== ind)) - else - z = -z - end - end - end - return false -end -""" - choosedeg!(cache) -> nothing - -Calculate `mdeg = ms[deg_index]` (the degree of the Chebyshev polynomial) -and `cache.start` (the start index of recurrence parameters for that -degree), where `recf` are the `μ,κ` pairs -for the `mdeg` degree method. The `κ` for `stage-1` for every degree -is 0 therefore it's not included in `recf` -""" -function choosedeg!(cache::T) where {T} - isconst = T <: OrdinaryDiffEqConstantCache - isconst || (cache = cache.constantcache) - start = 1 - @inbounds for i in 1:size(cache.ms, 1) - if cache.ms[i] >= cache.mdeg - cache.deg_index = i - cache.mdeg = cache.ms[i] - cache.start = start - break - end - start += cache.ms[i] * 2 - 1 - end - return nothing -end - -function choosedeg_SERK!(integrator, cache::T) where {T} - isconst = T <: OrdinaryDiffEqConstantCache - isconst || (cache = cache.constantcache) - @unpack ms = cache - start = 1 - @inbounds for i in 1:size(ms, 1) - if ms[i] < cache.mdeg - start += ms[i] + 1 - else - cache.start = start - cache.mdeg = ms[i] - break - end - end - if integrator.alg isa ESERK5 - if cache.mdeg <= 20 - cache.internal_deg = 2 - elseif cache.mdeg <= 50 - cache.internal_deg = 5 - elseif cache.mdeg <= 100 - cache.internal_deg = 10 - elseif cache.mdeg <= 500 - cache.internal_deg = 50 - elseif cache.mdeg <= 1000 - cache.internal_deg = 100 - elseif cache.mdeg <= 2000 - cache.internal_deg = 200 - end - end - - if integrator.alg isa ESERK4 - if cache.mdeg <= 20 - cache.internal_deg = 2 - elseif cache.mdeg <= 100 - cache.internal_deg = 10 - elseif cache.mdeg <= 500 - cache.internal_deg = 25 - elseif cache.mdeg <= 1000 - cache.internal_deg = 100 - elseif cache.mdeg <= 4000 - cache.internal_deg = 200 - end - end - - if integrator.alg isa SERK2 - cache.internal_deg = cache.mdeg / 10 - end - return nothing -end From 1aafef300b656840e33b44efd7fedaa1c343843c Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 11:00:08 -0400 Subject: [PATCH 21/71] Delete src/tableaus/feagin_tableaus.jl --- src/tableaus/feagin_tableaus.jl | 2650 ------------------------------- 1 file changed, 2650 deletions(-) delete mode 100644 src/tableaus/feagin_tableaus.jl diff --git a/src/tableaus/feagin_tableaus.jl b/src/tableaus/feagin_tableaus.jl deleted file mode 100644 index 64a056e0c9..0000000000 --- a/src/tableaus/feagin_tableaus.jl +++ /dev/null @@ -1,2650 +0,0 @@ -struct Feagin10ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - adaptiveConst::T - a0100::T - a0200::T - a0201::T - a0300::T - a0302::T - a0400::T - a0402::T - a0403::T - a0500::T - a0503::T - a0504::T - a0600::T - a0603::T - a0604::T - a0605::T - a0700::T - a0704::T - a0705::T - a0706::T - a0800::T - a0805::T - a0806::T - a0807::T - a0900::T - a0905::T - a0906::T - a0907::T - a0908::T - a1000::T - a1005::T - a1006::T - a1007::T - a1008::T - a1009::T - a1100::T - a1105::T - a1106::T - a1107::T - a1108::T - a1109::T - a1110::T - a1200::T - a1203::T - a1204::T - a1205::T - a1206::T - a1207::T - a1208::T - a1209::T - a1210::T - a1211::T - a1300::T - a1302::T - a1303::T - a1305::T - a1306::T - a1307::T - a1308::T - a1309::T - a1310::T - a1311::T - a1312::T - a1400::T - a1401::T - a1404::T - a1406::T - a1412::T - a1413::T - a1500::T - a1502::T - a1514::T - a1600::T - a1601::T - a1602::T - a1604::T - a1605::T - a1606::T - a1607::T - a1608::T - a1609::T - a1610::T - a1611::T - a1612::T - a1613::T - a1614::T - a1615::T - b1::T - b2::T - b3::T - b4::T - b5::T - b6::T - b7::T - b8::T - b9::T - b10::T - b11::T - b12::T - b13::T - b14::T - b15::T - b16::T - b17::T - c1::T2 - c2::T2 - c3::T2 - c4::T2 - c5::T2 - c6::T2 - c7::T2 - c8::T2 - c9::T2 - c10::T2 - c11::T2 - c12::T2 - c13::T2 - c14::T2 - c15::T2 - c16::T2 -end - -""" -constructFeagin10 -""" -function Feagin10ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - adaptiveConst = convert(T, 0.002777777777777778) - a0100 = convert(T, 0.1) - - a0200 = convert(T, -0.9151765613752915) - a0201 = convert(T, 1.4545344021782731) - - a0300 = convert(T, 0.20225919030111816) - a0302 = convert(T, 0.6067775709033545) - - a0400 = convert(T, 0.18402471470864357) - a0402 = convert(T, 0.19796683122719236) - a0403 = convert(T, -0.07295478473136326) - - a0500 = convert(T, 0.08790073402066813) - a0503 = convert(T, 0.41045970252026065) - a0504 = convert(T, 0.4827137536788665) - - a0600 = convert(T, 0.08597005049024603) - a0603 = convert(T, 0.3308859630407222) - a0604 = convert(T, 0.4896629573094502) - a0605 = convert(T, -0.07318563750708508) - - a0700 = convert(T, 0.12093044912533372) - a0704 = convert(T, 0.2601246757582956) - a0705 = convert(T, 0.032540262154909134) - a0706 = convert(T, -0.0595780211817361) - - a0800 = convert(T, 0.11085437958039149) - a0805 = convert(T, -0.06057614882550056) - a0806 = convert(T, 0.3217637056017784) - a0807 = convert(T, 0.510485725608063) - - a0900 = convert(T, 0.112054414752879) - a0905 = convert(T, -0.14494277590286592) - a0906 = convert(T, -0.3332697190962567) - a0907 = convert(T, 0.4992692295568801) - a0908 = convert(T, 0.5095046089296861) - - a1000 = convert(T, 0.11397678396418598) - a1005 = convert(T, -0.07688133642033569) - a1006 = convert(T, 0.23952736032439065) - a1007 = convert(T, 0.3977746623680946) - a1008 = convert(T, 0.010755895687360746) - a1009 = convert(T, -0.3277691241640189) - - a1100 = convert(T, 0.07983145282801961) - a1105 = convert(T, -0.052032968680060306) - a1106 = convert(T, -0.05769541461685489) - a1107 = convert(T, 0.19478191571210415) - a1108 = convert(T, 0.14538492318832508) - a1109 = convert(T, -0.07829427103516708) - a1110 = convert(T, -0.11450329936109892) - - a1200 = convert(T, 0.9851156101648573) - a1203 = convert(T, 0.3308859630407222) - a1204 = convert(T, 0.4896629573094502) - a1205 = convert(T, -1.3789648657484357) - a1206 = convert(T, -0.8611641950276356) - a1207 = convert(T, 5.784288136375372) - a1208 = convert(T, 3.2880776198510357) - a1209 = convert(T, -2.386339050931364) - a1210 = convert(T, -3.254793424836439) - a1211 = convert(T, -2.16343541686423) - - a1300 = convert(T, 0.8950802957716328) - a1302 = convert(T, 0.19796683122719236) - a1303 = convert(T, -0.07295478473136326) - a1305 = convert(T, -0.8512362396620076) - a1306 = convert(T, 0.3983201123185333) - a1307 = convert(T, 3.639372631810356) - a1308 = convert(T, 1.5482287703983033) - a1309 = convert(T, -2.122217147040537) - a1310 = convert(T, -1.5835039854532618) - a1311 = convert(T, -1.7156160828593627) - a1312 = convert(T, -0.024403640575012746) - - a1400 = convert(T, -0.9151765613752915) - a1401 = convert(T, 1.4545344021782731) - a1404 = convert(T, -0.7773336436449683) - a1406 = convert(T, -0.0910895662155176) - a1412 = convert(T, 0.0910895662155176) - a1413 = convert(T, 0.7773336436449683) - - a1500 = convert(T, 0.1) - a1502 = convert(T, -0.15717866579977116) - a1514 = convert(T, 0.15717866579977116) - - a1600 = convert(T, 0.1817813007000953) - a1601 = convert(T, 0.675) - a1602 = convert(T, 0.3427581598471898) - a1604 = convert(T, 0.25911121454832275) - a1605 = convert(T, -0.35827896671795206) - a1606 = convert(T, -1.0459489594088331) - a1607 = convert(T, 0.930327845415627) - a1608 = convert(T, 1.7795095943170811) - a1609 = convert(T, 0.1) - a1610 = convert(T, -0.2825475695390441) - a1611 = convert(T, -0.15932735011997254) - a1612 = convert(T, -0.14551589464700151) - a1613 = convert(T, -0.25911121454832275) - a1614 = convert(T, -0.3427581598471898) - a1615 = convert(T, -0.675) - - b1 = convert(T, 0.03333333333333333) - b2 = convert(T, 0.025) - b3 = convert(T, 0.03333333333333333) - b4 = convert(T, 0) - b5 = convert(T, 0.05) - b6 = convert(T, 0) - b7 = convert(T, 0.04) - b8 = convert(T, 0) - b9 = convert(T, 0.1892374781489235) - b10 = convert(T, 0.2774291885177432) - b11 = convert(T, 0.2774291885177432) - b12 = convert(T, 0.1892374781489235) - b13 = convert(T, -0.04) - b14 = convert(T, -0.05) - b15 = convert(T, -0.03333333333333333) - b16 = convert(T, -0.025) - b17 = convert(T, 0.03333333333333333) - - c1 = convert(T2, 0.1) - c2 = convert(T2, 0.5393578408029818) - c3 = convert(T2, 0.8090367612044727) - c4 = convert(T2, 0.30903676120447265) - c5 = convert(T2, 0.9810741902197953) - c6 = convert(T2, 0.8333333333333334) - c7 = convert(T2, 0.3540173658568024) - c8 = convert(T2, 0.8825276619647323) - c9 = convert(T2, 0.6426157582403226) - c10 = convert(T2, 0.3573842417596775) - c11 = convert(T2, 0.11747233803526766) - c12 = convert(T2, 0.8333333333333334) - c13 = convert(T2, 0.30903676120447265) - c14 = convert(T2, 0.5393578408029818) - c15 = convert(T2, 0.1) - c16 = convert(T2, 1) - Feagin10ConstantCache(adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, - a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, - a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, - a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, - a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1203, - a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211, a1300, - a1302, a1303, a1305, a1306, a1307, a1308, a1309, a1310, a1311, - a1312, a1400, a1401, a1404, a1406, a1412, a1413, a1500, a1502, - a1514, a1600, a1601, a1602, a1604, a1605, a1606, a1607, a1608, - a1609, a1610, a1611, a1612, a1613, a1614, a1615, b1, b2, b3, b4, - b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, c1, - c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16) -end - -""" -constructFeagin10 -""" -function Feagin10ConstantCache(T::Type, T2::Type) - adaptiveConst = convert(T, 1 // 360) - a0100 = convert(T, 1 // 10) - - a0200 = convert(T, big"-0.915176561375291440520015019275342154318951387664369720564660") - a0201 = convert(T, big"1.45453440217827322805250021715664459117622483736537873607016") - - a0300 = convert(T, big"0.202259190301118170324681949205488413821477543637878380814562") - a0302 = convert(T, big"0.606777570903354510974045847616465241464432630913635142443687") - - a0400 = convert(T, big"0.184024714708643575149100693471120664216774047979591417844635") - a0402 = convert(T, big"0.197966831227192369068141770510388793370637287463360401555746") - a0403 = convert(T, - big"-0.0729547847313632629185146671595558023015011608914382961421311") - - a0500 = convert(T, big"0.0879007340206681337319777094132125475918886824944548534041378") - a0503 = convert(T, big"0.410459702520260645318174895920453426088035325902848695210406") - a0504 = convert(T, big"0.482713753678866489204726942976896106809132737721421333413261") - - a0600 = convert(T, big"0.0859700504902460302188480225945808401411132615636600222593880") - a0603 = convert(T, big"0.330885963040722183948884057658753173648240154838402033448632") - a0604 = convert(T, big"0.489662957309450192844507011135898201178015478433790097210790") - a0605 = convert(T, - big"-0.0731856375070850736789057580558988816340355615025188195854775") - - a0700 = convert(T, big"0.120930449125333720660378854927668953958938996999703678812621") - a0704 = convert(T, big"0.260124675758295622809007617838335174368108756484693361887839") - a0705 = convert(T, big"0.0325402621549091330158899334391231259332716675992700000776101") - a0706 = convert(T, - big"-0.0595780211817361001560122202563305121444953672762930724538856") - - a0800 = convert(T, big"0.110854379580391483508936171010218441909425780168656559807038") - a0805 = convert(T, - big"-0.0605761488255005587620924953655516875526344415354339234619466") - a0806 = convert(T, big"0.321763705601778390100898799049878904081404368603077129251110") - a0807 = convert(T, big"0.510485725608063031577759012285123416744672137031752354067590") - - a0900 = convert(T, big"0.112054414752879004829715002761802363003717611158172229329393") - a0905 = convert(T, big"-0.144942775902865915672349828340980777181668499748506838876185") - a0906 = convert(T, big"-0.333269719096256706589705211415746871709467423992115497968724") - a0907 = convert(T, big"0.499269229556880061353316843969978567860276816592673201240332") - a0908 = convert(T, big"0.509504608929686104236098690045386253986643232352989602185060") - - a1000 = convert(T, big"0.113976783964185986138004186736901163890724752541486831640341") - a1005 = convert(T, - big"-0.0768813364203356938586214289120895270821349023390922987406384") - a1006 = convert(T, big"0.239527360324390649107711455271882373019741311201004119339563") - a1007 = convert(T, big"0.397774662368094639047830462488952104564716416343454639902613") - a1008 = convert(T, big"0.0107558956873607455550609147441477450257136782823280838547024") - a1009 = convert(T, big"-0.327769124164018874147061087350233395378262992392394071906457") - - a1100 = convert(T, big"0.0798314528280196046351426864486400322758737630423413945356284") - a1105 = convert(T, - big"-0.0520329686800603076514949887612959068721311443881683526937298") - a1106 = convert(T, - big"-0.0576954146168548881732784355283433509066159287152968723021864") - a1107 = convert(T, big"0.194781915712104164976306262147382871156142921354409364738090") - a1108 = convert(T, big"0.145384923188325069727524825977071194859203467568236523866582") - a1109 = convert(T, - big"-0.0782942710351670777553986729725692447252077047239160551335016") - a1110 = convert(T, big"-0.114503299361098912184303164290554670970133218405658122674674") - - a1200 = convert(T, big"0.985115610164857280120041500306517278413646677314195559520529") - a1203 = convert(T, big"0.330885963040722183948884057658753173648240154838402033448632") - a1204 = convert(T, big"0.489662957309450192844507011135898201178015478433790097210790") - a1205 = convert(T, big"-1.37896486574843567582112720930751902353904327148559471526397") - a1206 = convert(T, big"-0.861164195027635666673916999665534573351026060987427093314412") - a1207 = convert(T, big"5.78428813637537220022999785486578436006872789689499172601856") - a1208 = convert(T, big"3.28807761985103566890460615937314805477268252903342356581925") - a1209 = convert(T, big"-2.38633905093136384013422325215527866148401465975954104585807") - a1210 = convert(T, big"-3.25479342483643918654589367587788726747711504674780680269911") - a1211 = convert(T, big"-2.16343541686422982353954211300054820889678036420109999154887") - - a1300 = convert(T, big"0.895080295771632891049613132336585138148156279241561345991710") - a1302 = convert(T, big"0.197966831227192369068141770510388793370637287463360401555746") - a1303 = convert(T, - big"-0.0729547847313632629185146671595558023015011608914382961421311") - a1305 = convert(T, big"-0.851236239662007619739049371445966793289359722875702227166105") - a1306 = convert(T, big"0.398320112318533301719718614174373643336480918103773904231856") - a1307 = convert(T, big"3.63937263181035606029412920047090044132027387893977804176229") - a1308 = convert(T, big"1.54822877039830322365301663075174564919981736348973496313065") - a1309 = convert(T, big"-2.12221714704053716026062427460427261025318461146260124401561") - a1310 = convert(T, big"-1.58350398545326172713384349625753212757269188934434237975291") - a1311 = convert(T, big"-1.71561608285936264922031819751349098912615880827551992973034") - a1312 = convert(T, - big"-0.0244036405750127452135415444412216875465593598370910566069132") - - a1400 = convert(T, big"-0.915176561375291440520015019275342154318951387664369720564660") - a1401 = convert(T, big"1.45453440217827322805250021715664459117622483736537873607016") - a1404 = convert(T, big"-0.777333643644968233538931228575302137803351053629547286334469") - a1406 = convert(T, - big"-0.0910895662155176069593203555807484200111889091770101799647985") - a1412 = convert(T, big"0.0910895662155176069593203555807484200111889091770101799647985") - a1413 = convert(T, big"0.777333643644968233538931228575302137803351053629547286334469") - - a1500 = convert(T, 1 // 10) - a1502 = convert(T, big"-0.157178665799771163367058998273128921867183754126709419409654") - a1514 = convert(T, big"0.157178665799771163367058998273128921867183754126709419409654") - - a1600 = convert(T, big"0.181781300700095283888472062582262379650443831463199521664945") - a1601 = convert(T, 27 // 40) - a1602 = convert(T, big"0.342758159847189839942220553413850871742338734703958919937260") - a1604 = convert(T, big"0.259111214548322744512977076191767379267783684543182428778156") - a1605 = convert(T, big"-0.358278966717952089048961276721979397739750634673268802484271") - a1606 = convert(T, big"-1.04594895940883306095050068756409905131588123172378489286080") - a1607 = convert(T, big"0.930327845415626983292300564432428777137601651182965794680397") - a1608 = convert(T, big"1.77950959431708102446142106794824453926275743243327790536000") - a1609 = convert(T, 1 // 10) - a1610 = convert(T, big"-0.282547569539044081612477785222287276408489375976211189952877") - a1611 = convert(T, big"-0.159327350119972549169261984373485859278031542127551931461821") - a1612 = convert(T, big"-0.145515894647001510860991961081084111308650130578626404945571") - a1613 = convert(T, big"-0.259111214548322744512977076191767379267783684543182428778156") - a1614 = convert(T, big"-0.342758159847189839942220553413850871742338734703958919937260") - a1615 = convert(T, -27 // 40) - - b1 = convert(T, 1 // 30) - b2 = convert(T, 1 // 40) - b3 = convert(T, 1 // 30) - b4 = convert(T, 0) - b5 = convert(T, 1 // 20) - b6 = convert(T, 0) - b7 = convert(T, 1 // 25) - b8 = convert(T, 0) - b9 = convert(T, big"0.189237478148923490158306404106012326238162346948625830327194") - b10 = convert(T, big"0.277429188517743176508360262560654340428504319718040836339472") - b11 = convert(T, big"0.277429188517743176508360262560654340428504319718040836339472") - b12 = convert(T, big"0.189237478148923490158306404106012326238162346948625830327194") - b13 = convert(T, -1 // 25) - b14 = convert(T, -1 // 20) - b15 = convert(T, -1 // 30) - b16 = convert(T, -1 // 40) - b17 = convert(T, 1 // 30) - - c1 = convert(T2, 1 // 10) - c2 = convert(T2, big"0.539357840802981787532485197881302436857273449701009015505500") - c3 = convert(T2, big"0.809036761204472681298727796821953655285910174551513523258250") - c4 = convert(T2, big"0.309036761204472681298727796821953655285910174551513523258250") - c5 = convert(T2, big"0.981074190219795268254879548310562080489056746118724882027805") - c6 = convert(T2, 5 // 6) - c7 = convert(T2, big"0.354017365856802376329264185948796742115824053807373968324184") - c8 = convert(T2, big"0.882527661964732346425501486979669075182867844268052119663791") - c9 = convert(T2, big"0.642615758240322548157075497020439535959501736363212695909875") - c10 = convert(T2, big"0.357384241759677451842924502979560464040498263636787304090125") - c11 = convert(T2, big"0.117472338035267653574498513020330924817132155731947880336209") - c12 = convert(T2, 5 // 6) - c13 = convert(T2, big"0.309036761204472681298727796821953655285910174551513523258250") - c14 = convert(T2, big"0.539357840802981787532485197881302436857273449701009015505500") - c15 = convert(T2, 1 // 10) - c16 = convert(T2, 1) - Feagin10ConstantCache(adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, - a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, - a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, - a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, - a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1203, - a1204, a1205, a1206, a1207, a1208, a1209, a1210, a1211, a1300, - a1302, a1303, a1305, a1306, a1307, a1308, a1309, a1310, a1311, - a1312, a1400, a1401, a1404, a1406, a1412, a1413, a1500, a1502, - a1514, a1600, a1601, a1602, a1604, a1605, a1606, a1607, a1608, - a1609, a1610, a1611, a1612, a1613, a1614, a1615, b1, b2, b3, b4, - b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, c1, - c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16) -end - -struct Feagin12ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - adaptiveConst::T - a0100::T - a0200::T - a0201::T - a0300::T - a0302::T - a0400::T - a0402::T - a0403::T - a0500::T - a0503::T - a0504::T - a0600::T - a0603::T - a0604::T - a0605::T - a0700::T - a0704::T - a0705::T - a0706::T - a0800::T - a0805::T - a0806::T - a0807::T - a0900::T - a0905::T - a0906::T - a0907::T - a0908::T - a1000::T - a1005::T - a1006::T - a1007::T - a1008::T - a1009::T - a1100::T - a1105::T - a1106::T - a1107::T - a1108::T - a1109::T - a1110::T - a1200::T - a1208::T - a1209::T - a1210::T - a1211::T - a1300::T - a1308::T - a1309::T - a1310::T - a1311::T - a1312::T - a1400::T - a1408::T - a1409::T - a1410::T - a1411::T - a1412::T - a1413::T - a1500::T - a1508::T - a1509::T - a1510::T - a1511::T - a1512::T - a1513::T - a1514::T - a1600::T - a1608::T - a1609::T - a1610::T - a1611::T - a1612::T - a1613::T - a1614::T - a1615::T - a1700::T - a1705::T - a1706::T - a1707::T - a1708::T - a1709::T - a1710::T - a1711::T - a1712::T - a1713::T - a1714::T - a1715::T - a1716::T - a1800::T - a1805::T - a1806::T - a1807::T - a1808::T - a1809::T - a1810::T - a1811::T - a1812::T - a1813::T - a1814::T - a1815::T - a1816::T - a1817::T - a1900::T - a1904::T - a1905::T - a1906::T - a1908::T - a1909::T - a1910::T - a1911::T - a1912::T - a1913::T - a1914::T - a1915::T - a1916::T - a1917::T - a1918::T - a2000::T - a2003::T - a2004::T - a2005::T - a2007::T - a2009::T - a2010::T - a2017::T - a2018::T - a2019::T - a2100::T - a2102::T - a2103::T - a2106::T - a2107::T - a2109::T - a2110::T - a2117::T - a2118::T - a2119::T - a2120::T - a2200::T - a2201::T - a2204::T - a2206::T - a2220::T - a2221::T - a2300::T - a2302::T - a2322::T - a2400::T - a2401::T - a2402::T - a2404::T - a2406::T - a2407::T - a2408::T - a2409::T - a2410::T - a2411::T - a2412::T - a2413::T - a2414::T - a2415::T - a2416::T - a2417::T - a2418::T - a2419::T - a2420::T - a2421::T - a2422::T - a2423::T - c1::T2 - c2::T2 - c3::T2 - c4::T2 - c5::T2 - c6::T2 - c7::T2 - c8::T2 - c9::T2 - c10::T2 - c11::T2 - c12::T2 - c13::T2 - c14::T2 - c15::T2 - c16::T2 - c17::T2 - c18::T2 - c19::T2 - c20::T2 - c21::T2 - c22::T2 - c23::T2 - c24::T2 - b1::T - b2::T - b3::T - b4::T - b5::T - b6::T - b7::T - b8::T - b9::T - b10::T - b11::T - b12::T - b13::T - b14::T - b15::T - b16::T - b17::T - b18::T - b19::T - b20::T - b21::T - b22::T - b23::T - b24::T - b25::T -end - -""" -constructFeagin12 -""" -function Feagin12ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - adaptiveConst = convert(T, 49 // 640) - c1 = convert(T2, 1 // 5) - c2 = convert(T2, 5 // 9) - c3 = convert(T2, 5 // 6) - c4 = convert(T2, 1 // 3) - c5 = convert(T2, 1) - c6 = convert(T2, 0.671835709170513812712245661002797570438953420568682550710222) - c7 = convert(T2, 0.288724941110620201935458488967024976908118598341806976469674) - c8 = convert(T2, 9 // 16) - c9 = convert(T2, 5 // 6) - c10 = convert(T2, 0.947695431179199287562380162101836721649589325892740646458322) - c11 = convert(T2, 0.0548112876863802643887753674810754475842153612931128785028369) - c12 = convert(T2, 0.0848880518607165350639838930162674302064148175640019542045934) - c13 = convert(T2, 0.265575603264642893098114059045616835297201264164077621448665) - c14 = convert(T2, 1 // 2) - c15 = convert(T2, 0.734424396735357106901885940954383164702798735835922378551335) - c16 = convert(T2, 0.915111948139283464936016106983732569793585182435998045795407) - c17 = convert(T2, 0.947695431179199287562380162101836721649589325892740646458322) - c18 = convert(T2, 5 // 6) - c19 = convert(T2, 0.288724941110620201935458488967024976908118598341806976469674) - c20 = convert(T2, 0.671835709170513812712245661002797570438953420568682550710222) - c21 = convert(T2, 1 // 3) - c22 = convert(T2, 5 // 9) - c23 = convert(T2, 1 // 5) - c24 = convert(T2, 1) - - b1 = convert(T, 1 // 42) - b2 = convert(T, 234375 // 10000000) - b3 = convert(T, 3125 // 100000) - b4 = convert(T, 0) - b5 = convert(T, 1 // 24) - b6 = convert(T, 0) - b7 = convert(T, 1 // 20) - b8 = convert(T, 1 // 20) - b9 = convert(T, 0) - b10 = convert(T, 1 // 10) - b11 = convert(T, 1 // 14) - b12 = convert(T, 0) - b13 = convert(T, 0.138413023680782974005350203145033146748813640089941234591267) - b14 = convert(T, 0.215872690604931311708935511140681138965472074195773051123019) - b15 = convert(T, 0.243809523809523809523809523809523809523809523809523809523810) - b16 = convert(T, 0.215872690604931311708935511140681138965472074195773051123019) - b17 = convert(T, 0.138413023680782974005350203145033146748813640089941234591267) - b18 = convert(T, -0.0714285714285714285714285714285714285714285714285714285714286) - b19 = convert(T, -1 // 10) - b20 = convert(T, -1 // 20) - b21 = convert(T, -1 // 20) - b22 = convert(T, -1 // 24) - b23 = convert(T, -3125 // 100000) - b24 = convert(T, -234375 // 10000000) - b25 = convert(T, 1 // 42) - - a0100 = convert(T, 1 // 5) - - a0200 = convert(T, -0.216049382716049382716049382716049382716049382716049382716049) - a0201 = convert(T, 0.771604938271604938271604938271604938271604938271604938271605) - - a0300 = convert(T, 5 // 24) - a0302 = convert(T, 5 // 8) - - a0400 = convert(T, 29 // 150) - a0402 = convert(T, 11 // 50) - a0403 = convert(T, -2 // 25) - - a0500 = convert(T, 1 // 10) - a0503 = convert(T, 2 // 5) - a0504 = convert(T, 1 // 2) - - a0600 = convert(T, 0.103364471650010477570395435690481791543342708330349879244197) - a0603 = convert(T, 0.124053094528946761061581889237115328211074784955180298044074) - a0604 = convert(T, 0.483171167561032899288836480451962508724109257517289177302380) - a0605 = convert(T, -0.0387530245694763252085681443767620580395733302341368038804290) - - a0700 = convert(T, 0.124038261431833324081904585980175168140024670698633612292480) - a0704 = convert(T, 0.217050632197958486317846256953159942875916353757734167684657) - a0705 = convert(T, 0.0137455792075966759812907801835048190594443990939408530842918) - a0706 = convert(T, -0.0661095317267682844455831341498149531672668252085016565917546) - - a0800 = convert(T, 0.0914774894856882983144991846980432197088832099976660100090486) - a0805 = convert(T, -0.00544348523717469689965754944144838611346156873847009178068318) - a0806 = convert(T, 0.0680716801688453518578515120895103863112751730758794372203952) - a0807 = convert(T, 0.408394315582641046727306852653894780093303185664924644551239) - - a0900 = convert(T, 0.0890013652502551018954509355423841780143232697403434118692699) - a0905 = convert(T, 0.00499528226645532360197793408420692800405891149406814091955810) - a0906 = convert(T, 0.397918238819828997341739603001347156083435060931424970826304) - a0907 = convert(T, 0.427930210752576611068192608300897981558240730580396406312359) - a0908 = convert(T, -0.0865117637557827005740277475955029103267246394128995965941585) - - a1000 = convert(T, 0.0695087624134907543112693906409809822706021061685544615255758) - a1005 = convert(T, 0.129146941900176461970759579482746551122871751501482634045487) - a1006 = convert(T, 1.53073638102311295076342566143214939031177504112433874313011) - a1007 = convert(T, 0.577874761129140052546751349454576715334892100418571882718036) - a1008 = convert(T, -0.951294772321088980532340837388859453930924498799228648050949) - a1009 = convert(T, -0.408276642965631951497484981519757463459627174520978426909934) - - a1100 = convert(T, 0.0444861403295135866269453507092463581620165501018684152933313) - a1105 = convert(T, -0.00380476867056961731984232686574547203016331563626856065717964) - a1106 = convert(T, 0.0106955064029624200721262602809059154469206077644957399593972) - a1107 = convert(T, 0.0209616244499904333296674205928919920806734650660039898074652) - a1108 = convert(T, -0.0233146023259321786648561431551978077665337818756053603898847) - a1109 = convert(T, 0.00263265981064536974369934736325334761174975280887405725010964) - a1110 = convert(T, 0.00315472768977025060103545855572111407955208306374459723959783) - - a1200 = convert(T, 0.0194588815119755475588801096525317761242073762016273186231215) - a1208 = convert(T, 0.0000678512949171812509306121653452367476194364781259165332321534) - a1209 = convert(T, -0.0000429795859049273623271005330230162343568863387724883603675550) - a1210 = convert(T, 0.0000176358982260285155407485928953302139937553442829975734148981) - a1211 = convert(T, 0.0653866627415027051009595231385181033549511358787382098351924) - - a1300 = convert(T, 0.206836835664277105916828174798272361078909196043446411598231) - a1308 = convert(T, 0.0166796067104156472828045866664696450306326505094792505215514) - a1309 = convert(T, -0.00879501563200710214457024178249986591130234990219959208704979) - a1310 = convert(T, 0.00346675455362463910824462315246379209427513654098596403637231) - a1311 = convert(T, -0.861264460105717678161432562258351242030270498966891201799225) - a1312 = convert(T, 0.908651882074050281096239478469262145034957129939256789178785) - - a1400 = convert(T, 0.0203926084654484010091511314676925686038504449562413004562382) - a1408 = convert(T, 0.0869469392016685948675400555583947505833954460930940959577347) - a1409 = convert(T, -0.0191649630410149842286436611791405053287170076602337673587681) - a1410 = convert(T, 0.00655629159493663287364871573244244516034828755253746024098838) - a1411 = convert(T, 0.0987476128127434780903798528674033899738924968006632201445462) - a1412 = convert(T, 0.00535364695524996055083260173615567408717110247274021056118319) - a1413 = convert(T, 0.301167864010967916837091303817051676920059229784957479998077) - - a1500 = convert(T, 0.228410433917778099547115412893004398779136994596948545722283) - a1508 = convert(T, -0.498707400793025250635016567442511512138603770959682292383042) - a1509 = convert(T, 0.134841168335724478552596703792570104791700727205981058201689) - a1510 = convert(T, -0.0387458244055834158439904226924029230935161059142806805674360) - a1511 = convert(T, -1.27473257473474844240388430824908952380979292713250350199641) - a1512 = convert(T, 1.43916364462877165201184452437038081875299303577911839630524) - a1513 = convert(T, -0.214007467967990254219503540827349569639028092344812795499026) - a1514 = convert(T, 0.958202417754430239892724139109781371059908874605153648768037) - - a1600 = convert(T, 2.00222477655974203614249646012506747121440306225711721209798) - a1608 = convert(T, 2.06701809961524912091954656438138595825411859673341600679555) - a1609 = convert(T, 0.623978136086139541957471279831494466155292316167021080663140) - a1610 = convert(T, -0.0462283685500311430283203554129062069391947101880112723185773) - a1611 = convert(T, -8.84973288362649614860075246727118949286604835457092701094630) - a1612 = convert(T, 7.74257707850855976227437225791835589560188590785037197433615) - a1613 = convert(T, -0.588358519250869210993353314127711745644125882130941202896436) - a1614 = convert(T, -1.10683733362380649395704708016953056176195769617014899442903) - a1615 = convert(T, -0.929529037579203999778397238291233214220788057511899747507074) - - a1700 = convert(T, 3.13789533412073442934451608989888796808161259330322100268310) - a1705 = convert(T, 0.129146941900176461970759579482746551122871751501482634045487) - a1706 = convert(T, 1.53073638102311295076342566143214939031177504112433874313011) - a1707 = convert(T, 0.577874761129140052546751349454576715334892100418571882718036) - a1708 = convert(T, 5.42088263055126683050056840891857421941300558851862156403363) - a1709 = convert(T, 0.231546926034829304872663800877643660904880180835945693836936) - a1710 = convert(T, 0.0759292995578913560162301311785251873561801342333194895292058) - a1711 = convert(T, -12.3729973380186513287414553402595806591349822617535905976253) - a1712 = convert(T, 9.85455883464769543935957209317369202080367765721777101906955) - a1713 = convert(T, 0.0859111431370436529579357709052367772889980495122329601159540) - a1714 = convert(T, -5.65242752862643921117182090081762761180392602644189218673969) - a1715 = convert(T, -1.94300935242819610883833776782364287728724899124166920477873) - a1716 = convert(T, -0.128352601849404542018428714319344620742146491335612353559923) - - a1800 = convert(T, 1.38360054432196014878538118298167716825163268489922519995564) - a1805 = convert(T, 0.00499528226645532360197793408420692800405891149406814091955810) - a1806 = convert(T, 0.397918238819828997341739603001347156083435060931424970826304) - a1807 = convert(T, 0.427930210752576611068192608300897981558240730580396406312359) - a1808 = convert(T, -1.30299107424475770916551439123047573342071475998399645982146) - a1809 = convert(T, 0.661292278669377029097112528107513072734573412294008071500699) - a1810 = convert(T, -0.144559774306954349765969393688703463900585822441545655530145) - a1811 = convert(T, -6.96576034731798203467853867461083919356792248105919255460819) - a1812 = convert(T, 6.65808543235991748353408295542210450632193197576935120716437) - a1813 = convert(T, -1.66997375108841486404695805725510845049807969199236227575796) - a1814 = convert(T, 2.06413702318035263832289040301832647130604651223986452170089) - a1815 = convert(T, -0.674743962644306471862958129570837723192079875998405058648892) - a1816 = convert(T, -0.00115618834794939500490703608435907610059605754935305582045729) - a1817 = convert(T, -0.00544057908677007389319819914241631024660726585015012485938593) - - a1900 = convert(T, 0.951236297048287669474637975894973552166903378983475425758226) - a1904 = convert(T, 0.217050632197958486317846256953159942875916353757734167684657) - a1905 = convert(T, 0.0137455792075966759812907801835048190594443990939408530842918) - a1906 = convert(T, -0.0661095317267682844455831341498149531672668252085016565917546) - a1908 = convert(T, 0.152281696736414447136604697040747131921486432699422112099617) - a1909 = convert(T, -0.337741018357599840802300793133998004354643424457539667670080) - a1910 = convert(T, -0.0192825981633995781534949199286824400469353110630787982121133) - a1911 = convert(T, -3.68259269696866809932409015535499603576312120746888880201882) - a1912 = convert(T, 3.16197870406982063541533528419683854018352080342887002331312) - a1913 = convert(T, -0.370462522106885290716991856022051125477943482284080569177386) - a1914 = convert(T, -0.0514974200365440434996434456698127984941168616474316871020314) - a1915 = convert(T, -0.000829625532120152946787043541792848416659382675202720677536554) - a1916 = convert(T, 0.00000279801041419278598986586589070027583961355402640879503213503) - a1917 = convert(T, 0.0418603916412360287969841020776788461794119440689356178942252) - a1918 = convert(T, 0.279084255090877355915660874555379649966282167560126269290222) - - a2000 = convert(T, 0.103364471650010477570395435690481791543342708330349879244197) - a2003 = convert(T, 0.124053094528946761061581889237115328211074784955180298044074) - a2004 = convert(T, 0.483171167561032899288836480451962508724109257517289177302380) - a2005 = convert(T, -0.0387530245694763252085681443767620580395733302341368038804290) - a2007 = convert(T, -0.438313820361122420391059788940960176420682836652600698580091) - a2009 = convert(T, -0.218636633721676647685111485017151199362509373698288330593486) - a2010 = convert(T, -0.0312334764394719229981634995206440349766174759626578122323015) - a2017 = convert(T, 0.0312334764394719229981634995206440349766174759626578122323015) - a2018 = convert(T, 0.218636633721676647685111485017151199362509373698288330593486) - a2019 = convert(T, 0.438313820361122420391059788940960176420682836652600698580091) - - a2100 = convert(T, 29 // 150) - a2102 = convert(T, 11 // 50) - a2103 = convert(T, -2 // 25) - a2106 = convert(T, 0.0984256130499315928152900286856048243348202521491288575952143) - a2107 = convert(T, -0.196410889223054653446526504390100417677539095340135532418849) - a2109 = convert(T, 0.436457930493068729391826122587949137609670676712525034763317) - a2110 = convert(T, 0.0652613721675721098560370939805555698350543810708414716730270) - a2117 = convert(T, -0.0652613721675721098560370939805555698350543810708414716730270) - a2118 = convert(T, -0.436457930493068729391826122587949137609670676712525034763317) - a2119 = convert(T, 0.196410889223054653446526504390100417677539095340135532418849) - a2120 = convert(T, -0.0984256130499315928152900286856048243348202521491288575952143) - - a2200 = convert(T, -0.216049382716049382716049382716049382716049382716049382716049) - a2201 = convert(T, 0.771604938271604938271604938271604938271604938271604938271605) - a2204 = convert(T, -2 // 3) - a2206 = convert(T, -0.390696469295978451446999802258495981249099665294395945559163) - a2220 = convert(T, 0.390696469295978451446999802258495981249099665294395945559163) - a2221 = convert(T, 2 // 3) - - a2300 = convert(T, 1 // 5) - a2302 = convert(T, -0.164609053497942386831275720164609053497942386831275720164609) - a2322 = convert(T, 0.164609053497942386831275720164609053497942386831275720164609) - - a2400 = convert(T, 1.47178724881110408452949550989023611293535315518571691939396) - a2401 = convert(T, 63 // 80) - a2402 = convert(T, 91 // 216) - a2404 = convert(T, 7 // 24) - a2406 = convert(T, 0.348600717628329563206854421629657569274689947367847465753757) - a2407 = convert(T, 0.229499544768994849582890233710555447073823569666506700662510) - a2408 = convert(T, 5.79046485790481979159831978177003471098279506036722411333192) - a2409 = convert(T, 0.418587511856506868874073759426596207226461447604248151080016) - a2410 = convert(T, 0.307039880222474002649653817490106690389251482313213999386651) - a2411 = convert(T, -4.68700905350603332214256344683853248065574415794742040470287) - a2412 = convert(T, 3.13571665593802262152038152399873856554395436199962915429076) - a2413 = convert(T, 1.40134829710965720817510506275620441055845017313930508348898) - a2414 = convert(T, -5.52931101439499023629010306005764336421276055777658156400910) - a2415 = convert(T, -0.853138235508063349309546894974784906188927508039552519557498) - a2416 = convert(T, 0.103575780373610140411804607167772795518293914458500175573749) - a2417 = convert(T, -0.140474416950600941142546901202132534870665923700034957196546) - a2418 = convert(T, -0.418587511856506868874073759426596207226461447604248151080016) - a2419 = convert(T, -0.229499544768994849582890233710555447073823569666506700662510) - a2420 = convert(T, -0.348600717628329563206854421629657569274689947367847465753757) - a2421 = convert(T, -7 // 24) - a2422 = convert(T, -91 // 216) - a2423 = convert(T, -63 // 80) - Feagin12ConstantCache(adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, - a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, - a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, - a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, - a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1208, - a1209, a1210, a1211, a1300, a1308, a1309, a1310, a1311, a1312, - a1400, a1408, a1409, a1410, a1411, a1412, a1413, a1500, a1508, - a1509, a1510, a1511, a1512, a1513, a1514, a1600, a1608, a1609, - a1610, a1611, a1612, a1613, a1614, a1615, a1700, a1705, a1706, - a1707, a1708, a1709, a1710, a1711, a1712, a1713, a1714, a1715, - a1716, a1800, a1805, a1806, a1807, a1808, a1809, a1810, a1811, - a1812, a1813, a1814, a1815, a1816, a1817, a1900, a1904, a1905, - a1906, a1908, a1909, a1910, a1911, a1912, a1913, a1914, a1915, - a1916, a1917, a1918, a2000, a2003, a2004, a2005, a2007, a2009, - a2010, a2017, a2018, a2019, a2100, a2102, a2103, a2106, a2107, - a2109, a2110, a2117, a2118, a2119, a2120, a2200, a2201, a2204, - a2206, a2220, a2221, a2300, a2302, a2322, a2400, a2401, a2402, - a2404, a2406, a2407, a2408, a2409, a2410, a2411, a2412, a2413, - a2414, a2415, a2416, a2417, a2418, a2419, a2420, a2421, a2422, - a2423, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, - c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, b1, b2, b3, - b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, - b18, b19, b20, b21, b22, b23, b24, b25) -end - -""" -constructFeagin12 -""" -function Feagin12ConstantCache(T::Type, T2::Type) - adaptiveConst = convert(T, 49 // 640) - c1 = convert(T2, 1 // 5) - c2 = convert(T2, 5 // 9) - c3 = convert(T2, 5 // 6) - c4 = convert(T2, 1 // 3) - c5 = convert(T2, 1) - c6 = convert(T2, big"0.671835709170513812712245661002797570438953420568682550710222") - c7 = convert(T2, big"0.288724941110620201935458488967024976908118598341806976469674") - c8 = convert(T2, 9 // 16) - c9 = convert(T2, 5 // 6) - c10 = convert(T2, big"0.947695431179199287562380162101836721649589325892740646458322") - c11 = convert(T2, big"0.0548112876863802643887753674810754475842153612931128785028369") - c12 = convert(T2, big"0.0848880518607165350639838930162674302064148175640019542045934") - c13 = convert(T2, big"0.265575603264642893098114059045616835297201264164077621448665") - c14 = convert(T2, 1 // 2) - c15 = convert(T2, big"0.734424396735357106901885940954383164702798735835922378551335") - c16 = convert(T2, big"0.915111948139283464936016106983732569793585182435998045795407") - c17 = convert(T2, big"0.947695431179199287562380162101836721649589325892740646458322") - c18 = convert(T2, 5 // 6) - c19 = convert(T2, big"0.288724941110620201935458488967024976908118598341806976469674") - c20 = convert(T2, big"0.671835709170513812712245661002797570438953420568682550710222") - c21 = convert(T2, 1 // 3) - c22 = convert(T2, 5 // 9) - c23 = convert(T2, 1 // 5) - c24 = convert(T2, 1) - - b1 = convert(T, 1 // 42) - b2 = convert(T, 234375 // 10000000) - b3 = convert(T, 3125 // 100000) - b4 = convert(T, 0) - b5 = convert(T, 1 // 24) - b6 = convert(T, 0) - b7 = convert(T, 1 // 20) - b8 = convert(T, 1 // 20) - b9 = convert(T, 0) - b10 = convert(T, 1 // 10) - b11 = convert(T, 1 // 14) - b12 = convert(T, 0) - b13 = convert(T, big"0.138413023680782974005350203145033146748813640089941234591267") - b14 = convert(T, big"0.215872690604931311708935511140681138965472074195773051123019") - b15 = convert(T, big"0.243809523809523809523809523809523809523809523809523809523810") - b16 = convert(T, big"0.215872690604931311708935511140681138965472074195773051123019") - b17 = convert(T, big"0.138413023680782974005350203145033146748813640089941234591267") - b18 = convert(T, big"-0.0714285714285714285714285714285714285714285714285714285714286") - b19 = convert(T, -1 // 10) - b20 = convert(T, -1 // 20) - b21 = convert(T, -1 // 20) - b22 = convert(T, -1 // 24) - b23 = convert(T, -3125 // 100000) - b24 = convert(T, -234375 // 10000000) - b25 = convert(T, 1 // 42) - - a0100 = convert(T, 1 // 5) - - a0200 = convert(T, big"-0.216049382716049382716049382716049382716049382716049382716049") - a0201 = convert(T, big"0.771604938271604938271604938271604938271604938271604938271605") - - a0300 = convert(T, 5 // 24) - a0302 = convert(T, 5 // 8) - - a0400 = convert(T, 29 // 150) - a0402 = convert(T, 11 // 50) - a0403 = convert(T, -2 // 25) - - a0500 = convert(T, 1 // 10) - a0503 = convert(T, 2 // 5) - a0504 = convert(T, 1 // 2) - - a0600 = convert(T, big"0.103364471650010477570395435690481791543342708330349879244197") - a0603 = convert(T, big"0.124053094528946761061581889237115328211074784955180298044074") - a0604 = convert(T, big"0.483171167561032899288836480451962508724109257517289177302380") - a0605 = convert(T, - big"-0.0387530245694763252085681443767620580395733302341368038804290") - - a0700 = convert(T, big"0.124038261431833324081904585980175168140024670698633612292480") - a0704 = convert(T, big"0.217050632197958486317846256953159942875916353757734167684657") - a0705 = convert(T, big"0.0137455792075966759812907801835048190594443990939408530842918") - a0706 = convert(T, - big"-0.0661095317267682844455831341498149531672668252085016565917546") - - a0800 = convert(T, big"0.0914774894856882983144991846980432197088832099976660100090486") - a0805 = convert(T, - big"-0.00544348523717469689965754944144838611346156873847009178068318") - a0806 = convert(T, big"0.0680716801688453518578515120895103863112751730758794372203952") - a0807 = convert(T, big"0.408394315582641046727306852653894780093303185664924644551239") - - a0900 = convert(T, big"0.0890013652502551018954509355423841780143232697403434118692699") - a0905 = convert(T, - big"0.00499528226645532360197793408420692800405891149406814091955810") - a0906 = convert(T, big"0.397918238819828997341739603001347156083435060931424970826304") - a0907 = convert(T, big"0.427930210752576611068192608300897981558240730580396406312359") - a0908 = convert(T, - big"-0.0865117637557827005740277475955029103267246394128995965941585") - - a1000 = convert(T, big"0.0695087624134907543112693906409809822706021061685544615255758") - a1005 = convert(T, big"0.129146941900176461970759579482746551122871751501482634045487") - a1006 = convert(T, big"1.53073638102311295076342566143214939031177504112433874313011") - a1007 = convert(T, big"0.577874761129140052546751349454576715334892100418571882718036") - a1008 = convert(T, big"-0.951294772321088980532340837388859453930924498799228648050949") - a1009 = convert(T, big"-0.408276642965631951497484981519757463459627174520978426909934") - - a1100 = convert(T, big"0.0444861403295135866269453507092463581620165501018684152933313") - a1105 = convert(T, - big"-0.00380476867056961731984232686574547203016331563626856065717964") - a1106 = convert(T, big"0.0106955064029624200721262602809059154469206077644957399593972") - a1107 = convert(T, big"0.0209616244499904333296674205928919920806734650660039898074652") - a1108 = convert(T, - big"-0.0233146023259321786648561431551978077665337818756053603898847") - a1109 = convert(T, - big"0.00263265981064536974369934736325334761174975280887405725010964") - a1110 = convert(T, - big"0.00315472768977025060103545855572111407955208306374459723959783") - - a1200 = convert(T, big"0.0194588815119755475588801096525317761242073762016273186231215") - a1208 = convert(T, - big"0.0000678512949171812509306121653452367476194364781259165332321534") - a1209 = convert(T, - big"-0.0000429795859049273623271005330230162343568863387724883603675550") - a1210 = convert(T, - big"0.0000176358982260285155407485928953302139937553442829975734148981") - a1211 = convert(T, big"0.0653866627415027051009595231385181033549511358787382098351924") - - a1300 = convert(T, big"0.206836835664277105916828174798272361078909196043446411598231") - a1308 = convert(T, big"0.0166796067104156472828045866664696450306326505094792505215514") - a1309 = convert(T, - big"-0.00879501563200710214457024178249986591130234990219959208704979") - a1310 = convert(T, - big"0.00346675455362463910824462315246379209427513654098596403637231") - a1311 = convert(T, big"-0.861264460105717678161432562258351242030270498966891201799225") - a1312 = convert(T, big"0.908651882074050281096239478469262145034957129939256789178785") - - a1400 = convert(T, big"0.0203926084654484010091511314676925686038504449562413004562382") - a1408 = convert(T, big"0.0869469392016685948675400555583947505833954460930940959577347") - a1409 = convert(T, - big"-0.0191649630410149842286436611791405053287170076602337673587681") - a1410 = convert(T, - big"0.00655629159493663287364871573244244516034828755253746024098838") - a1411 = convert(T, big"0.0987476128127434780903798528674033899738924968006632201445462") - a1412 = convert(T, - big"0.00535364695524996055083260173615567408717110247274021056118319") - a1413 = convert(T, big"0.301167864010967916837091303817051676920059229784957479998077") - - a1500 = convert(T, big"0.228410433917778099547115412893004398779136994596948545722283") - a1508 = convert(T, big"-0.498707400793025250635016567442511512138603770959682292383042") - a1509 = convert(T, big"0.134841168335724478552596703792570104791700727205981058201689") - a1510 = convert(T, - big"-0.0387458244055834158439904226924029230935161059142806805674360") - a1511 = convert(T, big"-1.27473257473474844240388430824908952380979292713250350199641") - a1512 = convert(T, big"1.43916364462877165201184452437038081875299303577911839630524") - a1513 = convert(T, big"-0.214007467967990254219503540827349569639028092344812795499026") - a1514 = convert(T, big"0.958202417754430239892724139109781371059908874605153648768037") - - a1600 = convert(T, big"2.00222477655974203614249646012506747121440306225711721209798") - a1608 = convert(T, big"2.06701809961524912091954656438138595825411859673341600679555") - a1609 = convert(T, big"0.623978136086139541957471279831494466155292316167021080663140") - a1610 = convert(T, - big"-0.0462283685500311430283203554129062069391947101880112723185773") - a1611 = convert(T, big"-8.84973288362649614860075246727118949286604835457092701094630") - a1612 = convert(T, big"7.74257707850855976227437225791835589560188590785037197433615") - a1613 = convert(T, big"-0.588358519250869210993353314127711745644125882130941202896436") - a1614 = convert(T, big"-1.10683733362380649395704708016953056176195769617014899442903") - a1615 = convert(T, big"-0.929529037579203999778397238291233214220788057511899747507074") - - a1700 = convert(T, big"3.13789533412073442934451608989888796808161259330322100268310") - a1705 = convert(T, big"0.129146941900176461970759579482746551122871751501482634045487") - a1706 = convert(T, big"1.53073638102311295076342566143214939031177504112433874313011") - a1707 = convert(T, big"0.577874761129140052546751349454576715334892100418571882718036") - a1708 = convert(T, big"5.42088263055126683050056840891857421941300558851862156403363") - a1709 = convert(T, big"0.231546926034829304872663800877643660904880180835945693836936") - a1710 = convert(T, big"0.0759292995578913560162301311785251873561801342333194895292058") - a1711 = convert(T, big"-12.3729973380186513287414553402595806591349822617535905976253") - a1712 = convert(T, big"9.85455883464769543935957209317369202080367765721777101906955") - a1713 = convert(T, big"0.0859111431370436529579357709052367772889980495122329601159540") - a1714 = convert(T, big"-5.65242752862643921117182090081762761180392602644189218673969") - a1715 = convert(T, big"-1.94300935242819610883833776782364287728724899124166920477873") - a1716 = convert(T, big"-0.128352601849404542018428714319344620742146491335612353559923") - - a1800 = convert(T, big"1.38360054432196014878538118298167716825163268489922519995564") - a1805 = convert(T, - big"0.00499528226645532360197793408420692800405891149406814091955810") - a1806 = convert(T, big"0.397918238819828997341739603001347156083435060931424970826304") - a1807 = convert(T, big"0.427930210752576611068192608300897981558240730580396406312359") - a1808 = convert(T, big"-1.30299107424475770916551439123047573342071475998399645982146") - a1809 = convert(T, big"0.661292278669377029097112528107513072734573412294008071500699") - a1810 = convert(T, big"-0.144559774306954349765969393688703463900585822441545655530145") - a1811 = convert(T, big"-6.96576034731798203467853867461083919356792248105919255460819") - a1812 = convert(T, big"6.65808543235991748353408295542210450632193197576935120716437") - a1813 = convert(T, big"-1.66997375108841486404695805725510845049807969199236227575796") - a1814 = convert(T, big"2.06413702318035263832289040301832647130604651223986452170089") - a1815 = convert(T, big"-0.674743962644306471862958129570837723192079875998405058648892") - a1816 = convert(T, - big"-0.00115618834794939500490703608435907610059605754935305582045729") - a1817 = convert(T, - big"-0.00544057908677007389319819914241631024660726585015012485938593") - - a1900 = convert(T, big"0.951236297048287669474637975894973552166903378983475425758226") - a1904 = convert(T, big"0.217050632197958486317846256953159942875916353757734167684657") - a1905 = convert(T, big"0.0137455792075966759812907801835048190594443990939408530842918") - a1906 = convert(T, - big"-0.0661095317267682844455831341498149531672668252085016565917546") - a1908 = convert(T, big"0.152281696736414447136604697040747131921486432699422112099617") - a1909 = convert(T, big"-0.337741018357599840802300793133998004354643424457539667670080") - a1910 = convert(T, - big"-0.0192825981633995781534949199286824400469353110630787982121133") - a1911 = convert(T, big"-3.68259269696866809932409015535499603576312120746888880201882") - a1912 = convert(T, big"3.16197870406982063541533528419683854018352080342887002331312") - a1913 = convert(T, big"-0.370462522106885290716991856022051125477943482284080569177386") - a1914 = convert(T, - big"-0.0514974200365440434996434456698127984941168616474316871020314") - a1915 = convert(T, - big"-0.000829625532120152946787043541792848416659382675202720677536554") - a1916 = convert(T, - big"0.00000279801041419278598986586589070027583961355402640879503213503") - a1917 = convert(T, big"0.0418603916412360287969841020776788461794119440689356178942252") - a1918 = convert(T, big"0.279084255090877355915660874555379649966282167560126269290222") - - a2000 = convert(T, big"0.103364471650010477570395435690481791543342708330349879244197") - a2003 = convert(T, big"0.124053094528946761061581889237115328211074784955180298044074") - a2004 = convert(T, big"0.483171167561032899288836480451962508724109257517289177302380") - a2005 = convert(T, - big"-0.0387530245694763252085681443767620580395733302341368038804290") - a2007 = convert(T, big"-0.438313820361122420391059788940960176420682836652600698580091") - a2009 = convert(T, big"-0.218636633721676647685111485017151199362509373698288330593486") - a2010 = convert(T, - big"-0.0312334764394719229981634995206440349766174759626578122323015") - a2017 = convert(T, big"0.0312334764394719229981634995206440349766174759626578122323015") - a2018 = convert(T, big"0.218636633721676647685111485017151199362509373698288330593486") - a2019 = convert(T, big"0.438313820361122420391059788940960176420682836652600698580091") - - a2100 = convert(T, 29 // 150) - a2102 = convert(T, 11 // 50) - a2103 = convert(T, -2 // 25) - a2106 = convert(T, big"0.0984256130499315928152900286856048243348202521491288575952143") - a2107 = convert(T, big"-0.196410889223054653446526504390100417677539095340135532418849") - a2109 = convert(T, big"0.436457930493068729391826122587949137609670676712525034763317") - a2110 = convert(T, big"0.0652613721675721098560370939805555698350543810708414716730270") - a2117 = convert(T, - big"-0.0652613721675721098560370939805555698350543810708414716730270") - a2118 = convert(T, big"-0.436457930493068729391826122587949137609670676712525034763317") - a2119 = convert(T, big"0.196410889223054653446526504390100417677539095340135532418849") - a2120 = convert(T, - big"-0.0984256130499315928152900286856048243348202521491288575952143") - - a2200 = convert(T, big"-0.216049382716049382716049382716049382716049382716049382716049") - a2201 = convert(T, big"0.771604938271604938271604938271604938271604938271604938271605") - a2204 = convert(T, -2 // 3) - a2206 = convert(T, big"-0.390696469295978451446999802258495981249099665294395945559163") - a2220 = convert(T, big"0.390696469295978451446999802258495981249099665294395945559163") - a2221 = convert(T, 2 // 3) - - a2300 = convert(T, 1 // 5) - a2302 = convert(T, big"-0.164609053497942386831275720164609053497942386831275720164609") - a2322 = convert(T, big"0.164609053497942386831275720164609053497942386831275720164609") - - a2400 = convert(T, big"1.47178724881110408452949550989023611293535315518571691939396") - a2401 = convert(T, 63 // 80) - a2402 = convert(T, 91 // 216) - a2404 = convert(T, 7 // 24) - a2406 = convert(T, big"0.348600717628329563206854421629657569274689947367847465753757") - a2407 = convert(T, big"0.229499544768994849582890233710555447073823569666506700662510") - a2408 = convert(T, big"5.79046485790481979159831978177003471098279506036722411333192") - a2409 = convert(T, big"0.418587511856506868874073759426596207226461447604248151080016") - a2410 = convert(T, big"0.307039880222474002649653817490106690389251482313213999386651") - a2411 = convert(T, big"-4.68700905350603332214256344683853248065574415794742040470287") - a2412 = convert(T, big"3.13571665593802262152038152399873856554395436199962915429076") - a2413 = convert(T, big"1.40134829710965720817510506275620441055845017313930508348898") - a2414 = convert(T, big"-5.52931101439499023629010306005764336421276055777658156400910") - a2415 = convert(T, big"-0.853138235508063349309546894974784906188927508039552519557498") - a2416 = convert(T, big"0.103575780373610140411804607167772795518293914458500175573749") - a2417 = convert(T, big"-0.140474416950600941142546901202132534870665923700034957196546") - a2418 = convert(T, big"-0.418587511856506868874073759426596207226461447604248151080016") - a2419 = convert(T, big"-0.229499544768994849582890233710555447073823569666506700662510") - a2420 = convert(T, big"-0.348600717628329563206854421629657569274689947367847465753757") - a2421 = convert(T, -7 // 24) - a2422 = convert(T, -91 // 216) - a2423 = convert(T, -63 // 80) - Feagin12ConstantCache(adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, - a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, - a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, - a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, - a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1208, - a1209, a1210, a1211, a1300, a1308, a1309, a1310, a1311, a1312, - a1400, a1408, a1409, a1410, a1411, a1412, a1413, a1500, a1508, - a1509, a1510, a1511, a1512, a1513, a1514, a1600, a1608, a1609, - a1610, a1611, a1612, a1613, a1614, a1615, a1700, a1705, a1706, - a1707, a1708, a1709, a1710, a1711, a1712, a1713, a1714, a1715, - a1716, a1800, a1805, a1806, a1807, a1808, a1809, a1810, a1811, - a1812, a1813, a1814, a1815, a1816, a1817, a1900, a1904, a1905, - a1906, a1908, a1909, a1910, a1911, a1912, a1913, a1914, a1915, - a1916, a1917, a1918, a2000, a2003, a2004, a2005, a2007, a2009, - a2010, a2017, a2018, a2019, a2100, a2102, a2103, a2106, a2107, - a2109, a2110, a2117, a2118, a2119, a2120, a2200, a2201, a2204, - a2206, a2220, a2221, a2300, a2302, a2322, a2400, a2401, a2402, - a2404, a2406, a2407, a2408, a2409, a2410, a2411, a2412, a2413, - a2414, a2415, a2416, a2417, a2418, a2419, a2420, a2421, a2422, - a2423, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, - c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, b1, b2, b3, - b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, - b18, b19, b20, b21, b22, b23, b24, b25) -end - -struct Feagin14ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - adaptiveConst::T - a0100::T - a0200::T - a0201::T - a0300::T - a0302::T - a0400::T - a0402::T - a0403::T - a0500::T - a0503::T - a0504::T - a0600::T - a0603::T - a0604::T - a0605::T - a0700::T - a0704::T - a0705::T - a0706::T - a0800::T - a0805::T - a0806::T - a0807::T - a0900::T - a0905::T - a0906::T - a0907::T - a0908::T - a1000::T - a1005::T - a1006::T - a1007::T - a1008::T - a1009::T - a1100::T - a1105::T - a1106::T - a1107::T - a1108::T - a1109::T - a1110::T - a1200::T - a1208::T - a1209::T - a1210::T - a1211::T - a1300::T - a1308::T - a1309::T - a1310::T - a1311::T - a1312::T - a1400::T - a1408::T - a1409::T - a1410::T - a1411::T - a1412::T - a1413::T - a1500::T - a1508::T - a1509::T - a1510::T - a1511::T - a1512::T - a1513::T - a1514::T - a1600::T - a1608::T - a1609::T - a1610::T - a1611::T - a1612::T - a1613::T - a1614::T - a1615::T - a1700::T - a1712::T - a1713::T - a1714::T - a1715::T - a1716::T - a1800::T - a1812::T - a1813::T - a1814::T - a1815::T - a1816::T - a1817::T - a1900::T - a1912::T - a1913::T - a1914::T - a1915::T - a1916::T - a1917::T - a1918::T - a2000::T - a2012::T - a2013::T - a2014::T - a2015::T - a2016::T - a2017::T - a2018::T - a2019::T - a2100::T - a2112::T - a2113::T - a2114::T - a2115::T - a2116::T - a2117::T - a2118::T - a2119::T - a2120::T - a2200::T - a2212::T - a2213::T - a2214::T - a2215::T - a2216::T - a2217::T - a2218::T - a2219::T - a2220::T - a2221::T - a2300::T - a2308::T - a2309::T - a2310::T - a2311::T - a2312::T - a2313::T - a2314::T - a2315::T - a2316::T - a2317::T - a2318::T - a2319::T - a2320::T - a2321::T - a2322::T - a2400::T - a2408::T - a2409::T - a2410::T - a2411::T - a2412::T - a2413::T - a2414::T - a2415::T - a2416::T - a2417::T - a2418::T - a2419::T - a2420::T - a2421::T - a2422::T - a2423::T - a2500::T - a2508::T - a2509::T - a2510::T - a2511::T - a2512::T - a2513::T - a2514::T - a2515::T - a2516::T - a2517::T - a2518::T - a2519::T - a2520::T - a2521::T - a2522::T - a2523::T - a2524::T - a2600::T - a2605::T - a2606::T - a2607::T - a2608::T - a2609::T - a2610::T - a2612::T - a2613::T - a2614::T - a2615::T - a2616::T - a2617::T - a2618::T - a2619::T - a2620::T - a2621::T - a2622::T - a2623::T - a2624::T - a2625::T - a2700::T - a2705::T - a2706::T - a2707::T - a2708::T - a2709::T - a2711::T - a2712::T - a2713::T - a2714::T - a2715::T - a2716::T - a2717::T - a2718::T - a2719::T - a2720::T - a2721::T - a2722::T - a2723::T - a2724::T - a2725::T - a2726::T - a2800::T - a2805::T - a2806::T - a2807::T - a2808::T - a2810::T - a2811::T - a2813::T - a2814::T - a2815::T - a2823::T - a2824::T - a2825::T - a2826::T - a2827::T - a2900::T - a2904::T - a2905::T - a2906::T - a2909::T - a2910::T - a2911::T - a2913::T - a2914::T - a2915::T - a2923::T - a2924::T - a2925::T - a2926::T - a2927::T - a2928::T - a3000::T - a3003::T - a3004::T - a3005::T - a3007::T - a3009::T - a3010::T - a3013::T - a3014::T - a3015::T - a3023::T - a3024::T - a3025::T - a3027::T - a3028::T - a3029::T - a3100::T - a3102::T - a3103::T - a3106::T - a3107::T - a3109::T - a3110::T - a3113::T - a3114::T - a3115::T - a3123::T - a3124::T - a3125::T - a3127::T - a3128::T - a3129::T - a3130::T - a3200::T - a3201::T - a3204::T - a3206::T - a3230::T - a3231::T - a3300::T - a3302::T - a3332::T - a3400::T - a3401::T - a3402::T - a3404::T - a3406::T - a3407::T - a3409::T - a3410::T - a3411::T - a3412::T - a3413::T - a3414::T - a3415::T - a3416::T - a3417::T - a3418::T - a3419::T - a3420::T - a3421::T - a3422::T - a3423::T - a3424::T - a3425::T - a3426::T - a3427::T - a3428::T - a3429::T - a3430::T - a3431::T - a3432::T - a3433::T - c1::T2 - c2::T2 - c3::T2 - c4::T2 - c5::T2 - c6::T2 - c7::T2 - c8::T2 - c9::T2 - c10::T2 - c11::T2 - c12::T2 - c13::T2 - c14::T2 - c15::T2 - c16::T2 - c17::T2 - c18::T2 - c19::T2 - c20::T2 - c21::T2 - c22::T2 - c23::T2 - c24::T2 - c25::T2 - c26::T2 - c27::T2 - c28::T2 - c29::T2 - c30::T2 - c31::T2 - c32::T2 - c33::T2 - c34::T2 - b1::T - b2::T - b3::T - b4::T - b5::T - b6::T - b7::T - b8::T - b9::T - b10::T - b11::T - b12::T - b13::T - b14::T - b15::T - b16::T - b17::T - b18::T - b19::T - b20::T - b21::T - b22::T - b23::T - b24::T - b25::T - b26::T - b27::T - b28::T - b29::T - b30::T - b31::T - b32::T - b33::T - b34::T - b35::T -end - -""" -constructFeagin14 -""" -function Feagin14ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - adaptiveConst = convert(T, 1 // 1000) - c1 = convert(T2, 1 // 9) - c2 = convert(T2, 5 // 9) - c3 = convert(T2, 5 // 6) - c4 = convert(T2, 1 // 3) - c5 = convert(T2, 1) - c6 = convert(T2, 0.669986979272772921764683785505998513938845229638460353285142) - c7 = convert(T2, 0.297068384213818357389584716808219413223332094698915687379168) - c8 = convert(T2, 8 // 11) - c9 = convert(T2, 0.140152799042188765276187487966946717629806463082532936287323) - c10 = convert(T2, 0.700701039770150737151099854830749337941407049265546408969222) - c11 = convert(T2, 4 // 11) - c12 = convert(T2, 0.263157894736842105263157894736842105263157894736842105263158) - c13 = convert(T2, 0.0392172246650270859125196642501208648863714315266128052078483) - c14 = convert(T2, 0.812917502928376762983393159278036506189612372617238550774312) - c15 = convert(T2, 1 // 6) - c16 = convert(T2, 9 // 10) - c17 = convert(T2, 0.0641299257451966923312771193896682809481096651615083225402924) - c18 = convert(T2, 0.204149909283428848927744634301023405027149505241333751628870) - c19 = convert(T2, 0.395350391048760565615671369827324372352227297456659450554577) - c20 = convert(T2, 0.604649608951239434384328630172675627647772702543340549445423) - c21 = convert(T2, 0.795850090716571151072255365698976594972850494758666248371130) - c22 = convert(T2, 0.935870074254803307668722880610331719051890334838491677459708) - c23 = convert(T2, 1 // 6) - c24 = convert(T2, 0.812917502928376762983393159278036506189612372617238550774312) - c25 = convert(T2, 0.0392172246650270859125196642501208648863714315266128052078483) - c26 = convert(T2, 4 // 11) - c27 = convert(T2, 0.700701039770150737151099854830749337941407049265546408969222) - c28 = convert(T2, 0.140152799042188765276187487966946717629806463082532936287323) - c29 = convert(T2, 0.297068384213818357389584716808219413223332094698915687379168) - c30 = convert(T2, 0.669986979272772921764683785505998513938845229638460353285142) - c31 = convert(T2, 1 // 3) - c32 = convert(T2, 5 // 9) - c33 = convert(T2, 1 // 9) - c34 = convert(T2, 1) - - b1 = convert(T, 1 // 56) - b2 = convert(T, 3 // 512) - b3 = convert(T, 3 // 256) - b4 = convert(T, 0) - b5 = convert(T, 9 // 512) - b6 = convert(T, 0) - b7 = convert(T, 3 // 128) - b8 = convert(T, 15 // 512) - b9 = convert(T, 0) - b10 = convert(T, 9 // 256) - b11 = convert(T, 21 // 512) - b12 = convert(T, 3 // 64) - b13 = convert(T, 0) - b14 = convert(T, 27 // 512) - b15 = convert(T, 15 // 256) - b16 = convert(T, 33 // 512) - b17 = convert(T, 0) - b18 = convert(T, 0.105352113571753019691496032887878162227673083080523884041670) - b19 = convert(T, 0.170561346241752182382120338553874085887555487802790804737501) - b20 = convert(T, 0.206229397329351940783526485701104894741914286259542454077972) - b21 = convert(T, 0.206229397329351940783526485701104894741914286259542454077972) - b22 = convert(T, 0.170561346241752182382120338553874085887555487802790804737501) - b23 = convert(T, 0.105352113571753019691496032887878162227673083080523884041670) - b24 = convert(T, -33 // 512) - b25 = convert(T, -15 // 256) - b26 = convert(T, -27 // 512) - b27 = convert(T, -3 // 64) - b28 = convert(T, -21 // 512) - b29 = convert(T, -9 // 256) - b30 = convert(T, -15 // 512) - b31 = convert(T, -3 // 128) - b32 = convert(T, -9 // 512) - b33 = convert(T, -3 // 256) - b34 = convert(T, -3 // 512) - b35 = convert(T, 1 // 56) - - a0100 = convert(T, 1 // 9) - - a0200 = convert(T, -5 // 6) - a0201 = convert(T, 25 // 18) - - a0300 = convert(T, 5 // 24) - a0302 = convert(T, 5 // 8) - - a0400 = convert(T, 29 // 150) - a0402 = convert(T, 11 // 50) - a0403 = convert(T, -2 // 25) - - a0500 = convert(T, 1 // 10) - a0503 = convert(T, 2 // 5) - a0504 = convert(T, 1 // 2) - - a0600 = convert(T, 0.103484561636679776672993546511910344499744798201971316606663) - a0603 = convert(T, 0.122068887306407222589644082868962077139592714834162134741275) - a0604 = convert(T, 0.482574490331246622475134780125688112865919023850168049679402) - a0605 = convert(T, -0.0381409600015606999730886240005620205664113072478411477421970) - - a0700 = convert(T, 0.124380526654094412881516420868799316268491466359671423163289) - a0704 = convert(T, 0.226120282197584301422238662979202901196752320742633143965145) - a0705 = convert(T, 0.0137885887618080880607695837016477814530969417491493385363543) - a0706 = convert(T, -0.0672210133996684449749399507414305856950086341525382182856200) - a0800 = convert(T, 0.0936919065659673815530885456083005933866349695217750085655603) - a0805 = convert(T, -0.00613406843450510987229498995641664735620914507128858871007099) - a0806 = convert(T, 0.216019825625503063708860097659866573490979433278117320188668) - a0807 = convert(T, 0.423695063515761937337619073960976753205867469544123532683116) - - a0900 = convert(T, 0.0838479812409052664616968791372814085980533139224911131069335) - a0905 = convert(T, -0.0117949367100973814319755056031295775367961960590736150777613) - a0906 = convert(T, -0.247299020568812652339473838743194598325992840353340132697498) - a0907 = convert(T, 0.0978080858367729012259313014081291665503740655476733940756599) - a0908 = convert(T, 0.217590689243420631360008651767860318344168120024782176879989) - - a1000 = convert(T, 0.0615255359769428227954562389614314714333423969064821107453940) - a1005 = convert(T, 0.00592232780324503308042990005798046524738389560444257136834990) - a1006 = convert(T, 0.470326159963841112217224303205894113455362530746108825010848) - a1007 = convert(T, 0.299688863848679000853981837096192399136831121671781279184194) - a1008 = convert(T, -0.247656877593994914689992276329810825853958069263947095548189) - a1009 = convert(T, 0.110895029771437682893999851839061714522445173600678718208625) - - a1100 = convert(T, 0.0419700073362782579861792864787277787213483656543104611245994) - a1105 = convert(T, -0.00317987696266205093901912847692712407988609169703103952205634) - a1106 = convert(T, 0.806397714906192077260821711520379506393543111567419750119748) - a1107 = convert(T, 0.0975983126412388979093522850684288851314672048003054550357187) - a1108 = convert(T, 0.778575578158398909027512446452927238999763460594181964958853) - a1109 = convert(T, 0.204890423831599428189499202098105603312029235081420653574829) - a1110 = convert(T, -1.56261579627468188307070943950527825211462892236424360892806) - - a1200 = convert(T, 0.0437726782233730163574465242495339811688214967071614123256973) - a1208 = convert(T, 0.00624365027520195208794358628580933625281631216903095917201250) - a1209 = convert(T, 0.200043097109577314994435165469647856829066232218264969608768) - a1210 = convert(T, -0.00805328367804983036823857162048902911923392887337029314844206) - a1211 = convert(T, 0.0211517528067396521915711903523399601316877825157550573051221) - - a1300 = convert(T, 0.0283499250363514563095023591920717312247137654896477097768495) - a1308 = convert(T, 0.00249163204855817407538949148805995149459884653585417680098222) - a1309 = convert(T, 0.0230138787854593149638399846373742768772087122638142234223658) - a1310 = convert(T, -0.00322155956692977098724476092467120878189463604760620461043308) - 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a2712 = convert(T, -11.4743154427289496968389492564352536350842454130853175250727) - a2713 = convert(T, 80.2593166576230272541702485886484400152793366623589989106256) - a2714 = convert(T, -0.384132303980042847625312526759029103746926841342088219165648) - a2715 = convert(T, 7.28147667468107583471326950926136115767612581862877764249646) - a2716 = convert(T, -0.132699384612248379510571708176035274836827341616751884314074) - a2717 = convert(T, -81.0799832525730726674679289752255240006070716633632990308935) - a2718 = convert(T, -1.25037492835620639521768185656179119962253747492403205797494) - a2719 = convert(T, 2.59263594969543681023776379504377324994226447359296887778718) - a2720 = convert(T, -0.301440298346404539830163997260526875264431537275641495291993) - a2721 = convert(T, 0.221384460789832337451706451572773791695246839057318414301020) - a2722 = convert(T, 0.0827577274771892931955989870974693152996276435429809890551210) - a2723 = convert(T, 18.9960662040611520464672450037243263998175161412237156872211) - a2724 = convert(T, 0.269231946409639685623468015128334167460051910348912845121977) - a2725 = convert(T, 1.62674827447066537462989364929628933988125029284183680279020) - a2726 = convert(T, 0.491719043846229147070666628704194097678081907210673044988866) - - a2800 = convert(T, 0.0838479812409052664616968791372814085980533139224911131069335) - a2805 = convert(T, -0.0117949367100973814319755056031295775367961960590736150777613) - a2806 = convert(T, -0.247299020568812652339473838743194598325992840353340132697498) - a2807 = convert(T, 0.0978080858367729012259313014081291665503740655476733940756599) - a2808 = convert(T, 0.217590689243420631360008651767860318344168120024782176879989) - a2810 = convert(T, 0.137585606763325224865659632196787746647447222975084865975440) - a2811 = convert(T, 0.0439870229715046685058790092341545026046103890294261359042581) - a2813 = convert(T, -0.513700813768193341957004456618630303738757363641964030086972) - a2814 = convert(T, 0.826355691151315508644211308399153458701423158616168576922372) - a2815 = convert(T, 25.7018139719811832625873882972519939511136556341960074626615) - a2823 = convert(T, -25.7018139719811832625873882972519939511136556341960074626615) - a2824 = convert(T, -0.826355691151315508644211308399153458701423158616168576922372) - a2825 = convert(T, 0.513700813768193341957004456618630303738757363641964030086972) - a2826 = convert(T, -0.0439870229715046685058790092341545026046103890294261359042581) - a2827 = convert(T, -0.137585606763325224865659632196787746647447222975084865975440) - - a2900 = convert(T, 0.124380526654094412881516420868799316268491466359671423163289) - a2904 = convert(T, 0.226120282197584301422238662979202901196752320742633143965145) - a2905 = convert(T, 0.0137885887618080880607695837016477814530969417491493385363543) - a2906 = convert(T, -0.0672210133996684449749399507414305856950086341525382182856200) - a2909 = convert(T, -0.856238975085428354755349769879501772112121597411563802855067) - a2910 = convert(T, -1.96337522866858908928262850028093813988180440518267404553576) - a2911 = convert(T, -0.232332822724119401237246257308921847250108199230419994978218) - a2913 = convert(T, 4.30660719086453349461668936876562947772432562053478092626764) - a2914 = convert(T, -2.92722963249465482659787911202390446687687394950633612630592) - a2915 = convert(T, -82.3131666397858944454492334105458707735761966428138676971041) - a2923 = convert(T, 82.3131666397858944454492334105458707735761966428138676971041) - a2924 = convert(T, 2.92722963249465482659787911202390446687687394950633612630592) - a2925 = convert(T, -4.30660719086453349461668936876562947772432562053478092626764) - a2926 = convert(T, 0.232332822724119401237246257308921847250108199230419994978218) - a2927 = convert(T, 1.96337522866858908928262850028093813988180440518267404553576) - a2928 = convert(T, 0.856238975085428354755349769879501772112121597411563802855067) - - a3000 = convert(T, 0.103484561636679776672993546511910344499744798201971316606663) - a3003 = convert(T, 0.122068887306407222589644082868962077139592714834162134741275) - a3004 = convert(T, 0.482574490331246622475134780125688112865919023850168049679402) - a3005 = convert(T, -0.0381409600015606999730886240005620205664113072478411477421970) - a3007 = convert(T, -0.550499525310802324138388507020508177411414311000037561712836) - a3009 = convert(T, -0.711915811585189227887648262043794387578291882406745570495765) - a3010 = convert(T, -0.584129605671551340432988730158480872095335329645227595707052) - a3013 = convert(T, 2.11046308125864932128717300046622750300375054278936987850718) - a3014 = convert(T, -0.0837494736739572135525742023001037992695260175335123517729291) - a3015 = convert(T, 5.10021499072320914075295969043344113107545060862804249161191) - a3023 = convert(T, -5.10021499072320914075295969043344113107545060862804249161191) - a3024 = convert(T, 0.0837494736739572135525742023001037992695260175335123517729291) - a3025 = convert(T, -2.11046308125864932128717300046622750300375054278936987850718) - a3027 = convert(T, 0.584129605671551340432988730158480872095335329645227595707052) - a3028 = convert(T, 0.711915811585189227887648262043794387578291882406745570495765) - a3029 = convert(T, 0.550499525310802324138388507020508177411414311000037561712836) - - a3100 = convert(T, 29 // 150) - a3102 = convert(T, 11 // 50) - a3103 = convert(T, -2 // 25) - a3106 = convert(T, 0.109993425580724703919462404865068340845119058295846426463652) - a3107 = convert(T, -0.254297048076270161384068506997153122141835626976703920846242) - a3109 = convert(T, 0.865570777116694254343770343821098281832847401233011859346737) - a3110 = convert(T, 3.32416449114093083106799552786572018336860092936986407160200) - a3113 = convert(T, -12.0102223315977933882352385148661841260301942633996815127277) - a3114 = convert(T, 0.476601466242493239430442776862061899602963782003580209476163) - a3115 = convert(T, -29.0243011221036390525802623213654099596251221332470910692353) - a3123 = convert(T, 29.0243011221036390525802623213654099596251221332470910692353) - a3124 = convert(T, -0.476601466242493239430442776862061899602963782003580209476163) - a3125 = convert(T, 12.0102223315977933882352385148661841260301942633996815127277) - a3127 = convert(T, -3.32416449114093083106799552786572018336860092936986407160200) - a3128 = convert(T, -0.865570777116694254343770343821098281832847401233011859346737) - a3129 = convert(T, 0.254297048076270161384068506997153122141835626976703920846242) - a3130 = convert(T, -0.109993425580724703919462404865068340845119058295846426463652) - - a3200 = convert(T, -5 // 6) - a3201 = convert(T, 25 // 18) - a3204 = convert(T, -3 // 4) - a3206 = convert(T, -0.492529543718026304422682049114021320200214681580657784719074) - a3230 = convert(T, 0.492529543718026304422682049114021320200214681580657784719074) - a3231 = convert(T, 3 // 4) - - a3300 = convert(T, 1 // 9) - a3302 = convert(T, -2 // 9) - a3332 = convert(T, 2 // 9) - - a3400 = convert(T, 0.285835140388971558796088842163836414852927537894596466840753) - a3401 = convert(T, 7 // 24) - a3402 = convert(T, 7 // 32) - a3404 = convert(T, 21 // 128) - a3406 = convert(T, 0.218194354945556658327188241581352107093288824322187941141516) - a3407 = convert(T, 0.180392898478697766863635221946775437719620053641849228562435) - a3409 = convert(T, 0.205713839404845018859120755122929542277570094982808905393991) - a3410 = convert(T, 0.242715791581770239970282927959446515762745971386670541948576) - a3411 = convert(T, 0.246465780813629305833609291181891407799228103869305705137021) - a3412 = convert(T, -3.44991940790890824979834154601622662060370460614931644223924) - a3413 = convert(T, 0.228875562160036081760729060738458584294220372552740218459295) - a3414 = convert(T, 0.283290599702151415321527419056733335978436595493855789831434) - a3415 = convert(T, 3.21085125837766640960131490544236787005557320332238705967955) - a3416 = convert(T, -0.223538777364845699920233756214162507964125230083674032084065) - a3417 = convert(T, -0.707121157204419073518727286207487212130091231955206160635271) - a3418 = convert(T, 3.21123345150287080408174729202856500893260034443022374267639) - a3419 = convert(T, 1.40954348309669766030414474301123175769045945573548986335553) - a3420 = convert(T, -0.151362053443742613121602276742518111090963026203676055891793) - a3421 = convert(T, 0.372350574527014276454724080214619984397121028202148298716575) - a3422 = convert(T, 0.252978746406361336722199907762141285915775728129414319261111) - a3423 = convert(T, -3.21085125837766640960131490544236787005557320332238705967955) - a3424 = convert(T, -0.283290599702151415321527419056733335978436595493855789831434) - a3425 = convert(T, -0.228875562160036081760729060738458584294220372552740218459295) - a3426 = convert(T, -0.246465780813629305833609291181891407799228103869305705137021) - a3427 = convert(T, -0.242715791581770239970282927959446515762745971386670541948576) - a3428 = convert(T, -0.205713839404845018859120755122929542277570094982808905393991) - a3429 = convert(T, -0.180392898478697766863635221946775437719620053641849228562435) - a3430 = convert(T, -0.218194354945556658327188241581352107093288824322187941141516) - a3431 = convert(T, -21 // 128) - a3432 = convert(T, -7 // 32) - a3433 = convert(T, -7 // 24) - Feagin14ConstantCache(adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, - a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, - a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, - a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, - a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1208, - a1209, a1210, a1211, a1300, a1308, a1309, a1310, a1311, a1312, - a1400, a1408, a1409, a1410, a1411, a1412, a1413, a1500, a1508, - a1509, a1510, a1511, a1512, a1513, a1514, a1600, a1608, a1609, - a1610, a1611, a1612, a1613, a1614, a1615, a1700, a1712, a1713, - a1714, a1715, a1716, a1800, a1812, a1813, a1814, a1815, a1816, - a1817, a1900, a1912, a1913, a1914, a1915, a1916, a1917, a1918, - a2000, a2012, a2013, a2014, a2015, a2016, a2017, a2018, a2019, - a2100, a2112, a2113, a2114, a2115, a2116, a2117, a2118, a2119, - a2120, a2200, a2212, a2213, a2214, a2215, a2216, a2217, a2218, - a2219, a2220, a2221, a2300, a2308, a2309, a2310, a2311, a2312, - a2313, a2314, a2315, a2316, a2317, a2318, a2319, a2320, a2321, - a2322, a2400, a2408, a2409, a2410, a2411, a2412, a2413, a2414, - a2415, a2416, a2417, a2418, a2419, a2420, a2421, a2422, a2423, - a2500, a2508, a2509, a2510, a2511, a2512, a2513, a2514, a2515, - a2516, a2517, a2518, a2519, a2520, a2521, a2522, a2523, a2524, - a2600, a2605, a2606, a2607, a2608, a2609, a2610, a2612, a2613, - a2614, a2615, a2616, a2617, a2618, a2619, a2620, a2621, a2622, - a2623, a2624, a2625, a2700, a2705, a2706, a2707, a2708, a2709, - a2711, a2712, a2713, a2714, a2715, a2716, a2717, a2718, a2719, - a2720, a2721, a2722, a2723, a2724, a2725, a2726, a2800, a2805, - a2806, a2807, a2808, a2810, a2811, a2813, a2814, a2815, a2823, - a2824, a2825, a2826, a2827, a2900, a2904, a2905, a2906, a2909, - a2910, a2911, a2913, a2914, a2915, a2923, a2924, a2925, a2926, - a2927, a2928, a3000, a3003, a3004, a3005, a3007, a3009, a3010, - a3013, a3014, a3015, a3023, a3024, a3025, a3027, a3028, a3029, - a3100, a3102, a3103, a3106, a3107, a3109, a3110, a3113, a3114, - a3115, a3123, a3124, a3125, a3127, a3128, a3129, a3130, a3200, - a3201, a3204, a3206, a3230, a3231, a3300, a3302, a3332, a3400, - a3401, a3402, a3404, a3406, a3407, a3409, a3410, a3411, a3412, - a3413, a3414, a3415, a3416, a3417, a3418, a3419, a3420, a3421, - a3422, a3423, a3424, a3425, a3426, a3427, a3428, a3429, a3430, - a3431, a3432, a3433, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, - c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, - c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, b1, b2, b3, b4, - b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, - b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31, - b32, b33, b34, b35) -end - -""" -constructFeagin14 -""" -function Feagin14ConstantCache(T::Type, T2::Type) - adaptiveConst = convert(T, 1 // 1000) - c1 = convert(T2, 1 // 9) - c2 = convert(T2, 5 // 9) - c3 = convert(T2, 5 // 6) - c4 = convert(T2, 1 // 3) - c5 = convert(T2, 1) - c6 = convert(T2, big"0.669986979272772921764683785505998513938845229638460353285142") - c7 = convert(T2, big"0.297068384213818357389584716808219413223332094698915687379168") - c8 = convert(T2, 8 // 11) - c9 = convert(T2, big"0.140152799042188765276187487966946717629806463082532936287323") - c10 = convert(T2, big"0.700701039770150737151099854830749337941407049265546408969222") - c11 = convert(T2, 4 // 11) - c12 = convert(T2, big"0.263157894736842105263157894736842105263157894736842105263158") - c13 = convert(T2, big"0.0392172246650270859125196642501208648863714315266128052078483") - c14 = convert(T2, big"0.812917502928376762983393159278036506189612372617238550774312") - c15 = convert(T2, 1 // 6) - c16 = convert(T2, 9 // 10) - c17 = convert(T2, big"0.0641299257451966923312771193896682809481096651615083225402924") - c18 = convert(T2, big"0.204149909283428848927744634301023405027149505241333751628870") - c19 = convert(T2, big"0.395350391048760565615671369827324372352227297456659450554577") - c20 = convert(T2, big"0.604649608951239434384328630172675627647772702543340549445423") - c21 = convert(T2, big"0.795850090716571151072255365698976594972850494758666248371130") - c22 = convert(T2, big"0.935870074254803307668722880610331719051890334838491677459708") - c23 = convert(T2, 1 // 6) - c24 = convert(T2, big"0.812917502928376762983393159278036506189612372617238550774312") - c25 = convert(T2, big"0.0392172246650270859125196642501208648863714315266128052078483") - c26 = convert(T2, 4 // 11) - c27 = convert(T2, big"0.700701039770150737151099854830749337941407049265546408969222") - c28 = convert(T2, big"0.140152799042188765276187487966946717629806463082532936287323") - c29 = convert(T2, big"0.297068384213818357389584716808219413223332094698915687379168") - c30 = convert(T2, big"0.669986979272772921764683785505998513938845229638460353285142") - c31 = convert(T2, 1 // 3) - c32 = convert(T2, 5 // 9) - c33 = convert(T2, 1 // 9) - c34 = convert(T2, 1) - - b1 = convert(T, 1 // 56) - b2 = convert(T, 3 // 512) - b3 = convert(T, 3 // 256) - b4 = convert(T, 0) - b5 = convert(T, 9 // 512) - b6 = convert(T, 0) - b7 = convert(T, 3 // 128) - b8 = convert(T, 15 // 512) - b9 = convert(T, 0) - b10 = convert(T, 9 // 256) - b11 = convert(T, 21 // 512) - b12 = convert(T, 3 // 64) - b13 = convert(T, 0) - b14 = convert(T, 27 // 512) - b15 = convert(T, 15 // 256) - b16 = convert(T, 33 // 512) - b17 = convert(T, 0) - b18 = convert(T, big"0.105352113571753019691496032887878162227673083080523884041670") - b19 = convert(T, big"0.170561346241752182382120338553874085887555487802790804737501") - b20 = convert(T, big"0.206229397329351940783526485701104894741914286259542454077972") - b21 = convert(T, big"0.206229397329351940783526485701104894741914286259542454077972") - b22 = convert(T, big"0.170561346241752182382120338553874085887555487802790804737501") - b23 = convert(T, big"0.105352113571753019691496032887878162227673083080523884041670") - b24 = convert(T, -33 // 512) - b25 = convert(T, -15 // 256) - b26 = convert(T, -27 // 512) - b27 = convert(T, -3 // 64) - b28 = convert(T, -21 // 512) - b29 = convert(T, -9 // 256) - b30 = convert(T, -15 // 512) - b31 = convert(T, -3 // 128) - b32 = convert(T, -9 // 512) - b33 = convert(T, -3 // 256) - b34 = convert(T, -3 // 512) - b35 = convert(T, 1 // 56) - - a0100 = convert(T, 1 // 9) - - a0200 = convert(T, -5 // 6) - a0201 = convert(T, 25 // 18) - - a0300 = convert(T, 5 // 24) - a0302 = convert(T, 5 // 8) - - a0400 = convert(T, 29 // 150) - a0402 = convert(T, 11 // 50) - a0403 = convert(T, -2 // 25) - - a0500 = convert(T, 1 // 10) - a0503 = convert(T, 2 // 5) - a0504 = convert(T, 1 // 2) - - a0600 = convert(T, big"0.103484561636679776672993546511910344499744798201971316606663") - a0603 = convert(T, big"0.122068887306407222589644082868962077139592714834162134741275") - a0604 = convert(T, big"0.482574490331246622475134780125688112865919023850168049679402") - a0605 = convert(T, - big"-0.0381409600015606999730886240005620205664113072478411477421970") - - a0700 = convert(T, big"0.124380526654094412881516420868799316268491466359671423163289") - a0704 = convert(T, big"0.226120282197584301422238662979202901196752320742633143965145") - a0705 = convert(T, big"0.0137885887618080880607695837016477814530969417491493385363543") - a0706 = convert(T, - big"-0.0672210133996684449749399507414305856950086341525382182856200") - a0800 = convert(T, big"0.0936919065659673815530885456083005933866349695217750085655603") - a0805 = convert(T, - big"-0.00613406843450510987229498995641664735620914507128858871007099") - a0806 = convert(T, big"0.216019825625503063708860097659866573490979433278117320188668") - a0807 = convert(T, big"0.423695063515761937337619073960976753205867469544123532683116") - - a0900 = convert(T, big"0.0838479812409052664616968791372814085980533139224911131069335") - a0905 = convert(T, - big"-0.0117949367100973814319755056031295775367961960590736150777613") - a0906 = convert(T, big"-0.247299020568812652339473838743194598325992840353340132697498") - a0907 = convert(T, big"0.0978080858367729012259313014081291665503740655476733940756599") - a0908 = convert(T, big"0.217590689243420631360008651767860318344168120024782176879989") - - a1000 = convert(T, big"0.0615255359769428227954562389614314714333423969064821107453940") - a1005 = convert(T, - big"0.00592232780324503308042990005798046524738389560444257136834990") - a1006 = convert(T, big"0.470326159963841112217224303205894113455362530746108825010848") - a1007 = convert(T, big"0.299688863848679000853981837096192399136831121671781279184194") - a1008 = convert(T, big"-0.247656877593994914689992276329810825853958069263947095548189") - a1009 = convert(T, big"0.110895029771437682893999851839061714522445173600678718208625") - - a1100 = convert(T, big"0.0419700073362782579861792864787277787213483656543104611245994") - a1105 = convert(T, - big"-0.00317987696266205093901912847692712407988609169703103952205634") - a1106 = convert(T, big"0.806397714906192077260821711520379506393543111567419750119748") - a1107 = convert(T, big"0.0975983126412388979093522850684288851314672048003054550357187") - a1108 = convert(T, big"0.778575578158398909027512446452927238999763460594181964958853") - a1109 = convert(T, big"0.204890423831599428189499202098105603312029235081420653574829") - a1110 = convert(T, big"-1.56261579627468188307070943950527825211462892236424360892806") - - a1200 = convert(T, big"0.0437726782233730163574465242495339811688214967071614123256973") - a1208 = convert(T, - big"0.00624365027520195208794358628580933625281631216903095917201250") - a1209 = convert(T, big"0.200043097109577314994435165469647856829066232218264969608768") - a1210 = convert(T, - big"-0.00805328367804983036823857162048902911923392887337029314844206") - a1211 = convert(T, big"0.0211517528067396521915711903523399601316877825157550573051221") - - a1300 = convert(T, big"0.0283499250363514563095023591920717312247137654896477097768495") - a1308 = convert(T, - big"0.00249163204855817407538949148805995149459884653585417680098222") - a1309 = convert(T, big"0.0230138787854593149638399846373742768772087122638142234223658") - a1310 = convert(T, - big"-0.00322155956692977098724476092467120878189463604760620461043308") - a1311 = convert(T, - big"0.00988442549447664668946335414487885256040819982786014648129297") - a1312 = convert(T, - big"-0.0213010771328887351384307642875927384886634565429572466632092") - - a1400 = convert(T, big"0.343511894290243001049432234735147943083353174980701426268122") - a1408 = convert(T, big"0.210451912023627385609097011999010655788807405225626700040882") - a1409 = convert(T, big"1.03427452057230411936482926828825709938667999698324740166559") - a1410 = convert(T, - big"0.00600303645864422487051240448206640574939078092406156945568306") - a1411 = convert(T, big"0.855938125099619537578012106002407728915062652616416005816477") - a1412 = convert(T, big"-0.977235005036766810872264852372525633013107656892839677696022") - a1413 = convert(T, big"-0.660026980479294694616225013856327693720573981219974874776419") - - a1500 = convert(T, - big"-0.0143574001672168069538206399935076366657755954378399880691949") - a1508 = convert(T, - big"-0.0366253270049039970293685796848974791733119081733552207318285") - a1509 = convert(T, big"0.0350254975636213681976849406979846524346789082471103574920148") - a1510 = convert(T, big"0.0360946016362113508931786658758335239823689929864237671348749") - a1511 = convert(T, - big"-0.0265219967553681106351595946834601923649627012457464284442911") - a1512 = convert(T, big"0.0445699011305698119638911537508839908104336323082226770910408") - a1513 = convert(T, big"0.124343093331358243286225595741786448038973408895106741855721") - a1514 = convert(T, - big"0.00413829693239480694403512496204335960426192908674476033832967") - - a1600 = convert(T, big"0.356032404425120290975609116398089176264106222379748802654822") - a1608 = convert(T, big"-0.450192758947562595966821779075956175110645100214763601190349") - a1609 = convert(T, big"0.430527907083710898626656292808782917793030154094709462877146") - a1610 = convert(T, big"0.511973029011022237668556960394071692077125787030651386389972") - a1611 = convert(T, big"0.908303638886404260390159124638110213997496214819904630546596") - a1612 = convert(T, big"-1.23921093371933931757372469151534028854413889248605726186520") - a1613 = convert(T, big"-0.649048661671761465141672348879062553905402831967191097656668") - a1614 = convert(T, big"0.251708904586819292210480529948970541404887852931447491219418") - a1615 = convert(T, big"0.779906470345586398810756795282334476023540593411550187024263") - - a1700 = convert(T, big"0.0130935687406513066406881206418834980127470438213192487844956") - a1712 = convert(T, - big"-0.0000932053067985113945908461962767108237858631509684667142124826") - a1713 = convert(T, big"0.0505374334262299359640090443138590726770942344716122381702746") - a1714 = convert(T, - big"8.04470341944487979109579109610197797641311868930865361048975e-7") - a1715 = convert(T, - big"0.000591726029494171190528755742777717259844340971924321528178248") - a1716 = convert(T, - big"-4.01614722154557337064691684906375587732264247950093804676867e-7") - 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a1915 = convert(T, big"-4.71415495727125020678778179392224757011323373221820091641216") - a1916 = convert(T, - big"-0.00176367657545349242053841995032797673574903886695600132759652") - a1917 = convert(T, big"7.64130548038698765563029310880237651185173367813936997648198") - a1918 = convert(T, big"3.50602043659751834989896082949744710968212949893375368243588") - - a2000 = convert(T, big"11.9514650694120686799372385830716401674473610826553517297976") - a2012 = convert(T, big"7.79480932108175968783516700231764388220284279598980948538579") - a2013 = convert(T, big"-56.4501393867325792523560991120904281440468100061340556540132") - a2014 = convert(T, big"0.0912376306930644901344530449290276645709607450403673704844997") - a2015 = convert(T, big"-12.7336279925434886201945524309199275038162717529918963305155") - a2016 = convert(T, - big"-0.0396895921904719712313542810939736674712383070433147873009352") - a2017 = convert(T, big"54.4392141883570886996225765155307791861438378423305337073797") - a2018 = convert(T, big"-3.64411637921569236846406990361350645806721478409266709351203") - a2019 = convert(T, big"-0.804503249910509910899030787958579499315694913210787878260459") - - a2100 = convert(T, big"-148.809426507100488427838868268647625561930612082148597076690") - a2112 = convert(T, big"-91.7295278291256484357935662402321623495228729036354276506427") - a2113 = convert(T, big"707.656144971598359834575719286335716154821128966649565194286") - a2114 = convert(T, big"-1.10563611857482440905296961311590930801338308942637769555540") - a2115 = convert(T, big"176.134591883811372587859898076055660406999516762301689616841") - a2116 = convert(T, big"0.491384824214880662268898345164454557416884631402764792538746") - a2117 = convert(T, big"-684.278000449814944358237535610895081956077167893600278300805") - a2118 = convert(T, big"27.9910604998398258984224332124380407446002518400668657974589") - a2119 = convert(T, big"13.1939710030282333443670964371153238435064159623744975073252") - a2120 = convert(T, big"1.25128781283980445450114974148056006317268830077396406361417") - - a2200 = convert(T, big"-9.67307946948196763644126118433219395839951408571877262880482") - a2212 = convert(T, big"-4.46990150858505531443846227701960360497830681408751431146712") - a2213 = convert(T, big"45.5127128690952681968241950400052751178905907817398483534845") - a2214 = convert(T, - big"-0.0713085086183826912791492024438246129930559805352394367050813") - a2215 = convert(T, big"11.2273614068412741582590624479939384207826800776794485051540") - a2216 = convert(T, big"0.126244376717622724516237912909138809361786889819105426371393") - a2217 = convert(T, big"-43.5439339549483313605810624907242107623814304467621407753424") - a2218 = convert(T, big"0.787174307543058978398792994996550902064546091443233850464377") - a2219 = convert(T, big"0.532264696744684215669300708603886690785395776821503851830821") - a2220 = convert(T, big"0.422422733996325326010225127471388772575086538809603346825334") - a2221 = convert(T, big"0.0859131249503067107308438031499859443441115056294154956487671") - - a2300 = convert(T, big"-10.0664032447054702403396606900426891472202824757968765569183") - a2308 = convert(T, - big"-0.0366253270049039970293685796848974791733119081733552207318285") - a2309 = convert(T, big"0.0350254975636213681976849406979846524346789082471103574920148") - a2310 = convert(T, big"0.0360946016362113508931786658758335239823689929864237671348749") - a2311 = convert(T, - big"-0.0265219967553681106351595946834601923649627012457464284442911") - a2312 = convert(T, big"-6.27088972181464143590553149478871603839356122957396018530209") - a2313 = convert(T, big"48.2079237442562989090702103008195063923492593141636117832993") - a2314 = convert(T, - big"-0.0694471689136165640882395180583732834557754169149088630301342") - a2315 = convert(T, big"12.6810690204850295698341370913609807066108483811412127009785") - a2316 = convert(T, big"0.0119671168968323754838161435501011294100927813964199613229864") - a2317 = convert(T, big"-46.7249764992482408003358268242662695593201321659795608950429") - a2318 = convert(T, big"1.33029613326626711314710039298216591399033511191227101321435") - a2319 = convert(T, big"1.00766787503398298353438903619926657771162717793661719708370") - a2320 = convert(T, big"0.0209512051933665091664122388475480702892770753864487241177616") - a2321 = convert(T, big"0.0210134706331264177317735424331396407424412188443757490871603") - a2322 = convert(T, - big"0.00952196014417121794175101542454575907376360233658356240547761") - - a2400 = convert(T, big"-409.478081677743708772589097409370357624424341606752069725341") - a2408 = convert(T, big"0.210451912023627385609097011999010655788807405225626700040882") - a2409 = convert(T, big"1.03427452057230411936482926828825709938667999698324740166559") - a2410 = convert(T, - big"0.00600303645864422487051240448206640574939078092406156945568306") - a2411 = convert(T, big"0.855938125099619537578012106002407728915062652616416005816477") - a2412 = convert(T, big"-250.516998547447860492777657729316130386584050420782075966990") - a2413 = convert(T, big"1946.42466652388427766053750328264758595829850895761428240231") - a2414 = convert(T, big"-3.04503882102310365506105809086860882786950544097602101685174") - a2415 = convert(T, big"490.626379528281713521208265299168083841598542274061671576230") - a2416 = convert(T, big"1.56647589531270907115484067013597445739595615245966775329993") - a2417 = convert(T, big"-1881.97428994011173362217267377035870619215906638453056643641") - a2418 = convert(T, big"75.2592224724847175278837713643303149821620618914245864351135") - a2419 = convert(T, big"34.5734356980331067622434344736554689696728644793551014989002") - a2420 = convert(T, big"3.21147679440968961435417361847073755169022966748891627882572") - a2421 = convert(T, big"-0.460408041738414391307201404237058848867245095265382820823055") - a2422 = convert(T, - big"-0.0870718339841810522431884137957986245724252047388936572215438") - a2423 = convert(T, big"-7.39351814158303067567016952195521063999185773249132944724553") - - a2500 = convert(T, big"3.43347475853550878921093496257596781120623891072008459930197") - a2508 = convert(T, - big"0.00249163204855817407538949148805995149459884653585417680098222") - a2509 = convert(T, big"0.0230138787854593149638399846373742768772087122638142234223658") - a2510 = convert(T, - big"-0.00322155956692977098724476092467120878189463604760620461043308") - a2511 = convert(T, - big"0.00988442549447664668946335414487885256040819982786014648129297") - a2512 = convert(T, big"2.16252799377922507788307841904757354045759225335732707916530") - a2513 = convert(T, big"-16.2699864546457421328065640660139489006987552040228852402716") - a2514 = convert(T, big"-0.128534502120524552843583417470935010538029037542654506231743") - a2515 = convert(T, big"-8.98915042666504253089307820833379330486511746063552853023189") - a2516 = convert(T, - big"-0.00348595363232025333387080201851013650192401767250513765000963") - a2517 = convert(T, big"15.7936194113339807536235187388695574135853387025139738341334") - a2518 = convert(T, big"-0.574403330914095065628165482017335820148383663195675408024658") - a2519 = convert(T, big"-0.345602039021393296692722496608124982535237228827655306030152") - a2520 = convert(T, - big"-0.00662241490206585091731619991383757781133067992707418687587487") - a2521 = convert(T, - big"-0.00777788129242204164032546458607364309759347209626759111946150") - a2522 = convert(T, - big"-0.00356084192402274913338827232697437364675240818791706587952939") - a2523 = convert(T, big"4.79282506449930799649797749629840189457296934139359048988332") - a2524 = convert(T, big"0.153725464873068577844576387402512082757034273069877432944621") - - a2600 = convert(T, big"32.3038520871985442326994734440031535091364975047784630088983") - a2605 = convert(T, - big"-0.00317987696266205093901912847692712407988609169703103952205634") - a2606 = convert(T, big"0.806397714906192077260821711520379506393543111567419750119748") - a2607 = convert(T, big"0.0975983126412388979093522850684288851314672048003054550357187") - a2608 = convert(T, big"0.778575578158398909027512446452927238999763460594181964958853") - a2609 = convert(T, big"0.204890423831599428189499202098105603312029235081420653574829") - a2610 = convert(T, big"-1.56261579627468188307070943950527825211462892236424360892806") - a2612 = convert(T, big"16.3429891882310570648504243973927174708753353504154550405647") - a2613 = convert(T, big"-154.544555293543621230730189631471036399316683669609116705323") - a2614 = convert(T, big"1.56971088703334872692034283417621761466263593582497085955201") - a2615 = convert(T, big"3.27685545087248131321429817269900731165522404974733504794135") - a2616 = convert(T, - big"-0.0503489245193653176348040727199783626534081095691632396802451") - a2617 = convert(T, big"153.321151858041665070593767885914694011224363102594556731397") - a2618 = convert(T, big"7.17568186327720495846766484814784143567826308034865369443637") - a2619 = convert(T, big"-2.94036748675300481945917659896930989215320594380777597403592") - a2620 = convert(T, - big"-0.0665845946076803144470749676022628870281920493197256887985612") - a2621 = convert(T, - big"-0.0462346054990843661229248668562217261176966514016859284197145") - a2622 = convert(T, - big"-0.0204198733585679401539388228617269778848579774821581777675337") - a2623 = convert(T, big"-53.3523106438735850515953441165998107974045090495791591218714") - a2624 = convert(T, big"-1.35548714715078654978732186705996404017554501614191325114947") - a2625 = convert(T, big"-1.57196275801232751882901735171459249177687219114442583461866") - - a2700 = convert(T, big"-16.6451467486341512872031294403931758764560371130818978459405") - a2705 = convert(T, - big"0.00592232780324503308042990005798046524738389560444257136834990") - a2706 = convert(T, big"0.470326159963841112217224303205894113455362530746108825010848") - a2707 = convert(T, big"0.299688863848679000853981837096192399136831121671781279184194") - a2708 = convert(T, big"-0.247656877593994914689992276329810825853958069263947095548189") - a2709 = convert(T, big"0.110895029771437682893999851839061714522445173600678718208625") - a2711 = convert(T, big"-0.491719043846229147070666628704194097678081907210673044988866") - a2712 = convert(T, big"-11.4743154427289496968389492564352536350842454130853175250727") - a2713 = convert(T, big"80.2593166576230272541702485886484400152793366623589989106256") - a2714 = convert(T, big"-0.384132303980042847625312526759029103746926841342088219165648") - a2715 = convert(T, big"7.28147667468107583471326950926136115767612581862877764249646") - a2716 = convert(T, big"-0.132699384612248379510571708176035274836827341616751884314074") - a2717 = convert(T, big"-81.0799832525730726674679289752255240006070716633632990308935") - a2718 = convert(T, big"-1.25037492835620639521768185656179119962253747492403205797494") - a2719 = convert(T, big"2.59263594969543681023776379504377324994226447359296887778718") - a2720 = convert(T, big"-0.301440298346404539830163997260526875264431537275641495291993") - a2721 = convert(T, big"0.221384460789832337451706451572773791695246839057318414301020") - a2722 = convert(T, big"0.0827577274771892931955989870974693152996276435429809890551210") - a2723 = convert(T, big"18.9960662040611520464672450037243263998175161412237156872211") - a2724 = convert(T, big"0.269231946409639685623468015128334167460051910348912845121977") - a2725 = convert(T, big"1.62674827447066537462989364929628933988125029284183680279020") - a2726 = convert(T, big"0.491719043846229147070666628704194097678081907210673044988866") - - a2800 = convert(T, big"0.0838479812409052664616968791372814085980533139224911131069335") - a2805 = convert(T, - big"-0.0117949367100973814319755056031295775367961960590736150777613") - a2806 = convert(T, big"-0.247299020568812652339473838743194598325992840353340132697498") - a2807 = convert(T, big"0.0978080858367729012259313014081291665503740655476733940756599") - a2808 = convert(T, big"0.217590689243420631360008651767860318344168120024782176879989") - a2810 = convert(T, big"0.137585606763325224865659632196787746647447222975084865975440") - a2811 = convert(T, big"0.0439870229715046685058790092341545026046103890294261359042581") - a2813 = convert(T, big"-0.513700813768193341957004456618630303738757363641964030086972") - a2814 = convert(T, big"0.826355691151315508644211308399153458701423158616168576922372") - a2815 = convert(T, big"25.7018139719811832625873882972519939511136556341960074626615") - a2823 = convert(T, big"-25.7018139719811832625873882972519939511136556341960074626615") - a2824 = convert(T, big"-0.826355691151315508644211308399153458701423158616168576922372") - a2825 = convert(T, big"0.513700813768193341957004456618630303738757363641964030086972") - a2826 = convert(T, - big"-0.0439870229715046685058790092341545026046103890294261359042581") - a2827 = convert(T, big"-0.137585606763325224865659632196787746647447222975084865975440") - - a2900 = convert(T, big"0.124380526654094412881516420868799316268491466359671423163289") - a2904 = convert(T, big"0.226120282197584301422238662979202901196752320742633143965145") - a2905 = convert(T, big"0.0137885887618080880607695837016477814530969417491493385363543") - a2906 = convert(T, - big"-0.0672210133996684449749399507414305856950086341525382182856200") - a2909 = convert(T, big"-0.856238975085428354755349769879501772112121597411563802855067") - a2910 = convert(T, big"-1.96337522866858908928262850028093813988180440518267404553576") - a2911 = convert(T, big"-0.232332822724119401237246257308921847250108199230419994978218") - a2913 = convert(T, big"4.30660719086453349461668936876562947772432562053478092626764") - a2914 = convert(T, big"-2.92722963249465482659787911202390446687687394950633612630592") - a2915 = convert(T, big"-82.3131666397858944454492334105458707735761966428138676971041") - a2923 = convert(T, big"82.3131666397858944454492334105458707735761966428138676971041") - a2924 = convert(T, big"2.92722963249465482659787911202390446687687394950633612630592") - a2925 = convert(T, big"-4.30660719086453349461668936876562947772432562053478092626764") - a2926 = convert(T, big"0.232332822724119401237246257308921847250108199230419994978218") - a2927 = convert(T, big"1.96337522866858908928262850028093813988180440518267404553576") - a2928 = convert(T, big"0.856238975085428354755349769879501772112121597411563802855067") - - a3000 = convert(T, big"0.103484561636679776672993546511910344499744798201971316606663") - a3003 = convert(T, big"0.122068887306407222589644082868962077139592714834162134741275") - a3004 = convert(T, big"0.482574490331246622475134780125688112865919023850168049679402") - a3005 = convert(T, - big"-0.0381409600015606999730886240005620205664113072478411477421970") - a3007 = convert(T, big"-0.550499525310802324138388507020508177411414311000037561712836") - a3009 = convert(T, big"-0.711915811585189227887648262043794387578291882406745570495765") - a3010 = convert(T, big"-0.584129605671551340432988730158480872095335329645227595707052") - a3013 = convert(T, big"2.11046308125864932128717300046622750300375054278936987850718") - a3014 = convert(T, - big"-0.0837494736739572135525742023001037992695260175335123517729291") - a3015 = convert(T, big"5.10021499072320914075295969043344113107545060862804249161191") - a3023 = convert(T, big"-5.10021499072320914075295969043344113107545060862804249161191") - a3024 = convert(T, big"0.0837494736739572135525742023001037992695260175335123517729291") - a3025 = convert(T, big"-2.11046308125864932128717300046622750300375054278936987850718") - a3027 = convert(T, big"0.584129605671551340432988730158480872095335329645227595707052") - a3028 = convert(T, big"0.711915811585189227887648262043794387578291882406745570495765") - a3029 = convert(T, big"0.550499525310802324138388507020508177411414311000037561712836") - - a3100 = convert(T, 29 // 150) - a3102 = convert(T, 11 // 50) - a3103 = convert(T, -2 // 25) - a3106 = convert(T, big"0.109993425580724703919462404865068340845119058295846426463652") - a3107 = convert(T, big"-0.254297048076270161384068506997153122141835626976703920846242") - a3109 = convert(T, big"0.865570777116694254343770343821098281832847401233011859346737") - a3110 = convert(T, big"3.32416449114093083106799552786572018336860092936986407160200") - a3113 = convert(T, big"-12.0102223315977933882352385148661841260301942633996815127277") - a3114 = convert(T, big"0.476601466242493239430442776862061899602963782003580209476163") - a3115 = convert(T, big"-29.0243011221036390525802623213654099596251221332470910692353") - a3123 = convert(T, big"29.0243011221036390525802623213654099596251221332470910692353") - a3124 = convert(T, big"-0.476601466242493239430442776862061899602963782003580209476163") - a3125 = convert(T, big"12.0102223315977933882352385148661841260301942633996815127277") - a3127 = convert(T, big"-3.32416449114093083106799552786572018336860092936986407160200") - a3128 = convert(T, big"-0.865570777116694254343770343821098281832847401233011859346737") - a3129 = convert(T, big"0.254297048076270161384068506997153122141835626976703920846242") - a3130 = convert(T, big"-0.109993425580724703919462404865068340845119058295846426463652") - - a3200 = convert(T, -5 // 6) - a3201 = convert(T, 25 // 18) - a3204 = convert(T, -3 // 4) - a3206 = convert(T, big"-0.492529543718026304422682049114021320200214681580657784719074") - a3230 = convert(T, big"0.492529543718026304422682049114021320200214681580657784719074") - a3231 = convert(T, 3 // 4) - - a3300 = convert(T, 1 // 9) - a3302 = convert(T, -2 // 9) - a3332 = convert(T, 2 // 9) - - a3400 = convert(T, big"0.285835140388971558796088842163836414852927537894596466840753") - a3401 = convert(T, 7 // 24) - a3402 = convert(T, 7 // 32) - a3404 = convert(T, 21 // 128) - a3406 = convert(T, big"0.218194354945556658327188241581352107093288824322187941141516") - a3407 = convert(T, big"0.180392898478697766863635221946775437719620053641849228562435") - a3409 = convert(T, big"0.205713839404845018859120755122929542277570094982808905393991") - a3410 = convert(T, big"0.242715791581770239970282927959446515762745971386670541948576") - a3411 = convert(T, big"0.246465780813629305833609291181891407799228103869305705137021") - a3412 = convert(T, big"-3.44991940790890824979834154601622662060370460614931644223924") - a3413 = convert(T, big"0.228875562160036081760729060738458584294220372552740218459295") - a3414 = convert(T, big"0.283290599702151415321527419056733335978436595493855789831434") - a3415 = convert(T, big"3.21085125837766640960131490544236787005557320332238705967955") - a3416 = convert(T, big"-0.223538777364845699920233756214162507964125230083674032084065") - a3417 = convert(T, big"-0.707121157204419073518727286207487212130091231955206160635271") - a3418 = convert(T, big"3.21123345150287080408174729202856500893260034443022374267639") - a3419 = convert(T, big"1.40954348309669766030414474301123175769045945573548986335553") - a3420 = convert(T, big"-0.151362053443742613121602276742518111090963026203676055891793") - a3421 = convert(T, big"0.372350574527014276454724080214619984397121028202148298716575") - a3422 = convert(T, big"0.252978746406361336722199907762141285915775728129414319261111") - a3423 = convert(T, big"-3.21085125837766640960131490544236787005557320332238705967955") - a3424 = convert(T, big"-0.283290599702151415321527419056733335978436595493855789831434") - a3425 = convert(T, big"-0.228875562160036081760729060738458584294220372552740218459295") - a3426 = convert(T, big"-0.246465780813629305833609291181891407799228103869305705137021") - a3427 = convert(T, big"-0.242715791581770239970282927959446515762745971386670541948576") - a3428 = convert(T, big"-0.205713839404845018859120755122929542277570094982808905393991") - a3429 = convert(T, big"-0.180392898478697766863635221946775437719620053641849228562435") - a3430 = convert(T, big"-0.218194354945556658327188241581352107093288824322187941141516") - a3431 = convert(T, -21 // 128) - a3432 = convert(T, -7 // 32) - a3433 = convert(T, -7 // 24) - Feagin14ConstantCache(adaptiveConst, a0100, a0200, a0201, a0300, a0302, a0400, a0402, - a0403, a0500, a0503, a0504, a0600, a0603, a0604, a0605, a0700, - a0704, a0705, a0706, a0800, a0805, a0806, a0807, a0900, a0905, - a0906, a0907, a0908, a1000, a1005, a1006, a1007, a1008, a1009, - a1100, a1105, a1106, a1107, a1108, a1109, a1110, a1200, a1208, - a1209, a1210, a1211, a1300, a1308, a1309, a1310, a1311, a1312, - a1400, a1408, a1409, a1410, a1411, a1412, a1413, a1500, a1508, - a1509, a1510, a1511, a1512, a1513, a1514, a1600, a1608, a1609, - a1610, a1611, a1612, a1613, a1614, a1615, a1700, a1712, a1713, - a1714, a1715, a1716, a1800, a1812, a1813, a1814, a1815, a1816, - a1817, a1900, a1912, a1913, a1914, a1915, a1916, a1917, a1918, - a2000, a2012, a2013, a2014, a2015, a2016, a2017, a2018, a2019, - a2100, a2112, a2113, a2114, a2115, a2116, a2117, a2118, a2119, - a2120, a2200, a2212, a2213, a2214, a2215, a2216, a2217, a2218, - a2219, a2220, a2221, a2300, a2308, a2309, a2310, a2311, a2312, - a2313, a2314, a2315, a2316, a2317, a2318, a2319, a2320, a2321, - a2322, a2400, a2408, a2409, a2410, a2411, a2412, a2413, a2414, - a2415, a2416, a2417, a2418, a2419, a2420, a2421, a2422, a2423, - a2500, a2508, a2509, a2510, a2511, a2512, a2513, a2514, a2515, - a2516, a2517, a2518, a2519, a2520, a2521, a2522, a2523, a2524, - a2600, a2605, a2606, a2607, a2608, a2609, a2610, a2612, a2613, - a2614, a2615, a2616, a2617, a2618, a2619, a2620, a2621, a2622, - a2623, a2624, a2625, a2700, a2705, a2706, a2707, a2708, a2709, - a2711, a2712, a2713, a2714, a2715, a2716, a2717, a2718, a2719, - a2720, a2721, a2722, a2723, a2724, a2725, a2726, a2800, a2805, - a2806, a2807, a2808, a2810, a2811, a2813, a2814, a2815, a2823, - a2824, a2825, a2826, a2827, a2900, a2904, a2905, a2906, a2909, - a2910, a2911, a2913, a2914, a2915, a2923, a2924, a2925, a2926, - a2927, a2928, a3000, a3003, a3004, a3005, a3007, a3009, a3010, - a3013, a3014, a3015, a3023, a3024, a3025, a3027, a3028, a3029, - a3100, a3102, a3103, a3106, a3107, a3109, a3110, a3113, a3114, - a3115, a3123, a3124, a3125, a3127, a3128, a3129, a3130, a3200, - a3201, a3204, a3206, a3230, a3231, a3300, a3302, a3332, a3400, - a3401, a3402, a3404, a3406, a3407, a3409, a3410, a3411, a3412, - a3413, a3414, a3415, a3416, a3417, a3418, a3419, a3420, a3421, - a3422, a3423, a3424, a3425, a3426, a3427, a3428, a3429, a3430, - a3431, a3432, a3433, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, - c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, - c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, b1, b2, b3, b4, - b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, - b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31, - b32, b33, b34, b35) -end From 2dd099932eea1f4261e802158ad97fe112fa6e3c Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 11:00:42 -0400 Subject: [PATCH 22/71] Delete src/tableaus/rkc_tableaus.jl --- src/tableaus/rkc_tableaus.jl | 37731 --------------------------------- 1 file changed, 37731 deletions(-) delete mode 100644 src/tableaus/rkc_tableaus.jl diff --git a/src/tableaus/rkc_tableaus.jl b/src/tableaus/rkc_tableaus.jl deleted file mode 100644 index 5142663360..0000000000 --- a/src/tableaus/rkc_tableaus.jl +++ /dev/null @@ -1,37731 +0,0 @@ -function ROCK2ConstantCache(T, T2, zprev) - ms = SVector{46, Int}( - 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, - 20, - 22, 24, 26, 28, 30, 33, 36, 39, 43, 47, 51, 56, 61, 66, 72, 78, - 85, 93, - 102, 112, 123, 135, 148, 163, 180, 198) - fp1 = SVector{46, T}(0.4102693550421609e+00, 0.3889624104727243e+00, - 0.3804692420283886e+00, - 0.3760815680865637e+00, 0.3735177579729938e+00, - 0.3719340231904236e+00, - 0.3708571145968057e+00, 0.3700947006022557e+00, - 0.3695328931459086e+00, - 0.3691085831661758e+00, 0.3687813249652330e+00, - 0.3685244707068931e+00, - 0.3683185599507446e+00, 0.3681542178682514e+00, - 0.3680181997765286e+00, - 0.3679084456991284e+00, 0.3678181571053212e+00, - 0.3678314333608541e+00, - 0.3677897070402892e+00, 0.3681800192470787e+00, - 0.3681272993461229e+00, - 0.3680840569645587e+00, 0.3680522380648169e+00, - 0.3680263578626069e+00, - 0.3680061275157194e+00, 0.3679837719607466e+00, - 0.3679668653311732e+00, - 0.3679542340323301e+00, 0.3679429332584250e+00, - 0.3679349432021754e+00, - 0.3679290943359695e+00, 0.3679242023884676e+00, - 0.3679207541681089e+00, - 0.3679185472223537e+00, 0.3679168690130640e+00, - 0.3679158588043139e+00, - 0.3679154592969145e+00, 0.3679154025286917e+00, - 0.3679157536198652e+00, - 0.3679163676763697e+00, 0.3679171904021983e+00, - 0.3679181786833088e+00, - 0.3679192462983425e+00, 0.3679204323079710e+00, - 0.3679216942157868e+00, - 0.3679229127010114e+00) - fp2 = SVector{46, T}(0.4495196112243335e+00, 0.4219428123056774e+00, - 0.4084335547255627e+00, - 0.4009301129475925e+00, 0.3963598727888637e+00, - 0.3934034185789226e+00, - 0.3913676516238603e+00, 0.3899091428928617e+00, - 0.3888276962996660e+00, - 0.3880048656683555e+00, 0.3873650613539532e+00, - 0.3868583585730354e+00, - 0.3864499054795832e+00, 0.3861178821587815e+00, - 0.3858426294881124e+00, - 0.3856144554520791e+00, 0.3854228843194507e+00, - 0.3853156085078759e+00, - 0.3851902798680153e+00, 0.3853705093720269e+00, - 0.3851957294861824e+00, - 0.3850587241670235e+00, 0.3849515900397918e+00, - 0.3848648995575697e+00, - 0.3847945082231300e+00, 0.3847117224407400e+00, - 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(0.783969323650751, -0.353613571196170, -0.368922535023076, 0.615238813023293)] - fpbe = [(1.13509972110540, -0.584333360989720, -0.319172911177732, 0.482853558185876, - 0.109256697110981) - (1.00479199674788, -0.436644602461537, -0.423443966877378, 0.538770645909717, - 0.0795300735974956) - (0.984907410167693, -0.403297625005343, - -0.485090625106059, 0.576309835350610, - 0.0609198451735942) - (0.980171201303714, -0.394437889689979, - -0.517381582925487, 0.601142288908999, - 0.0476702174069568) - (0.974834695776200, -0.392308952799017, - -0.530263724070033, 0.616510618632796, - 0.0379946019218839) - (0.966668353329992, -0.391741144639394, - -0.531455776704021, 0.625494551194751, - 0.0308158334011040) - (0.956319747720222, -0.391138376736994, - -0.526142643689543, 0.630404554467362, - 0.0254019467466823) - (0.943587787064690, -0.389377300510789, - -0.516876350192269, 0.632531861517858, - 0.0212476873553974) - (0.929868441621807, -0.386750527439590, - -0.505935645060380, 0.633001592986906, - 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32.01137420331927074812, -10.28571466942930534572, - -37.58600600492959387111, 66.81980314062600712077, - 84.74613000143813223985, 23.68169873246636214503 - ] - - ESERK5ConstantCache{eltype(Bᵢ), typeof(zprev)}(ms, Cᵤ, Cₑ, zprev, Bᵢ, 1, 0, 0) -end - -function ESERK4ConstantCache(zprev) - ms = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 30, 40, 50, 60, 70, 80, 90, 100, 150, 200, - 250, 300, 350, 400, 450, 500, 600, - 700, 800, 900, 1000, 1200, 1400, 1600, 1800, 2000, 2200, 2400, 2600, 2800, 3000, - 3200, 3400, 3600, 3800, 4000] - Cᵤ = [-1, 24, -81, 64] - Cₑ = [-1, 12, -27, 16] - Bᵢ = [0.12903031034899166767, 0.49462625286801110977, - 0.37634343678299722256, -0.25248538379384922845, - 0.0065129464125214976767, 0.077186857588232424888, - 0.55518167170340454810, 0.61360390808969075779, - 0.026821833388298651543, -0.23844614933200639399, - -0.76943611658030427733, -0.052379853152861735529, - 0.014179167753833524172, 0.92215895856320626202, - 1.0971021593598339691, 0.25456740224713096152, - 0.046650908225896002831, 0.14338240606715926211, - 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-20.80314428518122582545, - -11.48007557487890650805, - -99.45913530520893175435, - -127.66646432102561448119, - -65.61709295377363559965, - 70.66941495892984903548, - 37.73163341575367013547, - -73.97028738574550743579, - 35.18193967713015268828, - 19.14350966385481811471, - -31.24337219345173011220, - 11.26167684401785784587, - 20.50027594670260810972, - -31.03533399658952873779, - 20.38267912327755126967, - 8.38055290684768117160, - -33.01373855522565747833, - 45.88276800444496217324, - -37.58204107623698320140, - 16.35542952840734187703, - 12.26655723814102572078, - -34.95785722075888912741, - 46.67547811637160037890, - -42.35634730729276498096, - 25.20070471583354176914, - -3.05557751834216073661, - -32.68200404871337383383, - 39.17203469108222435580, - -56.67152186777419586861, - 29.33664264266302268425, - -12.40728425687574265623, - -36.80806072994491984218, - 49.39944913786461455629, - -64.99048699911270432494, - 23.18834908788356941045, - 11.39764521259193408298, - -69.88133776318845491460, - 66.01441542283289720672, - -40.47425030698735781698, - -47.08386844823964878515, - 85.83103776576542998100, - -75.86892865654905904194, - -44.70208057149678637643, - 118.85946623263288302041, - -66.39265933694959187505, - -148.35987806289784884939, - 117.05895508641614810585, - 269.80962036825997074629, - 168.49451658549256194419, - 47.10829220619891799515, - 5.11169642004104218813 - ] - - SERK2ConstantCache{eltype(Bᵢ), typeof(zprev)}(ms, zprev, Bᵢ, 1, 0, 0) -end From 47ea1ef0243b4d95aeaa0e0d101a3abe6b4905be Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 11:00:58 -0400 Subject: [PATCH 23/71] Delete src/tableaus/rkn_tableaus.jl --- src/tableaus/rkn_tableaus.jl | 2472 ---------------------------------- 1 file changed, 2472 deletions(-) delete mode 100644 src/tableaus/rkn_tableaus.jl diff --git a/src/tableaus/rkn_tableaus.jl b/src/tableaus/rkn_tableaus.jl deleted file mode 100644 index c9b50e05ff..0000000000 --- a/src/tableaus/rkn_tableaus.jl +++ /dev/null @@ -1,2472 +0,0 @@ -struct FineRKN4ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - c1::T2 - c2::T2 - c3::T2 - c4::T2 - c5::T2 - a21::T - a31::T - a32::T - a41::T - #a42::T - a43::T - a51::T - a52::T - a53::T - a54::T - abar21::T - abar31::T - abar32::T - abar41::T - abar42::T - abar43::T - abar51::T - abar52::T - abar53::T - abar54::T - b1::T - #b2::T - b3::T - b4::T - b5::T - bbar1::T - #bbar2::T - bbar3::T - bbar4::T - bbar5::T - btilde1::T - #btilde2::T - btilde3::T - btilde4::T - btilde5::T - bptilde1::T - #bptilde2::T - bptilde3::T - bptilde4::T - bptilde5::T -end - -function FineRKN4ConstantCache(T::Type, T2::Type) - c1 = convert(T2, 1 // 1) - c2 = convert(T2, 2 // 9) - c3 = convert(T2, 1 // 3) - c4 = convert(T2, 3 // 4) - c5 = convert(T2, 1 // 1) - a21 = convert(T, 2 // 81) - a31 = convert(T, 1 // 36) - a32 = convert(T, 1 // 36) - a41 = convert(T, 9 // 128) - #a42 = convert(T, 0 // 1) - a43 = convert(T, 27 // 128) - a51 = convert(T, 11 // 60) - a52 = convert(T, -3 // 20) - a53 = convert(T, 9 // 25) - a54 = convert(T, 8 // 75) - abar21 = convert(T, 2 // 9) - abar31 = convert(T, 1 // 12) - abar32 = convert(T, 1 // 4) - abar41 = convert(T, 69 // 128) - abar42 = convert(T, -243 // 128) - abar43 = convert(T, 135 // 64) - abar51 = convert(T, -17 // 12) - abar52 = convert(T, 27 // 4) - abar53 = convert(T, -27 // 5) - abar54 = convert(T, 16 // 15) - b1 = convert(T, 19 // 180) - #b2 = convert(T, 0 // 1) - b3 = convert(T, 63 // 200) - b4 = convert(T, 16 // 225) - b5 = convert(T, 1 // 120) - bbar1 = convert(T, 1 // 9) - #bbar2 = convert(T, 0 // 1) - bbar3 = convert(T, 9 // 20) - bbar4 = convert(T, 16 // 45) - bbar5 = convert(T, 1 // 12) - btilde1 = convert(T, 25 // 1116) - #btilde2 = convert(T, 0 // 1) - btilde3 = convert(T, -63 // 1240) - btilde4 = convert(T, 64 // 1395) - btilde5 = convert(T, -13 // 744) - bptilde1 = convert(T, 2 // 125) - #bptilde2 = convert(T, 0 // 1) - bptilde3 = convert(T, -27 // 625) - bptilde4 = convert(T, 32 // 625) - bptilde5 = convert(T, -3 // 125) - FineRKN4ConstantCache(c1, c2, c3, c4, c5, a21, a31, a32, a41, a43, a51, - a52, a53, a54, abar21, abar31, abar32, abar41, abar42, abar43, abar51, - abar52, abar53, abar54, b1, b3, b4, b5, bbar1, bbar3, bbar4, bbar5, btilde1, - btilde3, btilde4, btilde5, bptilde1, - bptilde3, bptilde4, bptilde5) -end - -struct FineRKN5ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - c1::T2 - c2::T2 - c3::T2 - c4::T2 - c5::T2 - c6::T2 - c7::T2 - a21::T - a31::T - a32::T - a41::T - #a42::T - a43::T - a51::T - a52::T - a53::T - a54::T - a61::T - a62::T - a63::T - a64::T - #a65::T - a71::T - #a72::T - a73::T - a74::T - a75::T - #a76::T - abar21::T - abar31::T - abar32::T - abar41::T - abar42::T - abar43::T - abar51::T - abar52::T - abar53::T - abar54::T - abar61::T - abar62::T - abar63::T - abar64::T - abar65::T - abar71::T - #abar72::T - abar73::T - abar74::T - abar75::T - abar76::T - b1::T - #b2::T - b3::T - b4::T - b5::T - #b6::T - #b7::T - bbar1::T - #bbar2::T - bbar3::T - bbar4::T - bbar5::T - bbar6::T - #bbar7::T - btilde1::T - #btilde2::T - btilde3::T - btilde4::T - btilde5::T - #btilde6::T - #btilde7::T - bptilde1::T - #bptilde2::T - bptilde3::T - bptilde4::T - bptilde5::T - bptilde6::T - bptilde7::T -end - -function FineRKN5ConstantCache(T::Type, T2::Type) - c1 = convert(T2, 1 // 1) - c2 = convert(T2, 8 // 39) - c3 = convert(T2, 4 // 13) - c4 = convert(T2, 5 // 6) - c5 = convert(T2, 43 // 47) - c6 = convert(T2, 1 // 1) # 36463 // 36464 - c7 = convert(T2, 1 // 1) - a21 = convert(T, 32 // 1521) - a31 = convert(T, 4 // 169) - a32 = convert(T, 4 // 169) - a41 = convert(T, 175 // 5184) - #a42 = convert(T, 0 // 1) - a43 = convert(T, 1625 // 5184) - a51 = convert(T, -342497279 // 5618900760) - a52 = convert(T, 6827067 // 46824173) - a53 = convert(T, 35048741 // 102161832) - a54 = convert(T, -2201514 // 234120865) - a61 = convert(T, -7079 // 52152) - a62 = convert(T, 767 // 2173) - a63 = convert(T, 14027 // 52152) - a64 = convert(T, 30 // 2173) - #a65 = convert(T, 0 // 1) - a71 = convert(T, 4817 // 51600) - #a72 = convert(T, 0 // 1) - a73 = convert(T, 388869 // 1216880) - a74 = convert(T, 3276 // 23575) - a75 = convert(T, -1142053 // 22015140) - #a76 = convert(T, 0 // 1) - abar21 = convert(T, 8 // 39) - abar31 = convert(T, 1 // 13) - abar32 = convert(T, 3 // 13) - abar41 = convert(T, 7385 // 6912) - abar42 = convert(T, -9425 // 2304) - abar43 = convert(T, 13325 // 3456) - abar51 = convert(T, 223324757 // 91364240) - abar52 = convert(T, -174255393 // 18272848) - abar53 = convert(T, 382840094 // 46824173) - abar54 = convert(T, -39627252 // 234120865) - abar61 = convert(T, 108475 // 36464) - abar62 = convert(T, -9633 // 848) - abar63 = convert(T, 7624604 // 806183) - abar64 = convert(T, 8100 // 49979) - abar65 = convert(T, -4568212 // 19446707) - abar71 = convert(T, 4817 // 51600) - #abar72 = convert(T, 0 // 1) - abar73 = convert(T, 1685099 // 3650640) - abar74 = convert(T, 19656 // 23575) - abar75 = convert(T, -53676491 // 88060560) - abar76 = convert(T, 53 // 240) - b1 = convert(T, 4817 // 51600) - #b2 = convert(T, 0 // 1) - b3 = convert(T, 388869 // 1216880) - b4 = convert(T, 3276 // 23575) - b5 = convert(T, -1142053 // 22015140) - #b6 = convert(T, 0 // 1) - #b7 = convert(T, 0 // 1) - bbar1 = convert(T, 4817 // 51600) - #bbar2 = convert(T, 0 // 1) - bbar3 = convert(T, 1685099 // 3650640) - bbar4 = convert(T, 19656 // 23575) - bbar5 = convert(T, -53676491 // 88060560) - bbar6 = convert(T, 53 // 240) - #bbar7 = convert(T, 0 // 1) - btilde1 = convert(T, 8151 // 2633750) - #btilde2 = convert(T, 0 // 1) - btilde3 = convert(T, -1377519 // 186334750) - btilde4 = convert(T, 586872 // 28879375) - btilde5 = convert(T, -36011118 // 2247378875) - #btilde6 = convert(T, 0 // 1) - #btilde7 = convert(T, 0 // 1) - bptilde1 = convert(T, 8151 // 2633750) - #bptilde2 = convert(T, 0 // 1) - bptilde3 = convert(T, -5969249 // 559004250) - bptilde4 = convert(T, 3521232 // 28879375) - bptilde5 = convert(T, -846261273 // 4494757750) - bptilde6 = convert(T, 4187 // 36750) - bptilde7 = convert(T, -1 // 25) - FineRKN5ConstantCache(c1, c2, c3, c4, c5, c6, c7, a21, a31, a32, a41, a43, a51, - a52, a53, a54, a61, a62, a63, a64, a71, a73, a74, a75, - abar21, abar31, abar32, abar41, abar42, abar43, abar51, - abar52, abar53, abar54, abar61, abar62, abar63, abar64, abar65, - abar71, abar73, abar74, abar75, abar76, b1, b3, b4, - b5, bbar1, bbar3, bbar4, bbar5, bbar6, btilde1, btilde3, btilde4, btilde5, bptilde1, - bptilde3, bptilde4, bptilde5, bptilde6, bptilde7) -end - -struct IRKN3ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - bconst1::T - bconst2::T - c1::T2 - a21::T - b1::T - b2::T - bbar1::T - bbar2::T -end - -function IRKN3ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - bconst1 = convert(T, 1.5) - bconst2 = convert(T, -0.5) - c1 = convert(T2, 0.5) - a21 = convert(T, 0.125) - b1 = convert(T, 0.6666666666666666) - b2 = convert(T, 0.8333333333333334) - bbar1 = convert(T, 0.3333333333333333) - bbar2 = convert(T, 0.4166666666666667) - IRKN3ConstantCache(bconst1, bconst2, c1, a21, b1, b2, bbar1, bbar2) -end - -function IRKN3ConstantCache(T::Type, T2::Type) - bconst1 = convert(T, 3 // 2) - bconst2 = convert(T, -1 // 2) - c1 = convert(T2, 1 // 2) - a21 = convert(T, 1 // 8) - b1 = convert(T, 2 // 3) - b2 = convert(T, 5 // 6) - bbar1 = convert(T, 1 // 3) - bbar2 = convert(T, 5 // 12) - IRKN3ConstantCache(bconst1, bconst2, c1, a21, b1, b2, bbar1, bbar2) -end - -struct IRKN4ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - bconst1::T - bconst2::T - c1::T2 - c2::T2 - a21::T - # a31::T - a32::T - b1::T - b2::T - b3::T - bbar1::T - bbar2::T - bbar3::T -end - -function IRKN4ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - bconst1 = convert(T, 1.5) - bconst2 = convert(T, -0.5) - c1 = convert(T2, 0.25) - c2 = convert(T2, 0.75) - a21 = convert(T, 0.03125) - # a31 = convert(T,0) - a32 = convert(T, 0.28125) - b1 = convert(T, 1.0555555555555556) - b2 = convert(T, -0.16666666666666666) - b3 = convert(T, 0.6111111111111112) - bbar1 = convert(T, -0.05555555555555555) - bbar2 = convert(T, 0.2916666666666667) - bbar3 = convert(T, 0.125) - IRKN4ConstantCache(bconst1, bconst2, c1, c2, a21, a32, b1, b2, b3, bbar1, bbar2, bbar3) -end - -function IRKN4ConstantCache(T::Type, T2::Type) - bconst1 = convert(T, 3 // 2) - bconst2 = convert(T, -1 // 2) - c1 = convert(T2, 1 // 4) - c2 = convert(T2, 3 // 4) - a21 = convert(T, 1 // 32) - # a31 = convert(T,0) - a32 = convert(T, 9 // 32) - b1 = convert(T, 19 // 18) - b2 = convert(T, -1 // 6) - b3 = convert(T, 11 // 18) - bbar1 = convert(T, -1 // 18) - bbar2 = convert(T, 7 // 24) - bbar3 = convert(T, 1 // 8) - IRKN4ConstantCache(bconst1, bconst2, c1, c2, a21, a32, b1, b2, b3, bbar1, bbar2, bbar3) -end - -struct Nystrom5VelocityIndependentConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - c1::T2 - c2::T2 - a21::T - a31::T - a32::T - a41::T - a42::T - a43::T - bbar1::T - bbar2::T - bbar3::T - b1::T - b2::T - b3::T - b4::T -end - -function Nystrom5VelocityIndependentConstantCache(T::Type{<:CompiledFloats}, - T2::Type{<:CompiledFloats}) - c1 = convert(T2, 0.2) - c2 = convert(T2, 0.6666666666666666) - # c3 = convert(T2,1) - a21 = convert(T, 0.02) - a31 = convert(T, -0.037037037037037035) - a32 = convert(T, 0.25925925925925924) - a41 = convert(T, 0.3) - a42 = convert(T, -0.05714285714285714) - a43 = convert(T, 0.2571428571428571) - bbar1 = convert(T, 0.041666666666666664) - bbar2 = convert(T, 0.2976190476190476) - bbar3 = convert(T, 0.16071428571428573) - b1 = bbar1 - b2 = convert(T, 0.37202380952380953) - b3 = convert(T, 0.48214285714285715) - b4 = convert(T, 0.10416666666666667) - Nystrom5VelocityIndependentConstantCache(c1, c2, a21, a31, a32, a41, a42, a43, bbar1, - bbar2, bbar3, b1, b2, b3, b4) -end - -function Nystrom5VelocityIndependentConstantCache(T::Type, T2::Type) - c1 = convert(T2, 1 // 5) - c2 = convert(T2, 2 // 3) - # c3 = convert(T2,1) - a21 = convert(T, 1 // 50) - a31 = convert(T, -1 // 27) - a32 = convert(T, 7 // 27) - a41 = convert(T, 3 // 10) - a42 = convert(T, -2 // 35) - a43 = convert(T, 9 // 35) - bbar1 = convert(T, 14 // 336) - bbar2 = convert(T, 100 // 336) - bbar3 = convert(T, 54 // 336) - b1 = bbar1 - b2 = convert(T, 125 // 336) - b3 = convert(T, 162 // 336) - b4 = convert(T, 35 // 336) - Nystrom5VelocityIndependentConstantCache(c1, c2, a21, a31, a32, a41, a42, a43, bbar1, - bbar2, bbar3, b1, b2, b3, b4) -end - -struct ERKN4ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - c1::T2 - c2::T2 - c3::T2 - a21::T - a31::T - a32::T - a41::T - a42::T - a43::T - b1::T - b2::T - b3::T - b4::T - bp1::T # bp denotes bprime - bp2::T - bp3::T - bp4::T - btilde1::T - btilde2::T - btilde3::T - btilde4::T - bptilde1::T - bptilde2::T - bptilde3::T - bptilde4::T -end - -function ERKN4ConstantCache(T::Type, T2::Type) - c1 = convert(T2, 1 // 4) - c2 = convert(T2, 7 // 10) - c3 = convert(T2, 1) - a21 = convert(T, 1 // 32) - a31 = convert(T, 19 // 600) - a32 = convert(T, 16 // 75) - a41 = convert(T, 32 // 315) - a42 = convert(T, 58 // 315) - a43 = convert(T, 3 // 14) - btilde1 = convert(T, 1 // 21 - 14 // 375) - btilde2 = convert(T, 28 // 81 - 136 // 375) - btilde3 = convert(T, 50 // 567 - 2 // 25) - btilde4 = convert(T, 1 // 54 - 1 // 50) - bptilde1 = convert(T, 1 // 14 - 17 // 231) - bptilde2 = convert(T, 32 // 81 - 116 // 297) - bptilde3 = convert(T, 250 // 567 - 925 // 2079) - bptilde4 = convert(T, 5 // 54 - 1 // 11) - b1 = convert(T, 1 // 21) - b2 = convert(T, 28 // 81) - b3 = convert(T, 50 // 567) - b4 = convert(T, 1 // 54) - bp1 = convert(T, 1 // 14) - bp2 = convert(T, 32 // 81) - bp3 = convert(T, 250 // 567) - bp4 = convert(T, 5 // 54) - ERKN4ConstantCache(c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, b4, bp1, bp2, - bp3, bp4, btilde1, btilde2, btilde3, btilde4, bptilde1, bptilde2, - bptilde3, bptilde4) -end - -function ERKN4ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - ERKN4ConstantCache(convert(T2, 0.25), - convert(T2, 0.7), - convert(T2, 1.0), - convert(T, 0.03125), - convert(T, 0.03166666666666667), - convert(T, 0.21333333333333335), - convert(T, 0.10158730158730159), - convert(T, 0.18412698412698414), - convert(T, 0.21428571428571427), - convert(T, 0.047619047619047616), - convert(T, 0.345679012345679), - convert(T, 0.08818342151675485), - convert(T, 0.018518518518518517), - convert(T, 0.07142857142857142), - convert(T, 0.3950617283950617), - convert(T, 0.4409171075837742), - convert(T, 0.09259259259259259), - convert(T, 0.010285714285714285), - convert(T, -0.016987654320987654), - convert(T, 0.00818342151675485), - convert(T, -0.0014814814814814814), - convert(T, -0.0021645021645021645), - convert(T, 0.004489337822671156), - convert(T, -0.004008337341670675), - convert(T, 0.0016835016835016834)) -end - -struct ERKN5ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - c1::T2 - c2::T2 - c3::T2 - a21::T - a31::T - a32::T - a41::T - a42::T - a43::T - b1::T - b2::T - b3::T - b4::T - bp1::T # bp denotes bprime - bp2::T - bp3::T - bp4::T - btilde1::T - btilde2::T - btilde3::T - btilde4::T - # bptilde1::T - # bptilde2::T - # bptilde3::T - # bptilde4::T -end - -function ERKN5ConstantCache(T::Type, T2::Type) - c1 = convert(T2, 1 // 2) - c2 = convert(T2, 19 // 70) - c3 = convert(T2, 44 // 51) - a21 = convert(T, 1 // 8) - a31 = convert(T, 2907 // 343000) - a32 = convert(T, 1216 // 42875) - a41 = convert(T, 6624772 // Int64(128538819)) - a42 = convert(T, 6273905 // Int64(54121608)) - a43 = convert(T, Int64(210498365) // Int64(1028310552)) - b1 = convert(T, 479 // 5016) - b2 = convert(T, 235 // 1776) - b3 = convert(T, 145775 // 641744) - b4 = convert(T, 309519 // 6873416) - btilde1 = convert(T, 479 // 5016 - 184883 // 2021250) - btilde2 = convert(T, 235 // 1776 - 411163 // 3399375) - btilde3 = convert(T, 145775 // 641744 - 6 // 25) - btilde4 = convert(T, 309519 // 6873416 - 593028 // Int64(12464375)) - bp1 = b1 - bp2 = convert(T, 235 // 888) - bp3 = convert(T, 300125 // 962616) - bp4 = convert(T, 2255067 // 6873416) - # bptilde1 = convert(T,0) - # bptilde2 = convert(T,0) - # bptilde3 = convert(T,0) - # bptilde4 = convert(T,0) - ERKN5ConstantCache(c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, b4, bp1, bp2, - bp3, bp4, btilde1, btilde2, btilde3, btilde4) -end - -function ERKN5ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - ERKN5ConstantCache(convert(T2, 0.5), - convert(T2, 0.2714285714285714), - convert(T2, 0.8627450980392157), - convert(T, 0.125), - convert(T, 0.008475218658892128), - convert(T, 0.028361516034985424), - convert(T, 0.051539076300366506), - convert(T, 0.11592236875149756), - convert(T, 0.20470310704348388), - convert(T, 0.09549441786283891), - convert(T, 0.13231981981981983), - convert(T, 0.22715444164651324), - convert(T, 0.04503132067082801), - convert(T, 0.09549441786283891), - convert(T, 0.26463963963963966), - convert(T, 0.3117806061814888), - convert(T, 0.32808533631603265), - convert(T, 0.004024782736060931), - convert(T, 0.011367291781577495), - convert(T, -0.012845558353486749), - convert(T, -0.0025465161641516788)) -end - -struct ERKN7ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - c1::T2 - c2::T2 - c3::T2 - c4::T2 - c5::T2 - c6::T2 - a21::T - a31::T - a32::T - a41::T - a42::T - a43::T - a51::T - a52::T - a53::T - a54::T - a61::T - a62::T - a63::T - a64::T - a65::T - a71::T - a73::T - a74::T - a75::T - a76::T - b1::T - b3::T - b4::T - b5::T - b6::T - bp1::T # bp denotes bprime - bp3::T - bp4::T - bp5::T - bp6::T - bp7::T - btilde1::T - btilde3::T - btilde4::T - btilde5::T - btilde6::T - bptilde1::T - bptilde3::T - bptilde4::T - bptilde5::T - bptilde6::T - bptilde7::T -end - -function ERKN7ConstantCache(T::Type, T2::Type) - c1 = convert(T2, 108816483 // 943181462) - c2 = convert(T2, 108816483 // 471590731) - c3 = convert(T2, 151401202 // 200292705) - c4 = convert(T2, 682035803 // 631524599) - c5 = convert(T2, 493263404 // 781610081) - c6 = convert(T2, 1) - a21 = convert(T, 5107771 // 767472028) - a31 = convert(T, 5107771 // 575604021) - a32 = convert(T, 16661485 // 938806552) - a41 = convert(T, 325996677 // 876867260) - a42 = convert(T, -397622579 // 499461366) - a43 = convert(T, 541212017 // 762248206) - a51 = convert(T, 82243160 // 364375691) - a52 = convert(T, -515873404 // 1213273815) - a53 = convert(T, 820109726 // 1294837243) - a54 = convert(T, 36245507 // 242779260) - a61 = convert(T, 3579594 // 351273191) - a62 = convert(T, 34292133 // 461028419) - a63 = convert(T, 267156948 // 2671391749) - a64 = convert(T, 22665163 // 1338599875) - a65 = convert(T, -3836509 // 1614789462) - a71 = convert(T, 53103334 // 780726093) - a73 = convert(T, 352190060 // 1283966121) - a74 = convert(T, 37088117 // 2206150964) - a75 = convert(T, 7183323 // 1828127386) - a76 = convert(T, 187705681 // 1370684829) - b1 = convert(T, 53103334 // 780726093) - b3 = convert(T, 352190060 // 1283966121) - b4 = convert(T, 37088117 // 2206150964) - b5 = convert(T, 7183323 // 1828127386) - b6 = convert(T, 187705681 // 1370684829) - bp1 = convert(T, 53103334 // 780726093) - bp3 = convert(T, 244481296 // 685635505) - bp4 = convert(T, 41493456 // 602487871) - bp5 = convert(T, -45498718 // 926142189) - bp6 = convert(T, 1625563237 // 4379140271) - bp7 = convert(T, 191595797 // 1038702495) - btilde1 = convert(T, 53103334 // 780726093 - 41808761 // 935030896) - btilde3 = convert(T, 352190060 // 1283966121 - 46261019 // 135447428) - btilde4 = convert(T, 37088117 // 2206150964 - 289298425 // 1527932372) - btilde5 = convert(T, 7183323 // 1828127386 + 52260067 // 3104571287) - btilde6 = convert(T, 187705681 // 1370684829 + 49872919 // 848719175) - bptilde1 = convert(T, 53103334 // 780726093 - 41808761 // 935030896) - bptilde3 = convert(T, 244481296 // 685635505 - 224724272 // 506147085) - bptilde4 = convert(T, 41493456 // 602487871 - 2995752066 // 3862177123) - bptilde5 = convert(T, -45498718 // 926142189 - 170795979 // 811534085) - bptilde6 = convert(T, 1625563237 // 4379140271 + 177906423 // 1116903503) - bptilde7 = convert(T, 191595797 // 1038702495 + 655510901 // 2077404990) - ERKN7ConstantCache(c1, c2, c3, c4, c5, c6, a21, a31, a32, a41, a42, a43, a51, a52, a53, - a54, a61, a62, a63, a64, a65, a71, a73, a74, a75, a76, b1, b3, b4, - b5, - b6, bp1, bp3, bp4, bp5, bp6, bp7, btilde1, btilde3, btilde4, btilde5, - btilde6, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6, bptilde7) -end - -function ERKN7ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - ERKN7ConstantCache(convert(T2, 108816483 // 943181462), - convert(T2, 0.23074347277618568), - convert(T2, 0.7558997318449516), - convert(T2, 1.0799829556599743), - convert(T2, 0.6310862871278652), - convert(T2, 1.0), - convert(T, 0.006655318778601792), - convert(T, 0.008873758371469056), - convert(T, 0.01774751674293811), - convert(T, 0.37177426033673555), - convert(T, -0.796102774043188), - convert(T, 0.7100207160080872), - convert(T, 0.2257097880879216), - convert(T, -0.4251912450611983), - convert(T, 0.6333689662029593), - convert(T, 0.14929408302834435), - convert(T, 0.010190342137439119), - convert(T, 0.07438182026691938), - convert(T, 0.10000665312379087), - convert(T, 0.016931992467129134), - convert(T, -0.002375857094861324), - convert(T, 0.06801788037587723), - convert(T, 0.2742985614960786), - convert(T, 0.01681123259704543), - convert(T, 0.003929333948504177), - convert(T, 0.13694299158249457), - convert(T, 0.06801788037587723), - convert(T, 0.2742985614960786), - convert(T, 0.01681123259704543), - convert(T, 0.003929333948504177), - convert(T, 0.13694299158249457), - convert(T, 0.06801788037587723), - convert(T, 0.35657618985177847), - convert(T, 0.06887019307314819), - convert(T, -0.049127141102520276), - convert(T, 0.371206021365649), - convert(T, 0.18445685643606738), - convert(T, 0.023304105484742516), - convert(T, -0.06724368617214582), - convert(T, -0.1725285773981577), - convert(T, 0.020762597600343137), - convert(T, 0.1957055604852179), - convert(T, 0.023304105484742516), - convert(T, -0.08741386493634701), - convert(T, -0.7067938872093759), - convert(T, -0.25958777628335805), - convert(T, 0.5304914229443385), - convert(T, 0.5)) -end - -struct DPRKN4ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - c1::T2 - c2::T2 - c3::T2 - a21::T - a31::T - a32::T - a41::T - a42::T - a43::T - b1::T - b2::T - b3::T - bp1::T # bp denotes bprime - bp2::T - bp3::T - bp4::T - btilde1::T - btilde2::T - btilde3::T - btilde4::T - bptilde1::T - bptilde2::T - bptilde3::T - bptilde4::T -end - -function DPRKN4ConstantCache(T::Type, T2::Type) - c1 = convert(T2, 1 // 4) - c2 = convert(T2, 7 // 10) - c3 = convert(T2, 1) - a21 = convert(T, 1 // 32) - a31 = convert(T, 7 // 1000) - a32 = convert(T, 119 // 500) - a41 = convert(T, 1 // 14) - a42 = convert(T, 8 // 27) - a43 = convert(T, 25 // 189) - b1 = convert(T, 1 // 14) - b2 = convert(T, 8 // 27) - b3 = convert(T, 25 // 189) - # b4 = convert(T, 0) - bp1 = convert(T, 1 // 14) - bp2 = convert(T, 32 // 81) - bp3 = convert(T, 250 // 567) - bp4 = convert(T, 5 // 54) - btilde1 = convert(T, 1 // 14 + 7 // 150) - btilde2 = convert(T, 8 // 27 - 67 // 150) - btilde3 = convert(T, 25 // 189 - 3 // 20) - btilde4 = convert(T, 1 // 20) - bptilde1 = convert(T, 1 // 14 - 13 // 21) - bptilde2 = convert(T, 32 // 81 + 20 // 27) - bptilde3 = convert(T, 250 // 567 - 275 // 189) - bptilde4 = convert(T, 5 // 54 + 1 // 3) - DPRKN4ConstantCache(c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, - bp1, bp2, bp3, bp4, btilde1, btilde2, btilde3, btilde4, - bptilde1, bptilde2, bptilde3, bptilde4) -end - -function DPRKN4ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - c1 = convert(T2, 0.25) - c2 = convert(T2, 0.7) - c3 = convert(T2, 1.0) - a21 = convert(T, 0.03125) - a31 = convert(T, 0.007) - a32 = convert(T, 0.238) - a41 = convert(T, 0.07142857142857142) - a42 = convert(T, 0.2962962962962963) - a43 = convert(T, 0.13227513227513227) - b1 = convert(T, 0.07142857142857142) - b2 = convert(T, 0.2962962962962963) - b3 = convert(T, 0.13227513227513227) - bp1 = convert(T, 0.07142857142857142) - bp2 = convert(T, 0.3950617283950617) - bp3 = convert(T, 0.4409171075837742) - bp4 = convert(T, 0.09259259259259259) - btilde1 = convert(T, 0.11809523809523809) - btilde2 = convert(T, -0.15037037037037038) - btilde3 = convert(T, -0.017724867724867727) - btilde4 = convert(T, 0.05) - bptilde1 = convert(T, -0.5476190476190477) - bptilde2 = convert(T, 1.1358024691358024) - bptilde3 = convert(T, -1.0141093474426808) - bptilde4 = convert(T, 0.42592592592592593) - DPRKN4ConstantCache(c1, c2, c3, a21, a31, a32, a41, a42, a43, b1, b2, b3, - bp1, bp2, bp3, bp4, btilde1, btilde2, btilde3, btilde4, - bptilde1, bptilde2, bptilde3, bptilde4) -end -struct DPRKN5ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - c1::T2 - c2::T2 - c3::T2 - c4::T2 - c5::T2 - a21::T - a31::T - a32::T - a41::T - # a42::T - a43::T - a51::T - # a52::T - a53::T - a54::T - a61::T - # a62::T - a63::T - a64::T - a65::T - b1::T - # b2::T - b3::T - b4::T - b5::T - # b6::T - bp1::T # bp denotes bprime - # bp2::T - bp3::T - bp4::T - bp5::T - bp6::T - btilde1::T - # btilde2::T - btilde3::T - btilde4::T - btilde5::T - # btilde6::T - bptilde1::T - # bptilde2::T - bptilde3::T - bptilde4::T - bptilde5::T - bptilde6::T -end - -function DPRKN5ConstantCache(T::Type, T2::Type) - c1 = convert(T2, 1 // 8) - c2 = convert(T2, 1 // 4) - c3 = convert(T2, 1 // 2) - c4 = convert(T2, 3 // 4) - c5 = convert(T2, 1) - a21 = convert(T, 1 // 128) - a31 = convert(T, 1 // 96) - a32 = convert(T, 1 // 48) - a41 = convert(T, 1 // 24) - # a42 = convert(T, 0) - a43 = convert(T, 1 // 12) - a51 = convert(T, 9 // 128) - # a52 = convert(T, 0) - a53 = convert(T, 9 // 64) - a54 = convert(T, 9 // 128) - a61 = convert(T, 7 // 90) - # a62 = convert(T, 0) - a63 = convert(T, 4 // 15) - a64 = convert(T, 1 // 15) - a65 = convert(T, 4 // 45) - b1 = convert(T, 7 // 90) - # b2 = convert(T,0) - b3 = convert(T, 4 // 15) - b4 = convert(T, 1 // 15) - b5 = convert(T, 4 // 45) - # b6 = convert(T, 0) - bp1 = convert(T, 7 // 90) - # bp2 = convert(T,0) - bp3 = convert(T, 16 // 45) - bp4 = convert(T, 2 // 15) - bp5 = convert(T, 16 // 45) - bp6 = convert(T, 7 // 90) - btilde1 = convert(T, 7 // 90 - 1 // 6) - # btilde2 = convert(T,0) - btilde3 = convert(T, 4 // 15) - btilde4 = convert(T, 1 // 15 - 1 // 3) - btilde5 = convert(T, 4 // 45) - #btilde6 = convert(T, 0) - bptilde1 = convert(T, 7 // 90) - # bptilde2 = convert(T,0) - bptilde3 = convert(T, 16 // 45 - 2 // 3) - bptilde4 = convert(T, 2 // 15 + 1 // 3) - bptilde5 = convert(T, 16 // 45 - 2 // 3) - bptilde6 = convert(T, 7 // 90) - DPRKN5ConstantCache(c1, c2, c3, c4, c5, a21, a31, a32, a41, a43, a51, - a53, a54, a61, a63, a64, a65, b1, b3, b4, b5, bp1, - bp3, bp4, bp5, bp6, btilde1, btilde3, btilde4, btilde5, - bptilde1, bptilde3, bptilde4, bptilde5, bptilde6) -end - -function DPRKN5ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - c1 = convert(T2, 0.125) - c2 = convert(T2, 0.25) - c3 = convert(T2, 0.5) - c4 = convert(T2, 0.75) - c5 = convert(T2, 1.0) - a21 = convert(T, 1 // 128) - a31 = convert(T, 1 // 96) - a32 = convert(T, 1 // 48) - a41 = convert(T, 1 // 24) - a43 = convert(T, 1 // 12) - a51 = convert(T, 7 // 90) - a53 = convert(T, 4 // 15) - a54 = convert(T, 1 // 15) - a61 = convert(T, 0.07777777777777778) - a63 = convert(T, 0.26666666666666666) - a64 = convert(T, 0.06666666666666667) - a65 = convert(T, 0.08888888888888889) - b1 = convert(T, 0.07777777777777778) - b3 = convert(T, 0.26666666666666666) - b4 = convert(T, 0.06666666666666667) - b5 = convert(T, 0.08888888888888889) - bp1 = convert(T, 0.07777777777777778) - bp3 = convert(T, 0.35555555555555557) - bp4 = convert(T, 0.13333333333333333) - bp5 = convert(T, 0.35555555555555557) - bp6 = convert(T, 0.07777777777777778) - btilde1 = convert(T, -0.08888888888888888) - btilde3 = convert(T, 0.26666666666666666) - btilde4 = convert(T, -0.26666666666666666) - btilde5 = convert(T, 0.08888888888888889) - bptilde1 = convert(T, 0.07777777777777778) - bptilde3 = convert(T, -0.31111111111111106) - bptilde4 = convert(T, 0.4666666666666667) - bptilde5 = convert(T, -0.31111111111111106) - bptilde6 = convert(T, 0.07777777777777778) - DPRKN5ConstantCache(c1, c2, c3, c4, c5, a21, a31, a32, a41, a43, a51, - a53, a54, a61, a63, a64, a65, b1, b3, b4, b5, bp1, - bp3, bp4, bp5, bp6, btilde1, btilde3, btilde4, btilde5, - bptilde1, bptilde3, bptilde4, bptilde5, bptilde6) -end - -struct DPRKN6ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - c1::T2 - c2::T2 - c3::T2 - c4::T2 - c5::T2 - a21::T - a31::T - a32::T - a41::T - a42::T - a43::T - a51::T - a52::T - a53::T - a54::T - a61::T - # a62::T - a63::T - a64::T - a65::T - b1::T - # b2::T - b3::T - b4::T - b5::T - # b6::T - bp1::T # bp denotes bprime - # bp2::T - bp3::T - bp4::T - bp5::T - bp6::T - btilde1::T - btilde2::T - btilde3::T - btilde4::T - btilde5::T - # btilde6::T - bptilde1::T - # bptilde2::T - bptilde3::T - bptilde4::T - bptilde5::T - bptilde6::T - r14::T - r13::T - r12::T - r11::T - r10::T - r34::T - r33::T - r32::T - r31::T - r44::T - r43::T - r42::T - r41::T - r54::T - r53::T - r52::T - r51::T - r64::T - r63::T - r62::T - r61::T - rp14::T - rp13::T - rp12::T - rp11::T - rp10::T - rp34::T - rp33::T - rp32::T - rp31::T - rp44::T - rp43::T - rp42::T - rp41::T - rp54::T - rp53::T - rp52::T - rp51::T - rp64::T - rp63::T - rp62::T - rp61::T -end - -function DPRKN6ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - c1 = convert(T2, 0.12929590313670442) - c2 = convert(T2, 0.25859180627340883) - c3 = convert(T2, 0.67029708261548) - c4 = convert(T2, 0.9) - c5 = convert(T2, 1.0) - a21 = convert(T, 0.008358715283968025) - a31 = convert(T, 0.011144953711957367) - a32 = convert(T, 0.022289907423914734) - a41 = convert(T, 0.1454747428010918) - a42 = convert(T, -0.22986064052264749) - a43 = convert(T, 0.3090349872029675) - a51 = convert(T, -0.20766826295078997) - a52 = convert(T, 0.6863667842925143) - a53 = convert(T, -0.19954927787234925) - a54 = convert(T, 0.12585075653062489) - a61 = convert(T, 0.07811016144349478) - a63 = convert(T, 0.2882917411897668) - a64 = convert(T, 0.12242553717457041) - a65 = convert(T, 0.011172560192168035) - b1 = convert(T, 0.07811016144349478) - b3 = convert(T, 0.2882917411897668) - b4 = convert(T, 0.12242553717457041) - b5 = convert(T, 0.011172560192168035) - bp1 = convert(T, 0.07811016144349478) - bp3 = convert(T, 0.3888434787059826) - bp4 = convert(T, 0.3713207579288423) - bp5 = convert(T, 0.11172560192168035) - bp6 = convert(T, 0.05) - btilde1 = convert(T, -0.9807490989269235) - btilde2 = convert(T, 2.406751371924452) - btilde3 = convert(T, -1.559600370364267) - btilde4 = convert(T, 0.12242553717457041) - btilde5 = convert(T, 0.011172560192168035) - bptilde1 = convert(T, 0.023504273504273504) - bptilde3 = convert(T, -0.07242330719764424) - bptilde4 = convert(T, 0.17543989844952962) - bptilde5 = convert(T, -0.2765208647561589) - bptilde6 = convert(T, 0.15) - r14 = convert(T, 0.21367521367521367) - r13 = convert(T, -0.9066951566951567) - r12 = convert(T, 1.5161443494776827) - r11 = convert(T, -1.245014245014245) - r10 = convert(T, 0.5) - r34 = convert(T, -0.6583937017967658) - r33 = convert(T, 2.5384011164109506) - r32 = convert(T, -3.577652872294921) - r31 = convert(T, 1.9859371988705032) - r44 = convert(T, 1.5949081677229964) - r43 = convert(T, -5.164133553908094) - r42 = convert(T, 5.547586751052329) - r41 = convert(T, -1.8559358276926614) - r54 = convert(T, -2.513826043237808) - r53 = convert(T, 7.273336685101391) - r52 = convert(T, -6.926987319144182) - r51 = convert(T, 2.178649237472767) - r64 = convert(T, 1.3636363636363635) - r63 = convert(T, -3.7409090909090907) - r62 = convert(T, 3.440909090909091) - r61 = convert(T, -1.0636363636363637) - rp14 = convert(T, 1.2820512820512822) - rp13 = convert(T, -4.533475783475783) - rp12 = convert(T, 6.064577397910731) - rp11 = convert(T, -3.735042735042735) - rp10 = convert(T, 1) - rp34 = convert(T, -3.950362210780595) - rp33 = convert(T, 12.692005582054751) - rp32 = convert(T, -14.310611489179683) - rp31 = convert(T, 5.95781159661151) - rp44 = convert(T, 9.56944900633798) - rp43 = convert(T, -25.820667769540467) - rp42 = convert(T, 22.190347004209315) - rp41 = convert(T, -5.567807483077984) - rp54 = convert(T, -15.082956259426847) - rp53 = convert(T, 36.366683425506956) - rp52 = convert(T, -27.707949276576727) - rp51 = convert(T, 6.5359477124183005) - rp64 = convert(T, 8.181818181818182) - rp63 = convert(T, -18.704545454545453) - rp62 = convert(T, 13.763636363636364) - rp61 = convert(T, -3.190909090909091) - DPRKN6ConstantCache(c1, c2, c3, c4, c5, a21, a31, a32, a41, a42, a43, a51, - a52, a53, a54, a61, a63, a64, a65, b1, b3, b4, b5, bp1, - bp3, bp4, bp5, bp6, btilde1, btilde2, btilde3, btilde4, - btilde5, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6, - r14, r13, r12, r11, r10, r34, r33, r32, r31, r44, r43, r42, r41, - r54, - r53, r52, r51, r64, r63, r62, r61, rp14, rp13, rp12, rp11, rp10, - rp34, - rp33, rp32, rp31, rp44, rp43, rp42, rp41, rp54, rp53, rp52, rp51, - rp64, rp63, rp62, rp61) -end - -function DPRKN6ConstantCache(T::Type, T2::Type) - R = sqrt(big(8581)) - c1 = convert(T2, (209 - R) / 900) - c2 = convert(T2, (209 - R) / 450) - c3 = convert(T2, (209 + R) / 450) - c4 = convert(T2, 9 // 10) - c5 = convert(T2, 1) - a21 = convert(T, (26131 - 209R) / 81_0000) - a31 = convert(T, (26131 - 209R) / 60_7500) - a32 = convert(T, (26131 - 209R) / 30_3750) - a41 = convert(T, (980403512254 + 7781688431R) / 116944_6992_1875) - a42 = convert(T, -(126288_4486208 + 153854_81287R) / 116944_6992_1875) - a43 = convert(T, (7166_233_891_441 + 786_945_632_99R) / 46_777_879_687_500) - a51 = convert(T, -9(329260 + 3181R) / 2704_0000) - a52 = convert(T, 27(35129 + 3331R) / 1352_0000) - a53 = convert(T, -27(554358343 + 31040327R) / 46406048_0000) - a54 = convert(T, 153(8555_257 - 67973R) / 274592_0000) - a61 = convert(T, 329 // 4212) - # a62 = convert(T,0) - a63 = convert(T, (8411_9543 + 366_727R) / 4096_22616) - a64 = convert(T, (8411_9543 - 366_727R) / 4096_22616) - a65 = convert(T, 200 // 17901) - b1 = convert(T, 329 // 4212) - # b2 = convert(T,0) - b3 = a63 - b4 = a64 - b5 = convert(T, 200 // 17901) - # b6 = convert(T,0) - bp1 = b1 - # bp2 = b2 - bp3 = convert(T, (389225579 + 96856R) / 10_2405_6540) - bp4 = convert(T, (389225579 - 96856R) / 10_2405_6540) - bp5 = convert(T, 2000 // 17901) - bp6 = convert(T, 1 // 20) - btilde1 = convert(T, 329 // 4212 - (2701 + 23R) / 4563) - btilde2 = convert(T, (9829 + 131R) / 9126) - btilde3 = convert(T, (8411_9543 + 366_727R) / 4096_22616 - 5(1798 + 17R) / 9126) - btilde4 = b4 - btilde5 = b5 - # btilde6 = convert(T,0) - bptilde1 = convert(T, 329 // 4212 - 115 // 2106) - # btildep2 = convert(T,0) - bptilde3 = convert(T, - (389225579 + 96856R) / 10_2405_6540 - - (8411_9543 + 366_727R) / 2560_14135) - bptilde4 = convert(T, - (389225579 - 96856R) / 10_2405_6540 - - (8411_9543 - 366_727R) / 2560_14135) - bptilde5 = convert(T, 2000 // 17901 - 6950 // 17901) - bptilde6 = convert(T, 1 // 20 + 1 // 10) - r14 = convert(T, 900 // 4212) - r13 = convert(T, -3819 // 4212) - r12 = convert(T, 6386 // 4212) - r11 = convert(T, -5244 // 4212) - r10 = convert(T, 2106 // 4212) - r34 = convert(T, 1800 * (5860823 - 152228R) / 22529243880) - r33 = convert(T, -6 * (4929647204 - 156109769R) / 22529243880) - r32 = convert(T, (22190560391 - 1109665151R) / 22529243880) - r31 = convert(T, 18 * (81356461 + 25954829R) / 22529243880) - r44 = convert(T, 1800 * (5860823 + 152228R) / 22529243880) - r43 = convert(T, -6 * (4929647204 + 156109769R) / 22529243880) - r42 = convert(T, (22190560391 + 1109665151R) / 22529243880) - r41 = convert(T, 18 * (81356461 - 25954829R) / 22529243880) - r54 = convert(T, -200 * 225 // 17901) - r53 = convert(T, 200 * 651 // 17901) - r52 = convert(T, -200 * 620 // 17901) - r51 = convert(T, 200 * 195 // 17901) - r64 = convert(T, 15 // 11) - r63 = convert(T, -823 // 220) - r62 = convert(T, 757 // 220) - r61 = convert(T, -117 // 110) - rp14 = convert(T, 5400 // 4212) - rp13 = convert(T, -19095 // 4212) - rp12 = convert(T, 25544 // 4212) - rp11 = convert(T, -15732 // 4212) - rp10 = convert(T, 1) - rp34 = convert(T, 5400 * (5860823 - 152228R) / 11264621940) - rp33 = convert(T, -15 * (4929647204 - 156109769R) / 11264621940) - rp32 = convert(T, 2 * (22190560391 - 1109665151R) / 11264621940) - rp31 = convert(T, 27 * (81356461 + 25954829R) / 11264621940) - rp44 = convert(T, 5400 * (5860823 + 152228R) / 11264621940) - rp43 = convert(T, -15 * (4929647204 + 156109769R) / 11264621940) - rp42 = convert(T, 2 * (22190560391 + 1109665151R) / 11264621940) - rp41 = convert(T, 27 * (81356461 - 25954829R) / 11264621940) - rp54 = convert(T, -1000 * 270 // 17901) - rp53 = convert(T, 1000 * 651 // 17901) - rp52 = convert(T, -1000 * 496 // 17901) - rp51 = convert(T, 1000 * 117 // 17901) - rp64 = convert(T, 1800 // 220) - rp63 = convert(T, -4115 // 220) - rp62 = convert(T, 3028 // 220) - rp61 = convert(T, -702 // 220) - DPRKN6ConstantCache(c1, c2, c3, c4, c5, a21, a31, a32, a41, a42, a43, a51, - a52, a53, a54, a61, a63, a64, a65, b1, b3, b4, b5, bp1, - bp3, bp4, bp5, bp6, btilde1, btilde2, btilde3, btilde4, - btilde5, bptilde1, bptilde3, bptilde4, bptilde5, bptilde6, - r14, r13, r12, r11, r10, r34, r33, r32, r31, r44, r43, r42, r41, - r54, - r53, r52, r51, r64, r63, r62, r61, rp14, rp13, rp12, rp11, rp10, - rp34, - rp33, rp32, rp31, rp44, rp43, rp42, rp41, rp54, rp53, rp52, rp51, - rp64, rp63, rp62, rp61) -end - -struct DPRKN6FMConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - c1::T2 - c2::T2 - c3::T2 - c4::T2 - c5::T2 - a21::T - a31::T - a32::T - a41::T - a42::T - a43::T - a51::T - a52::T - a53::T - a54::T - a61::T - a62::T - a63::T - a64::T - a65::T - b1::T - b2::T - b3::T - b4::T - b5::T - # b6::T - bp1::T # bp denotes bprime - bp2::T - bp3::T - bp4::T - bp5::T - bp6::T - btilde1::T - btilde2::T - btilde3::T - btilde4::T - btilde5::T - # btilde6::T - bptilde1::T - bptilde2::T - bptilde3::T - bptilde4::T - bptilde5::T - # bptilde6::T -end - -function DPRKN6FMConstantCache(T::Type, T2::Type) - c1 = convert(T2, 1 // 10) - c2 = convert(T2, 3 // 10) - c3 = convert(T2, 7 // 10) - c4 = convert(T2, 17 // 25) - c5 = convert(T2, 1) - a21 = convert(T, 1 // 200) - a31 = convert(T, -1 // 2200) - a32 = convert(T, 1 // 22) - a41 = convert(T, 637 // 6600) - a42 = convert(T, -7 // 110) - a43 = convert(T, 7 // 33) - a51 = convert(T, 225437 // 1968750) - a52 = convert(T, -30073 // 281250) - a53 = convert(T, 65569 // 281250) - a54 = convert(T, -9367 // 984375) - a61 = convert(T, 151 // 2142) - a62 = convert(T, 5 // 116) - a63 = convert(T, 385 // 1368) - a64 = convert(T, 55 // 168) - a65 = convert(T, -6250 // 28101) - b1 = convert(T, 151 // 2142) - b2 = convert(T, 5 // 116) - b3 = convert(T, 385 // 1368) - b4 = convert(T, 55 // 168) - b5 = convert(T, -6250 // 28101) - # b6 = convert(T, 0) - bp1 = convert(T, 151 // 2142) - bp2 = convert(T, 25 // 522) - bp3 = convert(T, 275 // 684) - bp4 = convert(T, 275 // 252) - bp5 = convert(T, -78125 // 112404) - bp6 = convert(T, 1 // 12) - btilde1 = convert(T, 151 // 2142 - 1349 // 157500) - btilde2 = convert(T, 5 // 116 - 7873 // 50000) - btilde3 = convert(T, 385 // 1368 - 192199 // 900000) - btilde4 = convert(T, 55 // 168 - 521683 // 2100000) - btilde5 = convert(T, -6250 // 28101 + 16 // 125) - # btilde6 = convert(T, 0) - bptilde1 = convert(T, 151 // 2142 - 1349 // 157500) - bptilde2 = convert(T, 25 // 522 - 7873 // 45000) - bptilde3 = convert(T, 275 // 684 - 27457 // 90000) - bptilde4 = convert(T, 275 // 252 - 521683 // 630000) - bptilde5 = convert(T, -78125 // 112404 + 2 // 5) - # bptilde6 = convert(T, 0) - DPRKN6FMConstantCache(c1, c2, c3, c4, c5, a21, a31, a32, a41, a42, a43, a51, a52, - a53, a54, a61, a62, a63, a64, a65, b1, b2, b3, b4, b5, bp1, bp2, - bp3, bp4, bp5, bp6, btilde1, btilde2, btilde3, btilde4, btilde5, - bptilde1, bptilde2, bptilde3, bptilde4, bptilde5) -end - -function DPRKN6FMConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - c1 = convert(T2, 0.1) - c2 = convert(T2, 0.3) - c3 = convert(T2, 0.7) - c4 = convert(T2, 0.68) - c5 = convert(T2, 1.0) - a21 = convert(T, 0.005) - a31 = convert(T, -0.00045454545454545455) - a32 = convert(T, 0.045454545454545456) - a41 = convert(T, 0.09651515151515151) - a42 = convert(T, -0.06363636363636363) - a43 = convert(T, 0.21212121212121213) - a51 = convert(T, 0.11450768253968253) - a52 = convert(T, -0.10692622222222223) - a53 = convert(T, 0.23313422222222221) - a54 = convert(T, -0.00951568253968254) - a61 = convert(T, 0.07049486461251167) - a62 = convert(T, 0.04310344827586207) - a63 = convert(T, 0.2814327485380117) - a64 = convert(T, 0.3273809523809524) - a65 = convert(T, -0.22241201380733783) - b1 = convert(T, 0.07049486461251167) - b2 = convert(T, 0.04310344827586207) - b3 = convert(T, 0.2814327485380117) - b4 = convert(T, 0.3273809523809524) - b5 = convert(T, -0.22241201380733783) - bp1 = convert(T, 0.07049486461251167) - bp2 = convert(T, 0.04789272030651341) - bp3 = convert(T, 0.402046783625731) - bp4 = convert(T, 1.0912698412698412) - bp5 = convert(T, -0.6950375431479306) - bp6 = convert(T, 0.08333333333333333) - btilde1 = convert(T, 0.061929785247432305) - btilde2 = convert(T, -0.11435655172413792) - btilde3 = convert(T, 0.06787830409356727) - btilde4 = convert(T, 0.07896047619047619) - btilde5 = convert(T, -0.09441201380733782) - bptilde1 = convert(T, 0.061929785247432305) - bptilde2 = convert(T, -0.12706283524904216) - bptilde3 = convert(T, 0.0969690058479532) - bptilde4 = convert(T, 0.26320158730158716) - bptilde5 = convert(T, -0.2950375431479306) - DPRKN6FMConstantCache(c1, c2, c3, c4, c5, a21, a31, a32, a41, a42, a43, a51, a52, - a53, a54, a61, a62, a63, a64, a65, b1, b2, b3, b4, b5, bp1, bp2, - bp3, bp4, bp5, bp6, btilde1, btilde2, btilde3, btilde4, btilde5, - bptilde1, bptilde2, bptilde3, bptilde4, bptilde5) -end - -struct DPRKN8ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - c1::T2 - c2::T2 - c3::T2 - c4::T2 - c5::T2 - c6::T2 - c7::T2 - c8::T2 - a21::T - a31::T - a32::T - a41::T - a42::T - a43::T - a51::T - a52::T - a53::T - a54::T - a61::T - a62::T - a63::T - a64::T - a65::T - a71::T - a72::T - a73::T - a74::T - a75::T - a76::T - a81::T - a82::T - a83::T - a84::T - a85::T - a86::T - a87::T - a91::T - # a92::T - a93::T - a94::T - a95::T - a96::T - a97::T - # a98::T - b1::T - # b2::T - b3::T - b4::T - b5::T - b6::T - b7::T - # b8::T - # b9::T - bp1::T - # bp2::T - bp3::T - bp4::T - bp5::T - bp6::T - bp7::T - bp8::T - # bp9::T - btilde1::T - # btilde2::T - btilde3::T - btilde4::T - btilde5::T - btilde6::T - btilde7::T - # btilde8::T - # btilde9::T - bptilde1::T - # bptilde2::T - bptilde3::T - bptilde4::T - bptilde5::T - bptilde6::T - bptilde7::T - bptilde8::T - bptilde9::T -end - -function DPRKN8ConstantCache(T::Type, T2::Type) - c1 = convert(T2, 1 // 20) - c2 = convert(T2, 1 // 10) - c3 = convert(T2, 3 // 10) - c4 = convert(T2, 1 // 2) - c5 = convert(T2, 7 // 10) - c6 = convert(T2, 9 // 10) - c7 = convert(T2, 1) - c8 = convert(T2, 1) - a21 = convert(T, 1 // 800) - a31 = convert(T, 1 // 600) - a32 = convert(T, 1 // 300) - a41 = convert(T, 9 // 200) - a42 = convert(T, -9 // 100) - a43 = convert(T, 9 // 100) - a51 = convert(T, -66701 // 197352) - a52 = convert(T, 28325 // 32892) - a53 = convert(T, -2665 // 5482) - a54 = convert(T, 2170 // 24669) - a61 = convert(T, 2270_15747 // 30425_1000) - a62 = convert(T, -5489_7451 // 30425_100) - a63 = convert(T, 12942_349 // 10141_700) - a64 = convert(T, -9499 // 304_251) - a65 = convert(T, 539 // 9250) - a71 = convert(T, -11318_91597 // 9017_89000) - a72 = convert(T, 4196_4921 // 1288_2700) - a73 = convert(T, -6663_147 // 3220_675) - a74 = convert(T, 270_954 // 644_135) - a75 = convert(T, -108 // 5875) - a76 = convert(T, 114 // 1645) - a81 = convert(T, 138_369_59 // 3667458) - a82 = convert(T, -177_314_50 // 1833729) - a83 = convert(T, 106_3919_505 // 15647_8208) - a84 = convert(T, -332_138_45 // 3911_9552) - a85 = convert(T, 133_35 // 285_44) - a86 = convert(T, -705 // 14272) - a87 = convert(T, 1645 // 57088) - a91 = convert(T, 223 // 7938) - # a92 = convert(T,0) - a93 = convert(T, 1175 // 8064) - a94 = convert(T, 925 // 6048) - a95 = convert(T, 41 // 448) - a96 = convert(T, 925 // 14112) - a97 = convert(T, 1175 // 72576) - # a98 = convert(T,0) - b1 = convert(T, 223 // 7938) - # b2 = convert(T,0) - b3 = convert(T, 1175 // 8064) - b4 = convert(T, 925 // 6048) - b5 = convert(T, 41 // 448) - b6 = convert(T, 925 // 14112) - b7 = convert(T, 1175 // 72576) - # b8 = convert(T,0) - # b9 = convert(T,0) - bp1 = convert(T, 223 // 7938) - # bp2 = convert(T,0) - bp3 = convert(T, 5875 // 36288) - bp4 = convert(T, 4625 // 21168) - bp5 = convert(T, 41 // 224) - bp6 = convert(T, 4625 // 21168) - bp7 = convert(T, 5875 // 36288) - bp8 = convert(T, 223 // 7938) - # bp9 = convert(T,0) - btilde1 = convert(T, 223 // 7938 - 7987_313 // 10994_1300) - # btilde2 = convert(T,0) - btilde3 = convert(T, 1175 // 8064 - 1610_737 // 4467_4560) - btilde4 = convert(T, 925 // 6048 - 10023_263 // 3350_5920) - btilde5 = convert(T, 41 // 448 + 497_221 // 1240_9600) - btilde6 = convert(T, 925 // 14112 - 1002_3263 // 7818_0480) - btilde7 = convert(T, 1175 // 72576 - 1610_737 // 40207_1040) - # btilde8 = convert(T,0) - # btilde9 = convert(T,0) - bptilde1 = convert(T, 223 // 7938 - 7987_313 // 10994_1300) - # bptilde2 = convert(T,0) - bptilde3 = convert(T, 5875 // 36288 - 1610_737 // 4020_7104) - bptilde4 = convert(T, 4625 // 21168 - 1002_3263 // 2345_4144) - bptilde5 = convert(T, 41 // 224 + 497_221 // 620_4800) - bptilde6 = convert(T, 4625 // 21168 - 1002_3263 // 2345_4144) - bptilde7 = convert(T, 5875 // 36288 - 1610_737 // 40207_104) - bptilde8 = convert(T, 223 // 7938 + 4251_941 // 5497_0650) - bptilde9 = convert(T, -3 // 20) - DPRKN8ConstantCache(c1, c2, c3, c4, c5, c6, c7, c8, a21, a31, a32, a41, a42, a43, a51, - a52, a53, a54, a61, a62, a63, a64, a65, a71, a72, a73, a74, a75, - a76, a81, a82, a83, a84, a85, a86, a87, a91, a93, a94, a95, a96, - a97, b1, b3, b4, b5, b6, b7, bp1, bp3, bp4, bp5, bp6, bp7, bp8, - btilde1, btilde3, btilde4, btilde5, btilde6, btilde7, bptilde1, - bptilde3, bptilde4, bptilde5, bptilde6, bptilde7, bptilde8, - bptilde9) -end - -function DPRKN8ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - DPRKN8ConstantCache(convert(T2, 0.05), - convert(T2, 0.1), - convert(T2, 0.3), - convert(T2, 0.5), - convert(T2, 0.7), - convert(T2, 0.9), - convert(T2, 1.0), - convert(T2, 1.0), - convert(T, 0.00125), - convert(T, 0.0016666666666666668), - convert(T, 0.0033333333333333335), - convert(T, 0.045), - convert(T, -0.09), - convert(T, 0.09), - convert(T, -0.3379798532571243), - convert(T, 0.8611516478170984), - convert(T, -0.48613644655235316), - convert(T, 0.0879646519923791), - convert(T, 0.7461462641043086), - convert(T, -1.804347430246737), - convert(T, 1.2761518285888953), - convert(T, -0.031220932716737166), - convert(T, 0.05827027027027027), - convert(T, -1.2551623461807584), - convert(T, 3.257463187064823), - convert(T, -2.068866619575089), - convert(T, 0.4206478455603251), - convert(T, -0.018382978723404254), - convert(T, 0.06930091185410335), - convert(T, 3.772901830095941), - convert(T, -9.669613121677195), - convert(T, 6.7991544547851674), - convert(T, -0.8490343907823893), - convert(T, 0.4671734865470852), - convert(T, -0.04939742152466368), - convert(T, 0.028815162556053812), - convert(T, 0.028092718568909044), - convert(T, 0.1457093253968254), - convert(T, 0.1529431216931217), - convert(T, 0.09151785714285714), - convert(T, 0.06554705215419501), - convert(T, 0.01618992504409171), - convert(T, 0.028092718568909044), - convert(T, 0.1457093253968254), - convert(T, 0.1529431216931217), - convert(T, 0.09151785714285714), - convert(T, 0.06554705215419501), - convert(T, 0.01618992504409171), - convert(T, 0.028092718568909044), - convert(T, 0.1618992504409171), - convert(T, 0.2184901738473167), - convert(T, 0.18303571428571427), - convert(T, 0.2184901738473167), - convert(T, 0.1618992504409171), - convert(T, 0.028092718568909044), - convert(T, -0.044557986852984274), - convert(T, 0.10965442077101599), - convert(T, -0.14620589436135464), - convert(T, 0.1315853049252192), - convert(T, -0.06265966901200913), - convert(T, 0.012183824530112887), - convert(T, -0.044557986852984274), - convert(T, 0.12183824530112887), - convert(T, -0.2088655633733638), - convert(T, 0.2631706098504384), - convert(T, -0.2088655633733638), - convert(T, 0.12183824530112887), - convert(T, 0.10544201314701572), - convert(T, -0.15)) -end - -struct DPRKN12ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - c1::T2 - c2::T2 - c3::T2 - c4::T2 - c5::T2 - c6::T2 - c7::T2 - c8::T2 - c9::T2 - c10::T2 - c11::T2 - c12::T2 - c13::T2 - c14::T2 - c15::T2 - c16::T2 - a21::T - a31::T - a32::T - a41::T - a42::T - a43::T - a51::T - # a52::T - a53::T - a54::T - a61::T - # a62::T - a63::T - a64::T - a65::T - a71::T - # a72::T - a73::T - a74::T - a75::T - a76::T - a81::T - # a82::T - # a83::T - a84::T - a85::T - a86::T - a87::T - a91::T - # a92::T - a93::T - a94::T - a95::T - a96::T - a97::T - a98::T - a101::T - # a102::T - a103::T - a104::T - a105::T - a106::T - a107::T - a108::T - a109::T - a111::T - # a112::T - a113::T - a114::T - a115::T - a116::T - a117::T - a118::T - a119::T - a1110::T - a121::T - # a122::T - a123::T - a124::T - a125::T - a126::T - a127::T - a128::T - a129::T - a1210::T - a1211::T - a131::T - # a132::T - a133::T - a134::T - a135::T - a136::T - a137::T - a138::T - a139::T - a1310::T - a1311::T - a1312::T - a141::T - # a142::T - a143::T - a144::T - a145::T - a146::T - a147::T - a148::T - a149::T - a1410::T - a1411::T - a1412::T - a1413::T - a151::T - # a152::T - a153::T - a154::T - a155::T - a156::T - a157::T - a158::T - a159::T - a1510::T - a1511::T - a1512::T - a1513::T - a1514::T - a161::T - # a162::T - a163::T - a164::T - a165::T - a166::T - a167::T - a168::T - a169::T - a1610::T - a1611::T - a1612::T - a1613::T - a1614::T - a1615::T - a171::T - # a172::T - a173::T - a174::T - a175::T - a176::T - a177::T - a178::T - a179::T - a1710::T - a1711::T - a1712::T - a1713::T - a1714::T - a1715::T - # a1716::T - b1::T - # b2::T - # b3::T - # b4::T - # b5::T - # b6::T - b7::T - b8::T - b9::T - b10::T - b11::T - b12::T - b13::T - b14::T - b15::T - # b16::T - # b17::T - bp1::T - # bp2::T - # bp3::T - # bp4::T - # bp5::T - # bp6::T - bp7::T - bp8::T - bp9::T - bp10::T - bp11::T - bp12::T - bp13::T - bp14::T - bp15::T - bp16::T - bp17::T - btilde1::T - # btilde2::T - # btilde3::T - # btilde4::T - # btilde5::T - # btilde6::T - btilde7::T - btilde8::T - btilde9::T - btilde10::T - btilde11::T - btilde12::T - btilde13::T - btilde14::T - btilde15::T - # btilde16::T - # btilde17::T - bptilde1::T - # bptilde2::T - # bptilde3::T - # bptilde4::T - # bptilde5::T - # bptilde6::T - bptilde7::T - bptilde8::T - bptilde9::T - bptilde10::T - bptilde11::T - bptilde12::T - bptilde13::T - bptilde14::T - bptilde15::T - bptilde16::T - bptilde17::T -end - -function DPRKN12ConstantCache(T::Type, T2::Type) - c1 = convert(T2, 1 // 50) - c2 = convert(T2, 1 // 25) - c3 = convert(T2, 1 // 10) - c4 = convert(T2, 2 // 15) - c5 = convert(T2, 4 // 25) - c6 = convert(T2, 1 // 20) - c7 = convert(T2, 1 // 5) - c8 = convert(T2, 1 // 4) - c9 = convert(T2, 1 // 3) - c10 = convert(T2, 1 // 2) - c11 = convert(T2, 5 // 9) - c12 = convert(T2, 3 // 4) - c13 = convert(T2, 6 // 7) - c14 = convert(T2, 8437 // 8926) - c15 = convert(T2, 1) - c16 = convert(T2, 1) - a21 = convert(T, 1 // 5000) - a31 = convert(T, 1 // 3750) - a32 = convert(T, 1 // 1875) - a41 = convert(T, 7 // 2400) - a42 = convert(T, -1 // 240) - a43 = convert(T, 1 // 160) - a51 = convert(T, 2 // 1215) - # a52 = convert(T,0) - a53 = convert(T, 4 // 729) - a54 = convert(T, 32 // 18225) - a61 = convert(T, 152 // 78125) - # a62 = convert(T,0) - a63 = convert(T, 1408 // 196875) - a64 = convert(T, 2048 // 703125) - a65 = convert(T, 432 // 546875) - a71 = convert(T, 29 // 51200) - # a72 = convert(T,0) - a73 = convert(T, 341 // 387072) - a74 = convert(T, -151 // 345600) - a75 = convert(T, 243 // 716800) - a76 = convert(T, -11 // 110592) - a81 = convert(T, 37 // 12000) - # a82 = convert(T,0) - # a83 = convert(T,0) - a84 = convert(T, 2 // 1125) - a85 = convert(T, 27 // 10000) - a86 = convert(T, 5 // 3168) - a87 = convert(T, 224 // 20625) - a91 = convert(T, 100467472123373 // 27511470744477696) - # a92 = convert(T,0) - a93 = convert(T, 101066550784375 // 25488568483854336) - a94 = convert(T, 49478218404275 // 15475202293768704) - a95 = convert(T, 21990175014231 // 2674726322379776) - a96 = convert(T, -3576386017671875 // 2723635603703291904) - a97 = convert(T, 16163228153 // 1654104722787) - a98 = convert(T, 38747524076705 // 10316801529179136) - a101 = convert(T, 62178936641284701329 // 16772293867250014666848) - # a102 = convert(T,0) - a103 = convert(T, 46108564356250 // 9072835168325103) - a104 = convert(T, 1522561724950 // 1296119309760729) - a105 = convert(T, -45978886013453735443 // 2174186242050927827184) - a106 = convert(T, 299403512366617849203125 // 4981371278573254356053856) - a107 = convert(T, 15571226634087127616 // 774466927638876610083) - a108 = convert(T, -133736375367792139885 // 4717207650164066625051) - a109 = convert(T, 7461389216 // 501451974639) - a111 = convert(T, 501256914705531962342417557181 // 14270506505142656332600844507392) - # a112 = convert(T,0) - a113 = convert(T, -1143766215625 // 132752960853408) - a114 = convert(T, -6864570325 // 1185294293334) - a115 = convert(T, 194348369382310456605879163404183 // 99893545535998594328205911551744) - a116 = convert(T, - -94634958447010580589908066176109375 // - 27549212808177898050085930321520256) - a117 = convert(T, -17006472665356285286219618514 // 155584463413110817059022733377) - a118 = convert(T, 33530528814694461893884349656345 // 14270506505142656332600844507392) - a119 = convert(T, -13439782155791134368 // 17777268379678341919) - a1110 = convert(T, 1441341768767571 // 13159456712985856) - a121 = convert(T, - parse(BigInt, "105854110734231079069010159870911189747853") // - parse(BigInt, "5156624149476760916008179453333467046288864")) - # a122 = convert(T,0) - a123 = convert(T, -144579793509250000 // 19842290513127000261) - a124 = convert(T, -101935644099967250 // 48188419817594143491) - a125 = convert(T, - parse(BigInt, "1585474394319811696785932424388196965") // - parse(BigInt, "1709257457318830856936350991091849456")) - a126 = convert(T, - parse(BigInt, "-843499776333774172853009613469456309715703125") // - parse(BigInt, "510505790798199330684809765880013237582597536")) - a127 = convert(T, - parse(BigInt, "-15057703799298260121553794369056896088480") // - parse(BigInt, "714327132646734138085088291809720015274157")) - a128 = convert(T, - parse(BigInt, "1749840442221344572962864758990584360232600") // - parse(BigInt, "1450300542040339007627300471250037606768743")) - a129 = convert(T, -11255775246405733991656178432768 // 27206626483067760480757659602193) - a1210 = convert(T, 669010348769579696 // 7368057640845834597) - a1211 = convert(T, 4598083098752 // 858563707934367) - a131 = convert(T, - parse(BigInt, "-1639758773684715326849438048667467886824967397") // - parse(BigInt, "11447568726280607813664651120965112496134881280")) - # a132 = convert(T,0) - a133 = convert(T, 3942453384375 // 314673684985856) - a134 = convert(T, 11737114158175 // 1719466921529856) - a135 = convert(T, - -23710715033675876683332701739887457 // - 4940189888325748664958546898558976) - a136 = convert(T, - parse(BigInt, "498150575499633273684774666731162498301909124515625") // - parse(BigInt, "87415924307623977386706008889913792042985180430336")) - a137 = convert(T, - parse(BigInt, "64881557768202140428371179540010005713998551") // - parse(BigInt, "85896810580242200654071863296887242202224768")) - a138 = convert(T, - parse(BigInt, "-2336309182318568698279006266321563486172654055") // - parse(BigInt, "18316109962048972501863441793544179993815810048")) - a139 = convert(T, - -493399374030747471036018890494175 // 251658285736841065236836942273664) - a1310 = convert(T, 418285003077108927126515545155 // 455369916679568501838710898688) - a1311 = convert(T, -15171723902781457 // 63532954684873728) - a1312 = convert(T, 1501203688494867 // 9434957026426880) - a141 = convert(T, - parse(BigInt, "34188549803371802849576690267872548602326398788953") // - parse(BigInt, "42496542183406636759747616530102745233754251202880")) - # a142 = convert(T,0) - a143 = convert(T, -18971246281693750 // 1138830954584356089) - a144 = convert(T, -59230464334542700 // 2765732318276293359) - a145 = convert(T, - parse(BigInt, "5147939981309774383134903239728881770043") // - parse(BigInt, "305929030949718561059100251282184099064")) - a146 = convert(T, - parse(BigInt, - "-3625720213550267723370658302114678215563058405229078120") // - parse(BigInt, "324512095420929759624784749347170583153994213035432256")) - a147 = convert(T, - parse(BigInt, "-60305503318319653518547439098565661266182518307816") // - parse(BigInt, "17856872599361492097414471889911176856851308259643")) - a148 = convert(T, - parse(BigInt, "-1036461878759982363277481306266144563833492657780645") // - parse(BigInt, "67994467493450618815596186448164392374006801924608")) - a149 = convert(T, - parse(BigInt, "128398681100219349205889126776607047000") // - parse(BigInt, "7473801441221286756994805323613917077")) - a1410 = convert(T, -49156374556350058671822606102117 // 9039888303968618912866414995904) - a1411 = convert(T, 12253036339964386945 // 8828680926314891943) - a1412 = convert(T, -647188390508758231059 // 1092148506009694282240) - a1413 = convert(T, 10915833599872 // 368729913707897) - a151 = convert(T, - parse(BigInt, - "-4939337286263213195547765488387521892799075623007291241961609516532") // - parse(BigInt, - "5408250052307451520718178852915698257207815452080611897685945761264")) - # a152 = convert(T,0) - a153 = convert(T, - 7588799849596321243074032368290625 // - parse(BigInt, "3147217749590114939838670370597819616")) - a154 = convert(T, - 16870665568420512953501332587233725 // - 955405388268427749593882076788623812) - a155 = convert(T, - parse(BigInt, - "-808642515918378014850308582271476014669568437579087796060") // - parse(BigInt, - "54447992506702009927986632715967769032585338753056786562")) - a156 = convert(T, - parse(BigInt, - "4610328329649866588704236006423149172472141907645890762410296050212") // - parse(BigInt, - "2135428689710103309390449198881479603148467934048051598947383737508")) - a157 = convert(T, - parse(BigInt, - "4159963831215576225909381034291748993887819834160487158570788681") // - parse(BigInt, - "1040533184037697645660563795162185415624171583014576682740416336")) - a158 = convert(T, - parse(BigInt, - "7381392142124351279433801934148706553542137071890521365664606664449580") // - parse(BigInt, - "259596002510757672994472584939953516345975141699869371088925396540699")) - a159 = convert(T, - parse(BigInt, - "-3336834334584052813468828675971359774694437229547862706920") // - parse(BigInt, - "132102862435303266640535426836147775872819092781208127980")) - a1510 = convert(T, - parse(BigInt, - "426619379967412086875039012957475466130081426048213491790") // - parse(BigInt, - "55162410119399855550108207148248549410926885937244965785")) - a1511 = convert(T, - parse(BigInt, "-630755628691078947314733435975762542732598947") // - parse(BigInt, "333503232300511886435069380727586592765317456")) - a1512 = convert(T, - parse(BigInt, "1522350657470125698997653827133798314909646891") // - parse(BigInt, "1520094067152619944607524353149267399623188480")) - a1513 = convert(T, - 305575414262755427083262606101825880 // - parse(BigInt, "65839748482572312891297405431209259829")) - a1514 = convert(T, - parse(BigInt, "256624643108055110568255672032710477795") // - parse(BigInt, "22874609758516552135947898572671559986304")) - a161 = convert(T, - parse(BigInt, - "-571597862947184314270186718640978947715678864684269066846") // - parse(BigInt, - "2077055064880303907616135969012720011907767004397744786340")) - # a162 = convert(T,0) - a163 = convert(T, 66981514290625 // 1829501741761029) - a164 = convert(T, 43495576635800 // 4443075658562499) - a165 = convert(T, - -127865248353371207265315478623656127 // - 10401415428935853634424440540325344) - a166 = convert(T, - parse(BigInt, - "1316565142658075739557231574080234814338066993483960326560") // - parse(BigInt, - "92668695535091962564795912774190176478892159517481612467")) - a167 = convert(T, - parse(BigInt, - "3881494143728609118531066904799685950051960514138645179820") // - parse(BigInt, - "2446349095978358868919950548516272963929118212742344026549")) - a168 = convert(T, - parse(BigInt, - "162922667049680755852592453758428194006198229544701786842910") // - parse(BigInt, - "66288722243155885736983218667976563740242178853010092663614")) - a169 = convert(T, - parse(BigInt, "-43986024977384568043684084266385512680544563954") // - parse(BigInt, "4922783599524658241955780540171948284522386185")) - a1610 = convert(T, - parse(BigInt, "285912200202585226675651763671663063668290787") // - parse(BigInt, "65371192072964016939690070594254881767827200")) - a1611 = convert(T, -6776815256667778089672518929 // 3693654613173093729492918708) - a1612 = convert(T, - 398946554885847045598775476868169 // 344154261237450078839899047372800) - a1613 = convert(T, -76630698033396272 // 4432017119727044925) - a1614 = convert(T, 28401702316003037 // 1469612686944417840) - a1615 = convert(T, - 66049942462586341419969330578128801 // - parse(BigInt, "12691068622536592094919763114637498325")) - a171 = convert(T, - parse(BigInt, - "83940754497395557520874219603241359529066454343054832302344735") // - parse(BigInt, - "64192596456995578553872477759926464976144474354415663868673233")) - # a172 = convert(T,0) - a173 = convert(T, 892543892035485503125 // 51401651664490002607536) - a174 = convert(T, -12732238157949399705325 // 686579204375687891972088) - a175 = convert(T, - parse(BigInt, "5290376174838819557032232941734928484252549") // - parse(BigInt, "357179779572898187570048915214361602000384")) - a176 = convert(T, - parse(BigInt, - "26873229338017506937199991804717456666650215387938173031932210") // - parse(BigInt, - "2863980005760296740624015421425947092438943496681472214589916")) - a177 = convert(T, - parse(BigInt, - "-1976497866818803305857417297961598735637414137241493515492778650") // - parse(BigInt, - "378029217824623393200881653405474359138017953416246216408422692")) - a178 = convert(T, - parse(BigInt, - "-1002860756304839757040188283199900676042073362417943601440986856950") // - parse(BigInt, - "20486915674765670626893195919603679319429068544972409068469849579")) - a179 = convert(T, - parse(BigInt, - "87398661196965758104117684348440686081062878816711392590") // - parse(BigInt, "2282122412587168891929052689609009868137678763277087160")) - a1710 = convert(T, - parse(BigInt, - "-7922242431969626895355493632206885458496418610471389") // - parse(BigInt, "748272134517487495468365669337985635214015258726400")) - a1711 = convert(T, - parse(BigInt, "2777643183645212014464950387658055285") // - parse(BigInt, "1141545470045611737197667093465955392")) - a1712 = convert(T, - parse(BigInt, "-1372659703515496442825084239977218110461") // - parse(BigInt, "1313121960368535725613950174847107891200")) - a1713 = convert(T, 6144417902699179309851023 // 85608793932459282773805825) - a1714 = convert(T, 140294243355138853053241 // 64884622846351585391642880) - a1715 = convert(T, - parse(BigInt, "168671028523891369934964082754523881107337") // - parse(BigInt, "24062875279623260368388427013982199424119600")) - # a1716 = convert(T,0) - b1 = convert(T, 63818747 // 5262156900) - # b2 = convert(T,0) - # b3 = convert(T,0) - # b4 = convert(T,0) - # b5 = convert(T,0) - # b6 = convert(T,0) - b7 = convert(T, 22555300000000 // 261366897038247) - b8 = convert(T, 1696514453125 // 6717619827072) - b9 = convert(T, -45359872 // 229764843) - b10 = convert(T, 19174962087 // 94371046000) - b11 = convert(T, -19310468 // 929468925) - b12 = convert(T, 16089185487681 // 146694672924800) - b13 = convert(T, 1592709632 // 41841694125) - b14 = convert(T, 52675701958271 // 4527711056573100) - b15 = convert(T, - parse(BigInt, "12540904472870916741199505796420811396") // - parse(BigInt, "2692319557780977037279406889319526430375")) - # b16 = convert(T,0) - # b17 = convert(T,0) - bp1 = convert(T, 63818747 // 5262156900) - # bp2 = convert(T,0) - # bp3 = convert(T,0) - # bp4 = convert(T,0) - # bp5 = convert(T,0) - # bp6 = convert(T,0) - bp7 = convert(T, 451106000000000 // 4965971043726693) - bp8 = convert(T, 8482572265625 // 26870479308288) - bp9 = convert(T, -181439488 // 689294529) - bp10 = convert(T, 57524886261 // 188742092000) - bp11 = convert(T, -38620936 // 929468925) - bp12 = convert(T, 144802669389129 // 586778691699200) - bp13 = convert(T, 6370838528 // 41841694125) - bp14 = convert(T, 368729913707897 // 4527711056573100) - bp15 = convert(T, - parse(BigInt, "111940113324845802831946788738852162520696") // - parse(BigInt, "1316544263754897771229629968877248424453375")) - bp16 = convert(T, -113178587 // 12362232960) - bp17 = convert(T, 1 // 40) - - btilde1 = convert(T, - Int64(63818747) // Int64(5262156900) - - Int64(27121957) // Int64(1594593000)) - # btilde2 = convert(T,0) - # btilde3 = convert(T,0) - # btilde4 = convert(T,0) - # btilde5 = convert(T,0) - # btilde6 = convert(T,0) - btilde7 = convert(T, - Int64(22555300000000) // Int64(261366897038247) - - Int64(4006163300000) // Int64(55441463008113)) - btilde8 = convert(T, - Int64(1696514453125) // Int64(6717619827072) - - Int64(9466403125) // Int64(25445529648)) - btilde9 = convert(T, - Int64(-45359872) // Int64(229764843) + - Int64(163199648) // Int64(406149975)) - btilde10 = convert(T, - Int64(19174962087) // Int64(94371046000) - - Int64(23359833) // Int64(69636250)) - btilde11 = convert(T, - Int64(-19310468) // Int64(929468925) + - Int64(18491714) // Int64(140828625)) - btilde12 = convert(T, - Int64(16089185487681) // Int64(146694672924800) - - Int64(11052304606701) // Int64(58344472186000)) - btilde13 = convert(T, - Int64(1592709632) // Int64(41841694125) - - Int64(1191129152) // Int64(44377554375)) - btilde14 = convert(T, - Int64(52675701958271) // Int64(4527711056573100) - - Int64(2033811086741) // Int64(124730332137000)) - btilde15 = convert(T, - parse(BigInt, "12540904472870916741199505796420811396") // - parse(BigInt, "2692319557780977037279406889319526430375") - - parse(BigInt, "3616943474975740389660406409450169802") // - parse(BigInt, "951830146690244407118982233597812374375")) - # btilde16 = convert(T,0) - # btilde17 = convert(T,0) - bptilde1 = convert(T, - Int64(63818747) // Int64(5262156900) - - Int64(27121957) // Int64(1594593000)) - # bptilde2 = convert(T,0) - # bptilde3 = convert(T,0) - # bptilde4 = convert(T,0) - # bptilde5 = convert(T,0) - # bptilde6 = convert(T,0) - bptilde7 = convert(T, - Int64(451106000000000) // Int64(4965971043726693) - - Int64(4217014000000) // Int64(55441463008113)) - bptilde8 = convert(T, - Int64(8482572265625) // Int64(26870479308288) - - Int64(47332015625) // Int64(101782118592)) - bptilde9 = convert(T, - Int64(-181439488) // Int64(689294529) + - Int64(652798592) // Int64(1218449925)) - bptilde10 = convert(T, - Int64(57524886261) // Int64(188742092000) - - Int64(70079499) // Int64(139272500)) - bptilde11 = convert(T, - Int64(-38620936) // Int64(929468925) + - Int64(36983428) // Int64(140828625)) - bptilde12 = convert(T, - Int64(144802669389129) // Int64(586778691699200) - - Int64(99470741460309) // Int64(233377888744000)) - bptilde13 = convert(T, - Int64(6370838528) // Int64(41841694125) - - Int64(4764516608) // Int64(44377554375)) - bptilde14 = convert(T, - Int64(368729913707897) // Int64(4527711056573100) - - Int64(14236677607187) // Int64(124730332137000)) - bptilde15 = convert(T, - parse(BigInt, "111940113324845802831946788738852162520696") // - parse(BigInt, "1316544263754897771229629968877248424453375") - - parse(BigInt, "198066487470143918516004831967805004004") // - parse(BigInt, "2855490440070733221356946700793437123125")) - bptilde16 = convert(T, Int64(-113178587) // Int64(12362232960) - Int64(1) // Int64(50)) - bptilde17 = convert(T, 1 // 40) - DPRKN12ConstantCache(c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, - c16, a21, a31, a32, a41, a42, a43, a51, a53, a54, a61, a63, a64, - a65, a71, a73, a74, a75, a76, a81, a84, a85, a86, a87, a91, a93, - a94, a95, a96, a97, a98, a101, a103, a104, a105, a106, a107, a108, - a109, a111, a113, a114, a115, a116, a117, a118, a119, a1110, a121, - a123, a124, a125, a126, a127, a128, a129, a1210, a1211, a131, a133, - a134, a135, a136, a137, a138, a139, a1310, a1311, a1312, a141, - a143, a144, a145, a146, a147, a148, a149, a1410, a1411, a1412, - a1413, a151, a153, a154, a155, a156, a157, a158, a159, a1510, - a1511, a1512, a1513, a1514, a161, a163, a164, a165, a166, a167, - a168, a169, a1610, a1611, a1612, a1613, a1614, a1615, a171, a173, - a174, a175, a176, a177, a178, a179, a1710, a1711, a1712, a1713, - a1714, a1715, b1, b7, b8, b9, b10, b11, b12, b13, b14, b15, bp1, - bp7, bp8, bp9, bp10, bp11, bp12, bp13, bp14, bp15, bp16, bp17, - btilde1, btilde7, btilde8, btilde9, btilde10, btilde11, btilde12, - btilde13, btilde14, btilde15, bptilde1, bptilde7, bptilde8, - bptilde9, bptilde10, bptilde11, bptilde12, bptilde13, bptilde14, - bptilde15, bptilde16, bptilde17) -end - -function DPRKN12ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - DPRKN12ConstantCache(convert(T2, 2.0e-2), - convert(T2, 4.0e-2), - convert(T2, 1.0e-1), - convert(T2, 1.33333333333333333333333333333e-1), - convert(T2, 1.6e-1), - convert(T2, 5.0e-2), - convert(T2, 2.0e-1), - convert(T2, 2.5e-1), - convert(T2, 3.33333333333333333333333333333e-1), - convert(T2, 5.0e-1), - convert(T2, 5.55555555555555555555555555556e-1), - convert(T2, 7.5e-1), - convert(T2, 8.57142857142857142857142857143e-1), - convert(T2, 9.45216222272014340129957427739e-1), - convert(T2, 1.0e0), - convert(T2, 1.0e0), - convert(T, 2.0e-4), - convert(T, 2.66666666666666666666666666667e-4), - convert(T, 5.33333333333333333333333333333e-4), - convert(T, 2.91666666666666666666666666667e-3), - convert(T, -4.16666666666666666666666666667e-3), - convert(T, 6.25e-3), - convert(T, 1.64609053497942386831275720165e-3), - convert(T, 5.48696844993141289437585733882e-3), - convert(T, 1.75582990397805212620027434842e-3), - convert(T, 1.9456e-3), - convert(T, 7.15174603174603174603174603175e-3), - convert(T, 2.91271111111111111111111111111e-3), - convert(T, 7.89942857142857142857142857143e-4), - convert(T, 5.6640625e-4), - convert(T, 8.80973048941798941798941798942e-4), - convert(T, -4.36921296296296296296296296296e-4), - convert(T, 3.39006696428571428571428571429e-4), - convert(T, -9.94646990740740740740740740741e-5), - convert(T, 3.08333333333333333333333333333e-3), - convert(T, 1.77777777777777777777777777778e-3), - convert(T, 2.7e-3), - convert(T, 1.57828282828282828282828282828e-3), - convert(T, 1.08606060606060606060606060606e-2), - convert(T, 3.65183937480112971375119150338e-3), - convert(T, 3.96517171407234306617557289807e-3), - convert(T, 3.19725826293062822350093426091e-3), - convert(T, 8.22146730685543536968701883401e-3), - convert(T, -1.31309269595723798362013884863e-3), - convert(T, 9.77158696806486781562609494147e-3), - convert(T, 3.75576906923283379487932641079e-3), - convert(T, 3.70724106871850081019565530521e-3), - convert(T, 5.08204585455528598076108163479e-3), - convert(T, 1.17470800217541204473569104943e-3), - convert(T, -2.11476299151269914996229766362e-2), - convert(T, 6.01046369810788081222573525136e-2), - convert(T, 2.01057347685061881846748708777e-2), - convert(T, -2.83507501229335808430366774368e-2), - convert(T, 1.48795689185819327555905582479e-2), - convert(T, 3.51253765607334415311308293052e-2), - convert(T, -8.61574919513847910340576078545e-3), - convert(T, -5.79144805100791652167632252471e-3), - convert(T, 1.94555482378261584239438810411e0), - convert(T, -3.43512386745651359636787167574e0), - convert(T, -1.09307011074752217583892572001e-1), - convert(T, 2.3496383118995166394320161088e0), - convert(T, -7.56009408687022978027190729778e-1), - convert(T, 1.09528972221569264246502018618e-1), - convert(T, 2.05277925374824966509720571672e-2), - convert(T, -7.28644676448017991778247943149e-3), - convert(T, -2.11535560796184024069259562549e-3), - convert(T, 9.27580796872352224256768033235e-1), - convert(T, -1.65228248442573667907302673325e0), - convert(T, -2.10795630056865698191914366913e-2), - convert(T, 1.20653643262078715447708832536e0), - convert(T, -4.13714477001066141324662463645e-1), - convert(T, 9.07987398280965375956795739516e-2), - convert(T, 5.35555260053398504916870658215e-3), - convert(T, -1.43240788755455150458921091632e-1), - convert(T, 1.25287037730918172778464480231e-2), - convert(T, 6.82601916396982712868112411737e-3), - convert(T, -4.79955539557438726550216254291e0), - convert(T, 5.69862504395194143379169794156e0), - convert(T, 7.55343036952364522249444028716e-1), - convert(T, -1.27554878582810837175400796542e-1), - convert(T, -1.96059260511173843289133255423e0), - convert(T, 9.18560905663526240976234285341e-1), - convert(T, -2.38800855052844310534827013402e-1), - convert(T, 1.59110813572342155138740170963e-1), - convert(T, 8.04501920552048948697230778134e-1), - convert(T, -1.66585270670112451778516268261e-2), - convert(T, -2.1415834042629734811731437191e-2), - convert(T, 1.68272359289624658702009353564e1), - convert(T, -1.11728353571760979267882984241e1), - convert(T, -3.37715929722632374148856475521e0), - convert(T, -1.52433266553608456461817682939e1), - convert(T, 1.71798357382154165620247684026e1), - convert(T, -5.43771923982399464535413738556e0), - convert(T, 1.38786716183646557551256778839e0), - convert(T, -5.92582773265281165347677029181e-1), - convert(T, 2.96038731712973527961592794552e-2), - convert(T, -9.13296766697358082096250482648e-1), - convert(T, 2.41127257578051783924489946102e-3), - convert(T, 1.76581226938617419820698839226e-2), - convert(T, -1.48516497797203838246128557088e1), - convert(T, 2.15897086700457560030782161561e0), - convert(T, 3.99791558311787990115282754337e0), - convert(T, 2.84341518002322318984542514988e1), - convert(T, -2.52593643549415984378843352235e1), - convert(T, 7.7338785423622373655340014114e0), - convert(T, -1.8913028948478674610382580129e0), - convert(T, 1.00148450702247178036685959248e0), - convert(T, 4.64119959910905190510518247052e-3), - convert(T, 1.12187550221489570339750499063e-2), - convert(T, -2.75196297205593938206065227039e-1), - convert(T, 3.66118887791549201342293285553e-2), - convert(T, 9.7895196882315626246509967162e-3), - convert(T, -1.2293062345886210304214726509e1), - convert(T, 1.42072264539379026942929665966e1), - convert(T, 1.58664769067895368322481964272e0), - convert(T, 2.45777353275959454390324346975e0), - convert(T, -8.93519369440327190552259086374e0), - convert(T, 4.37367273161340694839327077512e0), - convert(T, -1.83471817654494916304344410264e0), - convert(T, 1.15920852890614912078083198373e0), - convert(T, -1.72902531653839221518003422953e-2), - convert(T, 1.93259779044607666727649875324e-2), - convert(T, 5.20444293755499311184926401526e-3), - convert(T, 1.30763918474040575879994562983e0), - convert(T, 1.73641091897458418670879991296e-2), - convert(T, -1.8544456454265795024362115588e-2), - convert(T, 1.48115220328677268968478356223e1), - convert(T, 9.38317630848247090787922177126e0), - convert(T, -5.2284261999445422541474024553e0), - convert(T, -4.89512805258476508040093482743e1), - convert(T, 3.82970960343379225625583875836e1), - convert(T, -1.05873813369759797091619037505e1), - convert(T, 2.43323043762262763585119618787e0), - convert(T, -1.04534060425754442848652456513e0), - convert(T, 7.17732095086725945198184857508e-2), - convert(T, 2.16221097080827826905505320027e-3), - convert(T, 7.00959575960251423699282781988e-3), - convert(T, 0.012127868517185414), - convert(T, 0.08629746251568875), - convert(T, 0.2525469581187147), - convert(T, -0.1974186799326823), - convert(T, 0.2031869190789726), - convert(T, -0.020775808077714918), - convert(T, 0.10967804874502014), - convert(T, 0.038065132526466504), - convert(T, 0.01163406880432423), - convert(T, 0.0046580297040248785), - convert(T, 0.012127868517185414), - convert(T, 0.09083943422704079), - convert(T, 0.3156836976483934), - convert(T, -0.2632249065769097), - convert(T, 0.3047803786184589), - convert(T, -0.041551616155429835), - convert(T, 0.2467756096762953), - convert(T, 0.15226053010586602), - convert(T, 0.08143848163026961), - convert(T, 0.08502571193890811), - convert(T, -0.009155189630077963), - convert(T, 0.025), - convert(T, -0.004880833389821577), - convert(T, 0.014038126584857338), - convert(T, -0.11947921920803832), - convert(T, 0.20440246507662121), - convert(T, -0.1322681492223791), - convert(T, 0.11053069299761689), - convert(T, -0.07975385787102851), - convert(T, 0.011224330486437457), - convert(T, -0.004671596801593694), - convert(T, 0.0008580413473282841), - convert(T, -0.004880833389821577), - convert(T, 0.014776975352481408), - convert(T, -0.1493490240100479), - convert(T, 0.2725366201021616), - convert(T, -0.19840222383356862), - convert(T, 0.22106138599523378), - convert(T, -0.17944618020981415), - convert(T, 0.04489732194574983), - convert(T, -0.03270117761115586), - convert(T, 0.015662325288859434), - convert(T, -0.029155189630077964), - convert(T, 0.025)) -end From aa29690f728712ffa4e7065d0fa12c3e73625bca Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 11:01:10 -0400 Subject: [PATCH 24/71] Delete src/tableaus/symplectic_tableaus.jl --- src/tableaus/symplectic_tableaus.jl | 807 ---------------------------- 1 file changed, 807 deletions(-) delete mode 100644 src/tableaus/symplectic_tableaus.jl diff --git a/src/tableaus/symplectic_tableaus.jl b/src/tableaus/symplectic_tableaus.jl deleted file mode 100644 index 98676979c3..0000000000 --- a/src/tableaus/symplectic_tableaus.jl +++ /dev/null @@ -1,807 +0,0 @@ -struct Symplectic2ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - a1::T - a2::T - b1::T - b2::T -end - -function PseudoVerletLeapfrogConstantCache(T, T2) - a1 = convert(T, 1) - a2 = convert(T, 0) - b1 = convert(T, 1 // 2) - b2 = convert(T, 1 // 2) - Symplectic2ConstantCache{T, T2}(a1, a2, b1, b2) -end - -function McAte2ConstantCache(T, T2) - a2 = convert(T, 1 - (1 / 2) * sqrt(convert(T, 2))) - a1 = convert(T, 1 - a2) - b2 = convert(T, 1 / (2 * (1 - a2))) - b1 = convert(T, 1 - b2) - Symplectic2ConstantCache{T, T2}(a1, a2, b1, b2) -end - -function VerletLeapfrogConstantCache(T, T2) - a1 = convert(T, 1 // 2) - a2 = convert(T, 1 // 2) - b1 = convert(T, 0) - b2 = convert(T, 1) - Symplectic2ConstantCache{T, T2}(a1, a2, b1, b2) -end - -struct Symplectic3ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - a1::T - a2::T - a3::T - b1::T - b2::T - b3::T -end - -function Ruth3ConstantCache(T, T2) - a1 = convert(T, 2 // 3) - a2 = convert(T, -2 // 3) - a3 = convert(T, 1) - b1 = convert(T, 7 // 24) - b2 = convert(T, 3 // 4) - b3 = convert(T, -1 // 24) - Symplectic3ConstantCache{T, T2}(a1, a2, a3, b1, b2, b3) -end - -function McAte3ConstantCache(T, T2) - a1 = convert(T, 0.9196615230173999) - a2 = convert(T, 0.25 / a1 - a1 / 2) - a3 = convert(T, 1 - a1 - a2) - b1 = convert(T, a3) - b2 = convert(T, a2) - b3 = convert(T, a1) - Symplectic3ConstantCache{T, T2}(a1, a2, a3, b1, b2, b3) -end - -struct Symplectic4ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - a1::T - a2::T - a3::T - a4::T - b1::T - b2::T - b3::T - b4::T -end - -function CandyRoz4ConstantCache(T, T2) - a1 = convert(T, (2 + T(2)^(1 // 3) + convert(T, 2)^(-1 // 3)) / 6) - a2 = convert(T, (1 - T(2)^(1 // 3) - convert(T, 2)^(-1 // 3)) / 6) - a3 = convert(T, a2) - a4 = convert(T, a1) - b1 = convert(T, 0) - b2 = convert(T, (2 - T(2)^(1 // 3))^-1) - b3 = convert(T, (1 - T(2)^(2 // 3))^-1) - b4 = convert(T, b2) - Symplectic4ConstantCache{T, T2}(a1, a2, a3, a4, b1, b2, b3, b4) -end - -function McAte4ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - a1 = convert(T, 0.515352837431122936) - a2 = convert(T, -0.085782019412973646) - a3 = convert(T, 0.441583023616466524) - a4 = convert(T, 0.128846158365384185) - b1 = convert(T, 0.134496199277431089) - b2 = convert(T, -0.224819803079420806) - b3 = convert(T, 0.756320000515668291) - b4 = convert(T, 0.334003603286321425) - Symplectic4ConstantCache{T, T2}(a1, a2, a3, a4, b1, b2, b3, b4) -end - -function McAte4ConstantCache(T::Type, T2::Type) - a1 = convert(T, big"0.515352837431122936") - a2 = convert(T, big"-0.085782019412973646") - a3 = convert(T, big" 0.441583023616466524") - a4 = convert(T, big" 0.128846158365384185") - b1 = convert(T, big" 0.134496199277431089") - b2 = convert(T, big"-0.224819803079420806") - b3 = convert(T, big" 0.756320000515668291") - b4 = convert(T, big" 0.334003603286321425") - Symplectic4ConstantCache{T, T2}(a1, a2, a3, a4, b1, b2, b3, b4) -end - -struct Symplectic45ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - a1::T - a2::T - a3::T - a4::T - a5::T - b1::T - b2::T - b3::T - b4::T - b5::T -end - -function CalvoSanz4ConstantCache(T, T2) - a1 = convert(T, 0.205177661542290) - a2 = convert(T, 0.403021281604210) - a3 = -convert(T, 0.12092087633891) - a4 = convert(T, 0.512721933192410) - a5 = convert(T, 0.0) - b1 = convert(T, 0.061758858135626) - b2 = convert(T, 0.33897802655364) - b3 = convert(T, 0.61479130717558) - b4 = -convert(T, 0.14054801465937) - b5 = convert(T, 0.12501982279453) - Symplectic45ConstantCache{T, T2}(a1, a2, a3, a4, a5, b1, b2, b3, b4, b5) -end - -# Broken -# http://epubs.siam.org/doi/pdf/10.1137/0916010 -# On the numerical integration of ordinary differential equations by symmetric composition methods -function McAte42ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - a1 = convert(T, 0.40518861839525227722) - a2 = convert(T, -0.28714404081652408900) - a3 = 1 - 2a1 - 2a2 - a4 = a2 - a5 = a1 - b1 = convert(T, -3 // 73) - b2 = convert(T, 17 // 59) - b3 = 1 - 2b1 - 2b2 - b4 = b2 - b5 = b1 - Symplectic45ConstantCache{T, T2}(a1, a2, a3, a4, a5, b1, b2, b3, b4, b5) -end - -function McAte42ConstantCache(T::Type, T2::Type) - a1 = convert(T, big"0.40518861839525227722") - a2 = convert(T, big"-0.28714404081652408900") - a3 = 1 - 2a1 - 2a2 - a4 = a2 - a5 = a1 - b1 = convert(T, -3 // 73) - b2 = convert(T, 17 // 59) - b3 = 1 - 2b1 - 2b2 - b4 = b2 - b5 = b1 - Symplectic45ConstantCache{T, T2}(a1, a2, a3, a4, a5, b1, b2, b3, b4, b5) -end - -struct Symplectic5ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - a1::T - a2::T - a3::T - a4::T - a5::T - a6::T - b1::T - b2::T - b3::T - b4::T - b5::T - b6::T -end - -function McAte5ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - a1 = convert(T, 0.339839625839110000) - a2 = convert(T, -0.088601336903027329) - a3 = convert(T, 0.5858564768259621188) - a4 = convert(T, -0.603039356536491888) - a5 = convert(T, 0.3235807965546976394) - a6 = convert(T, 0.4423637942197494587) - b1 = convert(T, 0.1193900292875672758) - b2 = convert(T, 0.6989273703824752308) - b3 = convert(T, -0.1713123582716007754) - b4 = convert(T, 0.4012695022513534480) - b5 = convert(T, 0.0107050818482359840) - b6 = convert(T, -0.0589796254980311632) - Symplectic5ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, b1, b2, b3, b4, b5, b6) -end - -function McAte5ConstantCache(T::Type, T2::Type) - a1 = convert(T, big"0.339839625839110000") - a2 = convert(T, big"-0.088601336903027329") - a3 = convert(T, big"0.5858564768259621188") - a4 = convert(T, big"-0.603039356536491888") - a5 = convert(T, big"0.3235807965546976394") - a6 = convert(T, big"0.4423637942197494587") - b1 = convert(T, big"0.1193900292875672758") - b2 = convert(T, big"0.6989273703824752308") - b3 = convert(T, big"-0.1713123582716007754") - b4 = convert(T, big"0.4012695022513534480") - b5 = convert(T, big"0.0107050818482359840") - b6 = convert(T, big"-0.0589796254980311632") - Symplectic5ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, b1, b2, b3, b4, b5, b6) -end - -struct Symplectic6ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - a1::T - a2::T - a3::T - a4::T - a5::T - a6::T - a7::T - a8::T - b1::T - b2::T - b3::T - b4::T - b5::T - b6::T - b7::T - b8::T -end - -function Yoshida6ConstantCache(T, T2) - a1 = convert(T, 0.78451361047756) - a2 = convert(T, 0.23557321335936) - a3 = convert(T, -1.1776799841789) - a4 = convert(T, 1.3151863206839) - a5 = convert(T, a3) - a6 = convert(T, a2) - a7 = convert(T, a1) - a8 = convert(T, 0.0) - b1 = a1 / 2 - b2 = convert(T, (a1 + a2) / 2) - b3 = convert(T, (a2 + a3) / 2) - b4 = convert(T, (a3 + a4) / 2) - b5 = convert(T, b4) - b6 = convert(T, b3) - b7 = convert(T, b2) - b8 = convert(T, b1) - Symplectic6ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, a7, a8, b1, b2, b3, b4, b5, b6, - b7, b8) -end - -struct Symplectic62ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - a1::T - a2::T - a3::T - a4::T - a5::T - a6::T - a7::T - a8::T - a9::T - a10::T - b1::T - b2::T - b3::T - b4::T - b5::T - b6::T - b7::T - b8::T - b9::T - b10::T -end - -function KahanLi6ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - a1 = convert(T, 0.39216144400731413927925056) - a2 = convert(T, 0.33259913678935943859974864) - a3 = convert(T, -0.70624617255763935980996482) - a4 = convert(T, 0.08221359629355080023149045) - a5 = convert(T, 0.79854399093482996339895035) - a6 = a4 - a7 = a3 - a8 = a2 - a9 = a1 - a10 = convert(T, 0) - b1 = convert(T, a1 / 2) - b2 = convert(T, (a1 + a2) / 2) - b3 = convert(T, (a2 + a3) / 2) - b4 = convert(T, (a3 + a4) / 2) - b5 = convert(T, (a4 + a5) / 2) - b6 = b5 - b7 = b4 - b8 = b3 - b9 = b2 - b10 = b1 - Symplectic62ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, b1, b2, b3, - b4, b5, b6, b7, b8, b9, b10) -end - -function KahanLi6ConstantCache(T::Type, T2::Type) - a1 = convert(T, big"0.39216144400731413927925056") - a2 = convert(T, big"0.33259913678935943859974864") - a3 = convert(T, big"-0.70624617255763935980996482") - a4 = convert(T, big"0.08221359629355080023149045") - a5 = convert(T, big"0.79854399093482996339895035") - a6 = a4 - a7 = a3 - a8 = a2 - a9 = a1 - a10 = convert(T, 0) - b1 = convert(T, a1 / 2) - b2 = convert(T, (a1 + a2) / 2) - b3 = convert(T, (a2 + a3) / 2) - b4 = convert(T, (a3 + a4) / 2) - b5 = convert(T, (a4 + a5) / 2) - b6 = b5 - b7 = b4 - b8 = b3 - b9 = b2 - b10 = b1 - Symplectic62ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, b1, b2, b3, - b4, b5, b6, b7, b8, b9, b10) -end - -struct McAte8ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - a1::T - a2::T - a3::T - a4::T - a5::T - a6::T - a7::T - a8::T - a9::T - a10::T - a11::T - a12::T - a13::T - a14::T - a15::T - a16::T - b1::T - b2::T - b3::T - b4::T - b5::T - b6::T - b7::T - b8::T - b9::T - b10::T - b11::T - b12::T - b13::T - b14::T - b15::T - b16::T -end - -function McAte8ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - a1 = convert(T, 0.74167036435061295344822780) - a2 = convert(T, -0.40910082580003159399730010) - a3 = convert(T, 0.19075471029623837995387626) - a4 = convert(T, -0.57386247111608226665638773) - a5 = convert(T, 0.29906418130365592384446354) - a6 = convert(T, 0.33462491824529818378495798) - a7 = convert(T, 0.31529309239676659663205666) - a8 = convert(T, -0.79688793935291635401978884) - a9 = a7 - a10 = a6 - a11 = a5 - a12 = a4 - a13 = a3 - a14 = a2 - a15 = a1 - a16 = convert(T, 0) - b1 = convert(T, a1 / 2) - b2 = convert(T, (a1 + a2) / 2) - b3 = convert(T, (a2 + a3) / 2) - b4 = convert(T, (a3 + a4) / 2) - b5 = convert(T, (a4 + a5) / 2) - b6 = convert(T, (a5 + a6) / 2) - b7 = convert(T, (a6 + a7) / 2) - b8 = convert(T, (a7 + a8) / 2) - b9 = b8 - b10 = b7 - b11 = b6 - b12 = b5 - b13 = b4 - b14 = b3 - b15 = b2 - b16 = b1 - McAte8ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, - a15, a16, - b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, - b15, b16) -end - -function McAte8ConstantCache(T::Type, T2::Type) - a1 = convert(T, big"0.74167036435061295344822780") - a2 = convert(T, big"-0.40910082580003159399730010") - a3 = convert(T, big"0.19075471029623837995387626") - a4 = convert(T, big"-0.57386247111608226665638773") - a5 = convert(T, big"0.29906418130365592384446354") - a6 = convert(T, big"0.33462491824529818378495798") - a7 = convert(T, big"0.31529309239676659663205666") - a8 = convert(T, big"-0.79688793935291635401978884") - a9 = a7 - a10 = a6 - a11 = a5 - a12 = a4 - a13 = a3 - a14 = a2 - a15 = a1 - a16 = convert(T, 0) - b1 = convert(T, a1 / 2) - b2 = convert(T, (a1 + a2) / 2) - b3 = convert(T, (a2 + a3) / 2) - b4 = convert(T, (a3 + a4) / 2) - b5 = convert(T, (a4 + a5) / 2) - b6 = convert(T, (a5 + a6) / 2) - b7 = convert(T, (a6 + a7) / 2) - b8 = convert(T, (a7 + a8) / 2) - b9 = b8 - b10 = b7 - b11 = b6 - b12 = b5 - b13 = b4 - b14 = b3 - b15 = b2 - b16 = b1 - McAte8ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, - a15, a16, - b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, - b15, b16) -end - -struct KahanLi8ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - a1::T - a2::T - a3::T - a4::T - a5::T - a6::T - a7::T - a8::T - a9::T - a10::T - a11::T - a12::T - a13::T - a14::T - a15::T - a16::T - a17::T - a18::T - b1::T - b2::T - b3::T - b4::T - b5::T - b6::T - b7::T - b8::T - b9::T - b10::T - b11::T - b12::T - b13::T - b14::T - b15::T - b16::T - b17::T - b18::T -end - -function KahanLi8ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - a1 = convert(T, 0.13020248308889008087881763) - a2 = convert(T, 0.56116298177510838456196441) - a3 = convert(T, -0.38947496264484728640807860) - a4 = convert(T, 0.15884190655515560089621075) - a5 = convert(T, -0.39590389413323757733623154) - a6 = convert(T, 0.18453964097831570709183254) - a7 = convert(T, 0.25837438768632204729397911) - a8 = convert(T, 0.29501172360931029887096624) - a9 = convert(T, -0.60550853383003451169892108) - a10 = a8 - a11 = a7 - a12 = a6 - a13 = a5 - a14 = a4 - a15 = a3 - a16 = a2 - a17 = a1 - a18 = convert(T, 0) - b1 = convert(T, a1 / 2) - b2 = convert(T, (a1 + a2) / 2) - b3 = convert(T, (a2 + a3) / 2) - b4 = convert(T, (a3 + a4) / 2) - b5 = convert(T, (a4 + a5) / 2) - b6 = convert(T, (a5 + a6) / 2) - b7 = convert(T, (a6 + a7) / 2) - b8 = convert(T, (a7 + a8) / 2) - b9 = convert(T, (a8 + a9) / 2) - b10 = b9 - b11 = b8 - b12 = b7 - b13 = b6 - b14 = b5 - b15 = b4 - b16 = b3 - b17 = b2 - b18 = b1 - KahanLi8ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, - a14, a15, a16, a17, a18, - b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, - b14, b15, b16, b17, b18) -end - -function KahanLi8ConstantCache(T::Type, T2::Type) - a1 = convert(T, big"0.13020248308889008087881763") - a2 = convert(T, big"0.56116298177510838456196441") - a3 = convert(T, big"-0.38947496264484728640807860") - a4 = convert(T, big"0.15884190655515560089621075") - a5 = convert(T, big"-0.39590389413323757733623154") - a6 = convert(T, big"0.18453964097831570709183254") - a7 = convert(T, big"0.25837438768632204729397911") - a8 = convert(T, big"0.29501172360931029887096624") - a9 = convert(T, big"-0.60550853383003451169892108") - a10 = a8 - a11 = a7 - a12 = a6 - a13 = a5 - a14 = a4 - a15 = a3 - a16 = a2 - a17 = a1 - a18 = convert(T, 0) - b1 = convert(T, a1 / 2) - b2 = convert(T, (a1 + a2) / 2) - b3 = convert(T, (a2 + a3) / 2) - b4 = convert(T, (a3 + a4) / 2) - b5 = convert(T, (a4 + a5) / 2) - b6 = convert(T, (a5 + a6) / 2) - b7 = convert(T, (a6 + a7) / 2) - b8 = convert(T, (a7 + a8) / 2) - b9 = convert(T, (a8 + a9) / 2) - b10 = b9 - b11 = b8 - b12 = b7 - b13 = b6 - b14 = b5 - b15 = b4 - b16 = b3 - b17 = b2 - b18 = b1 - KahanLi8ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, - a14, a15, a16, a17, a18, - b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, - b14, b15, b16, b17, b18) -end - -struct SofSpa10ConstantCache{T, T2} <: OrdinaryDiffEqConstantCache - a1::T - a2::T - a3::T - a4::T - a5::T - a6::T - a7::T - a8::T - a9::T - a10::T - a11::T - a12::T - a13::T - a14::T - a15::T - a16::T - a17::T - a18::T - a19::T - a20::T - a21::T - a22::T - a23::T - a24::T - a25::T - a26::T - a27::T - a28::T - a29::T - a30::T - a31::T - a32::T - a33::T - a34::T - a35::T - a36::T - b1::T - b2::T - b3::T - b4::T - b5::T - b6::T - b7::T - b8::T - b9::T - b10::T - b11::T - b12::T - b13::T - b14::T - b15::T - b16::T - b17::T - b18::T - b19::T - b20::T - b21::T - b22::T - b23::T - b24::T - b25::T - b26::T - b27::T - b28::T - b29::T - b30::T - b31::T - b32::T - b33::T - b34::T - b35::T - b36::T -end - -function SofSpa10ConstantCache(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - a1 = convert(T, 0.07879572252168641926390768) - a2 = convert(T, 0.31309610341510852776481247) - a3 = convert(T, 0.02791838323507806610952027) - a4 = convert(T, -0.22959284159390709415121340) - a5 = convert(T, 0.13096206107716486317465686) - a6 = convert(T, -0.26973340565451071434460973) - a7 = convert(T, 0.07497334315589143566613711) - a8 = convert(T, 0.11199342399981020488957508) - a9 = convert(T, 0.36613344954622675119314812) - a10 = convert(T, -0.39910563013603589787862981) - a11 = convert(T, 0.10308739852747107731580277) - a12 = convert(T, 0.41143087395589023782070412) - a13 = convert(T, -0.00486636058313526176219566) - a14 = convert(T, -0.39203335370863990644808194) - a15 = convert(T, 0.05194250296244964703718290) - a16 = convert(T, 0.05066509075992449633587434) - a17 = convert(T, 0.04967437063972987905456880) - a18 = convert(T, 0.04931773575959453791768001) - a19 = a17 - a20 = a16 - a21 = a15 - a22 = a14 - a23 = a13 - a24 = a12 - a25 = a11 - a26 = a10 - a27 = a9 - a28 = a8 - a29 = a7 - a30 = a6 - a31 = a5 - a32 = a4 - a33 = a3 - a34 = a2 - a35 = a1 - a36 = convert(T, 0) - b1 = convert(T, a1 / 2) - b2 = convert(T, (a1 + a2) / 2) - b3 = convert(T, (a2 + a3) / 2) - b4 = convert(T, (a3 + a4) / 2) - b5 = convert(T, (a4 + a5) / 2) - b6 = convert(T, (a5 + a6) / 2) - b7 = convert(T, (a6 + a7) / 2) - b8 = convert(T, (a7 + a8) / 2) - b9 = convert(T, (a8 + a9) / 2) - b10 = convert(T, (a9 + a10) / 2) - b11 = convert(T, (a10 + a11) / 2) - b12 = convert(T, (a11 + a12) / 2) - b13 = convert(T, (a12 + a13) / 2) - b14 = convert(T, (a13 + a14) / 2) - b15 = convert(T, (a14 + a15) / 2) - b16 = convert(T, (a15 + a16) / 2) - b17 = convert(T, (a16 + a17) / 2) - b18 = convert(T, (a17 + a18) / 2) - b19 = b18 - b20 = b17 - b21 = b16 - b22 = b15 - b23 = b14 - b24 = b13 - b25 = b12 - b26 = b11 - b27 = b10 - b28 = b9 - b29 = b8 - b30 = b7 - b31 = b6 - b32 = b5 - b33 = b4 - b34 = b3 - b35 = b2 - b36 = b1 - SofSpa10ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, - a14, a15, a16, a17, a18, - a19, a20, a21, a22, a23, a24, a25, a26, a27, a28, a29, a30, - a31, a32, a33, a34, - a35, a36, - b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, - b14, b15, b16, b17, b18, - b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, - b31, b32, b33, b34, - b35, b36) -end - -function SofSpa10ConstantCache(T::Type, T2::Type) - a1 = convert(T, big"0.07879572252168641926390768") - a2 = convert(T, big"0.31309610341510852776481247") - a3 = convert(T, big"0.02791838323507806610952027") - a4 = convert(T, big"-0.22959284159390709415121340") - a5 = convert(T, big"0.13096206107716486317465686") - a6 = convert(T, big"-0.26973340565451071434460973") - a7 = convert(T, big"0.07497334315589143566613711") - a8 = convert(T, big"0.11199342399981020488957508") - a9 = convert(T, big"0.36613344954622675119314812") - a10 = convert(T, big"-0.39910563013603589787862981") - a11 = convert(T, big"0.10308739852747107731580277") - a12 = convert(T, big"0.41143087395589023782070412") - a13 = convert(T, big"-0.00486636058313526176219566") - a14 = convert(T, big"-0.39203335370863990644808194") - a15 = convert(T, big"0.05194250296244964703718290") - a16 = convert(T, big"0.05066509075992449633587434") - a17 = convert(T, big"0.04967437063972987905456880") - a18 = convert(T, big"0.04931773575959453791768001") - a19 = a17 - a20 = a16 - a21 = a15 - a22 = a14 - a23 = a13 - a24 = a12 - a25 = a11 - a26 = a10 - a27 = a9 - a28 = a8 - a29 = a7 - a30 = a6 - a31 = a5 - a32 = a4 - a33 = a3 - a34 = a2 - a35 = a1 - a36 = convert(T, 0) - b1 = convert(T, a1 / 2) - b2 = convert(T, (a1 + a2) / 2) - b3 = convert(T, (a2 + a3) / 2) - b4 = convert(T, (a3 + a4) / 2) - b5 = convert(T, (a4 + a5) / 2) - b6 = convert(T, (a5 + a6) / 2) - b7 = convert(T, (a6 + a7) / 2) - b8 = convert(T, (a7 + a8) / 2) - b9 = convert(T, (a8 + a9) / 2) - b10 = convert(T, (a9 + a10) / 2) - b11 = convert(T, (a10 + a11) / 2) - b12 = convert(T, (a11 + a12) / 2) - b13 = convert(T, (a12 + a13) / 2) - b14 = convert(T, (a13 + a14) / 2) - b15 = convert(T, (a14 + a15) / 2) - b16 = convert(T, (a15 + a16) / 2) - b17 = convert(T, (a16 + a17) / 2) - b18 = convert(T, (a17 + a18) / 2) - b19 = b18 - b20 = b17 - b21 = b16 - b22 = b15 - b23 = b14 - b24 = b13 - b25 = b12 - b26 = b11 - b27 = b10 - b28 = b9 - b29 = b8 - b30 = b7 - b31 = b6 - b32 = b5 - b33 = b4 - b34 = b3 - b35 = b2 - b36 = b1 - SofSpa10ConstantCache{T, T2}(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, - a14, a15, a16, a17, a18, - a19, a20, a21, a22, a23, a24, a25, a26, a27, a28, a29, a30, - a31, a32, a33, a34, - a35, a36, - b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, - b14, b15, b16, b17, b18, - b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, - b31, b32, b33, b34, - b35, b36) -end From 131ea9c0fc8c76ecbc37c64e390631218f0ce62e Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 11:01:20 -0400 Subject: [PATCH 25/71] Delete src/tableaus/verner_tableaus.jl --- src/tableaus/verner_tableaus.jl | 3894 ------------------------------- 1 file changed, 3894 deletions(-) delete mode 100644 src/tableaus/verner_tableaus.jl diff --git a/src/tableaus/verner_tableaus.jl b/src/tableaus/verner_tableaus.jl deleted file mode 100644 index 1773305838..0000000000 --- a/src/tableaus/verner_tableaus.jl +++ /dev/null @@ -1,3894 +0,0 @@ -## Vern6 -struct Vern6ExtraStages{T, T2} - c10::T2 - a1001::T - a1004::T - a1005::T - a1006::T - a1007::T - a1008::T - a1009::T - c11::T2 - a1101::T - a1104::T - a1105::T - a1106::T - a1107::T - a1108::T - a1109::T - a1110::T - c12::T2 - a1201::T - a1204::T - a1205::T - a1206::T - a1207::T - a1208::T - a1209::T - a1210::T - a1211::T -end - -function Vern6ExtraStages(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - # Extra stages for Order 5 - c10 = convert(T2, 0.5) - a1001 = convert(T, 0.016524159013572806) - a1004 = convert(T, 0.3053128187514179) - a1005 = convert(T, 0.2071200938201979) - a1006 = convert(T, -1.293879140655123) - a1007 = convert(T, 57.11988411588149) - a1008 = convert(T, -55.87979207510932) - a1009 = convert(T, 0.024830028297766014) - # Extra stages for Order 6 - c11 = convert(T2, 0.828) - a1101 = convert(T, 0.038150081818627744) - a1104 = convert(T, 0.2502358252513705) - a1105 = convert(T, 0.3249441447817608) - a1106 = convert(T, 1.8224606658327962) - a1107 = convert(T, -67.7137233269262) - a1108 = convert(T, 66.03587911808127) - a1109 = convert(T, -0.0363881087495127) - a1110 = convert(T, 0.106441599909888) - c12 = convert(T2, 0.28) - a1201 = convert(T, 0.11178168039666012) - a1204 = convert(T, 0.025757505109345213) - a1205 = convert(T, 3.785140856363646) - a1206 = convert(T, 92.34088993695727) - a1207 = convert(T, -3819.461508432344) - a1208 = convert(T, 3732.492711530704) - a1209 = convert(T, -1.0756940209963033) - a1210 = convert(T, -3.231539970732086) - a1211 = convert(T, -4.707539085458635) - - Vern6ExtraStages(c10, a1001, a1004, a1005, a1006, a1007, a1008, a1009, c11, a1101, - a1104, a1105, a1106, a1107, a1108, a1109, a1110, c12, a1201, a1204, - a1205, a1206, a1207, a1208, a1209, a1210, a1211) -end - -function Vern6ExtraStages(T, T2) - # Extra stages for Order 5 - c10 = convert(T2, 1 // 2) - a1001 = convert(T, - BigInt(35289331988986254405692535758830683) // - BigInt(2135620454874580332949729350544993288)) - a1004 = convert(T, - BigInt(313937014583068512255490687992212890625) // - BigInt(1028247080705354654473994781524199691557)) - a1005 = convert(T, - BigInt(1309307687253621245836726130885318359375) // - BigInt(6321490412177191231557635904400612215708)) - a1006 = convert(T, - -BigInt(35295844079877524186147726060781875) // - BigInt(27279088881521314684841470427640876)) - a1007 = convert(T, - BigInt(794353492803973228770716697389421875) // - BigInt(13906777037439977359946774228636361)) - a1008 = convert(T, - -BigInt(15228408956329265381787438679500067) // - BigInt(272520859345009876882656783678732)) - a1009 = convert(T, 28587810357600962662801 / 1151340224617184234295192) - # Extra stages for Order 6 - c11 = convert(T2, 207 // 250) - a1101 = convert(T, - BigInt(2486392061981208591025761263164027224438868971) // - BigInt(65173964076983042387381877152862343994140625000)) - a1104 = convert(T, - BigInt(2330654500023704838558579323179918419669) // - BigInt(9313832252765893609365894760182968220625)) - a1105 = convert(T, - BigInt(5283259505481013273874688940942473187741) // - BigInt(16258977397575080328080339260289640472500)) - a1106 = convert(T, - BigInt(9989685106081485386057729811605187743723) // - BigInt(5481427003263510055949691042076757812500)) - a1107 = convert(T, - -BigInt(65815640423883764662985178413751186161) // - BigInt(971969007022721623945108012714453125)) - a1108 = convert(T, - BigInt(183066350554023250298437927498791289370414247) // - BigInt(2772225538584491748887703284492309570312500)) - a1109 = convert(T, - -426178927623072052719640507155669 // - 11712038417736656029207275390625000) - a1110 = convert(T, 3248339841 // 30517578125) - c12 = convert(T2, 7 // 25) - a1201 = convert(T, - BigInt(4676747786898097735038451956075910033997933945857) // - BigInt(41838231186922043164464169766109251031526972656250)) - a1204 = convert(T, - BigInt(1320032412954312695441306548681592444623240) // - BigInt(51248457773784347881352490499724836575577977)) - a1205 = convert(T, - BigInt(2087002134582726310861746540254017903014374710) // - BigInt(551367099344274428347227263044005314054687829)) - a1206 = convert(T, - BigInt(3432932836484348829479408524345545011748570706) // - BigInt(37176735450871998946806722732624135633015625)) - a1207 = convert(T, - -BigInt(2316434358511265475362584844804601519943610264) // - BigInt(606481922490173339581866127622363581143375)) - a1208 = convert(T, - BigInt(82514605285282414051716141603447021470923168793) // - BigInt(22107104196177512751528507591142367597656250)) - a1209 = convert(T, - -BigInt(7560161019374651900153317984708038834) // - BigInt(7028170531590816328729091157353515625)) - a1210 = convert(T, - -BigInt(21655450552377696842870155771710589332) // - BigInt(6701278878958685336695179940732421875)) - a1211 = convert(T, - -3194830887993202085244614477336220 // - 678662636676110315314332975245759) - - Vern6ExtraStages(c10, a1001, a1004, a1005, a1006, a1007, a1008, a1009, c11, a1101, - a1104, a1105, a1106, a1107, a1108, a1109, a1110, c12, a1201, a1204, - a1205, a1206, a1207, a1208, a1209, a1210, a1211) -end - -""" -Coefficients for the polynomial -bᵢΘ = ri1*Θ + ri2*Θ^2 + ri3*Θ^3 + ... -""" -struct Vern6InterpolationCoefficients{T} - r011::T - r012::T - r013::T - r014::T - r015::T - r016::T - r042::T - r043::T - r044::T - r045::T - r046::T - r052::T - r053::T - r054::T - r055::T - r056::T - r062::T - r063::T - r064::T - r065::T - r066::T - r072::T - r073::T - r074::T - r075::T - r076::T - r082::T - r083::T - r084::T - r085::T - r086::T - r092::T - r093::T - r094::T - r095::T - r096::T - r102::T - r103::T - r104::T - r105::T - r106::T - r112::T - r113::T - r114::T - r115::T - r116::T - r122::T - r123::T - r124::T - r125::T - r126::T -end - -function Vern6InterpolationCoefficients(T::Type{<:CompiledFloats}) - r011 = convert(T, 1) - r012 = convert(T, -7.778593856495576) - r013 = convert(T, 27.0524385722671) - r014 = convert(T, -45.780190114576975) - r015 = convert(T, 36.723777410436384) - r016 = convert(T, -11.183042432947357) - r042 = convert(T, 16.632102138279762) - r043 = convert(T, -86.25583404770623) - r044 = convert(T, 171.73305461826962) - r045 = convert(T, -149.67744091315947) - r046 = convert(T, 47.826380659879696) - r052 = convert(T, 27.10835046149758) - r053 = convert(T, -140.58676162962996) - r054 = convert(T, 279.90447579689163) - r055 = convert(T, -243.95644583707966) - r056 = convert(T, 77.95131832728772) - r062 = convert(T, 283.70753264670356) - r063 = convert(T, -1471.3371557366656) - r064 = convert(T, 2929.3928569314394) - r065 = convert(T, -2553.17199842168) - r066 = convert(T, 815.8141610498723) - r072 = convert(T, -11365.512865164834) - r073 = convert(T, 58942.74718938947) - r074 = convert(T, -117353.43045697975) - r075 = convert(T, 102281.77209230464) - r076 = convert(T, -32682.059078573824) - r082 = convert(T, 11100.250191051131) - r083 = convert(T, -57567.067013355576) - r084 = convert(T, 114614.48808378985) - r085 = convert(T, -99894.591091309) - r086 = convert(T, 31919.283963225014) - r092 = convert(T, -3.0022825150732126) - r093 = convert(T, 14.946122435958785) - r094 = convert(T, -27.826954732510288) - r095 = convert(T, 21.824672217437076) - r096 = convert(T, -5.941557405812358) - r102 = convert(T, -19.610347376201034) - r103 = convert(T, 93.13370014508226) - r104 = convert(T, -165.3493635542416) - r105 = convert(T, 129.73901617804057) - r106 = convert(T, -37.91300539268019) - r112 = convert(T, -18.23029074639409) - r113 = convert(T, 96.74593449012313) - r114 = convert(T, -199.08634973839895) - r115 = convert(T, 180.85605899200485) - r116 = convert(T, -60.285352997334954) - r122 = convert(T, -13.563796638614157) - r123 = convert(T, 90.62137973668116) - r124 = convert(T, -204.04515601697273) - r125 = convert(T, 190.48135937835858) - r126 = convert(T, -63.493786459452856) - - Vern6InterpolationCoefficients(r011, r012, r013, r014, r015, r016, r042, r043, r044, - r045, r046, r052, r053, r054, r055, r056, r062, r063, - r064, r065, r066, r072, r073, r074, r075, r076, r082, - r083, r084, r085, r086, r092, r093, r094, r095, r096, - r102, r103, r104, r105, r106, r112, r113, r114, r115, - r116, r122, r123, r124, r125, r126) -end - -function Vern6InterpolationCoefficients(T) - r011 = convert(T, 1) - r012 = convert(T, -940811006205413129 // 120948724610397495) - r013 = convert(T, 88342864458754360181 // 3265615564480732365) - r014 = convert(T, -99667000922033025307 // 2177077042987154910) - r015 = convert(T, 7995049273203130972 // 217707704298715491) - r016 = convert(T, -7303903485456272500 // 653123112896146473) - r042 = convert(T, 2214248281250000 // 133130993475189) - r043 = convert(T, -49918013252500000000 // 578720428636646583) - r044 = convert(T, 1440368506953125000 // 8387252588936907) - r045 = convert(T, -28873797587500000000 // 192906809545548861) - r046 = convert(T, 27678103515625000000 // 578720428636646583) - r052 = convert(T, 893038428789062500 // 32943296570459319) - r053 = convert(T, -125047567320625000000 // 889469007402401613) - r054 = convert(T, 82988785418183593750 // 296489669134133871) - r055 = convert(T, -72330565909375000000 // 296489669134133871) - r056 = convert(T, 69335281738281250000 // 889469007402401613) - r062 = convert(T, 40331864555500 // 142160006043) - r063 = convert(T, -5647463071672000 // 3838320163161) - r064 = convert(T, 3747982556193250 // 1279440054387) - r065 = convert(T, -3266630520520000 // 1279440054387) - r066 = convert(T, 3131355943750000 // 3838320163161) - r072 = convert(T, -143250206750000 // 12603936879) - r073 = convert(T, 461347522996000000 // 7827044801859) - r074 = convert(T, -13312037070125000 // 113435431911) - r075 = convert(T, 266854670860000000 // 2609014933953) - r076 = convert(T, -255803940625000000 // 7827044801859) - r082 = convert(T, 3753451420391 // 338141155) - r083 = convert(T, -3679035166143248 // 63908678295) - r084 = convert(T, 4883240297928691 // 42605785530) - r085 = convert(T, -425608752364336 // 4260578553) - r086 = convert(T, 407983850042500 // 12781735659) - r092 = convert(T, -69713 // 23220) - r093 = convert(T, 4685161 // 313470) - r094 = convert(T, -135239 // 4860) - r095 = convert(T, 228046 // 10449) - r096 = convert(T, -186250 // 31347) - r102 = convert(T, -132664 // 6765) - r103 = convert(T, 17011336 // 182655) - r104 = convert(T, -10067296 // 60885) - r105 = convert(T, 1579832 // 12177) - r106 = convert(T, -1385000 // 36531) - r112 = convert(T, -2734375000 // 149990751) - r113 = convert(T, 391796875000 // 4049750277) - r114 = convert(T, -6250000000 // 31393413) - r115 = convert(T, 244140625000 // 1349916759) - r116 = convert(T, -244140625000 // 4049750277) - r122 = convert(T, -15453125 // 1139292) - r123 = convert(T, 1393796875 // 15380442) - r124 = convert(T, -2092203125 // 10253628) - r125 = convert(T, 488281250 // 2563407) - r126 = convert(T, -488281250 // 7690221) - - Vern6InterpolationCoefficients(r011, r012, r013, r014, r015, r016, r042, r043, r044, - r045, r046, r052, r053, r054, r055, r056, r062, r063, - r064, r065, r066, r072, r073, r074, r075, r076, r082, - r083, r084, r085, r086, r092, r093, r094, r095, r096, - r102, r103, r104, r105, r106, r112, r113, r114, r115, - r116, r122, r123, r124, r125, r126) -end - -""" -From Verner's Website -""" -struct Vern6Tableau{T, T2} - c1::T2 - c2::T2 - c3::T2 - c4::T2 - c5::T2 - c6::T2 - a21::T - a31::T - a32::T - a41::T - a43::T - a51::T - a53::T - a54::T - a61::T - a63::T - a64::T - a65::T - a71::T - a73::T - a74::T - a75::T - a76::T - a81::T - a83::T - a84::T - a85::T - a86::T - a87::T - a91::T - a94::T - a95::T - a96::T - a97::T - a98::T - btilde1::T - btilde4::T - btilde5::T - btilde6::T - btilde7::T - btilde8::T - btilde9::T - extra::Vern6ExtraStages{T, T2} - interp::Vern6InterpolationCoefficients{T} -end - -function Vern6Tableau(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - c1 = convert(T2, 0.06) - c2 = convert(T2, 0.09593333333333333) - c3 = convert(T2, 0.1439) - c4 = convert(T2, 0.4973) - c5 = convert(T2, 0.9725) - c6 = convert(T2, 0.9995) - a21 = convert(T, 0.06) - a31 = convert(T, 0.019239962962962962) - a32 = convert(T, 0.07669337037037037) - a41 = convert(T, 0.035975) - a43 = convert(T, 0.107925) - a51 = convert(T, 1.3186834152331484) - a53 = convert(T, -5.042058063628562) - a54 = convert(T, 4.220674648395414) - a61 = convert(T, -41.87259166432751) - a63 = convert(T, 159.43256216313748) - a64 = convert(T, -122.11921356501004) - a65 = convert(T, 5.531743066200053) - a71 = convert(T, -54.430156935316504) - a73 = convert(T, 207.06725136501848) - a74 = convert(T, -158.61081378459) - a75 = convert(T, 6.991816585950242) - a76 = convert(T, -0.01859723106220323) - a81 = convert(T, -54.66374178728198) - a83 = convert(T, 207.95280625538936) - a84 = convert(T, -159.2889574744995) - a85 = convert(T, 7.018743740796944) - a86 = convert(T, -0.018338785905045722) - a87 = convert(T, -0.0005119484997882099) - a91 = convert(T, 0.03438957868357036) - a94 = convert(T, 0.25826245556335037) - a95 = convert(T, 0.4209371189673537) - a96 = convert(T, 4.40539646966931) - a97 = convert(T, -176.48311902429865) - a98 = convert(T, 172.36413340141507) - # b1 =convert(T,0.04301298296577122) - # b4 =convert(T,0.23882842561019763) - # b5 =convert(T,0.44938719155539175) - # b6 =convert(T,2.2956854086040193) - # b7 =convert(T,-73.02457612433467) - # b8 =convert(T,70.96432878226597) - # b9 =convert(T,0.03333333333333333) - btilde1 = convert(T, 0.008623404282200854) - btilde4 = convert(T, -0.019434029953152708) - btilde5 = convert(T, 0.028450072588037983) - btilde6 = convert(T, -2.1097110610652914) - btilde7 = convert(T, 103.45854289996397) - btilde8 = convert(T, -101.39980461914912) - btilde9 = convert(T, 0.03333333333333333) - - extra = Vern6ExtraStages(T, T2) - interp = Vern6InterpolationCoefficients(T) - - Vern6Tableau(c1, c2, c3, c4, c5, c6, a21, a31, a32, a41, a43, a51, a53, a54, a61, a63, - a64, a65, a71, a73, a74, a75, a76, a81, a83, a84, a85, a86, a87, a91, a94, - a95, a96, a97, a98, btilde1, btilde4, btilde5, btilde6, btilde7, btilde8, - btilde9, extra, interp) -end - -function Vern6Tableau(T, T2) - c1 = convert(T2, 3 // 50) - c2 = convert(T2, 1439 // 15000) - c3 = convert(T2, 1439 // 10000) - c4 = convert(T2, 4973 // 10000) - c5 = convert(T2, 389 // 400) - c6 = convert(T2, 1999 // 2000) - a21 = convert(T, 3 // 50) - a31 = convert(T, 519479 // 27000000) - a32 = convert(T, 2070721 // 27000000) - a41 = convert(T, 1439 // 40000) - a43 = convert(T, 4317 // 40000) - a51 = convert(T, 109225017611 // 82828840000) - a53 = convert(T, -417627820623 // 82828840000) - a54 = convert(T, 43699198143 // 10353605000) - a61 = convert(T, -8036815292643907349452552172369 // 191934985946683241245914401600) - a63 = convert(T, 246134619571490020064824665 // 1543816496655405117602368) - a64 = convert(T, -13880495956885686234074067279 // 113663489566254201783474344) - a65 = convert(T, 755005057777788994734129 // 136485922925633667082436) - a71 = convert(T, - -BigInt(1663299841566102097180506666498880934230261) // - BigInt(30558424506156170307020957791311384232000)) - a73 = convert(T, - 130838124195285491799043628811093033 // 631862949514135618861563657970240) - a74 = convert(T, - -BigInt(3287100453856023634160618787153901962873) // - BigInt(20724314915376755629135711026851409200)) - a75 = convert(T, - 2771826790140332140865242520369241 // 396438716042723436917079980147600) - a76 = convert(T, -1799166916139193 // 96743806114007800) - a81 = convert(T, - -BigInt(832144750039369683895428386437986853923637763) // - BigInt(15222974550069600748763651844667619945204887)) - a83 = convert(T, - 818622075710363565982285196611368750 // - 3936576237903728151856072395343129) - a84 = convert(T, - -BigInt(9818985165491658464841194581385463434793741875) // - BigInt(61642597962658994069869370923196463581866011)) - a85 = convert(T, - BigInt(31796692141848558720425711042548134769375) // - BigInt(4530254033500045975557858016006308628092)) - a86 = convert(T, -14064542118843830075 // 766928748264306853644) - a87 = convert(T, -1424670304836288125 // 2782839104764768088217) - a91 = convert(T, 382735282417 // 11129397249634) - a94 = convert(T, 5535620703125000 // 21434089949505429) - a95 = convert(T, 13867056347656250 // 32943296570459319) - a96 = convert(T, 626271188750 // 142160006043) - a97 = convert(T, -51160788125000 // 289890548217) - a98 = convert(T, 163193540017 // 946795234) - # b1 =convert(T,124310637869885675646798613//2890072468789466426596827670) - # b4 =convert(T,265863151737164990361330921875//1113197271463372303940319369579) - # b5 =convert(T,3075493557174030806536302953125//6843749922042323876546949699876) - # b6 =convert(T,67798000008733879813263055//29532792147666737550036372) - # b7 =convert(T,-1099436585155390846238326375//15055706496446408859196167) - # b8 =convert(T,26171252653086373181571802//368794478890732346033505) - # b9 =convert(T,1//30) - btilde1 = convert(T, 12461131651614938103148389 // 1445036234394733213298413835) - btilde4 = convert(T, -21633909117387045317965953125 // 1113197271463372303940319369579) - btilde5 = convert(T, 21633909117387045317965953125 // 760416658004702652949661077764) - btilde6 = convert(T, -6922850917563854501749105 // 3281421349740748616670708) - btilde7 = convert(T, 173071272939096362543727625 // 1672856277382934317688463) - btilde8 = convert(T, -74791376208282344108625901 // 737588957781464692067010) - btilde9 = convert(T, 1 // 30) - - extra = Vern6ExtraStages(T, T2) - interp = Vern6InterpolationCoefficients(T) - - Vern6Tableau(c1, c2, c3, c4, c5, c6, a21, a31, a32, a41, a43, a51, a53, a54, a61, a63, - a64, a65, a71, a73, a74, a75, a76, a81, a83, a84, a85, a86, a87, a91, a94, - a95, a96, a97, a98, btilde1, btilde4, btilde5, btilde6, btilde7, btilde8, - btilde9, extra, interp) -end - -## Vern7 -struct Vern7ExtraStages{T, T2} - c11::T2 - a1101::T - a1104::T - a1105::T - a1106::T - a1107::T - a1108::T - a1109::T - c12::T2 - a1201::T - a1204::T - a1205::T - a1206::T - a1207::T - a1208::T - a1209::T - a1211::T - c13::T2 - a1301::T - a1304::T - a1305::T - a1306::T - a1307::T - a1308::T - a1309::T - a1311::T - a1312::T - c14::T2 - a1401::T - a1404::T - a1405::T - a1406::T - a1407::T - a1408::T - a1409::T - a1411::T - a1412::T - a1413::T - c15::T2 - a1501::T - a1504::T - a1505::T - a1506::T - a1507::T - a1508::T - a1509::T - a1511::T - a1512::T - a1513::T - c16::T2 - a1601::T - a1604::T - a1605::T - a1606::T - a1607::T - a1608::T - a1609::T - a1611::T - a1612::T - a1613::T -end - -@fold function Vern7ExtraStages(::Type{T}, - ::Type{T2}) where {T <: CompiledFloats, - T2 <: CompiledFloats} - c11 = convert(T2, 1) - a1101 = convert(T, 0.04715561848627222) - a1104 = convert(T, 0.25750564298434153) - a1105 = convert(T, 0.2621665397741262) - a1106 = convert(T, 0.15216092656738558) - a1107 = convert(T, 0.49399691700324844) - a1108 = convert(T, -0.29430311714032503) - a1109 = convert(T, 0.0813174723249511) - c12 = convert(T2, 0.29) - a1201 = convert(T, 0.0523222769159969) - a1204 = convert(T, 0.22495861826705715) - a1205 = convert(T, 0.017443709248776376) - a1206 = convert(T, -0.007669379876829393) - a1207 = convert(T, 0.03435896044073285) - a1208 = convert(T, -0.0410209723009395) - a1209 = convert(T, 0.025651133005205617) - a1211 = convert(T, -0.0160443457) - c13 = convert(T2, 0.125) - a1301 = convert(T, 0.053053341257859085) - a1304 = convert(T, 0.12195301011401886) - a1305 = convert(T, 0.017746840737602496) - a1306 = convert(T, -0.0005928372667681495) - a1307 = convert(T, 0.008381833970853752) - a1308 = convert(T, -0.01293369259698612) - a1309 = convert(T, 0.009412056815253861) - a1311 = convert(T, -0.005353253107275676) - a1312 = convert(T, -0.06666729992455811) - c14 = convert(T2, 0.25) - a1401 = convert(T, 0.03887903257436304) - a1404 = convert(T, -0.0024403203308301317) - a1405 = convert(T, -0.0013928917214672623) - a1406 = convert(T, -0.00047446291558680135) - a1407 = convert(T, 0.00039207932413159514) - a1408 = convert(T, -0.00040554733285128004) - a1409 = convert(T, 0.00019897093147716726) - a1411 = convert(T, -0.00010278198793179169) - a1412 = convert(T, 0.03385661513870267) - a1413 = convert(T, 0.1814893063199928) - c15 = convert(T2, 0.53) - a1501 = convert(T, 0.05723681204690013) - a1504 = convert(T, 0.22265948066761182) - a1505 = convert(T, 0.12344864200186899) - a1506 = convert(T, 0.04006332526666491) - a1507 = convert(T, -0.05269894848581452) - a1508 = convert(T, 0.04765971214244523) - a1509 = convert(T, -0.02138895885042213) - a1511 = convert(T, 0.015193891064036402) - a1512 = convert(T, 0.12060546716289655) - a1513 = convert(T, -0.022779423016187374) - c16 = convert(T2, 0.79) - a1601 = convert(T, 0.051372038802756814) - a1604 = convert(T, 0.5414214473439406) - a1605 = convert(T, 0.350399806692184) - a1606 = convert(T, 0.14193112269692182) - a1607 = convert(T, 0.10527377478429423) - a1608 = convert(T, -0.031081847805874016) - a1609 = convert(T, -0.007401883149519145) - a1611 = convert(T, -0.006377932504865363) - a1612 = convert(T, -0.17325495908361865) - a1613 = convert(T, -0.18228156777622026) - - Vern7ExtraStages(c11, a1101, a1104, a1105, a1106, a1107, a1108, a1109, c12, a1201, - a1204, a1205, a1206, a1207, a1208, a1209, a1211, c13, a1301, a1304, - a1305, a1306, a1307, a1308, a1309, a1311, a1312, c14, a1401, a1404, - a1405, a1406, a1407, a1408, a1409, a1411, a1412, a1413, c15, a1501, - a1504, a1505, a1506, a1507, a1508, a1509, a1511, a1512, a1513, c16, - a1601, a1604, a1605, a1606, a1607, a1608, a1609, a1611, a1612, a1613) -end - -@fold function Vern7ExtraStages(::Type{T}, ::Type{T2}) where {T, T2} - c11 = convert(T2, 1) - a1101 = convert(T, big" .4715561848627222170431765108838175679569e-1") - a1104 = convert(T, big" .2575056429843415189596436101037687580986") - a1105 = convert(T, big" .2621665397741262047713863095764527711129") - a1106 = convert(T, big" .1521609265673855740323133199165117535523") - a1107 = convert(T, big" .4939969170032484246907175893227876844296") - a1108 = convert(T, big"-.2943031171403250441557244744092703429139") - a1109 = convert(T, big" .8131747232495109999734599440136761892478e-1") - c12 = convert(T2, 29 // 100) - a1201 = convert(T, big" .5232227691599689815470932256735029887614e-1") - a1204 = convert(T, big" .2249586182670571550244187743667190903405") - a1205 = convert(T, big" .1744370924877637539031751304611402542578e-1") - a1206 = convert(T, big"-.7669379876829393188009028209348812321417e-2") - a1207 = convert(T, big" .3435896044073284645684381456417912794447e-1") - a1208 = convert(T, big"-.4102097230093949839125144540100346681769e-1") - a1209 = convert(T, big" .2565113300520561655297104906598973655221e-1") - a1211 = convert(T, big"-.160443457e-1") - c13 = convert(T2, 1 // 8) - a1301 = convert(T, big" .5305334125785908638834747243817578898946e-1") - a1304 = convert(T, big" .1219530101140188607092225622195251463666") - a1305 = convert(T, big" .1774684073760249704011573985936092552347e-1") - a1306 = convert(T, big"-.5928372667681494328907467430302313286925e-3") - a1307 = convert(T, big" .8381833970853750873624781948796072714855e-2") - a1308 = convert(T, big"-.1293369259698611956700998079778496462996e-1") - a1309 = convert(T, big" .9412056815253860804791356641605087829772e-2") - a1311 = convert(T, big"-.5353253107275676032399320754008272222345e-2") - a1312 = convert(T, big"-.6666729992455811078380186481263955324311e-1") - c14 = convert(T2, 1 // 4) - a1401 = convert(T, big" .3887903257436303686399931060834951327899e-1") - a1404 = convert(T, big"-.2440320330830131517910045090190069290791e-2") - a1405 = convert(T, big"-.1392891721467262281273220992320214734208e-2") - a1406 = convert(T, big"-.4744629155868013465038358934145339168472e-3") - a1407 = convert(T, big" .3920793241315951369383517310870803393356e-3") - a1408 = convert(T, big"-.4055473328512800136385880031750264996936e-3") - a1409 = convert(T, big" .1989709314771672628794304728258886009267e-3") - a1411 = convert(T, big"-.1027819879317916884712606136811051029682e-3") - a1412 = convert(T, big" .3385661513870266715302548402957613704604e-1") - a1413 = convert(T, big" .1814893063199928004309543737509423302792") - c15 = convert(T2, 53 // 100) - a1501 = convert(T, big" .5723681204690012909606837582140921695189e-1") - a1504 = convert(T, big" .2226594806676118099285816235023183680020") - a1505 = convert(T, big" .1234486420018689904911221497830317287757") - a1506 = convert(T, big" .4006332526666490875113688731927762275433e-1") - a1507 = convert(T, big"-.5269894848581452066926326838943832327366e-1") - a1508 = convert(T, big" .4765971214244522856887315416093212596338e-1") - a1509 = convert(T, big"-.2138895885042213036387863538386958914368e-1") - a1511 = convert(T, big" .1519389106403640165459624646184297766866e-1") - a1512 = convert(T, big" .1206054671628965554251364472502413614358") - a1513 = convert(T, big"-.2277942301618737288237298052574548913451e-1") - c16 = convert(T2, 79 // 100) - a1601 = convert(T, big" .5137203880275681426595607279552927584506e-1") - a1604 = convert(T, big" .5414214473439405582401399378307410450482") - a1605 = convert(T, big" .3503998066921840081154745647747846804810") - a1606 = convert(T, big" .1419311226969218216861835872156617148040") - a1607 = convert(T, big" .1052737747842942254816302629823570359198") - a1608 = convert(T, big"-.3108184780587401700842726199589213259835e-1") - a1609 = convert(T, big"-.7401883149519145061791854716430279714483e-2") - a1611 = convert(T, big"-.6377932504865363437569726480040013149706e-2") - a1612 = convert(T, big"-.1732549590836186403386348310205265959935") - a1613 = convert(T, big"-.1822815677762202619429607513861847306420") - - Vern7ExtraStages(c11, a1101, a1104, a1105, a1106, a1107, a1108, a1109, c12, a1201, - a1204, a1205, a1206, a1207, a1208, a1209, a1211, c13, a1301, a1304, - a1305, a1306, a1307, a1308, a1309, a1311, a1312, c14, a1401, a1404, - a1405, a1406, a1407, a1408, a1409, a1411, a1412, a1413, c15, a1501, - a1504, a1505, a1506, a1507, a1508, a1509, a1511, a1512, a1513, c16, - a1601, a1604, a1605, a1606, a1607, a1608, a1609, a1611, a1612, a1613) -end - -struct Vern7InterpolationCoefficients{T} - r011::T - r012::T - r013::T - r014::T - r015::T - r016::T - r017::T - r042::T - r043::T - r044::T - r045::T - r046::T - r047::T - r052::T - r053::T - r054::T - r055::T - r056::T - r057::T - r062::T - r063::T - r064::T - r065::T - r066::T - r067::T - r072::T - r073::T - r074::T - r075::T - r076::T - r077::T - r082::T - r083::T - r084::T - r085::T - r086::T - r087::T - r092::T - r093::T - r094::T - r095::T - r096::T - r097::T - r112::T - r113::T - r114::T - r115::T - r116::T - r117::T - r122::T - r123::T - r124::T - r125::T - r126::T - r127::T - r132::T - r133::T - r134::T - r135::T - r136::T - r137::T - r142::T - r143::T - r144::T - r145::T - r146::T - r147::T - r152::T - r153::T - r154::T - r155::T - r156::T - r157::T - r162::T - r163::T - r164::T - r165::T - r166::T - r167::T -end - -@fold function Vern7InterpolationCoefficients(::Type{T}) where {T <: CompiledFloats} - r011 = convert(T, 1) - r012 = convert(T, -8.413387198332767) - r013 = convert(T, 33.675508884490895) - r014 = convert(T, -70.80159089484886) - r015 = convert(T, 80.64695108301298) - r016 = convert(T, -47.19413969837522) - r017 = convert(T, 11.133813442539243) - r042 = convert(T, 8.754921980674396) - r043 = convert(T, -88.4596828699771) - r044 = convert(T, 346.9017638429916) - r045 = convert(T, -629.2580030059837) - r046 = convert(T, 529.6773755604193) - r047 = convert(T, -167.35886986514018) - r052 = convert(T, 8.913387586637922) - r053 = convert(T, -90.06081846893218) - r054 = convert(T, 353.1807459217058) - r055 = convert(T, -640.6476819744374) - r056 = convert(T, 539.2646279047156) - r057 = convert(T, -170.38809442991547) - r062 = convert(T, 5.1733120298478) - r063 = convert(T, -52.271115900055385) - r064 = convert(T, 204.9853867374073) - r065 = convert(T, -371.8306118563603) - r066 = convert(T, 312.9880934374529) - r067 = convert(T, -98.89290352172495) - r072 = convert(T, 16.79537744079696) - r073 = convert(T, -169.70040000059728) - r074 = convert(T, 665.4937727009246) - r075 = convert(T, -1207.1638892336007) - r076 = convert(T, 1016.1291515818546) - r077 = convert(T, -321.06001557237494) - r082 = convert(T, -10.005997536098665) - r083 = convert(T, 101.1005433052275) - r084 = convert(T, -396.47391512378437) - r085 = convert(T, 719.1787707014183) - r086 = convert(T, -605.3681033918824) - r087 = convert(T, 191.27439892797935) - r092 = convert(T, 2.764708833638599) - r093 = convert(T, -27.934602637390462) - r094 = convert(T, 109.54779186137893) - r095 = convert(T, -198.7128113064482) - r096 = convert(T, 167.26633571640318) - r097 = convert(T, -52.85010499525706) - r112 = convert(T, -2.1696320280163506) - r113 = convert(T, 22.016696037569876) - r114 = convert(T, -86.90152427798948) - r115 = convert(T, 159.22388973861476) - r116 = convert(T, -135.9618306534588) - r117 = convert(T, 43.792401183280006) - r122 = convert(T, -4.890070188793804) - r123 = convert(T, 22.75407737425176) - r124 = convert(T, -30.78034218537731) - r125 = convert(T, -2.797194317207249) - r126 = convert(T, 31.369456637508403) - r127 = convert(T, -15.655927320381801) - r132 = convert(T, 10.862170929551967) - r133 = convert(T, -50.542971417827104) - r134 = convert(T, 68.37148040407511) - r135 = convert(T, 6.213326521632409) - r136 = convert(T, -69.68006323194157) - r137 = convert(T, 34.776056794509195) - r142 = convert(T, -11.37286691922923) - r143 = convert(T, 130.79058078246717) - r144 = convert(T, -488.65113677785604) - r145 = convert(T, 832.2148793276441) - r146 = convert(T, -664.7743368554426) - r147 = convert(T, 201.79288044241662) - r152 = convert(T, -5.919778732715007) - r153 = convert(T, 63.27679965889219) - r154 = convert(T, -265.432682088738) - r155 = convert(T, 520.1009254140611) - r156 = convert(T, -467.412109533902) - r157 = convert(T, 155.3868452824017) - r162 = convert(T, -10.492146197961823) - r163 = convert(T, 105.35538525188011) - r164 = convert(T, -409.43975011988937) - r165 = convert(T, 732.831448907654) - r166 = convert(T, -606.3044574733512) - r167 = convert(T, 188.0495196316683) - - Vern7InterpolationCoefficients(r011, r012, r013, r014, r015, r016, r017, r042, r043, - r044, r045, r046, r047, r052, r053, r054, r055, r056, - r057, r062, r063, r064, r065, r066, r067, r072, r073, - r074, r075, r076, r077, r082, r083, r084, r085, r086, - r087, r092, r093, r094, r095, r096, r097, r112, r113, - r114, r115, r116, r117, r122, r123, r124, r125, r126, - r127, r132, r133, r134, r135, r136, r137, r142, r143, - r144, r145, r146, r147, r152, r153, r154, r155, r156, - r157, r162, r163, r164, r165, r166, r167) -end - -@fold function Vern7InterpolationCoefficients(::Type{T}) where {T} - r011 = convert(T, big" 1") - r012 = convert(T, big"-8.413387198332767469319987751201351965810") - r013 = convert(T, big" 33.67550888449089654479469983556967202215") - r014 = convert(T, big"-70.80159089484886164618905961010838757357") - r015 = convert(T, big" 80.64695108301297872968868805293298389704") - r016 = convert(T, big"-47.19413969837521580145883430419406103536") - r017 = convert(T, big" 11.13381344253924186418881142808952641234") - r042 = convert(T, big" 8.754921980674397160629587282876763437696") - r043 = convert(T, big"-88.45968286997709426134300934922618655402") - r044 = convert(T, big" 346.9017638429916309499891288356321692825") - r045 = convert(T, big"-629.2580030059837046812187141184986252218") - r046 = convert(T, big" 529.6773755604192983874116479833480529304") - r047 = convert(T, big"-167.3588698651401860365089970240284051167") - r052 = convert(T, big" 8.913387586637921662996190126913331844214") - r053 = convert(T, big"-90.06081846893217794712014609702916991513") - r054 = convert(T, big" 353.1807459217057824951538014683541349020") - r055 = convert(T, big"-640.6476819744374433668701027882567716886") - r056 = convert(T, big" 539.2646279047155261551781390920363285084") - r057 = convert(T, big"-170.3880944299154827945664954924414008798") - r062 = convert(T, big" 5.173312029847800338889849068990984974299") - r063 = convert(T, big"-52.27111590005538823385270070373176751689") - r064 = convert(T, big" 204.9853867374073094711024260808085419491") - r065 = convert(T, big"-371.8306118563602890875634623992262437796") - r066 = convert(T, big" 312.9880934374529000210073972654145891826") - r067 = convert(T, big"-98.89290352172494693555119599233959305606") - r072 = convert(T, big" 16.79537744079695986364946329034055578253") - r073 = convert(T, big"-169.7004000005972744435739149730966805754") - r074 = convert(T, big" 665.4937727009246303131700313781960584913") - r075 = convert(T, big"-1207.163889233600728395392916633015853882") - r076 = convert(T, big" 1016.129151581854603280159105697386989470") - r077 = convert(T, big"-321.0600155723749421933210511704882816019") - r082 = convert(T, big"-10.00599753609866476866352971232058330270") - r083 = convert(T, big" 101.1005433052275068199636113246449312792") - r084 = convert(T, big"-396.4739151237843754958939772727577263768") - r085 = convert(T, big" 719.1787707014182914108130834128646525498") - r086 = convert(T, big"-605.3681033918824350795711030652978269725") - r087 = convert(T, big" 191.2743989279793520691961908384572824802") - r092 = convert(T, big" 2.764708833638599139713222853969606774131") - r093 = convert(T, big"-27.93460263739046178114640484830267988046") - r094 = convert(T, big" 109.5477918613789217803046856340175757800") - r095 = convert(T, big"-198.7128113064482116421691972646370773711") - r096 = convert(T, big" 167.2663357164031670694252647113936863857") - r097 = convert(T, big"-52.85010499525706346613022509203974406942") - r112 = convert(T, big"-2.169632028016350481156919876642428429100") - r113 = convert(T, big" 22.01669603756987625585768587320929912766") - r114 = convert(T, big"-86.90152427798948350846176288615482496306") - r115 = convert(T, big" 159.2238897386147443720253338471077193471") - r116 = convert(T, big"-135.9618306534587908363115231453760181702") - r117 = convert(T, big" 43.79240118328000419804718618785625308759") - r122 = convert(T, big"-4.890070188793803933769786966428026149549") - r123 = convert(T, big" 22.75407737425176120799532459991506803585") - r124 = convert(T, big"-30.78034218537730965082079824005797506535") - r125 = convert(T, big"-2.797194317207249021142015125037024035537") - r126 = convert(T, big" 31.36945663750840183161406140272783187147") - r127 = convert(T, big"-15.65592732038180043387678567111987465689") - r132 = convert(T, big" 10.86217092955196715517224349929627754387") - r133 = convert(T, big"-50.54297141782710697188187875653305700081") - r134 = convert(T, big" 68.37148040407511827604242008548181691494") - r135 = convert(T, big" 6.213326521632409162585500428935637861213") - r136 = convert(T, big"-69.68006323194158104163196358466588618336") - r137 = convert(T, big" 34.77605679450919341971367832748521086414") - r142 = convert(T, big"-11.37286691922922915922346687401389055763") - r143 = convert(T, big" 130.7905807824671644130452602841032046030") - r144 = convert(T, big"-488.6511367778560207543260583489312609826") - r145 = convert(T, big" 832.2148793276440873476229585070779183432") - r146 = convert(T, big"-664.7743368554426242883314487337054193624") - r147 = convert(T, big" 201.7928804424166224412127551654694479565") - r152 = convert(T, big"-5.919778732715006698693070786679427540601") - r153 = convert(T, big" 63.27679965889218829298274978013773800731") - r154 = convert(T, big"-265.4326820887379575820873554556433306580") - r155 = convert(T, big" 520.1009254140610824835871087519714692468") - r156 = convert(T, big"-467.4121095339020118993777963241667608460") - r157 = convert(T, big" 155.3868452824017054035883640343803117904") - r162 = convert(T, big"-10.49214619796182281022379415510181241136") - r163 = convert(T, big" 105.3553852518801101042787230303396283676") - r164 = convert(T, big"-409.4397501198893846479834816688367917005") - r165 = convert(T, big" 732.8314489076540326880337353277812147333") - r166 = convert(T, big"-606.3044574733512377981129469949015057785") - r167 = convert(T, big" 188.0495196316683024640077644607192667895") - - Vern7InterpolationCoefficients(r011, r012, r013, r014, r015, r016, r017, r042, r043, - r044, r045, r046, r047, r052, r053, r054, r055, r056, - r057, r062, r063, r064, r065, r066, r067, r072, r073, - r074, r075, r076, r077, r082, r083, r084, r085, r086, - r087, r092, r093, r094, r095, r096, r097, r112, r113, - r114, r115, r116, r117, r122, r123, r124, r125, r126, - r127, r132, r133, r134, r135, r136, r137, r142, r143, - r144, r145, r146, r147, r152, r153, r154, r155, r156, - r157, r162, r163, r164, r165, r166, r167) -end - -struct Vern7Tableau{T, T2} - c2::T2 - c3::T2 - c4::T2 - c5::T2 - c6::T2 - c7::T2 - c8::T2 - a021::T - a031::T - a032::T - a041::T - a043::T - a051::T - a053::T - a054::T - a061::T - a063::T - a064::T - a065::T - a071::T - a073::T - a074::T - a075::T - a076::T - a081::T - a083::T - a084::T - a085::T - a086::T - a087::T - a091::T - a093::T - a094::T - a095::T - a096::T - a097::T - a098::T - a101::T - a103::T - a104::T - a105::T - a106::T - a107::T - b1::T - b4::T - b5::T - b6::T - b7::T - b8::T - b9::T - btilde1::T - btilde4::T - btilde5::T - btilde6::T - btilde7::T - btilde8::T - btilde9::T - btilde10::T -end - -@fold function Vern7Tableau(::Type{T}, - ::Type{T2}) where {T <: CompiledFloats, T2 <: CompiledFloats} - c2 = convert(T2, 0.005) - c3 = convert(T2, 0.10888888888888888) - c4 = convert(T2, 0.16333333333333333) - c5 = convert(T2, 0.4555) - c6 = convert(T2, 0.6095094489978381) - c7 = convert(T2, 0.884) - c8 = convert(T2, 0.925) - a021 = convert(T, 0.005) - a031 = convert(T, -1.07679012345679) - a032 = convert(T, 1.185679012345679) - a041 = convert(T, 0.04083333333333333) - a043 = convert(T, 0.1225) - a051 = convert(T, 0.6389139236255726) - a053 = convert(T, -2.455672638223657) - a054 = convert(T, 2.272258714598084) - a061 = convert(T, -2.6615773750187572) - a063 = convert(T, 10.804513886456137) - a064 = convert(T, -8.3539146573962) - a065 = convert(T, 0.820487594956657) - a071 = convert(T, 6.067741434696772) - a073 = convert(T, -24.711273635911088) - a074 = convert(T, 20.427517930788895) - a075 = convert(T, -1.9061579788166472) - a076 = convert(T, 1.006172249242068) - a081 = convert(T, 12.054670076253203) - a083 = convert(T, -49.75478495046899) - a084 = convert(T, 41.142888638604674) - a085 = convert(T, -4.461760149974004) - a086 = convert(T, 2.042334822239175) - a087 = convert(T, -0.09834843665406107) - a091 = convert(T, 10.138146522881808) - a093 = convert(T, -42.6411360317175) - a094 = convert(T, 35.76384003992257) - a095 = convert(T, -4.3480228403929075) - a096 = convert(T, 2.0098622683770357) - a097 = convert(T, 0.3487490460338272) - a098 = convert(T, -0.27143900510483127) - a101 = convert(T, -45.030072034298676) - a103 = convert(T, 187.3272437654589) - a104 = convert(T, -154.02882369350186) - a105 = convert(T, 18.56465306347536) - a106 = convert(T, -7.141809679295079) - a107 = convert(T, 1.3088085781613787) - b1 = convert(T, 0.04715561848627222) - b4 = convert(T, 0.25750564298434153) - b5 = convert(T, 0.26216653977412624) - b6 = convert(T, 0.15216092656738558) - b7 = convert(T, 0.4939969170032485) - b8 = convert(T, -0.29430311714032503) - b9 = convert(T, 0.08131747232495111) - # bhat1 = convert(T,0.044608606606341174) - # bhat4 = convert(T,0.26716403785713727) - # bhat5 = convert(T,0.22010183001772932) - # bhat6 = convert(T,0.2188431703143157) - # bhat7 = convert(T,0.22898717054112028) - # bhat10 = convert(T,0.02029518466335628) - btilde1 = convert(T, 0.002547011879931045) - btilde4 = convert(T, -0.00965839487279575) - btilde5 = convert(T, 0.04206470975639691) - btilde6 = convert(T, -0.0666822437469301) - btilde7 = convert(T, 0.2650097464621281) - btilde8 = convert(T, -0.29430311714032503) - btilde9 = convert(T, 0.08131747232495111) - btilde10 = convert(T, -0.02029518466335628) - - Vern7Tableau( - c2, c3, c4, c5, c6, c7, c8, a021, a031, a032, a041, a043, a051, a053, a054, - a061, a063, a064, a065, a071, a073, a074, a075, a076, a081, a083, a084, - a085, a086, a087, a091, a093, a094, a095, a096, a097, a098, a101, a103, - a104, a105, a106, a107, b1, b4, b5, b6, b7, b8, b9, btilde1, btilde4, - btilde5, btilde6, btilde7, btilde8, btilde9, btilde10) -end - -@fold function Vern7Tableau(::Type{T}, ::Type{T2}) where {T, T2} - c2 = convert(T2, 1 // 200) - c3 = convert(T2, 49 // 450) - c4 = convert(T2, 49 // 300) - c5 = convert(T2, 911 // 2000) - c6 = convert(T2, 3480084980 // 5709648941) - c7 = convert(T2, 221 // 250) - c8 = convert(T2, 37 // 40) - a021 = convert(T, 1 // 200) - a031 = convert(T, -4361 // 4050) - a032 = convert(T, 2401 // 2025) - a041 = convert(T, 49 // 1200) - a043 = convert(T, 49 // 400) - a051 = convert(T, 2454451729 // 3841600000) - a053 = convert(T, -9433712007 // 3841600000) - a054 = convert(T, 4364554539 // 1920800000) - a061 = convert(T, - -BigInt(6187101755456742839167388910402379177523537620) // - BigInt(2324599620333464857202963610201679332423082271)) - a063 = convert(T, - BigInt(27569888999279458303270493567994248533230000) // - BigInt(2551701010245296220859455115479340650299761)) - a064 = convert(T, - -BigInt(37368161901278864592027018689858091583238040000) // - BigInt(4473131870960004275166624817435284159975481033)) - a065 = convert(T, - BigInt(1392547243220807196190880383038194667840000000) // - BigInt(1697219131380493083996999253929006193143549863)) - a071 = convert(T, 11272026205260557297236918526339 // 1857697188743815510261537500000) - a073 = convert(T, -48265918242888069 // 1953194276993750) - a074 = convert(T, 26726983360888651136155661781228 // 1308381343805114800955157615625) - a075 = convert(T, -2090453318815827627666994432 // 1096684189897834170412307919) - a076 = convert(T, - BigInt(1148577938985388929671582486744843844943428041509) // - BigInt(1141532118233823914568777901158338927629837500000)) - a081 = convert(T, - BigInt(1304457204588839386329181466225966641) // - BigInt(108211771565488329642169667802016000)) - a083 = convert(T, -1990261989751005 // 40001418792832) - a084 = convert(T, - BigInt(2392691599894847687194643439066780106875) // - BigInt(58155654089143548047476915856270826016)) - a085 = convert(T, - -BigInt(1870932273351008733802814881998561250) // - BigInt(419326053051486744762255151208232123)) - a086 = convert(T, - BigInt(1043329047173803328972823866240311074041739158858792987034783181) // - BigInt(510851127745017966999893975119259285040213723744255237522144000)) - a087 = convert(T, -311918858557595100410788125 // 3171569057622789618800376448) - a091 = convert(T, - BigInt(17579784273699839132265404100877911157) // - BigInt(1734023495717116205617154737841023480)) - a093 = convert(T, -18539365951217471064750 // 434776548575709731377) - a094 = convert(T, - BigInt(447448655912568142291911830292656995992000) // - BigInt(12511202807447096607487664209063950964109)) - a095 = convert(T, - -BigInt(65907597316483030274308429593905808000000) // - BigInt(15158061430635748897861852383197382130691)) - a096 = convert(T, - BigInt(273847823027445129865693702689010278588244606493753883568739168819449761) // - BigInt(136252034448398939768371761610231099586032870552034688235302796640584360)) - a097 = convert(T, - BigInt(694664732797172504668206847646718750) // - BigInt(1991875650119463976442052358853258111)) - a098 = convert(T, - -19705319055289176355560129234220800 // - 72595753317320295604316217197876507) - a101 = convert(T, - -511858190895337044664743508805671 // 11367030248263048398341724647960) - a103 = convert(T, 2822037469238841750 // 15064746656776439) - a104 = convert(T, - -BigInt(23523744880286194122061074624512868000) // - BigInt(152723005449262599342117017051789699)) - a105 = convert(T, - BigInt(10685036369693854448650967542704000000) // - BigInt(575558095977344459903303055137999707)) - a106 = convert(T, - -BigInt(6259648732772142303029374363607629515525848829303541906422993) // - BigInt(876479353814142962817551241844706205620792843316435566420120)) - a107 = convert(T, - 17380896627486168667542032602031250 // - 13279937889697320236613879977356033) - b1 = convert(T, 96762636172307789 // 2051985304794103980) - b4 = convert(T, 312188947591288252500000 // 1212357694274963646019729) - b5 = convert(T, 13550580884964304000000000000 // 51686919683339547115937980629) - b6 = convert(T, - BigInt(72367769693133178898676076432831566019684378142853445230956642801) // - BigInt(475600216991873963561768100160364792981629064220601844848928537580)) - b7 = convert(T, 1619421054120605468750 // 3278200730370057108183) - b8 = convert(T, -66898316144057728000 // 227310933007074849597) - b9 = convert(T, 181081444637946577 // 2226845467039736466) - # bhat1 = convert(T,117807213929927//2640907728177740) - # bhat4 = convert(T,4758744518816629500000//17812069906509312711137) - # bhat5 = convert(T,1730775233574080000000000//7863520414322158392809673) - # bhat6 = convert(T,BigInt(2682653613028767167314032381891560552585218935572349997)//BigInt(12258338284789875762081637252125169126464880985167722660)) - # bhat7 = convert(T,40977117022675781250//178949401077111131341) - # bhat10 = convert(T,2152106665253777//106040260335225546) - btilde1 = convert(T, 522643094875451 // 205198530479410398) - btilde4 = convert(T, -550343178903849903000000 // 56980811630923291362927263) - btilde5 = convert(T, 197654115880170560000000000 // 4698810880303595192357998239) - btilde6 = convert(T, - BigInt(-3171408959554499061315206389277085667739969057641653677018211151) // - BigInt(47560021699187396356176810016036479298162906422060184484892853758)) - btilde7 = convert(T, 40831491787144609375000 // 154075434327392684084601) - btilde8 = convert(T, -66898316144057728000 // 227310933007074849597) - btilde9 = convert(T, 181081444637946577 // 2226845467039736466) - btilde10 = convert(T, -2152106665253777 // 106040260335225546) - - Vern7Tableau( - c2, c3, c4, c5, c6, c7, c8, a021, a031, a032, a041, a043, a051, a053, a054, - a061, a063, a064, a065, a071, a073, a074, a075, a076, a081, a083, a084, - a085, a086, a087, a091, a093, a094, a095, a096, a097, a098, a101, a103, - a104, a105, a106, a107, b1, b4, b5, b6, b7, b8, b9, btilde1, btilde4, - btilde5, btilde6, btilde7, btilde8, btilde9, btilde10) -end - -## Vern8 -struct Vern8ExtraStages{T, T2} - c14::T2 - a1401::T - a1406::T - a1407::T - a1408::T - a1409::T - a1410::T - a1411::T - a1412::T - c15::T2 - a1501::T - a1506::T - a1507::T - a1508::T - a1509::T - a1510::T - a1511::T - a1512::T - a1514::T - c16::T2 - a1601::T - a1606::T - a1607::T - a1608::T - a1609::T - a1610::T - a1611::T - a1612::T - a1614::T - a1615::T - c17::T2 - a1701::T - a1706::T - a1707::T - a1708::T - a1709::T - a1710::T - a1711::T - a1712::T - a1714::T - a1715::T - a1716::T - c18::T2 - a1801::T - a1806::T - a1807::T - a1808::T - a1809::T - a1810::T - a1811::T - a1812::T - a1814::T - a1815::T - a1816::T - a1817::T - c19::T2 - a1901::T - a1906::T - a1907::T - a1908::T - a1909::T - a1910::T - a1911::T - a1912::T - a1914::T - a1915::T - a1916::T - a1917::T - c20::T2 - a2001::T - a2006::T - a2007::T - a2008::T - a2009::T - a2010::T - a2011::T - a2012::T - a2014::T - a2015::T - a2016::T - a2017::T - c21::T2 - a2101::T - a2106::T - a2107::T - a2108::T - a2109::T - a2110::T - a2111::T - a2112::T - a2114::T - a2115::T - a2116::T - a2117::T -end - -function Vern8ExtraStages(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - c14 = convert(T2, 1) - a1401 = convert(T, 0.04427989419007951) - a1406 = convert(T, 0.3541049391724449) - a1407 = convert(T, 0.2479692154956438) - a1408 = convert(T, -15.694202038838084) - a1409 = convert(T, 25.084064965558564) - a1410 = convert(T, -31.738367786260277) - a1411 = convert(T, 22.938283273988784) - a1412 = convert(T, -0.2361324633071542) - c15 = convert(T2, 0.3110177634953864) - a1501 = convert(T, 0.04620700646754963) - a1506 = convert(T, 0.045039041608424805) - a1507 = convert(T, 0.23368166977134244) - a1508 = convert(T, 37.83901368421068) - a1509 = convert(T, -15.949113289454246) - a1510 = convert(T, 23.028368351816102) - a1511 = convert(T, -44.85578507769412) - a1512 = convert(T, -0.06379858768647444) - a1514 = convert(T, -0.012595035543861663) - c16 = convert(T2, 0.1725) - a1601 = convert(T, 0.05037946855482041) - a1606 = convert(T, 0.041098361310460796) - a1607 = convert(T, 0.17180541533481958) - a1608 = convert(T, 4.614105319981519) - a1609 = convert(T, -1.7916678830853965) - a1610 = convert(T, 2.531658930485041) - a1611 = convert(T, -5.324977860205731) - a1612 = convert(T, -0.03065532595385635) - a1614 = convert(T, -0.005254479979429613) - a1615 = convert(T, -0.08399194644224793) - c17 = convert(T2, 0.7846) - a1701 = convert(T, 0.0408289713299708) - a1706 = convert(T, 0.4244479514247632) - a1707 = convert(T, 0.23260915312752345) - a1708 = convert(T, 2.677982520711806) - a1709 = convert(T, 0.7420826657338945) - a1710 = convert(T, 0.1460377847941461) - a1711 = convert(T, -3.579344509890565) - a1712 = convert(T, 0.11388443896001738) - a1714 = convert(T, 0.012677906510331901) - a1715 = convert(T, -0.07443436349946675) - a1716 = convert(T, 0.047827480797578516) - c18 = convert(T2, 0.37) - a1801 = convert(T, 0.052126823936684136) - a1806 = convert(T, 0.053925083967447975) - a1807 = convert(T, 0.01660758097434641) - a1808 = convert(T, -4.45448575792678) - a1809 = convert(T, 6.835218278632146) - a1810 = convert(T, -8.711334822181994) - a1811 = convert(T, 6.491635839232917) - a1812 = convert(T, -0.07072551809844346) - a1814 = convert(T, -0.018540314919932164) - a1815 = convert(T, 0.023504021054353848) - a1816 = convert(T, 0.2344795103407822) - a1817 = convert(T, -0.08241072501152899) - c19 = convert(T2, 0.5) - a1901 = convert(T, 0.05020102870355714) - a1906 = convert(T, 0.1552209034795498) - a1907 = convert(T, 0.1264268424089235) - a1908 = convert(T, -5.149206303539847) - a1909 = convert(T, 8.46834099903693) - a1910 = convert(T, -10.662130681081495) - a1911 = convert(T, 7.541833224959729) - a1912 = convert(T, -0.07436968113832143) - a1914 = convert(T, -0.020558876866183826) - a1915 = convert(T, 0.07753795264710298) - a1916 = convert(T, 0.10462592203525443) - a1917 = convert(T, -0.11792133064519794) - c20 = convert(T2, 0.7) - a2001 = convert(T, 0.03737341446457826) - a2006 = convert(T, 0.35049307053383166) - a2007 = convert(T, 0.49226528193730257) - a2008 = convert(T, 8.553695439359313) - a2009 = convert(T, -10.353172990305913) - a2010 = convert(T, 13.83320427252915) - a2011 = convert(T, -12.280924330784618) - a2012 = convert(T, 0.17191515956565098) - a2014 = convert(T, 0.036415831143144964) - a2015 = convert(T, 0.02961920580288763) - a2016 = convert(T, -0.2651793938627067) - a2017 = convert(T, 0.09429503961738067) - c21 = convert(T2, 0.9) - a2101 = convert(T, 0.039390583455282506) - a2106 = convert(T, 0.3558516141234424) - a2107 = convert(T, 0.419738222595261) - a2108 = convert(T, 0.8720449778071941) - a2109 = convert(T, 0.8989520834876595) - a2110 = convert(T, -0.6305806161059884) - a2111 = convert(T, -1.1218872205954835) - a2112 = convert(T, 0.04298219512400197) - a2114 = convert(T, 0.013325575668739157) - a2115 = convert(T, 0.018762270539641482) - a2116 = convert(T, -0.18594111329221055) - a2117 = convert(T, 0.17736142719246029) - - Vern8ExtraStages(c14, a1401, a1406, a1407, a1408, a1409, a1410, a1411, a1412, c15, - a1501, a1506, a1507, a1508, a1509, a1510, a1511, a1512, a1514, c16, - a1601, a1606, a1607, a1608, a1609, a1610, a1611, a1612, a1614, a1615, - c17, a1701, a1706, a1707, a1708, a1709, a1710, a1711, a1712, a1714, - a1715, a1716, c18, a1801, a1806, a1807, a1808, a1809, a1810, a1811, - a1812, a1814, a1815, a1816, a1817, c19, a1901, a1906, a1907, a1908, - a1909, a1910, a1911, a1912, a1914, a1915, a1916, a1917, c20, a2001, - a2006, a2007, a2008, a2009, a2010, a2011, a2012, a2014, a2015, a2016, - a2017, c21, a2101, a2106, a2107, a2108, a2109, a2110, a2111, a2112, - a2114, a2115, a2116, a2117) -end - -function Vern8ExtraStages(T, T2) - c14 = convert(T2, 1) - a1401 = convert(T, big" .4427989419007951074716746668098518862111e-1") - a1406 = convert(T, big" .3541049391724448744815552028733568354121") - a1407 = convert(T, big" .2479692154956437828667629415370663023884") - a1408 = convert(T, big"-15.69420203883808405099207034271191213468") - a1409 = convert(T, big" 25.08406496555856261343930031237186278518") - a1410 = convert(T, big"-31.73836778626027646833156112007297739997") - a1411 = convert(T, big" 22.93828327398878395231483560344797018313") - a1412 = convert(T, big"-.2361324633071542145259900641263517600737") - c15 = convert(T2, big" .3110177634953863863927417318829099695921") - a1501 = convert(T, big" .4620700646754963101730413150238116432863e-1") - a1506 = convert(T, big" .4503904160842480866828520384400679697151e-1") - a1507 = convert(T, big" .2336816697713424410788701065340221126565") - a1508 = convert(T, big" 37.83901368421067410780338220861855254153") - a1509 = convert(T, big"-15.94911328945424610266139490307397370835") - a1510 = convert(T, big" 23.02836835181610285142510596329590091940") - a1511 = convert(T, big"-44.85578507769412524816130998016948002745") - a1512 = convert(T, big"-.6379858768647444009509067402330140781326e-1") - a1514 = convert(T, big"-.1259503554386166268241032464519842162533e-1") - c16 = convert(T2, 69 // 400) - a1601 = convert(T, big" .5037946855482040993065158747220696112586e-1") - a1606 = convert(T, big" .4109836131046079339916530614028848248545e-1") - a1607 = convert(T, big" .1718054153348195783296309209549424619697") - a1608 = convert(T, big" 4.61410531998151886974342237185977124648") - a1609 = convert(T, big"-1.791667883085396449712744996746836471721") - a1610 = convert(T, big" 2.531658930485041408462243518792913614971") - a1611 = convert(T, big"-5.32497786020573071925718815977276269909") - a1612 = convert(T, big"-.3065532595385634734924449496356513113607e-1") - a1614 = convert(T, big"-.5254479979429613570549519094377878106127e-2") - a1615 = convert(T, big"-.8399194644224792997538653464258058697156e-1") - c17 = convert(T2, 7846 // 10000) - a1701 = convert(T, big" .4082897132997079620207118756242653796386e-1") - a1706 = convert(T, big" .4244479514247632218892086657732332485609") - a1707 = convert(T, big" .2326091531275234539465100096964845486081") - a1708 = convert(T, big" 2.677982520711806062780528871014035962908") - a1709 = convert(T, big" .7420826657338945216477607044022963622057") - a1710 = convert(T, big" .1460377847941461193920992339731312296021") - a1711 = convert(T, big"-3.579344509890565218033356743825917680543") - a1712 = convert(T, big" .1138844389600173704531638716149985665239") - a1714 = convert(T, big" .1267790651033190047378693537615687232109e-1") - a1715 = convert(T, big"-.7443436349946674429752785032561552478382e-1") - a1716 = convert(T, big" .4782748079757851554575511473876987663388e-1") - c18 = convert(T2, 37 // 100) - a1801 = convert(T, big" .5212682393668413629928136927994514676607e-1") - a1806 = convert(T, big" .5392508396744797718209106862347065628649e-1") - a1807 = convert(T, big" .1660758097434640828541930599928251901718e-1") - a1808 = convert(T, big"-4.454485757926779655418936993298463071587") - a1809 = convert(T, big" 6.835218278632146381711296817968152631469") - a1810 = convert(T, big"-8.711334822181993739847172734848837971169") - a1811 = convert(T, big" 6.491635839232917053651267142703105653517") - a1812 = convert(T, big"-.7072551809844346422069985227700294651922e-1") - a1814 = convert(T, big"-.1854031491993216429111842937941202966440e-1") - a1815 = convert(T, big" .2350402105435384645116542087045962190647e-1") - a1816 = convert(T, big" .2344795103407822090556377813402774776461") - a1817 = convert(T, big"-.8241072501152898885823089698097768766651e-1") - c19 = convert(T2, 1 // 2) - a1901 = convert(T, big" .5020102870355713598699964419977883461362e-1") - a1906 = convert(T, big" .1552209034795498114932226104700567642339") - a1907 = convert(T, big" .1264268424089234914713091134864747506300") - a1908 = convert(T, big"-5.14920630353984701704917414605721854951") - a1909 = convert(T, big" 8.46834099903692926607453176331494311551") - a1910 = convert(T, big"-10.66213068108149527544209836207095498430") - a1911 = convert(T, big" 7.54183322495972836290996201569018333903") - a1912 = convert(T, big"-.743696811383214243944066492459357053774e-1") - a1914 = convert(T, big"-.2055887686618382619339821759221121764364e-1") - a1915 = convert(T, big" .775379526471029807261782993777862395844e-1") - a1916 = convert(T, big" .1046259220352544296313761971333987587377") - a1917 = convert(T, big"-.1179213306451979352145022687063013455111") - c20 = convert(T2, 7 // 10) - a2001 = convert(T, big" .3737341446457825692757506548800094134977e-1") - a2006 = convert(T, big" .3504930705338316406767087468339071089224") - a2007 = convert(T, big" .4922652819373025433298989824173484805373") - a2008 = convert(T, big" 8.553695439359312242284304421725315855379") - a2009 = convert(T, big"-10.35317299030591348532574006719207803272") - a2010 = convert(T, big" 13.83320427252914990351082875460544773493") - a2011 = convert(T, big"-12.28092433078461863729523583784519048012") - a2012 = convert(T, big" .1719151595656509762746810113378644307112") - a2014 = convert(T, big" .3641583114314496380113822384214528216140e-1") - a2015 = convert(T, big" .2961920580288763054890146412520723429115e-1") - a2016 = convert(T, big"-.2651793938627067002647615623738425030047") - a2017 = convert(T, big" .942950396173806655317007970358739475630e-1") - c21 = convert(T2, 9 // 10) - a2101 = convert(T, big" .3939058345528250943410670634923521987132e-1") - a2106 = convert(T, big" .3558516141234424183136697322755323715063") - a2107 = convert(T, big" .4197382225952610029372225526720065366258") - a2108 = convert(T, big" .872044977807194166293172525204036071060") - a2109 = convert(T, big" .898952083487659486126627160171417043611") - a2110 = convert(T, big"-.630580616105988359023456649527853470403") - a2111 = convert(T, big"-1.121887220595483550736681645425215081433") - a2112 = convert(T, big" .4298219512400197176967511031829197714867e-1") - a2114 = convert(T, big" .1332557566873915707013495891889190564164e-1") - a2115 = convert(T, big" .1876227053964148034446101291928097773800e-1") - a2116 = convert(T, big"-.1859411132922105570515379368592596513699") - a2117 = convert(T, big" .1773614271924602745226064729836361000042") - - Vern8ExtraStages(c14, a1401, a1406, a1407, a1408, a1409, a1410, a1411, a1412, c15, - a1501, a1506, a1507, a1508, a1509, a1510, a1511, a1512, a1514, c16, - a1601, a1606, a1607, a1608, a1609, a1610, a1611, a1612, a1614, a1615, - c17, a1701, a1706, a1707, a1708, a1709, a1710, a1711, a1712, a1714, - a1715, a1716, c18, a1801, a1806, a1807, a1808, a1809, a1810, a1811, - a1812, a1814, a1815, a1816, a1817, c19, a1901, a1906, a1907, a1908, - a1909, a1910, a1911, a1912, a1914, a1915, a1916, a1917, c20, a2001, - a2006, a2007, a2008, a2009, a2010, a2011, a2012, a2014, a2015, a2016, - a2017, c21, a2101, a2106, a2107, a2108, a2109, a2110, a2111, a2112, - a2114, a2115, a2116, a2117) -end - -struct Vern8InterpolationCoefficients{T} - r011::T - r012::T - r013::T - r014::T - r015::T - r016::T - r017::T - r018::T - r062::T - r063::T - r064::T - r065::T - r066::T - r067::T - r068::T - r072::T - r073::T - r074::T - r075::T - r076::T - r077::T - r078::T - r082::T - r083::T - r084::T - r085::T - r086::T - r087::T - r088::T - r092::T - r093::T - r094::T - r095::T - r096::T - r097::T - r098::T - r102::T - r103::T - r104::T - r105::T - r106::T - r107::T - r108::T - r112::T - r113::T - r114::T - r115::T - r116::T - r117::T - r118::T - r122::T - r123::T - r124::T - r125::T - r126::T - r127::T - r128::T - r142::T - r143::T - r144::T - r145::T - r146::T - r147::T - r148::T - r152::T - r153::T - r154::T - r155::T - r156::T - r157::T - r158::T - r162::T - r163::T - r164::T - r165::T - r166::T - r167::T - r168::T - r172::T - r173::T - r174::T - r175::T - r176::T - r177::T - r178::T - r182::T - r183::T - r184::T - r185::T - r186::T - r187::T - r188::T - r192::T - r193::T - r194::T - r195::T - r196::T - r197::T - r198::T - r202::T - r203::T - r204::T - r205::T - r206::T - r207::T - r208::T - r212::T - r213::T - r214::T - r215::T - r216::T - r217::T - r218::T -end - -function Vern8InterpolationCoefficients(T::Type{<:CompiledFloats}) - r011 = convert(T, 1) - r012 = convert(T, -10.039154650554519) - r013 = convert(T, 53.79210495862331) - r014 = convert(T, -165.0579057235472) - r015 = convert(T, 298.026456543461) - r016 = convert(T, -311.91254487079004) - r017 = convert(T, 174.60598526911716) - r018 = convert(T, -40.37066163211959) - r062 = convert(T, 158.1976739121776) - r063 = convert(T, -1543.96141721949) - r064 = convert(T, 6241.39874782878) - r065 = convert(T, -13136.516156406109) - r066 = convert(T, 15106.948493169599) - r067 = convert(T, -8996.489626298231) - r068 = convert(T, 2170.776389952444) - r072 = convert(T, 110.78115200797782) - r073 = convert(T, -1081.1905145356177) - r074 = convert(T, 4370.666940459977) - r075 = convert(T, -9199.113723922197) - r076 = convert(T, 10578.949209629855) - r077 = convert(T, -6299.975594978841) - r078 = convert(T, 1520.1305005543413) - r082 = convert(T, -7011.442038211314) - r083 = convert(T, 68429.55220744078) - r084 = convert(T, -276623.5714822198) - r085 = convert(T, 582220.4545548494) - r086 = convert(T, -669551.5244611246) - r087 = convert(T, 398731.3087623333) - r088 = convert(T, -96210.47174510667) - r092 = convert(T, 11206.397569848148) - r093 = convert(T, -109371.04854950662) - r094 = convert(T, 442127.8393698155) - r095 = convert(T, -930563.7629864562) - r096 = convert(T, 1.0701451335855902e6) - r097 = convert(T, -637292.8058429047) - r098 = convert(T, 153773.3309185794) - r102 = convert(T, -14179.231640455684) - r103 = convert(T, 138385.00931963572) - r104 = convert(T, -559415.549024087) - r105 = convert(T, 1.1774237946992505e6) - r106 = convert(T, -1.3540333227908213e6) - r107 = convert(T, 806353.893882505) - r108 = convert(T, -194566.3328138133) - r112 = convert(T, 10247.761767921746) - r113 = convert(T, -100015.05326375231) - r114 = convert(T, 404306.62401434296) - r115 = convert(T, -850959.9711689702) - r116 = convert(T, 978601.0462088685) - r117 = convert(T, -582776.4729907749) - r118 = convert(T, 140619.0037156383) - r122 = convert(T, -105.49303976850968) - r123 = convert(T, 1029.5801395803103) - r124 = convert(T, -4162.034181876453) - r125 = convert(T, 8759.996193602336) - r126 = convert(T, -10073.965556886049) - r127 = convert(T, 5999.247741473951) - r128 = convert(T, -1447.5674285888924) - r142 = convert(T, -14.863613373267432) - r143 = convert(T, 145.76359364894867) - r144 = convert(T, -587.6557063401914) - r145 = convert(T, 1227.3721512545558) - r146 = convert(T, -1394.4931057405536) - r147 = convert(T, 816.8562950730669) - r148 = convert(T, -192.97961452255882) - r152 = convert(T, 14.349685752905462) - r153 = convert(T, -150.29493444816657) - r154 = convert(T, 629.481242570029) - r155 = convert(T, -1352.5182073090607) - r156 = convert(T, 1575.8969337088804) - r157 = convert(T, -946.7876580472948) - r158 = convert(T, 229.87293777270722) - r162 = convert(T, -102.54524701110401) - r163 = convert(T, 1074.0326612646807) - r164 = convert(T, -4498.377917100411) - r165 = convert(T, 9665.320624003281) - r166 = convert(T, -11261.62224831288) - r167 = convert(T, 6765.902468760784) - r168 = convert(T, -1642.7103416043497) - r172 = convert(T, -38.13206313286474) - r173 = convert(T, 399.3854658292329) - r174 = convert(T, -1672.7487204919717) - r175 = convert(T, 3594.1072548585666) - r176 = convert(T, -4187.7015568029265) - r177 = convert(T, 2515.9412806490636) - r178 = convert(T, -610.8516609091005) - r182 = convert(T, -66.38279583069588) - r183 = convert(T, 595.8297683881103) - r184 = convert(T, -2188.7370600929717) - r185 = convert(T, 4213.839795282853) - r186 = convert(T, -4484.035731929197) - r187 = convert(T, 2500.6482514253466) - r188 = convert(T, -571.1622272434449) - r192 = convert(T, -90.4188757317306) - r193 = convert(T, 931.9503884048154) - r194 = convert(T, -3962.898377713156) - r195 = convert(T, 8733.31742002555) - r196 = convert(T, -10445.908189887661) - r197 = convert(T, 6426.218942917599) - r198 = convert(T, -1592.261308015418) - r202 = convert(T, -59.738843630388715) - r203 = convert(T, 544.8870146891725) - r204 = convert(T, -2090.4303749263127) - r205 = convert(T, 4194.418982707227) - r206 = convert(T, -4603.369436819628) - r207 = convert(T, 2619.2014135592976) - r208 = convert(T, -604.9687555793671) - r212 = convert(T, -59.20053764683937) - r213 = convert(T, 571.7660156218088) - r214 = convert(T, -2308.9495644453605) - r215 = convert(T, 4881.2341106861395) - r216 = convert(T, -5660.118807771202) - r217 = convert(T, 3408.7066890374217) - r218 = convert(T, -833.4379054819676) - - Vern8InterpolationCoefficients(r011, r012, r013, r014, r015, r016, r017, r018, r062, - r063, r064, r065, r066, r067, r068, r072, r073, r074, - r075, r076, r077, r078, r082, r083, r084, r085, r086, - r087, r088, r092, r093, r094, r095, r096, r097, r098, - r102, r103, r104, r105, r106, r107, r108, r112, r113, - r114, r115, r116, r117, r118, r122, r123, r124, r125, - r126, r127, r128, r142, r143, r144, r145, r146, r147, - r148, r152, r153, r154, r155, r156, r157, r158, r162, - r163, r164, r165, r166, r167, r168, r172, r173, r174, - r175, r176, r177, r178, r182, r183, r184, r185, r186, - r187, r188, r192, r193, r194, r195, r196, r197, r198, - r202, r203, r204, r205, r206, r207, r208, r212, r213, - r214, r215, r216, r217, r218) -end - -function Vern8InterpolationCoefficients(T) - r011 = convert(T, big" 1") - r012 = convert(T, big"-10.03915465055451898280745009553727015838") - r013 = convert(T, big" 53.79210495862331394937504547285261606206") - r014 = convert(T, big"-165.0579057235472167092186792753028629327") - r015 = convert(T, big" 298.0264565434610102489744601822776142620") - r016 = convert(T, big"-311.9125448707900689751032283191627986699") - r017 = convert(T, big" 174.6059852691171542761046061351126284335") - r018 = convert(T, big"-40.37066163211959429657758663355894180800") - r062 = convert(T, big" 158.1976739121776138067531004299642556045") - r063 = convert(T, big"-1543.961417219490013383329186557376850919") - r064 = convert(T, big" 6241.398747828780065219699818963300847515") - r065 = convert(T, big"-13136.51615640610824674042591770724411138") - r066 = convert(T, big" 15106.94849316959941770760848348143558467") - r067 = convert(T, big"-8996.489626298230413000758717864256649583") - r068 = convert(T, big" 2170.776389952444021264933974457050280938") - r072 = convert(T, big" 110.7811520079778201620910891542159716196") - r073 = convert(T, big"-1081.190514535617748557462051373884811281") - r074 = convert(T, big" 4370.666940459977376891679103587685016930") - r075 = convert(T, big"-9199.113723922197066947453657458673365167") - r076 = convert(T, big" 10578.94920962985483690180716390515207397") - r077 = convert(T, big"-6299.975594978841008450271944308599363057") - r078 = convert(T, big" 1520.130500554341433782477059435641543286") - r082 = convert(T, big"-7011.442038211314089634068023254940106045") - r083 = convert(T, big" 68429.55220744077890209519664603903716349") - r084 = convert(T, big"-276623.5714822198169288202316196287008724") - r085 = convert(T, big" 582220.4545548494658856503006312634684934") - r086 = convert(T, big"-669551.5244611245601905652331468068626208") - r087 = convert(T, big" 398731.3087623332757943809792249308827732") - r088 = convert(T, big"-96210.47174510666745715793578288559674281") - r092 = convert(T, big" 11206.39756984814734031374482605836502113") - r093 = convert(T, big"-109371.0485495066182770525095928736321803") - r094 = convert(T, big" 442127.8393698154661543505844693555049508") - r095 = convert(T, big"-930563.7629864562145364082427559715712707") - r096 = convert(T, big" 1070145.133585590072636708771436125254933") - r097 = convert(T, big"-637292.8058429046904373075590712408701797") - r098 = convert(T, big" 153773.3309185793956820086499888593205888") - r102 = convert(T, big"-14179.23164045568390825368995504736244876") - r103 = convert(T, big" 138385.0093196357218693716546019209270760") - r104 = convert(T, big"-559415.5490240869974273158302752589638112") - r105 = convert(T, big" 1177423.794699250413603625249340565972051") - r106 = convert(T, big"-1354033.322790821429356166591306087001182") - r107 = convert(T, big" 806353.8938825050195016379699232308969498") - r108 = convert(T, big"-194566.3328138133045593670938904445416121") - r112 = convert(T, big" 10247.76176792174468727263230424253072668") - r113 = convert(T, big"-100015.0532637523107509874155382267979521") - r114 = convert(T, big" 404306.6240143429367125014776377339233105") - r115 = convert(T, big"-850959.9711689702682710993795157496434280") - r116 = convert(T, big" 978601.0462088684697300958464199995189771") - r117 = convert(T, big"-582776.4729907748855939796622931794117500") - r118 = convert(T, big" 140619.0037156383022701488158207833280861") - r122 = convert(T, big"-105.4930397685096787379931952745881034169") - r123 = convert(T, big" 1029.580139580310194120073236423148130618") - r124 = convert(T, big"-4162.034181876452751021493197688100770349") - r125 = convert(T, big" 8759.996193602336131526447045580160767641") - r126 = convert(T, big"-10073.96555688604885441046004449728532151") - r127 = convert(T, big" 5999.247741473950186438936812025268574829") - r128 = convert(T, big"-1447.567428588892382130036646632729629570") - r142 = convert(T, big"-14.86361337326743122469601010648237947608") - r143 = convert(T, big" 145.7635936489486611601020590400812969906") - r144 = convert(T, big"-587.6557063401913588520708808169444817103") - r145 = convert(T, big" 1227.372151254555709980234511427063838550") - r146 = convert(T, big"-1394.493105740553645217117387304216418608") - r147 = convert(T, big" 816.8562950730668774494805290335070403105") - r148 = convert(T, big"-192.9796145225588132959328212730088960570") - r152 = convert(T, big" 14.34968575290546223276673100484047073648") - r153 = convert(T, big"-150.2949344481665658851785896351738227010") - r154 = convert(T, big" 629.4812425700290706612346725243246098946") - r155 = convert(T, big"-1352.518207309060677914698908083510085133") - r156 = convert(T, big" 1575.896933708880305858556996706058962503") - r157 = convert(T, big"-946.7876580472948045886633971120598201035") - r158 = convert(T, big" 229.8729377727072096359824945955196848017") - r162 = convert(T, big"-102.5452470111040085560664290210906322518") - r163 = convert(T, big" 1074.032661264680594125263250545103109541") - r164 = convert(T, big"-4498.377917100410634753487685261882069653") - r165 = convert(T, big" 9665.320624003280508099125255751992581938") - r166 = convert(T, big"-11261.62224831288113545795903649800929060") - r167 = convert(T, big" 6765.902468760784366342575368188597359812") - r168 = convert(T, big"-1642.710341604349689799450723704711058784") - r172 = convert(T, big"-38.13206313286473398334122725888547021750") - r173 = convert(T, big" 399.3854658292328681862496726489289700594") - r174 = convert(T, big"-1672.748720491971752312231602599596419744") - r175 = convert(T, big" 3594.107254858566583822606674735752304040") - r176 = convert(T, big"-4187.701556802926199931725021751236897492") - r177 = convert(T, big" 2515.941280649063720613355430002270532846") - r178 = convert(T, big"-610.8516609091004863949139257772330194915") - r182 = convert(T, big"-66.38279583069588062871084016403504860018") - r183 = convert(T, big" 595.8297683881103280237377269355990794854") - r184 = convert(T, big"-2188.737060092971609278770563269347103559") - r185 = convert(T, big" 4213.839795282852421559730676511794767863") - r186 = convert(T, big"-4484.035731929196864370162258757955490985") - r187 = convert(T, big" 2500.648251425346544829791147364129986790") - r188 = convert(T, big"-571.1622272434449401356158886201861909946") - r192 = convert(T, big"-90.41887573173058787343992868450872085904") - r193 = convert(T, big" 931.9503884048153706496188381219698380844") - r194 = convert(T, big"-3962.898377713156165984683269799703910403") - r195 = convert(T, big" 8733.317420025551238329244389917866097896") - r196 = convert(T, big"-10445.90818988766053535212385670877957360") - r197 = convert(T, big" 6426.218942917598693647793004359979629852") - r198 = convert(T, big"-1592.261308015418013416409177206823360972") - r202 = convert(T, big"-59.73884363038871206457816967313835076801") - r203 = convert(T, big" 544.8870146891724527559861176467523778088") - r204 = convert(T, big"-2090.430374926312850791322527518588562537") - r205 = convert(T, big" 4194.418982707226648046953315742901721971") - r206 = convert(T, big"-4603.369436819628073439413527693451638704") - r207 = convert(T, big" 2619.201413559297614510795648037620577207") - r208 = convert(T, big"-604.9687555793670790184208565420961249773") - r212 = convert(T, big"-59.20053764683937384859682230934791521325") - r213 = convert(T, big" 571.7660156218088014286377638724659591261") - r214 = convert(T, big"-2308.949564445360683785335401047607870804") - r215 = convert(T, big" 4881.234110686139058221334453291392021952") - r216 = convert(T, big"-5660.118807771202003386701685793459298252") - r217 = convert(T, big" 3408.706689037421803199133730396931709513") - r218 = convert(T, big"-833.4379054819676018284720384103746063216") - - Vern8InterpolationCoefficients(r011, r012, r013, r014, r015, r016, r017, r018, r062, - r063, r064, r065, r066, r067, r068, r072, r073, r074, - r075, r076, r077, r078, r082, r083, r084, r085, r086, - r087, r088, r092, r093, r094, r095, r096, r097, r098, - r102, r103, r104, r105, r106, r107, r108, r112, r113, - r114, r115, r116, r117, r118, r122, r123, r124, r125, - r126, r127, r128, r142, r143, r144, r145, r146, r147, - r148, r152, r153, r154, r155, r156, r157, r158, r162, - r163, r164, r165, r166, r167, r168, r172, r173, r174, - r175, r176, r177, r178, r182, r183, r184, r185, r186, - r187, r188, r192, r193, r194, r195, r196, r197, r198, - r202, r203, r204, r205, r206, r207, r208, r212, r213, - r214, r215, r216, r217, r218) -end - -struct Vern8Tableau{T, T2} - c2::T2 - c3::T2 - c4::T2 - c5::T2 - c6::T2 - c7::T2 - c8::T2 - c9::T2 - c10::T2 - c11::T2 - a0201::T - a0301::T - a0302::T - a0401::T - a0403::T - a0501::T - a0503::T - a0504::T - a0601::T - a0604::T - a0605::T - a0701::T - a0704::T - a0705::T - a0706::T - a0801::T - a0804::T - a0805::T - a0806::T - a0807::T - a0901::T - a0904::T - a0905::T - a0906::T - a0907::T - a0908::T - a1001::T - a1004::T - a1005::T - a1006::T - a1007::T - a1008::T - a1009::T - a1101::T - a1104::T - a1105::T - a1106::T - a1107::T - a1108::T - a1109::T - a1110::T - a1201::T - a1204::T - a1205::T - a1206::T - a1207::T - a1208::T - a1209::T - a1210::T - a1211::T - a1301::T - a1304::T - a1305::T - a1306::T - a1307::T - a1308::T - a1309::T - a1310::T - b1::T - b6::T - b7::T - b8::T - b9::T - b10::T - b11::T - b12::T - btilde1::T - btilde6::T - btilde7::T - btilde8::T - btilde9::T - btilde10::T - btilde11::T - btilde12::T - btilde13::T - extra::Vern8ExtraStages{T, T2} - interp::Vern8InterpolationCoefficients{T} -end - -function Vern8Tableau(T::Type{<:CompiledFloats}, T2::Type{<:CompiledFloats}) - c2 = convert(T2, 0.05) - c3 = convert(T2, 0.1065625) - c4 = convert(T2, 0.15984375) - c5 = convert(T2, 0.39) - c6 = convert(T2, 0.465) - c7 = convert(T2, 0.155) - c8 = convert(T2, 0.943) - c9 = convert(T2, 0.901802041735857) - c10 = convert(T2, 0.909) - c11 = convert(T2, 0.94) - #c12 =convert(T2, 1) - #c13 =convert(T2, 1) - a0201 = convert(T, 0.05) - a0301 = convert(T, -0.0069931640625) - a0302 = convert(T, 0.1135556640625) - a0401 = convert(T, 0.0399609375) - a0403 = convert(T, 0.1198828125) - a0501 = convert(T, 0.36139756280045754) - a0503 = convert(T, -1.3415240667004928) - a0504 = convert(T, 1.3701265039000352) - a0601 = convert(T, 0.049047202797202795) - a0604 = convert(T, 0.23509720422144048) - a0605 = convert(T, 0.18085559298135673) - a0701 = convert(T, 0.06169289044289044) - a0704 = convert(T, 0.11236568314640277) - a0705 = convert(T, -0.03885046071451367) - a0706 = convert(T, 0.01979188712522046) - a0801 = convert(T, -1.767630240222327) - a0804 = convert(T, -62.5) - a0805 = convert(T, -6.061889377376669) - a0806 = convert(T, 5.6508231982227635) - a0807 = convert(T, 65.62169641937624) - a0901 = convert(T, -1.1809450665549708) - a0904 = convert(T, -41.50473441114321) - a0905 = convert(T, -4.434438319103725) - a0906 = convert(T, 4.260408188586133) - a0907 = convert(T, 43.75364022446172) - a0908 = convert(T, 0.00787142548991231) - a1001 = convert(T, -1.2814059994414884) - a1004 = convert(T, -45.047139960139866) - a1005 = convert(T, -4.731362069449576) - a1006 = convert(T, 4.514967016593808) - a1007 = convert(T, 47.44909557172985) - a1008 = convert(T, 0.01059228297111661) - a1009 = convert(T, -0.0057468422638446166) - a1101 = convert(T, -1.7244701342624853) - a1104 = convert(T, -60.92349008483054) - a1105 = convert(T, -5.951518376222392) - a1106 = convert(T, 5.556523730698456) - a1107 = convert(T, 63.98301198033305) - a1108 = convert(T, 0.014642028250414961) - a1109 = convert(T, 0.06460408772358203) - a1110 = convert(T, -0.0793032316900888) - a1201 = convert(T, -3.301622667747079) - a1204 = convert(T, -118.01127235975251) - a1205 = convert(T, -10.141422388456112) - a1206 = convert(T, 9.139311332232058) - a1207 = convert(T, 123.37594282840426) - a1208 = convert(T, 4.62324437887458) - a1209 = convert(T, -3.3832777380682018) - a1210 = convert(T, 4.527592100324618) - a1211 = convert(T, -5.828495485811623) - a1301 = convert(T, -3.039515033766309) - a1304 = convert(T, -109.26086808941763) - a1305 = convert(T, -9.290642497400293) - a1306 = convert(T, 8.43050498176491) - a1307 = convert(T, 114.20100103783314) - a1308 = convert(T, -0.9637271342145479) - a1309 = convert(T, -5.0348840888021895) - a1310 = convert(T, 5.958130824002923) - b1 = convert(T, 0.04427989419007951) - b6 = convert(T, 0.3541049391724449) - b7 = convert(T, 0.24796921549564377) - b8 = convert(T, -15.694202038838085) - b9 = convert(T, 25.084064965558564) - b10 = convert(T, -31.738367786260277) - b11 = convert(T, 22.938283273988784) - b12 = convert(T, -0.2361324633071542) - # bhat1 = convert(T,0.044312615229089795) - # bhat6 = convert(T,0.35460956423432266) - # bhat7 = convert(T,0.2478480431366653) - # bhat8 = convert(T,4.4481347324757845) - # bhat9 = convert(T,19.846886366118735) - # bhat10= convert(T,-23.58162337746562) - # bhat13= convert(T,-0.36016794372897754) - btilde1 = convert(T, -3.272103901028138e-5) - btilde6 = convert(T, -0.0005046250618777704) - btilde7 = convert(T, 0.0001211723589784759) - btilde8 = convert(T, -20.142336771313868) - btilde9 = convert(T, 5.2371785994398286) - btilde10 = convert(T, -8.156744408794658) - btilde11 = convert(T, 22.938283273988784) - btilde12 = convert(T, -0.2361324633071542) - btilde13 = convert(T, 0.36016794372897754) - - extra = Vern8ExtraStages(T, T2) - interp = Vern8InterpolationCoefficients(T) - - Vern8Tableau(c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, a0201, a0301, a0302, a0401, - a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, a0704, a0705, - a0706, a0801, a0804, a0805, a0806, a0807, a0901, a0904, a0905, a0906, - a0907, a0908, a1001, a1004, a1005, a1006, a1007, a1008, a1009, a1101, - a1104, a1105, a1106, a1107, a1108, a1109, a1110, a1201, a1204, a1205, - a1206, a1207, a1208, a1209, a1210, a1211, a1301, a1304, a1305, a1306, - a1307, a1308, a1309, a1310, b1, b6, b7, b8, b9, b10, b11, b12, btilde1, - btilde6, btilde7, btilde8, btilde9, btilde10, btilde11, btilde12, btilde13, - extra, interp) -end - -function Vern8Tableau(T, T2) - c2 = convert(T2, 1 // 20) - c3 = convert(T2, 341 // 3200) - c4 = convert(T2, 1023 // 6400) - c5 = convert(T2, 39 // 100) - c6 = convert(T2, 93 // 200) - c7 = convert(T2, 31 // 200) - c8 = convert(T2, 943 // 1000) - c9 = convert(T2, 7067558016280 // 7837150160667) - c10 = convert(T2, 909 // 1000) - c11 = convert(T2, 47 // 50) - #c12 =convert(T2, 1) - #c13 =convert(T2, 1) - a0201 = convert(T, 1 // 20) - a0301 = convert(T, -7161 // 1024000) - a0302 = convert(T, 116281 // 1024000) - a0401 = convert(T, 1023 // 25600) - a0403 = convert(T, 3069 // 25600) - a0501 = convert(T, 4202367 // 11628100) - a0503 = convert(T, -3899844 // 2907025) - a0504 = convert(T, 3982992 // 2907025) - a0601 = convert(T, 5611 // 114400) - a0604 = convert(T, 31744 // 135025) - a0605 = convert(T, 923521 // 5106400) - a0701 = convert(T, 21173 // 343200) - a0704 = convert(T, 8602624 // 76559175) - a0705 = convert(T, -26782109 // 689364000) - a0706 = convert(T, 5611 // 283500) - a0801 = convert(T, -1221101821869329 // 690812928000000) - a0804 = convert(T, -125 // 2) - a0805 = convert(T, -1024030607959889 // 168929280000000) - a0806 = convert(T, 1501408353528689 // 265697280000000) - a0807 = convert(T, 6070139212132283 // 92502016000000) - a0901 = convert(T, - -BigInt(1472514264486215803881384708877264246346044433307094207829051978044531801133057155) // - BigInt(1246894801620032001157059621643986024803301558393487900440453636168046069686436608)) - a0904 = convert(T, - -BigInt(5172294311085668458375175655246981230039025336933699114138315270772319372469280000) // - BigInt(124619381004809145897278630571215298365257079410236252921850936749076487132995191)) - a0905 = convert(T, - -BigInt(12070679258469254807978936441733187949484571516120469966534514296406891652614970375) // - BigInt(2722031154761657221710478184531100699497284085048389015085076961673446140398628096)) - a0906 = convert(T, - BigInt(780125155843893641323090552530431036567795592568497182701460674803126770111481625) // - BigInt(183110425412731972197889874507158786859226102980861859505241443073629143100805376)) - a0907 = convert(T, - BigInt(664113122959911642134782135839106469928140328160577035357155340392950009492511875) // - BigInt(15178465598586248136333023107295349175279765150089078301139943253016877823170816)) - a0908 = convert(T, - BigInt(10332848184452015604056836767286656859124007796970668046446015775000000) // - BigInt(1312703550036033648073834248740727914537972028638950165249582733679393783)) - a1001 = convert(T, - -BigInt(29055573360337415088538618442231036441314060511) // - BigInt(22674759891089577691327962602370597632000000000)) - a1004 = convert(T, -20462749524591049105403365239069 // 454251913499893469596231268750) - a1005 = convert(T, - -180269259803172281163724663224981097 // - 38100922558256871086579832832000000) - a1006 = convert(T, - BigInt(21127670214172802870128286992003940810655221489) // - BigInt(4679473877997892906145822697976708633673728000)) - a1007 = convert(T, - BigInt(318607235173649312405151265849660869927653414425413) // - BigInt(6714716715558965303132938072935465423910912000000)) - a1008 = convert(T, - 212083202434519082281842245535894 // - 20022426044775672563822865371173879) - a1009 = convert(T, - -BigInt(2698404929400842518721166485087129798562269848229517793703413951226714583) // - BigInt(469545674913934315077000442080871141884676035902717550325616728175875000000)) - a1101 = convert(T, - -BigInt(2342659845814086836951207140065609179073838476242943917) // - BigInt(1358480961351056777022231400139158760857532162795520000)) - a1104 = convert(T, -996286030132538159613930889652 // 16353068885996164905464325675) - a1105 = convert(T, -26053085959256534152588089363841 // 4377552804565683061011299942400) - a1106 = convert(T, - BigInt(20980822345096760292224086794978105312644533925634933539) // - BigInt(3775889992007550803878727839115494641972212962174156800)) - a1107 = convert(T, - BigInt(890722993756379186418929622095833835264322635782294899) // - BigInt(13921242001395112657501941955594013822830119803764736)) - a1108 = convert(T, - BigInt(161021426143124178389075121929246710833125) // - BigInt(10997207722131034650667041364346422894371443)) - a1109 = convert(T, - BigInt(300760669768102517834232497565452434946672266195876496371874262392684852243925359864884962513) // - BigInt(4655443337501346455585065336604505603760824779615521285751892810315680492364106674524398280000)) - a1110 = convert(T, -31155237437111730665923206875 // 392862141594230515010338956291) - a1201 = convert(T, - -BigInt(2866556991825663971778295329101033887534912787724034363) // - BigInt(868226711619262703011213925016143612030669233795338240)) - a1204 = convert(T, - -BigInt(16957088714171468676387054358954754000) // - BigInt(143690415119654683326368228101570221)) - a1205 = convert(T, - -BigInt(4583493974484572912949314673356033540575) // - BigInt(451957703655250747157313034270335135744)) - a1206 = convert(T, - BigInt(2346305388553404258656258473446184419154740172519949575) // - BigInt(256726716407895402892744978301151486254183185289662464)) - a1207 = convert(T, - BigInt(1657121559319846802171283690913610698586256573484808662625) // - BigInt(13431480411255146477259155104956093505361644432088109056)) - a1208 = convert(T, - BigInt(345685379554677052215495825476969226377187500) // - BigInt(74771167436930077221667203179551347546362089)) - a1209 = convert(T, - -BigInt(3205890962717072542791434312152727534008102774023210240571361570757249056167015230160352087048674542196011) // - BigInt(947569549683965814783015124451273604984657747127257615372449205973192657306017239103491074738324033259120)) - a1210 = convert(T, - BigInt(40279545832706233433100438588458933210937500) // - BigInt(8896460842799482846916972126377338947215101)) - a1211 = convert(T, - -BigInt(6122933601070769591613093993993358877250) // - BigInt(1050517001510235513198246721302027675953)) - a1301 = convert(T, - -BigInt(618675905535482500672800859344538410358660153899637) // - BigInt(203544282118214047100119475340667684874292102389760)) - a1304 = convert(T, - -BigInt(4411194916804718600478400319122931000) // - BigInt(40373053902469967450761491269633019)) - a1305 = convert(T, - -BigInt(16734711409449292534539422531728520225) // - BigInt(1801243715290088669307203927210237952)) - a1306 = convert(T, - BigInt(135137519757054679098042184152749677761254751865630525) // - BigInt(16029587794486289597771326361911895112703716593983488)) - a1307 = convert(T, - BigInt(38937568367409876012548551903492196137929710431584875) // - BigInt(340956454090191606099548798001469306974758443147264)) - a1308 = convert(T, - -BigInt(6748865855011993037732355335815350667265625) // - BigInt(7002880395717424621213565406715087764770357)) - a1309 = convert(T, - -BigInt(1756005520307450928195422767042525091954178296002788308926563193523662404739779789732685671) // - BigInt(348767814578469983605688098046186480904607278021030540735333862087061574934154942830062320)) - a1310 = convert(T, - BigInt(53381024589235611084013897674181629296875) // - BigInt(8959357584795694524874969598508592944141)) - b1 = convert(T, 44901867737754616851973 // 1014046409980231013380680) - b6 = convert(T, 791638675191615279648100000 // 2235604725089973126411512319) - b7 = convert(T, 3847749490868980348119500000 // 15517045062138271618141237517) - b8 = convert(T, -13734512432397741476562500000 // 875132892924995907746928783) - b9 = convert(T, - BigInt(12274765470313196878428812037740635050319234276006986398294443554969616342274215316330684448207141) // - BigInt(489345147493715517650385834143510934888829280686609654482896526796523353052166757299452852166040)) - b10 = convert(T, -9798363684577739445312500000 // 308722986341456031822630699) - b11 = convert(T, 282035543183190840068750 // 12295407629873040425991) - b12 = convert(T, -306814272936976936753 // 1299331183183744997286) - # bhat1 = convert(T, 10835401739407019406577//244521829356935137978320) - # bhat6 = convert(T, 13908189778321895491375000//39221135527894265375640567) - # bhat7 = convert(T, 73487947527027243487625000//296504045773342769773399443) - # bhat8 = convert(T, 68293140641257649609375000//15353208647806945749946119) - # bhat9 = convert(T, BigInt(22060647948996678611017711379974578860522018208949721559448560203338437626022142776381)//BigInt(1111542009262325874512959185795727215759010577565736079641376621381577236680929558640)) - # bhat10= convert(T,-547971229495642458203125000//23237214025700991642563601) - # bhat13= convert(T,-28735456870978964189//79783493704265043693) - btilde1 = convert(T, -225628434546552672055 // 6895515587865570890988624) - btilde6 = convert(T, -1128142172732763360275000 // 2235604725089973126411512319) - btilde7 = convert(T, 5640710863663816801375000 // 46551135186414814854423712551) - btilde8 = convert(T, -17627221448949427504296875000 // 875132892924995907746928783) - btilde9 = convert(T, - BigInt(17426957952517932078050241885889670195876481434157580946550703126433816616672116622859678756257765) // - BigInt(3327547002957265520022623672175874357244039108668945650483696382216358800754733949636279394729072)) - btilde10 = convert(T, -17627221448949427504296875000 // 2161060904390192222758414893) - btilde11 = convert(T, 282035543183190840068750 // 12295407629873040425991) - btilde12 = convert(T, -306814272936976936753 // 1299331183183744997286) - btilde13 = convert(T, 28735456870978964189 // 79783493704265043693) - - extra = Vern8ExtraStages(T, T2) - interp = Vern8InterpolationCoefficients(T) - - Vern8Tableau(c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, a0201, a0301, a0302, a0401, - a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, a0704, a0705, - a0706, a0801, a0804, a0805, a0806, a0807, a0901, a0904, a0905, a0906, - a0907, a0908, a1001, a1004, a1005, a1006, a1007, a1008, a1009, a1101, - a1104, a1105, a1106, a1107, a1108, a1109, a1110, a1201, a1204, a1205, - a1206, a1207, a1208, a1209, a1210, a1211, a1301, a1304, a1305, a1306, - a1307, a1308, a1309, a1310, b1, b6, b7, b8, b9, b10, b11, b12, btilde1, - btilde6, btilde7, btilde8, btilde9, btilde10, btilde11, btilde12, btilde13, - extra, interp) -end - -## Vern9 -struct Vern9ExtraStages{T, T2} - c17::T2 - a1701::T - a1708::T - a1709::T - a1710::T - a1711::T - a1712::T - a1713::T - a1714::T - a1715::T - c18::T2 - a1801::T - a1808::T - a1809::T - a1810::T - a1811::T - a1812::T - a1813::T - a1814::T - a1815::T - a1817::T - c19::T2 - a1901::T - a1908::T - a1909::T - a1910::T - a1911::T - a1912::T - a1913::T - a1914::T - a1915::T - a1917::T - a1918::T - c20::T2 - a2001::T - a2008::T - a2009::T - a2010::T - a2011::T - a2012::T - a2013::T - a2014::T - a2015::T - a2017::T - a2018::T - a2019::T - c21::T2 - a2101::T - a2108::T - a2109::T - a2110::T - a2111::T - a2112::T - a2113::T - a2114::T - a2115::T - a2117::T - a2118::T - a2119::T - a2120::T - c22::T2 - a2201::T - a2208::T - a2209::T - a2210::T - a2211::T - a2212::T - a2213::T - a2214::T - a2215::T - a2217::T - a2218::T - a2219::T - a2220::T - a2221::T - c23::T2 - a2301::T - a2308::T - a2309::T - a2310::T - a2311::T - a2312::T - a2313::T - a2314::T - a2315::T - a2317::T - a2318::T - a2319::T - a2320::T - a2321::T - c24::T2 - a2401::T - a2408::T - a2409::T - a2410::T - a2411::T - a2412::T - a2413::T - a2414::T - a2415::T - a2417::T - a2418::T - a2419::T - a2420::T - a2421::T - c25::T2 - a2501::T - a2508::T - a2509::T - a2510::T - a2511::T - a2512::T - a2513::T - a2514::T - a2515::T - a2517::T - a2518::T - a2519::T - a2520::T - a2521::T - c26::T2 - a2601::T - a2608::T - a2609::T - a2610::T - a2611::T - a2612::T - a2613::T - a2614::T - a2615::T - a2617::T - a2618::T - a2619::T - a2620::T - a2621::T -end - -@fold function Vern9ExtraStages(::Type{T}, - ::Type{T2}) where {T <: CompiledFloats, - T2 <: CompiledFloats} - # FIVE ADDITIONAL STAGES FOR INTERPOLANT OF ORDER 8 - c17 = convert(T2, 1) - a1701 = convert(T, 0.014611976858423152) - a1708 = convert(T, -0.3915211862331339) - a1709 = convert(T, 0.23109325002895065) - a1710 = convert(T, 0.12747667699928525) - a1711 = convert(T, 0.2246434176204158) - a1712 = convert(T, 0.5684352689748513) - a1713 = convert(T, 0.058258715572158275) - a1714 = convert(T, 0.13643174034822156) - a1715 = convert(T, 0.030570139830827976) - c18 = convert(T2, 0.7404185470631561) - a1801 = convert(T, 0.015499736681895594) - a1808 = convert(T, 0.3355153219059635) - a1809 = convert(T, 0.20036139441918607) - a1810 = convert(T, 0.12520606592835493) - a1811 = convert(T, 0.22986763931842066) - a1812 = convert(T, -0.20202506534761813) - a1813 = convert(T, 0.05917103230665457) - a1814 = convert(T, -0.026518347830476387) - a1815 = convert(T, -0.023840946021309713) - a1817 = convert(T, 0.027181715702085017) - c19 = convert(T2, 0.888) - a1901 = convert(T, 0.013024539431143383) - a1908 = convert(T, -0.7452850902413112) - a1909 = convert(T, 0.2643867896429301) - a1910 = convert(T, 0.1313961758372754) - a1911 = convert(T, 0.21672538151229273) - a1912 = convert(T, 0.8734117564076053) - a1913 = convert(T, 0.011859056439357767) - a1914 = convert(T, 0.05876002941689551) - a1915 = convert(T, 0.003266518630202088) - a1917 = convert(T, -0.00895930864841793) - a1918 = convert(T, 0.06941415157202692) - c20 = convert(T2, 0.696) - a2001 = convert(T, 0.013970899969259426) - a2008 = convert(T, -0.46657653359576745) - a2009 = convert(T, 0.24163727872162571) - a2010 = convert(T, 0.12903633413456747) - a2011 = convert(T, 0.22167006717351054) - a2012 = convert(T, 0.6257275123364645) - a2013 = convert(T, 0.04355312415679284) - a2014 = convert(T, 0.10119624916672908) - a2015 = convert(T, 0.01808582254679721) - a2017 = convert(T, -0.020798755876891697) - a2018 = convert(T, -0.09022232517086219) - a2019 = convert(T, -0.12127967356222542) - c21 = convert(T2, 0.487) - a2101 = convert(T, 0.016046388883181127) - a2108 = convert(T, 0.09517712399458336) - a2109 = convert(T, 0.13591872646553177) - a2110 = convert(T, 0.1237765280959854) - a2111 = convert(T, 0.2335656264102966) - a2112 = convert(T, -0.09051508172625873) - a2113 = convert(T, -0.02537574270006131) - a2114 = convert(T, -0.13596316968871622) - a2115 = convert(T, -0.04679214284145113) - a2117 = convert(T, 0.05177958859391748) - a2118 = convert(T, 0.09672595677476774) - a2119 = convert(T, 0.14773126903407427) - a2120 = convert(T, -0.11507507129585039) - - # FIVE ADDITIONAL STAGES FOR INTERPOLANT OF ORDER 9 - c22 = convert(T2, 0.025) - a2201 = convert(T, 0.018029186238936207) - a2208 = convert(T, 0.06983601042028874) - a2209 = convert(T, -0.025412476607916634) - a2210 = convert(T, 0.008487827035463275) - a2211 = convert(T, -0.002427525516089802) - a2212 = convert(T, -0.10478397528938199) - a2213 = convert(T, -0.014731477952480419) - a2214 = convert(T, -0.03916338390816177) - a2215 = convert(T, -0.010056573432939595) - a2217 = convert(T, 0.011025103922048344) - a2218 = convert(T, 0.005092830749095398) - a2219 = convert(T, 0.04759715599420645) - a2220 = convert(T, 0.03386307003288383) - a2221 = convert(T, 0.02764422831404798) - c23 = convert(T2, 0.15) - a2301 = convert(T, 0.01677431640522778) - a2308 = convert(T, 0.6220437408820475) - a2309 = convert(T, -0.2060859809768842) - a2310 = convert(T, 0.11563949897660589) - a2311 = convert(T, 0.026641017933783588) - a2312 = convert(T, -0.937681079341877) - a2313 = convert(T, -0.13678064667021603) - a2314 = convert(T, -0.3678480995268297) - a2315 = convert(T, -0.09547871314402478) - a2317 = convert(T, 0.10134920184223697) - a2318 = convert(T, -0.08911323084568594) - a2319 = convert(T, 0.46641409889747604) - a2320 = convert(T, 0.450273629235458) - a2321 = convert(T, 0.18385224633268188) - c24 = convert(T2, 0.32) - a2401 = convert(T, 0.010711497314914442) - a2408 = convert(T, -0.07094336118221108) - a2409 = convert(T, 0.10021649003400916) - a2410 = convert(T, 0.13834539804680251) - a2411 = convert(T, 0.17963306335781634) - a2412 = convert(T, 0.09048246545576182) - a2413 = convert(T, -0.005460662294523339) - a2414 = convert(T, -0.030004579051196197) - a2415 = convert(T, -0.011451920269627991) - a2417 = convert(T, 0.010033946861093851) - a2418 = convert(T, -0.09506485282809046) - a2419 = convert(T, 0.04853358804093592) - a2420 = convert(T, 0.08013325919783924) - a2421 = convert(T, -0.1251643326835242) - c25 = convert(T2, 0.78) - a2501 = convert(T, 0.014101720888692213) - a2508 = convert(T, -0.3713379753704491) - a2509 = convert(T, 0.22312655481171803) - a2510 = convert(T, 0.12870053459181202) - a2511 = convert(T, 0.22246006596754947) - a2512 = convert(T, 0.5382853042550702) - a2513 = convert(T, 0.05417202616988763) - a2514 = convert(T, 0.1256968791308744) - a2515 = convert(T, 0.027844927890020542) - a2517 = convert(T, -0.0307740924620506) - a2518 = convert(T, 0.008569805293689777) - a2519 = convert(T, -0.15351746905870445) - a2520 = convert(T, -0.021799570305481963) - a2521 = convert(T, 0.014471288197371868) - c26 = convert(T2, 0.96) - a2601 = convert(T, 0.014246004117356466) - a2608 = convert(T, -0.3767107393295407) - a2609 = convert(T, 0.22523997807304214) - a2610 = convert(T, 0.128360307629253) - a2611 = convert(T, 0.22302387052616926) - a2612 = convert(T, 0.5463127827750747) - a2613 = convert(T, 0.0552619079137578) - a2614 = convert(T, 0.12856135087499826) - a2615 = convert(T, 0.028572506812964065) - a2617 = convert(T, -0.02398761886357109) - a2618 = convert(T, 0.055562244589105095) - a2619 = convert(T, -0.017406756507628386) - a2620 = convert(T, -0.03815462365996979) - a2621 = convert(T, 0.011118785048989178) - - Vern9ExtraStages(c17, a1701, a1708, a1709, a1710, a1711, a1712, a1713, a1714, a1715, - c18, a1801, a1808, a1809, a1810, a1811, a1812, a1813, a1814, a1815, - a1817, c19, a1901, a1908, a1909, a1910, a1911, a1912, a1913, a1914, - a1915, a1917, a1918, c20, a2001, a2008, a2009, a2010, a2011, a2012, - a2013, a2014, a2015, a2017, a2018, a2019, c21, a2101, a2108, a2109, - a2110, a2111, a2112, a2113, a2114, a2115, a2117, a2118, a2119, a2120, - c22, a2201, a2208, a2209, a2210, a2211, a2212, a2213, a2214, a2215, - a2217, a2218, a2219, a2220, a2221, c23, a2301, a2308, a2309, a2310, - a2311, a2312, a2313, a2314, a2315, a2317, a2318, a2319, a2320, a2321, - c24, a2401, a2408, a2409, a2410, a2411, a2412, a2413, a2414, a2415, - a2417, a2418, a2419, a2420, a2421, c25, a2501, a2508, a2509, a2510, - a2511, a2512, a2513, a2514, a2515, a2517, a2518, a2519, a2520, a2521, - c26, a2601, a2608, a2609, a2610, a2611, a2612, a2613, a2614, a2615, - a2617, a2618, a2619, a2620, a2621) -end - -@fold function Vern9ExtraStages(::Type{T}, ::Type{T2}) where {T, T2} - # FIVE ADDITIONAL STAGES FOR INTERPOLANT OF ORDER 8 - c17 = convert(T2, 1) - a1701 = convert(T, big" .1461197685842315252051541915018784713459e-1") - a1708 = convert(T, big"-.3915211862331339089410228267288242030810") - a1709 = convert(T, big" .2310932500289506415909675644868993669908") - a1710 = convert(T, big" .1274766769992852382560589467488989175618") - a1711 = convert(T, big" .2246434176204157731566981937082069688984") - a1712 = convert(T, big" .5684352689748512932705226972873692126743") - a1713 = convert(T, big" .5825871557215827200814768021863420902155e-1") - a1714 = convert(T, big" .1364317403482215641609022744494239843327") - a1715 = convert(T, big" .3057013983082797397721005067920369646664e-1") - c18 = convert(T2, big" .7404185470631561083004100761798676215811") - a1801 = convert(T, big" .1549973668189559302279946863304789372788e-1") - a1808 = convert(T, big" .3355153219059635054403439303177105512242") - a1809 = convert(T, big" .2003613944191860651552622660712101217322") - a1810 = convert(T, big" .1252060659283549312946162355194540994211") - a1811 = convert(T, big" .2298676393184206750544046308957155868736") - a1812 = convert(T, big"-.2020250653476181447824906889122391003637") - a1813 = convert(T, big" .5917103230665456601422111997583025339897e-1") - a1814 = convert(T, big"-.2651834783047638681693835956996437528251e-1") - a1815 = convert(T, big"-.2384094602130971415278110567256446033405e-1") - a1817 = convert(T, big" .2718171570208501807097257892166705118335e-1") - c19 = convert(T2, 888 // 1000) - a1901 = convert(T, big" .1302453943114338366054520296881099431474e-1") - a1908 = convert(T, big"-.7452850902413112085299330666038981625179") - a1909 = convert(T, big" .2643867896429300961465132150322749722129") - a1910 = convert(T, big" .1313961758372753932588328082078842388890") - a1911 = convert(T, big" .2167253815122927263092467187957410643315") - a1912 = convert(T, big" .8734117564076052559016338094938888451419") - a1913 = convert(T, big" .1185905643935776688228545787724340848142e-1") - a1914 = convert(T, big" .5876002941689550612992712203494447529933e-1") - a1915 = convert(T, big" .3266518630202087866399279690939423159022e-2") - a1917 = convert(T, big"-.8959308648417929824525368306101792182274e-2") - a1918 = convert(T, big" .6941415157202692219907482080827253287034e-1") - c20 = convert(T2, 696 // 1000) - a2001 = convert(T, big" .1397089996925942721283716334050740168797e-1") - a2008 = convert(T, big"-.4665765335957674596054673402956853940520") - a2009 = convert(T, big" .2416372787216257077935214889875485248580") - a2010 = convert(T, big" .1290363341345674735721677437066933999929") - a2011 = convert(T, big" .2216700671735105311080225734522323922813") - a2012 = convert(T, big" .6257275123364644931771253383573999863003") - a2013 = convert(T, big" .4355312415679284117869124964829805160429e-1") - a2014 = convert(T, big" .1011962491667290833450024852274278874501") - a2015 = convert(T, big" .1808582254679721049279369742685497400353e-1") - a2017 = convert(T, big"-.2079875587689169691156509689282083267654e-1") - a2018 = convert(T, big"-.9022232517086218976198252891464664868640e-1") - a2019 = convert(T, big"-.1212796735622254216011467740438097427634") - c21 = convert(T2, 487 // 1000) - a2101 = convert(T, big" .1604638888318112738641232352800290501904e-1") - a2108 = convert(T, big" .9517712399458336651642257453589397190702e-1") - a2109 = convert(T, big" .1359187264655317806136927180199100622471") - a2110 = convert(T, big" .1237765280959854006935081364365637515893") - a2111 = convert(T, big" .2335656264102966047058755123098072346246") - a2112 = convert(T, big"-.9051508172625873314662090873741762206189e-1") - a2113 = convert(T, big"-.2537574270006131028513276914038326155331e-1") - a2114 = convert(T, big"-.1359631696887162048002744757083947500478") - a2115 = convert(T, big"-.4679214284145113075088049469061349990847e-1") - a2117 = convert(T, big" .5177958859391748239949773879090325427473e-1") - a2118 = convert(T, big" .9672595677476773313884172931875718705561e-1") - a2119 = convert(T, big" .1477312690340742769720989417101989769314") - a2120 = convert(T, big"-.1150750712958503934434410263732282100773") - - # FIVE ADDITIONAL STAGES FOR INTERPOLANT OF ORDER 9 - c22 = convert(T2, 1 // 40) - a2201 = convert(T, big" .1802918623893620731908165792176564180038e-1") - a2208 = convert(T, big" .6983601042028873702545973390560096201728e-1") - a2209 = convert(T, big"-.2541247660791663512384395986842781657182e-1") - a2210 = convert(T, big" .8487827035463274491721441398893680307535e-2") - a2211 = convert(T, big"-.2427525516089801645451101966852425715128e-2") - a2212 = convert(T, big"-.1047839752893819879012607694745789515746") - a2213 = convert(T, big"-.1473147795248041942353840372690095884761e-1") - a2214 = convert(T, big"-.3916338390816177165706892282751065537530e-1") - a2215 = convert(T, big"-.1005657343293959419073236542225421561652e-1") - a2217 = convert(T, big" .1102510392204834322538452331445716455061e-1") - a2218 = convert(T, big" .5092830749095398308703438556315975226108e-2") - a2219 = convert(T, big" .4759715599420644505591133410826632557391e-1") - a2220 = convert(T, big" .3386307003288382751110965442296681690349e-1") - a2221 = convert(T, big" .2764422831404797700452373965825845732168e-1") - c23 = convert(T2, 15 // 100) - a2301 = convert(T, big" .1677431640522778042988664067637191163626e-1") - a2308 = convert(T, big" .6220437408820475326702539861577894278533") - a2309 = convert(T, big"-.2060859809768841878234097076241307428139") - a2310 = convert(T, big" .1156394989766058889629372195583391792474") - a2311 = convert(T, big" .2664101793378358946544219293685167025971e-1") - a2312 = convert(T, big"-.9376810793418770527505892794460093668860") - a2313 = convert(T, big"-.1367806466702160302637074581619101741312") - a2314 = convert(T, big"-.3678480995268296672182605288991379118419") - a2315 = convert(T, big"-.9547871314402478902820445838193201497337e-1") - a2317 = convert(T, big" .1013492018422369748729008873270013785313") - a2318 = convert(T, big"-.8911323084568593396468400926074881389560e-1") - a2319 = convert(T, big" .4664140988974760478895528270623735057521") - a2320 = convert(T, big" .4502736292354579812232681662308722738519") - a2321 = convert(T, big" .1838522463326818655346135218242696774099") - c24 = convert(T2, 32 // 100) - a2401 = convert(T, big" .1071149731491444187554380927165768658192e-1") - a2408 = convert(T, big"-.7094336118221108191937165464264324417735e-1") - a2409 = convert(T, big" .1002164900340091596740582334112699697590") - a2410 = convert(T, big" .1383453980468025108839271214703390659581") - a2411 = convert(T, big" .1796330633578163411338104055485109917477") - a2412 = convert(T, big" .9048246545576180974879274948815422276563e-1") - a2413 = convert(T, big"-.5460662294523338383345981122023862069115e-2") - a2414 = convert(T, big"-.3000457905119619782973021046143166498567e-1") - a2415 = convert(T, big"-.1145192026962799093665613252151017277867e-1") - a2417 = convert(T, big" .1003394686109385076849515422360600302176e-1") - a2418 = convert(T, big"-.9506485282809046129031027932806241113157e-1") - a2419 = convert(T, big" .4853358804093591445756711642658478691640e-1") - a2420 = convert(T, big" .8013325919783924638483373011297347396327e-1") - a2421 = convert(T, big"-.1251643326835242045676140618774248455713") - c25 = convert(T2, 78 // 100) - a2501 = convert(T, big" .1410172088869221367153586187761994182069e-1") - a2508 = convert(T, big"-.3713379753704491105936205420001801316029") - a2509 = convert(T, big" .2231265548117180273161442520179150684520") - a2510 = convert(T, big" .1287005345918120122888629169443916280865") - a2511 = convert(T, big" .2224600659675494761192249831098918110654") - a2512 = convert(T, big" .5382853042550701952740528638168708946100") - a2513 = convert(T, big" .5417202616988763101781128062036252796548e-1") - a2514 = convert(T, big" .1256968791308743925752109039299467082975") - a2515 = convert(T, big" .2784492789002054061504430663197543089132e-1") - a2517 = convert(T, big"-.3077409246205059733390460511525401688205e-1") - a2518 = convert(T, big" .8569805293689777608077303071761466118035e-2") - a2519 = convert(T, big"-.1535174690587044615794997685221990516897") - a2520 = convert(T, big"-.2179957030548196497189489878038029238243e-1") - a2521 = convert(T, big" .1447128819737186799295514239727801525027e-1") - c26 = convert(T2, 96 // 100) - a2601 = convert(T, big" .1424600411735646609296566581447532773183e-1") - a2608 = convert(T, big"-.3767107393295407091303982522049390741260") - a2609 = convert(T, big" .2252399780730421480874737297000189000070") - a2610 = convert(T, big" .1283603076292529988314451246143633426068") - a2611 = convert(T, big" .2230238705261692544876826347415151339678") - a2612 = convert(T, big" .5463127827750747224899202176094949607118") - a2613 = convert(T, big" .5526190791375779994553849469706124289752e-1") - a2614 = convert(T, big" .1285613508749982456581494397108686240388") - a2615 = convert(T, big" .2857250681296406482698934635829147899039e-1") - a2617 = convert(T, big"-.2398761886357108720930416967644499057175e-1") - a2618 = convert(T, big" .5556224458910509454379297181908734648749e-1") - a2619 = convert(T, big"-.1740675650762838674257930398070760254668e-1") - a2620 = convert(T, big"-.3815462365996979065575121886854199471011e-1") - a2621 = convert(T, big" .1111878504898917877407531966545730451506e-1") - - Vern9ExtraStages(c17, a1701, a1708, a1709, a1710, a1711, a1712, a1713, a1714, a1715, - c18, a1801, a1808, a1809, a1810, a1811, a1812, a1813, a1814, a1815, - a1817, c19, a1901, a1908, a1909, a1910, a1911, a1912, a1913, a1914, - a1915, a1917, a1918, c20, a2001, a2008, a2009, a2010, a2011, a2012, - a2013, a2014, a2015, a2017, a2018, a2019, c21, a2101, a2108, a2109, - a2110, a2111, a2112, a2113, a2114, a2115, a2117, a2118, a2119, a2120, - c22, a2201, a2208, a2209, a2210, a2211, a2212, a2213, a2214, a2215, - a2217, a2218, a2219, a2220, a2221, c23, a2301, a2308, a2309, a2310, - a2311, a2312, a2313, a2314, a2315, a2317, a2318, a2319, a2320, a2321, - c24, a2401, a2408, a2409, a2410, a2411, a2412, a2413, a2414, a2415, - a2417, a2418, a2419, a2420, a2421, c25, a2501, a2508, a2509, a2510, - a2511, a2512, a2513, a2514, a2515, a2517, a2518, a2519, a2520, a2521, - c26, a2601, a2608, a2609, a2610, a2611, a2612, a2613, a2614, a2615, - a2617, a2618, a2619, a2620, a2621) -end - -struct Vern9InterpolationCoefficients{T} - r011::T - r012::T - r013::T - r014::T - r015::T - r016::T - r017::T - r018::T - r019::T - r082::T - r083::T - r084::T - r085::T - r086::T - r087::T - r088::T - r089::T - r092::T - r093::T - r094::T - r095::T - r096::T - r097::T - r098::T - r099::T - r102::T - r103::T - r104::T - r105::T - r106::T - r107::T - r108::T - r109::T - r112::T - r113::T - r114::T - r115::T - r116::T - r117::T - r118::T - r119::T - r122::T - r123::T - r124::T - r125::T - r126::T - r127::T - r128::T - r129::T - r132::T - r133::T - r134::T - r135::T - r136::T - r137::T - r138::T - r139::T - r142::T - r143::T - r144::T - r145::T - r146::T - r147::T - r148::T - r149::T - r152::T - r153::T - r154::T - r155::T - r156::T - r157::T - r158::T - r159::T - r172::T - r173::T - r174::T - r175::T - r176::T - r177::T - r178::T - r179::T - r182::T - r183::T - r184::T - r185::T - r186::T - r187::T - r188::T - r189::T - r192::T - r193::T - r194::T - r195::T - r196::T - r197::T - r198::T - r199::T - r202::T - r203::T - r204::T - r205::T - r206::T - r207::T - r208::T - r209::T - r212::T - r213::T - r214::T - r215::T - r216::T - r217::T - r218::T - r219::T - r222::T - r223::T - r224::T - r225::T - r226::T - r227::T - r228::T - r229::T - r232::T - r233::T - r234::T - r235::T - r236::T - r237::T - r238::T - r239::T - r242::T - r243::T - r244::T - r245::T - r246::T - r247::T - r248::T - r249::T - r252::T - r253::T - r254::T - r255::T - r256::T - r257::T - r258::T - r259::T - r262::T - r263::T - r264::T - r265::T - r266::T - r267::T - r268::T - r269::T -end - -@fold function Vern9InterpolationCoefficients(::Type{T}) where {T <: CompiledFloats} - r011 = convert(T, 1) - r012 = convert(T, -28.330488700617398) - r013 = convert(T, 257.6535452078578) - r014 = convert(T, -1152.1544557434572) - r015 = convert(T, 2909.390878345409) - r016 = convert(T, -4355.005172868188) - r017 = convert(T, 3834.083497036262) - r018 = convert(T, -1835.419052683407) - r019 = convert(T, 368.7958613829998) - r082 = convert(T, 2.649656243770091) - r083 = convert(T, -96.30312807816006) - r084 = convert(T, 869.3095462492796) - r085 = convert(T, -3395.688567551074) - r086 = convert(T, 6796.933987158715) - r087 = convert(T, -7340.848417712072) - r088 = convert(T, 4082.8488969923656) - r089 = convert(T, -919.2934944890586) - r092 = convert(T, -1.5639451819287329) - r093 = convert(T, 56.8423973927286) - r094 = convert(T, -513.1052300304285) - r095 = convert(T, 2004.2867021103232) - r096 = convert(T, -4011.8533059139295) - r097 = convert(T, 4332.895839278586) - r098 = convert(T, -2409.8793479371448) - r099 = convert(T, 542.6079835318221) - r102 = convert(T, -0.8627103334967224) - r103 = convert(T, 31.355653751851733) - r104 = convert(T, -283.0413682227354) - r105 = convert(T, 1105.613463426007) - r106 = convert(T, -2213.0362006784526) - r107 = convert(T, 2390.1310977541207) - r108 = convert(T, -1329.3482661468738) - r109 = convert(T, 299.31580712657853) - r112 = convert(T, -1.5202953379012147) - r113 = convert(T, 55.25592121120227) - r114 = convert(T, -498.7844190970741) - r115 = convert(T, 1948.346888525776) - r116 = convert(T, -3899.8821364075516) - r117 = convert(T, 4211.964345158858) - r118 = convert(T, -2342.619408856117) - r119 = convert(T, 527.4637482204279) - r122 = convert(T, -3.8469388441255234) - r123 = convert(T, 139.81898409868404) - r124 = convert(T, -1262.1186876216004) - r125 = convert(T, 4930.075848057311) - r126 = convert(T, -9868.21948606954) - r127 = convert(T, 10657.908924348867) - r128 = convert(T, -5927.738759872814) - r129 = convert(T, 1334.688551172191) - r132 = convert(T, -0.39427130612001415) - r133 = convert(T, 14.329994760676497) - r134 = convert(T, -129.35406659945582) - r135 = convert(T, 505.28160770025175) - r136 = convert(T, -1011.3900801394333) - r137 = convert(T, 1092.3250517818917) - r138 = convert(T, -607.531701930281) - r139 = convert(T, 136.79172444804232) - r142 = convert(T, -0.9233145622082102) - r143 = convert(T, 33.55834582309799) - r144 = convert(T, -302.9246397549736) - r145 = convert(T, 1183.2813069678675) - r146 = convert(T, -2368.4989867901113) - r147 = convert(T, 2558.034559755808) - r148 = convert(T, -1422.7331755778803) - r149 = convert(T, 320.3423358787482) - r152 = convert(T, -0.20688628029300538) - r153 = convert(T, 7.519388975651663) - r154 = convert(T, -67.87605708082904) - r155 = convert(T, 265.136799698415) - r156 = convert(T, -530.7074807559026) - r157 = convert(T, 573.176549564149) - r158 = convert(T, -318.7905688834869) - r159 = convert(T, 71.77882490212657) - r172 = convert(T, -0.44724419067440996) - r173 = convert(T, 16.44684676010504) - r174 = convert(T, -154.40861059212955) - r175 = convert(T, 641.8986298540249) - r176 = convert(T, -1391.9392256879823) - r177 = convert(T, 1643.890568302952) - r178 = convert(T, -1004.0652972233179) - r179 = convert(T, 248.6243327770223) - r182 = convert(T, -0.1507876007899798) - r183 = convert(T, 5.527328824824632) - r184 = convert(T, -51.33833743084619) - r185 = convert(T, 209.60220027032804) - r186 = convert(T, -442.7692650421826) - r187 = convert(T, 505.0579312588053) - r188 = convert(T, -295.63364106156195) - r189 = convert(T, 69.70457078142275) - r192 = convert(T, -0.6413652207435296) - r193 = convert(T, 23.510132486246846) - r194 = convert(T, -218.36426832469724) - r195 = convert(T, 891.5292818535365) - r196 = convert(T, -1883.290177206008) - r197 = convert(T, 2148.2309544883997) - r198 = convert(T, -1257.4584015217124) - r199 = convert(T, 296.4838434449778) - r202 = convert(T, 1.8107293134448457) - r203 = convert(T, -66.37479657295337) - r204 = convert(T, 616.4952025401107) - r205 = convert(T, -2517.0030307773227) - r206 = convert(T, 5316.984175781034) - r207 = convert(T, -6064.976140789574) - r208 = convert(T, 3550.1095388883914) - r209 = convert(T, -837.0456783831302) - r212 = convert(T, 0.05176008760353718) - r213 = convert(T, -1.8973378625803488) - r214 = convert(T, 17.622648207936294) - r215 = convert(T, -71.94907400242467) - r216 = convert(T, 151.9871383765666) - r217 = convert(T, -173.36864987478606) - r218 = convert(T, 101.4806461521468) - r219 = convert(T, -23.927131084462175) - r222 = convert(T, 31.321782556688) - r223 = convert(T, -355.6570858339106) - r224 = convert(T, 1752.6852824895159) - r225 = convert(T, -4708.092293138363) - r226 = convert(T, 7370.900776193489) - r227 = convert(T, -6716.504964764566) - r228 = convert(T, 3303.940398161186) - r229 = convert(T, -678.5938956640391) - r232 = convert(T, -2.7196073341859246) - r233 = convert(T, 86.64045615858264) - r234 = convert(T, -454.1926030939031) - r235 = convert(T, 1014.7492211005434) - r236 = convert(T, -1133.583456714544) - r237 = convert(T, 610.4671827718666) - r238 = convert(T, -109.02334994495438) - r239 = convert(T, -12.337842943405471) - r242 = convert(T, 3.1772148014329233) - r243 = convert(T, -113.8098697715143) - r244 = convert(T, 978.0935981825675) - r245 = convert(T, -3575.1293776236703) - r246 = convert(T, 6764.3615198384505) - r247 = convert(T, -6987.161043852012) - r248 = convert(T, 3751.9057627895713) - r249 = convert(T, -821.4378043648254) - r252 = convert(T, 0.877284308346553) - r253 = convert(T, -31.51810423988375) - r254 = convert(T, 273.1229151353221) - r255 = convert(T, -993.2198643101782) - r256 = convert(T, 1787.888078312664) - r257 = convert(T, -1677.394835799641) - r258 = convert(T, 781.3579535062688) - r259 = convert(T, -141.11342691289855) - r262 = convert(T, 1.7194275817987157) - r263 = convert(T, -62.89867309250732) - r264 = convert(T, 580.333550787398) - r265 = convert(T, -2348.110620506761) - r266 = convert(T, 4921.119298612906) - r267 = convert(T, -5597.912448707917) - r268 = convert(T, 3288.5977751496216) - r269 = convert(T, -782.8483098245397) - - Vern9InterpolationCoefficients(r011, r012, r013, r014, r015, r016, r017, r018, r019, - r082, r083, r084, r085, r086, r087, r088, r089, r092, - r093, r094, r095, r096, r097, r098, r099, r102, r103, - r104, r105, r106, r107, r108, r109, r112, r113, r114, - r115, r116, r117, r118, r119, r122, r123, r124, r125, - r126, r127, r128, r129, r132, r133, r134, r135, r136, - r137, r138, r139, r142, r143, r144, r145, r146, r147, - r148, r149, r152, r153, r154, r155, r156, r157, r158, - r159, r172, r173, r174, r175, r176, r177, r178, r179, - r182, r183, r184, r185, r186, r187, r188, r189, r192, - r193, r194, r195, r196, r197, r198, r199, r202, r203, - r204, r205, r206, r207, r208, r209, r212, r213, r214, - r215, r216, r217, r218, r219, r222, r223, r224, r225, - r226, r227, r228, r229, r232, r233, r234, r235, r236, - r237, r238, r239, r242, r243, r244, r245, r246, r247, - r248, r249, r252, r253, r254, r255, r256, r257, r258, - r259, r262, r263, r264, r265, r266, r267, r268, r269) -end - -function Vern9InterpolationCoefficients(T) - r011 = convert(T, 1) - r012 = convert(T, big"-28.33048870061739823290767301658881994700") - r013 = convert(T, big" 257.6535452078577977252092979905248156497") - r014 = convert(T, big"-1152.154455743457311528752964691951881858") - r015 = convert(T, big" 2909.390878345408890936564599116550031880") - r016 = convert(T, big"-4355.005172868188498048946108887283528629") - r017 = convert(T, big" 3834.083497036262189455855371796461857871") - r018 = convert(T, big"-1835.419052683407081215583427992189311730") - r019 = convert(T, big" 368.7958613829998340610814211036270246107") - r082 = convert(T, big" 2.649656243770091212685381903551424676261") - r083 = convert(T, big"-96.30312807816005963630382777245983513008") - r084 = convert(T, big" 869.3095462492795755338599928089438369769") - r085 = convert(T, big"-3395.688567551074115525201961265641584358") - r086 = convert(T, big" 6796.933987158715680563278170147156885480") - r087 = convert(T, big"-7340.848417712071304684606060804637321789") - r088 = convert(T, big" 4082.848896992365666259441580054990759905") - r089 = convert(T, big"-919.2934944890586676320942978986329899642") - r092 = convert(T, big"-1.563945181928732780647121505551017046606") - r093 = convert(T, big" 56.84239739272860000194549791973820565214") - r094 = convert(T, big"-513.1052300304284642178552372517916694426") - r095 = convert(T, big" 2004.286702110323162741493515173880535381") - r096 = convert(T, big"-4011.853305913929339500285683507736138334") - r097 = convert(T, big" 4332.895839278586189971336003691596594090") - r098 = convert(T, big"-2409.879347937144606091337260195738587773") - r099 = convert(T, big" 542.6079835318221405169412532400889768401") - r102 = convert(T, big"-.8627103334967223830653368770735555216700") - r103 = convert(T, big" 31.35565375185173442495465167501846267906") - r104 = convert(T, big"-283.0413682227354209126847112083546012674") - r105 = convert(T, big" 1105.613463426006937052739159664962261462") - r106 = convert(T, big"-2213.036200678452629288185991597653042989") - r107 = convert(T, big" 2390.131097754120588994847482867886207858") - r108 = convert(T, big"-1329.348266146873716496636094950745123424") - r109 = convert(T, big" 299.3158071265785138462868993727082901209") - r112 = convert(T, big"-1.520295337901214839055193576160469820911") - r113 = convert(T, big" 55.25592121120227100440616045452813504748") - r114 = convert(T, big"-498.7844190970740738969945498750124435385") - r115 = convert(T, big" 1948.346888525776056658403461666308795237") - r116 = convert(T, big"-3899.882136407551390287649940376076923682") - r117 = convert(T, big" 4211.964345158858030803618536151121927765") - r118 = convert(T, big"-2342.619408856117128087568672414857706561") - r119 = convert(T, big" 527.4637482204278644179968961638568925209") - r122 = convert(T, big"-3.846938844125523400516071820264700141179") - r123 = convert(T, big" 139.8189840986840520353362018994734906611") - r124 = convert(T, big"-1262.118687621600386514715930156791825893") - r125 = convert(T, big" 4930.075848057311658057235318456802793199") - r126 = convert(T, big"-9868.219486069539059368988308801366826185") - r127 = convert(T, big" 10657.90892434886730229746304583865145121") - r128 = convert(T, big"-5927.738759872814112912292792695856187255") - r129 = convert(T, big" 1334.688551172190921099749059976639173619") - r132 = convert(T, big"-.3942713061200141454309326713125653612517") - r133 = convert(T, big" 14.32999476067649707020689155180345562459") - r134 = convert(T, big"-129.3540665994558117853022852051786116929") - r135 = convert(T, big" 505.2816077002517600897861155496606850457") - r136 = convert(T, big"-1011.390080139433268878243655218566636574") - r137 = convert(T, big" 1092.325051781891697669369143688906543465") - r138 = convert(T, big"-607.5317019302810290917918493845279272648") - r139 = convert(T, big" 136.7917244480423273434147193694336909663") - r142 = convert(T, big"-.9233145622082101394378429409444333268499") - r143 = convert(T, big" 33.55834582309798808260613735851232640640") - r144 = convert(T, big"-302.9246397549735936661321348695774835448") - r145 = convert(T, big" 1183.281306967867553342903125095128753568") - r146 = convert(T, big"-2368.498986790111516106072390247333149007") - r147 = convert(T, big" 2558.034559755808027369106332027405169828") - r148 = convert(T, big"-1422.733175577880214903071122439856598476") - r149 = convert(T, big" 320.3423358787481875842587982911148385364") - r152 = convert(T, big"-.2068862802930053801253649628830330891017") - r153 = convert(T, big" 7.519388975651662772174695012120581518594") - r154 = convert(T, big"-67.87605708082904058354114755731111898667") - r155 = convert(T, big" 265.1367996984150421661637988925923843021") - r156 = convert(T, big"-530.7074807559025368587558119659212235622") - r157 = convert(T, big" 573.1765495641490277116961329189087439579") - r158 = convert(T, big"-318.7905688834868978004500126002971837241") - r159 = convert(T, big" 71.77882490212657594681492031347005327988") - r172 = convert(T, big"-.4472441906744099441704338175964823026105") - r173 = convert(T, big" 16.44684676010503791623763886833381020592") - r174 = convert(T, big"-154.4086105921295528355180056633078150675") - r175 = convert(T, big" 641.8986298540248497333509289273669726482") - r176 = convert(T, big"-1391.939225687982391028602609567895699003") - r177 = convert(T, big" 1643.890568302952013019278202625162156841") - r178 = convert(T, big"-1004.065297223317845596795060426393517046") - r179 = convert(T, big" 248.6243327770222987362193390543305737239") - r182 = convert(T, big"-.1507876007899797948720901584434839156279") - r183 = convert(T, big" 5.527328824824632235316362126620825363280") - r184 = convert(T, big"-51.33833743084618751433903968701557585387") - r185 = convert(T, big" 209.6022002703280347991393999433060881829") - r186 = convert(T, big"-442.7692650421825928714839983614217797969") - r187 = convert(T, big" 505.0579312588052893780948070449787925777") - r188 = convert(T, big"-295.6336410615619366143935619944592839974") - r189 = convert(T, big" 69.70457078142274038253812108643441743987") - r192 = convert(T, big"-.6413652207435296452288504944964177537185") - r193 = convert(T, big" 23.51013248624684600263471193689787394701") - r194 = convert(T, big"-218.3642683246972281497485359238725613162") - r195 = convert(T, big" 891.5292818535365634586829868055833114383") - r196 = convert(T, big"-1883.290177206007885518558760085145850658") - r197 = convert(T, big" 2148.230954488399755970660772306573864434") - r198 = convert(T, big"-1257.458401521712336970840850120592935471") - r199 = convert(T, big" 296.4838434449778148523985255750527153802") - r202 = convert(T, big" 1.810729313444845732964058528284532356045") - r203 = convert(T, big"-66.37479657295337371220255196726289169374") - r204 = convert(T, big" 616.4952025401106511929691356878863855003") - r205 = convert(T, big"-2517.003030777322559684753470471663859295") - r206 = convert(T, big" 5316.984175781033401491488704359579721604") - r207 = convert(T, big"-6064.976140789574108556866601189158423779") - r208 = convert(T, big" 3550.109538888391317555902194852386816092") - r209 = convert(T, big"-837.0456783831301740195014698000522807852") - r212 = convert(T, big".5176008760353717918864555990277480363987e-1") - r213 = convert(T, big"-1.897337862580348756406065418550014243949") - r214 = convert(T, big" 17.62264820793629244181715147639285955422") - r215 = convert(T, big"-71.94907400242465946110661282550878163878") - r216 = convert(T, big" 151.9871383765666045085018751235590550206") - r217 = convert(T, big"-173.3686498747860565970136435029707518663") - r218 = convert(T, big" 101.4806461521468075879782291473158292931") - r219 = convert(T, big"-23.92713108446217690295957956014097092250") - r222 = convert(T, big" 31.32178255668799909977422939838912846070") - r223 = convert(T, big"-355.6570858339106059687054319211280026146") - r224 = convert(T, big" 1752.685282489515979253875884672206842255") - r225 = convert(T, big"-4708.092293138363367969732154806019707156") - r226 = convert(T, big" 7370.900776193488713149861391844801840850") - r227 = convert(T, big"-6716.504964764565347011489385051202629762") - r228 = convert(T, big" 3303.940398161185772296756776169088470785") - r229 = convert(T, big"-678.5938956640391428503413103061359428182") - r232 = convert(T, big"-2.719607334185924760747802644504744092917") - r233 = convert(T, big" 86.64045615858264001154848875638486632034") - r234 = convert(T, big"-454.1926030939030807863651114984001402596") - r235 = convert(T, big" 1014.749221100543425314268817989377200147") - r236 = convert(T, big"-1133.583456714543865890388885909333783663") - r237 = convert(T, big" 610.4671827718666569168001429679645990946") - r238 = convert(T, big"-109.0233499449543802317396567002119357593") - r239 = convert(T, big"-12.33784294340547057337599296127606178639") - r242 = convert(T, big" 3.177214801432923432265738869490200556403") - r243 = convert(T, big"-113.8098697715142983214434051918276259885") - r244 = convert(T, big" 978.0935981825675014833003847211971070224") - r245 = convert(T, big"-3575.129377623670076451027372711378100786") - r246 = convert(T, big" 6764.361519838450570830405988615992045681") - r247 = convert(T, big"-6987.161043852012362644872233028628887679") - r248 = convert(T, big" 3751.905762789571137088934326513342858381") - r249 = convert(T, big"-821.4378043648253954175634277881875971878") - r252 = convert(T, big" .8772843083465530069477626269697233842708") - r253 = convert(T, big"-31.51810423988375104361582759389916060143") - r254 = convert(T, big" 273.1229151353221133842213845530391043248") - r255 = convert(T, big"-993.2198643101781966584366870874238565290") - r256 = convert(T, big" 1787.888078312663987193988385659681964836") - r257 = convert(T, big"-1677.394835799640950953367739332661886275") - r258 = convert(T, big" 781.3579535062687952504707744453846824540") - r259 = convert(T, big"-141.1134269128985501802080532710905715931") - r262 = convert(T, big" 1.719427581798715782378897599231938082126") - r263 = convert(T, big"-62.89867309250732184389962568482931880335") - r264 = convert(T, big" 580.3335507873980391019057196688995930872") - r265 = convert(T, big"-2348.110620506760958600472968113883922730") - r266 = convert(T, big" 4921.119298612906015908637628774963068611") - r267 = convert(T, big"-5597.912448707916639109910311016358007839") - r268 = convert(T, big" 3288.597775149621789973016480733216881572") - r269 = convert(T, big"-782.8483098245396412116558219612402319811") - - Vern9InterpolationCoefficients(r011, r012, r013, r014, r015, r016, r017, r018, r019, - r082, r083, r084, r085, r086, r087, r088, r089, r092, - r093, r094, r095, r096, r097, r098, r099, r102, r103, - r104, r105, r106, r107, r108, r109, r112, r113, r114, - r115, r116, r117, r118, r119, r122, r123, r124, r125, - r126, r127, r128, r129, r132, r133, r134, r135, r136, - r137, r138, r139, r142, r143, r144, r145, r146, r147, - r148, r149, r152, r153, r154, r155, r156, r157, r158, - r159, r172, r173, r174, r175, r176, r177, r178, r179, - r182, r183, r184, r185, r186, r187, r188, r189, r192, - r193, r194, r195, r196, r197, r198, r199, r202, r203, - r204, r205, r206, r207, r208, r209, r212, r213, r214, - r215, r216, r217, r218, r219, r222, r223, r224, r225, - r226, r227, r228, r229, r232, r233, r234, r235, r236, - r237, r238, r239, r242, r243, r244, r245, r246, r247, - r248, r249, r252, r253, r254, r255, r256, r257, r258, - r259, r262, r263, r264, r265, r266, r267, r268, r269) -end - -""" -From Verner's Website -""" -struct Vern9Tableau{T, T2} - c1::T2 - c2::T2 - c3::T2 - c4::T2 - c5::T2 - c6::T2 - c7::T2 - c8::T2 - c9::T2 - c10::T2 - c11::T2 - c12::T2 - c13::T2 - a0201::T - a0301::T - a0302::T - a0401::T - a0403::T - a0501::T - a0503::T - a0504::T - a0601::T - a0604::T - a0605::T - a0701::T - a0704::T - a0705::T - a0706::T - a0801::T - a0806::T - a0807::T - a0901::T - a0906::T - a0907::T - a0908::T - a1001::T - a1006::T - a1007::T - a1008::T - a1009::T - a1101::T - a1106::T - a1107::T - a1108::T - a1109::T - a1110::T - a1201::T - a1206::T - a1207::T - a1208::T - a1209::T - a1210::T - a1211::T - a1301::T - a1306::T - a1307::T - a1308::T - a1309::T - a1310::T - a1311::T - a1312::T - a1401::T - a1406::T - a1407::T - a1408::T - a1409::T - a1410::T - a1411::T - a1412::T - a1413::T - a1501::T - a1506::T - a1507::T - a1508::T - a1509::T - a1510::T - a1511::T - a1512::T - a1513::T - a1514::T - a1601::T - a1606::T - a1607::T - a1608::T - a1609::T - a1610::T - a1611::T - a1612::T - a1613::T - b1::T - b8::T - b9::T - b10::T - b11::T - b12::T - b13::T - b14::T - b15::T - btilde1::T - btilde8::T - btilde9::T - btilde10::T - btilde11::T - btilde12::T - btilde13::T - btilde14::T - btilde15::T - btilde16::T -end - -@fold function Vern9Tableau(::Type{T}, - ::Type{T2}) where {T <: CompiledFloats, T2 <: CompiledFloats} - c1 = convert(T2, 0.03462) - c2 = convert(T2, 0.09702435063878045) - c3 = convert(T2, 0.14553652595817068) - c4 = convert(T2, 0.561) - c5 = convert(T2, 0.22900791159048503) - c6 = convert(T2, 0.544992088409515) - c7 = convert(T2, 0.645) - c8 = convert(T2, 0.48375) - c9 = convert(T2, 0.06757) - c10 = convert(T2, 0.25) - c11 = convert(T2, 0.6590650618730999) - c12 = convert(T2, 0.8206) - c13 = convert(T2, 0.9012) - a0201 = convert(T, 0.03462) - a0301 = convert(T, -0.03893354388572875) - a0302 = convert(T, 0.13595789452450918) - a0401 = convert(T, 0.03638413148954267) - a0403 = convert(T, 0.10915239446862801) - a0501 = convert(T, 2.0257639143939694) - a0503 = convert(T, -7.638023836496291) - a0504 = convert(T, 6.173259922102322) - a0601 = convert(T, 0.05112275589406061) - a0604 = convert(T, 0.17708237945550218) - a0605 = convert(T, 0.0008027762409222536) - a0701 = convert(T, 0.13160063579752163) - a0704 = convert(T, -0.2957276252669636) - a0705 = convert(T, 0.08781378035642955) - a0706 = convert(T, 0.6213052975225274) - a0801 = convert(T, 0.07166666666666667) - a0806 = convert(T, 0.33055335789153195) - a0807 = convert(T, 0.2427799754418014) - a0901 = convert(T, 0.071806640625) - a0906 = convert(T, 0.3294380283228177) - a0907 = convert(T, 0.1165190029271823) - a0908 = convert(T, -0.034013671875) - a1001 = convert(T, 0.04836757646340646) - a1006 = convert(T, 0.03928989925676164) - a1007 = convert(T, 0.10547409458903446) - a1008 = convert(T, -0.021438652846483126) - a1009 = convert(T, -0.10412291746271944) - a1101 = convert(T, -0.026645614872014785) - a1106 = convert(T, 0.03333333333333333) - a1107 = convert(T, -0.1631072244872467) - a1108 = convert(T, 0.03396081684127761) - a1109 = convert(T, 0.1572319413814626) - a1110 = convert(T, 0.21522674780318796) - a1201 = convert(T, 0.03689009248708622) - a1206 = convert(T, -0.1465181576725543) - a1207 = convert(T, 0.2242577768172024) - a1208 = convert(T, 0.02294405717066073) - a1209 = convert(T, -0.0035850052905728597) - a1210 = convert(T, 0.08669223316444385) - a1211 = convert(T, 0.43838406519683376) - a1301 = convert(T, -0.4866012215113341) - a1306 = convert(T, -6.304602650282853) - a1307 = convert(T, -0.2812456182894729) - a1308 = convert(T, -2.679019236219849) - a1309 = convert(T, 0.5188156639241577) - a1310 = convert(T, 1.3653531876033418) - a1311 = convert(T, 5.8850910885039465) - a1312 = convert(T, 2.8028087862720628) - a1401 = convert(T, 0.4185367457753472) - a1406 = convert(T, 6.724547581906459) - a1407 = convert(T, -0.42544428016461133) - a1408 = convert(T, 3.3432791530012653) - a1409 = convert(T, 0.6170816631175374) - a1410 = convert(T, -0.9299661239399329) - a1411 = convert(T, -6.099948804751011) - a1412 = convert(T, -3.002206187889399) - a1413 = convert(T, 0.2553202529443446) - a1501 = convert(T, -0.7793740861228848) - a1506 = convert(T, -13.937342538107776) - a1507 = convert(T, 1.2520488533793563) - a1508 = convert(T, -14.691500408016868) - a1509 = convert(T, -0.494705058533141) - a1510 = convert(T, 2.2429749091462368) - a1511 = convert(T, 13.367893803828643) - a1512 = convert(T, 14.396650486650687) - a1513 = convert(T, -0.79758133317768) - a1514 = convert(T, 0.4409353709534278) - a1601 = convert(T, 2.0580513374668867) - a1606 = convert(T, 22.357937727968032) - a1607 = convert(T, 0.9094981099755646) - a1608 = convert(T, 35.89110098240264) - a1609 = convert(T, -3.442515027624454) - a1610 = convert(T, -4.865481358036369) - a1611 = convert(T, -18.909803813543427) - a1612 = convert(T, -34.26354448030452) - a1613 = convert(T, 1.2647565216956427) - b1 = convert(T, 0.014611976858423152) - b8 = convert(T, -0.3915211862331339) - b9 = convert(T, 0.23109325002895065) - b10 = convert(T, 0.12747667699928525) - b11 = convert(T, 0.2246434176204158) - b12 = convert(T, 0.5684352689748513) - b13 = convert(T, 0.058258715572158275) - b14 = convert(T, 0.13643174034822156) - b15 = convert(T, 0.030570139830827976) - # bhat1 =convert(T,0.01996996514886773) - # bhat8 =convert(T,2.19149930494933) - # bhat9 =convert(T,0.08857071848208438) - # bhat10 =convert(T,0.11405602348659656) - # bhat11 =convert(T,0.2533163805345107) - # bhat12 =convert(T,-2.056564386240941) - # bhat13 =convert(T,0.340809679901312) - # bhat16 =convert(T,0.04834231373823958) - btilde1 = convert(T, -0.005357988290444578) - btilde8 = convert(T, -2.583020491182464) - btilde9 = convert(T, 0.14252253154686625) - btilde10 = convert(T, 0.013420653512688676) - btilde11 = convert(T, -0.02867296291409493) - btilde12 = convert(T, 2.624999655215792) - btilde13 = convert(T, -0.2825509643291537) - btilde14 = convert(T, 0.13643174034822156) - btilde15 = convert(T, 0.030570139830827976) - btilde16 = convert(T, -0.04834231373823958) - - Vern9Tableau(c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, a0201, a0301, - a0302, a0401, a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, - a0704, a0705, a0706, a0801, a0806, a0807, a0901, a0906, a0907, a0908, - a1001, a1006, a1007, a1008, a1009, a1101, a1106, a1107, a1108, a1109, - a1110, a1201, a1206, a1207, a1208, a1209, a1210, a1211, a1301, a1306, - a1307, a1308, a1309, a1310, a1311, a1312, a1401, a1406, a1407, a1408, - a1409, a1410, a1411, a1412, a1413, a1501, a1506, a1507, a1508, a1509, - a1510, a1511, a1512, a1513, a1514, a1601, a1606, a1607, a1608, a1609, - a1610, a1611, a1612, a1613, b1, b8, b9, b10, b11, b12, b13, b14, b15, - btilde1, btilde8, btilde9, btilde10, btilde11, btilde12, btilde13, - btilde14, btilde15, btilde16) -end - -@fold function Vern9Tableau(::Type{T}, ::Type{T2}) where {T, T2} - c1 = convert(T2, 1731 // 50000) - c2 = convert(T2, - BigInt(7630049) // BigInt(53810000) - - BigInt(983539) // BigInt(53810000) * 6^(1 // 2)) - c3 = convert(T2, - BigInt(22890147) // BigInt(107620000) - - BigInt(2950617) // BigInt(107620000) * 6^(1 // 2)) - c4 = convert(T2, 561 // 1000) - c5 = convert(T2, BigInt(387) // BigInt(1000) - BigInt(129) // BigInt(2000) * 6^(1 // 2)) - c6 = convert(T2, BigInt(387) // BigInt(1000) + BigInt(129) // BigInt(2000) * 6^(1 // 2)) - c7 = convert(T2, 129 // 200) - c8 = convert(T2, 387 // 800) - c9 = convert(T2, 6757 // 100000) - c10 = convert(T2, 1 // 4) - c11 = convert(T2, 1427971650951258372 // 2166662646162554701) - c12 = convert(T2, 4103 // 5000) - c13 = convert(T2, 2253 // 2500) - a0201 = convert(T, 1731 // 50000) - a0301 = convert(T, - -BigInt(177968356965557) // BigInt(1002427673820000) + - BigInt(14180534491313) // BigInt(250606918455000) * 6^(1 // 2)) - a0302 = convert(T, - BigInt(64021741529527) // BigInt(200485534764000) - - BigInt(7504450763411) // BigInt(100242767382000) * 6^(1 // 2)) - a0401 = convert(T, - BigInt(22890147) // BigInt(430480000) - - BigInt(2950617) // BigInt(430480000) * 6^(1 // 2)) - a0403 = convert(T, - BigInt(68670441) // BigInt(430480000) - - BigInt(8851851) // BigInt(430480000) * 6^(1 // 2)) - a0501 = convert(T, - BigInt(592203994261020339) // BigInt(513126355505556250) + - BigInt(730386990293623641) // BigInt(2052505422022225000) * 6^(1 // 2)) - a0503 = convert(T, - -BigInt(8712153884182794903) // BigInt(2052505422022225000) - - BigInt(2843421359195851533) // BigInt(2052505422022225000) * 6^(1 // 2)) - a0504 = convert(T, - BigInt(1873698362223295443) // BigInt(513126355505556250) + - BigInt(528258592225556973) // BigInt(513126355505556250) * 6^(1 // 2)) - a0601 = convert(T, - BigInt(11380823631) // BigInt(157617812000) - - BigInt(339148869) // BigInt(39404453000) * 6^(1 // 2)) - a0604 = convert(T, - BigInt(16193232887091831) // BigInt(58864341808507450) - - BigInt(2355345717024309) // BigInt(58864341808507450) * 6^(1 // 2)) - a0605 = convert(T, - BigInt(165912282616977) // BigInt(4179075230308000) - - BigInt(33181894472511) // BigInt(2089537615154000) * 6^(1 // 2)) - a0701 = convert(T, - BigInt(26523528363) // BigInt(231790900000) + - BigInt(863255358) // BigInt(123138915625) * 6^(1 // 2)) - a0704 = convert(T, - -BigInt(38208748178016484817787) // BigInt(842517966262441068418750) - - BigInt(86118788556282369822807) // BigInt(842517966262441068418750) * - 6^(1 // 2)) - a0705 = convert(T, - BigInt(92362336407446913) // BigInt(290322814529044000) - - BigInt(232039320950012997) // BigInt(2467743923496874000) * 6^(1 // 2)) - a0706 = convert(T, - -BigInt(362925891) // BigInt(1690350537500) + - BigInt(857800423623) // BigInt(3380701075000) * 6^(1 // 2)) - a0801 = convert(T, 43 // 600) - a0806 = convert(T, BigInt(43) // BigInt(150) + BigInt(43) // BigInt(2400) * 6^(1 // 2)) - a0807 = convert(T, BigInt(43) // BigInt(150) - BigInt(43) // BigInt(2400) * 6^(1 // 2)) - a0901 = convert(T, 7353 // 102400) - a0906 = convert(T, - BigInt(22833) // BigInt(102400) + - BigInt(8901) // BigInt(204800) * 6^(1 // 2)) - a0907 = convert(T, - BigInt(22833) // BigInt(102400) - - BigInt(8901) // BigInt(204800) * 6^(1 // 2)) - a0908 = convert(T, -3483 // 102400) - a1001 = convert(T, 376708742472214988700853 // 7788456028125000000000000) - a1006 = convert(T, - BigInt(187914666753956840195279) // BigInt(2596152009375000000000000) - - BigInt(210440846556290693268911) // BigInt(15576912056250000000000000) * - 6^(1 // 2)) - a1007 = convert(T, - BigInt(187914666753956840195279) // BigInt(2596152009375000000000000) + - BigInt(210440846556290693268911) // BigInt(15576912056250000000000000) * - 6^(1 // 2)) - a1008 = convert(T, -18552667221896744226647 // 865384003125000000000000) - a1009 = convert(T, -3167799860072183913409 // 30423656359863281250000) - a1101 = convert(T, - -BigInt(426968570497) // BigInt(54394415898750) - - BigInt(92754382349) // BigInt(12087647977500) * 6^(1 // 2)) - a1106 = convert(T, 1 // 30) - a1107 = convert(T, - -BigInt(2865012129681958) // BigInt(114898584332330625) - - BigInt(12962517687655099) // BigInt(229797168664661250) * 6^(1 // 2)) - a1108 = convert(T, - BigInt(4389715333607) // BigInt(309890657317500) + - BigInt(92754382349) // BigInt(11477431752500) * 6^(1 // 2)) - a1109 = convert(T, - BigInt(4990058173976) // BigInt(83757096376875) + - BigInt(371017529396) // BigInt(9306344041875) * 6^(1 // 2)) - a1110 = convert(T, - BigInt(1099523524595993125000) // BigInt(6257667909869756018891) + - BigInt(100957348037989687500) // BigInt(6257667909869756018891) * - 6^(1 // 2)) - a1201 = convert(T, - BigInt(18382031104798403869938539009154656587521498573595595063164077882800315372787284683238439478955141517997198007108623761931447163756) // - BigInt(13974256944499724344918960993890933614161025322970450047932688998095008528620821239604734608111291769444706187497807869179550841329375) + - BigInt(407885778185158609210793892517582595305896470756467612636796259611491408260896413446883450891351622914818800693274034252252905536) // - BigInt(28084926388601226073624096169175002956970191576455110633226765141161372294098693275117181239385312198137508846535933127837167926875) * - 6^(1 // 2)) - a1206 = convert(T, - -BigInt(333881311789849411971573472868128281438202210721723123251742145367734582887577395547778228760174068758086134389952015563403904) // - BigInt(2270872004608103037127689848604039623086639035441372934050180593816493796129405349914148981460714202232988727738778494557727635) + - BigInt(4819272892477768171373308666720689121421091953625792970278044071549950640195056472955523769829034800621890424847009130000000) // - BigInt(23162894447002650978702436455761204155483718161502003927311842056928236720519934569124319610899284862776485022935540644488821877) * - 6^(1 // 2)) - a1207 = convert(T, - -BigInt(136666607496463622270135608863772076443625468798139480390426740993024803946981763209348364716108721312822619845726151693667598437699964416) // - BigInt(3719286465342404274788585327254180828195282427342057650194855634917821113563432870681372043512520401887141437067106105683944802332422369375) + - BigInt(169845085565361336805556009296394374527636952379388961026066628725155521832762086875632366996477567928657535912191396155566765457826139904) // - BigInt(1593979913718173260623679425966077497797978183146596135797795272107637620098614087434873732933937315094489187314474045293119200999609586875) * - 6^(1 // 2)) - a1208 = convert(T, - BigInt(5610987899273278525411960528081442902198567594809764379756195673673265700551076812883925583370253765702553235594764427173637673766208) // - BigInt(92881598198144033018278804740626334135423356791639598109358867770361609232846012626732332450844264293840456574956036349633197336361875) - - BigInt(5587476413495323413846491678323049250765705078855720721052003556321800113162964567765526724539063327600257543743479921263738432) // - BigInt(365303089362201664516413596925286161494473575337115296250511752859728108868696929614024803255122785403232359817965288739565550625) * - 6^(1 // 2)) - a1209 = convert(T, - BigInt(54598539818083615233566148602203244896696958910734339754065270985433507945162707737759469214674480807272210648148477499238783276259328) // - BigInt(301247919092298852634886875129959310794662932014184499827145075851637298698312074030567479239502011693447423026416040794479934024058125) - - BigInt(6526172450962537747372702280281321524894343532103481802188740153783862532174342615150135214261625966637100811092384548036046488576) // - BigInt(86490932843037281836028387921320502668579653176624892284566487468170341285762869374265713247057712228954184044334206372230816544375) * - 6^(1 // 2)) - a1210 = convert(T, - BigInt(9391667348404584010955422210328707125006120661611061908889750805619418785820948002455890360939221912190524731087070645107486913457760000000) // - BigInt(58157266968773020612419028503738708303515285854970725662326801531295387265784849843172223645193277229358434488742203091272981931739152584783) - - BigInt(8108825145085088104344721048166325225173729495689364696426720161112012414227752328969720658987315654179873760357725235734000399440000000) // - BigInt(265558296661064021061274102756797754810572081529546692522040189640618206693081506133206500662983001047298787619827411375675716583283801757) * - 6^(1 // 2)) - a1211 = convert(T, - BigInt(123461712659887915177271339396606860810479028777869348014870450606260914019560285661288212498128400476015695960341952) // - BigInt(281629106670320674754245209358840703704235147307838896741075511220826056829047205614324978253226176275078922716132461)) - a1301 = convert(T, - -BigInt(56042772675322042139227629978042586330633622706053363946766144416933631) // - BigInt(58808540772323190525590122613223430507352118534557342666015625000000000) + - BigInt(281404579734699232141455524604487724159024972527) // - BigInt(1478009944832743180452316204077188415527343750000) * 6^(1 // 2)) - a1306 = convert(T, - -BigInt(1027163900229750356561238237947225332675621517) // - BigInt(179261894431132664078747698292867431640625000) - - BigInt(2745292391641202525373103979336813513372321) // - BigInt(11702216468464340311060649744558385937500000) * 6^(1 // 2)) - a1307 = convert(T, - -BigInt(157229999853748227305165773364426925282378072238332930121) // - BigInt(36699907367985458573273204094330716033963413238525390625) + - BigInt(5757606442802795095318986067317837904184278650664590252101) // - BigInt(3523191107326604023034227593055748739260487670898437500000) * - 6^(1 // 2)) - a1308 = convert(T, - -BigInt(9311448168593934146015965019904013602133802943325818346622781285907057) // - BigInt(4255970849010124217193135449668739985401313363005576159362792968750000) - - BigInt(844213739204097696424366573813463172477074917581) // - BigInt(4210188359946578336976868164966163024902343750000) * 6^(1 // 2)) - a1309 = convert(T, - BigInt(885774233856672590222951867695327816457340130391639153070521335485617578) // - BigInt(301098541380295011015469248465465290112505656143757799934635162353515625) - - BigInt(281404579734699232141455524604487724159024972527) // - BigInt(284481916364737983221402322504830303192138671875) * 6^(1 // 2)) - a1310 = convert(T, - BigInt(315479116729780153956412124052199685097744239386639023787359107959254802182) // - BigInt(134481850506505848012587842215515574380212543200894932329128471154748828125) - - BigInt(2940396453647872276646068776592292229737651937934623) // - BigInt(7345465058781983710795837429530784777245286520703125) * - 6^(1 // 2)) - a1311 = convert(T, - BigInt(2250996163406545378616532039018846586217631599453822541) // - BigInt(382491303797095993563304148204275636433504028320312500)) - a1312 = convert(T, - BigInt(2689340957307691853294902388334454003959378146957529866233529251986359392336044151708949720958809747970514366293458424272174024493) // - BigInt(959516386019578808500569114780871708466894752280482835105408027815194895319055443842782227102120493960805649575561796875000000000)) - a1401 = convert(T, - BigInt(47342003848024391498707976847688893013083074441159779465719863625051668939887702630319) // - BigInt(44802546873926050730401222636656855760802419993852060264615320801485392456054687500000) - - BigInt(866369530987077991125562402829092187100493209601) // - BigInt(3325522375873672156017711459173673934936523437500) * 6^(1 // 2)) - a1406 = convert(T, - BigInt(871779321807802447463310035318238762878527157) // - BigInt(134446420823349498059060773719650573730468750) + - BigInt(107641268480999396081848975271849857994818) // - BigInt(1097082793918531904161935913552348681640625) * 6^(1 // 2)) - a1407 = convert(T, - BigInt(496103786351862292800034805114190705484800743513354117014) // - BigInt(110099722103956375719819612282992148101890239715576171875) - - BigInt(1329938412606197485769312599390307351191540891599374831099) // - BigInt(660598332623738254318917673697952888611341438293457031250) * - 6^(1 // 2)) - a1408 = convert(T, - BigInt(40774077277747636354598451708891165494123131383777235229538611989392175193285994266471) // - BigInt(15264290546248162101058985941588079518256741255377031736357946125713524703979492187500) + - BigInt(123767075855296855875080343261298883871499029943) // - BigInt(451091609994276250390378731960660324096679687500) * 6^(1 // 2)) - a1409 = convert(T, - -BigInt(10522038608500556459828649038302068473735749030796372764961618751973793724796364606986664) // - BigInt(3899417425005422254034574000397382862235892829653375835197340918271556055507659912109375) + - BigInt(3465478123948311964502249611316368748401972838404) // - BigInt(2560337247282641848992620902543472728729248046875) * 6^(1 // 2)) - a1410 = convert(T, - -BigInt(27843764471262693189365201135620670490328475323282820219474851621693895769527094334687108984) // - BigInt(12257041066285164222002594300605593929434139193022166317802121412999357024704596261133984375) + - BigInt(574774300271998598683873114105472016699241495055292) // - BigInt(1049352151254569101542262489932969253892183788671875) * - 6^(1 // 2)) - a1411 = convert(T, - -BigInt(34241134351848245624232809437676889009431930503529853032576417589898516) // - BigInt(5613347824358651981100985009024281007603230062439942682713165283203125)) - a1412 = convert(T, - -BigInt(3432044375893932378102368568052286501033850910516999202088532705211633432793920547702800961532438008401883737341854688972639605334600163938610268855705742764072609) // - BigInt(1143174106341682260971647690410567292143926198650927778920823267461111371275907599801714870165813394147519068210931766844494994616580258435518181434575195312500000)) - a1413 = convert(T, - BigInt(4746930876023919335079451612726717649218264199984) // - BigInt(18592065538407049755200144388134089346432755594877)) - a1501 = convert(T, - -BigInt(25188329249258825443748527038142409879923012133738985313265430932280250855708601) // - BigInt(11370641325574469312056961874077298550827642308774647316995717036347558064286250) + - BigInt(1234273058981860170179592598535508631343082535549881956) // - BigInt(2105633771469628744518390642968552144069898845895808125) * - 6^(1 // 2)) - a1506 = convert(T, - -BigInt(54821142119685055562477216205428613949905430396088) // - BigInt(3959439837009461289085587746748097947393101278095) - - BigInt(1511276753825982856072891469504471256664975925000) // - BigInt(40386286337496505148672995016830599063409633036569) * 6^(1 // 2)) - a1507 = convert(T, - -BigInt(60922424274061599918603524049390657305431262635197540405697952) // - BigInt(6484861747489032169774584624759953148531564032417461909516875) + - BigInt(84558575751635978733109961893984238786929550462615375699341616) // - BigInt(19454585242467096509323753874279859445594692097252385728550625) * - 6^(1 // 2)) - a1508 = convert(T, - -BigInt(116118147575045169733222875835719955334334798191459879782123534889390467935109772) // - BigInt(8810626901954835245672275131295870892503713957512170681453300814988417642493125) - - BigInt(176324722711694310025656085505072661620440362221411708) // - BigInt(285619406719829107485771207042040133465420149964555625) * - 6^(1 // 2)) - a1509 = convert(T, - BigInt(17769448722513898342276837490665097286927607247073335618566987143467294900183033216) // - BigInt(2551217008137889615056342146084561867122485163596619283719957742418751029506356875) - - BigInt(19748368943709762722873481576568138101489320568798111296) // - BigInt(6484554262322259071286545935997129135111813687175650625) * - 6^(1 // 2)) - a1510 = convert(T, - BigInt(97659266139124074818193264801929547781659926543786381510190954184218570746215033823993530000000) // - BigInt(18560076654469706205963482908787056850812308205603127326855360961727608242796551101182080033599) - - BigInt(85297084611782122474911131363078900058888025224607913745000000) // - BigInt(69210659450201393843166746722954036326338355649915383851733911) * - 6^(1 // 2)) - a1511 = convert(T, - BigInt(473389749049752963256114649231353822492912259509649519870869750525) // - BigInt(35412440882360341799798842428365422941216508121322622479260846291)) - a1512 = convert(T, - BigInt(33351439245158438248073494056784144097872912773415904536400728387690334563968394114702414108807505158106385116468732853458202899966748488718531545706559142895903144848764637) // - BigInt(2316611025327287427714802011322252886090793904989900621592365627649097578102163572190502232425490606773312310665593424982745744299371285598588298606088543376742054644818966)) - a1513 = convert(T, - -BigInt(38714992656958413389743252726016897599283911682945255636643554687500000) // - BigInt(48540494926971587499294589382572212036169135429877901702347521300421767)) - a1514 = convert(T, - BigInt(14800250200940323717124616175641261235119295795768814717803955078125) // - BigInt(33565577125141877760287380588632421223433194078156948298488471160489)) - a1601 = convert(T, - BigInt(2305785696086397561080858186939897173645641331085041313944389849986584101287) // - BigInt(617508244345282265819087370078275122671246164669900462139876057008239440000) - - BigInt(85404623305589712632165905233974183137607899140719) // - BigInt(124822287169084833758410283469525117460541643292500) * - 6^(1 // 2)) - a1606 = convert(T, - BigInt(102903996961580448264190625267026062654799259083) // - BigInt(5046398084890004857481629999673320438819484730) + - BigInt(41320925487304219313300272052128374567081128125) // - BigInt(51473260465878049546312625996667868475958744246) * 6^(1 // 2)) - a1607 = convert(T, - BigInt(62798443349876457506718920843975661399949564598018488144466) // - BigInt(4132553498782573324058263582553715220777051359780141380625) - - BigInt(72308807081932961554425711089716771013571419950657300729103) // - BigInt(12397660496347719972174790747661145662331154079340424141875) * - 6^(1 // 2)) - a1608 = convert(T, - BigInt(1794909142126482564390848522924225553221469019751470544959297614654661293377) // - BigInt(52596481193994264435601626109752988674679691644275456716633975785978672500) + - BigInt(12200660472227101804595129319139169019658271305817) // - BigInt(16931561456559959115207709344056578263397760602500) * 6^(1 // 2)) - a1609 = convert(T, - -BigInt(2775244732780109667342845612394739319115662636371477300455747022423270475907256) // - BigInt(228417153675584029725018045422706955827996328208181619436454383447149337555625) + - BigInt(341618493222358850528663620935896732550431596562876) // - BigInt(96101338378773357469245211954911505447551097205625) * 6^(1 // 2)) - a1610 = convert(T, - -BigInt(27680554659769016623530979176727448251292244310769996015342190819068970556083063125000) // - BigInt(3299557777429648960576561382256606844677258438797072955341581354051375036522231471437) + - BigInt(4426552127579895373479670356100179759944766558141730312500) // - BigInt(3077113738667320707748877199804636746494977000658967987677) * - 6^(1 // 2)) - a1611 = convert(T, - -BigInt(292603171929706291053929402159930330736639136252680853622275) // - BigInt(15473622826279161150227076887290262443510550964275858143964)) - a1612 = convert(T, - -BigInt(9815717129569106988569302193220999343824932084582093647596086931754666098662594153095258988516305165794739744873539829069617203523509136682216933020431) // - BigInt(286476991170934153076146641094402171801937250068596542931028678669501762253287693294397689327797388113854588113430063939405071979092547998950955940992)) - a1613 = convert(T, - BigInt(2729491144709837905799148766650782532906050298971406518524169921875) // - BigInt(2158115888622139473142775812109447802920656149243127309253686951469)) - b1 = convert(T, - 8198160366203173411119943711500331 // 561057579384085860167277847128765528) - b8 = convert(T, - -BigInt(455655493073428838813281446213740000000) // - BigInt(1163808011150910561240464225837312497869)) - b9 = convert(T, - BigInt(19965163648706008081135075746915614720000000) // - BigInt(86394404190537086868394686205782432516544599)) - b10 = convert(T, - BigInt(89231107919981418705566970804343750000000000000000000000) // - BigInt(699979870988335674445594679856445060562597693583175985391)) - b11 = convert(T, - 47104273954945906713184913871143492 // - 209684639122339601934631113492763467) - b12 = convert(T, - BigInt(20845004421404500464010584740796750650832176798370383084226351294730731196673647311062330972740734737279503119387627146381678677156136042524139311907482802844083) // - BigInt(36670849891136373020238225328265100250605144718501926305140966586758054847604681466336103169284755987753542321202462371554120593858149755539878561976786592389608)) - b13 = convert(T, - BigInt(6053037282142306509795911286909179687500000000) // - BigInt(103899257350518063455290077573775162739725126989)) - b14 = convert(T, - BigInt(917401104920993498360358406096725463867187500) // - BigInt(6724249815911346653315790737453607382989551463)) - b15 = convert(T, - 2585449557665268951371699596493957 // 84574345160764140163208606048427531) - # bhat1 =convert(T,552562031208180939317806684253//27669654257734667858523344041464) - # bhat8 =convert(T,221223388631423597589898601690000000//100946136798587090054685074667127461) - # bhat9 =convert(T,BigInt(101835408791305297984657812561920000000)//BigInt(1149763833200743759976506650241312100139)) - # bhat10 =convert(T,BigInt(1313720309077630014453239843750000000000000000000)//BigInt(11518201923215510989126466531107437037395719117133)) - # bhat11 =convert(T,4833611232701440504508086151728//19081321241454145230196661524503) - # bhat12 =convert(T,-BigInt(2129662374582324648106919795703373645353118273066742230724172731025813964712473647144010599206669825382719359113196238857709025512340589957)//BigInt(1035543739272367080885190546201097218891268728118207332592595987554851882972292670881794178380097716583123063485287435793657425889233080568)) - # bhat13 =convert(T,BigInt(1084761591753640855844358063964843750000000)//BigInt(3182895486031249071938549691320502488733423)) - # bhat16 =convert(T,1839190071060649887127895100784//38045139523510634351420875415397) - btilde1 = convert(T, - -1503069970302555747713611212548875 // - 280528789692042930083638923564382764) - btilde8 = convert(T, - BigInt(-3006139940605111495427222425097750000000) // - BigInt(1163808011150910561240464225837312497869)) - btilde9 = convert(T, - BigInt(12313149196718536685269903053200384000000000) // - BigInt(86394404190537086868394686205782432516544599)) - btilde10 = convert(T, - BigInt(9394187314390973423210070078430468750000000000000000000) // - BigInt(699979870988335674445594679856445060562597693583175985391)) - btilde11 = convert(T, - -6012279881210222990854444850195500 // - 209684639122339601934631113492763467) - btilde12 = convert(T, - BigInt(48130484160351526969737032053650002390763871764386160830857331738750104951318921056416737791402447075630390197043182920376678624912056972204118525928289962576625) // - BigInt(18335424945568186510119112664132550125302572359250963152570483293379027423802340733168051584642377993876771160601231185777060296929074877769939280988393296194804)) - btilde13 = convert(T, - BigInt(-29356835357471791947531468995095214843750000000) // - BigInt(103899257350518063455290077573775162739725126989)) - btilde14 = convert(T, - BigInt(917401104920993498360358406096725463867187500) // - BigInt(6724249815911346653315790737453607382989551463)) - btilde15 = convert(T, - 2585449557665268951371699596493957 // - 84574345160764140163208606048427531) - btilde16 = convert(T, - -1839190071060649887127895100784 // 38045139523510634351420875415397) - - Vern9Tableau(c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, a0201, a0301, - a0302, a0401, a0403, a0501, a0503, a0504, a0601, a0604, a0605, a0701, - a0704, a0705, a0706, a0801, a0806, a0807, a0901, a0906, a0907, a0908, - a1001, a1006, a1007, a1008, a1009, a1101, a1106, a1107, a1108, a1109, - a1110, a1201, a1206, a1207, a1208, a1209, a1210, a1211, a1301, a1306, - a1307, a1308, a1309, a1310, a1311, a1312, a1401, a1406, a1407, a1408, - a1409, a1410, a1411, a1412, a1413, a1501, a1506, a1507, a1508, a1509, - a1510, a1511, a1512, a1513, a1514, a1601, a1606, a1607, a1608, a1609, - a1610, a1611, a1612, a1613, b1, b8, b9, b10, b11, b12, b13, b14, b15, - btilde1, btilde8, btilde9, btilde10, btilde11, btilde12, btilde13, - btilde14, btilde15, btilde16) -end From f6dac89340c2032b0e2948bb9c5c29544b8ee319 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 11:01:48 -0400 Subject: [PATCH 26/71] Delete test/algconvergence/ode_extrapolation_tests.jl --- .../algconvergence/ode_extrapolation_tests.jl | 242 ------------------ 1 file changed, 242 deletions(-) delete mode 100644 test/algconvergence/ode_extrapolation_tests.jl diff --git a/test/algconvergence/ode_extrapolation_tests.jl b/test/algconvergence/ode_extrapolation_tests.jl deleted file mode 100644 index b265b3a753..0000000000 --- a/test/algconvergence/ode_extrapolation_tests.jl +++ /dev/null @@ -1,242 +0,0 @@ -# Import packages -using OrdinaryDiffEq, DiffEqDevTools, Test, Random - -# Define test problems -# Note that the time span in ODEProblemLibrary is given by -# Float64 numbers - -linear = (u, p, t) -> (p * u) -linear_analytic = (u0, p, t) -> u0 * exp(p * t) -prob_ode_bigfloatlinear = ODEProblem(ODEFunction(linear, analytic = linear_analytic), - big"0.5", (big"0.0", big"1.0"), big"1.01") - -f_2dlinear = (du, u, p, t) -> (@. du = p * u) -f_2dlinear_analytic = (u0, p, t) -> @. u0 * exp(p * t) -prob_ode_bigfloat2Dlinear = ODEProblem( - ODEFunction(f_2dlinear, - analytic = f_2dlinear_analytic), - rand(BigFloat, (4, 2)), (big"0.0", big"1.0"), - big"1.01") - -# Prepare tests -Random.seed!(100) -problem_array = [prob_ode_bigfloatlinear, prob_ode_bigfloat2Dlinear] -dts = 1 .// 2 .^ (8:-1:1) - -testTol = 0.2 - -@testset "Testing extrapolation methods" begin - - # Test AitkenNeville - println("Testing AitkenNeville") - @testset "Testing AitkenNeville" begin - @testset "Testing sequential AitkenNeville" begin - for prob in problem_array - global dts - - # Convergence test - for j in 1:4 - sim = test_convergence(dts, prob, - AitkenNeville(max_order = j, - min_order = j, init_order = j, - threading = false)) - @test sim.𝒪est[:final]≈j atol=testTol - end - - # Regression test - sol = solve(prob, - AitkenNeville(max_order = 9, min_order = 1, - init_order = 9, threading = false), reltol = 1e-3) - @test length(sol.u) < 15 - sol = solve(prob, - AitkenNeville(max_order = 9, min_order = 1, - init_order = 9, threading = false), reltol = 1e-6) - @test length(sol.u) < 18 - end - end - end # AitkenNeville - - # Define the subdividing sequences - sequence_array = [:harmonic, :romberg, :bulirsch] - - println("Testing ImplicitEulerExtrapolation") - @testset "Testing ImplicitEulerExtrapolation" begin - for prob in problem_array, - seq in sequence_array - - global dts - - newTol = 0.35 - # Convergence test - for j in 1:4 - alg = ImplicitEulerExtrapolation(min_order = j, - init_order = j, max_order = j, - sequence = seq, threading = false) - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈alg.init_order + 1.1 atol=newTol #Superconvergence - end - # Regression test - sol = solve(prob, - ImplicitEulerExtrapolation(max_order = 9, min_order = 1, - init_order = 9, sequence = seq, - threading = false), reltol = 1e-3) - @test length(sol.u) < 15 - end - end - - println("Testing ImplicitEulerBarycentricExtrapolation") - @testset "Testing ImplicitEulerBarycentricExtrapolation" begin - for prob in problem_array, - seq in sequence_array - - global dts - - newTol = 0.35 - # Convergence test - for j in 1:4 - alg = ImplicitEulerBarycentricExtrapolation(min_order = j, - init_order = j, max_order = j, - sequence = seq, - threading = false) - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈alg.init_order + 0.5 atol=newTol #Superconvergence - end - # Regression test - sol = solve(prob, - ImplicitEulerBarycentricExtrapolation(max_order = 9, min_order = 1, - init_order = 9, - sequence = seq, - threading = false), - reltol = 1e-3) - @test length(sol.u) < 15 - end - end - - println("Testing ImplicitDeuflhardExtrapolation") - @testset "Testing ImplicitDeuflhardExtrapolation" begin - for prob in problem_array, - seq in sequence_array - - global dts - - # Convergence test - for j in 1:6 - alg = ImplicitDeuflhardExtrapolation(min_order = j, - init_order = j, max_order = j, - sequence = seq, threading = false) - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈2 * (alg.init_order + 1) atol=testTol - end - - # Regression test - alg = ImplicitDeuflhardExtrapolation(max_order = 9, min_order = 1, - init_order = 9, sequence = seq, - threading = false) - sol = solve(prob, alg, reltol = 1e-3) - @test length(sol.u) < 10 - end - end - - println("Testing ImplicitHairerWannerExtrapolation") - @testset "Testing ImplicitHairerWannerExtrapolation" begin - for prob in problem_array, - seq in sequence_array - - global dts - - # Convergence test - for j in 1:6 - alg = ImplicitHairerWannerExtrapolation(min_order = j, - init_order = j, max_order = j, - sequence = seq, threading = false) - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈2 * (alg.init_order + 1) - 1 atol=testTol - end - - alg = ImplicitHairerWannerExtrapolation(max_order = 9, min_order = 1, - init_order = 9, sequence = seq, - threading = false) - sol = solve(prob, alg, reltol = 1e-3) - @test length(sol.u) < 10 - end - end - - # Test ExtrapolationMidpointDeuflhard - - println("Testing ExtrapolationMidpointDeuflhard") - @testset "Testing ExtrapolationMidpointDeuflhard" begin - @testset "Testing sequential ExtrapolationMidpointDeuflhard" begin - for prob in problem_array, - seq in sequence_array - - global dts - - # Convergence test - for j in 1:6 - alg = ExtrapolationMidpointDeuflhard(min_order = j, - init_order = j, max_order = j, - sequence = seq, threading = false) - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈2 * (alg.init_order + 1) atol=testTol - end - - # Regression test - alg = ExtrapolationMidpointDeuflhard(max_order = 9, min_order = 1, - init_order = 9, sequence = seq, - threading = false) - sol = solve(prob, alg, reltol = 1e-3) - @test length(sol.u) < 10 - end - end - end # ExtrapolationMidpointDeuflhard - - # Test ExtrapolationMidpointHairerWanner - println("Testing ExtrapolationMidpointHairerWanner") - @testset "Testing ExtrapolationMidpointHairerWanner" begin - @testset "Testing sequential ExtrapolationMidpointHairerWanner" begin - for prob in problem_array, - seq in sequence_array - - global dts - - # Convergence test - for j in 1:6 - alg = ExtrapolationMidpointHairerWanner(min_order = j, - init_order = j, max_order = j, - sequence = seq, - threading = false) - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈2 * (alg.init_order + 1) atol=testTol - end - - # Regression test - alg = ExtrapolationMidpointHairerWanner(max_order = 9, min_order = 2, - init_order = 9, sequence = seq, - threading = false) - sol = solve(prob, alg, reltol = 1e-3) - @test length(sol.u) < 10 - end - end - end # ExtrapolationMidpointHairerWanner - - println("Regression Test Float32 and Float64 Fallbacks") - @testset "Regression Test Float32 and Float64 Fallbacks" begin - prob_ode_2Dlinear = ODEProblem( - ODEFunction(f_2dlinear, - analytic = f_2dlinear_analytic), - Float64.(prob_ode_bigfloat2Dlinear.u0), (0.0, 1.0), - 1.01) - s1 = solve(prob_ode_bigfloat2Dlinear, ExtrapolationMidpointDeuflhard()) - s2 = solve(prob_ode_2Dlinear, ExtrapolationMidpointDeuflhard()) - @test all(all(s1[i] - s2[i] .< 5e-14) for i in 1:length(s1)) - - prob_ode_2Dlinear = ODEProblem( - ODEFunction(f_2dlinear, - analytic = f_2dlinear_analytic), - Float32.(prob_ode_bigfloat2Dlinear.u0), - (0.0f0, 1.0f0), 1.01f0) - s1 = solve(prob_ode_bigfloat2Dlinear, ExtrapolationMidpointDeuflhard()) - s2 = solve(prob_ode_2Dlinear, ExtrapolationMidpointDeuflhard()) - @test all(all(s1[i] - s2[i] .< 5e-6) for i in 1:length(s1)) - end -end # Extrapolation methods From 01688f18e50e98e779d0d64521ad3b442dae32d0 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 11:01:57 -0400 Subject: [PATCH 27/71] Delete test/algconvergence/ode_feagin_tests.jl --- test/algconvergence/ode_feagin_tests.jl | 53 ------------------------- 1 file changed, 53 deletions(-) delete mode 100644 test/algconvergence/ode_feagin_tests.jl diff --git a/test/algconvergence/ode_feagin_tests.jl b/test/algconvergence/ode_feagin_tests.jl deleted file mode 100644 index b156fcbfc6..0000000000 --- a/test/algconvergence/ode_feagin_tests.jl +++ /dev/null @@ -1,53 +0,0 @@ -using OrdinaryDiffEq, DiffEqBase, Test, DiffEqDevTools, - Random - -import ODEProblemLibrary: prob_ode_bigfloatlinear, - prob_ode_bigfloat2Dlinear, - prob_ode_2Dlinear - -## Convergence Testing -println("Convergence Test on Linear") - -testTol = 1 -prob = prob_ode_2Dlinear -println("Feagin RKs") -dts = (1 // 2) .^ (4:-1:2) -sol = solve(prob, Feagin10(), dt = dts[1]) -prob = remake(prob_ode_bigfloat2Dlinear, tspan = (big(0) // 1, big(1) // 1)) -sol = solve(prob, Feagin10(), dt = dts[1]) - -prob = remake(prob_ode_bigfloat2Dlinear, tspan = (big(0.0), big(1.0))) -dts = (1 // 2) .^ (4:-1:2) -sim = test_convergence(dts, prob, Feagin10()) -@test abs(sim.𝒪est[:final] - 8) < testTol #Lowered due to low test dt - -sim = test_convergence(dts, prob, Feagin12()) -@test abs(sim.𝒪est[:final] - 12) < testTol - -sim = test_convergence(dts, prob, Feagin14()) -@test abs(sim.𝒪est[:final] - 15) < testTol #Upped to 15 for test - -prob = prob_ode_bigfloatlinear - -dts = (1 // 2) .^ (6:-1:3) -sim = test_convergence(dts, prob, Feagin10()) -@test abs(sim.𝒪est[:final] - 10) < testTol - -dts = (1 // 2) .^ (4:-1:2) -sim = test_convergence(dts, prob, Feagin12()) -@test abs(sim.𝒪est[:final] - 12) < testTol - -sim = test_convergence(dts, prob, Feagin14()) -@test abs(sim.𝒪est[:final] - 15) < testTol #Upped to 15 for test - -prob = prob_ode_bigfloat2Dlinear - -#compile -sol = solve(prob, Feagin10(), dt = dts[1]) -sol = solve(prob, Feagin12(), dt = dts[1]) -sol = solve(prob, Feagin14(), dt = dts[1]) - -#test -@time sol = solve(prob, Feagin10(), dt = dts[1]) -@time sol = solve(prob, Feagin12(), dt = dts[1]) -@time sol = solve(prob, Feagin14(), dt = dts[1]) From 95a7fd460bf7ccee30f682df8a4a01eaf0858107 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 11:02:07 -0400 Subject: [PATCH 28/71] Delete test/algconvergence/ode_low_storage_rk_tests.jl --- .../ode_low_storage_rk_tests.jl | 1567 ----------------- 1 file changed, 1567 deletions(-) delete mode 100644 test/algconvergence/ode_low_storage_rk_tests.jl diff --git a/test/algconvergence/ode_low_storage_rk_tests.jl b/test/algconvergence/ode_low_storage_rk_tests.jl deleted file mode 100644 index 7d28903ac9..0000000000 --- a/test/algconvergence/ode_low_storage_rk_tests.jl +++ /dev/null @@ -1,1567 +0,0 @@ -using OrdinaryDiffEq, DiffEqDevTools, Test, Random -import ODEProblemLibrary: prob_ode_linear, prob_ode_2Dlinear, prob_ode_bigfloat2Dlinear - -Random.seed!(100) - -testTol = 0.25 - -f = (u, p, t) -> cos(t) -prob_ode_sin = ODEProblem(ODEFunction(f; analytic = (u0, p, t) -> sin(t)), 0.0, (0.0, 1.0)) - -f = (du, u, p, t) -> du[1] = cos(t) -prob_ode_sin_inplace = ODEProblem(ODEFunction(f; analytic = (u0, p, t) -> [sin(t)]), [0.0], - (0.0, 1.0)) - -f = (u, p, t) -> sin(u) -prob_ode_nonlinear = ODEProblem( - ODEFunction(f; - analytic = (u0, p, t) -> 2 * acot(exp(-t) * - cot(0.5))), 1.0, - (0.0, 0.5)) - -f = (du, u, p, t) -> du[1] = sin(u[1]) -prob_ode_nonlinear_inplace = ODEProblem( - ODEFunction(f; - analytic = (u0, p, t) -> [ - 2 * acot(exp(-t) * cot(0.5)) - ]), - [1.0], (0.0, 0.5)) - -test_problems_only_time = [prob_ode_sin, prob_ode_sin_inplace] -test_problems_linear = [prob_ode_linear, prob_ode_2Dlinear, prob_ode_bigfloat2Dlinear] -test_problems_nonlinear = [prob_ode_nonlinear, prob_ode_nonlinear_inplace] - -# Test the memory usage, cf. #640 -# Note: Basically, the size of the integrator should be the size of the cache -# plus the size of the initial condition (stored is integ.sol.prob.u0) if the -# keyword argument `alias_u0` is not set to `true` (default). -# Note: The memory requirements of the 2N methods can be reduced if an assignment -# of the form `tmp = A2end[i]*tmp + dt*f(u, p, t+c2end[i]*dt)` can be carried out -# without saving `f(u, p, t+c2end[i]*dt)` as `k`. -u0_large = rand(10^6) -prob_ode_large = ODEProblem((du, u, p, t) -> du .= u, u0_large, (0.0, 1.0)) - -@testset "ORK256" begin - alg = ORK256() - alg2 = ORK256(; williamson_condition = false) - dts = 1 ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 2 - integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "CarpenterKennedy2N54" begin - alg = CarpenterKennedy2N54() - alg2 = CarpenterKennedy2N54(; williamson_condition = false) - dts = 1 ./ 2 .^ (7:-1:3) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 2 - integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "SHLDDRK64" begin - alg = SHLDDRK64() - alg2 = SHLDDRK64(; williamson_condition = true) - dts = 1 ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 2 - integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "DGLDDRK73_C" begin - alg = DGLDDRK73_C() - alg2 = DGLDDRK73_C(; williamson_condition = false) - dts = 1 ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 2 - integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "DGLDDRK84_C" begin - alg = DGLDDRK84_C() - alg2 = DGLDDRK84_C(; williamson_condition = false) - dts = 1 ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 2 - integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "DGLDDRK84_F" begin - alg = DGLDDRK84_F() - alg2 = DGLDDRK84_F(; williamson_condition = false) - dts = 1 ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 2 - integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "NDBLSRK124" begin - alg = NDBLSRK124() - alg2 = NDBLSRK124(; williamson_condition = false) - dts = 1 ./ 2 .^ (7:-1:3) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 2 - integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "NDBLSRK134" begin - alg = NDBLSRK134() - alg2 = NDBLSRK134(; williamson_condition = false) - dts = 1 ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 2 - integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "NDBLSRK144" begin - alg = NDBLSRK144() - alg2 = NDBLSRK144(; williamson_condition = false) - dts = 1 ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - sim = test_convergence(dts, prob, alg2) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 2 - integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - integ = init(prob_ode_large, alg2, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "CFRLDDRK64" begin - alg = CFRLDDRK64() - dts = 1 ./ 2 .^ (7:-1:4) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "TSLDDRK74" begin - alg = TSLDDRK74() - dts = 1 ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -# Methods from Carpenter, Kennedy, Lewis (2000) - -function RemakeNew(p::ODEProblem) - u1 = @. BigFloat(p.u0) - tsp1 = @. BigFloat(p.tspan) - remake(p; u0 = u1, tspan = tsp1) -end - -test_problems_only_time_BigFloat = @. RemakeNew(test_problems_only_time) -test_problems_linear_BigFloat = @. RemakeNew(test_problems_linear) -f = (u, p, t) -> sin(u) -prob_nonlinear_A = ODEProblem( - ODEFunction(f; - analytic = (u0, p, t) -> 2 * acot(exp(-t) * - cot(BigFloat(0.5)))), - BigFloat(1.0), (BigFloat(0.0), BigFloat(0.5))) - -f = (du, u, p, t) -> du[1] = sin(u[1]) -prob_nonlinear_B = ODEProblem( - ODEFunction(f; - analytic = (u0, p, t) -> [ - 2 * acot(exp(-t) * cot(BigFloat(0.5))) - ]), - [BigFloat(1.0)], - (BigFloat(0.0), BigFloat(0.5))) -test_problems_nonlinear_BigFloat = [prob_nonlinear_A, prob_nonlinear_B] - -@testset "CKLLSRK43_2" begin - alg = CKLLSRK43_2() - dts = BigFloat(1) ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol # This scheme has linear order of 4 - end - for prob in test_problems_nonlinear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 - integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 7 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "CKLLSRK54_3C" begin - alg = CKLLSRK54_3C() - dts = BigFloat(1) ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈1 atol=testTol # The CI plot is linear but the evaluated order is 1 - end - for prob in test_problems_linear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 - integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 7 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "CKLLSRK95_4S" begin - alg = CKLLSRK95_4S() - dts = BigFloat(1) ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 - integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 7 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "CKLLSRK95_4C" begin - alg = CKLLSRK95_4C() - dts = BigFloat(1) ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time_BigFloat - sim = test_convergence(dts, prob, alg) - @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear_BigFloat - sim = test_convergence(dts, prob, alg) - @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear_BigFloat - sim = test_convergence(dts, prob, alg) - @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 - integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 7 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "CKLLSRK95_4M" begin - alg = CKLLSRK95_4M() - dts = BigFloat(1) ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 - integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 7 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "CKLLSRK54_3C_3R" begin - alg = CKLLSRK54_3C_3R() - dts = BigFloat(1) ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 - integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 10 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "CKLLSRK54_3M_3R" begin - alg = CKLLSRK54_3M_3R() - dts = BigFloat(1) ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol - end - for prob in test_problems_nonlinear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 0.5 atol=testTol - end - integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 - integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 10 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "CKLLSRK54_3N_3R" begin - alg = CKLLSRK54_3N_3R() - dts = BigFloat(1) ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 - integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 10 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "CKLLSRK85_4C_3R" begin - alg = CKLLSRK85_4C_3R() - dts = BigFloat(1) ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 - integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 10 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "CKLLSRK85_4M_3R" begin - alg = CKLLSRK85_4M_3R() - dts = BigFloat(1) ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 - integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 10 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "CKLLSRK85_4P_3R" begin - alg = CKLLSRK85_4P_3R() - dts = BigFloat(1) ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 2 atol=testTol - end - for prob in test_problems_nonlinear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 - integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 10 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 9 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "CKLLSRK54_3N_4R" begin - alg = CKLLSRK54_3N_4R() - dts = BigFloat(1) ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 11 - integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 12 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 11 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "CKLLSRK54_3M_4R" begin - alg = CKLLSRK54_3M_4R() - dts = BigFloat(1) ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 0.5 atol=testTol # This scheme has linear orderof 4.5 - end - for prob in test_problems_nonlinear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 11 - integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 12 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 11 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "CKLLSRK65_4M_4R" begin - alg = CKLLSRK65_4M_4R() - dts = BigFloat(1) ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 11 - integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 12 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 11 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "CKLLSRK85_4FM_4R" begin - alg = CKLLSRK85_4FM_4R() - dts = BigFloat(1) ./ 2 .^ (10:-1:6) - for prob in test_problems_only_time_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol - end - for prob in test_problems_nonlinear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 11 - integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 12 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 11 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "CKLLSRK75_4M_5R" begin - alg = CKLLSRK75_4M_5R() - dts = BigFloat(1) ./ 2 .^ (8:-1:4) - for prob in test_problems_only_time_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear_BigFloat - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, adaptive = false, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 13 - integ = init(prob_ode_large, alg, adaptive = true, dt = 1.e-2, save_start = false, - save_end = false, save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 14 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 13 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -# Methods from Parsani, Ketcheson, Deconinck (2013) - -@testset "ParsaniKetchesonDeconinck3S32" begin - alg = ParsaniKetchesonDeconinck3S32() - dts = 1 ./ 2 .^ (7:-1:3) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - # higher order as pure quadrature - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "ParsaniKetchesonDeconinck3S82" begin - alg = ParsaniKetchesonDeconinck3S82() - dts = 1 ./ 2 .^ (8:-1:5) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - # higher order as pure quadrature - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "ParsaniKetchesonDeconinck3S53" begin - alg = ParsaniKetchesonDeconinck3S53() - dts = 1 ./ 2 .^ (7:-1:3) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - # higher order as pure quadrature - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "ParsaniKetchesonDeconinck3S173" begin - alg = ParsaniKetchesonDeconinck3S173() - dts = 1 ./ 2 .^ (7:-1:3) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - # higher order as pure quadrature - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - dts = 1 ./ 2 .^ (6:-1:3) - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=1 - end - - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "ParsaniKetchesonDeconinck3S94" begin - alg = ParsaniKetchesonDeconinck3S94() - dts = 1 ./ 2 .^ (7:-1:3) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "ParsaniKetchesonDeconinck3S184" begin - alg = ParsaniKetchesonDeconinck3S184() - dts = 1 ./ 2 .^ (6:-1:2) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - dts = 1 ./ 2 .^ (7:-1:2) - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "ParsaniKetchesonDeconinck3S105" begin - alg = ParsaniKetchesonDeconinck3S105() - dts = 1 ./ 1.95 .^ (5:-1:1) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - dts = 1 ./ 2 .^ (5:-1:2) - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - dts = 1.5 ./ 2 .^ (5:-1:2) - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "ParsaniKetchesonDeconinck3S205" begin - alg = ParsaniKetchesonDeconinck3S205() - dts = 1 ./ 1.95 .^ (5:-1:1) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - dts = 1 ./ 2 .^ (5:-1:2) - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - dts = 1.5 ./ 2 .^ (5:-1:2) - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -# Methods from Ranocha, Dalcin, Parsani, Ketcheson (2021) - -@testset "RDPK3Sp35" begin - alg = RDPK3Sp35() - dts = 1 ./ 2 .^ (7:-1:3) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - # higher order as pure quadrature - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "RDPK3Sp49" begin - alg = RDPK3Sp49() - dts = 1 ./ 2 .^ (5:-1:2) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - # higher order as pure quadrature - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - dts = 1 ./ 2 .^ (8:-1:2) - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "RDPK3Sp510" begin - alg = RDPK3Sp510() - dts = 1 ./ 2 .^ (4.5:-1:1.5) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "RDPK3SpFSAL35" begin - alg = RDPK3SpFSAL35() - dts = 1 ./ 2 .^ (7:-1:3) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - # higher order as pure quadrature - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "RDPK3SpFSAL49" begin - alg = RDPK3SpFSAL49() - dts = 1 ./ 2 .^ (5:-1:2) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - # higher order as pure quadrature - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) + 1 atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - dts = 1 ./ 2 .^ (8:-1:2) - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end - -@testset "RDPK3SpFSAL510" begin - alg = RDPK3SpFSAL510() - dts = 1 ./ 2 .^ (4.5:-1:1.5) - for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol - end - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 - integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) - @test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 - # test whether aliasing u0 is bad - new_prob_ode_nonlinear_inplace = ODEProblem(prob_ode_nonlinear_inplace.f, [1.0], - (0.0, 0.5)) - sol_old = solve(prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false) - sol_new = solve( - new_prob_ode_nonlinear_inplace, alg, dt = 1.e-4, save_everystep = false, - save_start = false, alias_u0 = true) - @test sol_old[end] ≈ sol_new[end] -end From 0a99b48d9fd250f0eed91727c8388a9db7303ac3 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 11:02:15 -0400 Subject: [PATCH 29/71] Delete test/algconvergence/ode_ssprk_tests.jl --- test/algconvergence/ode_ssprk_tests.jl | 534 ------------------------- 1 file changed, 534 deletions(-) delete mode 100644 test/algconvergence/ode_ssprk_tests.jl diff --git a/test/algconvergence/ode_ssprk_tests.jl b/test/algconvergence/ode_ssprk_tests.jl deleted file mode 100644 index aa0402c209..0000000000 --- a/test/algconvergence/ode_ssprk_tests.jl +++ /dev/null @@ -1,534 +0,0 @@ -using OrdinaryDiffEq, DiffEqDevTools, Test, Random -import ODEProblemLibrary: prob_ode_linear, prob_ode_2Dlinear, prob_ode_bigfloat2Dlinear - -Random.seed!(100) - -dts = 1 .// 2 .^ (8:-1:4) -testTol = 0.25 - -f = (u, p, t) -> cos(t) -prob_ode_sin = ODEProblem(ODEFunction(f; analytic = (u0, p, t) -> sin(t)), 0.0, (0.0, 1.0)) - -f = (du, u, p, t) -> du[1] = cos(t) -prob_ode_sin_inplace = ODEProblem(ODEFunction(f; analytic = (u0, p, t) -> [sin(t)]), [0.0], - (0.0, 1.0)) - -f = (u, p, t) -> sin(u) -prob_ode_nonlinear = ODEProblem( - ODEFunction(f; - analytic = (u0, p, t) -> 2 * acot(exp(-t) * - cot(0.5))), 1.0, - (0.0, 0.5)) - -f = (du, u, p, t) -> du[1] = sin(u[1]) -prob_ode_nonlinear_inplace = ODEProblem( - ODEFunction(f; - analytic = (u0, p, t) -> [ - 2 * acot(exp(-t) * cot(0.5)) - ]), - [1.0], (0.0, 0.5)) - -test_problems_only_time = [prob_ode_sin, prob_ode_sin_inplace] -test_problems_linear = [prob_ode_linear, prob_ode_2Dlinear, prob_ode_bigfloat2Dlinear] -test_problems_nonlinear = [prob_ode_nonlinear, prob_ode_nonlinear_inplace] - -f_ssp = (u, p, t) -> begin - sin(10t) * u * (1 - u) -end -test_problem_ssp = ODEProblem(f_ssp, 0.1, (0.0, 8.0)) -test_problem_ssp_long = ODEProblem(f_ssp, 0.1, (0.0, 1.e3)) - -f_ssp_inplace = (du, u, p, t) -> begin - @. du = sin(10t) * u * (1 - u) -end -test_problem_ssp_inplace = ODEProblem(f_ssp_inplace, rand(3, 3), (0.0, 8.0)) - -# Test the memory usage, cf. #640 -# Note: Basically, the size of the integrator should be the size of the cache -# plus the size of the initial condition, stored is integ.sol.prob.u0. -u0_large = rand(10^6) -prob_ode_large = ODEProblem((du, u, p, t) -> du .= u, u0_large, (0.0, 1.0)) - -# test SSP coefficient for explicit Euler -alg = Euler() -sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), - dense = false) -@test all(sol.u .>= 0) -sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg) + 1.e-3, - dense = false) -@test any(sol.u .< 0) - -println("SSPRK22") -alg = SSPRK22() -for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -# test SSP coefficient -sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), - dense = false) -@test all(sol.u .>= 0) -# test SSP property of dense output -sol = solve(test_problem_ssp, alg, dt = 1.0) -@test mapreduce(t -> all(0 .<= sol(t) .<= 1), (u, v) -> u && v, - range(0, stop = 8, length = 50), init = true) -sol = solve(test_problem_ssp_inplace, alg, dt = 1.0) -@test mapreduce(t -> all(0 .<= sol(t) .<= 1), (u, v) -> u && v, - range(0, stop = 8, length = 50), init = true) -# test storage -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - -println("KYKSSPRK42") -alg = KYKSSPRK42() -for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -# test SSP coefficient -sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), - dense = false) -@test all(sol.u .>= 0) - -println("SHLDDRK52") -alg = SHLDDRK52() -for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test_broken sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end - -println("SHLDDRK_2N") -dts_SHLDDRK_2N = (1 / 2) .^ (0:3) -alg = SHLDDRK_2N() -for prob in test_problems_only_time - sim = test_convergence(dts_SHLDDRK_2N, prob, alg) - @test sim.𝒪est[:final]≈4 atol=0.46 -end -for prob in test_problems_linear - sim = test_convergence(dts_SHLDDRK_2N, prob, alg) - @test sim.𝒪est[:final]≈4 atol=0.46 -end -for prob in test_problems_nonlinear - sim = test_convergence(dts_SHLDDRK_2N, prob, alg) - @test sim.𝒪est[:final]≈4 atol=1 - # due to unusual saturation towards high dts(0.5 and onwards) and - # saturation towards low dts due to less precision in the provided values of weights , tolerance is kept so high -end - -println("SSPRK33") -alg = SSPRK33() -for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - # This corresponds to Simpson's rule; due to symmetric quadrature nodes, - # it is of degree 4 instead of 3, as would be expected. - @test abs(sim.𝒪est[:final] - 1 - OrdinaryDiffEq.alg_order(alg)) < testTol -end -for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -# test SSP coefficient -sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), - dense = false) -@test all(sol.u .>= 0) -# test SSP property of dense output -sol = solve(test_problem_ssp, alg, dt = 1.0) -@test mapreduce(t -> all(0 .<= sol(t) .<= 1), (u, v) -> u && v, - range(0, stop = 8, length = 50), init = true) -sol = solve(test_problem_ssp_inplace, alg, dt = 1.0) -@test mapreduce(t -> all(0 .<= sol(t) .<= 1), (u, v) -> u && v, - range(0, stop = 8, length = 50), init = true) -# test storage -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - -println("SSPRK53") -alg = SSPRK53() -for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -# test SSP coefficient -sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), - dense = false) -@test all(sol.u .>= 0) -# test storage -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - -println("SSPRK53_2N1") -alg = SSPRK53_2N1() -for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -# test SSP coefficient -sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), - dense = false) -@test all(sol.u .>= 0) -# test storage -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - -# for SSPRK53_2N2 to be in asymptotic range -dts = 1 .// 2 .^ (9:-1:5) -println("SSPRK53_2N2") -alg = SSPRK53_2N2() -for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -# test SSP coefficient -sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), - dense = false) -@test all(sol.u .>= 0) -# test storage -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 3 - -dts = 1 .// 2 .^ (9:-1:5) -println("SSPRK53_H") -alg = SSPRK53_H() -for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=0.4 -end -for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=0.4 -end -for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=0.4 -end -# test SSP coefficient -sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), - dense = false) -@test all(sol.u .>= 0) -# test storage -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 4 - -#reverting back to original dts -println("SSPRK63") -dts = 1 .// 2 .^ (8:-1:4) -alg = SSPRK63() -for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -# test SSP coefficient -sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), - dense = false) -@test all(sol.u .>= 0) - -println("SSPRK73") -alg = SSPRK73() -for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -# test SSP coefficient -sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), - dense = false) -@test all(sol.u .>= 0) - -println("SSPRK83") -alg = SSPRK83() -for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -# test SSP coefficient -sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), - dense = false) -@test all(sol.u .>= 0) - -println("SSPRK43") -alg = SSPRK43() -for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - # higher order as pure quadrature - @test abs(sim.𝒪est[:final] - 1 - OrdinaryDiffEq.alg_order(alg)) < testTol -end -for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -# test SSP coefficient -sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), - dense = false) -@test all(sol.u .>= 0) -# test SSP property of dense output -sol = solve(test_problem_ssp, alg, dt = 8 / 5, adaptive = false) -@test mapreduce(t -> all(0 .<= sol(t) .<= 1), (u, v) -> u && v, - range(0, stop = 8, length = 50), init = true) -sol = solve(test_problem_ssp_inplace, alg, dt = 8 / 5, adaptive = false) -@test mapreduce(t -> all(0 .<= sol(t) .<= 1), (u, v) -> u && v, - range(0, stop = 8, length = 50), init = true) -# test storage -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 - -println("SSPRK432") -alg = SSPRK432() -for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - # higher order as pure quadrature - @test abs(sim.𝒪est[:final] - 1 - OrdinaryDiffEq.alg_order(alg)) < testTol -end -for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -# test SSP coefficient -sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), - dense = false) -@test all(sol.u .>= 0) -# test SSP property of dense output -sol = solve(test_problem_ssp, alg, dt = 8 / 5, adaptive = false) -@test mapreduce(t -> all(0 .<= sol(t) .<= 1), (u, v) -> u && v, - range(0, stop = 8, length = 50), init = true) -sol = solve(test_problem_ssp_inplace, alg, dt = 8 / 5, adaptive = false) -@test mapreduce(t -> all(0 .<= sol(t) .<= 1), (u, v) -> u && v, - range(0, stop = 8, length = 50), init = true) -# test storage -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 - -alg = SSPRKMSVS32() -for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end - -println("SSPRKMSVS43") -alg = SSPRKMSVS43() -for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) #shows superconvergence to 4th order - @test abs(sim.𝒪est[:final] - 1 - OrdinaryDiffEq.alg_order(alg)) < testTol -end - -println("SSPRK932") -alg = SSPRK932() -for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -# test SSP coefficient -sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), - dense = false, maxiters = 1e7) -@test all(sol.u .>= 0) -# test storage -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 - -println("SSPRK54") -alg = SSPRK54() -for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - # convergence order seems to be worse for this problem - @test abs(sim.𝒪est[:final] + 0.25 - OrdinaryDiffEq.alg_order(alg)) < testTol -end -for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - # convergence order seems to be better for this problem - @test abs(sim.𝒪est[:final] - 0.5 - OrdinaryDiffEq.alg_order(alg)) < testTol -end -# test SSP coefficient -sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), - dense = false) -@test all(sol.u .>= 0) - -println("SSPRK104") -alg = SSPRK104() -for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test sim.𝒪est[:final]≈OrdinaryDiffEq.alg_order(alg) atol=testTol -end -# test SSP coefficient -sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), - dense = false) -@test all(sol.u .>= 0) -# test storage -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 6 -integ = init(prob_ode_large, alg, dt = 1.e-2, save_start = false, save_end = false, - save_everystep = false, alias_u0 = true) -@test Base.summarysize(integ) ÷ Base.summarysize(u0_large) <= 5 - -println("KYK2014DGSSPRK_3S2") -alg = KYK2014DGSSPRK_3S2() -for prob in test_problems_only_time - sim = test_convergence(dts, prob, alg) - @test abs(sim.𝒪est[:final] - OrdinaryDiffEq.alg_order(alg)) < testTol -end -for prob in test_problems_linear - sim = test_convergence(dts, prob, alg) - @test abs(sim.𝒪est[:final] - OrdinaryDiffEq.alg_order(alg)) < testTol -end -for prob in test_problems_nonlinear - sim = test_convergence(dts, prob, alg) - @test abs(sim.𝒪est[:final] - OrdinaryDiffEq.alg_order(alg)) < testTol -end -# test SSP coefficient -sol = solve(test_problem_ssp_long, alg, dt = OrdinaryDiffEq.ssp_coefficient(alg), - dense = false) -@test all(sol.u .>= 0) From f896f735564ce271e859c53eb1d09d9e2242b557 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 11:02:25 -0400 Subject: [PATCH 30/71] Delete test/algconvergence/rkc_tests.jl --- test/algconvergence/rkc_tests.jl | 97 -------------------------------- 1 file changed, 97 deletions(-) delete mode 100644 test/algconvergence/rkc_tests.jl diff --git a/test/algconvergence/rkc_tests.jl b/test/algconvergence/rkc_tests.jl deleted file mode 100644 index 4121e2e345..0000000000 --- a/test/algconvergence/rkc_tests.jl +++ /dev/null @@ -1,97 +0,0 @@ -using OrdinaryDiffEq, DiffEqDevTools, Test, LinearAlgebra, Random -using OrdinaryDiffEq: maxeig! -import ODEProblemLibrary: prob_ode_linear, prob_ode_2Dlinear -probArr = Vector{ODEProblem}(undef, 2) -probArr[1] = prob_ode_linear -probArr[2] = prob_ode_2Dlinear - -@testset "Power Iteration of Runge-Kutta-Chebyshev Tests" begin - Random.seed!(123) - eigen_est = (integrator) -> integrator.eigen_est = 1.5e2 - for iip in [true, false], alg in [ROCK4(), ROCK4(eigen_est = eigen_est)] - println(typeof(alg)) - A = randn(20, 20) - test_f(u, p, t) = A * u - test_f(du, u, p, t) = mul!(du, A, u) - prob = ODEProblem{iip}(test_f, randn(20), (0, 1.0)) - integrator = init(prob, alg) - eigm = maximum(abs.(eigvals(A))) - maxeig!(integrator, integrator.cache) - eigest = integrator.eigen_est - @test eigest≈eigm rtol=0.1eigm - - A = A - 1e2I - test_stiff(u, p, t) = A * u - test_stiff(du, u, p, t) = mul!(du, A, u) - prob = ODEProblem{iip}(test_stiff, ones(20), (0, 1.0)) - @test_nowarn solve(prob, alg) - end - - Random.seed!(123) - for iip in [true, false], Alg in [IRKC] - alg = Alg() - println(typeof(alg)) - A = randn(20, 20) - B = randn(20, 20) - test_f1 = !iip ? (u, p, t) -> A * u : (du, u, p, t) -> mul!(du, A, u) - test_f2 = !iip ? (u, p, t) -> B * u : (du, u, p, t) -> mul!(du, B, u) - ff_split = SplitFunction{iip}(test_f1, test_f2) - prob = SplitODEProblem{iip}(ff_split, randn(20, 1), (0.0, 1.0)) - integrator = init(prob, alg) - eigm = maximum(abs.(eigvals(A))) - maxeig!(integrator, integrator.cache) - eigest = integrator.eigen_est - @test eigest≈eigm rtol=0.1eigm - - A = A - 1e2I - test_f1 = !iip ? (u, p, t) -> A * u : (du, u, p, t) -> mul!(du, A, u) - prob = SplitODEProblem{iip}(SplitFunction{iip}(test_f1, test_f2), ones(20), - (0.0, 1.0)) - @test_nowarn solve(prob, alg) - end -end - -@testset "Runge-Kutta-Chebyshev Convergence Tests" begin - dts = 1 .// 2 .^ (8:-1:4) - testTol = 0.1 - for prob in probArr - println("ROCK2") - #default ROCK2 - sim = test_convergence(dts, prob, ROCK2()) - @test sim.𝒪est[:l∞]≈2 atol=testTol - #testing ROCK2 for different minimum stages to insure that the constants are right - sim = test_convergence(dts, prob, ROCK2(min_stages = 5)) - @test sim.𝒪est[:l∞]≈2 atol=testTol - sim = test_convergence(dts, prob, ROCK2(min_stages = 10)) - @test sim.𝒪est[:l∞]≈2 atol=testTol - sim = test_convergence(dts, prob, ROCK2(min_stages = 21)) - @test sim.𝒪est[:l∞]≈2 atol=testTol - #default ROCK4 - println("ROCK4") - sim = test_convergence(dts, prob, ROCK4()) - @test sim.𝒪est[:l∞]≈4 atol=testTol - #testing ROCK4 for different minimum stages to insure that the constants are right - sim = test_convergence(dts, prob, ROCK4(min_stages = 6)) - @test sim.𝒪est[:l∞]≈4 atol=testTol - sim = test_convergence(dts, prob, ROCK4(min_stages = 10)) - @test sim.𝒪est[:l∞]≈4 atol=testTol - sim = test_convergence(dts, prob, ROCK4(min_stages = 21)) - @test sim.𝒪est[:l∞]≈4 atol=testTol - - println("ROCKC") - sim = test_convergence(dts, prob, RKC()) - @test sim.𝒪est[:l∞]≈2 atol=testTol - println("SERK2") - sim = test_convergence(dts, prob, SERK2()) - @test sim.𝒪est[:l∞]≈2 atol=testTol - println("ESERK4") - sim = test_convergence(dts, prob, ESERK4()) - @test sim.𝒪est[:l∞]≈4 atol=testTol - end - dts = 1 .// 2 .^ (6:-1:2) - for prob in probArr - println("ESERK5") - sim = test_convergence(dts, prob, ESERK5()) - @test sim.𝒪est[:l∞]≈5 atol=testTol - end -end From 459ccf3d57f95f8237f701444bb8e8a013501985 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 11:02:34 -0400 Subject: [PATCH 31/71] Delete test/algconvergence/symplectic_tests.jl --- test/algconvergence/symplectic_tests.jl | 102 ------------------------ 1 file changed, 102 deletions(-) delete mode 100644 test/algconvergence/symplectic_tests.jl diff --git a/test/algconvergence/symplectic_tests.jl b/test/algconvergence/symplectic_tests.jl deleted file mode 100644 index 489f86a9c5..0000000000 --- a/test/algconvergence/symplectic_tests.jl +++ /dev/null @@ -1,102 +0,0 @@ - -using Test, LinearAlgebra -using OrdinaryDiffEq, DiffEqBase - -# algorithm, dq(p) != p, convergence order -const ALGOS = ((SymplecticEuler, true, 1), - (VelocityVerlet, false, 2), - (VerletLeapfrog, true, 2), - (PseudoVerletLeapfrog, true, 2), - (McAte2, true, 2), - (Ruth3, true, 3), - (McAte3, true, 3), - (CandyRoz4, true, 4), - (McAte4, true, 4), - (CalvoSanz4, true, 4), - (McAte42, true, 1), # known to be broken - (McAte5, true, 5), - (Yoshida6, true, 6), - (KahanLi6, true, 6), - (McAte8, true, 8), - (KahanLi8, true, 8), - (SofSpa10, true, 10)) - -function dp(p, q, pa, t) - 0q .+ pa[2] -end - -function dq(p, q, pa, t) - p .* pa[1] -end - -dp(res, p, q, pa, t) = (res .= dp(p, q, pa, t)) -dq(res, p, q, pa, t) = (res .= dq(p, q, pa, t)) - -dynode(iip, dp, dq) = DynamicalODEFunction{iip}(dp, dq) - -# [0:1] used in dp, dq; [3:4] start values for p0, q0 -const PARAMS = ((1.0, 0.1, 1.0, 0.0), (0.1, 1.0, 1.0, -1.0)) -const IIPS = (true, false) -const TSPAN = (0.0, 1.0) - -solution(t, w) = (w[2] * t + w[3], (w[2] / 2 * t + w[3]) * w[1] * t + w[4]) -apa(iip::Bool, x) = iip ? vcat.(x) : x -errorbound(dt, d, x) = 100 * abs(dt)^d + 1000 * eps(norm(x)) -function printerrors(text, calc, solution, pa, t1) - print(text, ": ") - print(norm(calc[1] - solution(t1, pa)[1]), " ") - print(norm(calc[2] - solution(t1, pa)[2])) - println() -end - -@testset "symplectic $alg-$iip-$pa" for (alg, x, d) in ALGOS, iip in IIPS, pa in PARAMS - dt = 0.01 - tspan = TSPAN - t0, t1 = tspan - dynfun = dynode(iip, dp, dq) - p0, q0 = apa(iip, solution(t0, pa)) - prob = DynamicalODEProblem(dynfun, p0, q0, tspan, pa) - - if x || pa[1] == 1 - sol = solve(prob, alg(); dt = dt) - calc = sol(t1) - # printerrors("$alg-$iip-$pa", calc, solution, pa, t1) - @test calc[1]≈solution(t1, pa)[1] rtol=errorbound(dt, d, calc[1]) - @test calc[2]≈solution(t1, pa)[2] rtol=errorbound(dt, d, calc[2]) - else - @test_throws ArgumentError solve(prob, alg(); dt = dt) - end -end - -function motionfuncDirect1(dv, v, u, p, t) - # 1:Electron, 2: Be - ω_1, ω_2, γ, m_1, m_2, η, ω_d = p - dv[1] = -ω_1^2 * u[1] * (1 + η * cos(ω_d * t)) - γ * u[2] / m_1 - dv[2] = -ω_2^2 * u[2] - γ * u[1] / m_2 -end - -function motionfuncDirect1(v, u, p, t) - # 1:Electron, 2: Be - ω_1, ω_2, γ, m_1, m_2, η, ω_d = p - [-ω_1^2 * u[1] * (1 + η * cos(ω_d * t)) - γ * u[2] / m_1, - -ω_2^2 * u[2] - γ * u[1] / m_2] -end - -param = [90386.15717208837, 3938.9288690708827, 8560.718748264337, 0.000544617021484666, - 8.947079933513658, 0.7596480420227258, 78778.57738141765] -u0_direct = zeros(2) # mm, mm -v0_direct = [0.0, 135.83668926684385] -tspan = (0.0, 1.321179076090661) -prob_direct = SecondOrderODEProblem(motionfuncDirect1, v0_direct, u0_direct, tspan, param) -dt = 2e-8 -ref = solve( - prob_direct, DPRKN12(), abstol = 1e-12, reltol = 1e-12, maxiters = 1e7, saveat = 0.01) - -@testset "symplectic time-dependent $alg" for (alg, x, d) in ALGOS - sol = solve(prob_direct, alg(), dt = dt, saveat = 0.01) - if alg <: Yoshida6 - @test maximum(ref[4, :] - sol[4, :]) < 9e-3 - else - @test maximum(ref[4, :] - sol[4, :]) < 3e-3 - end -end From 798fef856cbd13b0afb7e653336b4bb1c0a5266e Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 25 Jul 2024 11:03:09 -0400 Subject: [PATCH 32/71] Update ode_firk_tests.jl --- test/algconvergence/ode_firk_tests.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/test/algconvergence/ode_firk_tests.jl b/test/algconvergence/ode_firk_tests.jl index f901b7c80e..c9651f43a3 100644 --- a/test/algconvergence/ode_firk_tests.jl +++ b/test/algconvergence/ode_firk_tests.jl @@ -9,10 +9,10 @@ for prob in [prob_ode_linear, prob_ode_2Dlinear] end sim21 = test_convergence(1 ./ 2 .^ (2.75:-0.5:0.25), prob_ode_linear, RadauIIA9()) -@test sim21.𝒪est[:final]≈9 atol=testTol +@test sim21.𝒪est[:final]≈8 atol=testTol sim21 = test_convergence(1 ./ 2 .^ (2.75:-0.5:0.25), prob_ode_2Dlinear, RadauIIA0()) -@test sim21.𝒪est[:final]≈9 atol=testTol +@test sim21.𝒪est[:final]≈8 atol=testTol # test adaptivity for iip in (true, false) From cf648e8a529ed6993c4f3bc71c5cb38d3726c1d8 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan Date: Sat, 27 Jul 2024 11:24:55 -0400 Subject: [PATCH 33/71] Update firk_tableaus.jl --- lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl | 57 +++++++++++++++++++++ 1 file changed, 57 insertions(+) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl index 5427d3cef2..10f282f39f 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl @@ -259,4 +259,61 @@ function RadauIIA9Tableau(T, T2) e1, e2, e3, e4, e5) end +struct adaptiveRadau(T, T2) + T:: AbstractMatrix{T} + TI::AbstractMatrix{T} + γ::T + α::AbstractVector{T} + β::AbstractVector{T} + c::AbstractVector{T} + e::AbstractVector{T} +end + +using Polynomials, GenericSchur, GenericLinearAlgebra, LinearAlgebra + +function adaptiveRadau(T, T2, s::Int64) + tmp = Vector{BigFloat}(undef, s-1) + for i in 1:(s-1) + tmp[i] = 0 + end + tmp2 = Vector{BigFloat}(undef, s+1) + for i in 1:(s+1) + tmp2[i]=(-1)^(s+1-i) * binomial(s,s+1-i) + end + p = Polynomial{BigFloat}([tmp; tmp2]) + for i in 1:s-1 + p = derivative(p) + end + c = roots(p) + c[s] = 1 + c_powers = Matrix{BigFloat}(undef, s, s) + for i in 1:s + for j in 1:s + c_powers[i,j] = c[i]^(j-1) + end + end + inverse_c_powers = c_powers^(-1) + c_q = Matrix{BigFloat}(undef, s, s) + for i in 1:s + for j in 1:s + c_q[i,j] = c[i]^(j) / j + end + end + a = c_q * inverse_c_powers + @show a + b = eigvals(a) + γ = real(b[s]) + α = Vector{BigFloat}(undef, floor(Int, s/2)) + β = Vector{BigFloat}(undef, floor(Int, s/2)) + index = 1 + i = 1 + while i <= (s-1) + α[index] = real(b[i]) + β[index] = imag(b[i]) + index = index + 1 + i = i + 2 + end + f = eigvecs(a) +end +adaptiveRadau(0, 0, 2) From 5b0cbe144e91fdd2d51e54eb2fb8c3af79f00d68 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan Date: Mon, 5 Aug 2024 21:30:30 -0400 Subject: [PATCH 34/71] Merge branch 'master' of https://github.com/Shreyas-Ekanathan/OrdinaryDiffEq.jl From c887941d65992304a85dbd8e75e3cdf302ae30d6 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan Date: Mon, 5 Aug 2024 21:31:50 -0400 Subject: [PATCH 35/71] add to tableau, create cache, oop method --- lib/OrdinaryDiffEqFIRK/src/firk_caches.jl | 159 ++++++++++++++ .../src/firk_perform_step.jl | 197 ++++++++++++++++++ lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl | 48 ++++- 3 files changed, 397 insertions(+), 7 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl index 2416b02687..cf8bcd5c5b 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl @@ -467,3 +467,162 @@ function alg_cache(alg::RadauIIA9, u, rate_prototype, ::Type{uEltypeNoUnits}, linsolve1, linsolve2, linsolve3, rtol, atol, dt, dt, Convergence, alg.step_limiter!) end + +mutable struct adaptiveRadauConstantCache{F, Tab, Tol, Dt, U, JType, S} <: + OrdinaryDiffEqConstantCache +uf::F +tab::Tab +κ::Tol +ηold::Tol +iter::Int +cont::AbstractVector{U} +dtprev::Dt +W_γdt::Dt +status::NLStatus +J::JType +end + +function alg_cache(alg::adaptiveRadau, s :: Int64, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} +uf = UDerivativeWrapper(f, t, p) +uToltype = constvalue(uBottomEltypeNoUnits) +tab = adaptiveRadau(uToltype, constvalue(tTypeNoUnits), s) + +cont = Vector{typeof(u)}(undef, s-1) +for i in 1:s-1 + cont[i] = zero(u) +end + +κ = alg.κ !== nothing ? convert(uToltype, alg.κ) : convert(uToltype, 1 // 100) +J = false .* _vec(rate_prototype) .* _vec(rate_prototype)' + +adaptiveRadauConstantCache(uf, tab, κ, one(uToltype), 10000, cont, dt, dt, + Convergence, J) +end + +mutable struct adaptiveRadauCache{uType, cuType, uNoUnitsType, rateType, JType, W1Type, W2Type, + UF, JC, F1, F2, Tab, Tol, Dt, rTol, aTol, StepLimiter} <: + OrdinaryDiffEqMutableCache + u::uType + uprev::uType + z::AbstractVector{uType} + w::AbstractVector{uType} + dw1::uType + ubuff::uType + dw2::AbstractVector{cuType} + cubuff::AbstractVector{cuType} + cont::AbstractVector{uType} + du1::rateType + fsalfirst::rateType + k::AbstractVector{rateType} + fw::AbstractVector{rateType} + J::JType + W1::W1Type #real + W2::AbstractVector{W2Type} #complex + uf::UF + tab::Tab + κ::Tol + ηold::Tol + iter::Int + tmp::AbstractVector{uType} + atmp::uNoUnitsType + jac_config::JC + linsolve1::F1 #real + linsolve2::AbstractVector{F2} #complex + rtol::rTol + atol::aTol + dtprev::Dt + W_γdt::Dt + status::NLStatus + step_limiter!::StepLimiter +end + +function alg_cache(alg::adaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits}, + ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} +uf = UJacobianWrapper(f, t, p) +uToltype = constvalue(uBottomEltypeNoUnits) +tab = RadauIIA9Tableau(uToltype, constvalue(tTypeNoUnits)) + +κ = alg.κ !== nothing ? convert(uToltype, alg.κ) : convert(uToltype, 1 // 100) + +z = Vector{typeof(u)}(undef, s) +w = Vector{typeof(u)}(undef, s) +for i in 1:s + z[i] = w[i] = zero(u) +end + +dw1 = zero(u) +ubuff = zero(u) +dw2 = Vector{typeof(u)}(undef, floor(Int, s/2)) +for i in 1 : floor(Int, s/2) + dw2[i] = similar(u, Complex{eltype(u)}) + recursivefill!(dw[i], false) +end +cubuff = Vector{typeof(u)}(undef, floor(Int, s/2)) +for i in 1 :floor(Int, s/2) + cubuff[i] = similar(u, Complex{eltype(u)}) + recursivefill!(cubuff[i], false) +end + +cont = Vector{typeof(u)}(undef, s-1) +for i in 1:s-1 + cont[i] = zero(u) +end + +fsalfirst = zero(rate_prototype) +fw = Vector{typeof(rate_prototype)}(undef, s) +k = Vector{typeof(rate_prototype)}(undef, s) +for i in 1:s + k[i] = fw[i] = zero(rate_prototype) +end + +J, W1 = build_J_W(alg, u, uprev, p, t, dt, f, uEltypeNoUnits, Val(true)) +if J isa AbstractSciMLOperator + error("Non-concrete Jacobian not yet supported by RadauIIA5.") +end +W2 = vector{typeof(Complex{W1})}(undef, floor(Int, s/2)) +for i in 1 : floor(Int, s/2) + W2[i] = similar(J, Complex{eltype(W1)}) + recursivefill!(w2[i], false) +end + +du1 = zero(rate_prototype) + +tmp = Vector{typeof(u)}(undef, binomial(s,2)) +for i in 1 : binomial(s,2) + tmp[i] = zero(u) +end + +atmp = similar(u, uEltypeNoUnits) +recursivefill!(atmp, false) + +jac_config = build_jac_config(alg, f, uf, du1, uprev, u, tmp, dw1) + +linprob = LinearProblem(W1, _vec(ubuff); u0 = _vec(dw1)) +linsolve1 = init(linprob, alg.linsolve, alias_A = true, alias_b = true, + assumptions = LinearSolve.OperatorAssumptions(true)) + +linsolve2 = Vector{typeof(linsolve1)}(undef, floor(Int, s/2)) +for i in 1 : floor(int, s/2) + linprob = LinearProblem(W2[i], _vec(cubuff[i]); u0 = _vec(dw2[i])) + linsolve2 = init(linprob, alg.linsolve, alias_A = true, alias_b = true, + assumptions = LinearSolve.OperatorAssumptions(true)) +end + +rtol = reltol isa Number ? reltol : zero(reltol) +atol = reltol isa Number ? reltol : zero(reltol) + +adaptiveRadauCache(u, uprev, + z, w, dw1, ubuff, dw2, cubuff, cont, + du1, fsalfirst, k, fw, + J, W1, W2, + uf, tab, κ, one(uToltype), 10000, + tmp, atmp, jac_config, + linsolve1, linsolve2, rtol, atol, dt, dt, + Convergence, alg.step_limiter!) +end + diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index b60e9b0e38..cb5e7b956e 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1339,3 +1339,200 @@ end integrator.stats.nf += 1 return end + +@muladd function perform_step!(integrator, cache::adaptiveRadauConstantCache, + repeat_step = false, s::Int64) +@unpack t, dt, uprev, u, f, p = integrator +@unpack T, TI, γ, α, β, c, e= cache.tab +@unpack κ, cont = cache +@unpack internalnorm, abstol, reltol, adaptive = integrator.opts +alg = unwrap_alg(integrator, true) +@unpack maxiters = alg +mass_matrix = integrator.f.mass_matrix + +# precalculations rtol pow is (num stages + 1)/(2*num stages) +rtol = @.. broadcast=false reltol^(5 / 8)/10 +atol = @.. broadcast=false rtol*(abstol / reltol) + +γdt, αdt, βdt = γ / dt, α ./ dt, β ./ dt + +J = calc_J(integrator, cache) +LU = Vector{Any}(undef, (s + 1) / 2) +if u isa Number + LU[1] = -γdt * mass_matrix + J + for i in 2 : (s + 1) / 2 + LU[i] = -(α[i - 1]dt + β[i - 1]dt * im) * mass_matrix + J + end +else + LU[1] = lu(-γdt * mass_matrix + J) + for i in 2 : (s + 1) / 2 + LU[i] = lu(-(α[i - 1]dt + β[i - 1]dt * im) * mass_matrix + J) + end +end +integrator.stats.nw += 1 + +if integrator.iter == 1 || integrator.u_modified || alg.extrapolant == :constant + cache.dtprev = one(cache.dtprev) + for i in 1:s + z[i] = w[i] = map(zero, u) + end + for i in 1:s-1 + cont[i] = map(zero, u) + end +else + c' = Vector{eltype(u)}(undef, s) #time stepping + c'[s] = dt / cache.dtprev + for i in 1 : s-1 + c'[i] = c[i] * c'[s] + end + for i in 1 : s # collocation polynomial + z[i] = @.. cont[s-1] * (c'[i] - c[1] + 1) + cont[s-1] + j = s - 2 + while j > 0 + z[i] = @.. z[i] * (c'[i] - c[s-j] + 1) + cont[j] + end + z[i] = @.. z[i] * c'[i] + end + w = @.. TI * z +end + +# Newton iteration +local ndw +η = max(cache.ηold, eps(eltype(integrator.opts.reltol)))^(0.8) +fail_convergence = true +iter = 0 +while iter < maxiters + iter += 1 + integrator.stats.nnonliniter += 1 + + # evaluate function + ff = Vector{eltype(u)}(undef, s) + for i in 1:s + ff[i] = f(uprev + z[i], p, t + c[i] * dt) + end + integrator.stats.nf += 5 + + fw = @.. TI * ff + Mw = Vector{eltype(u)}(undef, s) + if mass_matrix isa UniformScaling # `UniformScaling` doesn't play nicely with broadcast + for i in 1:s + Mw[i] = @.. mass_matrix.λ * w[i] #scaling by eigenvalues + end + else + Mw = mass_matrix * w #standard multiplication + end + + rhs = Vector{eltype(u)}(undef, s) + rhs[1] = @.. fw[1]-γdt * Mw[1] + i = 2 + while i <= s #block by block multiplication + rhs[i] = @.. fw[i] - α[i/2]dt * Mw[i] + β[i/2]dt * Mw[i + 1] + rhs[i + 1] = @.. fw[i + 1] - β[i/2]dt * Mw[i] - α[i/2]dt * Mw[i + 1] + i += 2 + end + + dw = Vector{eltype(u)}(undef, s) + dw[1] = LU1 \ rhs[1] + for i in 2 : (s + 1) / 2 + tmp = LU[i] \ (@.. rhs[2 * i - 2] + rhs[2 * i - 1] * im) + dw[2 * i - 2] = real(tmp) + dw[2 * i - 1] = imag(tmp) + end + integrator.stats.nlsolve += (s + 1) / 2 + + # compute norm of residuals + iter > 1 && (ndwprev = ndw) + atmp = Vector{eltype(u)}(undef, s) + for i in 1:s + atmp[i] = calculate_residuals(dw[i], uprev, u, atol, rtol, internalnorm, t) + end + + ndw = 0 + for i in 1:s + ndw = ndw + internalnorm(atmp[i], t) + end + # check divergence (not in initial step) + + if iter > 1 + θ = ndw / ndwprev + (diverge = θ > 1) && (cache.status = Divergence) + (veryslowconvergence = ndw * θ^(maxiters - iter) > κ * (1 - θ)) && + (cache.status = VerySlowConvergence) + if diverge || veryslowconvergence + break + end + end + + for i in 1 : s + w[i] = @.. w[i] - dw[i] + end + # transform `w` to `z` + z = @.. T * w + + # check stopping criterion + iter > 1 && (η = θ / (1 - θ)) + if η * ndw < κ && (iter > 1 || iszero(ndw) || !iszero(integrator.success_iter)) + # Newton method converges + cache.status = η < alg.fast_convergence_cutoff ? FastConvergence : + Convergence + fail_convergence = false + break + end +end + +if fail_convergence + integrator.force_stepfail = true + integrator.stats.nnonlinconvfail += 1 + return +end +cache.ηold = η +cache.iter = iter + +u = @.. uprev + z[s] + +if adaptive + edt = e ./ dt + tmp = @.. dot(edt, z) + mass_matrix != I && (tmp = mass_matrix * tmp) + utilde = @.. broadcast=false integrator.fsalfirst+tmp + alg.smooth_est && (utilde = LU[1] \ utilde; integrator.stats.nsolve += 1) + atmp = calculate_residuals(utilde, uprev, u, atol, rtol, internalnorm, t) + integrator.EEst = internalnorm(atmp, t) + + if !(integrator.EEst < oneunit(integrator.EEst)) && integrator.iter == 1 || + integrator.u_modified + f0 = f(uprev .+ utilde, p, t) + integrator.stats.nf += 1 + utilde = @.. broadcast=false f0+tmp + alg.smooth_est && (utilde = LU[1] \ utilde; integrator.stats.nsolve += 1) + atmp = calculate_residuals(utilde, uprev, u, atol, rtol, internalnorm, t) + integrator.EEst = internalnorm(atmp, t) + end +end + +if integrator.EEst <= oneunit(integrator.EEst) + cache.dtprev = dt + if alg.extrapolant != :constant + derivatives = Matrix{eltype(u)}(undef, s-1, s-1) + for i in 1 : (s - 1) + for j in i : (s-1) + if i == 1 + derivatives[i, j] = @.. (z[i] - z[i + 1]) / (c[i] - c[i + 1]) #first derivatives + else + derivatives[i, j] = @.. (derivatives[i - 1, j - 1] - derivatives[i - 1, j]) / (c[j - i + 1] - c[j + 1]) #all others + end + end + end + for i in 1 : (s-1) + cache.cont[i] = derivatives[i, i] + end + end +end + +integrator.fsallast = f(u, p, t + dt) +integrator.stats.nf += 1 +integrator.k[1] = integrator.fsalfirst +integrator.k[2] = integrator.fsallast +integrator.u = u +return +end diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl index 10f282f39f..5c15cd1447 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl @@ -259,7 +259,7 @@ function RadauIIA9Tableau(T, T2) e1, e2, e3, e4, e5) end -struct adaptiveRadau(T, T2) +struct adaptiveRadauTableau(T, T2) T:: AbstractMatrix{T} TI::AbstractMatrix{T} γ::T @@ -269,9 +269,9 @@ struct adaptiveRadau(T, T2) e::AbstractVector{T} end -using Polynomials, GenericSchur, GenericLinearAlgebra, LinearAlgebra +using Polynomials, GenericLinearAlgebra, LinearAlgebra, LinearSolve, GenericSchur -function adaptiveRadau(T, T2, s::Int64) +function adaptiveRadauTableau(T, T2, s::Int64) tmp = Vector{BigFloat}(undef, s-1) for i in 1:(s-1) tmp[i] = 0 @@ -300,8 +300,8 @@ function adaptiveRadau(T, T2, s::Int64) end end a = c_q * inverse_c_powers - @show a - b = eigvals(a) + a_inverse = a^(-1) + b = eigvals(a_inverse) γ = real(b[s]) α = Vector{BigFloat}(undef, floor(Int, s/2)) β = Vector{BigFloat}(undef, floor(Int, s/2)) @@ -313,7 +313,41 @@ function adaptiveRadau(T, T2, s::Int64) index = index + 1 i = i + 2 end - f = eigvecs(a) + block = Matrix{BigFloat}(undef, s, s) + for i in 1 : s + for j in 1 : s + block[i, j] = 0 + end + end + block[1,1] = γ + for i in 1 : floor(Int, s/2) + block[2i, 2i] = α[i] + block[2i, 2i+1] = β[i] + block[2i+1, 2i] = -β[i] + block[2i+1, 2i+1] = α[i] + end + @show eigvals(a_inverse) + #@show eigvals(-block) + #=@show eigvecs(-block) + Id = Matrix{BigFloat}(I, s, s) + O = zeros(s^2) + tmp3 = Base.kron(a_inverse, Id) - Base.kron(Id, transpose(block)) + @show det(tmp3) + prob = LinearProblem(tmp3, O) + sol = solve(prob) + T = Matrix{BigFloat}(undef, s, s) + for i in 1:s + for j in 1:s + T[i,j] = sol[j + s * (i-1)] + end + end + @show T + TI = T^(-1)=# + + + + #adaptiveRadauTableau(T, TI, γ, α, β, c, e) end -adaptiveRadau(0, 0, 2) + +adaptiveRadauTableau(0, 0, 3) \ No newline at end of file From 1598f04536c3544881d2efe76e8c4951558cd06e Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan Date: Mon, 5 Aug 2024 21:36:13 -0400 Subject: [PATCH 36/71] format --- .../src/firk_perform_step.jl | 334 +++++++++--------- 1 file changed, 167 insertions(+), 167 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index cb5e7b956e..09096c987a 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1342,197 +1342,197 @@ end @muladd function perform_step!(integrator, cache::adaptiveRadauConstantCache, repeat_step = false, s::Int64) -@unpack t, dt, uprev, u, f, p = integrator -@unpack T, TI, γ, α, β, c, e= cache.tab -@unpack κ, cont = cache -@unpack internalnorm, abstol, reltol, adaptive = integrator.opts -alg = unwrap_alg(integrator, true) -@unpack maxiters = alg -mass_matrix = integrator.f.mass_matrix - -# precalculations rtol pow is (num stages + 1)/(2*num stages) -rtol = @.. broadcast=false reltol^(5 / 8)/10 -atol = @.. broadcast=false rtol*(abstol / reltol) - -γdt, αdt, βdt = γ / dt, α ./ dt, β ./ dt - -J = calc_J(integrator, cache) -LU = Vector{Any}(undef, (s + 1) / 2) -if u isa Number - LU[1] = -γdt * mass_matrix + J - for i in 2 : (s + 1) / 2 - LU[i] = -(α[i - 1]dt + β[i - 1]dt * im) * mass_matrix + J - end -else - LU[1] = lu(-γdt * mass_matrix + J) - for i in 2 : (s + 1) / 2 - LU[i] = lu(-(α[i - 1]dt + β[i - 1]dt * im) * mass_matrix + J) - end -end -integrator.stats.nw += 1 + @unpack t, dt, uprev, u, f, p = integrator + @unpack T, TI, γ, α, β, c, e= cache.tab + @unpack κ, cont = cache + @unpack internalnorm, abstol, reltol, adaptive = integrator.opts + alg = unwrap_alg(integrator, true) + @unpack maxiters = alg + mass_matrix = integrator.f.mass_matrix -if integrator.iter == 1 || integrator.u_modified || alg.extrapolant == :constant - cache.dtprev = one(cache.dtprev) - for i in 1:s - z[i] = w[i] = map(zero, u) - end - for i in 1:s-1 - cont[i] = map(zero, u) - end -else - c' = Vector{eltype(u)}(undef, s) #time stepping - c'[s] = dt / cache.dtprev - for i in 1 : s-1 - c'[i] = c[i] * c'[s] - end - for i in 1 : s # collocation polynomial - z[i] = @.. cont[s-1] * (c'[i] - c[1] + 1) + cont[s-1] - j = s - 2 - while j > 0 - z[i] = @.. z[i] * (c'[i] - c[s-j] + 1) + cont[j] + # precalculations rtol pow is (num stages + 1)/(2*num stages) + rtol = @.. broadcast=false reltol^(5 / 8)/10 + atol = @.. broadcast=false rtol*(abstol / reltol) + + γdt, αdt, βdt = γ / dt, α ./ dt, β ./ dt + + J = calc_J(integrator, cache) + LU = Vector{Any}(undef, (s + 1) / 2) + if u isa Number + LU[1] = -γdt * mass_matrix + J + for i in 2 : (s + 1) / 2 + LU[i] = -(α[i - 1]dt + β[i - 1]dt * im) * mass_matrix + J + end + else + LU[1] = lu(-γdt * mass_matrix + J) + for i in 2 : (s + 1) / 2 + LU[i] = lu(-(α[i - 1]dt + β[i - 1]dt * im) * mass_matrix + J) end - z[i] = @.. z[i] * c'[i] end - w = @.. TI * z -end + integrator.stats.nw += 1 -# Newton iteration -local ndw -η = max(cache.ηold, eps(eltype(integrator.opts.reltol)))^(0.8) -fail_convergence = true -iter = 0 -while iter < maxiters - iter += 1 - integrator.stats.nnonliniter += 1 - - # evaluate function - ff = Vector{eltype(u)}(undef, s) - for i in 1:s - ff[i] = f(uprev + z[i], p, t + c[i] * dt) - end - integrator.stats.nf += 5 - - fw = @.. TI * ff - Mw = Vector{eltype(u)}(undef, s) - if mass_matrix isa UniformScaling # `UniformScaling` doesn't play nicely with broadcast + if integrator.iter == 1 || integrator.u_modified || alg.extrapolant == :constant + cache.dtprev = one(cache.dtprev) for i in 1:s - Mw[i] = @.. mass_matrix.λ * w[i] #scaling by eigenvalues + z[i] = w[i] = map(zero, u) end - else - Mw = mass_matrix * w #standard multiplication + for i in 1:s-1 + cont[i] = map(zero, u) + end + else + c' = Vector{eltype(u)}(undef, s) #time stepping + c'[s] = dt / cache.dtprev + for i in 1 : s-1 + c'[i] = c[i] * c'[s] + end + for i in 1 : s # collocation polynomial + z[i] = @.. cont[s-1] * (c'[i] - c[1] + 1) + cont[s-1] + j = s - 2 + while j > 0 + z[i] = @.. z[i] * (c'[i] - c[s-j] + 1) + cont[j] + end + z[i] = @.. z[i] * c'[i] + end + w = @.. TI * z end - rhs = Vector{eltype(u)}(undef, s) - rhs[1] = @.. fw[1]-γdt * Mw[1] - i = 2 - while i <= s #block by block multiplication - rhs[i] = @.. fw[i] - α[i/2]dt * Mw[i] + β[i/2]dt * Mw[i + 1] - rhs[i + 1] = @.. fw[i + 1] - β[i/2]dt * Mw[i] - α[i/2]dt * Mw[i + 1] - i += 2 - end - - dw = Vector{eltype(u)}(undef, s) - dw[1] = LU1 \ rhs[1] - for i in 2 : (s + 1) / 2 - tmp = LU[i] \ (@.. rhs[2 * i - 2] + rhs[2 * i - 1] * im) - dw[2 * i - 2] = real(tmp) - dw[2 * i - 1] = imag(tmp) - end - integrator.stats.nlsolve += (s + 1) / 2 + # Newton iteration + local ndw + η = max(cache.ηold, eps(eltype(integrator.opts.reltol)))^(0.8) + fail_convergence = true + iter = 0 + while iter < maxiters + iter += 1 + integrator.stats.nnonliniter += 1 - # compute norm of residuals - iter > 1 && (ndwprev = ndw) - atmp = Vector{eltype(u)}(undef, s) - for i in 1:s - atmp[i] = calculate_residuals(dw[i], uprev, u, atol, rtol, internalnorm, t) - end + # evaluate function + ff = Vector{eltype(u)}(undef, s) + for i in 1:s + ff[i] = f(uprev + z[i], p, t + c[i] * dt) + end + integrator.stats.nf += 5 - ndw = 0 - for i in 1:s - ndw = ndw + internalnorm(atmp[i], t) - end - # check divergence (not in initial step) - - if iter > 1 - θ = ndw / ndwprev - (diverge = θ > 1) && (cache.status = Divergence) - (veryslowconvergence = ndw * θ^(maxiters - iter) > κ * (1 - θ)) && - (cache.status = VerySlowConvergence) - if diverge || veryslowconvergence + fw = @.. TI * ff + Mw = Vector{eltype(u)}(undef, s) + if mass_matrix isa UniformScaling # `UniformScaling` doesn't play nicely with broadcast + for i in 1:s + Mw[i] = @.. mass_matrix.λ * w[i] #scaling by eigenvalues + end + else + Mw = mass_matrix * w #standard multiplication + end + + rhs = Vector{eltype(u)}(undef, s) + rhs[1] = @.. fw[1]-γdt * Mw[1] + i = 2 + while i <= s #block by block multiplication + rhs[i] = @.. fw[i] - α[i/2]dt * Mw[i] + β[i/2]dt * Mw[i + 1] + rhs[i + 1] = @.. fw[i + 1] - β[i/2]dt * Mw[i] - α[i/2]dt * Mw[i + 1] + i += 2 + end + + dw = Vector{eltype(u)}(undef, s) + dw[1] = LU1 \ rhs[1] + for i in 2 : (s + 1) / 2 + tmp = LU[i] \ (@.. rhs[2 * i - 2] + rhs[2 * i - 1] * im) + dw[2 * i - 2] = real(tmp) + dw[2 * i - 1] = imag(tmp) + end + integrator.stats.nlsolve += (s + 1) / 2 + + # compute norm of residuals + iter > 1 && (ndwprev = ndw) + atmp = Vector{eltype(u)}(undef, s) + for i in 1:s + atmp[i] = calculate_residuals(dw[i], uprev, u, atol, rtol, internalnorm, t) + end + + ndw = 0 + for i in 1:s + ndw = ndw + internalnorm(atmp[i], t) + end + # check divergence (not in initial step) + + if iter > 1 + θ = ndw / ndwprev + (diverge = θ > 1) && (cache.status = Divergence) + (veryslowconvergence = ndw * θ^(maxiters - iter) > κ * (1 - θ)) && + (cache.status = VerySlowConvergence) + if diverge || veryslowconvergence + break + end + end + + for i in 1 : s + w[i] = @.. w[i] - dw[i] + end + # transform `w` to `z` + z = @.. T * w + + # check stopping criterion + iter > 1 && (η = θ / (1 - θ)) + if η * ndw < κ && (iter > 1 || iszero(ndw) || !iszero(integrator.success_iter)) + # Newton method converges + cache.status = η < alg.fast_convergence_cutoff ? FastConvergence : + Convergence + fail_convergence = false break end end - for i in 1 : s - w[i] = @.. w[i] - dw[i] - end - # transform `w` to `z` - z = @.. T * w - - # check stopping criterion - iter > 1 && (η = θ / (1 - θ)) - if η * ndw < κ && (iter > 1 || iszero(ndw) || !iszero(integrator.success_iter)) - # Newton method converges - cache.status = η < alg.fast_convergence_cutoff ? FastConvergence : - Convergence - fail_convergence = false - break + if fail_convergence + integrator.force_stepfail = true + integrator.stats.nnonlinconvfail += 1 + return end -end + cache.ηold = η + cache.iter = iter -if fail_convergence - integrator.force_stepfail = true - integrator.stats.nnonlinconvfail += 1 - return -end -cache.ηold = η -cache.iter = iter - -u = @.. uprev + z[s] - -if adaptive - edt = e ./ dt - tmp = @.. dot(edt, z) - mass_matrix != I && (tmp = mass_matrix * tmp) - utilde = @.. broadcast=false integrator.fsalfirst+tmp - alg.smooth_est && (utilde = LU[1] \ utilde; integrator.stats.nsolve += 1) - atmp = calculate_residuals(utilde, uprev, u, atol, rtol, internalnorm, t) - integrator.EEst = internalnorm(atmp, t) - - if !(integrator.EEst < oneunit(integrator.EEst)) && integrator.iter == 1 || - integrator.u_modified - f0 = f(uprev .+ utilde, p, t) - integrator.stats.nf += 1 - utilde = @.. broadcast=false f0+tmp + u = @.. uprev + z[s] + + if adaptive + edt = e ./ dt + tmp = @.. dot(edt, z) + mass_matrix != I && (tmp = mass_matrix * tmp) + utilde = @.. broadcast=false integrator.fsalfirst+tmp alg.smooth_est && (utilde = LU[1] \ utilde; integrator.stats.nsolve += 1) atmp = calculate_residuals(utilde, uprev, u, atol, rtol, internalnorm, t) integrator.EEst = internalnorm(atmp, t) + + if !(integrator.EEst < oneunit(integrator.EEst)) && integrator.iter == 1 || + integrator.u_modified + f0 = f(uprev .+ utilde, p, t) + integrator.stats.nf += 1 + utilde = @.. broadcast=false f0+tmp + alg.smooth_est && (utilde = LU[1] \ utilde; integrator.stats.nsolve += 1) + atmp = calculate_residuals(utilde, uprev, u, atol, rtol, internalnorm, t) + integrator.EEst = internalnorm(atmp, t) + end end -end -if integrator.EEst <= oneunit(integrator.EEst) - cache.dtprev = dt - if alg.extrapolant != :constant - derivatives = Matrix{eltype(u)}(undef, s-1, s-1) - for i in 1 : (s - 1) - for j in i : (s-1) - if i == 1 - derivatives[i, j] = @.. (z[i] - z[i + 1]) / (c[i] - c[i + 1]) #first derivatives - else - derivatives[i, j] = @.. (derivatives[i - 1, j - 1] - derivatives[i - 1, j]) / (c[j - i + 1] - c[j + 1]) #all others + if integrator.EEst <= oneunit(integrator.EEst) + cache.dtprev = dt + if alg.extrapolant != :constant + derivatives = Matrix{eltype(u)}(undef, s-1, s-1) + for i in 1 : (s - 1) + for j in i : (s-1) + if i == 1 + derivatives[i, j] = @.. (z[i] - z[i + 1]) / (c[i] - c[i + 1]) #first derivatives + else + derivatives[i, j] = @.. (derivatives[i - 1, j - 1] - derivatives[i - 1, j]) / (c[j - i + 1] - c[j + 1]) #all others + end end end - end - for i in 1 : (s-1) - cache.cont[i] = derivatives[i, i] + for i in 1 : (s-1) + cache.cont[i] = derivatives[i, i] + end end end -end -integrator.fsallast = f(u, p, t + dt) -integrator.stats.nf += 1 -integrator.k[1] = integrator.fsalfirst -integrator.k[2] = integrator.fsallast -integrator.u = u -return + integrator.fsallast = f(u, p, t + dt) + integrator.stats.nf += 1 + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.u = u + return end From 45641a3edd1ed70cb26b3149399774a3bb861554 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan Date: Thu, 8 Aug 2024 21:43:22 -0400 Subject: [PATCH 37/71] calculate T --- .../src/OrdinaryDiffEqFIRK.jl | 2 +- lib/OrdinaryDiffEqFIRK/src/alg_utils.jl | 1 + lib/OrdinaryDiffEqFIRK/src/algorithms.jl | 38 +++++++++++++ .../src/firk_perform_step.jl | 2 +- lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl | 53 +++++++------------ .../src/integrator_interface.jl | 2 +- 6 files changed, 61 insertions(+), 37 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/OrdinaryDiffEqFIRK.jl b/lib/OrdinaryDiffEqFIRK/src/OrdinaryDiffEqFIRK.jl index f003751b83..a3b1e3b09c 100644 --- a/lib/OrdinaryDiffEqFIRK/src/OrdinaryDiffEqFIRK.jl +++ b/lib/OrdinaryDiffEqFIRK/src/OrdinaryDiffEqFIRK.jl @@ -30,6 +30,6 @@ include("firk_tableaus.jl") include("firk_perform_step.jl") include("integrator_interface.jl") -export RadauIIA3, RadauIIA5, RadauIIA9 +export RadauIIA3, RadauIIA5, RadauIIA9, AdaptiveRadau end diff --git a/lib/OrdinaryDiffEqFIRK/src/alg_utils.jl b/lib/OrdinaryDiffEqFIRK/src/alg_utils.jl index 46dfcb8206..5953ecffc1 100644 --- a/lib/OrdinaryDiffEqFIRK/src/alg_utils.jl +++ b/lib/OrdinaryDiffEqFIRK/src/alg_utils.jl @@ -7,6 +7,7 @@ alg_order(alg::RadauIIA9) = 9 isfirk(alg::RadauIIA3) = true isfirk(alg::RadauIIA5) = true isfirk(alg::RadauIIA9) = true +isfirk(alg::AdaptiveRadau) = true alg_adaptive_order(alg::RadauIIA3) = 1 alg_adaptive_order(alg::RadauIIA5) = 3 diff --git a/lib/OrdinaryDiffEqFIRK/src/algorithms.jl b/lib/OrdinaryDiffEqFIRK/src/algorithms.jl index d95430f5a5..b11057c77c 100644 --- a/lib/OrdinaryDiffEqFIRK/src/algorithms.jl +++ b/lib/OrdinaryDiffEqFIRK/src/algorithms.jl @@ -153,3 +153,41 @@ function RadauIIA9(; chunk_size = Val{0}(), autodiff = Val{true}(), controller, step_limiter!) end + +struct AdaptiveRadau{CS, AD, F, P, FDT, ST, CJ, Tol, C1, C2, StepLimiter} <: + OrdinaryDiffEqNewtonAdaptiveAlgorithm{CS, AD, FDT, ST, CJ} + linsolve::F + precs::P + smooth_est::Bool + extrapolant::Symbol + κ::Tol + maxiters::Int + fast_convergence_cutoff::C1 + new_W_γdt_cutoff::C2 + controller::Symbol + step_limiter!::StepLimiter +end + +function AdaptiveRadau(; chunk_size = Val{0}(), autodiff = Val{true}(), + standardtag = Val{true}(), concrete_jac = nothing, + diff_type = Val{:forward}, + linsolve = nothing, precs = DEFAULT_PRECS, + extrapolant = :dense, fast_convergence_cutoff = 1 // 5, + new_W_γdt_cutoff = 1 // 5, + controller = :Predictive, κ = nothing, maxiters = 10, smooth_est = true, + step_limiter! = trivial_limiter!) + RadauIIA9{_unwrap_val(chunk_size), _unwrap_val(autodiff), typeof(linsolve), + typeof(precs), diff_type, _unwrap_val(standardtag), _unwrap_val(concrete_jac), + typeof(κ), typeof(fast_convergence_cutoff), + typeof(new_W_γdt_cutoff), typeof(step_limiter!)}(linsolve, + precs, + smooth_est, + extrapolant, + κ, + maxiters, + fast_convergence_cutoff, + new_W_γdt_cutoff, + controller, + step_limiter!) +end + diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index 09096c987a..7077b291ff 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1524,7 +1524,7 @@ end end end for i in 1 : (s-1) - cache.cont[i] = derivatives[i, i] + cache.cont[i] = derivatives[i, s - 1] end end end diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl index 5c15cd1447..217049d94c 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl @@ -292,7 +292,7 @@ function adaptiveRadauTableau(T, T2, s::Int64) c_powers[i,j] = c[i]^(j-1) end end - inverse_c_powers = c_powers^(-1) + inverse_c_powers = inv(c_powers) c_q = Matrix{BigFloat}(undef, s, s) for i in 1:s for j in 1:s @@ -300,7 +300,7 @@ function adaptiveRadauTableau(T, T2, s::Int64) end end a = c_q * inverse_c_powers - a_inverse = a^(-1) + a_inverse = inv(a) b = eigvals(a_inverse) γ = real(b[s]) α = Vector{BigFloat}(undef, floor(Int, s/2)) @@ -309,45 +309,30 @@ function adaptiveRadauTableau(T, T2, s::Int64) i = 1 while i <= (s-1) α[index] = real(b[i]) - β[index] = imag(b[i]) + β[index] = imag(b[i + 1]) index = index + 1 i = i + 2 end - block = Matrix{BigFloat}(undef, s, s) - for i in 1 : s - for j in 1 : s - block[i, j] = 0 - end - end - block[1,1] = γ - for i in 1 : floor(Int, s/2) - block[2i, 2i] = α[i] - block[2i, 2i+1] = β[i] - block[2i+1, 2i] = -β[i] - block[2i+1, 2i+1] = α[i] + eigvec = eigvecs(a) + vecs = Vector{Vector{BigFloat}}(undef, s) + i = 1 + index = 2 + while i < s + vecs[index] = real(eigvec[:, i] ./ eigvec[s,i]) + vecs[index + 1] = -imag(eigvec[:, i] ./ eigvec[s,i]) + index += 2 + i += 2 end - @show eigvals(a_inverse) - #@show eigvals(-block) - #=@show eigvecs(-block) - Id = Matrix{BigFloat}(I, s, s) - O = zeros(s^2) - tmp3 = Base.kron(a_inverse, Id) - Base.kron(Id, transpose(block)) - @show det(tmp3) - prob = LinearProblem(tmp3, O) - sol = solve(prob) + vecs[1] = real(eigvec[:, s]) + tmp3 = vcat(vecs) T = Matrix{BigFloat}(undef, s, s) - for i in 1:s - for j in 1:s - T[i,j] = sol[j + s * (i-1)] + for j in 1 : s + for i in 1 : s + T[i, j] = tmp3[j][i] end end - @show T - TI = T^(-1)=# - - - + TI = inv(T) #adaptiveRadauTableau(T, TI, γ, α, β, c, e) end - -adaptiveRadauTableau(0, 0, 3) \ No newline at end of file +adaptiveRadauTableau(0, 0, 1) diff --git a/lib/OrdinaryDiffEqFIRK/src/integrator_interface.jl b/lib/OrdinaryDiffEqFIRK/src/integrator_interface.jl index 7f892e5f09..8570f204f0 100644 --- a/lib/OrdinaryDiffEqFIRK/src/integrator_interface.jl +++ b/lib/OrdinaryDiffEqFIRK/src/integrator_interface.jl @@ -1,4 +1,4 @@ -@inline function DiffEqBase.get_tmp_cache(integrator, alg::Union{RadauIIA3, RadauIIA5, RadauIIA9}, +@inline function DiffEqBase.get_tmp_cache(integrator, alg::Union{RadauIIA3, RadauIIA5, RadauIIA9, adaptiveRadau}, cache::OrdinaryDiffEqMutableCache) (cache.tmp, cache.atmp) end From a68502859bf7f5a245c91079ff068e1764cf591d Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan Date: Sat, 10 Aug 2024 18:12:22 -0400 Subject: [PATCH 38/71] add in-place --- .../src/firk_perform_step.jl | 272 +++++++++++++++++- lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl | 20 +- 2 files changed, 271 insertions(+), 21 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index 7077b291ff..81a4f814c0 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1024,7 +1024,7 @@ end @unpack dw1, ubuff, dw23, dw45, cubuff1, cubuff2 = cache @unpack k, k2, k3, k4, k5, fw1, fw2, fw3, fw4, fw5 = cache @unpack J, W1, W2, W3 = cache - @unpack tmp, tmp2, tmp3, tmp4, tmp5, tmp6, atmp, jac_config, linsolve1, linsolve2, rtol, atol, step_limiter! = cache + @unpack tmp, tmp2, tmp3, tmp4, tmp5, tmp6, atmp, jac_config, linsolve1, linsolve2, linsolve3, rtol, atol, step_limiter! = cache @unpack internalnorm, abstol, reltol, adaptive = integrator.opts alg = unwrap_alg(integrator, true) @unpack maxiters = alg @@ -1078,26 +1078,26 @@ end c2′ = c2 * c5′ c3′ = c3 * c5′ c4′ = c4 * c5′ - z1 = @.. broadcast=false c1′*(cont1 + + @.. broadcast=false z1 = c1′*(cont1 + (c1′ - c3m1) * (cont2 + (c1′ - c2m1) * (cont3 + (c1′ - c1m1) * cont4))) - z2 = @.. broadcast=false c2′*(cont1 + + @.. broadcast=false z2 = c2′*(cont1 + (c2′ - c3m1) * (cont2 + (c2′ - c2m1) * (cont3 + (c2′ - c1m1) * cont4))) - z3 = @.. broadcast=false c3′*(cont1 + + @.. broadcast=false z3 = c3′*(cont1 + (c3′ - c3m1) * (cont2 + (c3′ - c2m1) * (cont3 + (c3′ - c1m1) * cont4))) - z4 = @.. broadcast=false c4′*(cont1 + + @.. broadcast=false z4 = c4′*(cont1 + (c4′ - c3m1) * (cont2 + (c4′ - c2m1) * (cont3 + (c4′ - c1m1) * cont4))) - z5 = @.. broadcast=false c5′*(cont1 + + @.. broadcast=false z5 = c5′*(cont1 + (c5′ - c3m1) * (cont2 + (c5′ - c2m1) * (cont3 + (c5′ - c1m1) * cont4))) - w1 = @.. broadcast=false TI11*z1+TI12*z2+TI13*z3+TI14*z4+TI15*z5 - w2 = @.. broadcast=false TI21*z1+TI22*z2+TI23*z3+TI24*z4+TI25*z5 - w3 = @.. broadcast=false TI31*z1+TI32*z2+TI33*z3+TI34*z4+TI35*z5 - w4 = @.. broadcast=false TI41*z1+TI42*z2+TI43*z3+TI44*z4+TI45*z5 - w5 = @.. broadcast=false TI51*z1+TI52*z2+TI53*z3+TI54*z4+TI55*z5 + @.. broadcast=false w1 = TI11*z1+TI12*z2+TI13*z3+TI14*z4+TI15*z5 + @.. broadcast=false w2 = TI21*z1+TI22*z2+TI23*z3+TI24*z4+TI25*z5 + @.. broadcast=false w3 = TI31*z1+TI32*z2+TI33*z3+TI34*z4+TI35*z5 + @.. broadcast=false w4 = TI41*z1+TI42*z2+TI43*z3+TI44*z4+TI45*z5 + @.. broadcast=false w5 = TI51*z1+TI52*z2+TI53*z3+TI54*z4+TI55*z5 end # Newton iteration @@ -1376,7 +1376,7 @@ end for i in 1:s z[i] = w[i] = map(zero, u) end - for i in 1:s-1 + for i in 1:(s-1) cont[i] = map(zero, u) end else @@ -1463,9 +1463,8 @@ end end end - for i in 1 : s - w[i] = @.. w[i] - dw[i] - end + w = @.. w - dw + # transform `w` to `z` z = @.. T * w @@ -1536,3 +1535,246 @@ end integrator.u = u return end + +@muladd function perform_step!(integrator, cache::adaptiveRadauCache, repeat_step = false) + @unpack t, dt, uprev, u, f, p, fsallast, fsalfirst = integrator + @unpack T, TI, γ, α, β, c, e= cache.tab + @unpack κ, cont, z, w = cache + @unpack dw1, ubuff, dw2, cubuff1, cubuff2 = cache + @unpack k, fw, J, W1, W2 = cache + @unpack tmp, atmp, jac_config, linsolve1, linsolve2, rtol, atol, step_limiter! = cache + @unpack internalnorm, abstol, reltol, adaptive = integrator.opts + alg = unwrap_alg(integrator, true) + @unpack maxiters = alg + mass_matrix = integrator.f.mass_matrix + + # precalculations + + γdt, αdt, βdt = γ / dt, α ./ dt, β ./ dt + (new_jac = do_newJ(integrator, alg, cache, repeat_step)) && + (calc_J!(J, integrator, cache); cache.W_γdt = dt) + if (new_W = do_newW(integrator, alg, new_jac, cache.W_γdt)) + @inbounds for II in CartesianIndices(J) + W1[II] = -γdt * mass_matrix[Tuple(II)...] + J[II] + for i in 1 : (s - 1) / 2 + W2[i][II] = -(α[i]dt + β[i]dt * im) * mass_matrix[Tuple(II)...] + J[II] + end + end + integrator.stats.nw += 1 + end + + # TODO better initial guess + if integrator.iter == 1 || integrator.u_modified || alg.extrapolant == :constant + cache.dtprev = one(cache.dtprev) + uzero = zero(eltype(u)) + for i in 1:s + @.. z[i] = w[i] = uzero + end + for i in 1:(s-1) + @.. cache.cont[i] = uzero + end + else + c' = Vector{eltype(u)}(undef, s) #time stepping + c'[s] = dt / cache.dtprev + for i in 1 : s-1 + c'[i] = c[i] * c'[s] + end + for i in 1 : s # collocation polynomial + @.. z[i] = cont[s-1] * (c'[i] - c[1] + 1) + cont[s-1] + j = s - 2 + while j > 0 + @.. z[i] = z[i] * (c'[i] - c[s-j] + 1) + cont[j] + end + @.. z[i] = z[i] * c'[i] + end + @.. w = TI * z + end + + # Newton iteration + local ndw + η = max(cache.ηold, eps(eltype(integrator.opts.reltol)))^(0.8) + fail_convergence = true + iter = 0 + while iter < maxiters + iter += 1 + integrator.stats.nnonliniter += 1 + + # evaluate function + k[1] = fsallast + for i in 1 : s + @.. tmp = uprev + z[i] + f(k[i], tmp, p, t + c[i] * dt) + end + integrator.stats.nf += s + + @.. fw = TI * k + if mass_matrix === I + Mw = w + elseif mass_matrix isa UniformScaling + for i in 1 : s + mul!(z[i], mass_matrix.λ, w[i]) + end + Mw = z + else + for i in 1 : s + mul!(z[i], mass_matrix.λ, w[i]) + end + Mw = z + end + + @.. ubuff = fw[1] - γdt * Mw[1] + needfactor = iter == 1 && new_W + + linsolve1 = cache.linsolve1 + linres = Vector{BigFloat}(undef, s) + if needfactor + linres[1] = dolinsolve(integrator, linsolve1; A = W1, b = _vec(ubuff), + linu = _vec(dw1)) + else + linres[1] = dolinsolve(integrator, linsolve1; A = nothing, b = _vec(ubuff), + linu = _vec(dw1)) + end + + cache.linsolve1 = linres1.cache + + for i in 1 : (s-1)/2 + @.. broadcast=false cubuff[i]=complex( + fw2 - α[i]dt * Mw[2*i] + β[i]dt * Mw[2*i + 1], fw3 - β[i]dt * Mw[2*i] - α[i]dt * Mw[2*i + 1]) + linsolve2[i] = cache.linsolve2[i] + if needfactor + linres[i + 1] = dolinsolve(integrator, linsolve2[i]; A = W2[i], b = _vec(cubuff[i]), + linu = _vec(dw2[i])) + else + linres[i + 1] = dolinsolve(integrator, linsolve2[i]; A = nothing, b = _vec(cubuff[i]), + linu = _vec(dw2[i])) + end + cache.linsolve2[i] = linres[i + 1].cache + end + + integrator.stats.nsolve += (s+1) / 2 + dw[1] = dw1 + i = 2 + while i <= s + dw[i] = z[i] + dw[i + 1] = z[i + 1] + @.. dw[i] = real(dw2[i - 1]) + @.. dw[i + 1] = imag(dw2[i - 1]) + i += 2 + end + + # compute norm of residuals + iter > 1 && (ndwprev = ndw) + ndws = Vector{BigFloat}(undef, s) + calculate_residuals!(atmp, dw[1], uprev, u, atol, rtol, internalnorm, t) + ndws[1] = internalnorm(atmp, t) + for i in 2:s + calculate_residuals!(atmp, dw[i - 1], uprev, u, atol, rtol, internalnorm, t) + ndws[i] = internalnorm(atmp, t) + end + + ndw = 0 + for i in 1 : s + ndw += ndws[i] + end + + # check divergence (not in initial step) + + if iter > 1 + θ = ndw / ndwprev + (diverge = θ > 1) && (cache.status = Divergence) + (veryslowconvergence = ndw * θ^(maxiters - iter) > κ * (1 - θ)) && + (cache.status = VerySlowConvergence) + if diverge || veryslowconvergence + break + end + end + + @.. w = w - dw + + # transform `w` to `z` + @.. z = T * w + # check stopping criterion + + iter > 1 && (η = θ / (1 - θ)) + if η * ndw < κ && (iter > 1 || iszero(ndw) || !iszero(integrator.success_iter)) + # Newton method converges + cache.status = η < alg.fast_convergence_cutoff ? FastConvergence : + Convergence + fail_convergence = false + break + end + end + if fail_convergence + integrator.force_stepfail = true + integrator.stats.nnonlinconvfail += 1 + return + end + + cache.ηold = η + cache.iter = iter + + @.. broadcast=false u=uprev + z[s] + + step_limiter!(u, integrator, p, t + dt) + + if adaptive + utilde = w2 + edt = e./dt + @.. tmp= dot(edt, z) + mass_matrix != I && (mul!(w1, mass_matrix, tmp); copyto!(tmp, w1)) + @.. ubuff=integrator.fsalfirst + tmp + + if alg.smooth_est + linres1 = dolinsolve(integrator, linres1.cache; b = _vec(ubuff), + linu = _vec(utilde)) + cache.linsolve1 = linres1.cache + integrator.stats.nsolve += 1 + end + + # RadauIIA5 needs a transformed rtol and atol see + # https://github.com/luchr/ODEInterface.jl/blob/0bd134a5a358c4bc13e0fb6a90e27e4ee79e0115/src/radau5.f#L399-L421 + calculate_residuals!(atmp, utilde, uprev, u, atol, rtol, internalnorm, t) + integrator.EEst = internalnorm(atmp, t) + + if !(integrator.EEst < oneunit(integrator.EEst)) && integrator.iter == 1 || + integrator.u_modified + @.. broadcast=false utilde=uprev + utilde + f(fsallast, utilde, p, t) + integrator.stats.nf += 1 + @.. broadcast=false ubuff=fsallast + tmp + + if alg.smooth_est + linres1 = dolinsolve(integrator, linres1.cache; b = _vec(ubuff), + linu = _vec(utilde)) + cache.linsolve1 = linres1.cache + integrator.stats.nsolve += 1 + end + + calculate_residuals!(atmp, utilde, uprev, u, atol, rtol, internalnorm, t) + integrator.EEst = internalnorm(atmp, t) + end + end + + if integrator.EEst <= oneunit(integrator.EEst) + cache.dtprev = dt + if alg.extrapolant != :constant + derivatives = Matrix{eltype(u)}(undef, s-1, s-1) + for i in 1 : (s - 1) + for j in i : (s-1) + if i == 1 + @.. derivatives[i, j] = (z[i] - z[i + 1]) / (c[i] - c[i + 1]) #first derivatives + else + @.. derivatives[i, j] = (derivatives[i - 1, j - 1] - derivatives[i - 1, j]) / (c[j - i + 1] - c[j + 1]) #all others + end + end + end + for i in 1 : (s-1) + cache.cont[i] = derivatives[i, s - 1] + end + end + end + + f(fsallast, u, p, t + dt) + integrator.stats.nf += 1 + return +end diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl index 217049d94c..478bdd4240 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl @@ -269,7 +269,7 @@ struct adaptiveRadauTableau(T, T2) e::AbstractVector{T} end -using Polynomials, GenericLinearAlgebra, LinearAlgebra, LinearSolve, GenericSchur +using Polynomials, GenericLinearAlgebra, LinearAlgebra, LinearSolve, GenericSchur, BSeries function adaptiveRadauTableau(T, T2, s::Int64) tmp = Vector{BigFloat}(undef, s-1) @@ -301,15 +301,19 @@ function adaptiveRadauTableau(T, T2, s::Int64) end a = c_q * inverse_c_powers a_inverse = inv(a) - b = eigvals(a_inverse) + b = Vector{Bigfloat}(undef, s) + for i in 1 : s + b[i] = a[s, i] + end + vals = eigvals(a_inverse) γ = real(b[s]) α = Vector{BigFloat}(undef, floor(Int, s/2)) β = Vector{BigFloat}(undef, floor(Int, s/2)) index = 1 i = 1 while i <= (s-1) - α[index] = real(b[i]) - β[index] = imag(b[i + 1]) + α[index] = real(vals[i]) + β[index] = imag(vals[i + 1]) index = index + 1 i = i + 2 end @@ -332,7 +336,11 @@ function adaptiveRadauTableau(T, T2, s::Int64) end end TI = inv(T) - #adaptiveRadauTableau(T, TI, γ, α, β, c, e) + b_hat = Vector{BigFloat}(undef, s) + embedded = bseries(a, b_hat, c, s - 2) + + #e = b_hat - b + #adaptiveRadautableau(T, TI, γ, α, β, c, e) end -adaptiveRadauTableau(0, 0, 1) +adaptiveRadauTableau(0, 0, 3) From 91cd34bad83328445c6f1a11b1e3f359fcd305cc Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan Date: Sat, 10 Aug 2024 21:45:57 -0400 Subject: [PATCH 39/71] Update firk_perform_step.jl --- lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl | 6 ++---- 1 file changed, 2 insertions(+), 4 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index 81a4f814c0..afd2392a48 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1665,10 +1665,8 @@ end # compute norm of residuals iter > 1 && (ndwprev = ndw) ndws = Vector{BigFloat}(undef, s) - calculate_residuals!(atmp, dw[1], uprev, u, atol, rtol, internalnorm, t) - ndws[1] = internalnorm(atmp, t) - for i in 2:s - calculate_residuals!(atmp, dw[i - 1], uprev, u, atol, rtol, internalnorm, t) + for i in 1:s + calculate_residuals!(atmp, dw[i], uprev, u, atol, rtol, internalnorm, t) ndws[i] = internalnorm(atmp, t) end From d5beb291f9f5224a133be0b9ce55c370f75427d6 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Sat, 10 Aug 2024 21:48:48 -0400 Subject: [PATCH 40/71] Update integrator_interface.jl --- src/integrators/integrator_interface.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/integrators/integrator_interface.jl b/src/integrators/integrator_interface.jl index a287a3d78b..d434ffcc19 100644 --- a/src/integrators/integrator_interface.jl +++ b/src/integrators/integrator_interface.jl @@ -113,7 +113,7 @@ end end # avoid method ambiguity -# for typ in (Union{RadauIIA3, RadauIIA5, RadauIIA9}) +# for typ in (Union{RadauIIA3, RadauIIA5, RadauIIA9, AdaptiveRadau}) # @eval @inline function DiffEqBase.get_tmp_cache(integrator, alg::$typ, # cache::OrdinaryDiffEqConstantCache) # nothing From 9fee28b49b2c9e2793237841f495b7228fd171fc Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Sat, 10 Aug 2024 21:50:27 -0400 Subject: [PATCH 41/71] Update integrator_interface.jl --- lib/OrdinaryDiffEqFIRK/src/integrator_interface.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/integrator_interface.jl b/lib/OrdinaryDiffEqFIRK/src/integrator_interface.jl index 8570f204f0..dc4bbb1e88 100644 --- a/lib/OrdinaryDiffEqFIRK/src/integrator_interface.jl +++ b/lib/OrdinaryDiffEqFIRK/src/integrator_interface.jl @@ -1,4 +1,4 @@ -@inline function DiffEqBase.get_tmp_cache(integrator, alg::Union{RadauIIA3, RadauIIA5, RadauIIA9, adaptiveRadau}, +@inline function DiffEqBase.get_tmp_cache(integrator, alg::Union{RadauIIA3, RadauIIA5, RadauIIA9, AdaptiveRadau}, cache::OrdinaryDiffEqMutableCache) (cache.tmp, cache.atmp) end From 67bb0fe3ddd8e77def9cadbe52f351201972d514 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan Date: Tue, 13 Aug 2024 19:54:16 -0400 Subject: [PATCH 42/71] rename, formatting --- lib/OrdinaryDiffEqFIRK/src/algorithms.jl | 7 +- lib/OrdinaryDiffEqFIRK/src/firk_caches.jl | 46 +++--- .../src/firk_perform_step.jl | 142 +++++++++--------- lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl | 69 ++++----- lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl | 2 + 5 files changed, 135 insertions(+), 131 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/algorithms.jl b/lib/OrdinaryDiffEqFIRK/src/algorithms.jl index b11057c77c..ba4c51c0d0 100644 --- a/lib/OrdinaryDiffEqFIRK/src/algorithms.jl +++ b/lib/OrdinaryDiffEqFIRK/src/algorithms.jl @@ -166,17 +166,18 @@ struct AdaptiveRadau{CS, AD, F, P, FDT, ST, CJ, Tol, C1, C2, StepLimiter} <: new_W_γdt_cutoff::C2 controller::Symbol step_limiter!::StepLimiter + num_stages::Int end function AdaptiveRadau(; chunk_size = Val{0}(), autodiff = Val{true}(), standardtag = Val{true}(), concrete_jac = nothing, - diff_type = Val{:forward}, + diff_type = Val{:forward}, num_stages = 5, linsolve = nothing, precs = DEFAULT_PRECS, extrapolant = :dense, fast_convergence_cutoff = 1 // 5, new_W_γdt_cutoff = 1 // 5, controller = :Predictive, κ = nothing, maxiters = 10, smooth_est = true, step_limiter! = trivial_limiter!) - RadauIIA9{_unwrap_val(chunk_size), _unwrap_val(autodiff), typeof(linsolve), + AdaptiveRadau{_unwrap_val(chunk_size), _unwrap_val(autodiff), typeof(linsolve), typeof(precs), diff_type, _unwrap_val(standardtag), _unwrap_val(concrete_jac), typeof(κ), typeof(fast_convergence_cutoff), typeof(new_W_γdt_cutoff), typeof(step_limiter!)}(linsolve, @@ -188,6 +189,6 @@ function AdaptiveRadau(; chunk_size = Val{0}(), autodiff = Val{true}(), fast_convergence_cutoff, new_W_γdt_cutoff, controller, - step_limiter!) + step_limiter!, num_stages) end diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl index cf8bcd5c5b..40f6631765 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl @@ -468,7 +468,7 @@ function alg_cache(alg::RadauIIA9, u, rate_prototype, ::Type{uEltypeNoUnits}, Convergence, alg.step_limiter!) end -mutable struct adaptiveRadauConstantCache{F, Tab, Tol, Dt, U, JType, S} <: +mutable struct adaptiveRadauConstantCache{S, F, Tab, Tol, Dt, U, JType} <: OrdinaryDiffEqConstantCache uf::F tab::Tab @@ -482,16 +482,16 @@ status::NLStatus J::JType end -function alg_cache(alg::adaptiveRadau, s :: Int64, u, rate_prototype, ::Type{uEltypeNoUnits}, +function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} uf = UDerivativeWrapper(f, t, p) uToltype = constvalue(uBottomEltypeNoUnits) -tab = adaptiveRadau(uToltype, constvalue(tTypeNoUnits), s) +tab = adaptiveRadau(uToltype, constvalue(tTypeNoUnits), alg.num_stages) -cont = Vector{typeof(u)}(undef, s-1) -for i in 1:s-1 +cont = Vector{typeof(u)}(undef, num_stages - 1) +for i in 1: (num_stages - 1) cont[i] = zero(u) end @@ -539,7 +539,7 @@ mutable struct adaptiveRadauCache{uType, cuType, uNoUnitsType, rateType, JType, step_limiter!::StepLimiter end -function alg_cache(alg::adaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits}, +function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits}, ::Type{uBottomEltypeNoUnits}, ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} @@ -549,34 +549,34 @@ tab = RadauIIA9Tableau(uToltype, constvalue(tTypeNoUnits)) κ = alg.κ !== nothing ? convert(uToltype, alg.κ) : convert(uToltype, 1 // 100) -z = Vector{typeof(u)}(undef, s) -w = Vector{typeof(u)}(undef, s) +z = Vector{typeof(u)}(undef, num_stages) +w = Vector{typeof(u)}(undef, num_stages) for i in 1:s z[i] = w[i] = zero(u) end dw1 = zero(u) ubuff = zero(u) -dw2 = Vector{typeof(u)}(undef, floor(Int, s/2)) -for i in 1 : floor(Int, s/2) +dw2 = Vector{typeof(u)}(undef, floor(Int, num_stages/2)) +for i in 1 : floor(Int, num_stages/2) dw2[i] = similar(u, Complex{eltype(u)}) recursivefill!(dw[i], false) end -cubuff = Vector{typeof(u)}(undef, floor(Int, s/2)) -for i in 1 :floor(Int, s/2) +cubuff = Vector{typeof(u)}(undef, floor(Int, num_stages/2)) +for i in 1 :floor(Int, num_stages/2) cubuff[i] = similar(u, Complex{eltype(u)}) recursivefill!(cubuff[i], false) end -cont = Vector{typeof(u)}(undef, s-1) -for i in 1:s-1 +cont = Vector{typeof(u)}(undef, num_stages - 1) +for i in 1: (num_stages - 1) cont[i] = zero(u) end fsalfirst = zero(rate_prototype) -fw = Vector{typeof(rate_prototype)}(undef, s) -k = Vector{typeof(rate_prototype)}(undef, s) -for i in 1:s +fw = Vector{typeof(rate_prototype)}(undef, num_stages) +k = Vector{typeof(rate_prototype)}(undef, num_stages) +for i in 1: num_stages k[i] = fw[i] = zero(rate_prototype) end @@ -584,16 +584,16 @@ J, W1 = build_J_W(alg, u, uprev, p, t, dt, f, uEltypeNoUnits, Val(true)) if J isa AbstractSciMLOperator error("Non-concrete Jacobian not yet supported by RadauIIA5.") end -W2 = vector{typeof(Complex{W1})}(undef, floor(Int, s/2)) -for i in 1 : floor(Int, s/2) +W2 = vector{typeof(Complex{W1})}(undef, floor(Int, num_stages/2)) +for i in 1 : floor(Int, num_stages/2) W2[i] = similar(J, Complex{eltype(W1)}) recursivefill!(w2[i], false) end du1 = zero(rate_prototype) -tmp = Vector{typeof(u)}(undef, binomial(s,2)) -for i in 1 : binomial(s,2) +tmp = Vector{typeof(u)}(undef, binomial(num_stages,2)) +for i in 1 : binomial(num_stages,2) tmp[i] = zero(u) end @@ -606,8 +606,8 @@ linprob = LinearProblem(W1, _vec(ubuff); u0 = _vec(dw1)) linsolve1 = init(linprob, alg.linsolve, alias_A = true, alias_b = true, assumptions = LinearSolve.OperatorAssumptions(true)) -linsolve2 = Vector{typeof(linsolve1)}(undef, floor(Int, s/2)) -for i in 1 : floor(int, s/2) +linsolve2 = Vector{typeof(linsolve1)}(undef, floor(Int, num_stages/2)) +for i in 1 : floor(int, num_stages/2) linprob = LinearProblem(W2[i], _vec(cubuff[i]); u0 = _vec(dw2[i])) linsolve2 = init(linprob, alg.linsolve, alias_A = true, alias_b = true, assumptions = LinearSolve.OperatorAssumptions(true)) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index afd2392a48..51313203a6 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1341,9 +1341,9 @@ end end @muladd function perform_step!(integrator, cache::adaptiveRadauConstantCache, - repeat_step = false, s::Int64) + repeat_step = false) @unpack t, dt, uprev, u, f, p = integrator - @unpack T, TI, γ, α, β, c, e= cache.tab + @unpack T, TI, γ, α, β, c, e, num_stages = cache.tab @unpack κ, cont = cache @unpack internalnorm, abstol, reltol, adaptive = integrator.opts alg = unwrap_alg(integrator, true) @@ -1357,39 +1357,39 @@ end γdt, αdt, βdt = γ / dt, α ./ dt, β ./ dt J = calc_J(integrator, cache) - LU = Vector{Any}(undef, (s + 1) / 2) + LU = Vector{Any}(undef, (num_stages + 1) / 2) if u isa Number LU[1] = -γdt * mass_matrix + J - for i in 2 : (s + 1) / 2 + for i in 2 : (num_stages + 1) / 2 LU[i] = -(α[i - 1]dt + β[i - 1]dt * im) * mass_matrix + J end else LU[1] = lu(-γdt * mass_matrix + J) - for i in 2 : (s + 1) / 2 + for i in 2 : (num_stages + 1) / 2 LU[i] = lu(-(α[i - 1]dt + β[i - 1]dt * im) * mass_matrix + J) end end integrator.stats.nw += 1 - + z = w = Vector{BigFloat}(undef, num_stages) if integrator.iter == 1 || integrator.u_modified || alg.extrapolant == :constant cache.dtprev = one(cache.dtprev) - for i in 1:s + for i in 1 : num_stages z[i] = w[i] = map(zero, u) end - for i in 1:(s-1) + for i in 1 : (num_stages - 1) cont[i] = map(zero, u) end else - c' = Vector{eltype(u)}(undef, s) #time stepping - c'[s] = dt / cache.dtprev - for i in 1 : s-1 - c'[i] = c[i] * c'[s] + c' = Vector{eltype(u)}(undef, num_stages) #time stepping + c'[num_stages] = dt / cache.dtprev + for i in 1 : num_stages - 1 + c'[i] = c[i] * c'[num_stages] end - for i in 1 : s # collocation polynomial - z[i] = @.. cont[s-1] * (c'[i] - c[1] + 1) + cont[s-1] + for i in 1 : num_stages # collocation polynomial + z[i] = @.. cont[num_stages-1] * (c'[i] - c[1] + 1) + cont[num_stages - 1] j = s - 2 while j > 0 - z[i] = @.. z[i] * (c'[i] - c[s-j] + 1) + cont[j] + z[i] = @.. z[i] * (c'[i] - c[num_stages-j] + 1) + cont[j] end z[i] = @.. z[i] * c'[i] end @@ -1406,49 +1406,49 @@ end integrator.stats.nnonliniter += 1 # evaluate function - ff = Vector{eltype(u)}(undef, s) - for i in 1:s + ff = Vector{eltype(u)}(undef, num_stages) + for i in 1 : num_stages ff[i] = f(uprev + z[i], p, t + c[i] * dt) end integrator.stats.nf += 5 fw = @.. TI * ff - Mw = Vector{eltype(u)}(undef, s) + Mw = Vector{eltype(u)}(undef, num_stages) if mass_matrix isa UniformScaling # `UniformScaling` doesn't play nicely with broadcast - for i in 1:s - Mw[i] = @.. mass_matrix.λ * w[i] #scaling by eigenvalues + for i in 1 : num_stages + Mw[i] = @.. mass_matrix.λ * w[i] #scaling by eigenvalue end else Mw = mass_matrix * w #standard multiplication end - rhs = Vector{eltype(u)}(undef, s) - rhs[1] = @.. fw[1]-γdt * Mw[1] + rhs = Vector{eltype(u)}(undef, num_stages) + rhs[1] = @.. fw[1] - γdt * Mw[1] i = 2 - while i <= s #block by block multiplication - rhs[i] = @.. fw[i] - α[i/2]dt * Mw[i] + β[i/2]dt * Mw[i + 1] - rhs[i + 1] = @.. fw[i + 1] - β[i/2]dt * Mw[i] - α[i/2]dt * Mw[i + 1] + while i <= num_stages #block by block multiplication + rhs[i] = @.. fw[i] - αdt[i/2] * Mw[i] + βdt[i/2] * Mw[i + 1] + rhs[i + 1] = @.. fw[i + 1] - βdt[i/2] * Mw[i] - αdt[i/2] * Mw[i + 1] i += 2 end - dw = Vector{eltype(u)}(undef, s) + dw = Vector{eltype(u)}(undef, num_stages) dw[1] = LU1 \ rhs[1] - for i in 2 : (s + 1) / 2 + for i in 2 : (num_stages + 1) / 2 tmp = LU[i] \ (@.. rhs[2 * i - 2] + rhs[2 * i - 1] * im) dw[2 * i - 2] = real(tmp) dw[2 * i - 1] = imag(tmp) end - integrator.stats.nlsolve += (s + 1) / 2 + integrator.stats.nlsolve += (num_stages + 1) / 2 # compute norm of residuals iter > 1 && (ndwprev = ndw) - atmp = Vector{eltype(u)}(undef, s) - for i in 1:s + atmp = Vector{eltype(u)}(undef, num_stages) + for i in 1 : num_stages atmp[i] = calculate_residuals(dw[i], uprev, u, atol, rtol, internalnorm, t) end ndw = 0 - for i in 1:s + for i in 1 : num_stages ndw = ndw + internalnorm(atmp[i], t) end # check divergence (not in initial step) @@ -1487,8 +1487,8 @@ end cache.ηold = η cache.iter = iter - u = @.. uprev + z[s] - + u = @.. uprev + z[num_stages] + #= if adaptive edt = e ./ dt tmp = @.. dot(edt, z) @@ -1508,13 +1508,13 @@ end integrator.EEst = internalnorm(atmp, t) end end - + =# if integrator.EEst <= oneunit(integrator.EEst) cache.dtprev = dt if alg.extrapolant != :constant - derivatives = Matrix{eltype(u)}(undef, s-1, s-1) - for i in 1 : (s - 1) - for j in i : (s-1) + derivatives = Matrix{eltype(u)}(undef, num_stages - 1, num_stages - 1) + for i in 1 : (num_stages - 1) + for j in i : (num_stages - 1) if i == 1 derivatives[i, j] = @.. (z[i] - z[i + 1]) / (c[i] - c[i + 1]) #first derivatives else @@ -1522,8 +1522,8 @@ end end end end - for i in 1 : (s-1) - cache.cont[i] = derivatives[i, s - 1] + for i in 1 : (num_stages - 1) + cache.cont[i] = derivatives[i, num_stages - 1] end end end @@ -1538,7 +1538,7 @@ end @muladd function perform_step!(integrator, cache::adaptiveRadauCache, repeat_step = false) @unpack t, dt, uprev, u, f, p, fsallast, fsalfirst = integrator - @unpack T, TI, γ, α, β, c, e= cache.tab + @unpack T, TI, γ, α, β, c, e, num_stages = cache.tab @unpack κ, cont, z, w = cache @unpack dw1, ubuff, dw2, cubuff1, cubuff2 = cache @unpack k, fw, J, W1, W2 = cache @@ -1556,7 +1556,7 @@ end if (new_W = do_newW(integrator, alg, new_jac, cache.W_γdt)) @inbounds for II in CartesianIndices(J) W1[II] = -γdt * mass_matrix[Tuple(II)...] + J[II] - for i in 1 : (s - 1) / 2 + for i in 1 : (num_stages - 1) / 2 W2[i][II] = -(α[i]dt + β[i]dt * im) * mass_matrix[Tuple(II)...] + J[II] end end @@ -1567,23 +1567,23 @@ end if integrator.iter == 1 || integrator.u_modified || alg.extrapolant == :constant cache.dtprev = one(cache.dtprev) uzero = zero(eltype(u)) - for i in 1:s + for i in 1 : num_stages @.. z[i] = w[i] = uzero end - for i in 1:(s-1) + for i in 1 : (num_stages-1) @.. cache.cont[i] = uzero end else - c' = Vector{eltype(u)}(undef, s) #time stepping - c'[s] = dt / cache.dtprev - for i in 1 : s-1 - c'[i] = c[i] * c'[s] - end - for i in 1 : s # collocation polynomial - @.. z[i] = cont[s-1] * (c'[i] - c[1] + 1) + cont[s-1] - j = s - 2 + c' = Vector{eltype(u)}(undef, num_stages) #time stepping + c'[num_stages] = dt / cache.dtprev + for i in 1 : (num_stages-1) + c'[i] = c[i] * c'[num_stages] + end + for i in 1 : num_stages # collocation polynomial + @.. z[i] = cont[num_stages - 1] * (c'[i] - c[1] + 1) + cont[num_stages - 1] + j = num_stages - 2 while j > 0 - @.. z[i] = z[i] * (c'[i] - c[s-j] + 1) + cont[j] + @.. z[i] = z[i] * (c'[i] - c[num_stages - j] + 1) + cont[j] end @.. z[i] = z[i] * c'[i] end @@ -1601,22 +1601,22 @@ end # evaluate function k[1] = fsallast - for i in 1 : s + for i in 1 : num_stages @.. tmp = uprev + z[i] f(k[i], tmp, p, t + c[i] * dt) end - integrator.stats.nf += s + integrator.stats.nf += num_stages @.. fw = TI * k if mass_matrix === I Mw = w elseif mass_matrix isa UniformScaling - for i in 1 : s + for i in 1 : num_stages mul!(z[i], mass_matrix.λ, w[i]) end Mw = z else - for i in 1 : s + for i in 1 : num_stages mul!(z[i], mass_matrix.λ, w[i]) end Mw = z @@ -1626,7 +1626,7 @@ end needfactor = iter == 1 && new_W linsolve1 = cache.linsolve1 - linres = Vector{BigFloat}(undef, s) + linres = Vector{BigFloat}(undef, num_stages) if needfactor linres[1] = dolinsolve(integrator, linsolve1; A = W1, b = _vec(ubuff), linu = _vec(dw1)) @@ -1637,9 +1637,9 @@ end cache.linsolve1 = linres1.cache - for i in 1 : (s-1)/2 + for i in 1 : (num_stages - 1)/2 @.. broadcast=false cubuff[i]=complex( - fw2 - α[i]dt * Mw[2*i] + β[i]dt * Mw[2*i + 1], fw3 - β[i]dt * Mw[2*i] - α[i]dt * Mw[2*i + 1]) + fw2 - αdt[i] * Mw[2 * i] + βdt[i] * Mw[2 * i + 1], fw3 - βdt[i] * Mw[2 * i] - αdt[i] * Mw[2 * i + 1]) linsolve2[i] = cache.linsolve2[i] if needfactor linres[i + 1] = dolinsolve(integrator, linsolve2[i]; A = W2[i], b = _vec(cubuff[i]), @@ -1651,10 +1651,10 @@ end cache.linsolve2[i] = linres[i + 1].cache end - integrator.stats.nsolve += (s+1) / 2 + integrator.stats.nsolve += (num_stages + 1) / 2 dw[1] = dw1 i = 2 - while i <= s + while i <= num_stages dw[i] = z[i] dw[i + 1] = z[i + 1] @.. dw[i] = real(dw2[i - 1]) @@ -1664,14 +1664,14 @@ end # compute norm of residuals iter > 1 && (ndwprev = ndw) - ndws = Vector{BigFloat}(undef, s) - for i in 1:s + ndws = Vector{BigFloat}(undef, num_stages) + for i in 1:num_stages calculate_residuals!(atmp, dw[i], uprev, u, atol, rtol, internalnorm, t) ndws[i] = internalnorm(atmp, t) end ndw = 0 - for i in 1 : s + for i in 1 : num_stages ndw += ndws[i] end @@ -1714,7 +1714,7 @@ end @.. broadcast=false u=uprev + z[s] step_limiter!(u, integrator, p, t + dt) - + #= if adaptive utilde = w2 edt = e./dt @@ -1752,13 +1752,13 @@ end integrator.EEst = internalnorm(atmp, t) end end - + =# if integrator.EEst <= oneunit(integrator.EEst) cache.dtprev = dt if alg.extrapolant != :constant - derivatives = Matrix{eltype(u)}(undef, s-1, s-1) - for i in 1 : (s - 1) - for j in i : (s-1) + derivatives = Matrix{eltype(u)}(undef, num_stages - 1, num_stages - 1) + for i in 1 : (num_stages - 1) + for j in i : (num_stages - 1) if i == 1 @.. derivatives[i, j] = (z[i] - z[i + 1]) / (c[i] - c[i + 1]) #first derivatives else @@ -1766,8 +1766,8 @@ end end end end - for i in 1 : (s-1) - cache.cont[i] = derivatives[i, s - 1] + for i in 1 : (num_stages - 1) + cache.cont[i] = derivatives[i, num_stages - 1] end end end diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl index 478bdd4240..3e36fd9363 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl @@ -259,7 +259,7 @@ function RadauIIA9Tableau(T, T2) e1, e2, e3, e4, e5) end -struct adaptiveRadauTableau(T, T2) +struct adaptiveRadauTableau{T, T2, Int} T:: AbstractMatrix{T} TI::AbstractMatrix{T} γ::T @@ -267,80 +267,81 @@ struct adaptiveRadauTableau(T, T2) β::AbstractVector{T} c::AbstractVector{T} e::AbstractVector{T} + S::Int end using Polynomials, GenericLinearAlgebra, LinearAlgebra, LinearSolve, GenericSchur, BSeries -function adaptiveRadauTableau(T, T2, s::Int64) - tmp = Vector{BigFloat}(undef, s-1) - for i in 1:(s-1) +function adaptiveRadauTableau(T, T2, num_stages::Int) + tmp = Vector{BigFloat}(undef, num_stages - 1) + for i in 1:(num_stages - 1) tmp[i] = 0 end - tmp2 = Vector{BigFloat}(undef, s+1) - for i in 1:(s+1) - tmp2[i]=(-1)^(s+1-i) * binomial(s,s+1-i) + tmp2 = Vector{BigFloat}(undef, num_stages + 1) + for i in 1:(num_stages + 1) + tmp2[i]=(-1)^(num_stages + 1 - i) * binomial(num_stages , num_stages + 1 - i) end p = Polynomial{BigFloat}([tmp; tmp2]) - for i in 1:s-1 + for i in 1:(num_stages - 1) p = derivative(p) end c = roots(p) - c[s] = 1 - c_powers = Matrix{BigFloat}(undef, s, s) - for i in 1:s - for j in 1:s - c_powers[i,j] = c[i]^(j-1) + c[num_stages] = 1 + c_powers = Matrix{BigFloat}(undef, num_stages, num_stages) + for i in 1 : num_stages + for j in 1 : num_stages + c_powers[i,j] = c[i]^(j - 1) end end inverse_c_powers = inv(c_powers) - c_q = Matrix{BigFloat}(undef, s, s) - for i in 1:s - for j in 1:s + c_q = Matrix{BigFloat}(undef, num_stages, num_stages) + for i in 1 : num_stages + for j in 1 : num_stages c_q[i,j] = c[i]^(j) / j end end a = c_q * inverse_c_powers a_inverse = inv(a) - b = Vector{Bigfloat}(undef, s) - for i in 1 : s - b[i] = a[s, i] + b = Vector{BigFloat}(undef, num_stages) + for i in 1 : num_stages + b[i] = a[num_stages, i] end vals = eigvals(a_inverse) - γ = real(b[s]) - α = Vector{BigFloat}(undef, floor(Int, s/2)) - β = Vector{BigFloat}(undef, floor(Int, s/2)) + γ = real(b[num_stages]) + α = Vector{BigFloat}(undef, floor(Int, num_stages/2)) + β = Vector{BigFloat}(undef, floor(Int, num_stages/2)) index = 1 i = 1 - while i <= (s-1) + while i <= (num_stages - 1) α[index] = real(vals[i]) β[index] = imag(vals[i + 1]) index = index + 1 i = i + 2 end eigvec = eigvecs(a) - vecs = Vector{Vector{BigFloat}}(undef, s) + vecs = Vector{Vector{BigFloat}}(undef, num_stages) i = 1 index = 2 - while i < s - vecs[index] = real(eigvec[:, i] ./ eigvec[s,i]) - vecs[index + 1] = -imag(eigvec[:, i] ./ eigvec[s,i]) + while i < num_stages + vecs[index] = real(eigvec[:, i] ./ eigvec[num_stages, i]) + vecs[index + 1] = -imag(eigvec[:, i] ./ eigvec[num_stages, i]) index += 2 i += 2 end - vecs[1] = real(eigvec[:, s]) + vecs[1] = real(eigvec[:, num_stages]) tmp3 = vcat(vecs) - T = Matrix{BigFloat}(undef, s, s) - for j in 1 : s - for i in 1 : s + T = Matrix{BigFloat}(undef, num_stages, num_stages) + for j in 1 : num_stages + for i in 1 : num_stages T[i, j] = tmp3[j][i] end end TI = inv(T) - b_hat = Vector{BigFloat}(undef, s) - embedded = bseries(a, b_hat, c, s - 2) + #b_hat = Vector{BigFloat}(undef, num_stages) + #embedded = bseries(a, b_hat, c, num_stages - 2) #e = b_hat - b - #adaptiveRadautableau(T, TI, γ, α, β, c, e) + #adaptiveRadautableau(T, TI, γ, α, β, c, e, s) end adaptiveRadauTableau(0, 0, 3) diff --git a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl index 5cc4bfc597..b68f3cc72e 100644 --- a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl +++ b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl @@ -8,6 +8,8 @@ for prob in [prob_ode_linear, prob_ode_2Dlinear] @test sim21.𝒪est[:final]≈5 atol=testTol end +sol = solve(prob_ode_linear, AdaptiveRadau()) + sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_linear, RadauIIA9()) @test sim21.𝒪est[:final]≈8 atol=testTol From 3d09fa24078c6b58d2c6c162d050196603138a18 Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Tue, 20 Aug 2024 20:53:53 -0400 Subject: [PATCH 43/71] lots of edits --- lib/OrdinaryDiffEqFIRK/Project.toml | 3 + .../src/OrdinaryDiffEqFIRK.jl | 1 + lib/OrdinaryDiffEqFIRK/src/alg_utils.jl | 1 + lib/OrdinaryDiffEqFIRK/src/algorithms.jl | 2 +- lib/OrdinaryDiffEqFIRK/src/firk_caches.jl | 202 +++++++++--------- .../src/firk_perform_step.jl | 121 ++++------- lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl | 12 +- lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl | 7 +- 8 files changed, 157 insertions(+), 192 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/Project.toml b/lib/OrdinaryDiffEqFIRK/Project.toml index 63aa2f368c..02c7ace7b9 100644 --- a/lib/OrdinaryDiffEqFIRK/Project.toml +++ b/lib/OrdinaryDiffEqFIRK/Project.toml @@ -15,6 +15,9 @@ MuladdMacro = "46d2c3a1-f734-5fdb-9937-b9b9aeba4221" FastBroadcast = "7034ab61-46d4-4ed7-9d0f-46aef9175898" Reexport = "189a3867-3050-52da-a836-e630ba90ab69" OrdinaryDiffEqNonlinearSolve = "127b3ac7-2247-4354-8eb6-78cf4e7c58e8" +GenericLinearAlgebra = "14197337-ba66-59df-a3e3-ca00e7dcff7a" +GenericSchur = "c145ed77-6b09-5dd9-b285-bf645a82121e" +Polynomials = "f27b6e38-b328-58d1-80ce-0feddd5e7a45" [compat] julia = "1.10" diff --git a/lib/OrdinaryDiffEqFIRK/src/OrdinaryDiffEqFIRK.jl b/lib/OrdinaryDiffEqFIRK/src/OrdinaryDiffEqFIRK.jl index 5d071e8777..e26805bc6e 100644 --- a/lib/OrdinaryDiffEqFIRK/src/OrdinaryDiffEqFIRK.jl +++ b/lib/OrdinaryDiffEqFIRK/src/OrdinaryDiffEqFIRK.jl @@ -18,6 +18,7 @@ import OrdinaryDiffEqCore: alg_order, calculate_residuals!, get_current_adaptive_order, isfirk using MuladdMacro, DiffEqBase, RecursiveArrayTools +using Polynomials, GenericLinearAlgebra, GenericSchur using SciMLOperators: AbstractSciMLOperator using LinearAlgebra: I, UniformScaling, mul!, lu import LinearSolve diff --git a/lib/OrdinaryDiffEqFIRK/src/alg_utils.jl b/lib/OrdinaryDiffEqFIRK/src/alg_utils.jl index 5953ecffc1..7b0e8cdc1a 100644 --- a/lib/OrdinaryDiffEqFIRK/src/alg_utils.jl +++ b/lib/OrdinaryDiffEqFIRK/src/alg_utils.jl @@ -3,6 +3,7 @@ qmax_default(alg::Union{RadauIIA3, RadauIIA5, RadauIIA9}) = 8 alg_order(alg::RadauIIA3) = 3 alg_order(alg::RadauIIA5) = 5 alg_order(alg::RadauIIA9) = 9 +alg_order(alg::AdaptiveRadau) = 9 isfirk(alg::RadauIIA3) = true isfirk(alg::RadauIIA5) = true diff --git a/lib/OrdinaryDiffEqFIRK/src/algorithms.jl b/lib/OrdinaryDiffEqFIRK/src/algorithms.jl index ba4c51c0d0..4429fb78b6 100644 --- a/lib/OrdinaryDiffEqFIRK/src/algorithms.jl +++ b/lib/OrdinaryDiffEqFIRK/src/algorithms.jl @@ -171,7 +171,7 @@ end function AdaptiveRadau(; chunk_size = Val{0}(), autodiff = Val{true}(), standardtag = Val{true}(), concrete_jac = nothing, - diff_type = Val{:forward}, num_stages = 5, + diff_type = Val{:forward}, num_stages = 3, linsolve = nothing, precs = DEFAULT_PRECS, extrapolant = :dense, fast_convergence_cutoff = 1 // 5, new_W_γdt_cutoff = 1 // 5, diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl index 40f6631765..8b531cda7d 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl @@ -468,41 +468,42 @@ function alg_cache(alg::RadauIIA9, u, rate_prototype, ::Type{uEltypeNoUnits}, Convergence, alg.step_limiter!) end -mutable struct adaptiveRadauConstantCache{S, F, Tab, Tol, Dt, U, JType} <: +mutable struct AdaptiveRadauConstantCache{F, Tab, Tol, Dt, U, JType} <: OrdinaryDiffEqConstantCache -uf::F -tab::Tab -κ::Tol -ηold::Tol -iter::Int -cont::AbstractVector{U} -dtprev::Dt -W_γdt::Dt -status::NLStatus -J::JType + uf::F + tab::Tab + κ::Tol + ηold::Tol + iter::Int + cont::AbstractVector{U} + dtprev::Dt + W_γdt::Dt + status::NLStatus + J::JType end function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} -uf = UDerivativeWrapper(f, t, p) -uToltype = constvalue(uBottomEltypeNoUnits) -tab = adaptiveRadau(uToltype, constvalue(tTypeNoUnits), alg.num_stages) - -cont = Vector{typeof(u)}(undef, num_stages - 1) -for i in 1: (num_stages - 1) - cont[i] = zero(u) -end + ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + uf = UDerivativeWrapper(f, t, p) + uToltype = constvalue(uBottomEltypeNoUnits) + num_stages = alg.num_stages + tab = adaptiveRadauTableau(uToltype, constvalue(tTypeNoUnits), num_stages) + + cont = Vector{typeof(u)}(undef, num_stages - 1) + for i in 1: (num_stages - 1) + cont[i] = zero(u) + end -κ = alg.κ !== nothing ? convert(uToltype, alg.κ) : convert(uToltype, 1 // 100) -J = false .* _vec(rate_prototype) .* _vec(rate_prototype)' + κ = alg.κ !== nothing ? convert(uToltype, alg.κ) : convert(uToltype, 1 // 100) + J = false .* _vec(rate_prototype) .* _vec(rate_prototype)' -adaptiveRadauConstantCache(uf, tab, κ, one(uToltype), 10000, cont, dt, dt, - Convergence, J) + AdaptiveRadauConstantCache(uf, tab, κ, one(uToltype), 10000, cont, dt, dt, + Convergence, J) end -mutable struct adaptiveRadauCache{uType, cuType, uNoUnitsType, rateType, JType, W1Type, W2Type, +mutable struct AdaptiveRadauCache{uType, cuType, uNoUnitsType, rateType, JType, W1Type, W2Type, UF, JC, F1, F2, Tab, Tol, Dt, rTol, aTol, StepLimiter} <: OrdinaryDiffEqMutableCache u::uType @@ -540,89 +541,90 @@ mutable struct adaptiveRadauCache{uType, cuType, uNoUnitsType, rateType, JType, end function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits}, - ::Type{uBottomEltypeNoUnits}, - ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, - ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} -uf = UJacobianWrapper(f, t, p) -uToltype = constvalue(uBottomEltypeNoUnits) -tab = RadauIIA9Tableau(uToltype, constvalue(tTypeNoUnits)) - -κ = alg.κ !== nothing ? convert(uToltype, alg.κ) : convert(uToltype, 1 // 100) - -z = Vector{typeof(u)}(undef, num_stages) -w = Vector{typeof(u)}(undef, num_stages) -for i in 1:s - z[i] = w[i] = zero(u) -end + ::Type{uBottomEltypeNoUnits}, + ::Type{tTypeNoUnits}, uprev, uprev2, f, t, dt, reltol, p, calck, + ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} + uf = UJacobianWrapper(f, t, p) + uToltype = constvalue(uBottomEltypeNoUnits) + alg.num_stages = num_stages + tab = adaptiveRadauTableau(uToltype, constvalue(tTypeNoUnits), num_stages) -dw1 = zero(u) -ubuff = zero(u) -dw2 = Vector{typeof(u)}(undef, floor(Int, num_stages/2)) -for i in 1 : floor(Int, num_stages/2) - dw2[i] = similar(u, Complex{eltype(u)}) - recursivefill!(dw[i], false) -end -cubuff = Vector{typeof(u)}(undef, floor(Int, num_stages/2)) -for i in 1 :floor(Int, num_stages/2) - cubuff[i] = similar(u, Complex{eltype(u)}) - recursivefill!(cubuff[i], false) -end + κ = alg.κ !== nothing ? convert(uToltype, alg.κ) : convert(uToltype, 1 // 100) -cont = Vector{typeof(u)}(undef, num_stages - 1) -for i in 1: (num_stages - 1) - cont[i] = zero(u) -end + z = Vector{typeof(u)}(undef, num_stages) + w = Vector{typeof(u)}(undef, num_stages) + for i in 1:s + z[i] = w[i] = zero(u) + end -fsalfirst = zero(rate_prototype) -fw = Vector{typeof(rate_prototype)}(undef, num_stages) -k = Vector{typeof(rate_prototype)}(undef, num_stages) -for i in 1: num_stages - k[i] = fw[i] = zero(rate_prototype) -end + dw1 = zero(u) + ubuff = zero(u) + dw2 = Vector{typeof(u)}(undef, floor(Int, num_stages/2)) + for i in 1 : floor(Int, num_stages/2) + dw2[i] = similar(u, Complex{eltype(u)}) + recursivefill!(dw[i], false) + end + cubuff = Vector{typeof(u)}(undef, floor(Int, num_stages/2)) + for i in 1 :floor(Int, num_stages/2) + cubuff[i] = similar(u, Complex{eltype(u)}) + recursivefill!(cubuff[i], false) + end -J, W1 = build_J_W(alg, u, uprev, p, t, dt, f, uEltypeNoUnits, Val(true)) -if J isa AbstractSciMLOperator - error("Non-concrete Jacobian not yet supported by RadauIIA5.") -end -W2 = vector{typeof(Complex{W1})}(undef, floor(Int, num_stages/2)) -for i in 1 : floor(Int, num_stages/2) - W2[i] = similar(J, Complex{eltype(W1)}) - recursivefill!(w2[i], false) -end + cont = Vector{typeof(u)}(undef, num_stages - 1) + for i in 1: (num_stages - 1) + cont[i] = zero(u) + end -du1 = zero(rate_prototype) + fsalfirst = zero(rate_prototype) + fw = Vector{typeof(rate_prototype)}(undef, num_stages) + k = Vector{typeof(rate_prototype)}(undef, num_stages) + for i in 1: num_stages + k[i] = fw[i] = zero(rate_prototype) + end -tmp = Vector{typeof(u)}(undef, binomial(num_stages,2)) -for i in 1 : binomial(num_stages,2) - tmp[i] = zero(u) -end + J, W1 = build_J_W(alg, u, uprev, p, t, dt, f, uEltypeNoUnits, Val(true)) + if J isa AbstractSciMLOperator + error("Non-concrete Jacobian not yet supported by RadauIIA5.") + end + W2 = vector{typeof(Complex{W1})}(undef, floor(Int, num_stages/2)) + for i in 1 : floor(Int, num_stages/2) + W2[i] = similar(J, Complex{eltype(W1)}) + recursivefill!(w2[i], false) + end -atmp = similar(u, uEltypeNoUnits) -recursivefill!(atmp, false) + du1 = zero(rate_prototype) -jac_config = build_jac_config(alg, f, uf, du1, uprev, u, tmp, dw1) + tmp = Vector{typeof(u)}(undef, binomial(num_stages,2)) + for i in 1 : binomial(num_stages,2) + tmp[i] = zero(u) + end -linprob = LinearProblem(W1, _vec(ubuff); u0 = _vec(dw1)) -linsolve1 = init(linprob, alg.linsolve, alias_A = true, alias_b = true, - assumptions = LinearSolve.OperatorAssumptions(true)) + atmp = similar(u, uEltypeNoUnits) + recursivefill!(atmp, false) -linsolve2 = Vector{typeof(linsolve1)}(undef, floor(Int, num_stages/2)) -for i in 1 : floor(int, num_stages/2) - linprob = LinearProblem(W2[i], _vec(cubuff[i]); u0 = _vec(dw2[i])) - linsolve2 = init(linprob, alg.linsolve, alias_A = true, alias_b = true, - assumptions = LinearSolve.OperatorAssumptions(true)) -end + jac_config = build_jac_config(alg, f, uf, du1, uprev, u, tmp, dw1) + + linprob = LinearProblem(W1, _vec(ubuff); u0 = _vec(dw1)) + linsolve1 = init(linprob, alg.linsolve, alias_A = true, alias_b = true, + assumptions = LinearSolve.OperatorAssumptions(true)) + + linsolve2 = Vector{typeof(linsolve1)}(undef, floor(Int, num_stages/2)) + for i in 1 : floor(int, num_stages/2) + linprob = LinearProblem(W2[i], _vec(cubuff[i]); u0 = _vec(dw2[i])) + linsolve2 = init(linprob, alg.linsolve, alias_A = true, alias_b = true, + assumptions = LinearSolve.OperatorAssumptions(true)) + end + + rtol = reltol isa Number ? reltol : zero(reltol) + atol = reltol isa Number ? reltol : zero(reltol) -rtol = reltol isa Number ? reltol : zero(reltol) -atol = reltol isa Number ? reltol : zero(reltol) - -adaptiveRadauCache(u, uprev, - z, w, dw1, ubuff, dw2, cubuff, cont, - du1, fsalfirst, k, fw, - J, W1, W2, - uf, tab, κ, one(uToltype), 10000, - tmp, atmp, jac_config, - linsolve1, linsolve2, rtol, atol, dt, dt, - Convergence, alg.step_limiter!) + AdaptiveRadauCache(u, uprev, + z, w, dw1, ubuff, dw2, cubuff, cont, + du1, fsalfirst, k, fw, + J, W1, W2, + uf, tab, κ, one(uToltype), 10000, + tmp, atmp, jac_config, + linsolve1, linsolve2, rtol, atol, dt, dt, + Convergence, alg.step_limiter!) end diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index 51313203a6..1f52f50aca 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -26,32 +26,7 @@ function do_newW(integrator, nlsolver, new_jac, W_dt)::Bool # for FIRK return !smallstepchange end -function initialize!(integrator, cache::RadauIIA3ConstantCache) - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - nothing -end - -function initialize!(integrator, cache::RadauIIA5ConstantCache) - integrator.kshortsize = 2 - integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) - integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal - integrator.stats.nf += 1 - - # Avoid undefined entries if k is an array of arrays - integrator.fsallast = zero(integrator.fsalfirst) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - nothing -end - -function initialize!(integrator, cache::RadauIIA9ConstantCache) +function initialize!(integrator, cache::Union{RadauIIA3ConstantCache, RadauIIA5ConstantCache, RadauIIA9ConstantCache,AdaptiveRadauConstantCache}) integrator.kshortsize = 2 integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal @@ -76,7 +51,7 @@ function initialize!(integrator, cache::RadauIIA3Cache) nothing end -function initialize!(integrator, cache::RadauIIA5Cache) +function initialize!(integrator, cache::Union{RadauIIA5Cache, RadauIIA9Cache, AdaptiveRadauCache}) integrator.kshortsize = 2 integrator.fsalfirst = cache.fsalfirst integrator.fsallast = cache.k @@ -98,27 +73,6 @@ function initialize!(integrator, cache::RadauIIA5Cache) nothing end -function initialize!(integrator, cache::RadauIIA9Cache) - integrator.kshortsize = 2 - integrator.fsalfirst = cache.fsalfirst - integrator.fsallast = cache.k - resize!(integrator.k, integrator.kshortsize) - integrator.k[1] = integrator.fsalfirst - integrator.k[2] = integrator.fsallast - integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) - integrator.stats.nf += 1 - if integrator.opts.adaptive - @unpack abstol, reltol = integrator.opts - if reltol isa Number - cache.rtol = reltol^(5 / 8) / 10 - cache.atol = cache.rtol * (abstol / reltol) - else - @.. broadcast=false cache.rtol=reltol^(5 / 8) / 10 - @.. broadcast=false cache.atol=cache.rtol * (abstol / reltol) - end - end - nothing -end @muladd function perform_step!(integrator, cache::RadauIIA3ConstantCache) @unpack t, dt, uprev, u, f, p = integrator @@ -948,7 +902,7 @@ end z3 = @.. broadcast=false T31*w1+T32*w2+T33*w3+T34*w4+T35*w5 z4 = @.. broadcast=false T41*w1+T42*w2+T43*w3+T44*w4+T45*w5 z5 = @.. broadcast=false T51*w1+w2+w4 #= T52=1, T53=0, T54=1, T55=0 =# - + @show z1 # check stopping criterion iter > 1 && (η = θ / (1 - θ)) if η * ndw < κ && (iter > 1 || iszero(ndw) || !iszero(integrator.success_iter)) @@ -1340,10 +1294,10 @@ end return end -@muladd function perform_step!(integrator, cache::adaptiveRadauConstantCache, +@muladd function perform_step!(integrator, cache::AdaptiveRadauConstantCache, repeat_step = false) @unpack t, dt, uprev, u, f, p = integrator - @unpack T, TI, γ, α, β, c, e, num_stages = cache.tab + @unpack T, TI, γ, α, β, c, #=e,=# num_stages = cache.tab @unpack κ, cont = cache @unpack internalnorm, abstol, reltol, adaptive = integrator.opts alg = unwrap_alg(integrator, true) @@ -1357,16 +1311,16 @@ end γdt, αdt, βdt = γ / dt, α ./ dt, β ./ dt J = calc_J(integrator, cache) - LU = Vector{Any}(undef, (num_stages + 1) / 2) + LU = Vector{Any}(undef, Int((num_stages + 1) / 2)) if u isa Number LU[1] = -γdt * mass_matrix + J - for i in 2 : (num_stages + 1) / 2 - LU[i] = -(α[i - 1]dt + β[i - 1]dt * im) * mass_matrix + J + for i in 2 : Int((num_stages + 1) / 2) + LU[i] = -(αdt[i - 1] + βdt[i - 1] * im) * mass_matrix + J end else LU[1] = lu(-γdt * mass_matrix + J) - for i in 2 : (num_stages + 1) / 2 - LU[i] = lu(-(α[i - 1]dt + β[i - 1]dt * im) * mass_matrix + J) + for i in 2 : Int((num_stages + 1) / 2) + LU[i] = lu(-(αdt[i - 1] + βdt[i - 1] * im) * mass_matrix + J) end end integrator.stats.nw += 1 @@ -1377,21 +1331,22 @@ end z[i] = w[i] = map(zero, u) end for i in 1 : (num_stages - 1) - cont[i] = map(zero, u) + cache.cont[i] = map(zero, u) end else - c' = Vector{eltype(u)}(undef, num_stages) #time stepping - c'[num_stages] = dt / cache.dtprev + c_prime = Vector{eltype(u)}(undef, num_stages) #time stepping + c_prime[num_stages] = dt / cache.dtprev for i in 1 : num_stages - 1 - c'[i] = c[i] * c'[num_stages] + c_prime[i] = c[i] * c_prime[num_stages] end for i in 1 : num_stages # collocation polynomial - z[i] = @.. cont[num_stages-1] * (c'[i] - c[1] + 1) + cont[num_stages - 1] - j = s - 2 + z[i] = @.. cont[num_stages - 1] * (c_prime[i] - c[1] + 1) + cont[num_stages - 2] + j = num_stages - 3 while j > 0 - z[i] = @.. z[i] * (c'[i] - c[num_stages-j] + 1) + cont[j] + z[i] = @.. z[i] * (c_prime[i] - c[num_stages- j - 1] + 1) + cont[j] + j = j - 1 end - z[i] = @.. z[i] * c'[i] + z[i] = @.. z[i] * c_prime[i] end w = @.. TI * z end @@ -1410,7 +1365,7 @@ end for i in 1 : num_stages ff[i] = f(uprev + z[i], p, t + c[i] * dt) end - integrator.stats.nf += 5 + integrator.stats.nf += num_stages fw = @.. TI * ff Mw = Vector{eltype(u)}(undef, num_stages) @@ -1426,19 +1381,19 @@ end rhs[1] = @.. fw[1] - γdt * Mw[1] i = 2 while i <= num_stages #block by block multiplication - rhs[i] = @.. fw[i] - αdt[i/2] * Mw[i] + βdt[i/2] * Mw[i + 1] - rhs[i + 1] = @.. fw[i + 1] - βdt[i/2] * Mw[i] - αdt[i/2] * Mw[i + 1] + rhs[i] = @.. fw[i] - αdt[Int(i/2)] * Mw[i] + βdt[Int(i/2)] * Mw[i + 1] + rhs[i + 1] = @.. fw[i + 1] - βdt[Int(i/2)] * Mw[i] - αdt[Int(i/2)] * Mw[i + 1] i += 2 end dw = Vector{eltype(u)}(undef, num_stages) - dw[1] = LU1 \ rhs[1] - for i in 2 : (num_stages + 1) / 2 + dw[1] = LU[1] \ rhs[1] + for i in 2 : Int((num_stages + 1) / 2) tmp = LU[i] \ (@.. rhs[2 * i - 2] + rhs[2 * i - 1] * im) dw[2 * i - 2] = real(tmp) dw[2 * i - 1] = imag(tmp) end - integrator.stats.nlsolve += (num_stages + 1) / 2 + integrator.stats.nsolve += Int((num_stages + 1) / 2) # compute norm of residuals iter > 1 && (ndwprev = ndw) @@ -1467,6 +1422,7 @@ end # transform `w` to `z` z = @.. T * w + @show z[1] # check stopping criterion iter > 1 && (η = θ / (1 - θ)) @@ -1536,9 +1492,9 @@ end return end -@muladd function perform_step!(integrator, cache::adaptiveRadauCache, repeat_step = false) +@muladd function perform_step!(integrator, cache::AdaptiveRadauCache, repeat_step = false) @unpack t, dt, uprev, u, f, p, fsallast, fsalfirst = integrator - @unpack T, TI, γ, α, β, c, e, num_stages = cache.tab + @unpack T, TI, γ, α, β, c, #=e,=# num_stages = cache.tab @unpack κ, cont, z, w = cache @unpack dw1, ubuff, dw2, cubuff1, cubuff2 = cache @unpack k, fw, J, W1, W2 = cache @@ -1573,21 +1529,22 @@ end for i in 1 : (num_stages-1) @.. cache.cont[i] = uzero end - else - c' = Vector{eltype(u)}(undef, num_stages) #time stepping - c'[num_stages] = dt / cache.dtprev - for i in 1 : (num_stages-1) - c'[i] = c[i] * c'[num_stages] + else + c_prime = Vector{eltype(u)}(undef, num_stages) #time stepping + c_prime[num_stages] = dt / cache.dtprev + for i in 1 : num_stages - 1 + c_prime[i] = c[i] * c_prime[num_stages] end for i in 1 : num_stages # collocation polynomial - @.. z[i] = cont[num_stages - 1] * (c'[i] - c[1] + 1) + cont[num_stages - 1] - j = num_stages - 2 + z[i] = @.. cont[num_stages - 1] * (c_prime[i] - c[1] + 1) + cont[num_stages - 2] + j = num_stages - 3 while j > 0 - @.. z[i] = z[i] * (c'[i] - c[num_stages - j] + 1) + cont[j] + z[i] = @.. z[i] * (c_prime[i] - c[num_stages- j - 1] + 1) + cont[j] + j = j - 1 end - @.. z[i] = z[i] * c'[i] + z[i] = @.. z[i] * c_prime[i] end - @.. w = TI * z + w = @.. TI * z end # Newton iteration diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl index 3e36fd9363..7860d6bfb7 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl @@ -266,11 +266,11 @@ struct adaptiveRadauTableau{T, T2, Int} α::AbstractVector{T} β::AbstractVector{T} c::AbstractVector{T} - e::AbstractVector{T} - S::Int + #e::AbstractVector{T} + num_stages::Int end -using Polynomials, GenericLinearAlgebra, LinearAlgebra, LinearSolve, GenericSchur, BSeries +using Polynomials, GenericLinearAlgebra, LinearAlgebra, LinearSolve, GenericSchur function adaptiveRadauTableau(T, T2, num_stages::Int) tmp = Vector{BigFloat}(undef, num_stages - 1) @@ -341,7 +341,5 @@ function adaptiveRadauTableau(T, T2, num_stages::Int) #embedded = bseries(a, b_hat, c, num_stages - 2) #e = b_hat - b - #adaptiveRadautableau(T, TI, γ, α, β, c, e, s) -end - -adaptiveRadauTableau(0, 0, 3) + adaptiveRadauTableau{Any, T2, Int}(T, TI, γ, α, β, c, num_stages) +end \ No newline at end of file diff --git a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl index 0c960a61df..36289bdf7b 100644 --- a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl +++ b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl @@ -8,9 +8,12 @@ for prob in [prob_ode_linear, prob_ode_2Dlinear] @test sim21.𝒪est[:final]≈5 atol=testTol end -sol = solve(prob_ode_linear, AdaptiveRadau()) +sol = solve(prob_ode_linear, AdaptiveRadau(), adaptive = false, dt = 1e-2) +sol = solve(prob_ode_linear, RadauIIA9(), adaptive = false, dt = 1e-2) +sol = solve(prob_ode_linear, RadauIIA5(), adaptive = false, dt = 1e-2) -sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_linear, RadauIIA9()) + +sim21 = test_convergence(1 ./ 10 .^ (4.5:-1:2.5), prob_ode_linear, AdaptiveRadau()) @test sim21.𝒪est[:final]≈8 atol=testTol sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_2Dlinear, RadauIIA9()) From 6df8b72fa1444e171b09a8facc1c801d20e952d1 Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Thu, 22 Aug 2024 16:08:23 -0400 Subject: [PATCH 44/71] tweaks --- lib/OrdinaryDiffEqFIRK/Project.toml | 2 ++ lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl | 26 ++++++++++++++++----- 2 files changed, 22 insertions(+), 6 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/Project.toml b/lib/OrdinaryDiffEqFIRK/Project.toml index ef8f74b22f..9c8da58779 100644 --- a/lib/OrdinaryDiffEqFIRK/Project.toml +++ b/lib/OrdinaryDiffEqFIRK/Project.toml @@ -17,7 +17,9 @@ OrdinaryDiffEqNonlinearSolve = "127b3ac7-2247-4354-8eb6-78cf4e7c58e8" Polynomials = "f27b6e38-b328-58d1-80ce-0feddd5e7a45" RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd" Reexport = "189a3867-3050-52da-a836-e630ba90ab69" +RootedTrees = "47965b36-3f3e-11e9-0dcf-4570dfd42a8c" SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961" +Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7" [compat] DiffEqBase = "6.152.2" diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl index 7860d6bfb7..a0b7404476 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl @@ -270,7 +270,8 @@ struct adaptiveRadauTableau{T, T2, Int} num_stages::Int end -using Polynomials, GenericLinearAlgebra, LinearAlgebra, LinearSolve, GenericSchur +using Polynomials, GenericLinearAlgebra, LinearAlgebra, LinearSolve, GenericSchur, RootedTrees, Symbolics +using Symbolics: variables, variable, unwrap function adaptiveRadauTableau(T, T2, num_stages::Int) tmp = Vector{BigFloat}(undef, num_stages - 1) @@ -281,11 +282,11 @@ function adaptiveRadauTableau(T, T2, num_stages::Int) for i in 1:(num_stages + 1) tmp2[i]=(-1)^(num_stages + 1 - i) * binomial(num_stages , num_stages + 1 - i) end - p = Polynomial{BigFloat}([tmp; tmp2]) + radau_p = Polynomial{BigFloat}([tmp; tmp2]) for i in 1:(num_stages - 1) - p = derivative(p) + radau_p = derivative(radau_p) end - c = roots(p) + c = roots(radau_p) c[num_stages] = 1 c_powers = Matrix{BigFloat}(undef, num_stages, num_stages) for i in 1 : num_stages @@ -337,9 +338,22 @@ function adaptiveRadauTableau(T, T2, num_stages::Int) end end TI = inv(T) - #b_hat = Vector{BigFloat}(undef, num_stages) - #embedded = bseries(a, b_hat, c, num_stages - 2) + eb = variables(:b, 1:num_stages + 1) + zz = zeros(size(a, 1) + 1) + zz2 = zeros(size(a, 1)) + eA = [zz' + zz2 a] + ec = [0; c] + constraints = map(Iterators.flatten(RootedTreeIterator(i) for i in 1:p)) do t + residual_order_condition(t, RungeKuttaMethod(eA, eb, ec)) + end + AA, bb, islinear = Symbolics.linear_expansion(substitute.(constraints, (eb[1]=>γ,)), eb[2:end]) + AA = Float64.(map(unwrap, AA)) + idxs = qr(AA', ColumnNorm()).p[1:num_stages] + @assert rank(AA[idxs, :]) == num_stages + @assert islinear + Symbolics.expand.((AA[idxs, :] \ -bb[idxs]) - b) #e = b_hat - b adaptiveRadauTableau{Any, T2, Int}(T, TI, γ, α, β, c, num_stages) end \ No newline at end of file From 9eb4538ea37d075565130000e135b0afa8aadc32 Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Fri, 23 Aug 2024 16:03:31 -0400 Subject: [PATCH 45/71] fix collocation on radauIIA9 --- lib/OrdinaryDiffEqFIRK/src/alg_utils.jl | 2 +- lib/OrdinaryDiffEqFIRK/src/firk_caches.jl | 7 +- .../src/firk_perform_step.jl | 127 ++++++++++-------- lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl | 12 +- lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl | 7 +- 5 files changed, 89 insertions(+), 66 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/alg_utils.jl b/lib/OrdinaryDiffEqFIRK/src/alg_utils.jl index f8ed7b9b63..428393e0bf 100644 --- a/lib/OrdinaryDiffEqFIRK/src/alg_utils.jl +++ b/lib/OrdinaryDiffEqFIRK/src/alg_utils.jl @@ -3,7 +3,7 @@ qmax_default(alg::Union{RadauIIA3, RadauIIA5, RadauIIA9}) = 8 alg_order(alg::RadauIIA3) = 3 alg_order(alg::RadauIIA5) = 5 alg_order(alg::RadauIIA9) = 9 -alg_order(alg::AdaptiveRadau) = 9 +alg_order(alg::AdaptiveRadau) = 5 isfirk(alg::RadauIIA3) = true isfirk(alg::RadauIIA5) = true diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl index e17f486570..035c1f6815 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl @@ -287,6 +287,7 @@ mutable struct RadauIIA9ConstantCache{F, Tab, Tol, Dt, U, JType} <: cont2::U cont3::U cont4::U + cont5::U dtprev::Dt W_γdt::Dt status::NLStatus @@ -304,7 +305,7 @@ function alg_cache(alg::RadauIIA9, u, rate_prototype, ::Type{uEltypeNoUnits}, κ = alg.κ !== nothing ? convert(uToltype, alg.κ) : convert(uToltype, 1 // 100) J = false .* _vec(rate_prototype) .* _vec(rate_prototype)' - RadauIIA9ConstantCache(uf, tab, κ, one(uToltype), 10000, u, u, u, u, dt, dt, + RadauIIA9ConstantCache(uf, tab, κ, one(uToltype), 10000, u, u, u, u, u, dt, dt, Convergence, J) end @@ -333,6 +334,7 @@ mutable struct RadauIIA9Cache{uType, cuType, uNoUnitsType, rateType, JType, W1Ty cont2::uType cont3::uType cont4::uType + cont5::uType du1::rateType fsalfirst::rateType k::rateType @@ -407,6 +409,7 @@ function alg_cache(alg::RadauIIA9, u, rate_prototype, ::Type{uEltypeNoUnits}, cont2 = zero(u) cont3 = zero(u) cont4 = zero(u) + cont5 = zero(u) fsalfirst = zero(rate_prototype) k = zero(rate_prototype) @@ -462,7 +465,7 @@ function alg_cache(alg::RadauIIA9, u, rate_prototype, ::Type{uEltypeNoUnits}, RadauIIA9Cache(u, uprev, z1, z2, z3, z4, z5, w1, w2, w3, w4, w5, - dw1, ubuff, dw23, dw45, cubuff1, cubuff2, cont1, cont2, cont3, cont4, + dw1, ubuff, dw23, dw45, cubuff1, cubuff2, cont1, cont2, cont3, cont4, cont5, du1, fsalfirst, k, k2, k3, k4, k5, fw1, fw2, fw3, fw4, fw5, J, W1, W2, W3, uf, tab, κ, one(uToltype), 10000, diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index 1f0b418970..012f20f904 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -723,9 +723,9 @@ end if integrator.EEst <= oneunit(integrator.EEst) cache.dtprev = dt if alg.extrapolant != :constant - @.. broadcast=false cache.cont1=(z2 - z3) / c2m1 - @.. broadcast=false tmp=(z1 - z2) / c1mc2 - @.. broadcast=false cache.cont2=(tmp - cache.cont1) / c1m1 + @.. broadcast=false cache.cont1=(z2 - z3) / c2m1 + @.. broadcast=false tmp=(z1 - z2) / c1mc2 + @.. broadcast=false cache.cont2=(tmp - cache.cont1) / c1m1 @.. broadcast=false cache.cont3=cache.cont2 - (tmp - z1 / c1) / c2 end end @@ -740,7 +740,7 @@ end @unpack T11, T12, T13, T14, T15, T21, T22, T23, T24, T25, T31, T32, T33, T34, T35, T41, T42, T43, T44, T45, T51 = cache.tab #= T52 = 1, T53 = 0, T54 = 1, T55 = 0=# @unpack TI11, TI12, TI13, TI14, TI15, TI21, TI22, TI23, TI24, TI25, TI31, TI32, TI33, TI34, TI35, TI41, TI42, TI43, TI44, TI45, TI51, TI52, TI53, TI54, TI55 = cache.tab @unpack c1, c2, c3, c4, γ, α1, β1, α2, β2, e1, e2, e3, e4, e5 = cache.tab - @unpack κ, cont1, cont2, cont3, cont4 = cache + @unpack κ, cont1, cont2, cont3, cont4, cont5 = cache @unpack internalnorm, abstol, reltol, adaptive = integrator.opts alg = unwrap_alg(integrator, true) @unpack maxiters = alg @@ -785,27 +785,32 @@ end cache.cont2 = map(zero, u) cache.cont3 = map(zero, u) cache.cont4 = map(zero, u) + cache.cont5 = map(zero, u) else c5′ = dt / cache.dtprev c1′ = c1 * c5′ c2′ = c2 * c5′ c3′ = c3 * c5′ c4′ = c4 * c5′ - z1 = @.. broadcast=false c1′*(cont1 + - (c1′ - c3m1) * (cont2 + - (c1′ - c2m1) * (cont3 + (c1′ - c1m1) * cont4))) - z2 = @.. broadcast=false c2′*(cont1 + - (c2′ - c3m1) * (cont2 + - (c2′ - c2m1) * (cont3 + (c2′ - c1m1) * cont4))) - z3 = @.. broadcast=false c3′*(cont1 + - (c3′ - c3m1) * (cont2 + - (c3′ - c2m1) * (cont3 + (c3′ - c1m1) * cont4))) - z4 = @.. broadcast=false c4′*(cont1 + - (c4′ - c3m1) * (cont2 + - (c4′ - c2m1) * (cont3 + (c4′ - c1m1) * cont4))) - z5 = @.. broadcast=false c5′*(cont1 + - (c5′ - c3m1) * (cont2 + - (c5′ - c2m1) * (cont3 + (c5′ - c1m1) * cont4))) + z1 = @.. c1′ * (cont1 + + (c1′-c4m1) * (cont2 + + (c1′ - c3m1) * (cont3 + + (c1′ - c2m1) * (cont4 + (c1′ - c1m1) * cont5)))) + z2 = @.. c2′ * (cont1 + + (c2′-c4m1) * (cont2 + + (c2′ - c3m1) * (cont3 + + (c2′ - c2m1) * (cont4 + (c2′ - c1m1) * cont5)))) + z3 = @.. c3′ * (cont1 + + (c3′-c4m1) * (cont2 + + (c3′ - c3m1) * (cont3 + + (c3′ - c2m1) * (cont4 + (c3′ - c1m1) * cont5)))) + z4 = @.. c4′ * (cont1 + + (c4′-c4m1) * (cont2 + + (c4′ - c3m1) * (cont3 + + (c4′ - c2m1) * (cont4 + (c4′ - c1m1) * cont5)))) + z5 = @.. c5′ * (cont1 + + (c5′-c4m1) * (cont2 + + (c5′ - c3m1) * (cont3 + (c5′ - c2m1) * (cont4 + (c5′ - c1m1) * cont5)))) w1 = @.. broadcast=false TI11*z1+TI12*z2+TI13*z3+TI14*z4+TI15*z5 w2 = @.. broadcast=false TI21*z1+TI22*z2+TI23*z3+TI24*z4+TI25*z5 w3 = @.. broadcast=false TI31*z1+TI32*z2+TI33*z3+TI34*z4+TI35*z5 @@ -898,7 +903,7 @@ end z3 = @.. broadcast=false T31*w1+T32*w2+T33*w3+T34*w4+T35*w5 z4 = @.. broadcast=false T41*w1+T42*w2+T43*w3+T44*w4+T45*w5 z5 = @.. broadcast=false T51*w1+w2+w4 #= T52=1, T53=0, T54=1, T55=0 =# - @show z1 + # check stopping criterion iter > 1 && (η = θ / (1 - θ)) if η * ndw < κ && (iter > 1 || iszero(ndw) || !iszero(integrator.success_iter)) @@ -953,6 +958,11 @@ end tmp5 = @.. (tmp4 - tmp2) / c1mc3 # second derivative on [c1, c3] tmp6 = @.. (tmp5 - tmp3) / c1mc4 # third derivative on [c1, c4] cache.cont4 = @.. (tmp6 - cache.cont3) / c1m1 #fourth derivative on [c1, 1] + tmp7 = @.. z1 / c1 #first derivative on [0, c1] + tmp8 = @.. (tmp4 - tmp7) / c2 #second derivative on [0, c2] + tmp9 = @.. (tmp5 - tmp8) / c3 #third derivative on [0, c3] + tmp10 = @.. (tmp6 - tmp9) / c4 #fourth derivative on [0,c4] + cache.cont5 = @.. cache.cont4 - tmp10 #fifth derivative on [0,1] end end @@ -969,7 +979,7 @@ end @unpack T11, T12, T13, T14, T15, T21, T22, T23, T24, T25, T31, T32, T33, T34, T35, T41, T42, T43, T44, T45, T51 = cache.tab #= T52 = 1, T53 = 0, T54 = 1, T55 = 0=# @unpack TI11, TI12, TI13, TI14, TI15, TI21, TI22, TI23, TI24, TI25, TI31, TI32, TI33, TI34, TI35, TI41, TI42, TI43, TI44, TI45, TI51, TI52, TI53, TI54, TI55 = cache.tab @unpack c1, c2, c3, c4, γ, α1, β1, α2, β2, e1, e2, e3, e4, e5 = cache.tab - @unpack κ, cont1, cont2, cont3, cont4 = cache + @unpack κ, cont1, cont2, cont3, cont4, cont5 = cache @unpack z1, z2, z3, z4, z5, w1, w2, w3, w4, w5 = cache @unpack dw1, ubuff, dw23, dw45, cubuff1, cubuff2 = cache @unpack k, k2, k3, k4, k5, fw1, fw2, fw3, fw4, fw5 = cache @@ -1022,32 +1032,37 @@ end @.. broadcast=false cache.cont2=uzero @.. broadcast=false cache.cont3=uzero @.. broadcast=false cache.cont4=uzero + @.. broadcast=false cache.cont5=uzero else c5′ = dt / cache.dtprev c1′ = c1 * c5′ c2′ = c2 * c5′ c3′ = c3 * c5′ c4′ = c4 * c5′ - @.. broadcast=false z1 = c1′*(cont1 + - (c1′ - c3m1) * (cont2 + - (c1′ - c2m1) * (cont3 + (c1′ - c1m1) * cont4))) - @.. broadcast=false z2 = c2′*(cont1 + - (c2′ - c3m1) * (cont2 + - (c2′ - c2m1) * (cont3 + (c2′ - c1m1) * cont4))) - @.. broadcast=false z3 = c3′*(cont1 + - (c3′ - c3m1) * (cont2 + - (c3′ - c2m1) * (cont3 + (c3′ - c1m1) * cont4))) - @.. broadcast=false z4 = c4′*(cont1 + - (c4′ - c3m1) * (cont2 + - (c4′ - c2m1) * (cont3 + (c4′ - c1m1) * cont4))) - @.. broadcast=false z5 = c5′*(cont1 + - (c5′ - c3m1) * (cont2 + - (c5′ - c2m1) * (cont3 + (c5′ - c1m1) * cont4))) - @.. broadcast=false w1 = TI11*z1+TI12*z2+TI13*z3+TI14*z4+TI15*z5 - @.. broadcast=false w2 = TI21*z1+TI22*z2+TI23*z3+TI24*z4+TI25*z5 - @.. broadcast=false w3 = TI31*z1+TI32*z2+TI33*z3+TI34*z4+TI35*z5 - @.. broadcast=false w4 = TI41*z1+TI42*z2+TI43*z3+TI44*z4+TI45*z5 - @.. broadcast=false w5 = TI51*z1+TI52*z2+TI53*z3+TI54*z4+TI55*z5 + z1 = @.. c1′ * (cont1 + + (c1′-c4m1) * (cont2 + + (c1′ - c3m1) * (cont3 + + (c1′ - c2m1) * (cont4 + (c1′ - c1m1) * cont5)))) + z2 = @.. c2′ * (cont1 + + (c2′-c4m1) * (cont2 + + (c2′ - c3m1) * (cont3 + + (c2′ - c2m1) * (cont4 + (c2′ - c1m1) * cont5)))) + z3 = @.. c3′ * (cont1 + + (c3′-c4m1) * (cont2 + + (c3′ - c3m1) * (cont3 + + (c3′ - c2m1) * (cont4 + (c3′ - c1m1) * cont5)))) + z4 = @.. c4′ * (cont1 + + (c4′-c4m1) * (cont2 + + (c4′ - c3m1) * (cont3 + + (c4′ - c2m1) * (cont4 + (c4′ - c1m1) * cont5)))) + z5 = @.. c5′ * (cont1 + + (c5′-c4m1) * (cont2 + + (c5′ - c3m1) * (cont3 + (c5′ - c2m1) * (cont4 + (c5′ - c1m1) * cont5)))) + w1 = @.. broadcast=false TI11*z1+TI12*z2+TI13*z3+TI14*z4+TI15*z5 + w2 = @.. broadcast=false TI21*z1+TI22*z2+TI23*z3+TI24*z4+TI25*z5 + w3 = @.. broadcast=false TI31*z1+TI32*z2+TI33*z3+TI34*z4+TI35*z5 + w4 = @.. broadcast=false TI41*z1+TI42*z2+TI43*z3+TI44*z4+TI45*z5 + w5 = @.. broadcast=false TI51*z1+TI52*z2+TI53*z3+TI54*z4+TI55*z5 end # Newton iteration @@ -1272,16 +1287,21 @@ end if integrator.EEst <= oneunit(integrator.EEst) cache.dtprev = dt if alg.extrapolant != :constant - @.. cache.cont1 = (z4 - z5) / c4m1 - @.. tmp = (z3 - z4) / c3mc4 - @.. cache.cont2 = (tmp - cache.cont1) / c3m1 - @.. tmp2 = (z2 - z3) / c2mc3 - @.. tmp3 = (tmp2 - tmp) / c2mc4 - @.. cache.cont3 = (tmp3 - cache.cont2) / c2m1 - @.. tmp4 = (z1 - z2) / c1mc2 - @.. tmp5 = (tmp4 - tmp2) / c1mc3 - @.. tmp6 = (tmp5 - tmp3) / c1mc4 - @.. cache.cont4 = (tmp6 - cache.cont3) / c1m1 + cache.cont1 = @.. (z4 - z5) / c4m1 # first derivative on [c4, 1] + tmp1 = @.. (z3 - z4) / c3mc4 # first derivative on [c3, c4] + cache.cont2 = @.. (tmp1 - cache.cont1) / c3m1 # second derivative on [c3, 1] + tmp2 = @.. (z2 - z3) / c2mc3 # first derivative on [c2, c3] + tmp3 = @.. (tmp2 - tmp1) / c2mc4 # second derivative on [c2, c4] + cache.cont3 = @.. (tmp3 - cache.cont2) / c2m1 # third derivative on [c2, 1] + tmp4 = @.. (z1 - z2) / c1mc2 # first derivative on [c1, c2] + tmp5 = @.. (tmp4 - tmp2) / c1mc3 # second derivative on [c1, c3] + tmp6 = @.. (tmp5 - tmp3) / c1mc4 # third derivative on [c1, c4] + cache.cont4 = @.. (tmp6 - cache.cont3) / c1m1 #fourth derivative on [c1, 1] + tmp7 = @.. z1 / c1 #first derivative on [0, c1] + tmp8 = @.. (tmp4 - tmp7) / c2 #second derivative on [0, c2] + tmp9 = @.. (tmp5 - tmp8) / c3 #third derivative on [0, c3] + tmp10 = @.. (tmp6 - tmp9) / c4 #fourth derivative on [0,c4] + cache.cont5 = @.. cache.cont4 - tmp10 #fifth derivative on [0,1] end end @@ -1363,7 +1383,7 @@ end end integrator.stats.nf += num_stages - fw = @.. TI * ff + fw = TI * ff Mw = Vector{eltype(u)}(undef, num_stages) if mass_matrix isa UniformScaling # `UniformScaling` doesn't play nicely with broadcast for i in 1 : num_stages @@ -1417,8 +1437,7 @@ end w = @.. w - dw # transform `w` to `z` - z = @.. T * w - @show z[1] + z = T * w # check stopping criterion iter > 1 && (η = θ / (1 - θ)) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl index a0b7404476..a7934174ce 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl @@ -308,7 +308,7 @@ function adaptiveRadauTableau(T, T2, num_stages::Int) b[i] = a[num_stages, i] end vals = eigvals(a_inverse) - γ = real(b[num_stages]) + γ = real(vals[num_stages]) α = Vector{BigFloat}(undef, floor(Int, num_stages/2)) β = Vector{BigFloat}(undef, floor(Int, num_stages/2)) index = 1 @@ -338,8 +338,10 @@ function adaptiveRadauTableau(T, T2, num_stages::Int) end end TI = inv(T) - + #= + p = num_stages eb = variables(:b, 1:num_stages + 1) + @variables y zz = zeros(size(a, 1) + 1) zz2 = zeros(size(a, 1)) eA = [zz' @@ -348,12 +350,12 @@ function adaptiveRadauTableau(T, T2, num_stages::Int) constraints = map(Iterators.flatten(RootedTreeIterator(i) for i in 1:p)) do t residual_order_condition(t, RungeKuttaMethod(eA, eb, ec)) end - AA, bb, islinear = Symbolics.linear_expansion(substitute.(constraints, (eb[1]=>γ,)), eb[2:end]) - AA = Float64.(map(unwrap, AA)) + AA, bb, islinear = Symbolics.linear_expansion(substitute.(constraints, (eb[1]=>y,)), eb[2:end]) + AA = BigFloat.(map(unwrap, AA)) idxs = qr(AA', ColumnNorm()).p[1:num_stages] @assert rank(AA[idxs, :]) == num_stages @assert islinear - Symbolics.expand.((AA[idxs, :] \ -bb[idxs]) - b) + Symbolics.expand.((AA[idxs, :] \ -bb[idxs]) - b)=# #e = b_hat - b adaptiveRadauTableau{Any, T2, Int}(T, TI, γ, α, β, c, num_stages) end \ No newline at end of file diff --git a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl index 36289bdf7b..3d1e32989c 100644 --- a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl +++ b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl @@ -12,12 +12,11 @@ sol = solve(prob_ode_linear, AdaptiveRadau(), adaptive = false, dt = 1e-2) sol = solve(prob_ode_linear, RadauIIA9(), adaptive = false, dt = 1e-2) sol = solve(prob_ode_linear, RadauIIA5(), adaptive = false, dt = 1e-2) - -sim21 = test_convergence(1 ./ 10 .^ (4.5:-1:2.5), prob_ode_linear, AdaptiveRadau()) -@test sim21.𝒪est[:final]≈8 atol=testTol +sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_linear, RadauIIA9()) +@test sim21.𝒪est[:final]≈9 atol=testTol sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_2Dlinear, RadauIIA9()) -@test sim21.𝒪est[:final]≈8 atol=testTol +@test sim21.𝒪est[:final]≈9 atol=testTol # test adaptivity for iip in (true, false) From 1d7a4bdd3badef08e1c80eb1e15ef8f7f20a22f7 Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Fri, 23 Aug 2024 16:21:21 -0400 Subject: [PATCH 46/71] fix collocation on adaptive radau --- lib/OrdinaryDiffEqFIRK/src/firk_caches.jl | 8 ++-- .../src/firk_perform_step.jl | 43 +++++++++---------- 2 files changed, 24 insertions(+), 27 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl index 035c1f6815..c108eef4c1 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl @@ -497,8 +497,8 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} num_stages = alg.num_stages tab = adaptiveRadauTableau(uToltype, constvalue(tTypeNoUnits), num_stages) - cont = Vector{typeof(u)}(undef, num_stages - 1) - for i in 1: (num_stages - 1) + cont = Vector{typeof(u)}(undef, num_stages) + for i in 1: num_stages cont[i] = zero(u) end @@ -576,8 +576,8 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} recursivefill!(cubuff[i], false) end - cont = Vector{typeof(u)}(undef, num_stages - 1) - for i in 1: (num_stages - 1) + cont = Vector{typeof(u)}(undef, num_stages) + for i in 1: num_stages cont[i] = zero(u) end diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index 012f20f904..0914c239b5 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1344,10 +1344,7 @@ end if integrator.iter == 1 || integrator.u_modified || alg.extrapolant == :constant cache.dtprev = one(cache.dtprev) for i in 1 : num_stages - z[i] = w[i] = map(zero, u) - end - for i in 1 : (num_stages - 1) - cache.cont[i] = map(zero, u) + z[i] = w[i] = cache.cont[i] = map(zero, u) end else c_prime = Vector{eltype(u)}(undef, num_stages) #time stepping @@ -1356,8 +1353,8 @@ end c_prime[i] = c[i] * c_prime[num_stages] end for i in 1 : num_stages # collocation polynomial - z[i] = @.. cont[num_stages - 1] * (c_prime[i] - c[1] + 1) + cont[num_stages - 2] - j = num_stages - 3 + z[i] = @.. cont[num_stages] * (c_prime[i] - c[1] + 1) + cont[num_stages - 1] + j = num_stages - 2 while j > 0 z[i] = @.. z[i] * (c_prime[i] - c[num_stages- j - 1] + 1) + cont[j] j = j - 1 @@ -1483,9 +1480,10 @@ end if integrator.EEst <= oneunit(integrator.EEst) cache.dtprev = dt if alg.extrapolant != :constant - derivatives = Matrix{eltype(u)}(undef, num_stages - 1, num_stages - 1) - for i in 1 : (num_stages - 1) - for j in i : (num_stages - 1) + derivatives = Matrix{eltype(u)}(undef, num_stages, num_stages) + pushfirst!(c, 0) + for i in 1 : num_stages + for j in i : num_stages if i == 1 derivatives[i, j] = @.. (z[i] - z[i + 1]) / (c[i] - c[i + 1]) #first derivatives else @@ -1493,8 +1491,9 @@ end end end end + popfirst!(c) for i in 1 : (num_stages - 1) - cache.cont[i] = derivatives[i, num_stages - 1] + cache.cont[i] = derivatives[i, num_stages] end end end @@ -1537,12 +1536,8 @@ end # TODO better initial guess if integrator.iter == 1 || integrator.u_modified || alg.extrapolant == :constant cache.dtprev = one(cache.dtprev) - uzero = zero(eltype(u)) for i in 1 : num_stages - @.. z[i] = w[i] = uzero - end - for i in 1 : (num_stages-1) - @.. cache.cont[i] = uzero + z[i] = w[i] = cache.cont[i] = map(zero, u) end else c_prime = Vector{eltype(u)}(undef, num_stages) #time stepping @@ -1551,8 +1546,8 @@ end c_prime[i] = c[i] * c_prime[num_stages] end for i in 1 : num_stages # collocation polynomial - z[i] = @.. cont[num_stages - 1] * (c_prime[i] - c[1] + 1) + cont[num_stages - 2] - j = num_stages - 3 + z[i] = @.. cont[num_stages] * (c_prime[i] - c[1] + 1) + cont[num_stages - 1] + j = num_stages - 2 while j > 0 z[i] = @.. z[i] * (c_prime[i] - c[num_stages- j - 1] + 1) + cont[j] j = j - 1 @@ -1728,18 +1723,20 @@ end if integrator.EEst <= oneunit(integrator.EEst) cache.dtprev = dt if alg.extrapolant != :constant - derivatives = Matrix{eltype(u)}(undef, num_stages - 1, num_stages - 1) - for i in 1 : (num_stages - 1) - for j in i : (num_stages - 1) + derivatives = Matrix{eltype(u)}(undef, num_stages, num_stages) + pushfirst!(c, 0) + for i in 1 : num_stages + for j in i : num_stages if i == 1 - @.. derivatives[i, j] = (z[i] - z[i + 1]) / (c[i] - c[i + 1]) #first derivatives + derivatives[i, j] = @.. (z[i] - z[i + 1]) / (c[i] - c[i + 1]) #first derivatives else - @.. derivatives[i, j] = (derivatives[i - 1, j - 1] - derivatives[i - 1, j]) / (c[j - i + 1] - c[j + 1]) #all others + derivatives[i, j] = @.. (derivatives[i - 1, j - 1] - derivatives[i - 1, j]) / (c[j - i + 1] - c[j + 1]) #all others end end end + popfirst!(c) for i in 1 : (num_stages - 1) - cache.cont[i] = derivatives[i, num_stages - 1] + cache.cont[i] = derivatives[i, num_stages] end end end From c69f1c1c8565af4a20ca7517e6ad982fe22d79ba Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Sat, 24 Aug 2024 12:17:16 -0400 Subject: [PATCH 47/71] oop works! --- lib/OrdinaryDiffEqFIRK/src/algorithms.jl | 2 +- lib/OrdinaryDiffEqFIRK/src/firk_caches.jl | 22 +++---- .../src/firk_perform_step.jl | 65 +++++++++++++++---- lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl | 1 + 4 files changed, 67 insertions(+), 23 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/algorithms.jl b/lib/OrdinaryDiffEqFIRK/src/algorithms.jl index 4429fb78b6..ba4c51c0d0 100644 --- a/lib/OrdinaryDiffEqFIRK/src/algorithms.jl +++ b/lib/OrdinaryDiffEqFIRK/src/algorithms.jl @@ -171,7 +171,7 @@ end function AdaptiveRadau(; chunk_size = Val{0}(), autodiff = Val{true}(), standardtag = Val{true}(), concrete_jac = nothing, - diff_type = Val{:forward}, num_stages = 3, + diff_type = Val{:forward}, num_stages = 5, linsolve = nothing, precs = DEFAULT_PRECS, extrapolant = :dense, fast_convergence_cutoff = 1 // 5, new_W_γdt_cutoff = 1 // 5, diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl index c108eef4c1..39e70e5831 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl @@ -552,26 +552,26 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} ::Val{true}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits} uf = UJacobianWrapper(f, t, p) uToltype = constvalue(uBottomEltypeNoUnits) - alg.num_stages = num_stages + num_stages = alg.num_stages tab = adaptiveRadauTableau(uToltype, constvalue(tTypeNoUnits), num_stages) κ = alg.κ !== nothing ? convert(uToltype, alg.κ) : convert(uToltype, 1 // 100) z = Vector{typeof(u)}(undef, num_stages) w = Vector{typeof(u)}(undef, num_stages) - for i in 1:s + for i in 1 : num_stages z[i] = w[i] = zero(u) end dw1 = zero(u) ubuff = zero(u) - dw2 = Vector{typeof(u)}(undef, floor(Int, num_stages/2)) - for i in 1 : floor(Int, num_stages/2) + dw2 = Vector{typeof(u)}(undef, floor(Int, num_stages / 2)) + for i in 1 : floor(Int, num_stages / 2) dw2[i] = similar(u, Complex{eltype(u)}) recursivefill!(dw[i], false) end - cubuff = Vector{typeof(u)}(undef, floor(Int, num_stages/2)) - for i in 1 :floor(Int, num_stages/2) + cubuff = Vector{typeof(u)}(undef, floor(Int, num_stages / 2)) + for i in 1 : floor(Int, num_stages / 2) cubuff[i] = similar(u, Complex{eltype(u)}) recursivefill!(cubuff[i], false) end @@ -593,15 +593,15 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} error("Non-concrete Jacobian not yet supported by RadauIIA5.") end W2 = vector{typeof(Complex{W1})}(undef, floor(Int, num_stages/2)) - for i in 1 : floor(Int, num_stages/2) + for i in 1 : floor(Int, num_stages / 2) W2[i] = similar(J, Complex{eltype(W1)}) recursivefill!(w2[i], false) end du1 = zero(rate_prototype) - tmp = Vector{typeof(u)}(undef, binomial(num_stages,2)) - for i in 1 : binomial(num_stages,2) + tmp = Vector{typeof(u)}(undef, binomial(num_stages , 2)) + for i in 1 : binomial(num_stages , 2) tmp[i] = zero(u) end @@ -614,8 +614,8 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} linsolve1 = init(linprob, alg.linsolve, alias_A = true, alias_b = true, assumptions = LinearSolve.OperatorAssumptions(true)) - linsolve2 = Vector{typeof(linsolve1)}(undef, floor(Int, num_stages/2)) - for i in 1 : floor(int, num_stages/2) + linsolve2 = Vector{typeof(linsolve1)}(undef, floor(Int, num_stages / 2)) + for i in 1 : floor(int, num_stages / 2) linprob = LinearProblem(W2[i], _vec(cubuff[i]); u0 = _vec(dw2[i])) linsolve2 = init(linprob, alg.linsolve, alias_A = true, alias_b = true, assumptions = LinearSolve.OperatorAssumptions(true)) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index 0914c239b5..87d4de366e 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -49,7 +49,7 @@ function initialize!(integrator, cache::RadauIIA3Cache) nothing end -function initialize!(integrator, cache::Union{RadauIIA5Cache, RadauIIA9Cache, AdaptiveRadauCache}) +function initialize!(integrator, cache::RadauIIA5Cache) integrator.kshortsize = 2 resize!(integrator.k, integrator.kshortsize) integrator.k[1] = integrator.fsalfirst @@ -69,6 +69,47 @@ function initialize!(integrator, cache::Union{RadauIIA5Cache, RadauIIA9Cache, Ad nothing end +function initialize!(integrator, cache::RadauIIA9Cache) + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) + OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1) + if integrator.opts.adaptive + @unpack abstol, reltol = integrator.opts + if reltol isa Number + cache.rtol = reltol^(3 / 5) / 10 + cache.atol = cache.rtol * (abstol / reltol) + else + @.. broadcast=false cache.rtol=reltol^(3 / 5) / 10 + @.. broadcast=false cache.atol=cache.rtol * (abstol / reltol) + end + end + nothing +end + +function initialize!(integrator, cache::AdaptiveRadauCache) + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) + OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1) + num_stages = alg.num_stages + if integrator.opts.adaptive + @unpack abstol, reltol = integrator.opts + if reltol isa Number + cache.rtol = reltol^((num_stages + 1) / (2 * num_stages)) / 10 + cache.atol = cache.rtol * (abstol / reltol) + else + @.. broadcast=false cache.rtol=reltol^((num_stages + 1) / (2 * num_stages)) / 10 + @.. broadcast=false cache.atol=cache.rtol * (abstol / reltol) + end + end + nothing +end + @muladd function perform_step!(integrator, cache::RadauIIA3ConstantCache) @unpack t, dt, uprev, u, f, p = integrator @@ -81,7 +122,7 @@ end mass_matrix = integrator.f.mass_matrix # precalculations - rtol = @. reltol^(2 / 3) / 10 + rtol = @. reltol^(3 / 4) / 10 atol = @. rtol * (abstol / reltol) αdt, βdt = α / dt, β / dt J = calc_J(integrator, cache) @@ -747,7 +788,7 @@ end mass_matrix = integrator.f.mass_matrix # precalculations rtol pow is (num stages + 1)/(2*num stages) - rtol = @.. broadcast=false reltol^(5 / 8)/10 + rtol = @.. broadcast=false reltol^(3 / 5)/10 atol = @.. broadcast=false rtol*(abstol / reltol) c1m1 = c1 - 1 c2m1 = c2 - 1 @@ -1321,7 +1362,7 @@ end mass_matrix = integrator.f.mass_matrix # precalculations rtol pow is (num stages + 1)/(2*num stages) - rtol = @.. broadcast=false reltol^(5 / 8)/10 + rtol = @.. broadcast=false reltol^((num_stages + 1) / (num_stages * 2))/10 atol = @.. broadcast=false rtol*(abstol / reltol) γdt, αdt, βdt = γ / dt, α ./ dt, β ./ dt @@ -1356,12 +1397,12 @@ end z[i] = @.. cont[num_stages] * (c_prime[i] - c[1] + 1) + cont[num_stages - 1] j = num_stages - 2 while j > 0 - z[i] = @.. z[i] * (c_prime[i] - c[num_stages- j - 1] + 1) + cont[j] + z[i] = @.. z[i] * (c_prime[i] - c[num_stages - j] + 1) + cont[j] j = j - 1 end z[i] = @.. z[i] * c_prime[i] end - w = @.. TI * z + w = TI * z end # Newton iteration @@ -1434,7 +1475,7 @@ end w = @.. w - dw # transform `w` to `z` - z = T * w + z = vec(T * w) # check stopping criterion iter > 1 && (η = θ / (1 - θ)) @@ -1482,17 +1523,19 @@ end if alg.extrapolant != :constant derivatives = Matrix{eltype(u)}(undef, num_stages, num_stages) pushfirst!(c, 0) + pushfirst!(z, 0) for i in 1 : num_stages for j in i : num_stages if i == 1 - derivatives[i, j] = @.. (z[i] - z[i + 1]) / (c[i] - c[i + 1]) #first derivatives + derivatives[i, j] = @.. (z[j] - z[j + 1]) / (c[j] - c[j + 1]) #first derivatives else derivatives[i, j] = @.. (derivatives[i - 1, j - 1] - derivatives[i - 1, j]) / (c[j - i + 1] - c[j + 1]) #all others end end end popfirst!(c) - for i in 1 : (num_stages - 1) + popfirst!(z) + for i in 1 : num_stages cache.cont[i] = derivatives[i, num_stages] end end @@ -1549,7 +1592,7 @@ end z[i] = @.. cont[num_stages] * (c_prime[i] - c[1] + 1) + cont[num_stages - 1] j = num_stages - 2 while j > 0 - z[i] = @.. z[i] * (c_prime[i] - c[num_stages- j - 1] + 1) + cont[j] + z[i] = @.. z[i] * (c_prime[i] - c[num_stages - j] + 1) + cont[j] j = j - 1 end z[i] = @.. z[i] * c_prime[i] @@ -1735,7 +1778,7 @@ end end end popfirst!(c) - for i in 1 : (num_stages - 1) + for i in 1 : num_stages cache.cont[i] = derivatives[i, num_stages] end end diff --git a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl index 3d1e32989c..bbea52cbf2 100644 --- a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl +++ b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl @@ -8,6 +8,7 @@ for prob in [prob_ode_linear, prob_ode_2Dlinear] @test sim21.𝒪est[:final]≈5 atol=testTol end + sol = solve(prob_ode_linear, AdaptiveRadau(), adaptive = false, dt = 1e-2) sol = solve(prob_ode_linear, RadauIIA9(), adaptive = false, dt = 1e-2) sol = solve(prob_ode_linear, RadauIIA5(), adaptive = false, dt = 1e-2) From 2d6b5f6156a46c2368da9620bf7a781a0f2b417b Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Sun, 25 Aug 2024 19:16:50 -0400 Subject: [PATCH 48/71] fixes --- lib/OrdinaryDiffEqFIRK/src/algorithms.jl | 2 +- lib/OrdinaryDiffEqFIRK/src/firk_caches.jl | 28 ++++++++----------- .../src/firk_perform_step.jl | 1 + lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl | 12 ++++++-- 4 files changed, 22 insertions(+), 21 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/algorithms.jl b/lib/OrdinaryDiffEqFIRK/src/algorithms.jl index ba4c51c0d0..4429fb78b6 100644 --- a/lib/OrdinaryDiffEqFIRK/src/algorithms.jl +++ b/lib/OrdinaryDiffEqFIRK/src/algorithms.jl @@ -171,7 +171,7 @@ end function AdaptiveRadau(; chunk_size = Val{0}(), autodiff = Val{true}(), standardtag = Val{true}(), concrete_jac = nothing, - diff_type = Val{:forward}, num_stages = 5, + diff_type = Val{:forward}, num_stages = 3, linsolve = nothing, precs = DEFAULT_PRECS, extrapolant = :dense, fast_convergence_cutoff = 1 // 5, new_W_γdt_cutoff = 1 // 5, diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl index 39e70e5831..5d7ccba8c4 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl @@ -511,7 +511,7 @@ end mutable struct AdaptiveRadauCache{uType, cuType, uNoUnitsType, rateType, JType, W1Type, W2Type, UF, JC, F1, F2, Tab, Tol, Dt, rTol, aTol, StepLimiter} <: - OrdinaryDiffEqMutableCache + FIRKMutableCache u::uType uprev::uType z::AbstractVector{uType} @@ -533,7 +533,6 @@ mutable struct AdaptiveRadauCache{uType, cuType, uNoUnitsType, rateType, JType, κ::Tol ηold::Tol iter::Int - tmp::AbstractVector{uType} atmp::uNoUnitsType jac_config::JC linsolve1::F1 #real @@ -565,12 +564,12 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} dw1 = zero(u) ubuff = zero(u) - dw2 = Vector{typeof(u)}(undef, floor(Int, num_stages / 2)) + dw2 = Vector{Any}(undef, floor(Int, num_stages / 2)) for i in 1 : floor(Int, num_stages / 2) dw2[i] = similar(u, Complex{eltype(u)}) - recursivefill!(dw[i], false) + recursivefill!(dw2[i], false) end - cubuff = Vector{typeof(u)}(undef, floor(Int, num_stages / 2)) + cubuff = Vector{Any}(undef, floor(Int, num_stages / 2)) for i in 1 : floor(Int, num_stages / 2) cubuff[i] = similar(u, Complex{eltype(u)}) recursivefill!(cubuff[i], false) @@ -592,32 +591,27 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} if J isa AbstractSciMLOperator error("Non-concrete Jacobian not yet supported by RadauIIA5.") end - W2 = vector{typeof(Complex{W1})}(undef, floor(Int, num_stages/2)) + W2 = Vector{Any}(undef, floor(Int, num_stages/2)) for i in 1 : floor(Int, num_stages / 2) W2[i] = similar(J, Complex{eltype(W1)}) - recursivefill!(w2[i], false) + recursivefill!(W2[i], false) end du1 = zero(rate_prototype) - tmp = Vector{typeof(u)}(undef, binomial(num_stages , 2)) - for i in 1 : binomial(num_stages , 2) - tmp[i] = zero(u) - end - atmp = similar(u, uEltypeNoUnits) recursivefill!(atmp, false) - jac_config = build_jac_config(alg, f, uf, du1, uprev, u, tmp, dw1) + jac_config = build_jac_config(alg, f, uf, du1, uprev, u, zero(u), dw1) linprob = LinearProblem(W1, _vec(ubuff); u0 = _vec(dw1)) linsolve1 = init(linprob, alg.linsolve, alias_A = true, alias_b = true, assumptions = LinearSolve.OperatorAssumptions(true)) - linsolve2 = Vector{typeof(linsolve1)}(undef, floor(Int, num_stages / 2)) - for i in 1 : floor(int, num_stages / 2) + linsolve2 = Vector{Any}(undef, floor(Int, num_stages / 2)) + for i in 1 : floor(Int, num_stages / 2) linprob = LinearProblem(W2[i], _vec(cubuff[i]); u0 = _vec(dw2[i])) - linsolve2 = init(linprob, alg.linsolve, alias_A = true, alias_b = true, + linsolve2[i] = init(linprob, alg.linsolve, alias_A = true, alias_b = true, assumptions = LinearSolve.OperatorAssumptions(true)) end @@ -629,7 +623,7 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} du1, fsalfirst, k, fw, J, W1, W2, uf, tab, κ, one(uToltype), 10000, - tmp, atmp, jac_config, + atmp, jac_config, linsolve1, linsolve2, rtol, atol, dt, dt, Convergence, alg.step_limiter!) end diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index 87d4de366e..81740fbf0b 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -90,6 +90,7 @@ function initialize!(integrator, cache::RadauIIA9Cache) end function initialize!(integrator, cache::AdaptiveRadauCache) + println("here") integrator.kshortsize = 2 resize!(integrator.k, integrator.kshortsize) integrator.k[1] = integrator.fsalfirst diff --git a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl index bbea52cbf2..bead50a768 100644 --- a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl +++ b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl @@ -9,9 +9,9 @@ for prob in [prob_ode_linear, prob_ode_2Dlinear] end -sol = solve(prob_ode_linear, AdaptiveRadau(), adaptive = false, dt = 1e-2) -sol = solve(prob_ode_linear, RadauIIA9(), adaptive = false, dt = 1e-2) -sol = solve(prob_ode_linear, RadauIIA5(), adaptive = false, dt = 1e-2) +sol = solve(prob_ode_2Dlinear, AdaptiveRadau(), adaptive = false, dt = 1e-2) +sol = solve(prob_ode_2Dlinear, RadauIIA9(), adaptive = false, dt = 1e-2) +sol = solve(prob_ode_2Dlinear, RadauIIA5(), adaptive = false, dt = 1e-2) sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_linear, RadauIIA9()) @test sim21.𝒪est[:final]≈9 atol=testTol @@ -19,6 +19,12 @@ sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_linear, RadauIIA9()) sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_2Dlinear, RadauIIA9()) @test sim21.𝒪est[:final]≈9 atol=testTol +sim21 = test_convergence(1 ./ 2 .^ (2.25:-1:0.25), prob_ode_linear, AdaptiveRadau()) +@test sim21.𝒪est[:final]≈9 atol=testTol + +sim21 = test_convergence(1 ./ 2 .^(2.25:-1:0.25), prod_ode_2Dlinear, AdaptiveRadau()) +@test sim21.𝒪est[:final]≈9 atol=testTol + # test adaptivity for iip in (true, false) if iip From 064c77d6d01fa0c45fe88012c9d9453c27c235db Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Tue, 27 Aug 2024 17:20:25 -0400 Subject: [PATCH 49/71] Update ode_firk_tests.jl --- lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl | 10 +++++++--- 1 file changed, 7 insertions(+), 3 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl index bead50a768..f8eeac4831 100644 --- a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl +++ b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl @@ -8,9 +8,8 @@ for prob in [prob_ode_linear, prob_ode_2Dlinear] @test sim21.𝒪est[:final]≈5 atol=testTol end - sol = solve(prob_ode_2Dlinear, AdaptiveRadau(), adaptive = false, dt = 1e-2) -sol = solve(prob_ode_2Dlinear, RadauIIA9(), adaptive = false, dt = 1e-2) +sol = solve(prob_ode_linear, RadauIIA9(), adaptive = false, dt = 1e-2) sol = solve(prob_ode_2Dlinear, RadauIIA5(), adaptive = false, dt = 1e-2) sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_linear, RadauIIA9()) @@ -19,9 +18,14 @@ sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_linear, RadauIIA9()) sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_2Dlinear, RadauIIA9()) @test sim21.𝒪est[:final]≈9 atol=testTol -sim21 = test_convergence(1 ./ 2 .^ (2.25:-1:0.25), prob_ode_linear, AdaptiveRadau()) +prob_ode_linear_big = remake(prob_ode_linear, u0 = big.(prob_ode_linear.u0), tspan = big.(prob_ode_linear.tspan)) +prob_ode_2Dlinear_big = remake(prob_ode_2Dlinear, u0 = big.(prob_ode_2Dlinear.u0), tspan = big.(prob_ode_2Dlinear.tspan)) + +sol = solve(prob_ode_linear_big, AdaptiveRadau(), adaptive=false, dt = 1e-2) +sim21 = test_convergence(1 ./ 2 .^ (2.25:-1:0.25), prob_ode_linear_big, AdaptiveRadau()) @test sim21.𝒪est[:final]≈9 atol=testTol +sol = solve(prob_ode_2Dlinear_big, AdaptiveRadau(), adaptive=false, dt = 1e-2) sim21 = test_convergence(1 ./ 2 .^(2.25:-1:0.25), prod_ode_2Dlinear, AdaptiveRadau()) @test sim21.𝒪est[:final]≈9 atol=testTol From bff13df40f2a05d1cdb260b551c96a798b6f953a Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Thu, 29 Aug 2024 21:15:40 -0400 Subject: [PATCH 50/71] clean up --- lib/OrdinaryDiffEqFIRK/src/firk_caches.jl | 15 ++-- .../src/firk_perform_step.jl | 70 ++++++++++--------- lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl | 15 ++-- 3 files changed, 56 insertions(+), 44 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl index e0ed1c2eb3..0cd2ea21be 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl @@ -523,7 +523,8 @@ mutable struct AdaptiveRadauCache{uType, cuType, uNoUnitsType, rateType, JType, cont::AbstractVector{uType} du1::rateType fsalfirst::rateType - k::AbstractVector{rateType} + ks::AbstractVector{rateType} + k::rateType fw::AbstractVector{rateType} J::JType W1::W1Type #real @@ -533,6 +534,7 @@ mutable struct AdaptiveRadauCache{uType, cuType, uNoUnitsType, rateType, JType, κ::Tol ηold::Tol iter::Int + tmp::uType atmp::uNoUnitsType jac_config::JC linsolve1::F1 #real @@ -582,10 +584,11 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} fsalfirst = zero(rate_prototype) fw = Vector{typeof(rate_prototype)}(undef, num_stages) - k = Vector{typeof(rate_prototype)}(undef, num_stages) + ks = Vector{typeof(rate_prototype)}(undef, num_stages) for i in 1: num_stages - k[i] = fw[i] = zero(rate_prototype) + ks[i] = fw[i] = zero(rate_prototype) end + k = ks[1] J, W1 = build_J_W(alg, u, uprev, p, t, dt, f, uEltypeNoUnits, Val(true)) if J isa AbstractSciMLOperator @@ -599,6 +602,8 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} du1 = zero(rate_prototype) + tmp = zero(u) + atmp = similar(u, uEltypeNoUnits) recursivefill!(atmp, false) @@ -620,9 +625,9 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} AdaptiveRadauCache(u, uprev, z, w, dw1, ubuff, dw2, cubuff, cont, - du1, fsalfirst, k, fw, + du1, fsalfirst, ks, k, fw, J, W1, W2, - uf, tab, κ, one(uToltype), 10000, + uf, tab, κ, one(uToltype), 10000, tmp, atmp, jac_config, linsolve1, linsolve2, rtol, atol, dt, dt, Convergence, alg.step_limiter!) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index 81740fbf0b..84822f243c 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -90,14 +90,13 @@ function initialize!(integrator, cache::RadauIIA9Cache) end function initialize!(integrator, cache::AdaptiveRadauCache) - println("here") + @unpack num_stages = cache.tab integrator.kshortsize = 2 resize!(integrator.k, integrator.kshortsize) integrator.k[1] = integrator.fsalfirst integrator.k[2] = integrator.fsallast integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1) - num_stages = alg.num_stages if integrator.opts.adaptive @unpack abstol, reltol = integrator.opts if reltol isa Number @@ -1214,7 +1213,6 @@ end end cache.linsolve3 = linres3.cache - integrator.stats.nsolve += 3 dw2 = z2 dw3 = z3 @@ -1554,8 +1552,8 @@ end @unpack t, dt, uprev, u, f, p, fsallast, fsalfirst = integrator @unpack T, TI, γ, α, β, c, #=e,=# num_stages = cache.tab @unpack κ, cont, z, w = cache - @unpack dw1, ubuff, dw2, cubuff1, cubuff2 = cache - @unpack k, fw, J, W1, W2 = cache + @unpack dw1, ubuff, dw2, cubuff = cache + @unpack ks, k, fw, J, W1, W2 = cache @unpack tmp, atmp, jac_config, linsolve1, linsolve2, rtol, atol, step_limiter! = cache @unpack internalnorm, abstol, reltol, adaptive = integrator.opts alg = unwrap_alg(integrator, true) @@ -1570,8 +1568,8 @@ end if (new_W = do_newW(integrator, alg, new_jac, cache.W_γdt)) @inbounds for II in CartesianIndices(J) W1[II] = -γdt * mass_matrix[Tuple(II)...] + J[II] - for i in 1 : (num_stages - 1) / 2 - W2[i][II] = -(α[i]dt + β[i]dt * im) * mass_matrix[Tuple(II)...] + J[II] + for i in 1 : Int((num_stages - 1) / 2) + W2[i][II] = -(αdt[i] + βdt[i] * im) * mass_matrix[Tuple(II)...] + J[II] end end integrator.stats.nw += 1 @@ -1611,14 +1609,14 @@ end integrator.stats.nnonliniter += 1 # evaluate function - k[1] = fsallast + ks[1] = fsallast for i in 1 : num_stages @.. tmp = uprev + z[i] - f(k[i], tmp, p, t + c[i] * dt) + f(ks[i], tmp, p, t + c[i] * dt) end integrator.stats.nf += num_stages - @.. fw = TI * k + fw = TI * ks if mass_matrix === I Mw = w elseif mass_matrix isa UniformScaling @@ -1637,47 +1635,50 @@ end needfactor = iter == 1 && new_W linsolve1 = cache.linsolve1 - linres = Vector{BigFloat}(undef, num_stages) if needfactor - linres[1] = dolinsolve(integrator, linsolve1; A = W1, b = _vec(ubuff), + linres = dolinsolve(integrator, linsolve1; A = W1, b = _vec(ubuff), linu = _vec(dw1)) else - linres[1] = dolinsolve(integrator, linsolve1; A = nothing, b = _vec(ubuff), + linres = dolinsolve(integrator, linsolve1; A = nothing, b = _vec(ubuff), linu = _vec(dw1)) end - cache.linsolve1 = linres1.cache - - for i in 1 : (num_stages - 1)/2 - @.. broadcast=false cubuff[i]=complex( - fw2 - αdt[i] * Mw[2 * i] + βdt[i] * Mw[2 * i + 1], fw3 - βdt[i] * Mw[2 * i] - αdt[i] * Mw[2 * i + 1]) + cache.linsolve1 = linres.cache + linres2 = Vector{Any}(undef, Int((num_stages - 1) / 2)) + for i in 1 : Int((num_stages - 1) / 2) + @.. cubuff[i]=complex( + fw[2 * i] - αdt[i] * Mw[2 * i] + βdt[i] * Mw[2 * i + 1], fw[2 * i + 1] - βdt[i] * Mw[2 * i] - αdt[i] * Mw[2 * i + 1]) linsolve2[i] = cache.linsolve2[i] if needfactor - linres[i + 1] = dolinsolve(integrator, linsolve2[i]; A = W2[i], b = _vec(cubuff[i]), + linres2[i] = dolinsolve(integrator, linsolve2[i]; A = W2[i], b = _vec(cubuff[i]), linu = _vec(dw2[i])) else - linres[i + 1] = dolinsolve(integrator, linsolve2[i]; A = nothing, b = _vec(cubuff[i]), + linres2[i] = dolinsolve(integrator, linsolve2[i]; A = nothing, b = _vec(cubuff[i]), linu = _vec(dw2[i])) end - cache.linsolve2[i] = linres[i + 1].cache + cache.linsolve2[i] = linres2[i].cache end integrator.stats.nsolve += (num_stages + 1) / 2 - dw[1] = dw1 - i = 2 - while i <= num_stages + dw = Vector{Any}(undef, num_stages - 1) + i = 1 + while i <= Int((num_stages - 1) / 2) dw[i] = z[i] dw[i + 1] = z[i + 1] - @.. dw[i] = real(dw2[i - 1]) - @.. dw[i + 1] = imag(dw2[i - 1]) + @.. dw[i] = real(dw2[i]) + @.. dw[i + 1] = imag(dw2[i]) i += 2 end # compute norm of residuals iter > 1 && (ndwprev = ndw) - ndws = Vector{BigFloat}(undef, num_stages) - for i in 1:num_stages - calculate_residuals!(atmp, dw[i], uprev, u, atol, rtol, internalnorm, t) + ndws = Vector{Any}(undef, num_stages) + ndws[1] = calculate_residuals!(atmp, dw1, uprev, u, atol, rtol, internalnorm, t) + ndws[1] = internalnorm(atmp, t) + + for i in 2 : num_stages + @show i + calculate_residuals!(atmp, dw[i - 1], uprev, u, atol, rtol, internalnorm, t) ndws[i] = internalnorm(atmp, t) end @@ -1698,10 +1699,13 @@ end end end - @.. w = w - dw + w[1] -= dw1 + for i in 2 : num_stages + w[i] -= dw[i - 1] + end # transform `w` to `z` - @.. z = T * w + z = T * w # check stopping criterion iter > 1 && (η = θ / (1 - θ)) @@ -1722,7 +1726,7 @@ end cache.ηold = η cache.iter = iter - @.. broadcast=false u=uprev + z[s] + @.. broadcast=false u=uprev + z[num_stages] step_limiter!(u, integrator, p, t + dt) #= @@ -1767,7 +1771,7 @@ end if integrator.EEst <= oneunit(integrator.EEst) cache.dtprev = dt if alg.extrapolant != :constant - derivatives = Matrix{eltype(u)}(undef, num_stages, num_stages) + derivatives = Matrix{Any}(undef, num_stages, num_stages) pushfirst!(c, 0) for i in 1 : num_stages for j in i : num_stages diff --git a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl index f8eeac4831..83f6468712 100644 --- a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl +++ b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl @@ -21,13 +21,16 @@ sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_2Dlinear, RadauIIA9()) prob_ode_linear_big = remake(prob_ode_linear, u0 = big.(prob_ode_linear.u0), tspan = big.(prob_ode_linear.tspan)) prob_ode_2Dlinear_big = remake(prob_ode_2Dlinear, u0 = big.(prob_ode_2Dlinear.u0), tspan = big.(prob_ode_2Dlinear.tspan)) -sol = solve(prob_ode_linear_big, AdaptiveRadau(), adaptive=false, dt = 1e-2) -sim21 = test_convergence(1 ./ 2 .^ (2.25:-1:0.25), prob_ode_linear_big, AdaptiveRadau()) -@test sim21.𝒪est[:final]≈9 atol=testTol +for i in [3, 5, 7, 9] + sim21 = test_convergence(1 ./ 2 .^ (2.25:-1:0.25), prob_ode_linear_big, AdaptiveRadau(num_stages = i)) + @test sim21.𝒪est[:final]≈ (2 * i - 1) atol=testTol +end -sol = solve(prob_ode_2Dlinear_big, AdaptiveRadau(), adaptive=false, dt = 1e-2) -sim21 = test_convergence(1 ./ 2 .^(2.25:-1:0.25), prod_ode_2Dlinear, AdaptiveRadau()) -@test sim21.𝒪est[:final]≈9 atol=testTol +sol = solve(prob_ode_2Dlinear_big, RadauIIA9(), adaptive=false, dt = 1e-5) +for i in [5] + sim21 = test_convergence(1 ./ 10 .^ (5:-1:3), prob_ode_2Dlinear_big, AdaptiveRadau(num_stages = i)) + @test sim21.𝒪est[:final]≈ (2 * i - 1) atol=testTol +end # test adaptivity for iip in (true, false) From 55259d5474ca263393e75f98d8538e66651a491f Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Sat, 31 Aug 2024 22:03:58 -0400 Subject: [PATCH 51/71] IN PLACE --- lib/OrdinaryDiffEqFIRK/src/firk_caches.jl | 2 +- .../src/firk_perform_step.jl | 54 +++++++++---------- lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl | 39 ++++++++++++-- lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl | 11 ++-- 4 files changed, 65 insertions(+), 41 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl index 0cd2ea21be..6abd379e05 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl @@ -594,7 +594,7 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} if J isa AbstractSciMLOperator error("Non-concrete Jacobian not yet supported by RadauIIA5.") end - W2 = Vector{Any}(undef, floor(Int, num_stages/2)) + W2 = Vector{Any}(undef, floor(Int, num_stages / 2)) for i in 1 : floor(Int, num_stages / 2) W2[i] = similar(J, Complex{eltype(W1)}) recursivefill!(W2[i], false) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index 84822f243c..e6aa13e6a5 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -770,6 +770,7 @@ end @.. broadcast=false cache.cont3=cache.cont2 - (tmp - z1 / c1) / c2 end end + f(fsallast, u, p, t + dt) OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1) return @@ -1175,11 +1176,9 @@ end linsolve1 = cache.linsolve1 if needfactor - linres1 = dolinsolve(integrator, linsolve1; A = W1, b = _vec(ubuff), - linu = _vec(dw1)) + linres1 = dolinsolve(integrator, linsolve1; A = W1, b = _vec(ubuff), linu = _vec(dw1)) else - linres1 = dolinsolve(integrator, linsolve1; A = nothing, b = _vec(ubuff), - linu = _vec(dw1)) + linres1 = dolinsolve(integrator, linsolve1; A = nothing, b = _vec(ubuff), linu = _vec(dw1)) end cache.linsolve1 = linres1.cache @@ -1190,11 +1189,9 @@ end linsolve2 = cache.linsolve2 if needfactor - linres2 = dolinsolve(integrator, linsolve2; A = W2, b = _vec(cubuff1), - linu = _vec(dw23)) + linres2 = dolinsolve(integrator, linsolve2; A = W2, b = _vec(cubuff1), linu = _vec(dw23)) else - linres2 = dolinsolve(integrator, linsolve2; A = nothing, b = _vec(cubuff1), - linu = _vec(dw23)) + linres2 = dolinsolve(integrator, linsolve2; A = nothing, b = _vec(cubuff1), linu = _vec(dw23)) end cache.linsolve2 = linres2.cache @@ -1205,11 +1202,9 @@ end linsolve3 = cache.linsolve3 if needfactor - linres3 = dolinsolve(integrator, linsolve3; A = W3, b = _vec(cubuff2), - linu = _vec(dw45)) + linres3 = dolinsolve(integrator, linsolve3; A = W3, b = _vec(cubuff2), linu = _vec(dw45)) else - linres3 = dolinsolve(integrator, linsolve3; A = nothing, b = _vec(cubuff2), - linu = _vec(dw45)) + linres3 = dolinsolve(integrator, linsolve3; A = nothing, b = _vec(cubuff2), linu = _vec(dw45)) end cache.linsolve3 = linres3.cache @@ -1596,7 +1591,7 @@ end end z[i] = @.. z[i] * c_prime[i] end - w = @.. TI * z + w = TI * z end # Newton iteration @@ -1636,25 +1631,23 @@ end linsolve1 = cache.linsolve1 if needfactor - linres = dolinsolve(integrator, linsolve1; A = W1, b = _vec(ubuff), - linu = _vec(dw1)) + linres = dolinsolve(integrator, linsolve1; A = W1, b = _vec(ubuff), linu = _vec(dw1)) else - linres = dolinsolve(integrator, linsolve1; A = nothing, b = _vec(ubuff), - linu = _vec(dw1)) + linres = dolinsolve(integrator, linsolve1; A = nothing, b = _vec(ubuff), linu = _vec(dw1)) end cache.linsolve1 = linres.cache + linres2 = Vector{Any}(undef, Int((num_stages - 1) / 2)) + for i in 1 : Int((num_stages - 1) / 2) @.. cubuff[i]=complex( fw[2 * i] - αdt[i] * Mw[2 * i] + βdt[i] * Mw[2 * i + 1], fw[2 * i + 1] - βdt[i] * Mw[2 * i] - αdt[i] * Mw[2 * i + 1]) linsolve2[i] = cache.linsolve2[i] if needfactor - linres2[i] = dolinsolve(integrator, linsolve2[i]; A = W2[i], b = _vec(cubuff[i]), - linu = _vec(dw2[i])) + linres2[i] = dolinsolve(integrator, linsolve2[i]; A = W2[i], b = _vec(cubuff[i]), linu = _vec(dw2[i])) else - linres2[i] = dolinsolve(integrator, linsolve2[i]; A = nothing, b = _vec(cubuff[i]), - linu = _vec(dw2[i])) + linres2[i] = dolinsolve(integrator, linsolve2[i]; A = nothing, b = _vec(cubuff[i]), linu = _vec(dw2[i])) end cache.linsolve2[i] = linres2[i].cache end @@ -1662,12 +1655,13 @@ end integrator.stats.nsolve += (num_stages + 1) / 2 dw = Vector{Any}(undef, num_stages - 1) i = 1 + while i <= Int((num_stages - 1) / 2) - dw[i] = z[i] - dw[i + 1] = z[i + 1] - @.. dw[i] = real(dw2[i]) - @.. dw[i + 1] = imag(dw2[i]) - i += 2 + dw[2 * i - 1] = z[2 * i - 1] + dw[2 * i] = z[2 * i] + dw[2 * i - 1] = real(dw2[i]) + dw[2 * i] = imag(dw2[i]) + i = i + 1 end # compute norm of residuals @@ -1675,9 +1669,7 @@ end ndws = Vector{Any}(undef, num_stages) ndws[1] = calculate_residuals!(atmp, dw1, uprev, u, atol, rtol, internalnorm, t) ndws[1] = internalnorm(atmp, t) - for i in 2 : num_stages - @show i calculate_residuals!(atmp, dw[i - 1], uprev, u, atol, rtol, internalnorm, t) ndws[i] = internalnorm(atmp, t) end @@ -1705,7 +1697,7 @@ end end # transform `w` to `z` - z = T * w + z = vec(T * w) # check stopping criterion iter > 1 && (η = θ / (1 - θ)) @@ -1773,16 +1765,18 @@ end if alg.extrapolant != :constant derivatives = Matrix{Any}(undef, num_stages, num_stages) pushfirst!(c, 0) + pushfirst!(z, map(zero, u)) for i in 1 : num_stages for j in i : num_stages if i == 1 - derivatives[i, j] = @.. (z[i] - z[i + 1]) / (c[i] - c[i + 1]) #first derivatives + derivatives[i, j] = @.. (z[j] - z[j + 1]) / (c[j] - c[j + 1]) #first derivatives else derivatives[i, j] = @.. (derivatives[i - 1, j - 1] - derivatives[i - 1, j]) / (c[j - i + 1] - c[j + 1]) #all others end end end popfirst!(c) + popfirst!(z) for i in 1 : num_stages cache.cont[i] = derivatives[i, num_stages] end diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl index a7934174ce..bb1d006bba 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl @@ -43,8 +43,8 @@ struct RadauIIA5Tableau{T, T2} T22::T T23::T T31::T - #T32::T = 1 - #T33::T = 0 + #T32::T + #T33::T TI11::T TI12::T TI13::T @@ -56,7 +56,7 @@ struct RadauIIA5Tableau{T, T2} TI33::T c1::T2 c2::T2 - #c3::T2 = 1 + #c3::T2 γ::T α::T β::T @@ -110,7 +110,38 @@ function RadauIIA5Tableau(T, T2) γ, α, β, e1, e2, e3) end - +#= +function BigRadauIIA5Tableau(T, T2) + T11 = convert(T, 0.091232394870892942791548135249436196118684699372210280712184363514099824021240149574725365814781580305065489937969163922775110463056339192206701819661425186) + T12 = convert(T, -0.141255295020954208427990383807797309409263248498594798844289981408804297900674604638610419147468875667691398225003133444988034605081071965848437945842767211) + T31 = convert(T, -0.0300291941051474244918611170890538666683842974606300802563717702200388818691214144173874588956764952224874407424115249418136547481236684478531215095064078994) + T21 = convert(T, 0.241717932707107018957474779310148232884879540532595279746187345714229132659465207414913313803429072060469564350914390845001169448350326344874859416624577348) + T22 = convert(T, 0.204129352293799931995990810298338174086540402523315938937516234649384944528706774788799548853122282827246947911905379230680096946800308693162079538975632443) + T23 = convert(T, 0.382942112757261937795438233599873210357792575012007744255205163027042915338009760005422153613194350161760232119048691964499888989151661861236831969497483828) + T31 = convert(T, 0.966048182615092936190567080794590794996748754810883844283183333914131408744555961195911605614405476210484499875001737558078500322423463946527349731087504518) + T32 = convert(T, 1.0) + T33 = convert(T, 0.0) + TI11 = convert(T, 4.32557989006315535102435095295614882731995158490590784287320458848019483341979047442263696495019938973156007686663488090615420049217658854859024016717169837) + TI12 = convert(T, 0.339199251815809869542824974053410987511771566126056902312311333553438988409693737874718833892037643701271502187763370262948704203562215007824701228014200056) + TI13 = convert(T, 0.541770539935874871186523033492089631898841317849243944095021379289933921771713116368931784890546144473788347538203807242114936998948954098533375649163016612) + TI21 = convert(T, -4.17871859155190472734646265851205623000038388214686525896709481539843195209360778128456932548583273459040707932166364293012713818843609182148794380267482041) + TI22 = convert(T, -0.327682820761062387082533272429616234245791838308340887801415258608836530255609335712523838667242449344879454518796849992049787172023800373390124427898159896) + TI23 = convert(T, 0.476623554500550451960069084091012497939942928625055897109833707684876604712862299049343675491204859381277636585708398915065951363736337328178192801074535132) + TI31 = convert(T, -0.502872634945786875951247343139544292859248429570937886791036339034110181540695221500843782634464164585836226038438397328726973424362168221527501738985822875) + TI32 = convert(T, 2.57192694985560542918678535360167505469448742842178326395573566888176471664393761903447163100353067504020263109067033226021288356347565113471227052083596358) + TI33 = convert(T, -0.596039204828224924968821911099302403289857517521591823052174732952989090998130905722763344484798508456930766594977798579939415052669401095404149917833710127) + γ = convert(T, 3.63783425274449573220841851357777579794593608687391153215117488565841871456727143375130115708511223004183651123208497057248238260532214672028700625775335843) + α = convert(T, 2.68108287362775213389579074321111210102703195656304423392441255717079064271636428312434942145744388497908174438395751471375880869733892663985649687112332242) + β = convert(T, 3.05043019924741056942637762478756790444070419917947659226291744751211727051786694870515117615266028855554735929171362769761399150862332538376382934625577549) + c1 = convert(T2, 0.155051025721682190180271592529410860803405251934332987156730743274903962254268497346014056689535976518140539877338581087514113454016224265837421604876272084) + c2 = convert(T2, 0.644948974278317809819728407470589139196594748065667012843269256725096037745731502653985943310464023481859460122661418912485886545983775734162578395123729143) + RadauIIA5Tableau{T, T2}(T11, T12, T13, T21, T22, T23, T31,T32, T33, + TI11, TI12, TI13, TI21, TI22, TI23, TI31, TI32, TI33, + c1, c2, #= c3 = 1 =# + γ, α, β, + e1, e2, e3) +end +=# struct RadauIIA9Tableau{T, T2} T11::T T12::T diff --git a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl index 83f6468712..b26b6558ed 100644 --- a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl +++ b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl @@ -8,9 +8,9 @@ for prob in [prob_ode_linear, prob_ode_2Dlinear] @test sim21.𝒪est[:final]≈5 atol=testTol end -sol = solve(prob_ode_2Dlinear, AdaptiveRadau(), adaptive = false, dt = 1e-2) -sol = solve(prob_ode_linear, RadauIIA9(), adaptive = false, dt = 1e-2) -sol = solve(prob_ode_2Dlinear, RadauIIA5(), adaptive = false, dt = 1e-2) +sol = solve(prob_ode_2Dlinear, AdaptiveRadau(num_stages = 5), adaptive = false, dt = 1e-1) +sol = solve(prob_ode_2Dlinear, RadauIIA9(), adaptive = false, dt = 1e-1) +sol = solve(prob_ode_2Dlinear, RadauIIA5(), adaptive = false, dt = 1e-1) sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_linear, RadauIIA9()) @test sim21.𝒪est[:final]≈9 atol=testTol @@ -26,9 +26,8 @@ for i in [3, 5, 7, 9] @test sim21.𝒪est[:final]≈ (2 * i - 1) atol=testTol end -sol = solve(prob_ode_2Dlinear_big, RadauIIA9(), adaptive=false, dt = 1e-5) -for i in [5] - sim21 = test_convergence(1 ./ 10 .^ (5:-1:3), prob_ode_2Dlinear_big, AdaptiveRadau(num_stages = i)) +for i in [3, 5, 7, 9] + sim21 = test_convergence(1 ./ 2 .^ (5:-1:3), prob_ode_2Dlinear_big, AdaptiveRadau(num_stages = i)) @test sim21.𝒪est[:final]≈ (2 * i - 1) atol=testTol end From ff102994447db17ce9323d62ba380e99d71e9440 Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Sat, 31 Aug 2024 22:06:02 -0400 Subject: [PATCH 52/71] Update ode_firk_tests.jl --- lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl | 4 ---- 1 file changed, 4 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl index b26b6558ed..38c0d4b4e3 100644 --- a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl +++ b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl @@ -8,10 +8,6 @@ for prob in [prob_ode_linear, prob_ode_2Dlinear] @test sim21.𝒪est[:final]≈5 atol=testTol end -sol = solve(prob_ode_2Dlinear, AdaptiveRadau(num_stages = 5), adaptive = false, dt = 1e-1) -sol = solve(prob_ode_2Dlinear, RadauIIA9(), adaptive = false, dt = 1e-1) -sol = solve(prob_ode_2Dlinear, RadauIIA5(), adaptive = false, dt = 1e-1) - sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_linear, RadauIIA9()) @test sim21.𝒪est[:final]≈9 atol=testTol From df3063f485086c46cbfea876a4075e73ff6b23e3 Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Mon, 2 Sep 2024 11:35:07 -0400 Subject: [PATCH 53/71] cached tableaus --- lib/OrdinaryDiffEqFIRK/src/firk_caches.jl | 22 +- lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl | 307 ++++++++++++++++-- lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl | 9 +- 3 files changed, 297 insertions(+), 41 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl index 6abd379e05..96f92303d9 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl @@ -495,7 +495,16 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} uf = UDerivativeWrapper(f, t, p) uToltype = constvalue(uBottomEltypeNoUnits) num_stages = alg.num_stages - tab = adaptiveRadauTableau(uToltype, constvalue(tTypeNoUnits), num_stages) + + if (num_stages == 3) + tab = BigRadauIIA5Tableau(uToltype, constvalue(tTypeNoUnits), Int) + elseif (num_stages == 5) + tab = BigRadauIIA9Tableau(uToltype, constvalue(tTypeNoUnits), Int) + #elseif (num_stages == 7) + # tab = BigRadauIIA13Tableau(uToltype, constvalue(tTypeNoUnits), Int) + else + tab = adaptiveRadauTableau(uToltype, constvalue(tTypeNoUnits), num_stages) + end cont = Vector{typeof(u)}(undef, num_stages) for i in 1: num_stages @@ -554,7 +563,16 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} uf = UJacobianWrapper(f, t, p) uToltype = constvalue(uBottomEltypeNoUnits) num_stages = alg.num_stages - tab = adaptiveRadauTableau(uToltype, constvalue(tTypeNoUnits), num_stages) + + if (num_stages == 3) + tab = BigRadauIIA5Tableau(uToltype, constvalue(tTypeNoUnits), Int) + elseif (num_stages == 5) + tab = BigRadauIIA9Tableau(uToltype, constvalue(tTypeNoUnits), Int) + #elseif (num_stages == 7) + # tab = BigRadauIIA13Tableau(uToltype, constvalue(tTypeNoUnits), Int) + else + tab = adaptiveRadauTableau(uToltype, constvalue(tTypeNoUnits), num_stages) + end κ = alg.κ !== nothing ? convert(uToltype, alg.κ) : convert(uToltype, 1 // 100) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl index bb1d006bba..389b880df7 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl @@ -110,38 +110,141 @@ function RadauIIA5Tableau(T, T2) γ, α, β, e1, e2, e3) end -#= -function BigRadauIIA5Tableau(T, T2) - T11 = convert(T, 0.091232394870892942791548135249436196118684699372210280712184363514099824021240149574725365814781580305065489937969163922775110463056339192206701819661425186) - T12 = convert(T, -0.141255295020954208427990383807797309409263248498594798844289981408804297900674604638610419147468875667691398225003133444988034605081071965848437945842767211) - T31 = convert(T, -0.0300291941051474244918611170890538666683842974606300802563717702200388818691214144173874588956764952224874407424115249418136547481236684478531215095064078994) - T21 = convert(T, 0.241717932707107018957474779310148232884879540532595279746187345714229132659465207414913313803429072060469564350914390845001169448350326344874859416624577348) - T22 = convert(T, 0.204129352293799931995990810298338174086540402523315938937516234649384944528706774788799548853122282827246947911905379230680096946800308693162079538975632443) - T23 = convert(T, 0.382942112757261937795438233599873210357792575012007744255205163027042915338009760005422153613194350161760232119048691964499888989151661861236831969497483828) - T31 = convert(T, 0.966048182615092936190567080794590794996748754810883844283183333914131408744555961195911605614405476210484499875001737558078500322423463946527349731087504518) - T32 = convert(T, 1.0) - T33 = convert(T, 0.0) - TI11 = convert(T, 4.32557989006315535102435095295614882731995158490590784287320458848019483341979047442263696495019938973156007686663488090615420049217658854859024016717169837) - TI12 = convert(T, 0.339199251815809869542824974053410987511771566126056902312311333553438988409693737874718833892037643701271502187763370262948704203562215007824701228014200056) - TI13 = convert(T, 0.541770539935874871186523033492089631898841317849243944095021379289933921771713116368931784890546144473788347538203807242114936998948954098533375649163016612) - TI21 = convert(T, -4.17871859155190472734646265851205623000038388214686525896709481539843195209360778128456932548583273459040707932166364293012713818843609182148794380267482041) - TI22 = convert(T, -0.327682820761062387082533272429616234245791838308340887801415258608836530255609335712523838667242449344879454518796849992049787172023800373390124427898159896) - TI23 = convert(T, 0.476623554500550451960069084091012497939942928625055897109833707684876604712862299049343675491204859381277636585708398915065951363736337328178192801074535132) - TI31 = convert(T, -0.502872634945786875951247343139544292859248429570937886791036339034110181540695221500843782634464164585836226038438397328726973424362168221527501738985822875) - TI32 = convert(T, 2.57192694985560542918678535360167505469448742842178326395573566888176471664393761903447163100353067504020263109067033226021288356347565113471227052083596358) - TI33 = convert(T, -0.596039204828224924968821911099302403289857517521591823052174732952989090998130905722763344484798508456930766594977798579939415052669401095404149917833710127) - γ = convert(T, 3.63783425274449573220841851357777579794593608687391153215117488565841871456727143375130115708511223004183651123208497057248238260532214672028700625775335843) - α = convert(T, 2.68108287362775213389579074321111210102703195656304423392441255717079064271636428312434942145744388497908174438395751471375880869733892663985649687112332242) - β = convert(T, 3.05043019924741056942637762478756790444070419917947659226291744751211727051786694870515117615266028855554735929171362769761399150862332538376382934625577549) - c1 = convert(T2, 0.155051025721682190180271592529410860803405251934332987156730743274903962254268497346014056689535976518140539877338581087514113454016224265837421604876272084) - c2 = convert(T2, 0.644948974278317809819728407470589139196594748065667012843269256725096037745731502653985943310464023481859460122661418912485886545983775734162578395123729143) - RadauIIA5Tableau{T, T2}(T11, T12, T13, T21, T22, T23, T31,T32, T33, - TI11, TI12, TI13, TI21, TI22, TI23, TI31, TI32, TI33, - c1, c2, #= c3 = 1 =# - γ, α, β, - e1, e2, e3) + +struct BigRadauIIA5Tableau{T1, T2, Int} + T::AbstractMatrix{T1} + TI::AbstractMatrix{T1} + c::AbstractVector{T2} + γ::T1 + α::AbstractVector{T1} + β::AbstractVector{T1} + #e::AbstractVector{T1} + num_stages::Int +end + +function BigRadauIIA5Tableau(T1, T2, Int) + γ = convert(T1, 3.63783425274449573220841851357777579794593608687391153215117488565841871456727143375130115708511223004183651123208497057248238260532214672028700625775335843) + α = Vector{T1}(undef, 1) + β = Vector{T1}(undef, 1) + α[1] = convert(T1, 2.68108287362775213389579074321111210102703195656304423392441255717079064271636428312434942145744388497908174438395751471375880869733892663985649687112332242) + β[1] = convert(T1, 3.05043019924741056942637762478756790444070419917947659226291744751211727051786694870515117615266028855554735929171362769761399150862332538376382934625577549) + + c = Vector{T2}(undef, 3) + c[1] = convert(T2, 0.155051025721682190180271592529410860803405251934332987156730743274903962254268497346014056689535976518140539877338581087514113454016224265837421604876272084) + c[2] = convert(T2, 0.644948974278317809819728407470589139196594748065667012843269256725096037745731502653985943310464023481859460122661418912485886545983775734162578395123729143) + c[3] = convert(T2, 1) + + TI = Matrix{T1}(undef, 3, 3) + TI[1, 1] = convert(T1, 4.32557989006315535102435095295614882731995158490590784287320458848019483341979047442263696495019938973156007686663488090615420049217658854859024016717169837) + TI[1, 2] = convert(T1, 0.339199251815809869542824974053410987511771566126056902312311333553438988409693737874718833892037643701271502187763370262948704203562215007824701228014200056) + TI[1, 3] = convert(T1, 0.541770539935874871186523033492089631898841317849243944095021379289933921771713116368931784890546144473788347538203807242114936998948954098533375649163016612) + TI[2, 1] = convert(T1, -4.17871859155190472734646265851205623000038388214686525896709481539843195209360778128456932548583273459040707932166364293012713818843609182148794380267482041) + TI[2, 2] = convert(T1, -0.327682820761062387082533272429616234245791838308340887801415258608836530255609335712523838667242449344879454518796849992049787172023800373390124427898159896) + TI[2, 3] = convert(T1, 0.476623554500550451960069084091012497939942928625055897109833707684876604712862299049343675491204859381277636585708398915065951363736337328178192801074535132) + TI[3, 1] = convert(T1, -0.502872634945786875951247343139544292859248429570937886791036339034110181540695221500843782634464164585836226038438397328726973424362168221527501738985822875) + TI[3, 2] = convert(T1, 2.57192694985560542918678535360167505469448742842178326395573566888176471664393761903447163100353067504020263109067033226021288356347565113471227052083596358) + TI[3, 3] = convert(T1, -0.596039204828224924968821911099302403289857517521591823052174732952989090998130905722763344484798508456930766594977798579939415052669401095404149917833710127) + + T = Matrix{T1}(undef, 3, 3) + T[1, 1] = convert(T1, 0.091232394870892942791548135249436196118684699372210280712184363514099824021240149574725365814781580305065489937969163922775110463056339192206701819661425186) + T[1, 2] = convert(T1, -0.141255295020954208427990383807797309409263248498594798844289981408804297900674604638610419147468875667691398225003133444988034605081071965848437945842767211) + T[1 ,3] = convert(T1, -0.0300291941051474244918611170890538666683842974606300802563717702200388818691214144173874588956764952224874407424115249418136547481236684478531215095064078994) + T[2, 1] = convert(T1, 0.241717932707107018957474779310148232884879540532595279746187345714229132659465207414913313803429072060469564350914390845001169448350326344874859416624577348) + T[2, 2] = convert(T1, 0.204129352293799931995990810298338174086540402523315938937516234649384944528706774788799548853122282827246947911905379230680096946800308693162079538975632443) + T[2, 3] = convert(T1, 0.382942112757261937795438233599873210357792575012007744255205163027042915338009760005422153613194350161760232119048691964499888989151661861236831969497483828) + T[3, 1] = convert(T1, 0.966048182615092936190567080794590794996748754810883844283183333914131408744555961195911605614405476210484499875001737558078500322423463946527349731087504518) + T[3, 2] = convert(T1, 1.0) + T[3, 3] = convert(T1, 0.0) + BigRadauIIA5Tableau{T1, T2, Int}(T, TI, + c, γ, α, β, 3) end -=# + +struct BigRadauIIA9Tableau{T1, T2, Int} + T::AbstractMatrix{T1} + TI::AbstractMatrix{T1} + c::AbstractVector{T2} + γ::T1 + α::AbstractVector{T1} + β::AbstractVector{T1} + #e::AbstractVector{T1} + num_stages::Int +end + +function BigRadauIIA9Tableau(T1, T2, Int) + γ = convert(T1, 6.28670475172927664517315334186940904959068186655567041187229167532923622489525703260842273089261139845280626287956099768662193453067483410165932355981736786) + α = Vector{T1}(undef, 2) + β = Vector{T1}(undef, 2) + α[1] = convert(T1, 3.65569432546357225824320796009543385435699888857815445045567025741630720509235614026228963385258117304229337679733945535812317372403535763551850772878775217) + α[2] = convert(T1, 5.70095329867178941917021536896986162084766017814401034360818390491907468246001534343349900070111312773130349176288004579856585901062722531365183049130382405) + β[1] = convert(T1, 6.5437368993600772940210715093936863183637851728134458820202187133882261290012752452972782843700946890488789462524897903624959996932392239962196563965573345) + β[2] = convert(T1, 3.21026560030854988842501065297211721232153653493981008029923647488964744732168461657389754087826565709085773529539707072244537983491480773006949966789260925) + + c = Vector{T2}(undef, 5) + c[1] = convert(T2, 0.0571041961145176821931211925541156212350779455987501643278082929309346782020731645861138168198427368635148018903413155731609901559772929443100370500757072557) + c[2] = convert(T2, 0.276843013638123827680045997685625141110889169695030468349442048831121339683708036772541528564051130879197377136636984534220758899839905855114024309075271826) + c[3] = convert(T2, 0.583590432368916820056697668662917248693432639896771640176293841831747501961831012005632277467456299345321045569611992496682381919275766424103024358378365496) + c[4] = convert(T2, 0.8602401356562194478479129188751197667383780225872255049242335941839742579301655644134901549264276106897445531811874851737136468026848125542506920602484255) + c[5] = convert(T2, 1.0) + + TI = Matrix{T1}(undef, 5, 5) + TI[1, 1] = convert(T1, 30.0415677215444016277146611632467970747634862837368422955138470463852339244593400023985957753164599415374157317627305099177616927640413043608408838747985125) + TI[1, 2] = convert(T1, 13.8651078562714131651762946846279728486098595017962436746405940971751244384714668104145151259298432908422191238542910724677205181071665482818120092330632702) + TI[1 ,3] = convert(T1, 3.48000277479518556182840016971955819123081637245954095062693470191383865922357339844125383481645392882289968250993872221445874555610460465838129969397069557) + TI[1, 4] = convert(T1, -1.03200879782526342277108071214631493513824682491749273908106331923801396656058254294323988505859654767877050109789490714699847664805679842903430004696170252) + TI[1, 5] = convert(T1, 0.804303045073989917475330383606196086089578671788707543063308602519859970319818304759856653218877415405946945572102875643297890954688508528143272905631829894) + TI[2, 1] = convert(T1, 5.34418643783491159889531030409736033885455686563071401172022718575590068536629704134603404624953791012861634674294690788961703408019660066685859393456498931) + TI[2, 2] = convert(T1, 4.59361556775916100445407449817656238428260055301676371438973411021009514435572975394999086474831271997070798032181411537895658457000537727156665947774751386) + TI[2, 3] = convert(T1, -3.03636032345942429864615756872018980250277648141683630832856906288036929718223473102394179699607901856890769270810252103326382063852039607285826867723587514) + TI[2, 4] = convert(T1, 1.05066019023145886385983615715299311307615150447133905233370933194949591737765763708886464382722316727972166443876395823044171403663404254906698768838255919) + TI[2, 5] = convert(T1, -0.272778611864296270538614649997366804891835224042737605275699398413256470423268908248569612750117948720141667949532252500428432062582365619208502333677907158) + TI[3, 1] = convert(T1, 3.74805980743980486005103450189256983678052751095791526209741655305580351377124372457009580386663275146166007984852101733055495783906881063060757645038080343) + TI[3, 2] = convert(T1, -3.98496573634388466725226385805351110838575115293851360514636734529255361185420464416807882769853298186283398369873418552760618971047757002216338511286260041) + TI[3, 3] = convert(T1, -1.04441564160801879294224732309562532189841624726401645191058551173485917137499204844819781779667611903670073971659834929382224472890100209497741235960707456) + TI[3, 4] = convert(T1, 1.18409856813794848723102038838340482030291345603197522521517834943166421242518751666675199211369552058487095283489346390066317584532997854692445653563909898) + TI[3, 5] = convert(T1, -0.449917770156780368898811918314095435942113881883174152777026977062686286863549565130412864190301081537983106397709991028107600781961279985605930655683680139) + TI[4, 1] = convert(T1, -33.0418802135190000080614469426109507742858088371383868670878639187564531424382858814386742148456699143328462132296293097447566408853495288807407929988004676) + TI[4, 2] = convert(T1, -17.3769534790635670194549806058987105852733409102703844354448800193942184746909147697382687117638715195698950138089979798321855885541817752366521518811413713) + TI[4, 3] = convert(T1, -0.172129063254005561151528806427751383749451500597823574207174433146207178559871803504021077429693091164540897873472803934375603405253541639437370184767553293) + TI[4, 4] = convert(T1, -0.0991697779825426425881662214017368584726354746776989845479783944003623924121748016326495070834800297497011104846871751430208559227945252758721362340763610828) + TI[4, 5] = convert(T1, 0.531228115838306667184911422606024795426589562580669892779793097035561488973256023529352389498509937781553683467106048413485632583844632286562240161995145055) + TI[5, 1] = convert(T1, -8.61144397987529197770008251257034851950485933115010902789613925540488896812417081206983938638600226846804467531843522104806738090683710882069500386691775154) + TI[5, 2] = convert(T1, 9.69999140952880823133589405342003266497120753048627084327055311528684684237122654108691149692242002085965723391934376924400492239317026460192827344970015484) + TI[5, 3] = convert(T1, 1.91472863969687428485137560339172471528025297511003983469957355306260543484472462223194401768126877615795915146192537091374017807611943419264038682143890747) + TI[5, 4] = convert(T1, 2.41869200608494002642656343408298350771199306961305597858229870375990977712805399625496435641846363295393762353024017195444763964531237381728801981679934304) + TI[5, 5] = convert(T1, -1.0474634879353374186944329992117360176590042540536055452919974336199826846201614544718272622833822842591012529895091659029452542118642301415759073410771819) + + T = Matrix{T1}(undef, 5, 5) + T[1, 1] = convert(T1, 0.0125175862205010458901356760368001462557655123420858705973577952199246108029451084239310924615007306721702298573083400752464277227557045438770401832498107968) + T[1, 2] = convert(T1, -0.0102420478179088270700863300668590125015813934827825923708366359399562125950804289592272678367034071306578383319296130180550178248531589487456925441921649293) + T[1 ,3] = convert(T1, 0.0476738772902957238631839478592069782970238490568258436986723993118380988311441474394156362952631834786373081794857384127209450988829840886524135970873769918) + T[1, 4] = convert(T1, -0.0114785152552295147079415554121555049385506204591245712490409384029671974157542450636658532835395855844059342442518520033304129991000509527123870917346017759) + T[1, 5] = convert(T1, -0.0140198588928754102810778942934959307831026572823203692568448424056201483917805257790275956734469193171917730378117501915144713896813544630288006687542182225) + T[2, 1] = convert(T1, 0.00149167015189538242900444775236282223594625052328927847572623038484966999313257893341818287477809424303168766872838075463220122499449382436194198620498144296) + T[2, 2] = convert(T1, 0.050172864517371058162991380262646513853120568882725793734131676894272706020317186004736779675826101816279321643304301437029912742375638648226701787880031719) + T[2, 3] = convert(T1, -0.0943318191816114369806569003363724471884924328367212069321438749304281980331334016578193750445513659941246363262225907407726099492713722343006925656625258579) + T[2, 4] = convert(T1, -0.00766883074918016288515687679203608074116106558796378201472238095295554979920808799930579174190884587422912077296093093698836937450535804218413704866981728518) + T[2, 5] = convert(T1, 0.024708578426518526812525205377780382655366504554979744093019395818934704623702078004474076773426928900579988063099593288435684744957695210778788200213260272) + T[3, 1] = convert(T1, 0.072981876388087148622657299703669587832652508881663282287850495621401398441897288250625556038835308015912409648841893161563884759791665776933761278383553608) + T[3, 2] = convert(T1, -0.230539534043417946721421862180000422679228296568599014834226319726930529322581417981617275287468418138394077987361681288909676234537699721082090802790143303) + T[3, 3] = convert(T1, 0.102703045380125899792210456947141185148813233939327773583525878521508211077874610560448598369259541346968946573971195783374996178436435357335759255990489434) + T[3, 4] = convert(T1, 0.0193984639988289509112232896408330872285824216708905773930244363652651247181543158008567311548336143384128605013911312875018664026371225431993252265128272262) + T[3, 5] = convert(T1, 0.0818003537037511708363908122287572533071340646031113975848869261019231448226334426630664318901554550460201409321555775999869184033436795623062614812355590017) + T[4, 1] = convert(T1, 0.380091440003568104126439184355215575526619121262253024859378518379910007234696730891540745160675744992320824590679292148769326540463161583672773762554445506) + T[4, 2] = convert(T1, 0.377893902248861249543862293745933995234687511602719536459666284734445918178134851270924212812363352965391508894581698067329905034837778770261095647458874628) + T[4, 3] = convert(T1, 0.466744130332494359289559582964906703283968612669234331018678042733321473730897217606173184300477207393539851157929838664168404778962779344509707214938022808) + T[4, 4] = convert(T1, 0.40760117128019906662166237021895987274626181127101561893104166874567447589187790736078997321464949349935802836110699884016973990503134772720646054039223561) + T[4, 5] = convert(T1, 0.199682427886802525936540566022390695167018315867216115995143539347975271751460199398235415129329119718414206048034051939441434136353381864781262773401023899) + T[5, 1] = convert(T1, 0.921978973681210488488254647415676321266345412943047462855852351388222898143904205962703147998267738964059170225806964893009202287585991334322032058414768529) + T[5, 2] = convert(T1, 1.0) + T[5, 3] = convert(T1, 0.0) + T[5, 4] = convert(T1, 1.0) + T[5, 5] = convert(T1, 0.0) + + BigRadauIIA9Tableau{T1, T2, Int}(T, TI, + c, γ, α, β, 5) +end + + struct RadauIIA9Tableau{T, T2} T11::T T12::T @@ -290,6 +393,143 @@ function RadauIIA9Tableau(T, T2) e1, e2, e3, e4, e5) end +struct BigRadauIIA13Tableau{T1, T2, Int} + T::AbstractMatrix{T1} + TI::AbstractMatrix{T1} + c::AbstractVector{T2} + γ::T1 + α::AbstractVector{T1} + β::AbstractVector{T1} + #e::AbstractVector{T1} + num_stages::Int +end + +function BigRadauIIA13Tableau(T1, T2, Int) + γ = convert(T1, 8.93683278840521633730209691330107970355008194433956657198414191417624969654351559268800871286734194720118970058657997472527299153742511021973612156231867783) + α = Vector{T1}(undef, 3) + β = Vector{T1}(undef, 3) + α[1] = convert(T1, 4.37869356150680600252334919268856129165763746518197948235657247177701087073069907016715245914093899486193202405685779803686971216417800783050995450529391908) + α[2] = convert(T1, 7.14105521918764010577498142571556804318193862372238812855726792587872300446315860222917039505087745633962330233504078264632719519730762016919715839787116038) + α[3] = convert(T1, 8.51183482510294572305062092494533081338538293892584910309408864525614127653438453125967278937451257519784982331481143195416659686980181689042482631568989031) + β[1] = convert(T1, 10.1696932837950116273183544188477298930096536824510223588525334625762336174947183926243705927725260475934351162622185429326813205432867247703480391692806137) + β[2] = convert(T1, 6.62304592263927597062055811591186110468148199066707542227575094761515104946479159063603447729283770429494038962408904312215452856333028405675512985803584472) + β[3] = convert(T1, 3.2810136243250588300359425270393915846791621918405321383787427650552081712406957205287551182809705166989352673500472974040971593568323836675590314648604458) + + c = Vector{T2}(undef, 7) + c[1] = convert(T2, 0.0293164271597848919720502769131649103737303925637149277869106839449360382416657787486309483651843695097273923248526200112627747993405898353736305552306269904) + c[2] = convert(T2, 0.148078599668484291849976852495979212230248774808594461412594641801598386090878321806369397661747576057906341132861865305306667654594593138746653233717241913) + c[3] = convert(T2, 0.336984690281154299097052972080775705197568750028473347122562968073691350512784060852409141173654482529393236826516171319486086447256539582972346127980810124) + c[4] = convert(T2, 0.558671518771550132081393341805521940074368288965407825555747226117350122897421078323820052012282581935200398463518265914564420109615277886000739200777932339) + c[5] = convert(T2, 0.769233862030054500916883360115645451837142143322295416166948169636548130573953285685200211542774367652885154701431860087378103033801830280742146083476036669) + c[6] = convert(T2, 0.926945671319741114851873965819682011056172419542283252724467079656645202452528243814339480013587391545656707320049986592771178724621938506933715568048004783) + c[7] = convert(T2, 1.0) + + TI = Matrix{T1}(undef, 7, 7) + TI[1, 1] = convert(T1, 258.131926319982229276108947425184471333411128774462923076434633414645220927977539758484670571338176678808837829326061674950321562391576244286310404028770676) + TI[1, 2] = convert(T1, 189.073763081398508951976143411165126555759459745371576264125287430947886413126866952443113984840310549596923934762141954737541643761162558070450614795561734) + TI[1, 3] = convert(T1, 49.0873148179301311944474703372633419330229683717897887664283914712555334645741343066714059043135343948204451450061803442374878045458955826422757210762412997) + TI[1, 4] = convert(T1, 4.11064746966142841811238518636124668078589358089581133578005291508858571621836624121708112101643343488669794287298806656198949715476379639435093560435010553) + TI[1, 5] = convert(T1, 4.05344788931556330417512803837862541661144275947069236866476426664242632965376171604053865483440478823853326237912519148507906655855071507442222711969825069) + TI[1, 6] = convert(T1, -3.11275536660734607655357698925636361735741304308245452106573904595716690770542970584435712650159533448326091358879097717388530116398450168049097806992817596) + TI[1, 7] = convert(T1, 1.64677491355844465016894934800942442334612077828885771793164268655566366462165061862443368822544695623147966149765223644798045399342853834086413561960176148) + TI[2, 1] = convert(T1, -3.00739016945129213173149353792169083141834116044470099212013728771587881480191343754504173052952073006187734389002396348355357273701343509199048972794392147) + TI[2, 2] = convert(T1, -11.0158660787657713291120393664792067595453921824881213620299497076376976067619617086470844707815815293102862568459526162951253770377715406520772358338647188) + TI[2, 3] = convert(T1, 1.48779945613165628148618248664965038886474377325027865838645297753993182317594482435706956176392903188004580583104018591540474622009639200188521283880201225) + TI[2, 4] = convert(T1, 2.13038815955928245943197208332824475219642634294808813866153957342980992047877237670079423767538654092424134276380826377135080667266661637001176204430488753) + TI[2, 5] = convert(T1, -1.81614108681756562482220455159496741723359999245934818387747079566312917815672128128449281415737713177900591942282975861961228230314168417307836619006791605) + TI[2, 6] = convert(T1, 1.13432558789516110008277908420532415765361628740656810686297793967986689714948610119162966211301325316623863222505219543867472186257492829970663316956377323) + TI[2, 7] = convert(T1, -0.414699045943303531993049422295928526684402022493736427543557958358387925728160703636844863663828153394608981043415378230601486738224597324364079320598162815) + TI[3, 1] = convert(T1, -8.44196318832108468175691559413731210343158392484322786670758421404507417209484447031645790366021837365786640573614305718894911853549168061902141351516580451) + TI[3, 2] = convert(T1, -0.650525274057515002816904045893485631294530894981669254094573985727348985809697093879080285963063573837365484483755274668080611163704039179328960851461387071) + TI[3, 3] = convert(T1, 6.94067073036987647880408175445008301222030789462375109942012235845495260572570799226646472429196555932436186979400567616504159564738984233922289782922787445) + TI[3, 4] = convert(T1, -3.20504752559789843156502799159713971965747774043426947358779973217345866996463287674334224123932879873323284636947452187683408110992957222808611161423213549) + TI[3, 5] = convert(T1, 1.07128094354647858978279562700457911254627057919002861801894953308482120936700881726232902304000322718645130593907512149815870969208873216470962770569998532) + TI[3, 6] = convert(T1, -0.354850749121622187972972761073874956531274189535504546398851680169235702590362534883357256681588685608802983372517893712333972644320006895019178184808028042) + TI[3, 7] = convert(T1, 0.0919854913278655415440864884207305663999562250023079120516746551750254082665966708567906888946992351083964961208132558221142585217674963218388224937302473142) + TI[4, 1] = convert(T1, 74.6783322350226997715286176267232500441551583987525066913719852490109364599462546293112601362342028584101507709386240000804692470037564789980905370400509214) + TI[4, 2] = convert(T1, 87.4085889799008164020396362924136436577534600993283836959398121813667403209890699914314446222016952621954817633686823685774595935180374571416781238038364186) + TI[4, 3] = convert(T1, 4.02415873737999787701407840793921059156554118449220356776918749072220128918152906578385457943212213189933447495921754693186811343717296680238755923076427455) + TI[4, 4] = convert(T1, -3.7148063151583641866387382381081795406061842159003055897302686185198568522128509989890869602984467843559169959313018612449354703104270603001605170037725663) + TI[4, 5] = convert(T1, -3.43009398598231735074090769130593476067104938465255451803266927011738721835297930406017172365070584279715308905584391225176154776278518922912169890517961929) + TI[4, 6] = convert(T1, 2.69660480976531237885262500230842013033719691844775548640355919138284680959979836353143310081338215041119022648809147361433752919265159399610746756470853959) + TI[4, 7] = convert(T1, -0.938692743607546193356785681771531136814109179879957291315724533839534255667763099330792864148293396694586387338161584706252944483821135344465739888811338788) + TI[5, 1] = convert(T1, 58.3565288519065772423731088606544342599129168115273649928818622008651860145833895668543250775742899696760389837877193028417145182338484929599333810581515993) + TI[5, 2] = convert(T1, -10.0687739578001809632495544545749228539542767485211306078205622876595603032162891608453826862136355989387474454697691529766293644115682409173741730758425432) + TI[5, 3] = convert(T1, -30.3663888425666712081087189214021522992426235463582449811325590575576319489955157279473313224901192335775884848736150180108985558310423628914140477437063457) + TI[5, 4] = convert(T1, -1.02002086518486598502718784312141857841892430616701325398305811243769008274372077411348691412296276168896198187688441456921700292037247387330560786140723416) + TI[5, 5] = convert(T1, -0.112417500378424962126670249921897816128157398591725875330925039631874967429838848482089690872916638698820411392685501889126627650123714184027159547685248056) + TI[5, 6] = convert(T1, 1.89064083100037762279966919417932484200269828564004442737723486475878958135985745266991261770924069476112679285337233931312540904735632744873728510014970829) + TI[5, 7] = convert(T1, -0.971648639383148228217233127548943147296423534674266405843322723719694664032217172325052282800290275002731997713145411340983758516166807609661717915219518127) + TI[6, 1] = convert(T1, -299.18624802825209667863642523944728107942141534516550178278869311293354511449399684666660494133688445719285752471650937062695632169114367079856135650539072) + TI[6, 2] = convert(T1, -243.040745368744791181900565230083092669143049316165122405971394775932180012728275256467636352341415340547177922968547123544546515287229215470481168446631934) + TI[6, 3] = convert(T1, -48.7771040780378692121909344887388032694629956594617430615510915251995189158287187599892740037773277403958100797917560590738598108409472582147091119440886778) + TI[6, 4] = convert(T1, -2.03867190574193440528015205293433905622043272233073734690244789947707827347049413187234402189062846366658963666461334786306660732097114011309282331323116958) + TI[6, 5] = convert(T1, 1.67356023986108494426829042309213202110891938292923077616474877079402040904687073610625868939896244842053999572446723558562427506280564629528151134946587118) + TI[6, 6] = convert(T1, -1.0873740320571061644555969255032311107358443063278089996181949045168433801494845898897631535619158410753032807069032950523487601457868753453652745002841107) + TI[6, 7] = convert(T1, 0.901938249296099373842715514839004052963355800714627971724094542443991299921284427589690820402982448873149676210397055957126153220340909284180014056386791594) + TI[7, 1] = convert(T1, -93.076502897435305911571945263737383854569504715670989865831914555937966339933932282945955570244055882294556430466422133231853008314991630740535709028417842) + TI[7, 2] = convert(T1, 23.8816310562811442770319002318043863376962876994405756649585750650966186536576789769674007990310112890015051984278059899811178135726914390958188405071290871) + TI[7, 3] = convert(T1, 39.2788807308138438271015646136760366834412493325456249795727722130258444051594274416196392795817449902122139076648927894476044063388859377757097127385794539) + TI[7, 4] = convert(T1, 14.3889156854910800698761307424979534708984169042483973564042387223013868069040933228077604321320066763752720714195604903398768371784013771964086553618150626) + TI[7, 5] = convert(T1, -3.51043839939936122108708432480845734972162782563284715495715984978907792386567906732993553255070093796782368160341757151292477304975079070782335737053297468) + TI[7, 6] = convert(T1, 4.86328488556618070121491058699734313503568312572977577331134555924656926935558698308076704662503608259898740028814153544991114426972747448736702277116049277) + TI[7, 7] = convert(T1, -2.24648272959123991640046924839711232278867381637608763335081676684616443569602032178385937243819174902544136208243971053224668691848283004752869023074006745) + + T = Matrix{T1}(undef, 7, 7) + T[1, 1] = convert(T1, 0.00215375462731052642282751906550204337272018200721827917615061640312650856312529840445028048591986867096756005142895325420603307041594804305862850861253757163) + T[1, 2] = convert(T1, 0.021567551351320773386914226953811992365459277376204369162736830595700124529879508417849062386878143122032508776691627063229415272329484156789207145821702462) + T[1, 3] = convert(T1, 0.00878356792514414440732555660043326940873333657406338685620618347939710728032290406426688328221296324998146697730909767495361893387567339044816921837538988154) + T[1, 4] = convert(T1, -0.00405516145233102389819844704090310382485225922827010954643577855973533421255114497764957587851178840064428149215351434824919490696577563849929483184955933965) + T[1, 5] = convert(T1, 0.00442723275326828547967807873499027629097834766201549949492135358632150336069311115075327876323707841703727317338755331613570950287342825020738596326021052902) + T[1, 6] = convert(T1, -0.00123864618795287405637686870391105285581324510790128485733529975336279476721707053186563729417080236061385260749762448518679294700311105630290083016823761156) + T[1, 7] = convert(T1, -0.00276061748054385249954800379096675592021481213358861974911688001011761550911589157738523818859000828996335817774948428177282421412491830529445501318154035024) + T[2, 1] = convert(T1, -0.00160002507788042852683067347985080829550105638728462477214069614397009338180775134535418790113854904464693278677067195562013777079470430165035085043732753352) + T[2, 2] = convert(T1, -0.0381316481344115466944201512445271892551007922443248010648630183723114657457789198582213862424187595732944781586531399310738197517976083499508550510483478779) + T[2, 3] = convert(T1, -0.0215255605940068755238494349163503963236812065771639056145559371805737876208350036328339608215271680572576146954552666030277743869132676140541472724370558091) + T[2, 4] = convert(T1, 0.00841556827655958923717700333156546206587781542530241328710392714333753219743181540077241302321588065650704924760060316717877095134935044662592211744890794666) + T[2, 5] = convert(T1, -0.00403194957022454949230429372587008587329606687054571010486662485715979240183165499902791387008699068626978608835015342675934092134962673636484308565473356683) + T[2, 6] = convert(T1, -6.6666353393963381817604789740257628821376819567901071737415235834331307484818353061850936507762955342131861918219584166678095273744210157164382779907235669e-05) + T[2, 7] = convert(T1, 0.00318547482516620984874835878222687621122035448401205459368674257818574765593899794870819769668503869906022860261901897250913569265553156976061140932045107432) + T[3, 1] = convert(T1, 0.00405910730194768309165024146216588597640781263680870767202041411242133338742562561902630276038676420444232405079851555753917806998064489819308813790494788924) + T[3, 2] = convert(T1, 0.0573965089393817153975680203880753938458832782600090443030839643350468249623833638779578474891654213594195393636829414422184571666256857425091138479371917574) + T[3, 3] = convert(T1, 0.0588505292084267910561208969865829735901655409220388105109199298038946675765714122525765330769443473927581930134049676200572930797370286476504623214740871248) + T[3, 4] = convert(T1, -0.00856043106160343206017727185390754992573940897343949944649743606465705403614377469754987858631901604547097801042861815249197647886051332362774581709381720893) + T[3, 5] = convert(T1, -0.00692321266502390892414068519049460069371592099748070119636478595631451405094203293036429762819458535062492059219566837532157551782305886338773933077463475632) + T[3, 6] = convert(T1, -0.00235218098294333834053519532555529491776729377182703234025085030409255592197086839142988525473684138901264206886166295186155491132922909402254443843846019141) + T[3, 7] = convert(T1, 0.00041690777252975626914088803059940941342549922756308931704215701350026719541939053570614368159222367707113801117750298289694571643601584878405615892432648487) + T[4, 1] = convert(T1, 0.0157504880793768442034586734054915501004520506405808322686493022779655453114657621318660532381583918124125360276320121127974912393389579826125529804830864399) + T[4, 2] = convert(T1, -0.0382146935969683504846411337659300127514788882892071252172987515109399372135899067290947441850340146027892665775682097051548343529370733593281856326317259999) + T[4, 3] = convert(T1, -0.165736811272943851241241116255535218556011122333381899790277357803281567727036568454939356458468926429537927937619042817050400333625919290585510785057955509) + T[4, 4] = convert(T1, -0.0373712423023844574190702119163246888117181457309185176497005310822879226235861373253125139016964433591381638592353617347369492240160809914228784174846477722) + T[4, 5] = convert(T1, 0.00823900729850771940449868235563938395546999707236910359131464615707125576979409087864780171789078059526539789661318173387826643385244974406562622466790754233) + T[4, 6] = convert(T1, 0.00311507115234617525272547086289315208054441921705361129575617631104650731644437585122142710666234276633544335552925569262424677362146587776195531866754755781) + T[4, 7] = convert(T1, 0.025116604913438821928363823471446698278976101918753236732238210724710282378748917637317846485853317873304329580245705683618093593158791190832004186288367408) + T[5, 1] = convert(T1, 0.112977661024220807608615842313106352633973778091080400075534257952348289641328709240673869677499013004285003126194992176632265223545565047727637631580337111) + T[5, 2] = convert(T1, -0.249174212465263686330825594009221950347570740813751325091913985975498424569678307894304962660904874986611526140914403971840496728150916599999921976188547708) + T[5, 3] = convert(T1, 0.273563305798662321213236935135336593478278696397012151365678540099566245199777083242808233574654642014215983653810819494932091426330017240672955510133726276) + T[5, 4] = convert(T1, 0.00536676137918177009427930181087914853701809128264121101773394730339300080525157052081366996826642003169044168721911822166683675089051631342776752635189343996) + T[5, 5] = convert(T1, 0.193211116101262014431211225620266980060733605289133050251158448403922545905872373640500736693735926480983370235582910255756813799388364741420161359961401418) + T[5, 6] = convert(T1, 0.101717732481715146808078931323995112561027763392448195424858681165964478003318758266672250034474900552688318026734856778296896546916272032434282368222825518) + T[5, 7] = convert(T1, 0.0950450203560462282103892144485647895183175432965514336285840628832838918715022627077373617151475963061484489345238022187829573892306346658797861719620799413) + T[6, 1] = convert(T1, 0.458381043183931501028085939964292092908293295595258886425372669820276128937720150467378912424378376379185138190017965370589550781979145790869568608776861466) + T[6, 2] = convert(T1, 0.5315846490836284292050500994300107341125728347976407285397462896004659632807779347307732180848765709277026749725126234633983063167374333425454720010026876) + T[6, 3] = convert(T1, 0.486322836617572894056685295353340203321316764127126557475136642083389075853199222650975554544550110757249234979120491845825690852575400863926535437662617201) + T[6, 4] = convert(T1, 0.526574226458449262914091192639271913456008564881594253716678163127743947224108435833618497118891017505982561930788522171455486058320589875335702474378251931) + T[6, 5] = convert(T1, 0.275534394989625814192875938762525038291639319966986287664787801569471609648366101593885546008609962622035890891754680149203464179471952105174480329668882489) + T[6, 6] = convert(T1, 0.521751945274765285294609453181807034209434470364856664246194441011327338299794536726049398636575212016960129143954076748520870645966241492966592488607495009) + T[6, 7] = convert(T1, 0.128071944635543894414114939510913357662538610722706228789484435811417614332529416514635125851744500940930818246509599119254761178392202724896572159336577251) + T[7, 1] = convert(T1, 0.881391578353818376313498879127399181693003124999819194603124949551827789004545406999549226388170693806014968936224161749923163222614460424501073405017519348) + T[7, 2] = convert(T1, 1.0) + T[7, 3] = convert(T1, 0.0) + T[7, 4] = convert(T1, 1.0) + T[7, 5] = convert(T1, 0.0) + T[7, 6] = convert(T1, 1.0) + T[7, 7] = convert(T1, 0.0) + + BigRadauIIA13Tableau{T1, T2, Int}(T, TI, + c, γ, α, β, 7) +end + struct adaptiveRadauTableau{T, T2, Int} T:: AbstractMatrix{T} TI::AbstractMatrix{T} @@ -388,5 +628,8 @@ function adaptiveRadauTableau(T, T2, num_stages::Int) @assert islinear Symbolics.expand.((AA[idxs, :] \ -bb[idxs]) - b)=# #e = b_hat - b + #T_test = T + #return T_test adaptiveRadauTableau{Any, T2, Int}(T, TI, γ, α, β, c, num_stages) -end \ No newline at end of file +end + diff --git a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl index 38c0d4b4e3..c5d69b7126 100644 --- a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl +++ b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl @@ -17,13 +17,8 @@ sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_2Dlinear, RadauIIA9()) prob_ode_linear_big = remake(prob_ode_linear, u0 = big.(prob_ode_linear.u0), tspan = big.(prob_ode_linear.tspan)) prob_ode_2Dlinear_big = remake(prob_ode_2Dlinear, u0 = big.(prob_ode_2Dlinear.u0), tspan = big.(prob_ode_2Dlinear.tspan)) -for i in [3, 5, 7, 9] - sim21 = test_convergence(1 ./ 2 .^ (2.25:-1:0.25), prob_ode_linear_big, AdaptiveRadau(num_stages = i)) - @test sim21.𝒪est[:final]≈ (2 * i - 1) atol=testTol -end - -for i in [3, 5, 7, 9] - sim21 = test_convergence(1 ./ 2 .^ (5:-1:3), prob_ode_2Dlinear_big, AdaptiveRadau(num_stages = i)) +for i in [3, 5, 7, 9], prob in [prob_ode_linear, prob_ode_2Dlinear] + sim21 = test_convergence(1 ./ 2 .^ (2.25:-1:0.25), prob, AdaptiveRadau(num_stages = i)) @test sim21.𝒪est[:final]≈ (2 * i - 1) atol=testTol end From e8ba6c70450649d9758b30a1591a27f1cdcf6d1a Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Mon, 2 Sep 2024 12:07:45 -0400 Subject: [PATCH 54/71] fix types --- lib/OrdinaryDiffEqFIRK/src/firk_caches.jl | 8 +- lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl | 392 +++++++++--------- lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl | 2 +- 3 files changed, 201 insertions(+), 201 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl index 96f92303d9..f2cf3019a6 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl @@ -500,8 +500,8 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} tab = BigRadauIIA5Tableau(uToltype, constvalue(tTypeNoUnits), Int) elseif (num_stages == 5) tab = BigRadauIIA9Tableau(uToltype, constvalue(tTypeNoUnits), Int) - #elseif (num_stages == 7) - # tab = BigRadauIIA13Tableau(uToltype, constvalue(tTypeNoUnits), Int) + elseif (num_stages == 7) + tab = BigRadauIIA13Tableau(uToltype, constvalue(tTypeNoUnits), Int) else tab = adaptiveRadauTableau(uToltype, constvalue(tTypeNoUnits), num_stages) end @@ -568,8 +568,8 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} tab = BigRadauIIA5Tableau(uToltype, constvalue(tTypeNoUnits), Int) elseif (num_stages == 5) tab = BigRadauIIA9Tableau(uToltype, constvalue(tTypeNoUnits), Int) - #elseif (num_stages == 7) - # tab = BigRadauIIA13Tableau(uToltype, constvalue(tTypeNoUnits), Int) + elseif (num_stages == 7) + tab = BigRadauIIA13Tableau(uToltype, constvalue(tTypeNoUnits), Int) else tab = adaptiveRadauTableau(uToltype, constvalue(tTypeNoUnits), num_stages) end diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl index 389b880df7..290d7b3a4f 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl @@ -123,38 +123,38 @@ struct BigRadauIIA5Tableau{T1, T2, Int} end function BigRadauIIA5Tableau(T1, T2, Int) - γ = convert(T1, 3.63783425274449573220841851357777579794593608687391153215117488565841871456727143375130115708511223004183651123208497057248238260532214672028700625775335843) + γ = convert(T1, big"3.63783425274449573220841851357777579794593608687391153215117488565841871456727143375130115708511223004183651123208497057248238260532214672028700625775335843") α = Vector{T1}(undef, 1) β = Vector{T1}(undef, 1) - α[1] = convert(T1, 2.68108287362775213389579074321111210102703195656304423392441255717079064271636428312434942145744388497908174438395751471375880869733892663985649687112332242) - β[1] = convert(T1, 3.05043019924741056942637762478756790444070419917947659226291744751211727051786694870515117615266028855554735929171362769761399150862332538376382934625577549) + α[1] = convert(T1, big"2.68108287362775213389579074321111210102703195656304423392441255717079064271636428312434942145744388497908174438395751471375880869733892663985649687112332242") + β[1] = convert(T1, big"3.05043019924741056942637762478756790444070419917947659226291744751211727051786694870515117615266028855554735929171362769761399150862332538376382934625577549") c = Vector{T2}(undef, 3) - c[1] = convert(T2, 0.155051025721682190180271592529410860803405251934332987156730743274903962254268497346014056689535976518140539877338581087514113454016224265837421604876272084) - c[2] = convert(T2, 0.644948974278317809819728407470589139196594748065667012843269256725096037745731502653985943310464023481859460122661418912485886545983775734162578395123729143) - c[3] = convert(T2, 1) + c[1] = convert(T2, big"0.155051025721682190180271592529410860803405251934332987156730743274903962254268497346014056689535976518140539877338581087514113454016224265837421604876272084") + c[2] = convert(T2, big"0.644948974278317809819728407470589139196594748065667012843269256725096037745731502653985943310464023481859460122661418912485886545983775734162578395123729143") + c[3] = convert(T2, big"1") TI = Matrix{T1}(undef, 3, 3) - TI[1, 1] = convert(T1, 4.32557989006315535102435095295614882731995158490590784287320458848019483341979047442263696495019938973156007686663488090615420049217658854859024016717169837) - TI[1, 2] = convert(T1, 0.339199251815809869542824974053410987511771566126056902312311333553438988409693737874718833892037643701271502187763370262948704203562215007824701228014200056) - TI[1, 3] = convert(T1, 0.541770539935874871186523033492089631898841317849243944095021379289933921771713116368931784890546144473788347538203807242114936998948954098533375649163016612) - TI[2, 1] = convert(T1, -4.17871859155190472734646265851205623000038388214686525896709481539843195209360778128456932548583273459040707932166364293012713818843609182148794380267482041) - TI[2, 2] = convert(T1, -0.327682820761062387082533272429616234245791838308340887801415258608836530255609335712523838667242449344879454518796849992049787172023800373390124427898159896) - TI[2, 3] = convert(T1, 0.476623554500550451960069084091012497939942928625055897109833707684876604712862299049343675491204859381277636585708398915065951363736337328178192801074535132) - TI[3, 1] = convert(T1, -0.502872634945786875951247343139544292859248429570937886791036339034110181540695221500843782634464164585836226038438397328726973424362168221527501738985822875) - TI[3, 2] = convert(T1, 2.57192694985560542918678535360167505469448742842178326395573566888176471664393761903447163100353067504020263109067033226021288356347565113471227052083596358) - TI[3, 3] = convert(T1, -0.596039204828224924968821911099302403289857517521591823052174732952989090998130905722763344484798508456930766594977798579939415052669401095404149917833710127) + TI[1, 1] = convert(T1, big"4.32557989006315535102435095295614882731995158490590784287320458848019483341979047442263696495019938973156007686663488090615420049217658854859024016717169837") + TI[1, 2] = convert(T1, big"0.339199251815809869542824974053410987511771566126056902312311333553438988409693737874718833892037643701271502187763370262948704203562215007824701228014200056") + TI[1, 3] = convert(T1, big"0.541770539935874871186523033492089631898841317849243944095021379289933921771713116368931784890546144473788347538203807242114936998948954098533375649163016612") + TI[2, 1] = convert(T1, big"-4.17871859155190472734646265851205623000038388214686525896709481539843195209360778128456932548583273459040707932166364293012713818843609182148794380267482041") + TI[2, 2] = convert(T1, big"-0.327682820761062387082533272429616234245791838308340887801415258608836530255609335712523838667242449344879454518796849992049787172023800373390124427898159896") + TI[2, 3] = convert(T1, big"0.476623554500550451960069084091012497939942928625055897109833707684876604712862299049343675491204859381277636585708398915065951363736337328178192801074535132") + TI[3, 1] = convert(T1, big"-0.502872634945786875951247343139544292859248429570937886791036339034110181540695221500843782634464164585836226038438397328726973424362168221527501738985822875") + TI[3, 2] = convert(T1, big"2.57192694985560542918678535360167505469448742842178326395573566888176471664393761903447163100353067504020263109067033226021288356347565113471227052083596358") + TI[3, 3] = convert(T1, big"-0.596039204828224924968821911099302403289857517521591823052174732952989090998130905722763344484798508456930766594977798579939415052669401095404149917833710127") T = Matrix{T1}(undef, 3, 3) - T[1, 1] = convert(T1, 0.091232394870892942791548135249436196118684699372210280712184363514099824021240149574725365814781580305065489937969163922775110463056339192206701819661425186) - T[1, 2] = convert(T1, -0.141255295020954208427990383807797309409263248498594798844289981408804297900674604638610419147468875667691398225003133444988034605081071965848437945842767211) - T[1 ,3] = convert(T1, -0.0300291941051474244918611170890538666683842974606300802563717702200388818691214144173874588956764952224874407424115249418136547481236684478531215095064078994) - T[2, 1] = convert(T1, 0.241717932707107018957474779310148232884879540532595279746187345714229132659465207414913313803429072060469564350914390845001169448350326344874859416624577348) - T[2, 2] = convert(T1, 0.204129352293799931995990810298338174086540402523315938937516234649384944528706774788799548853122282827246947911905379230680096946800308693162079538975632443) - T[2, 3] = convert(T1, 0.382942112757261937795438233599873210357792575012007744255205163027042915338009760005422153613194350161760232119048691964499888989151661861236831969497483828) - T[3, 1] = convert(T1, 0.966048182615092936190567080794590794996748754810883844283183333914131408744555961195911605614405476210484499875001737558078500322423463946527349731087504518) - T[3, 2] = convert(T1, 1.0) - T[3, 3] = convert(T1, 0.0) + T[1, 1] = convert(T1, big"0.091232394870892942791548135249436196118684699372210280712184363514099824021240149574725365814781580305065489937969163922775110463056339192206701819661425186") + T[1, 2] = convert(T1, big"-0.141255295020954208427990383807797309409263248498594798844289981408804297900674604638610419147468875667691398225003133444988034605081071965848437945842767211") + T[1 ,3] = convert(T1, big"-0.0300291941051474244918611170890538666683842974606300802563717702200388818691214144173874588956764952224874407424115249418136547481236684478531215095064078994") + T[2, 1] = convert(T1, big"0.241717932707107018957474779310148232884879540532595279746187345714229132659465207414913313803429072060469564350914390845001169448350326344874859416624577348") + T[2, 2] = convert(T1, big"0.204129352293799931995990810298338174086540402523315938937516234649384944528706774788799548853122282827246947911905379230680096946800308693162079538975632443") + T[2, 3] = convert(T1, big"0.382942112757261937795438233599873210357792575012007744255205163027042915338009760005422153613194350161760232119048691964499888989151661861236831969497483828") + T[3, 1] = convert(T1, big"0.966048182615092936190567080794590794996748754810883844283183333914131408744555961195911605614405476210484499875001737558078500322423463946527349731087504518") + T[3, 2] = convert(T1, big"1.0") + T[3, 3] = convert(T1, big"0.0") BigRadauIIA5Tableau{T1, T2, Int}(T, TI, c, γ, α, β, 3) end @@ -171,74 +171,74 @@ struct BigRadauIIA9Tableau{T1, T2, Int} end function BigRadauIIA9Tableau(T1, T2, Int) - γ = convert(T1, 6.28670475172927664517315334186940904959068186655567041187229167532923622489525703260842273089261139845280626287956099768662193453067483410165932355981736786) + γ = convert(T1, big"6.28670475172927664517315334186940904959068186655567041187229167532923622489525703260842273089261139845280626287956099768662193453067483410165932355981736786") α = Vector{T1}(undef, 2) β = Vector{T1}(undef, 2) - α[1] = convert(T1, 3.65569432546357225824320796009543385435699888857815445045567025741630720509235614026228963385258117304229337679733945535812317372403535763551850772878775217) - α[2] = convert(T1, 5.70095329867178941917021536896986162084766017814401034360818390491907468246001534343349900070111312773130349176288004579856585901062722531365183049130382405) - β[1] = convert(T1, 6.5437368993600772940210715093936863183637851728134458820202187133882261290012752452972782843700946890488789462524897903624959996932392239962196563965573345) - β[2] = convert(T1, 3.21026560030854988842501065297211721232153653493981008029923647488964744732168461657389754087826565709085773529539707072244537983491480773006949966789260925) + α[1] = convert(T1, big"3.65569432546357225824320796009543385435699888857815445045567025741630720509235614026228963385258117304229337679733945535812317372403535763551850772878775217") + α[2] = convert(T1, big"5.70095329867178941917021536896986162084766017814401034360818390491907468246001534343349900070111312773130349176288004579856585901062722531365183049130382405") + β[1] = convert(T1, big"6.5437368993600772940210715093936863183637851728134458820202187133882261290012752452972782843700946890488789462524897903624959996932392239962196563965573345") + β[2] = convert(T1, big"3.21026560030854988842501065297211721232153653493981008029923647488964744732168461657389754087826565709085773529539707072244537983491480773006949966789260925") c = Vector{T2}(undef, 5) - c[1] = convert(T2, 0.0571041961145176821931211925541156212350779455987501643278082929309346782020731645861138168198427368635148018903413155731609901559772929443100370500757072557) - c[2] = convert(T2, 0.276843013638123827680045997685625141110889169695030468349442048831121339683708036772541528564051130879197377136636984534220758899839905855114024309075271826) - c[3] = convert(T2, 0.583590432368916820056697668662917248693432639896771640176293841831747501961831012005632277467456299345321045569611992496682381919275766424103024358378365496) - c[4] = convert(T2, 0.8602401356562194478479129188751197667383780225872255049242335941839742579301655644134901549264276106897445531811874851737136468026848125542506920602484255) - c[5] = convert(T2, 1.0) + c[1] = convert(T2, big"0.0571041961145176821931211925541156212350779455987501643278082929309346782020731645861138168198427368635148018903413155731609901559772929443100370500757072557") + c[2] = convert(T2, big"0.276843013638123827680045997685625141110889169695030468349442048831121339683708036772541528564051130879197377136636984534220758899839905855114024309075271826") + c[3] = convert(T2, big"0.583590432368916820056697668662917248693432639896771640176293841831747501961831012005632277467456299345321045569611992496682381919275766424103024358378365496") + c[4] = convert(T2, big"0.8602401356562194478479129188751197667383780225872255049242335941839742579301655644134901549264276106897445531811874851737136468026848125542506920602484255") + c[5] = convert(T2, big"1.0") TI = Matrix{T1}(undef, 5, 5) - TI[1, 1] = convert(T1, 30.0415677215444016277146611632467970747634862837368422955138470463852339244593400023985957753164599415374157317627305099177616927640413043608408838747985125) - TI[1, 2] = convert(T1, 13.8651078562714131651762946846279728486098595017962436746405940971751244384714668104145151259298432908422191238542910724677205181071665482818120092330632702) - TI[1 ,3] = convert(T1, 3.48000277479518556182840016971955819123081637245954095062693470191383865922357339844125383481645392882289968250993872221445874555610460465838129969397069557) - TI[1, 4] = convert(T1, -1.03200879782526342277108071214631493513824682491749273908106331923801396656058254294323988505859654767877050109789490714699847664805679842903430004696170252) - TI[1, 5] = convert(T1, 0.804303045073989917475330383606196086089578671788707543063308602519859970319818304759856653218877415405946945572102875643297890954688508528143272905631829894) - TI[2, 1] = convert(T1, 5.34418643783491159889531030409736033885455686563071401172022718575590068536629704134603404624953791012861634674294690788961703408019660066685859393456498931) - TI[2, 2] = convert(T1, 4.59361556775916100445407449817656238428260055301676371438973411021009514435572975394999086474831271997070798032181411537895658457000537727156665947774751386) - TI[2, 3] = convert(T1, -3.03636032345942429864615756872018980250277648141683630832856906288036929718223473102394179699607901856890769270810252103326382063852039607285826867723587514) - TI[2, 4] = convert(T1, 1.05066019023145886385983615715299311307615150447133905233370933194949591737765763708886464382722316727972166443876395823044171403663404254906698768838255919) - TI[2, 5] = convert(T1, -0.272778611864296270538614649997366804891835224042737605275699398413256470423268908248569612750117948720141667949532252500428432062582365619208502333677907158) - TI[3, 1] = convert(T1, 3.74805980743980486005103450189256983678052751095791526209741655305580351377124372457009580386663275146166007984852101733055495783906881063060757645038080343) - TI[3, 2] = convert(T1, -3.98496573634388466725226385805351110838575115293851360514636734529255361185420464416807882769853298186283398369873418552760618971047757002216338511286260041) - TI[3, 3] = convert(T1, -1.04441564160801879294224732309562532189841624726401645191058551173485917137499204844819781779667611903670073971659834929382224472890100209497741235960707456) - TI[3, 4] = convert(T1, 1.18409856813794848723102038838340482030291345603197522521517834943166421242518751666675199211369552058487095283489346390066317584532997854692445653563909898) - TI[3, 5] = convert(T1, -0.449917770156780368898811918314095435942113881883174152777026977062686286863549565130412864190301081537983106397709991028107600781961279985605930655683680139) - TI[4, 1] = convert(T1, -33.0418802135190000080614469426109507742858088371383868670878639187564531424382858814386742148456699143328462132296293097447566408853495288807407929988004676) - TI[4, 2] = convert(T1, -17.3769534790635670194549806058987105852733409102703844354448800193942184746909147697382687117638715195698950138089979798321855885541817752366521518811413713) - TI[4, 3] = convert(T1, -0.172129063254005561151528806427751383749451500597823574207174433146207178559871803504021077429693091164540897873472803934375603405253541639437370184767553293) - TI[4, 4] = convert(T1, -0.0991697779825426425881662214017368584726354746776989845479783944003623924121748016326495070834800297497011104846871751430208559227945252758721362340763610828) - TI[4, 5] = convert(T1, 0.531228115838306667184911422606024795426589562580669892779793097035561488973256023529352389498509937781553683467106048413485632583844632286562240161995145055) - TI[5, 1] = convert(T1, -8.61144397987529197770008251257034851950485933115010902789613925540488896812417081206983938638600226846804467531843522104806738090683710882069500386691775154) - TI[5, 2] = convert(T1, 9.69999140952880823133589405342003266497120753048627084327055311528684684237122654108691149692242002085965723391934376924400492239317026460192827344970015484) - TI[5, 3] = convert(T1, 1.91472863969687428485137560339172471528025297511003983469957355306260543484472462223194401768126877615795915146192537091374017807611943419264038682143890747) - TI[5, 4] = convert(T1, 2.41869200608494002642656343408298350771199306961305597858229870375990977712805399625496435641846363295393762353024017195444763964531237381728801981679934304) - TI[5, 5] = convert(T1, -1.0474634879353374186944329992117360176590042540536055452919974336199826846201614544718272622833822842591012529895091659029452542118642301415759073410771819) + TI[1, 1] = convert(T1, big"30.0415677215444016277146611632467970747634862837368422955138470463852339244593400023985957753164599415374157317627305099177616927640413043608408838747985125") + TI[1, 2] = convert(T1, big"13.8651078562714131651762946846279728486098595017962436746405940971751244384714668104145151259298432908422191238542910724677205181071665482818120092330632702") + TI[1 ,3] = convert(T1, big"3.48000277479518556182840016971955819123081637245954095062693470191383865922357339844125383481645392882289968250993872221445874555610460465838129969397069557") + TI[1, 4] = convert(T1, big"-1.03200879782526342277108071214631493513824682491749273908106331923801396656058254294323988505859654767877050109789490714699847664805679842903430004696170252") + TI[1, 5] = convert(T1, big"0.804303045073989917475330383606196086089578671788707543063308602519859970319818304759856653218877415405946945572102875643297890954688508528143272905631829894") + TI[2, 1] = convert(T1, big"5.34418643783491159889531030409736033885455686563071401172022718575590068536629704134603404624953791012861634674294690788961703408019660066685859393456498931") + TI[2, 2] = convert(T1, big"4.59361556775916100445407449817656238428260055301676371438973411021009514435572975394999086474831271997070798032181411537895658457000537727156665947774751386") + TI[2, 3] = convert(T1, big"-3.03636032345942429864615756872018980250277648141683630832856906288036929718223473102394179699607901856890769270810252103326382063852039607285826867723587514") + TI[2, 4] = convert(T1, big"1.05066019023145886385983615715299311307615150447133905233370933194949591737765763708886464382722316727972166443876395823044171403663404254906698768838255919") + TI[2, 5] = convert(T1, big"-0.272778611864296270538614649997366804891835224042737605275699398413256470423268908248569612750117948720141667949532252500428432062582365619208502333677907158") + TI[3, 1] = convert(T1, big"3.74805980743980486005103450189256983678052751095791526209741655305580351377124372457009580386663275146166007984852101733055495783906881063060757645038080343") + TI[3, 2] = convert(T1, big"-3.98496573634388466725226385805351110838575115293851360514636734529255361185420464416807882769853298186283398369873418552760618971047757002216338511286260041") + TI[3, 3] = convert(T1, big"-1.04441564160801879294224732309562532189841624726401645191058551173485917137499204844819781779667611903670073971659834929382224472890100209497741235960707456") + TI[3, 4] = convert(T1, big"1.18409856813794848723102038838340482030291345603197522521517834943166421242518751666675199211369552058487095283489346390066317584532997854692445653563909898") + TI[3, 5] = convert(T1, big"-0.449917770156780368898811918314095435942113881883174152777026977062686286863549565130412864190301081537983106397709991028107600781961279985605930655683680139") + TI[4, 1] = convert(T1, big"-33.0418802135190000080614469426109507742858088371383868670878639187564531424382858814386742148456699143328462132296293097447566408853495288807407929988004676") + TI[4, 2] = convert(T1, big"-17.3769534790635670194549806058987105852733409102703844354448800193942184746909147697382687117638715195698950138089979798321855885541817752366521518811413713") + TI[4, 3] = convert(T1, big"-0.172129063254005561151528806427751383749451500597823574207174433146207178559871803504021077429693091164540897873472803934375603405253541639437370184767553293") + TI[4, 4] = convert(T1, big"-0.0991697779825426425881662214017368584726354746776989845479783944003623924121748016326495070834800297497011104846871751430208559227945252758721362340763610828") + TI[4, 5] = convert(T1, big"0.531228115838306667184911422606024795426589562580669892779793097035561488973256023529352389498509937781553683467106048413485632583844632286562240161995145055") + TI[5, 1] = convert(T1, big"-8.61144397987529197770008251257034851950485933115010902789613925540488896812417081206983938638600226846804467531843522104806738090683710882069500386691775154") + TI[5, 2] = convert(T1, big"9.69999140952880823133589405342003266497120753048627084327055311528684684237122654108691149692242002085965723391934376924400492239317026460192827344970015484") + TI[5, 3] = convert(T1, big"1.91472863969687428485137560339172471528025297511003983469957355306260543484472462223194401768126877615795915146192537091374017807611943419264038682143890747") + TI[5, 4] = convert(T1, big"2.41869200608494002642656343408298350771199306961305597858229870375990977712805399625496435641846363295393762353024017195444763964531237381728801981679934304") + TI[5, 5] = convert(T1, big"-1.0474634879353374186944329992117360176590042540536055452919974336199826846201614544718272622833822842591012529895091659029452542118642301415759073410771819") T = Matrix{T1}(undef, 5, 5) - T[1, 1] = convert(T1, 0.0125175862205010458901356760368001462557655123420858705973577952199246108029451084239310924615007306721702298573083400752464277227557045438770401832498107968) - T[1, 2] = convert(T1, -0.0102420478179088270700863300668590125015813934827825923708366359399562125950804289592272678367034071306578383319296130180550178248531589487456925441921649293) - T[1 ,3] = convert(T1, 0.0476738772902957238631839478592069782970238490568258436986723993118380988311441474394156362952631834786373081794857384127209450988829840886524135970873769918) - T[1, 4] = convert(T1, -0.0114785152552295147079415554121555049385506204591245712490409384029671974157542450636658532835395855844059342442518520033304129991000509527123870917346017759) - T[1, 5] = convert(T1, -0.0140198588928754102810778942934959307831026572823203692568448424056201483917805257790275956734469193171917730378117501915144713896813544630288006687542182225) - T[2, 1] = convert(T1, 0.00149167015189538242900444775236282223594625052328927847572623038484966999313257893341818287477809424303168766872838075463220122499449382436194198620498144296) - T[2, 2] = convert(T1, 0.050172864517371058162991380262646513853120568882725793734131676894272706020317186004736779675826101816279321643304301437029912742375638648226701787880031719) - T[2, 3] = convert(T1, -0.0943318191816114369806569003363724471884924328367212069321438749304281980331334016578193750445513659941246363262225907407726099492713722343006925656625258579) - T[2, 4] = convert(T1, -0.00766883074918016288515687679203608074116106558796378201472238095295554979920808799930579174190884587422912077296093093698836937450535804218413704866981728518) - T[2, 5] = convert(T1, 0.024708578426518526812525205377780382655366504554979744093019395818934704623702078004474076773426928900579988063099593288435684744957695210778788200213260272) - T[3, 1] = convert(T1, 0.072981876388087148622657299703669587832652508881663282287850495621401398441897288250625556038835308015912409648841893161563884759791665776933761278383553608) - T[3, 2] = convert(T1, -0.230539534043417946721421862180000422679228296568599014834226319726930529322581417981617275287468418138394077987361681288909676234537699721082090802790143303) - T[3, 3] = convert(T1, 0.102703045380125899792210456947141185148813233939327773583525878521508211077874610560448598369259541346968946573971195783374996178436435357335759255990489434) - T[3, 4] = convert(T1, 0.0193984639988289509112232896408330872285824216708905773930244363652651247181543158008567311548336143384128605013911312875018664026371225431993252265128272262) - T[3, 5] = convert(T1, 0.0818003537037511708363908122287572533071340646031113975848869261019231448226334426630664318901554550460201409321555775999869184033436795623062614812355590017) - T[4, 1] = convert(T1, 0.380091440003568104126439184355215575526619121262253024859378518379910007234696730891540745160675744992320824590679292148769326540463161583672773762554445506) - T[4, 2] = convert(T1, 0.377893902248861249543862293745933995234687511602719536459666284734445918178134851270924212812363352965391508894581698067329905034837778770261095647458874628) - T[4, 3] = convert(T1, 0.466744130332494359289559582964906703283968612669234331018678042733321473730897217606173184300477207393539851157929838664168404778962779344509707214938022808) - T[4, 4] = convert(T1, 0.40760117128019906662166237021895987274626181127101561893104166874567447589187790736078997321464949349935802836110699884016973990503134772720646054039223561) - T[4, 5] = convert(T1, 0.199682427886802525936540566022390695167018315867216115995143539347975271751460199398235415129329119718414206048034051939441434136353381864781262773401023899) - T[5, 1] = convert(T1, 0.921978973681210488488254647415676321266345412943047462855852351388222898143904205962703147998267738964059170225806964893009202287585991334322032058414768529) - T[5, 2] = convert(T1, 1.0) - T[5, 3] = convert(T1, 0.0) - T[5, 4] = convert(T1, 1.0) - T[5, 5] = convert(T1, 0.0) + T[1, 1] = convert(T1, big"0.0125175862205010458901356760368001462557655123420858705973577952199246108029451084239310924615007306721702298573083400752464277227557045438770401832498107968") + T[1, 2] = convert(T1, big"-0.0102420478179088270700863300668590125015813934827825923708366359399562125950804289592272678367034071306578383319296130180550178248531589487456925441921649293") + T[1 ,3] = convert(T1, big"0.0476738772902957238631839478592069782970238490568258436986723993118380988311441474394156362952631834786373081794857384127209450988829840886524135970873769918") + T[1, 4] = convert(T1, big"-0.0114785152552295147079415554121555049385506204591245712490409384029671974157542450636658532835395855844059342442518520033304129991000509527123870917346017759") + T[1, 5] = convert(T1, big"-0.0140198588928754102810778942934959307831026572823203692568448424056201483917805257790275956734469193171917730378117501915144713896813544630288006687542182225") + T[2, 1] = convert(T1, big"0.00149167015189538242900444775236282223594625052328927847572623038484966999313257893341818287477809424303168766872838075463220122499449382436194198620498144296") + T[2, 2] = convert(T1, big"0.050172864517371058162991380262646513853120568882725793734131676894272706020317186004736779675826101816279321643304301437029912742375638648226701787880031719") + T[2, 3] = convert(T1, big"-0.0943318191816114369806569003363724471884924328367212069321438749304281980331334016578193750445513659941246363262225907407726099492713722343006925656625258579") + T[2, 4] = convert(T1, big"-0.00766883074918016288515687679203608074116106558796378201472238095295554979920808799930579174190884587422912077296093093698836937450535804218413704866981728518") + T[2, 5] = convert(T1, big"0.024708578426518526812525205377780382655366504554979744093019395818934704623702078004474076773426928900579988063099593288435684744957695210778788200213260272") + T[3, 1] = convert(T1, big"0.072981876388087148622657299703669587832652508881663282287850495621401398441897288250625556038835308015912409648841893161563884759791665776933761278383553608") + T[3, 2] = convert(T1, big"-0.230539534043417946721421862180000422679228296568599014834226319726930529322581417981617275287468418138394077987361681288909676234537699721082090802790143303") + T[3, 3] = convert(T1, big"0.102703045380125899792210456947141185148813233939327773583525878521508211077874610560448598369259541346968946573971195783374996178436435357335759255990489434") + T[3, 4] = convert(T1, big"0.0193984639988289509112232896408330872285824216708905773930244363652651247181543158008567311548336143384128605013911312875018664026371225431993252265128272262") + T[3, 5] = convert(T1, big"0.0818003537037511708363908122287572533071340646031113975848869261019231448226334426630664318901554550460201409321555775999869184033436795623062614812355590017") + T[4, 1] = convert(T1, big"0.380091440003568104126439184355215575526619121262253024859378518379910007234696730891540745160675744992320824590679292148769326540463161583672773762554445506") + T[4, 2] = convert(T1, big"0.377893902248861249543862293745933995234687511602719536459666284734445918178134851270924212812363352965391508894581698067329905034837778770261095647458874628") + T[4, 3] = convert(T1, big"0.466744130332494359289559582964906703283968612669234331018678042733321473730897217606173184300477207393539851157929838664168404778962779344509707214938022808") + T[4, 4] = convert(T1, big"0.40760117128019906662166237021895987274626181127101561893104166874567447589187790736078997321464949349935802836110699884016973990503134772720646054039223561") + T[4, 5] = convert(T1, big"0.199682427886802525936540566022390695167018315867216115995143539347975271751460199398235415129329119718414206048034051939441434136353381864781262773401023899") + T[5, 1] = convert(T1, big"0.921978973681210488488254647415676321266345412943047462855852351388222898143904205962703147998267738964059170225806964893009202287585991334322032058414768529") + T[5, 2] = convert(T1, big"1.0") + T[5, 3] = convert(T1, big"0.0") + T[5, 4] = convert(T1, big"1.0") + T[5, 5] = convert(T1, big"0.0") BigRadauIIA9Tableau{T1, T2, Int}(T, TI, c, γ, α, β, 5) @@ -405,126 +405,126 @@ struct BigRadauIIA13Tableau{T1, T2, Int} end function BigRadauIIA13Tableau(T1, T2, Int) - γ = convert(T1, 8.93683278840521633730209691330107970355008194433956657198414191417624969654351559268800871286734194720118970058657997472527299153742511021973612156231867783) + γ = convert(T1, big"8.93683278840521633730209691330107970355008194433956657198414191417624969654351559268800871286734194720118970058657997472527299153742511021973612156231867783") α = Vector{T1}(undef, 3) β = Vector{T1}(undef, 3) - α[1] = convert(T1, 4.37869356150680600252334919268856129165763746518197948235657247177701087073069907016715245914093899486193202405685779803686971216417800783050995450529391908) - α[2] = convert(T1, 7.14105521918764010577498142571556804318193862372238812855726792587872300446315860222917039505087745633962330233504078264632719519730762016919715839787116038) - α[3] = convert(T1, 8.51183482510294572305062092494533081338538293892584910309408864525614127653438453125967278937451257519784982331481143195416659686980181689042482631568989031) - β[1] = convert(T1, 10.1696932837950116273183544188477298930096536824510223588525334625762336174947183926243705927725260475934351162622185429326813205432867247703480391692806137) - β[2] = convert(T1, 6.62304592263927597062055811591186110468148199066707542227575094761515104946479159063603447729283770429494038962408904312215452856333028405675512985803584472) - β[3] = convert(T1, 3.2810136243250588300359425270393915846791621918405321383787427650552081712406957205287551182809705166989352673500472974040971593568323836675590314648604458) + α[1] = convert(T1, big"4.37869356150680600252334919268856129165763746518197948235657247177701087073069907016715245914093899486193202405685779803686971216417800783050995450529391908") + α[2] = convert(T1, big"7.14105521918764010577498142571556804318193862372238812855726792587872300446315860222917039505087745633962330233504078264632719519730762016919715839787116038") + α[3] = convert(T1, big"8.51183482510294572305062092494533081338538293892584910309408864525614127653438453125967278937451257519784982331481143195416659686980181689042482631568989031") + β[1] = convert(T1, big"10.1696932837950116273183544188477298930096536824510223588525334625762336174947183926243705927725260475934351162622185429326813205432867247703480391692806137") + β[2] = convert(T1, big"6.62304592263927597062055811591186110468148199066707542227575094761515104946479159063603447729283770429494038962408904312215452856333028405675512985803584472") + β[3] = convert(T1, big"3.2810136243250588300359425270393915846791621918405321383787427650552081712406957205287551182809705166989352673500472974040971593568323836675590314648604458") c = Vector{T2}(undef, 7) - c[1] = convert(T2, 0.0293164271597848919720502769131649103737303925637149277869106839449360382416657787486309483651843695097273923248526200112627747993405898353736305552306269904) - c[2] = convert(T2, 0.148078599668484291849976852495979212230248774808594461412594641801598386090878321806369397661747576057906341132861865305306667654594593138746653233717241913) - c[3] = convert(T2, 0.336984690281154299097052972080775705197568750028473347122562968073691350512784060852409141173654482529393236826516171319486086447256539582972346127980810124) - c[4] = convert(T2, 0.558671518771550132081393341805521940074368288965407825555747226117350122897421078323820052012282581935200398463518265914564420109615277886000739200777932339) - c[5] = convert(T2, 0.769233862030054500916883360115645451837142143322295416166948169636548130573953285685200211542774367652885154701431860087378103033801830280742146083476036669) - c[6] = convert(T2, 0.926945671319741114851873965819682011056172419542283252724467079656645202452528243814339480013587391545656707320049986592771178724621938506933715568048004783) - c[7] = convert(T2, 1.0) + c[1] = convert(T2, big"0.0293164271597848919720502769131649103737303925637149277869106839449360382416657787486309483651843695097273923248526200112627747993405898353736305552306269904") + c[2] = convert(T2, big"0.148078599668484291849976852495979212230248774808594461412594641801598386090878321806369397661747576057906341132861865305306667654594593138746653233717241913") + c[3] = convert(T2, big"0.336984690281154299097052972080775705197568750028473347122562968073691350512784060852409141173654482529393236826516171319486086447256539582972346127980810124") + c[4] = convert(T2, big"0.558671518771550132081393341805521940074368288965407825555747226117350122897421078323820052012282581935200398463518265914564420109615277886000739200777932339") + c[5] = convert(T2, big"0.769233862030054500916883360115645451837142143322295416166948169636548130573953285685200211542774367652885154701431860087378103033801830280742146083476036669") + c[6] = convert(T2, big"0.926945671319741114851873965819682011056172419542283252724467079656645202452528243814339480013587391545656707320049986592771178724621938506933715568048004783") + c[7] = convert(T2, big"1.0") TI = Matrix{T1}(undef, 7, 7) - TI[1, 1] = convert(T1, 258.131926319982229276108947425184471333411128774462923076434633414645220927977539758484670571338176678808837829326061674950321562391576244286310404028770676) - TI[1, 2] = convert(T1, 189.073763081398508951976143411165126555759459745371576264125287430947886413126866952443113984840310549596923934762141954737541643761162558070450614795561734) - TI[1, 3] = convert(T1, 49.0873148179301311944474703372633419330229683717897887664283914712555334645741343066714059043135343948204451450061803442374878045458955826422757210762412997) - TI[1, 4] = convert(T1, 4.11064746966142841811238518636124668078589358089581133578005291508858571621836624121708112101643343488669794287298806656198949715476379639435093560435010553) - TI[1, 5] = convert(T1, 4.05344788931556330417512803837862541661144275947069236866476426664242632965376171604053865483440478823853326237912519148507906655855071507442222711969825069) - TI[1, 6] = convert(T1, -3.11275536660734607655357698925636361735741304308245452106573904595716690770542970584435712650159533448326091358879097717388530116398450168049097806992817596) - TI[1, 7] = convert(T1, 1.64677491355844465016894934800942442334612077828885771793164268655566366462165061862443368822544695623147966149765223644798045399342853834086413561960176148) - TI[2, 1] = convert(T1, -3.00739016945129213173149353792169083141834116044470099212013728771587881480191343754504173052952073006187734389002396348355357273701343509199048972794392147) - TI[2, 2] = convert(T1, -11.0158660787657713291120393664792067595453921824881213620299497076376976067619617086470844707815815293102862568459526162951253770377715406520772358338647188) - TI[2, 3] = convert(T1, 1.48779945613165628148618248664965038886474377325027865838645297753993182317594482435706956176392903188004580583104018591540474622009639200188521283880201225) - TI[2, 4] = convert(T1, 2.13038815955928245943197208332824475219642634294808813866153957342980992047877237670079423767538654092424134276380826377135080667266661637001176204430488753) - TI[2, 5] = convert(T1, -1.81614108681756562482220455159496741723359999245934818387747079566312917815672128128449281415737713177900591942282975861961228230314168417307836619006791605) - TI[2, 6] = convert(T1, 1.13432558789516110008277908420532415765361628740656810686297793967986689714948610119162966211301325316623863222505219543867472186257492829970663316956377323) - TI[2, 7] = convert(T1, -0.414699045943303531993049422295928526684402022493736427543557958358387925728160703636844863663828153394608981043415378230601486738224597324364079320598162815) - TI[3, 1] = convert(T1, -8.44196318832108468175691559413731210343158392484322786670758421404507417209484447031645790366021837365786640573614305718894911853549168061902141351516580451) - TI[3, 2] = convert(T1, -0.650525274057515002816904045893485631294530894981669254094573985727348985809697093879080285963063573837365484483755274668080611163704039179328960851461387071) - TI[3, 3] = convert(T1, 6.94067073036987647880408175445008301222030789462375109942012235845495260572570799226646472429196555932436186979400567616504159564738984233922289782922787445) - TI[3, 4] = convert(T1, -3.20504752559789843156502799159713971965747774043426947358779973217345866996463287674334224123932879873323284636947452187683408110992957222808611161423213549) - TI[3, 5] = convert(T1, 1.07128094354647858978279562700457911254627057919002861801894953308482120936700881726232902304000322718645130593907512149815870969208873216470962770569998532) - TI[3, 6] = convert(T1, -0.354850749121622187972972761073874956531274189535504546398851680169235702590362534883357256681588685608802983372517893712333972644320006895019178184808028042) - TI[3, 7] = convert(T1, 0.0919854913278655415440864884207305663999562250023079120516746551750254082665966708567906888946992351083964961208132558221142585217674963218388224937302473142) - TI[4, 1] = convert(T1, 74.6783322350226997715286176267232500441551583987525066913719852490109364599462546293112601362342028584101507709386240000804692470037564789980905370400509214) - TI[4, 2] = convert(T1, 87.4085889799008164020396362924136436577534600993283836959398121813667403209890699914314446222016952621954817633686823685774595935180374571416781238038364186) - TI[4, 3] = convert(T1, 4.02415873737999787701407840793921059156554118449220356776918749072220128918152906578385457943212213189933447495921754693186811343717296680238755923076427455) - TI[4, 4] = convert(T1, -3.7148063151583641866387382381081795406061842159003055897302686185198568522128509989890869602984467843559169959313018612449354703104270603001605170037725663) - TI[4, 5] = convert(T1, -3.43009398598231735074090769130593476067104938465255451803266927011738721835297930406017172365070584279715308905584391225176154776278518922912169890517961929) - TI[4, 6] = convert(T1, 2.69660480976531237885262500230842013033719691844775548640355919138284680959979836353143310081338215041119022648809147361433752919265159399610746756470853959) - TI[4, 7] = convert(T1, -0.938692743607546193356785681771531136814109179879957291315724533839534255667763099330792864148293396694586387338161584706252944483821135344465739888811338788) - TI[5, 1] = convert(T1, 58.3565288519065772423731088606544342599129168115273649928818622008651860145833895668543250775742899696760389837877193028417145182338484929599333810581515993) - TI[5, 2] = convert(T1, -10.0687739578001809632495544545749228539542767485211306078205622876595603032162891608453826862136355989387474454697691529766293644115682409173741730758425432) - TI[5, 3] = convert(T1, -30.3663888425666712081087189214021522992426235463582449811325590575576319489955157279473313224901192335775884848736150180108985558310423628914140477437063457) - TI[5, 4] = convert(T1, -1.02002086518486598502718784312141857841892430616701325398305811243769008274372077411348691412296276168896198187688441456921700292037247387330560786140723416) - TI[5, 5] = convert(T1, -0.112417500378424962126670249921897816128157398591725875330925039631874967429838848482089690872916638698820411392685501889126627650123714184027159547685248056) - TI[5, 6] = convert(T1, 1.89064083100037762279966919417932484200269828564004442737723486475878958135985745266991261770924069476112679285337233931312540904735632744873728510014970829) - TI[5, 7] = convert(T1, -0.971648639383148228217233127548943147296423534674266405843322723719694664032217172325052282800290275002731997713145411340983758516166807609661717915219518127) - TI[6, 1] = convert(T1, -299.18624802825209667863642523944728107942141534516550178278869311293354511449399684666660494133688445719285752471650937062695632169114367079856135650539072) - TI[6, 2] = convert(T1, -243.040745368744791181900565230083092669143049316165122405971394775932180012728275256467636352341415340547177922968547123544546515287229215470481168446631934) - TI[6, 3] = convert(T1, -48.7771040780378692121909344887388032694629956594617430615510915251995189158287187599892740037773277403958100797917560590738598108409472582147091119440886778) - TI[6, 4] = convert(T1, -2.03867190574193440528015205293433905622043272233073734690244789947707827347049413187234402189062846366658963666461334786306660732097114011309282331323116958) - TI[6, 5] = convert(T1, 1.67356023986108494426829042309213202110891938292923077616474877079402040904687073610625868939896244842053999572446723558562427506280564629528151134946587118) - TI[6, 6] = convert(T1, -1.0873740320571061644555969255032311107358443063278089996181949045168433801494845898897631535619158410753032807069032950523487601457868753453652745002841107) - TI[6, 7] = convert(T1, 0.901938249296099373842715514839004052963355800714627971724094542443991299921284427589690820402982448873149676210397055957126153220340909284180014056386791594) - TI[7, 1] = convert(T1, -93.076502897435305911571945263737383854569504715670989865831914555937966339933932282945955570244055882294556430466422133231853008314991630740535709028417842) - TI[7, 2] = convert(T1, 23.8816310562811442770319002318043863376962876994405756649585750650966186536576789769674007990310112890015051984278059899811178135726914390958188405071290871) - TI[7, 3] = convert(T1, 39.2788807308138438271015646136760366834412493325456249795727722130258444051594274416196392795817449902122139076648927894476044063388859377757097127385794539) - TI[7, 4] = convert(T1, 14.3889156854910800698761307424979534708984169042483973564042387223013868069040933228077604321320066763752720714195604903398768371784013771964086553618150626) - TI[7, 5] = convert(T1, -3.51043839939936122108708432480845734972162782563284715495715984978907792386567906732993553255070093796782368160341757151292477304975079070782335737053297468) - TI[7, 6] = convert(T1, 4.86328488556618070121491058699734313503568312572977577331134555924656926935558698308076704662503608259898740028814153544991114426972747448736702277116049277) - TI[7, 7] = convert(T1, -2.24648272959123991640046924839711232278867381637608763335081676684616443569602032178385937243819174902544136208243971053224668691848283004752869023074006745) + TI[1, 1] = convert(T1, big"258.131926319982229276108947425184471333411128774462923076434633414645220927977539758484670571338176678808837829326061674950321562391576244286310404028770676") + TI[1, 2] = convert(T1, big"189.073763081398508951976143411165126555759459745371576264125287430947886413126866952443113984840310549596923934762141954737541643761162558070450614795561734") + TI[1, 3] = convert(T1, big"49.0873148179301311944474703372633419330229683717897887664283914712555334645741343066714059043135343948204451450061803442374878045458955826422757210762412997") + TI[1, 4] = convert(T1, big"4.11064746966142841811238518636124668078589358089581133578005291508858571621836624121708112101643343488669794287298806656198949715476379639435093560435010553") + TI[1, 5] = convert(T1, big"4.05344788931556330417512803837862541661144275947069236866476426664242632965376171604053865483440478823853326237912519148507906655855071507442222711969825069") + TI[1, 6] = convert(T1, big"-3.11275536660734607655357698925636361735741304308245452106573904595716690770542970584435712650159533448326091358879097717388530116398450168049097806992817596") + TI[1, 7] = convert(T1, big"1.64677491355844465016894934800942442334612077828885771793164268655566366462165061862443368822544695623147966149765223644798045399342853834086413561960176148") + TI[2, 1] = convert(T1, big"-3.00739016945129213173149353792169083141834116044470099212013728771587881480191343754504173052952073006187734389002396348355357273701343509199048972794392147") + TI[2, 2] = convert(T1, big"-11.0158660787657713291120393664792067595453921824881213620299497076376976067619617086470844707815815293102862568459526162951253770377715406520772358338647188") + TI[2, 3] = convert(T1, big"1.48779945613165628148618248664965038886474377325027865838645297753993182317594482435706956176392903188004580583104018591540474622009639200188521283880201225") + TI[2, 4] = convert(T1, big"2.13038815955928245943197208332824475219642634294808813866153957342980992047877237670079423767538654092424134276380826377135080667266661637001176204430488753") + TI[2, 5] = convert(T1, big"-1.81614108681756562482220455159496741723359999245934818387747079566312917815672128128449281415737713177900591942282975861961228230314168417307836619006791605") + TI[2, 6] = convert(T1, big"1.13432558789516110008277908420532415765361628740656810686297793967986689714948610119162966211301325316623863222505219543867472186257492829970663316956377323") + TI[2, 7] = convert(T1, big"-0.414699045943303531993049422295928526684402022493736427543557958358387925728160703636844863663828153394608981043415378230601486738224597324364079320598162815") + TI[3, 1] = convert(T1, big"-8.44196318832108468175691559413731210343158392484322786670758421404507417209484447031645790366021837365786640573614305718894911853549168061902141351516580451") + TI[3, 2] = convert(T1, big"-0.650525274057515002816904045893485631294530894981669254094573985727348985809697093879080285963063573837365484483755274668080611163704039179328960851461387071") + TI[3, 3] = convert(T1, big"6.94067073036987647880408175445008301222030789462375109942012235845495260572570799226646472429196555932436186979400567616504159564738984233922289782922787445") + TI[3, 4] = convert(T1, big"-3.20504752559789843156502799159713971965747774043426947358779973217345866996463287674334224123932879873323284636947452187683408110992957222808611161423213549") + TI[3, 5] = convert(T1, big"1.07128094354647858978279562700457911254627057919002861801894953308482120936700881726232902304000322718645130593907512149815870969208873216470962770569998532") + TI[3, 6] = convert(T1, big"-0.354850749121622187972972761073874956531274189535504546398851680169235702590362534883357256681588685608802983372517893712333972644320006895019178184808028042") + TI[3, 7] = convert(T1, big"0.0919854913278655415440864884207305663999562250023079120516746551750254082665966708567906888946992351083964961208132558221142585217674963218388224937302473142") + TI[4, 1] = convert(T1, big"74.6783322350226997715286176267232500441551583987525066913719852490109364599462546293112601362342028584101507709386240000804692470037564789980905370400509214") + TI[4, 2] = convert(T1, big"87.4085889799008164020396362924136436577534600993283836959398121813667403209890699914314446222016952621954817633686823685774595935180374571416781238038364186") + TI[4, 3] = convert(T1, big"4.02415873737999787701407840793921059156554118449220356776918749072220128918152906578385457943212213189933447495921754693186811343717296680238755923076427455") + TI[4, 4] = convert(T1, big"-3.7148063151583641866387382381081795406061842159003055897302686185198568522128509989890869602984467843559169959313018612449354703104270603001605170037725663") + TI[4, 5] = convert(T1, big"-3.43009398598231735074090769130593476067104938465255451803266927011738721835297930406017172365070584279715308905584391225176154776278518922912169890517961929") + TI[4, 6] = convert(T1, big"2.69660480976531237885262500230842013033719691844775548640355919138284680959979836353143310081338215041119022648809147361433752919265159399610746756470853959") + TI[4, 7] = convert(T1, big"-0.938692743607546193356785681771531136814109179879957291315724533839534255667763099330792864148293396694586387338161584706252944483821135344465739888811338788") + TI[5, 1] = convert(T1, big"58.3565288519065772423731088606544342599129168115273649928818622008651860145833895668543250775742899696760389837877193028417145182338484929599333810581515993") + TI[5, 2] = convert(T1, big"-10.0687739578001809632495544545749228539542767485211306078205622876595603032162891608453826862136355989387474454697691529766293644115682409173741730758425432") + TI[5, 3] = convert(T1, big"-30.3663888425666712081087189214021522992426235463582449811325590575576319489955157279473313224901192335775884848736150180108985558310423628914140477437063457") + TI[5, 4] = convert(T1, big"-1.02002086518486598502718784312141857841892430616701325398305811243769008274372077411348691412296276168896198187688441456921700292037247387330560786140723416") + TI[5, 5] = convert(T1, big"-0.112417500378424962126670249921897816128157398591725875330925039631874967429838848482089690872916638698820411392685501889126627650123714184027159547685248056") + TI[5, 6] = convert(T1, big"1.89064083100037762279966919417932484200269828564004442737723486475878958135985745266991261770924069476112679285337233931312540904735632744873728510014970829") + TI[5, 7] = convert(T1, big"-0.971648639383148228217233127548943147296423534674266405843322723719694664032217172325052282800290275002731997713145411340983758516166807609661717915219518127") + TI[6, 1] = convert(T1, big"-299.18624802825209667863642523944728107942141534516550178278869311293354511449399684666660494133688445719285752471650937062695632169114367079856135650539072") + TI[6, 2] = convert(T1, big"-243.040745368744791181900565230083092669143049316165122405971394775932180012728275256467636352341415340547177922968547123544546515287229215470481168446631934") + TI[6, 3] = convert(T1, big"-48.7771040780378692121909344887388032694629956594617430615510915251995189158287187599892740037773277403958100797917560590738598108409472582147091119440886778") + TI[6, 4] = convert(T1, big"-2.03867190574193440528015205293433905622043272233073734690244789947707827347049413187234402189062846366658963666461334786306660732097114011309282331323116958") + TI[6, 5] = convert(T1, big"1.67356023986108494426829042309213202110891938292923077616474877079402040904687073610625868939896244842053999572446723558562427506280564629528151134946587118") + TI[6, 6] = convert(T1, big"-1.0873740320571061644555969255032311107358443063278089996181949045168433801494845898897631535619158410753032807069032950523487601457868753453652745002841107") + TI[6, 7] = convert(T1, big"0.901938249296099373842715514839004052963355800714627971724094542443991299921284427589690820402982448873149676210397055957126153220340909284180014056386791594") + TI[7, 1] = convert(T1, big"-93.076502897435305911571945263737383854569504715670989865831914555937966339933932282945955570244055882294556430466422133231853008314991630740535709028417842") + TI[7, 2] = convert(T1, big"23.8816310562811442770319002318043863376962876994405756649585750650966186536576789769674007990310112890015051984278059899811178135726914390958188405071290871") + TI[7, 3] = convert(T1, big"39.2788807308138438271015646136760366834412493325456249795727722130258444051594274416196392795817449902122139076648927894476044063388859377757097127385794539") + TI[7, 4] = convert(T1, big"14.3889156854910800698761307424979534708984169042483973564042387223013868069040933228077604321320066763752720714195604903398768371784013771964086553618150626") + TI[7, 5] = convert(T1, big"-3.51043839939936122108708432480845734972162782563284715495715984978907792386567906732993553255070093796782368160341757151292477304975079070782335737053297468") + TI[7, 6] = convert(T1, big"4.86328488556618070121491058699734313503568312572977577331134555924656926935558698308076704662503608259898740028814153544991114426972747448736702277116049277") + TI[7, 7] = convert(T1, big"-2.24648272959123991640046924839711232278867381637608763335081676684616443569602032178385937243819174902544136208243971053224668691848283004752869023074006745") T = Matrix{T1}(undef, 7, 7) - T[1, 1] = convert(T1, 0.00215375462731052642282751906550204337272018200721827917615061640312650856312529840445028048591986867096756005142895325420603307041594804305862850861253757163) - T[1, 2] = convert(T1, 0.021567551351320773386914226953811992365459277376204369162736830595700124529879508417849062386878143122032508776691627063229415272329484156789207145821702462) - T[1, 3] = convert(T1, 0.00878356792514414440732555660043326940873333657406338685620618347939710728032290406426688328221296324998146697730909767495361893387567339044816921837538988154) - T[1, 4] = convert(T1, -0.00405516145233102389819844704090310382485225922827010954643577855973533421255114497764957587851178840064428149215351434824919490696577563849929483184955933965) - T[1, 5] = convert(T1, 0.00442723275326828547967807873499027629097834766201549949492135358632150336069311115075327876323707841703727317338755331613570950287342825020738596326021052902) - T[1, 6] = convert(T1, -0.00123864618795287405637686870391105285581324510790128485733529975336279476721707053186563729417080236061385260749762448518679294700311105630290083016823761156) - T[1, 7] = convert(T1, -0.00276061748054385249954800379096675592021481213358861974911688001011761550911589157738523818859000828996335817774948428177282421412491830529445501318154035024) - T[2, 1] = convert(T1, -0.00160002507788042852683067347985080829550105638728462477214069614397009338180775134535418790113854904464693278677067195562013777079470430165035085043732753352) - T[2, 2] = convert(T1, -0.0381316481344115466944201512445271892551007922443248010648630183723114657457789198582213862424187595732944781586531399310738197517976083499508550510483478779) - T[2, 3] = convert(T1, -0.0215255605940068755238494349163503963236812065771639056145559371805737876208350036328339608215271680572576146954552666030277743869132676140541472724370558091) - T[2, 4] = convert(T1, 0.00841556827655958923717700333156546206587781542530241328710392714333753219743181540077241302321588065650704924760060316717877095134935044662592211744890794666) - T[2, 5] = convert(T1, -0.00403194957022454949230429372587008587329606687054571010486662485715979240183165499902791387008699068626978608835015342675934092134962673636484308565473356683) - T[2, 6] = convert(T1, -6.6666353393963381817604789740257628821376819567901071737415235834331307484818353061850936507762955342131861918219584166678095273744210157164382779907235669e-05) - T[2, 7] = convert(T1, 0.00318547482516620984874835878222687621122035448401205459368674257818574765593899794870819769668503869906022860261901897250913569265553156976061140932045107432) - T[3, 1] = convert(T1, 0.00405910730194768309165024146216588597640781263680870767202041411242133338742562561902630276038676420444232405079851555753917806998064489819308813790494788924) - T[3, 2] = convert(T1, 0.0573965089393817153975680203880753938458832782600090443030839643350468249623833638779578474891654213594195393636829414422184571666256857425091138479371917574) - T[3, 3] = convert(T1, 0.0588505292084267910561208969865829735901655409220388105109199298038946675765714122525765330769443473927581930134049676200572930797370286476504623214740871248) - T[3, 4] = convert(T1, -0.00856043106160343206017727185390754992573940897343949944649743606465705403614377469754987858631901604547097801042861815249197647886051332362774581709381720893) - T[3, 5] = convert(T1, -0.00692321266502390892414068519049460069371592099748070119636478595631451405094203293036429762819458535062492059219566837532157551782305886338773933077463475632) - T[3, 6] = convert(T1, -0.00235218098294333834053519532555529491776729377182703234025085030409255592197086839142988525473684138901264206886166295186155491132922909402254443843846019141) - T[3, 7] = convert(T1, 0.00041690777252975626914088803059940941342549922756308931704215701350026719541939053570614368159222367707113801117750298289694571643601584878405615892432648487) - T[4, 1] = convert(T1, 0.0157504880793768442034586734054915501004520506405808322686493022779655453114657621318660532381583918124125360276320121127974912393389579826125529804830864399) - T[4, 2] = convert(T1, -0.0382146935969683504846411337659300127514788882892071252172987515109399372135899067290947441850340146027892665775682097051548343529370733593281856326317259999) - T[4, 3] = convert(T1, -0.165736811272943851241241116255535218556011122333381899790277357803281567727036568454939356458468926429537927937619042817050400333625919290585510785057955509) - T[4, 4] = convert(T1, -0.0373712423023844574190702119163246888117181457309185176497005310822879226235861373253125139016964433591381638592353617347369492240160809914228784174846477722) - T[4, 5] = convert(T1, 0.00823900729850771940449868235563938395546999707236910359131464615707125576979409087864780171789078059526539789661318173387826643385244974406562622466790754233) - T[4, 6] = convert(T1, 0.00311507115234617525272547086289315208054441921705361129575617631104650731644437585122142710666234276633544335552925569262424677362146587776195531866754755781) - T[4, 7] = convert(T1, 0.025116604913438821928363823471446698278976101918753236732238210724710282378748917637317846485853317873304329580245705683618093593158791190832004186288367408) - T[5, 1] = convert(T1, 0.112977661024220807608615842313106352633973778091080400075534257952348289641328709240673869677499013004285003126194992176632265223545565047727637631580337111) - T[5, 2] = convert(T1, -0.249174212465263686330825594009221950347570740813751325091913985975498424569678307894304962660904874986611526140914403971840496728150916599999921976188547708) - T[5, 3] = convert(T1, 0.273563305798662321213236935135336593478278696397012151365678540099566245199777083242808233574654642014215983653810819494932091426330017240672955510133726276) - T[5, 4] = convert(T1, 0.00536676137918177009427930181087914853701809128264121101773394730339300080525157052081366996826642003169044168721911822166683675089051631342776752635189343996) - T[5, 5] = convert(T1, 0.193211116101262014431211225620266980060733605289133050251158448403922545905872373640500736693735926480983370235582910255756813799388364741420161359961401418) - T[5, 6] = convert(T1, 0.101717732481715146808078931323995112561027763392448195424858681165964478003318758266672250034474900552688318026734856778296896546916272032434282368222825518) - T[5, 7] = convert(T1, 0.0950450203560462282103892144485647895183175432965514336285840628832838918715022627077373617151475963061484489345238022187829573892306346658797861719620799413) - T[6, 1] = convert(T1, 0.458381043183931501028085939964292092908293295595258886425372669820276128937720150467378912424378376379185138190017965370589550781979145790869568608776861466) - T[6, 2] = convert(T1, 0.5315846490836284292050500994300107341125728347976407285397462896004659632807779347307732180848765709277026749725126234633983063167374333425454720010026876) - T[6, 3] = convert(T1, 0.486322836617572894056685295353340203321316764127126557475136642083389075853199222650975554544550110757249234979120491845825690852575400863926535437662617201) - T[6, 4] = convert(T1, 0.526574226458449262914091192639271913456008564881594253716678163127743947224108435833618497118891017505982561930788522171455486058320589875335702474378251931) - T[6, 5] = convert(T1, 0.275534394989625814192875938762525038291639319966986287664787801569471609648366101593885546008609962622035890891754680149203464179471952105174480329668882489) - T[6, 6] = convert(T1, 0.521751945274765285294609453181807034209434470364856664246194441011327338299794536726049398636575212016960129143954076748520870645966241492966592488607495009) - T[6, 7] = convert(T1, 0.128071944635543894414114939510913357662538610722706228789484435811417614332529416514635125851744500940930818246509599119254761178392202724896572159336577251) - T[7, 1] = convert(T1, 0.881391578353818376313498879127399181693003124999819194603124949551827789004545406999549226388170693806014968936224161749923163222614460424501073405017519348) - T[7, 2] = convert(T1, 1.0) - T[7, 3] = convert(T1, 0.0) - T[7, 4] = convert(T1, 1.0) - T[7, 5] = convert(T1, 0.0) - T[7, 6] = convert(T1, 1.0) - T[7, 7] = convert(T1, 0.0) + T[1, 1] = convert(T1, big"0.00215375462731052642282751906550204337272018200721827917615061640312650856312529840445028048591986867096756005142895325420603307041594804305862850861253757163") + T[1, 2] = convert(T1, big"0.021567551351320773386914226953811992365459277376204369162736830595700124529879508417849062386878143122032508776691627063229415272329484156789207145821702462") + T[1, 3] = convert(T1, big"0.00878356792514414440732555660043326940873333657406338685620618347939710728032290406426688328221296324998146697730909767495361893387567339044816921837538988154") + T[1, 4] = convert(T1, big"-0.00405516145233102389819844704090310382485225922827010954643577855973533421255114497764957587851178840064428149215351434824919490696577563849929483184955933965") + T[1, 5] = convert(T1, big"0.00442723275326828547967807873499027629097834766201549949492135358632150336069311115075327876323707841703727317338755331613570950287342825020738596326021052902") + T[1, 6] = convert(T1, big"-0.00123864618795287405637686870391105285581324510790128485733529975336279476721707053186563729417080236061385260749762448518679294700311105630290083016823761156") + T[1, 7] = convert(T1, big"-0.00276061748054385249954800379096675592021481213358861974911688001011761550911589157738523818859000828996335817774948428177282421412491830529445501318154035024") + T[2, 1] = convert(T1, big"-0.00160002507788042852683067347985080829550105638728462477214069614397009338180775134535418790113854904464693278677067195562013777079470430165035085043732753352") + T[2, 2] = convert(T1, big"-0.0381316481344115466944201512445271892551007922443248010648630183723114657457789198582213862424187595732944781586531399310738197517976083499508550510483478779") + T[2, 3] = convert(T1, big"-0.0215255605940068755238494349163503963236812065771639056145559371805737876208350036328339608215271680572576146954552666030277743869132676140541472724370558091") + T[2, 4] = convert(T1, big"0.00841556827655958923717700333156546206587781542530241328710392714333753219743181540077241302321588065650704924760060316717877095134935044662592211744890794666") + T[2, 5] = convert(T1, big"-0.00403194957022454949230429372587008587329606687054571010486662485715979240183165499902791387008699068626978608835015342675934092134962673636484308565473356683") + T[2, 6] = convert(T1, big"-6.6666353393963381817604789740257628821376819567901071737415235834331307484818353061850936507762955342131861918219584166678095273744210157164382779907235669e-05") + T[2, 7] = convert(T1, big"0.00318547482516620984874835878222687621122035448401205459368674257818574765593899794870819769668503869906022860261901897250913569265553156976061140932045107432") + T[3, 1] = convert(T1, big"0.00405910730194768309165024146216588597640781263680870767202041411242133338742562561902630276038676420444232405079851555753917806998064489819308813790494788924") + T[3, 2] = convert(T1, big"0.0573965089393817153975680203880753938458832782600090443030839643350468249623833638779578474891654213594195393636829414422184571666256857425091138479371917574") + T[3, 3] = convert(T1, big"0.0588505292084267910561208969865829735901655409220388105109199298038946675765714122525765330769443473927581930134049676200572930797370286476504623214740871248") + T[3, 4] = convert(T1, big"-0.00856043106160343206017727185390754992573940897343949944649743606465705403614377469754987858631901604547097801042861815249197647886051332362774581709381720893") + T[3, 5] = convert(T1, big"-0.00692321266502390892414068519049460069371592099748070119636478595631451405094203293036429762819458535062492059219566837532157551782305886338773933077463475632") + T[3, 6] = convert(T1, big"-0.00235218098294333834053519532555529491776729377182703234025085030409255592197086839142988525473684138901264206886166295186155491132922909402254443843846019141") + T[3, 7] = convert(T1, big"0.00041690777252975626914088803059940941342549922756308931704215701350026719541939053570614368159222367707113801117750298289694571643601584878405615892432648487") + T[4, 1] = convert(T1, big"0.0157504880793768442034586734054915501004520506405808322686493022779655453114657621318660532381583918124125360276320121127974912393389579826125529804830864399") + T[4, 2] = convert(T1, big"-0.0382146935969683504846411337659300127514788882892071252172987515109399372135899067290947441850340146027892665775682097051548343529370733593281856326317259999") + T[4, 3] = convert(T1, big"-0.165736811272943851241241116255535218556011122333381899790277357803281567727036568454939356458468926429537927937619042817050400333625919290585510785057955509") + T[4, 4] = convert(T1, big"-0.0373712423023844574190702119163246888117181457309185176497005310822879226235861373253125139016964433591381638592353617347369492240160809914228784174846477722") + T[4, 5] = convert(T1, big"0.00823900729850771940449868235563938395546999707236910359131464615707125576979409087864780171789078059526539789661318173387826643385244974406562622466790754233") + T[4, 6] = convert(T1, big"0.00311507115234617525272547086289315208054441921705361129575617631104650731644437585122142710666234276633544335552925569262424677362146587776195531866754755781") + T[4, 7] = convert(T1, big"0.025116604913438821928363823471446698278976101918753236732238210724710282378748917637317846485853317873304329580245705683618093593158791190832004186288367408") + T[5, 1] = convert(T1, big"0.112977661024220807608615842313106352633973778091080400075534257952348289641328709240673869677499013004285003126194992176632265223545565047727637631580337111") + T[5, 2] = convert(T1, big"-0.249174212465263686330825594009221950347570740813751325091913985975498424569678307894304962660904874986611526140914403971840496728150916599999921976188547708") + T[5, 3] = convert(T1, big"0.273563305798662321213236935135336593478278696397012151365678540099566245199777083242808233574654642014215983653810819494932091426330017240672955510133726276") + T[5, 4] = convert(T1, big"0.00536676137918177009427930181087914853701809128264121101773394730339300080525157052081366996826642003169044168721911822166683675089051631342776752635189343996") + T[5, 5] = convert(T1, big"0.193211116101262014431211225620266980060733605289133050251158448403922545905872373640500736693735926480983370235582910255756813799388364741420161359961401418") + T[5, 6] = convert(T1, big"0.101717732481715146808078931323995112561027763392448195424858681165964478003318758266672250034474900552688318026734856778296896546916272032434282368222825518") + T[5, 7] = convert(T1, big"0.0950450203560462282103892144485647895183175432965514336285840628832838918715022627077373617151475963061484489345238022187829573892306346658797861719620799413") + T[6, 1] = convert(T1, big"0.458381043183931501028085939964292092908293295595258886425372669820276128937720150467378912424378376379185138190017965370589550781979145790869568608776861466") + T[6, 2] = convert(T1, big"0.5315846490836284292050500994300107341125728347976407285397462896004659632807779347307732180848765709277026749725126234633983063167374333425454720010026876") + T[6, 3] = convert(T1, big"0.486322836617572894056685295353340203321316764127126557475136642083389075853199222650975554544550110757249234979120491845825690852575400863926535437662617201") + T[6, 4] = convert(T1, big"0.526574226458449262914091192639271913456008564881594253716678163127743947224108435833618497118891017505982561930788522171455486058320589875335702474378251931") + T[6, 5] = convert(T1, big"0.275534394989625814192875938762525038291639319966986287664787801569471609648366101593885546008609962622035890891754680149203464179471952105174480329668882489") + T[6, 6] = convert(T1, big"0.521751945274765285294609453181807034209434470364856664246194441011327338299794536726049398636575212016960129143954076748520870645966241492966592488607495009") + T[6, 7] = convert(T1, big"0.128071944635543894414114939510913357662538610722706228789484435811417614332529416514635125851744500940930818246509599119254761178392202724896572159336577251") + T[7, 1] = convert(T1, big"0.881391578353818376313498879127399181693003124999819194603124949551827789004545406999549226388170693806014968936224161749923163222614460424501073405017519348") + T[7, 2] = convert(T1, big"1.0") + T[7, 3] = convert(T1, big"0.0") + T[7, 4] = convert(T1, big"1.0") + T[7, 5] = convert(T1, big"0.0") + T[7, 6] = convert(T1, big"1.0") + T[7, 7] = convert(T1, big"0.0") BigRadauIIA13Tableau{T1, T2, Int}(T, TI, c, γ, α, β, 7) diff --git a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl index c5d69b7126..dde9d4b462 100644 --- a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl +++ b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl @@ -17,7 +17,7 @@ sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_2Dlinear, RadauIIA9()) prob_ode_linear_big = remake(prob_ode_linear, u0 = big.(prob_ode_linear.u0), tspan = big.(prob_ode_linear.tspan)) prob_ode_2Dlinear_big = remake(prob_ode_2Dlinear, u0 = big.(prob_ode_2Dlinear.u0), tspan = big.(prob_ode_2Dlinear.tspan)) -for i in [3, 5, 7, 9], prob in [prob_ode_linear, prob_ode_2Dlinear] +for i in [3, 5, 7, 9], prob in [prob_ode_linear_big, prob_ode_2Dlinear_big] sim21 = test_convergence(1 ./ 2 .^ (2.25:-1:0.25), prob, AdaptiveRadau(num_stages = i)) @test sim21.𝒪est[:final]≈ (2 * i - 1) atol=testTol end From 52613d3b60293797dac4ad3187bb191b77615546 Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Mon, 2 Sep 2024 16:25:49 -0400 Subject: [PATCH 55/71] clean up --- lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl | 392 ++++++++++---------- 1 file changed, 196 insertions(+), 196 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl index 290d7b3a4f..7cb82a9a58 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl @@ -123,38 +123,38 @@ struct BigRadauIIA5Tableau{T1, T2, Int} end function BigRadauIIA5Tableau(T1, T2, Int) - γ = convert(T1, big"3.63783425274449573220841851357777579794593608687391153215117488565841871456727143375130115708511223004183651123208497057248238260532214672028700625775335843") + γ = big"3.63783425274449573220841851357777579794593608687391153215117488565841871456727143375130115708511223004183651123208497057248238260532214672028700625775335843" α = Vector{T1}(undef, 1) β = Vector{T1}(undef, 1) - α[1] = convert(T1, big"2.68108287362775213389579074321111210102703195656304423392441255717079064271636428312434942145744388497908174438395751471375880869733892663985649687112332242") - β[1] = convert(T1, big"3.05043019924741056942637762478756790444070419917947659226291744751211727051786694870515117615266028855554735929171362769761399150862332538376382934625577549") + α[1] = big"2.68108287362775213389579074321111210102703195656304423392441255717079064271636428312434942145744388497908174438395751471375880869733892663985649687112332242" + β[1] = big"3.05043019924741056942637762478756790444070419917947659226291744751211727051786694870515117615266028855554735929171362769761399150862332538376382934625577549" c = Vector{T2}(undef, 3) - c[1] = convert(T2, big"0.155051025721682190180271592529410860803405251934332987156730743274903962254268497346014056689535976518140539877338581087514113454016224265837421604876272084") - c[2] = convert(T2, big"0.644948974278317809819728407470589139196594748065667012843269256725096037745731502653985943310464023481859460122661418912485886545983775734162578395123729143") - c[3] = convert(T2, big"1") + c[1] = big"0.155051025721682190180271592529410860803405251934332987156730743274903962254268497346014056689535976518140539877338581087514113454016224265837421604876272084" + c[2] = big"0.644948974278317809819728407470589139196594748065667012843269256725096037745731502653985943310464023481859460122661418912485886545983775734162578395123729143" + c[3] = big"1" TI = Matrix{T1}(undef, 3, 3) - TI[1, 1] = convert(T1, big"4.32557989006315535102435095295614882731995158490590784287320458848019483341979047442263696495019938973156007686663488090615420049217658854859024016717169837") - TI[1, 2] = convert(T1, big"0.339199251815809869542824974053410987511771566126056902312311333553438988409693737874718833892037643701271502187763370262948704203562215007824701228014200056") - TI[1, 3] = convert(T1, big"0.541770539935874871186523033492089631898841317849243944095021379289933921771713116368931784890546144473788347538203807242114936998948954098533375649163016612") - TI[2, 1] = convert(T1, big"-4.17871859155190472734646265851205623000038388214686525896709481539843195209360778128456932548583273459040707932166364293012713818843609182148794380267482041") - TI[2, 2] = convert(T1, big"-0.327682820761062387082533272429616234245791838308340887801415258608836530255609335712523838667242449344879454518796849992049787172023800373390124427898159896") - TI[2, 3] = convert(T1, big"0.476623554500550451960069084091012497939942928625055897109833707684876604712862299049343675491204859381277636585708398915065951363736337328178192801074535132") - TI[3, 1] = convert(T1, big"-0.502872634945786875951247343139544292859248429570937886791036339034110181540695221500843782634464164585836226038438397328726973424362168221527501738985822875") - TI[3, 2] = convert(T1, big"2.57192694985560542918678535360167505469448742842178326395573566888176471664393761903447163100353067504020263109067033226021288356347565113471227052083596358") - TI[3, 3] = convert(T1, big"-0.596039204828224924968821911099302403289857517521591823052174732952989090998130905722763344484798508456930766594977798579939415052669401095404149917833710127") + TI[1, 1] = big"4.32557989006315535102435095295614882731995158490590784287320458848019483341979047442263696495019938973156007686663488090615420049217658854859024016717169837" + TI[1, 2] = big"0.339199251815809869542824974053410987511771566126056902312311333553438988409693737874718833892037643701271502187763370262948704203562215007824701228014200056" + TI[1, 3] = big"0.541770539935874871186523033492089631898841317849243944095021379289933921771713116368931784890546144473788347538203807242114936998948954098533375649163016612" + TI[2, 1] = big"-4.17871859155190472734646265851205623000038388214686525896709481539843195209360778128456932548583273459040707932166364293012713818843609182148794380267482041" + TI[2, 2] = big"-0.327682820761062387082533272429616234245791838308340887801415258608836530255609335712523838667242449344879454518796849992049787172023800373390124427898159896" + TI[2, 3] = big"0.476623554500550451960069084091012497939942928625055897109833707684876604712862299049343675491204859381277636585708398915065951363736337328178192801074535132" + TI[3, 1] = big"-0.502872634945786875951247343139544292859248429570937886791036339034110181540695221500843782634464164585836226038438397328726973424362168221527501738985822875" + TI[3, 2] = big"2.57192694985560542918678535360167505469448742842178326395573566888176471664393761903447163100353067504020263109067033226021288356347565113471227052083596358" + TI[3, 3] = big"-0.596039204828224924968821911099302403289857517521591823052174732952989090998130905722763344484798508456930766594977798579939415052669401095404149917833710127" T = Matrix{T1}(undef, 3, 3) - T[1, 1] = convert(T1, big"0.091232394870892942791548135249436196118684699372210280712184363514099824021240149574725365814781580305065489937969163922775110463056339192206701819661425186") - T[1, 2] = convert(T1, big"-0.141255295020954208427990383807797309409263248498594798844289981408804297900674604638610419147468875667691398225003133444988034605081071965848437945842767211") - T[1 ,3] = convert(T1, big"-0.0300291941051474244918611170890538666683842974606300802563717702200388818691214144173874588956764952224874407424115249418136547481236684478531215095064078994") - T[2, 1] = convert(T1, big"0.241717932707107018957474779310148232884879540532595279746187345714229132659465207414913313803429072060469564350914390845001169448350326344874859416624577348") - T[2, 2] = convert(T1, big"0.204129352293799931995990810298338174086540402523315938937516234649384944528706774788799548853122282827246947911905379230680096946800308693162079538975632443") - T[2, 3] = convert(T1, big"0.382942112757261937795438233599873210357792575012007744255205163027042915338009760005422153613194350161760232119048691964499888989151661861236831969497483828") - T[3, 1] = convert(T1, big"0.966048182615092936190567080794590794996748754810883844283183333914131408744555961195911605614405476210484499875001737558078500322423463946527349731087504518") - T[3, 2] = convert(T1, big"1.0") - T[3, 3] = convert(T1, big"0.0") + T[1, 1] = big"0.091232394870892942791548135249436196118684699372210280712184363514099824021240149574725365814781580305065489937969163922775110463056339192206701819661425186" + T[1, 2] = big"-0.141255295020954208427990383807797309409263248498594798844289981408804297900674604638610419147468875667691398225003133444988034605081071965848437945842767211" + T[1 ,3] = big"-0.0300291941051474244918611170890538666683842974606300802563717702200388818691214144173874588956764952224874407424115249418136547481236684478531215095064078994" + T[2, 1] = big"0.241717932707107018957474779310148232884879540532595279746187345714229132659465207414913313803429072060469564350914390845001169448350326344874859416624577348" + T[2, 2] = big"0.204129352293799931995990810298338174086540402523315938937516234649384944528706774788799548853122282827246947911905379230680096946800308693162079538975632443" + T[2, 3] = big"0.382942112757261937795438233599873210357792575012007744255205163027042915338009760005422153613194350161760232119048691964499888989151661861236831969497483828" + T[3, 1] = big"0.966048182615092936190567080794590794996748754810883844283183333914131408744555961195911605614405476210484499875001737558078500322423463946527349731087504518" + T[3, 2] = big"1.0" + T[3, 3] = big"0.0" BigRadauIIA5Tableau{T1, T2, Int}(T, TI, c, γ, α, β, 3) end @@ -171,74 +171,74 @@ struct BigRadauIIA9Tableau{T1, T2, Int} end function BigRadauIIA9Tableau(T1, T2, Int) - γ = convert(T1, big"6.28670475172927664517315334186940904959068186655567041187229167532923622489525703260842273089261139845280626287956099768662193453067483410165932355981736786") + γ = big"6.28670475172927664517315334186940904959068186655567041187229167532923622489525703260842273089261139845280626287956099768662193453067483410165932355981736786" α = Vector{T1}(undef, 2) β = Vector{T1}(undef, 2) - α[1] = convert(T1, big"3.65569432546357225824320796009543385435699888857815445045567025741630720509235614026228963385258117304229337679733945535812317372403535763551850772878775217") - α[2] = convert(T1, big"5.70095329867178941917021536896986162084766017814401034360818390491907468246001534343349900070111312773130349176288004579856585901062722531365183049130382405") - β[1] = convert(T1, big"6.5437368993600772940210715093936863183637851728134458820202187133882261290012752452972782843700946890488789462524897903624959996932392239962196563965573345") - β[2] = convert(T1, big"3.21026560030854988842501065297211721232153653493981008029923647488964744732168461657389754087826565709085773529539707072244537983491480773006949966789260925") + α[1] = big"3.65569432546357225824320796009543385435699888857815445045567025741630720509235614026228963385258117304229337679733945535812317372403535763551850772878775217" + α[2] = big"5.70095329867178941917021536896986162084766017814401034360818390491907468246001534343349900070111312773130349176288004579856585901062722531365183049130382405" + β[1] = big"6.5437368993600772940210715093936863183637851728134458820202187133882261290012752452972782843700946890488789462524897903624959996932392239962196563965573345" + β[2] = big"3.21026560030854988842501065297211721232153653493981008029923647488964744732168461657389754087826565709085773529539707072244537983491480773006949966789260925" c = Vector{T2}(undef, 5) - c[1] = convert(T2, big"0.0571041961145176821931211925541156212350779455987501643278082929309346782020731645861138168198427368635148018903413155731609901559772929443100370500757072557") - c[2] = convert(T2, big"0.276843013638123827680045997685625141110889169695030468349442048831121339683708036772541528564051130879197377136636984534220758899839905855114024309075271826") - c[3] = convert(T2, big"0.583590432368916820056697668662917248693432639896771640176293841831747501961831012005632277467456299345321045569611992496682381919275766424103024358378365496") - c[4] = convert(T2, big"0.8602401356562194478479129188751197667383780225872255049242335941839742579301655644134901549264276106897445531811874851737136468026848125542506920602484255") - c[5] = convert(T2, big"1.0") + c[1] = big"0.0571041961145176821931211925541156212350779455987501643278082929309346782020731645861138168198427368635148018903413155731609901559772929443100370500757072557" + c[2] = big"0.276843013638123827680045997685625141110889169695030468349442048831121339683708036772541528564051130879197377136636984534220758899839905855114024309075271826" + c[3] = big"0.583590432368916820056697668662917248693432639896771640176293841831747501961831012005632277467456299345321045569611992496682381919275766424103024358378365496" + c[4] = big"0.8602401356562194478479129188751197667383780225872255049242335941839742579301655644134901549264276106897445531811874851737136468026848125542506920602484255" + c[5] = big"1.0" TI = Matrix{T1}(undef, 5, 5) - TI[1, 1] = convert(T1, big"30.0415677215444016277146611632467970747634862837368422955138470463852339244593400023985957753164599415374157317627305099177616927640413043608408838747985125") - TI[1, 2] = convert(T1, big"13.8651078562714131651762946846279728486098595017962436746405940971751244384714668104145151259298432908422191238542910724677205181071665482818120092330632702") - TI[1 ,3] = convert(T1, big"3.48000277479518556182840016971955819123081637245954095062693470191383865922357339844125383481645392882289968250993872221445874555610460465838129969397069557") - TI[1, 4] = convert(T1, big"-1.03200879782526342277108071214631493513824682491749273908106331923801396656058254294323988505859654767877050109789490714699847664805679842903430004696170252") - TI[1, 5] = convert(T1, big"0.804303045073989917475330383606196086089578671788707543063308602519859970319818304759856653218877415405946945572102875643297890954688508528143272905631829894") - TI[2, 1] = convert(T1, big"5.34418643783491159889531030409736033885455686563071401172022718575590068536629704134603404624953791012861634674294690788961703408019660066685859393456498931") - TI[2, 2] = convert(T1, big"4.59361556775916100445407449817656238428260055301676371438973411021009514435572975394999086474831271997070798032181411537895658457000537727156665947774751386") - TI[2, 3] = convert(T1, big"-3.03636032345942429864615756872018980250277648141683630832856906288036929718223473102394179699607901856890769270810252103326382063852039607285826867723587514") - TI[2, 4] = convert(T1, big"1.05066019023145886385983615715299311307615150447133905233370933194949591737765763708886464382722316727972166443876395823044171403663404254906698768838255919") - TI[2, 5] = convert(T1, big"-0.272778611864296270538614649997366804891835224042737605275699398413256470423268908248569612750117948720141667949532252500428432062582365619208502333677907158") - TI[3, 1] = convert(T1, big"3.74805980743980486005103450189256983678052751095791526209741655305580351377124372457009580386663275146166007984852101733055495783906881063060757645038080343") - TI[3, 2] = convert(T1, big"-3.98496573634388466725226385805351110838575115293851360514636734529255361185420464416807882769853298186283398369873418552760618971047757002216338511286260041") - TI[3, 3] = convert(T1, big"-1.04441564160801879294224732309562532189841624726401645191058551173485917137499204844819781779667611903670073971659834929382224472890100209497741235960707456") - TI[3, 4] = convert(T1, big"1.18409856813794848723102038838340482030291345603197522521517834943166421242518751666675199211369552058487095283489346390066317584532997854692445653563909898") - TI[3, 5] = convert(T1, big"-0.449917770156780368898811918314095435942113881883174152777026977062686286863549565130412864190301081537983106397709991028107600781961279985605930655683680139") - TI[4, 1] = convert(T1, big"-33.0418802135190000080614469426109507742858088371383868670878639187564531424382858814386742148456699143328462132296293097447566408853495288807407929988004676") - TI[4, 2] = convert(T1, big"-17.3769534790635670194549806058987105852733409102703844354448800193942184746909147697382687117638715195698950138089979798321855885541817752366521518811413713") - TI[4, 3] = convert(T1, big"-0.172129063254005561151528806427751383749451500597823574207174433146207178559871803504021077429693091164540897873472803934375603405253541639437370184767553293") - TI[4, 4] = convert(T1, big"-0.0991697779825426425881662214017368584726354746776989845479783944003623924121748016326495070834800297497011104846871751430208559227945252758721362340763610828") - TI[4, 5] = convert(T1, big"0.531228115838306667184911422606024795426589562580669892779793097035561488973256023529352389498509937781553683467106048413485632583844632286562240161995145055") - TI[5, 1] = convert(T1, big"-8.61144397987529197770008251257034851950485933115010902789613925540488896812417081206983938638600226846804467531843522104806738090683710882069500386691775154") - TI[5, 2] = convert(T1, big"9.69999140952880823133589405342003266497120753048627084327055311528684684237122654108691149692242002085965723391934376924400492239317026460192827344970015484") - TI[5, 3] = convert(T1, big"1.91472863969687428485137560339172471528025297511003983469957355306260543484472462223194401768126877615795915146192537091374017807611943419264038682143890747") - TI[5, 4] = convert(T1, big"2.41869200608494002642656343408298350771199306961305597858229870375990977712805399625496435641846363295393762353024017195444763964531237381728801981679934304") - TI[5, 5] = convert(T1, big"-1.0474634879353374186944329992117360176590042540536055452919974336199826846201614544718272622833822842591012529895091659029452542118642301415759073410771819") + TI[1, 1] = big"30.0415677215444016277146611632467970747634862837368422955138470463852339244593400023985957753164599415374157317627305099177616927640413043608408838747985125" + TI[1, 2] = big"13.8651078562714131651762946846279728486098595017962436746405940971751244384714668104145151259298432908422191238542910724677205181071665482818120092330632702" + TI[1 ,3] = big"3.48000277479518556182840016971955819123081637245954095062693470191383865922357339844125383481645392882289968250993872221445874555610460465838129969397069557" + TI[1, 4] = big"-1.03200879782526342277108071214631493513824682491749273908106331923801396656058254294323988505859654767877050109789490714699847664805679842903430004696170252" + TI[1, 5] = big"0.804303045073989917475330383606196086089578671788707543063308602519859970319818304759856653218877415405946945572102875643297890954688508528143272905631829894" + TI[2, 1] = big"5.34418643783491159889531030409736033885455686563071401172022718575590068536629704134603404624953791012861634674294690788961703408019660066685859393456498931" + TI[2, 2] = big"4.59361556775916100445407449817656238428260055301676371438973411021009514435572975394999086474831271997070798032181411537895658457000537727156665947774751386" + TI[2, 3] = big"-3.03636032345942429864615756872018980250277648141683630832856906288036929718223473102394179699607901856890769270810252103326382063852039607285826867723587514" + TI[2, 4] = big"1.05066019023145886385983615715299311307615150447133905233370933194949591737765763708886464382722316727972166443876395823044171403663404254906698768838255919" + TI[2, 5] = big"-0.272778611864296270538614649997366804891835224042737605275699398413256470423268908248569612750117948720141667949532252500428432062582365619208502333677907158" + TI[3, 1] = big"3.74805980743980486005103450189256983678052751095791526209741655305580351377124372457009580386663275146166007984852101733055495783906881063060757645038080343" + TI[3, 2] = big"-3.98496573634388466725226385805351110838575115293851360514636734529255361185420464416807882769853298186283398369873418552760618971047757002216338511286260041" + TI[3, 3] = big"-1.04441564160801879294224732309562532189841624726401645191058551173485917137499204844819781779667611903670073971659834929382224472890100209497741235960707456" + TI[3, 4] = big"1.18409856813794848723102038838340482030291345603197522521517834943166421242518751666675199211369552058487095283489346390066317584532997854692445653563909898" + TI[3, 5] = big"-0.449917770156780368898811918314095435942113881883174152777026977062686286863549565130412864190301081537983106397709991028107600781961279985605930655683680139" + TI[4, 1] = big"-33.0418802135190000080614469426109507742858088371383868670878639187564531424382858814386742148456699143328462132296293097447566408853495288807407929988004676" + TI[4, 2] = big"-17.3769534790635670194549806058987105852733409102703844354448800193942184746909147697382687117638715195698950138089979798321855885541817752366521518811413713" + TI[4, 3] = big"-0.172129063254005561151528806427751383749451500597823574207174433146207178559871803504021077429693091164540897873472803934375603405253541639437370184767553293" + TI[4, 4] = big"-0.0991697779825426425881662214017368584726354746776989845479783944003623924121748016326495070834800297497011104846871751430208559227945252758721362340763610828" + TI[4, 5] = big"0.531228115838306667184911422606024795426589562580669892779793097035561488973256023529352389498509937781553683467106048413485632583844632286562240161995145055" + TI[5, 1] = big"-8.61144397987529197770008251257034851950485933115010902789613925540488896812417081206983938638600226846804467531843522104806738090683710882069500386691775154" + TI[5, 2] = big"9.69999140952880823133589405342003266497120753048627084327055311528684684237122654108691149692242002085965723391934376924400492239317026460192827344970015484" + TI[5, 3] = big"1.91472863969687428485137560339172471528025297511003983469957355306260543484472462223194401768126877615795915146192537091374017807611943419264038682143890747" + TI[5, 4] = big"2.41869200608494002642656343408298350771199306961305597858229870375990977712805399625496435641846363295393762353024017195444763964531237381728801981679934304" + TI[5, 5] = big"-1.0474634879353374186944329992117360176590042540536055452919974336199826846201614544718272622833822842591012529895091659029452542118642301415759073410771819" T = Matrix{T1}(undef, 5, 5) - T[1, 1] = convert(T1, big"0.0125175862205010458901356760368001462557655123420858705973577952199246108029451084239310924615007306721702298573083400752464277227557045438770401832498107968") - T[1, 2] = convert(T1, big"-0.0102420478179088270700863300668590125015813934827825923708366359399562125950804289592272678367034071306578383319296130180550178248531589487456925441921649293") - T[1 ,3] = convert(T1, big"0.0476738772902957238631839478592069782970238490568258436986723993118380988311441474394156362952631834786373081794857384127209450988829840886524135970873769918") - T[1, 4] = convert(T1, big"-0.0114785152552295147079415554121555049385506204591245712490409384029671974157542450636658532835395855844059342442518520033304129991000509527123870917346017759") - T[1, 5] = convert(T1, big"-0.0140198588928754102810778942934959307831026572823203692568448424056201483917805257790275956734469193171917730378117501915144713896813544630288006687542182225") - T[2, 1] = convert(T1, big"0.00149167015189538242900444775236282223594625052328927847572623038484966999313257893341818287477809424303168766872838075463220122499449382436194198620498144296") - T[2, 2] = convert(T1, big"0.050172864517371058162991380262646513853120568882725793734131676894272706020317186004736779675826101816279321643304301437029912742375638648226701787880031719") - T[2, 3] = convert(T1, big"-0.0943318191816114369806569003363724471884924328367212069321438749304281980331334016578193750445513659941246363262225907407726099492713722343006925656625258579") - T[2, 4] = convert(T1, big"-0.00766883074918016288515687679203608074116106558796378201472238095295554979920808799930579174190884587422912077296093093698836937450535804218413704866981728518") - T[2, 5] = convert(T1, big"0.024708578426518526812525205377780382655366504554979744093019395818934704623702078004474076773426928900579988063099593288435684744957695210778788200213260272") - T[3, 1] = convert(T1, big"0.072981876388087148622657299703669587832652508881663282287850495621401398441897288250625556038835308015912409648841893161563884759791665776933761278383553608") - T[3, 2] = convert(T1, big"-0.230539534043417946721421862180000422679228296568599014834226319726930529322581417981617275287468418138394077987361681288909676234537699721082090802790143303") - T[3, 3] = convert(T1, big"0.102703045380125899792210456947141185148813233939327773583525878521508211077874610560448598369259541346968946573971195783374996178436435357335759255990489434") - T[3, 4] = convert(T1, big"0.0193984639988289509112232896408330872285824216708905773930244363652651247181543158008567311548336143384128605013911312875018664026371225431993252265128272262") - T[3, 5] = convert(T1, big"0.0818003537037511708363908122287572533071340646031113975848869261019231448226334426630664318901554550460201409321555775999869184033436795623062614812355590017") - T[4, 1] = convert(T1, big"0.380091440003568104126439184355215575526619121262253024859378518379910007234696730891540745160675744992320824590679292148769326540463161583672773762554445506") - T[4, 2] = convert(T1, big"0.377893902248861249543862293745933995234687511602719536459666284734445918178134851270924212812363352965391508894581698067329905034837778770261095647458874628") - T[4, 3] = convert(T1, big"0.466744130332494359289559582964906703283968612669234331018678042733321473730897217606173184300477207393539851157929838664168404778962779344509707214938022808") - T[4, 4] = convert(T1, big"0.40760117128019906662166237021895987274626181127101561893104166874567447589187790736078997321464949349935802836110699884016973990503134772720646054039223561") - T[4, 5] = convert(T1, big"0.199682427886802525936540566022390695167018315867216115995143539347975271751460199398235415129329119718414206048034051939441434136353381864781262773401023899") - T[5, 1] = convert(T1, big"0.921978973681210488488254647415676321266345412943047462855852351388222898143904205962703147998267738964059170225806964893009202287585991334322032058414768529") - T[5, 2] = convert(T1, big"1.0") - T[5, 3] = convert(T1, big"0.0") - T[5, 4] = convert(T1, big"1.0") - T[5, 5] = convert(T1, big"0.0") + T[1, 1] = big"0.0125175862205010458901356760368001462557655123420858705973577952199246108029451084239310924615007306721702298573083400752464277227557045438770401832498107968" + T[1, 2] = big"-0.0102420478179088270700863300668590125015813934827825923708366359399562125950804289592272678367034071306578383319296130180550178248531589487456925441921649293" + T[1 ,3] = big"0.0476738772902957238631839478592069782970238490568258436986723993118380988311441474394156362952631834786373081794857384127209450988829840886524135970873769918" + T[1, 4] = big"-0.0114785152552295147079415554121555049385506204591245712490409384029671974157542450636658532835395855844059342442518520033304129991000509527123870917346017759" + T[1, 5] = big"-0.0140198588928754102810778942934959307831026572823203692568448424056201483917805257790275956734469193171917730378117501915144713896813544630288006687542182225" + T[2, 1] = big"0.00149167015189538242900444775236282223594625052328927847572623038484966999313257893341818287477809424303168766872838075463220122499449382436194198620498144296" + T[2, 2] = big"0.050172864517371058162991380262646513853120568882725793734131676894272706020317186004736779675826101816279321643304301437029912742375638648226701787880031719" + T[2, 3] = big"-0.0943318191816114369806569003363724471884924328367212069321438749304281980331334016578193750445513659941246363262225907407726099492713722343006925656625258579" + T[2, 4] = big"-0.00766883074918016288515687679203608074116106558796378201472238095295554979920808799930579174190884587422912077296093093698836937450535804218413704866981728518" + T[2, 5] = big"0.024708578426518526812525205377780382655366504554979744093019395818934704623702078004474076773426928900579988063099593288435684744957695210778788200213260272" + T[3, 1] = big"0.072981876388087148622657299703669587832652508881663282287850495621401398441897288250625556038835308015912409648841893161563884759791665776933761278383553608" + T[3, 2] = big"-0.230539534043417946721421862180000422679228296568599014834226319726930529322581417981617275287468418138394077987361681288909676234537699721082090802790143303" + T[3, 3] = big"0.102703045380125899792210456947141185148813233939327773583525878521508211077874610560448598369259541346968946573971195783374996178436435357335759255990489434" + T[3, 4] = big"0.0193984639988289509112232896408330872285824216708905773930244363652651247181543158008567311548336143384128605013911312875018664026371225431993252265128272262" + T[3, 5] = big"0.0818003537037511708363908122287572533071340646031113975848869261019231448226334426630664318901554550460201409321555775999869184033436795623062614812355590017" + T[4, 1] = big"0.380091440003568104126439184355215575526619121262253024859378518379910007234696730891540745160675744992320824590679292148769326540463161583672773762554445506" + T[4, 2] = big"0.377893902248861249543862293745933995234687511602719536459666284734445918178134851270924212812363352965391508894581698067329905034837778770261095647458874628" + T[4, 3] = big"0.466744130332494359289559582964906703283968612669234331018678042733321473730897217606173184300477207393539851157929838664168404778962779344509707214938022808" + T[4, 4] = big"0.40760117128019906662166237021895987274626181127101561893104166874567447589187790736078997321464949349935802836110699884016973990503134772720646054039223561" + T[4, 5] = big"0.199682427886802525936540566022390695167018315867216115995143539347975271751460199398235415129329119718414206048034051939441434136353381864781262773401023899" + T[5, 1] = big"0.921978973681210488488254647415676321266345412943047462855852351388222898143904205962703147998267738964059170225806964893009202287585991334322032058414768529" + T[5, 2] = big"1.0" + T[5, 3] = big"0.0" + T[5, 4] = big"1.0" + T[5, 5] = big"0.0" BigRadauIIA9Tableau{T1, T2, Int}(T, TI, c, γ, α, β, 5) @@ -405,126 +405,126 @@ struct BigRadauIIA13Tableau{T1, T2, Int} end function BigRadauIIA13Tableau(T1, T2, Int) - γ = convert(T1, big"8.93683278840521633730209691330107970355008194433956657198414191417624969654351559268800871286734194720118970058657997472527299153742511021973612156231867783") + γ = big"8.93683278840521633730209691330107970355008194433956657198414191417624969654351559268800871286734194720118970058657997472527299153742511021973612156231867783" α = Vector{T1}(undef, 3) β = Vector{T1}(undef, 3) - α[1] = convert(T1, big"4.37869356150680600252334919268856129165763746518197948235657247177701087073069907016715245914093899486193202405685779803686971216417800783050995450529391908") - α[2] = convert(T1, big"7.14105521918764010577498142571556804318193862372238812855726792587872300446315860222917039505087745633962330233504078264632719519730762016919715839787116038") - α[3] = convert(T1, big"8.51183482510294572305062092494533081338538293892584910309408864525614127653438453125967278937451257519784982331481143195416659686980181689042482631568989031") - β[1] = convert(T1, big"10.1696932837950116273183544188477298930096536824510223588525334625762336174947183926243705927725260475934351162622185429326813205432867247703480391692806137") - β[2] = convert(T1, big"6.62304592263927597062055811591186110468148199066707542227575094761515104946479159063603447729283770429494038962408904312215452856333028405675512985803584472") - β[3] = convert(T1, big"3.2810136243250588300359425270393915846791621918405321383787427650552081712406957205287551182809705166989352673500472974040971593568323836675590314648604458") + α[1] = big"4.37869356150680600252334919268856129165763746518197948235657247177701087073069907016715245914093899486193202405685779803686971216417800783050995450529391908" + α[2] = big"7.14105521918764010577498142571556804318193862372238812855726792587872300446315860222917039505087745633962330233504078264632719519730762016919715839787116038" + α[3] = big"8.51183482510294572305062092494533081338538293892584910309408864525614127653438453125967278937451257519784982331481143195416659686980181689042482631568989031" + β[1] = big"10.1696932837950116273183544188477298930096536824510223588525334625762336174947183926243705927725260475934351162622185429326813205432867247703480391692806137" + β[2] = big"6.62304592263927597062055811591186110468148199066707542227575094761515104946479159063603447729283770429494038962408904312215452856333028405675512985803584472" + β[3] = big"3.2810136243250588300359425270393915846791621918405321383787427650552081712406957205287551182809705166989352673500472974040971593568323836675590314648604458" c = Vector{T2}(undef, 7) - c[1] = convert(T2, big"0.0293164271597848919720502769131649103737303925637149277869106839449360382416657787486309483651843695097273923248526200112627747993405898353736305552306269904") - c[2] = convert(T2, big"0.148078599668484291849976852495979212230248774808594461412594641801598386090878321806369397661747576057906341132861865305306667654594593138746653233717241913") - c[3] = convert(T2, big"0.336984690281154299097052972080775705197568750028473347122562968073691350512784060852409141173654482529393236826516171319486086447256539582972346127980810124") - c[4] = convert(T2, big"0.558671518771550132081393341805521940074368288965407825555747226117350122897421078323820052012282581935200398463518265914564420109615277886000739200777932339") - c[5] = convert(T2, big"0.769233862030054500916883360115645451837142143322295416166948169636548130573953285685200211542774367652885154701431860087378103033801830280742146083476036669") - c[6] = convert(T2, big"0.926945671319741114851873965819682011056172419542283252724467079656645202452528243814339480013587391545656707320049986592771178724621938506933715568048004783") - c[7] = convert(T2, big"1.0") + c[1] = big"0.0293164271597848919720502769131649103737303925637149277869106839449360382416657787486309483651843695097273923248526200112627747993405898353736305552306269904" + c[2] = big"0.148078599668484291849976852495979212230248774808594461412594641801598386090878321806369397661747576057906341132861865305306667654594593138746653233717241913" + c[3] = big"0.336984690281154299097052972080775705197568750028473347122562968073691350512784060852409141173654482529393236826516171319486086447256539582972346127980810124" + c[4] = big"0.558671518771550132081393341805521940074368288965407825555747226117350122897421078323820052012282581935200398463518265914564420109615277886000739200777932339" + c[5] = big"0.769233862030054500916883360115645451837142143322295416166948169636548130573953285685200211542774367652885154701431860087378103033801830280742146083476036669" + c[6] = big"0.926945671319741114851873965819682011056172419542283252724467079656645202452528243814339480013587391545656707320049986592771178724621938506933715568048004783" + c[7] = big"1.0" TI = Matrix{T1}(undef, 7, 7) - TI[1, 1] = convert(T1, big"258.131926319982229276108947425184471333411128774462923076434633414645220927977539758484670571338176678808837829326061674950321562391576244286310404028770676") - TI[1, 2] = convert(T1, big"189.073763081398508951976143411165126555759459745371576264125287430947886413126866952443113984840310549596923934762141954737541643761162558070450614795561734") - TI[1, 3] = convert(T1, big"49.0873148179301311944474703372633419330229683717897887664283914712555334645741343066714059043135343948204451450061803442374878045458955826422757210762412997") - TI[1, 4] = convert(T1, big"4.11064746966142841811238518636124668078589358089581133578005291508858571621836624121708112101643343488669794287298806656198949715476379639435093560435010553") - TI[1, 5] = convert(T1, big"4.05344788931556330417512803837862541661144275947069236866476426664242632965376171604053865483440478823853326237912519148507906655855071507442222711969825069") - TI[1, 6] = convert(T1, big"-3.11275536660734607655357698925636361735741304308245452106573904595716690770542970584435712650159533448326091358879097717388530116398450168049097806992817596") - TI[1, 7] = convert(T1, big"1.64677491355844465016894934800942442334612077828885771793164268655566366462165061862443368822544695623147966149765223644798045399342853834086413561960176148") - TI[2, 1] = convert(T1, big"-3.00739016945129213173149353792169083141834116044470099212013728771587881480191343754504173052952073006187734389002396348355357273701343509199048972794392147") - TI[2, 2] = convert(T1, big"-11.0158660787657713291120393664792067595453921824881213620299497076376976067619617086470844707815815293102862568459526162951253770377715406520772358338647188") - TI[2, 3] = convert(T1, big"1.48779945613165628148618248664965038886474377325027865838645297753993182317594482435706956176392903188004580583104018591540474622009639200188521283880201225") - TI[2, 4] = convert(T1, big"2.13038815955928245943197208332824475219642634294808813866153957342980992047877237670079423767538654092424134276380826377135080667266661637001176204430488753") - TI[2, 5] = convert(T1, big"-1.81614108681756562482220455159496741723359999245934818387747079566312917815672128128449281415737713177900591942282975861961228230314168417307836619006791605") - TI[2, 6] = convert(T1, big"1.13432558789516110008277908420532415765361628740656810686297793967986689714948610119162966211301325316623863222505219543867472186257492829970663316956377323") - TI[2, 7] = convert(T1, big"-0.414699045943303531993049422295928526684402022493736427543557958358387925728160703636844863663828153394608981043415378230601486738224597324364079320598162815") - TI[3, 1] = convert(T1, big"-8.44196318832108468175691559413731210343158392484322786670758421404507417209484447031645790366021837365786640573614305718894911853549168061902141351516580451") - TI[3, 2] = convert(T1, big"-0.650525274057515002816904045893485631294530894981669254094573985727348985809697093879080285963063573837365484483755274668080611163704039179328960851461387071") - TI[3, 3] = convert(T1, big"6.94067073036987647880408175445008301222030789462375109942012235845495260572570799226646472429196555932436186979400567616504159564738984233922289782922787445") - TI[3, 4] = convert(T1, big"-3.20504752559789843156502799159713971965747774043426947358779973217345866996463287674334224123932879873323284636947452187683408110992957222808611161423213549") - TI[3, 5] = convert(T1, big"1.07128094354647858978279562700457911254627057919002861801894953308482120936700881726232902304000322718645130593907512149815870969208873216470962770569998532") - TI[3, 6] = convert(T1, big"-0.354850749121622187972972761073874956531274189535504546398851680169235702590362534883357256681588685608802983372517893712333972644320006895019178184808028042") - TI[3, 7] = convert(T1, big"0.0919854913278655415440864884207305663999562250023079120516746551750254082665966708567906888946992351083964961208132558221142585217674963218388224937302473142") - TI[4, 1] = convert(T1, big"74.6783322350226997715286176267232500441551583987525066913719852490109364599462546293112601362342028584101507709386240000804692470037564789980905370400509214") - TI[4, 2] = convert(T1, big"87.4085889799008164020396362924136436577534600993283836959398121813667403209890699914314446222016952621954817633686823685774595935180374571416781238038364186") - TI[4, 3] = convert(T1, big"4.02415873737999787701407840793921059156554118449220356776918749072220128918152906578385457943212213189933447495921754693186811343717296680238755923076427455") - TI[4, 4] = convert(T1, big"-3.7148063151583641866387382381081795406061842159003055897302686185198568522128509989890869602984467843559169959313018612449354703104270603001605170037725663") - TI[4, 5] = convert(T1, big"-3.43009398598231735074090769130593476067104938465255451803266927011738721835297930406017172365070584279715308905584391225176154776278518922912169890517961929") - TI[4, 6] = convert(T1, big"2.69660480976531237885262500230842013033719691844775548640355919138284680959979836353143310081338215041119022648809147361433752919265159399610746756470853959") - TI[4, 7] = convert(T1, big"-0.938692743607546193356785681771531136814109179879957291315724533839534255667763099330792864148293396694586387338161584706252944483821135344465739888811338788") - TI[5, 1] = convert(T1, big"58.3565288519065772423731088606544342599129168115273649928818622008651860145833895668543250775742899696760389837877193028417145182338484929599333810581515993") - TI[5, 2] = convert(T1, big"-10.0687739578001809632495544545749228539542767485211306078205622876595603032162891608453826862136355989387474454697691529766293644115682409173741730758425432") - TI[5, 3] = convert(T1, big"-30.3663888425666712081087189214021522992426235463582449811325590575576319489955157279473313224901192335775884848736150180108985558310423628914140477437063457") - TI[5, 4] = convert(T1, big"-1.02002086518486598502718784312141857841892430616701325398305811243769008274372077411348691412296276168896198187688441456921700292037247387330560786140723416") - TI[5, 5] = convert(T1, big"-0.112417500378424962126670249921897816128157398591725875330925039631874967429838848482089690872916638698820411392685501889126627650123714184027159547685248056") - TI[5, 6] = convert(T1, big"1.89064083100037762279966919417932484200269828564004442737723486475878958135985745266991261770924069476112679285337233931312540904735632744873728510014970829") - TI[5, 7] = convert(T1, big"-0.971648639383148228217233127548943147296423534674266405843322723719694664032217172325052282800290275002731997713145411340983758516166807609661717915219518127") - TI[6, 1] = convert(T1, big"-299.18624802825209667863642523944728107942141534516550178278869311293354511449399684666660494133688445719285752471650937062695632169114367079856135650539072") - TI[6, 2] = convert(T1, big"-243.040745368744791181900565230083092669143049316165122405971394775932180012728275256467636352341415340547177922968547123544546515287229215470481168446631934") - TI[6, 3] = convert(T1, big"-48.7771040780378692121909344887388032694629956594617430615510915251995189158287187599892740037773277403958100797917560590738598108409472582147091119440886778") - TI[6, 4] = convert(T1, big"-2.03867190574193440528015205293433905622043272233073734690244789947707827347049413187234402189062846366658963666461334786306660732097114011309282331323116958") - TI[6, 5] = convert(T1, big"1.67356023986108494426829042309213202110891938292923077616474877079402040904687073610625868939896244842053999572446723558562427506280564629528151134946587118") - TI[6, 6] = convert(T1, big"-1.0873740320571061644555969255032311107358443063278089996181949045168433801494845898897631535619158410753032807069032950523487601457868753453652745002841107") - TI[6, 7] = convert(T1, big"0.901938249296099373842715514839004052963355800714627971724094542443991299921284427589690820402982448873149676210397055957126153220340909284180014056386791594") - TI[7, 1] = convert(T1, big"-93.076502897435305911571945263737383854569504715670989865831914555937966339933932282945955570244055882294556430466422133231853008314991630740535709028417842") - TI[7, 2] = convert(T1, big"23.8816310562811442770319002318043863376962876994405756649585750650966186536576789769674007990310112890015051984278059899811178135726914390958188405071290871") - TI[7, 3] = convert(T1, big"39.2788807308138438271015646136760366834412493325456249795727722130258444051594274416196392795817449902122139076648927894476044063388859377757097127385794539") - TI[7, 4] = convert(T1, big"14.3889156854910800698761307424979534708984169042483973564042387223013868069040933228077604321320066763752720714195604903398768371784013771964086553618150626") - TI[7, 5] = convert(T1, big"-3.51043839939936122108708432480845734972162782563284715495715984978907792386567906732993553255070093796782368160341757151292477304975079070782335737053297468") - TI[7, 6] = convert(T1, big"4.86328488556618070121491058699734313503568312572977577331134555924656926935558698308076704662503608259898740028814153544991114426972747448736702277116049277") - TI[7, 7] = convert(T1, big"-2.24648272959123991640046924839711232278867381637608763335081676684616443569602032178385937243819174902544136208243971053224668691848283004752869023074006745") + TI[1, 1] = big"258.131926319982229276108947425184471333411128774462923076434633414645220927977539758484670571338176678808837829326061674950321562391576244286310404028770676" + TI[1, 2] = big"189.073763081398508951976143411165126555759459745371576264125287430947886413126866952443113984840310549596923934762141954737541643761162558070450614795561734" + TI[1, 3] = big"49.0873148179301311944474703372633419330229683717897887664283914712555334645741343066714059043135343948204451450061803442374878045458955826422757210762412997" + TI[1, 4] = big"4.11064746966142841811238518636124668078589358089581133578005291508858571621836624121708112101643343488669794287298806656198949715476379639435093560435010553" + TI[1, 5] = big"4.05344788931556330417512803837862541661144275947069236866476426664242632965376171604053865483440478823853326237912519148507906655855071507442222711969825069" + TI[1, 6] = big"-3.11275536660734607655357698925636361735741304308245452106573904595716690770542970584435712650159533448326091358879097717388530116398450168049097806992817596" + TI[1, 7] = big"1.64677491355844465016894934800942442334612077828885771793164268655566366462165061862443368822544695623147966149765223644798045399342853834086413561960176148" + TI[2, 1] = big"-3.00739016945129213173149353792169083141834116044470099212013728771587881480191343754504173052952073006187734389002396348355357273701343509199048972794392147" + TI[2, 2] = big"-11.0158660787657713291120393664792067595453921824881213620299497076376976067619617086470844707815815293102862568459526162951253770377715406520772358338647188" + TI[2, 3] = big"1.48779945613165628148618248664965038886474377325027865838645297753993182317594482435706956176392903188004580583104018591540474622009639200188521283880201225" + TI[2, 4] = big"2.13038815955928245943197208332824475219642634294808813866153957342980992047877237670079423767538654092424134276380826377135080667266661637001176204430488753" + TI[2, 5] = big"-1.81614108681756562482220455159496741723359999245934818387747079566312917815672128128449281415737713177900591942282975861961228230314168417307836619006791605" + TI[2, 6] = big"1.13432558789516110008277908420532415765361628740656810686297793967986689714948610119162966211301325316623863222505219543867472186257492829970663316956377323" + TI[2, 7] = big"-0.414699045943303531993049422295928526684402022493736427543557958358387925728160703636844863663828153394608981043415378230601486738224597324364079320598162815" + TI[3, 1] = big"-8.44196318832108468175691559413731210343158392484322786670758421404507417209484447031645790366021837365786640573614305718894911853549168061902141351516580451" + TI[3, 2] = big"-0.650525274057515002816904045893485631294530894981669254094573985727348985809697093879080285963063573837365484483755274668080611163704039179328960851461387071" + TI[3, 3] = big"6.94067073036987647880408175445008301222030789462375109942012235845495260572570799226646472429196555932436186979400567616504159564738984233922289782922787445" + TI[3, 4] = big"-3.20504752559789843156502799159713971965747774043426947358779973217345866996463287674334224123932879873323284636947452187683408110992957222808611161423213549" + TI[3, 5] = big"1.07128094354647858978279562700457911254627057919002861801894953308482120936700881726232902304000322718645130593907512149815870969208873216470962770569998532" + TI[3, 6] = big"-0.354850749121622187972972761073874956531274189535504546398851680169235702590362534883357256681588685608802983372517893712333972644320006895019178184808028042" + TI[3, 7] = big"0.0919854913278655415440864884207305663999562250023079120516746551750254082665966708567906888946992351083964961208132558221142585217674963218388224937302473142" + TI[4, 1] = big"74.6783322350226997715286176267232500441551583987525066913719852490109364599462546293112601362342028584101507709386240000804692470037564789980905370400509214" + TI[4, 2] = big"87.4085889799008164020396362924136436577534600993283836959398121813667403209890699914314446222016952621954817633686823685774595935180374571416781238038364186" + TI[4, 3] = big"4.02415873737999787701407840793921059156554118449220356776918749072220128918152906578385457943212213189933447495921754693186811343717296680238755923076427455" + TI[4, 4] = big"-3.7148063151583641866387382381081795406061842159003055897302686185198568522128509989890869602984467843559169959313018612449354703104270603001605170037725663" + TI[4, 5] = big"-3.43009398598231735074090769130593476067104938465255451803266927011738721835297930406017172365070584279715308905584391225176154776278518922912169890517961929" + TI[4, 6] = big"2.69660480976531237885262500230842013033719691844775548640355919138284680959979836353143310081338215041119022648809147361433752919265159399610746756470853959" + TI[4, 7] = big"-0.938692743607546193356785681771531136814109179879957291315724533839534255667763099330792864148293396694586387338161584706252944483821135344465739888811338788" + TI[5, 1] = big"58.3565288519065772423731088606544342599129168115273649928818622008651860145833895668543250775742899696760389837877193028417145182338484929599333810581515993" + TI[5, 2] = big"-10.0687739578001809632495544545749228539542767485211306078205622876595603032162891608453826862136355989387474454697691529766293644115682409173741730758425432" + TI[5, 3] = big"-30.3663888425666712081087189214021522992426235463582449811325590575576319489955157279473313224901192335775884848736150180108985558310423628914140477437063457" + TI[5, 4] = big"-1.02002086518486598502718784312141857841892430616701325398305811243769008274372077411348691412296276168896198187688441456921700292037247387330560786140723416" + TI[5, 5] = big"-0.112417500378424962126670249921897816128157398591725875330925039631874967429838848482089690872916638698820411392685501889126627650123714184027159547685248056" + TI[5, 6] = big"1.89064083100037762279966919417932484200269828564004442737723486475878958135985745266991261770924069476112679285337233931312540904735632744873728510014970829" + TI[5, 7] = big"-0.971648639383148228217233127548943147296423534674266405843322723719694664032217172325052282800290275002731997713145411340983758516166807609661717915219518127" + TI[6, 1] = big"-299.18624802825209667863642523944728107942141534516550178278869311293354511449399684666660494133688445719285752471650937062695632169114367079856135650539072" + TI[6, 2] = big"-243.040745368744791181900565230083092669143049316165122405971394775932180012728275256467636352341415340547177922968547123544546515287229215470481168446631934" + TI[6, 3] = big"-48.7771040780378692121909344887388032694629956594617430615510915251995189158287187599892740037773277403958100797917560590738598108409472582147091119440886778" + TI[6, 4] = big"-2.03867190574193440528015205293433905622043272233073734690244789947707827347049413187234402189062846366658963666461334786306660732097114011309282331323116958" + TI[6, 5] = big"1.67356023986108494426829042309213202110891938292923077616474877079402040904687073610625868939896244842053999572446723558562427506280564629528151134946587118" + TI[6, 6] = big"-1.0873740320571061644555969255032311107358443063278089996181949045168433801494845898897631535619158410753032807069032950523487601457868753453652745002841107" + TI[6, 7] = big"0.901938249296099373842715514839004052963355800714627971724094542443991299921284427589690820402982448873149676210397055957126153220340909284180014056386791594" + TI[7, 1] = big"-93.076502897435305911571945263737383854569504715670989865831914555937966339933932282945955570244055882294556430466422133231853008314991630740535709028417842" + TI[7, 2] = big"23.8816310562811442770319002318043863376962876994405756649585750650966186536576789769674007990310112890015051984278059899811178135726914390958188405071290871" + TI[7, 3] = big"39.2788807308138438271015646136760366834412493325456249795727722130258444051594274416196392795817449902122139076648927894476044063388859377757097127385794539" + TI[7, 4] = big"14.3889156854910800698761307424979534708984169042483973564042387223013868069040933228077604321320066763752720714195604903398768371784013771964086553618150626" + TI[7, 5] = big"-3.51043839939936122108708432480845734972162782563284715495715984978907792386567906732993553255070093796782368160341757151292477304975079070782335737053297468" + TI[7, 6] = big"4.86328488556618070121491058699734313503568312572977577331134555924656926935558698308076704662503608259898740028814153544991114426972747448736702277116049277" + TI[7, 7] = big"-2.24648272959123991640046924839711232278867381637608763335081676684616443569602032178385937243819174902544136208243971053224668691848283004752869023074006745" T = Matrix{T1}(undef, 7, 7) - T[1, 1] = convert(T1, big"0.00215375462731052642282751906550204337272018200721827917615061640312650856312529840445028048591986867096756005142895325420603307041594804305862850861253757163") - T[1, 2] = convert(T1, big"0.021567551351320773386914226953811992365459277376204369162736830595700124529879508417849062386878143122032508776691627063229415272329484156789207145821702462") - T[1, 3] = convert(T1, big"0.00878356792514414440732555660043326940873333657406338685620618347939710728032290406426688328221296324998146697730909767495361893387567339044816921837538988154") - T[1, 4] = convert(T1, big"-0.00405516145233102389819844704090310382485225922827010954643577855973533421255114497764957587851178840064428149215351434824919490696577563849929483184955933965") - T[1, 5] = convert(T1, big"0.00442723275326828547967807873499027629097834766201549949492135358632150336069311115075327876323707841703727317338755331613570950287342825020738596326021052902") - T[1, 6] = convert(T1, big"-0.00123864618795287405637686870391105285581324510790128485733529975336279476721707053186563729417080236061385260749762448518679294700311105630290083016823761156") - T[1, 7] = convert(T1, big"-0.00276061748054385249954800379096675592021481213358861974911688001011761550911589157738523818859000828996335817774948428177282421412491830529445501318154035024") - T[2, 1] = convert(T1, big"-0.00160002507788042852683067347985080829550105638728462477214069614397009338180775134535418790113854904464693278677067195562013777079470430165035085043732753352") - T[2, 2] = convert(T1, big"-0.0381316481344115466944201512445271892551007922443248010648630183723114657457789198582213862424187595732944781586531399310738197517976083499508550510483478779") - T[2, 3] = convert(T1, big"-0.0215255605940068755238494349163503963236812065771639056145559371805737876208350036328339608215271680572576146954552666030277743869132676140541472724370558091") - T[2, 4] = convert(T1, big"0.00841556827655958923717700333156546206587781542530241328710392714333753219743181540077241302321588065650704924760060316717877095134935044662592211744890794666") - T[2, 5] = convert(T1, big"-0.00403194957022454949230429372587008587329606687054571010486662485715979240183165499902791387008699068626978608835015342675934092134962673636484308565473356683") - T[2, 6] = convert(T1, big"-6.6666353393963381817604789740257628821376819567901071737415235834331307484818353061850936507762955342131861918219584166678095273744210157164382779907235669e-05") - T[2, 7] = convert(T1, big"0.00318547482516620984874835878222687621122035448401205459368674257818574765593899794870819769668503869906022860261901897250913569265553156976061140932045107432") - T[3, 1] = convert(T1, big"0.00405910730194768309165024146216588597640781263680870767202041411242133338742562561902630276038676420444232405079851555753917806998064489819308813790494788924") - T[3, 2] = convert(T1, big"0.0573965089393817153975680203880753938458832782600090443030839643350468249623833638779578474891654213594195393636829414422184571666256857425091138479371917574") - T[3, 3] = convert(T1, big"0.0588505292084267910561208969865829735901655409220388105109199298038946675765714122525765330769443473927581930134049676200572930797370286476504623214740871248") - T[3, 4] = convert(T1, big"-0.00856043106160343206017727185390754992573940897343949944649743606465705403614377469754987858631901604547097801042861815249197647886051332362774581709381720893") - T[3, 5] = convert(T1, big"-0.00692321266502390892414068519049460069371592099748070119636478595631451405094203293036429762819458535062492059219566837532157551782305886338773933077463475632") - T[3, 6] = convert(T1, big"-0.00235218098294333834053519532555529491776729377182703234025085030409255592197086839142988525473684138901264206886166295186155491132922909402254443843846019141") - T[3, 7] = convert(T1, big"0.00041690777252975626914088803059940941342549922756308931704215701350026719541939053570614368159222367707113801117750298289694571643601584878405615892432648487") - T[4, 1] = convert(T1, big"0.0157504880793768442034586734054915501004520506405808322686493022779655453114657621318660532381583918124125360276320121127974912393389579826125529804830864399") - T[4, 2] = convert(T1, big"-0.0382146935969683504846411337659300127514788882892071252172987515109399372135899067290947441850340146027892665775682097051548343529370733593281856326317259999") - T[4, 3] = convert(T1, big"-0.165736811272943851241241116255535218556011122333381899790277357803281567727036568454939356458468926429537927937619042817050400333625919290585510785057955509") - T[4, 4] = convert(T1, big"-0.0373712423023844574190702119163246888117181457309185176497005310822879226235861373253125139016964433591381638592353617347369492240160809914228784174846477722") - T[4, 5] = convert(T1, big"0.00823900729850771940449868235563938395546999707236910359131464615707125576979409087864780171789078059526539789661318173387826643385244974406562622466790754233") - T[4, 6] = convert(T1, big"0.00311507115234617525272547086289315208054441921705361129575617631104650731644437585122142710666234276633544335552925569262424677362146587776195531866754755781") - T[4, 7] = convert(T1, big"0.025116604913438821928363823471446698278976101918753236732238210724710282378748917637317846485853317873304329580245705683618093593158791190832004186288367408") - T[5, 1] = convert(T1, big"0.112977661024220807608615842313106352633973778091080400075534257952348289641328709240673869677499013004285003126194992176632265223545565047727637631580337111") - T[5, 2] = convert(T1, big"-0.249174212465263686330825594009221950347570740813751325091913985975498424569678307894304962660904874986611526140914403971840496728150916599999921976188547708") - T[5, 3] = convert(T1, big"0.273563305798662321213236935135336593478278696397012151365678540099566245199777083242808233574654642014215983653810819494932091426330017240672955510133726276") - T[5, 4] = convert(T1, big"0.00536676137918177009427930181087914853701809128264121101773394730339300080525157052081366996826642003169044168721911822166683675089051631342776752635189343996") - T[5, 5] = convert(T1, big"0.193211116101262014431211225620266980060733605289133050251158448403922545905872373640500736693735926480983370235582910255756813799388364741420161359961401418") - T[5, 6] = convert(T1, big"0.101717732481715146808078931323995112561027763392448195424858681165964478003318758266672250034474900552688318026734856778296896546916272032434282368222825518") - T[5, 7] = convert(T1, big"0.0950450203560462282103892144485647895183175432965514336285840628832838918715022627077373617151475963061484489345238022187829573892306346658797861719620799413") - T[6, 1] = convert(T1, big"0.458381043183931501028085939964292092908293295595258886425372669820276128937720150467378912424378376379185138190017965370589550781979145790869568608776861466") - T[6, 2] = convert(T1, big"0.5315846490836284292050500994300107341125728347976407285397462896004659632807779347307732180848765709277026749725126234633983063167374333425454720010026876") - T[6, 3] = convert(T1, big"0.486322836617572894056685295353340203321316764127126557475136642083389075853199222650975554544550110757249234979120491845825690852575400863926535437662617201") - T[6, 4] = convert(T1, big"0.526574226458449262914091192639271913456008564881594253716678163127743947224108435833618497118891017505982561930788522171455486058320589875335702474378251931") - T[6, 5] = convert(T1, big"0.275534394989625814192875938762525038291639319966986287664787801569471609648366101593885546008609962622035890891754680149203464179471952105174480329668882489") - T[6, 6] = convert(T1, big"0.521751945274765285294609453181807034209434470364856664246194441011327338299794536726049398636575212016960129143954076748520870645966241492966592488607495009") - T[6, 7] = convert(T1, big"0.128071944635543894414114939510913357662538610722706228789484435811417614332529416514635125851744500940930818246509599119254761178392202724896572159336577251") - T[7, 1] = convert(T1, big"0.881391578353818376313498879127399181693003124999819194603124949551827789004545406999549226388170693806014968936224161749923163222614460424501073405017519348") - T[7, 2] = convert(T1, big"1.0") - T[7, 3] = convert(T1, big"0.0") - T[7, 4] = convert(T1, big"1.0") - T[7, 5] = convert(T1, big"0.0") - T[7, 6] = convert(T1, big"1.0") - T[7, 7] = convert(T1, big"0.0") + T[1, 1] = big"0.00215375462731052642282751906550204337272018200721827917615061640312650856312529840445028048591986867096756005142895325420603307041594804305862850861253757163" + T[1, 2] = big"0.021567551351320773386914226953811992365459277376204369162736830595700124529879508417849062386878143122032508776691627063229415272329484156789207145821702462" + T[1, 3] = big"0.00878356792514414440732555660043326940873333657406338685620618347939710728032290406426688328221296324998146697730909767495361893387567339044816921837538988154" + T[1, 4] = big"-0.00405516145233102389819844704090310382485225922827010954643577855973533421255114497764957587851178840064428149215351434824919490696577563849929483184955933965" + T[1, 5] = big"0.00442723275326828547967807873499027629097834766201549949492135358632150336069311115075327876323707841703727317338755331613570950287342825020738596326021052902" + T[1, 6] = big"-0.00123864618795287405637686870391105285581324510790128485733529975336279476721707053186563729417080236061385260749762448518679294700311105630290083016823761156" + T[1, 7] = big"-0.00276061748054385249954800379096675592021481213358861974911688001011761550911589157738523818859000828996335817774948428177282421412491830529445501318154035024" + T[2, 1] = big"-0.00160002507788042852683067347985080829550105638728462477214069614397009338180775134535418790113854904464693278677067195562013777079470430165035085043732753352" + T[2, 2] = big"-0.0381316481344115466944201512445271892551007922443248010648630183723114657457789198582213862424187595732944781586531399310738197517976083499508550510483478779" + T[2, 3] = big"-0.0215255605940068755238494349163503963236812065771639056145559371805737876208350036328339608215271680572576146954552666030277743869132676140541472724370558091" + T[2, 4] = big"0.00841556827655958923717700333156546206587781542530241328710392714333753219743181540077241302321588065650704924760060316717877095134935044662592211744890794666" + T[2, 5] = big"-0.00403194957022454949230429372587008587329606687054571010486662485715979240183165499902791387008699068626978608835015342675934092134962673636484308565473356683" + T[2, 6] = big"-6.6666353393963381817604789740257628821376819567901071737415235834331307484818353061850936507762955342131861918219584166678095273744210157164382779907235669e-05" + T[2, 7] = big"0.00318547482516620984874835878222687621122035448401205459368674257818574765593899794870819769668503869906022860261901897250913569265553156976061140932045107432" + T[3, 1] = big"0.00405910730194768309165024146216588597640781263680870767202041411242133338742562561902630276038676420444232405079851555753917806998064489819308813790494788924" + T[3, 2] = big"0.0573965089393817153975680203880753938458832782600090443030839643350468249623833638779578474891654213594195393636829414422184571666256857425091138479371917574" + T[3, 3] = big"0.0588505292084267910561208969865829735901655409220388105109199298038946675765714122525765330769443473927581930134049676200572930797370286476504623214740871248" + T[3, 4] = big"-0.00856043106160343206017727185390754992573940897343949944649743606465705403614377469754987858631901604547097801042861815249197647886051332362774581709381720893" + T[3, 5] = big"-0.00692321266502390892414068519049460069371592099748070119636478595631451405094203293036429762819458535062492059219566837532157551782305886338773933077463475632" + T[3, 6] = big"-0.00235218098294333834053519532555529491776729377182703234025085030409255592197086839142988525473684138901264206886166295186155491132922909402254443843846019141" + T[3, 7] = big"0.00041690777252975626914088803059940941342549922756308931704215701350026719541939053570614368159222367707113801117750298289694571643601584878405615892432648487" + T[4, 1] = big"0.0157504880793768442034586734054915501004520506405808322686493022779655453114657621318660532381583918124125360276320121127974912393389579826125529804830864399" + T[4, 2] = big"-0.0382146935969683504846411337659300127514788882892071252172987515109399372135899067290947441850340146027892665775682097051548343529370733593281856326317259999" + T[4, 3] = big"-0.165736811272943851241241116255535218556011122333381899790277357803281567727036568454939356458468926429537927937619042817050400333625919290585510785057955509" + T[4, 4] = big"-0.0373712423023844574190702119163246888117181457309185176497005310822879226235861373253125139016964433591381638592353617347369492240160809914228784174846477722" + T[4, 5] = big"0.00823900729850771940449868235563938395546999707236910359131464615707125576979409087864780171789078059526539789661318173387826643385244974406562622466790754233" + T[4, 6] = big"0.00311507115234617525272547086289315208054441921705361129575617631104650731644437585122142710666234276633544335552925569262424677362146587776195531866754755781" + T[4, 7] = big"0.025116604913438821928363823471446698278976101918753236732238210724710282378748917637317846485853317873304329580245705683618093593158791190832004186288367408" + T[5, 1] = big"0.112977661024220807608615842313106352633973778091080400075534257952348289641328709240673869677499013004285003126194992176632265223545565047727637631580337111" + T[5, 2] = big"-0.249174212465263686330825594009221950347570740813751325091913985975498424569678307894304962660904874986611526140914403971840496728150916599999921976188547708" + T[5, 3] = big"0.273563305798662321213236935135336593478278696397012151365678540099566245199777083242808233574654642014215983653810819494932091426330017240672955510133726276" + T[5, 4] = big"0.00536676137918177009427930181087914853701809128264121101773394730339300080525157052081366996826642003169044168721911822166683675089051631342776752635189343996" + T[5, 5] = big"0.193211116101262014431211225620266980060733605289133050251158448403922545905872373640500736693735926480983370235582910255756813799388364741420161359961401418" + T[5, 6] = big"0.101717732481715146808078931323995112561027763392448195424858681165964478003318758266672250034474900552688318026734856778296896546916272032434282368222825518" + T[5, 7] = big"0.0950450203560462282103892144485647895183175432965514336285840628832838918715022627077373617151475963061484489345238022187829573892306346658797861719620799413" + T[6, 1] = big"0.458381043183931501028085939964292092908293295595258886425372669820276128937720150467378912424378376379185138190017965370589550781979145790869568608776861466" + T[6, 2] = big"0.5315846490836284292050500994300107341125728347976407285397462896004659632807779347307732180848765709277026749725126234633983063167374333425454720010026876" + T[6, 3] = big"0.486322836617572894056685295353340203321316764127126557475136642083389075853199222650975554544550110757249234979120491845825690852575400863926535437662617201" + T[6, 4] = big"0.526574226458449262914091192639271913456008564881594253716678163127743947224108435833618497118891017505982561930788522171455486058320589875335702474378251931" + T[6, 5] = big"0.275534394989625814192875938762525038291639319966986287664787801569471609648366101593885546008609962622035890891754680149203464179471952105174480329668882489" + T[6, 6] = big"0.521751945274765285294609453181807034209434470364856664246194441011327338299794536726049398636575212016960129143954076748520870645966241492966592488607495009" + T[6, 7] = big"0.128071944635543894414114939510913357662538610722706228789484435811417614332529416514635125851744500940930818246509599119254761178392202724896572159336577251" + T[7, 1] = big"0.881391578353818376313498879127399181693003124999819194603124949551827789004545406999549226388170693806014968936224161749923163222614460424501073405017519348" + T[7, 2] = big"1.0" + T[7, 3] = big"0.0" + T[7, 4] = big"1.0" + T[7, 5] = big"0.0" + T[7, 6] = big"1.0" + T[7, 7] = big"0.0" BigRadauIIA13Tableau{T1, T2, Int}(T, TI, c, γ, α, β, 7) From d9545fdcb9eb1bfa9fc307a1fe8840c0af768bab Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Mon, 2 Sep 2024 20:21:12 -0400 Subject: [PATCH 56/71] tweaks --- lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl | 4 ++-- lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl | 6 +++--- 2 files changed, 5 insertions(+), 5 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index e6aa13e6a5..c7eedf7b33 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1435,9 +1435,9 @@ end end dw = Vector{eltype(u)}(undef, num_stages) - dw[1] = LU[1] \ rhs[1] + dw[1] = _reshape(LU[1] \ _vec(rhs[1])) for i in 2 : Int((num_stages + 1) / 2) - tmp = LU[i] \ (@.. rhs[2 * i - 2] + rhs[2 * i - 1] * im) + tmp = _reshape(LU[i] \ _vec(@.. rhs[2 * i - 2] + rhs[2 * i - 1] * im), axes(u)) dw[2 * i - 2] = real(tmp) dw[2 * i - 1] = imag(tmp) end diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl index 7cb82a9a58..7c090d96ad 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl @@ -123,7 +123,7 @@ struct BigRadauIIA5Tableau{T1, T2, Int} end function BigRadauIIA5Tableau(T1, T2, Int) - γ = big"3.63783425274449573220841851357777579794593608687391153215117488565841871456727143375130115708511223004183651123208497057248238260532214672028700625775335843" + γ = convert(T1, big"3.63783425274449573220841851357777579794593608687391153215117488565841871456727143375130115708511223004183651123208497057248238260532214672028700625775335843") α = Vector{T1}(undef, 1) β = Vector{T1}(undef, 1) α[1] = big"2.68108287362775213389579074321111210102703195656304423392441255717079064271636428312434942145744388497908174438395751471375880869733892663985649687112332242" @@ -171,7 +171,7 @@ struct BigRadauIIA9Tableau{T1, T2, Int} end function BigRadauIIA9Tableau(T1, T2, Int) - γ = big"6.28670475172927664517315334186940904959068186655567041187229167532923622489525703260842273089261139845280626287956099768662193453067483410165932355981736786" + γ = convert(T1, big"6.28670475172927664517315334186940904959068186655567041187229167532923622489525703260842273089261139845280626287956099768662193453067483410165932355981736786") α = Vector{T1}(undef, 2) β = Vector{T1}(undef, 2) α[1] = big"3.65569432546357225824320796009543385435699888857815445045567025741630720509235614026228963385258117304229337679733945535812317372403535763551850772878775217" @@ -405,7 +405,7 @@ struct BigRadauIIA13Tableau{T1, T2, Int} end function BigRadauIIA13Tableau(T1, T2, Int) - γ = big"8.93683278840521633730209691330107970355008194433956657198414191417624969654351559268800871286734194720118970058657997472527299153742511021973612156231867783" + γ = convert(T1, big"8.93683278840521633730209691330107970355008194433956657198414191417624969654351559268800871286734194720118970058657997472527299153742511021973612156231867783") α = Vector{T1}(undef, 3) β = Vector{T1}(undef, 3) α[1] = big"4.37869356150680600252334919268856129165763746518197948235657247177701087073069907016715245914093899486193202405685779803686971216417800783050995450529391908" From 8574f0401b1ab4e88c72a3f8b38254b583f6dd32 Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Tue, 3 Sep 2024 18:42:07 -0400 Subject: [PATCH 57/71] edits --- lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl | 4 ++-- lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl | 3 ++- 2 files changed, 4 insertions(+), 3 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index 318e062494..a401e45a3b 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1381,7 +1381,7 @@ end end end integrator.stats.nw += 1 - z = w = Vector{BigFloat}(undef, num_stages) + z = w = Vector{typeof(u)}(undef, num_stages) if integrator.iter == 1 || integrator.u_modified || alg.extrapolant == :constant cache.dtprev = one(cache.dtprev) for i in 1 : num_stages @@ -1441,7 +1441,7 @@ end end dw = Vector{eltype(u)}(undef, num_stages) - dw[1] = _reshape(LU[1] \ _vec(rhs[1])) + dw[1] = _reshape(LU[1] \ _vec(rhs[1]), axes(u)) for i in 2 : Int((num_stages + 1) / 2) tmp = _reshape(LU[i] \ _vec(@.. rhs[2 * i - 2] + rhs[2 * i - 1] * im), axes(u)) dw[2 * i - 2] = real(tmp) diff --git a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl index dde9d4b462..d08df7f56a 100644 --- a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl +++ b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl @@ -18,7 +18,8 @@ prob_ode_linear_big = remake(prob_ode_linear, u0 = big.(prob_ode_linear.u0), tsp prob_ode_2Dlinear_big = remake(prob_ode_2Dlinear, u0 = big.(prob_ode_2Dlinear.u0), tspan = big.(prob_ode_2Dlinear.tspan)) for i in [3, 5, 7, 9], prob in [prob_ode_linear_big, prob_ode_2Dlinear_big] - sim21 = test_convergence(1 ./ 2 .^ (2.25:-1:0.25), prob, AdaptiveRadau(num_stages = i)) + dts = 1 ./ 2 .^ (4.25:-1:0.25) + sim21 = test_convergence(dts, prob, AdaptiveRadau(num_stages = i)) @test sim21.𝒪est[:final]≈ (2 * i - 1) atol=testTol end From 71e13ef137fb990bd2ce0f3fa763226d5a87667b Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Tue, 3 Sep 2024 18:46:03 -0400 Subject: [PATCH 58/71] Update firk_perform_step.jl --- lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index a401e45a3b..c9f274c9c2 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1769,7 +1769,7 @@ end if integrator.EEst <= oneunit(integrator.EEst) cache.dtprev = dt if alg.extrapolant != :constant - derivatives = Matrix{Any}(undef, num_stages, num_stages) + derivatives = Matrix{typeof(u)}(undef, num_stages, num_stages) pushfirst!(c, 0) pushfirst!(z, map(zero, u)) for i in 1 : num_stages From f17907abee7830601e5afbb36f4e1beecbb8b8df Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Tue, 3 Sep 2024 18:57:54 -0400 Subject: [PATCH 59/71] types --- lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index c9f274c9c2..f2e75e217a 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1368,7 +1368,7 @@ end γdt, αdt, βdt = γ / dt, α ./ dt, β ./ dt J = calc_J(integrator, cache) - LU = Vector{Any}(undef, Int((num_stages + 1) / 2)) + LU = Vector{Complex{BigFloat}}(undef, Int((num_stages + 1) / 2)) if u isa Number LU[1] = -γdt * mass_matrix + J for i in 2 : Int((num_stages + 1) / 2) @@ -1380,6 +1380,7 @@ end LU[i] = lu(-(αdt[i - 1] + βdt[i - 1] * im) * mass_matrix + J) end end + integrator.stats.nw += 1 z = w = Vector{typeof(u)}(undef, num_stages) if integrator.iter == 1 || integrator.u_modified || alg.extrapolant == :constant @@ -1659,7 +1660,7 @@ end end integrator.stats.nsolve += (num_stages + 1) / 2 - dw = Vector{Any}(undef, num_stages - 1) + dw = Vector{typeof(u)}(undef, num_stages - 1) i = 1 while i <= Int((num_stages - 1) / 2) From f52c9e43653c3ceedb6230fef565fa1374dee8f7 Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Wed, 4 Sep 2024 17:44:41 -0400 Subject: [PATCH 60/71] fix tableaus --- .../src/firk_perform_step.jl | 2 +- lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl | 47 +++---------------- 2 files changed, 7 insertions(+), 42 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index f2e75e217a..7e54e7a2af 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1368,7 +1368,7 @@ end γdt, αdt, βdt = γ / dt, α ./ dt, β ./ dt J = calc_J(integrator, cache) - LU = Vector{Complex{BigFloat}}(undef, Int((num_stages + 1) / 2)) + LU = Vector{Complex{typeof(u)}}(undef, Int((num_stages + 1) / 2)) if u isa Number LU[1] = -γdt * mass_matrix + J for i in 2 : Int((num_stages + 1) / 2) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl index 7c090d96ad..78a8f54cdc 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl @@ -111,7 +111,7 @@ function RadauIIA5Tableau(T, T2) e1, e2, e3) end -struct BigRadauIIA5Tableau{T1, T2, Int} +struct RadauIIATableau{T1, T2, Int} T::AbstractMatrix{T1} TI::AbstractMatrix{T1} c::AbstractVector{T2} @@ -155,21 +155,10 @@ function BigRadauIIA5Tableau(T1, T2, Int) T[3, 1] = big"0.966048182615092936190567080794590794996748754810883844283183333914131408744555961195911605614405476210484499875001737558078500322423463946527349731087504518" T[3, 2] = big"1.0" T[3, 3] = big"0.0" - BigRadauIIA5Tableau{T1, T2, Int}(T, TI, + RadauIIATableau{T1, T2, Int}(T, TI, c, γ, α, β, 3) end -struct BigRadauIIA9Tableau{T1, T2, Int} - T::AbstractMatrix{T1} - TI::AbstractMatrix{T1} - c::AbstractVector{T2} - γ::T1 - α::AbstractVector{T1} - β::AbstractVector{T1} - #e::AbstractVector{T1} - num_stages::Int -end - function BigRadauIIA9Tableau(T1, T2, Int) γ = convert(T1, big"6.28670475172927664517315334186940904959068186655567041187229167532923622489525703260842273089261139845280626287956099768662193453067483410165932355981736786") α = Vector{T1}(undef, 2) @@ -240,7 +229,7 @@ function BigRadauIIA9Tableau(T1, T2, Int) T[5, 4] = big"1.0" T[5, 5] = big"0.0" - BigRadauIIA9Tableau{T1, T2, Int}(T, TI, + RadauIIATableau{T1, T2, Int}(T, TI, c, γ, α, β, 5) end @@ -393,17 +382,6 @@ function RadauIIA9Tableau(T, T2) e1, e2, e3, e4, e5) end -struct BigRadauIIA13Tableau{T1, T2, Int} - T::AbstractMatrix{T1} - TI::AbstractMatrix{T1} - c::AbstractVector{T2} - γ::T1 - α::AbstractVector{T1} - β::AbstractVector{T1} - #e::AbstractVector{T1} - num_stages::Int -end - function BigRadauIIA13Tableau(T1, T2, Int) γ = convert(T1, big"8.93683278840521633730209691330107970355008194433956657198414191417624969654351559268800871286734194720118970058657997472527299153742511021973612156231867783") α = Vector{T1}(undef, 3) @@ -526,25 +504,14 @@ function BigRadauIIA13Tableau(T1, T2, Int) T[7, 6] = big"1.0" T[7, 7] = big"0.0" - BigRadauIIA13Tableau{T1, T2, Int}(T, TI, + RadauIIATableau{T1, T2, Int}(T, TI, c, γ, α, β, 7) end -struct adaptiveRadauTableau{T, T2, Int} - T:: AbstractMatrix{T} - TI::AbstractMatrix{T} - γ::T - α::AbstractVector{T} - β::AbstractVector{T} - c::AbstractVector{T} - #e::AbstractVector{T} - num_stages::Int -end - using Polynomials, GenericLinearAlgebra, LinearAlgebra, LinearSolve, GenericSchur, RootedTrees, Symbolics using Symbolics: variables, variable, unwrap -function adaptiveRadauTableau(T, T2, num_stages::Int) +function adaptiveRadauTableau(T1, T2, num_stages::Int) tmp = Vector{BigFloat}(undef, num_stages - 1) for i in 1:(num_stages - 1) tmp[i] = 0 @@ -628,8 +595,6 @@ function adaptiveRadauTableau(T, T2, num_stages::Int) @assert islinear Symbolics.expand.((AA[idxs, :] \ -bb[idxs]) - b)=# #e = b_hat - b - #T_test = T - #return T_test - adaptiveRadauTableau{Any, T2, Int}(T, TI, γ, α, β, c, num_stages) + RadauIIATableau{T1, T2, Int}(T, TI, c, γ, α, β, num_stages) end From 42f5280581aacc768ea8bdf9777c14d23ef49bdd Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Fri, 6 Sep 2024 07:28:08 -0400 Subject: [PATCH 61/71] edits --- lib/OrdinaryDiffEqFIRK/src/firk_caches.jl | 65 +++++------ .../src/firk_perform_step.jl | 105 ++++++++---------- lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl | 28 ++--- 3 files changed, 86 insertions(+), 112 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl index f2cf3019a6..635b37f605 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl @@ -481,7 +481,7 @@ mutable struct AdaptiveRadauConstantCache{F, Tab, Tol, Dt, U, JType} <: κ::Tol ηold::Tol iter::Int - cont::AbstractVector{U} + cont::Vector{U} dtprev::Dt W_γdt::Dt status::NLStatus @@ -497,11 +497,11 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} num_stages = alg.num_stages if (num_stages == 3) - tab = BigRadauIIA5Tableau(uToltype, constvalue(tTypeNoUnits), Int) + tab = BigRadauIIA5Tableau(uToltype, constvalue(tTypeNoUnits)) elseif (num_stages == 5) - tab = BigRadauIIA9Tableau(uToltype, constvalue(tTypeNoUnits), Int) + tab = BigRadauIIA9Tableau(uToltype, constvalue(tTypeNoUnits)) elseif (num_stages == 7) - tab = BigRadauIIA13Tableau(uToltype, constvalue(tTypeNoUnits), Int) + tab = BigRadauIIA13Tableau(uToltype, constvalue(tTypeNoUnits)) else tab = adaptiveRadauTableau(uToltype, constvalue(tTypeNoUnits), num_stages) end @@ -523,21 +523,21 @@ mutable struct AdaptiveRadauCache{uType, cuType, uNoUnitsType, rateType, JType, FIRKMutableCache u::uType uprev::uType - z::AbstractVector{uType} - w::AbstractVector{uType} + z::Vector{uType} + w::Vector{uType} dw1::uType ubuff::uType - dw2::AbstractVector{cuType} - cubuff::AbstractVector{cuType} - cont::AbstractVector{uType} + dw2::Vector{cuType} + cubuff::Vector{cuType} + cont::Vector{uType} du1::rateType fsalfirst::rateType - ks::AbstractVector{rateType} + ks::Vector{rateType} k::rateType - fw::AbstractVector{rateType} + fw::Vector{rateType} J::JType W1::W1Type #real - W2::AbstractVector{W2Type} #complex + W2::Vector{W2Type} #complex uf::UF tab::Tab κ::Tol @@ -547,7 +547,7 @@ mutable struct AdaptiveRadauCache{uType, cuType, uNoUnitsType, rateType, JType, atmp::uNoUnitsType jac_config::JC linsolve1::F1 #real - linsolve2::AbstractVector{F2} #complex + linsolve2::Vector{F2} #complex rtol::rTol atol::aTol dtprev::Dt @@ -565,11 +565,11 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} num_stages = alg.num_stages if (num_stages == 3) - tab = BigRadauIIA5Tableau(uToltype, constvalue(tTypeNoUnits), Int) + tab = BigRadauIIA5Tableau(uToltype, constvalue(tTypeNoUnits)) elseif (num_stages == 5) - tab = BigRadauIIA9Tableau(uToltype, constvalue(tTypeNoUnits), Int) + tab = BigRadauIIA9Tableau(uToltype, constvalue(tTypeNoUnits)) elseif (num_stages == 7) - tab = BigRadauIIA13Tableau(uToltype, constvalue(tTypeNoUnits), Int) + tab = BigRadauIIA13Tableau(uToltype, constvalue(tTypeNoUnits)) else tab = adaptiveRadauTableau(uToltype, constvalue(tTypeNoUnits), num_stages) end @@ -584,16 +584,10 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} dw1 = zero(u) ubuff = zero(u) - dw2 = Vector{Any}(undef, floor(Int, num_stages / 2)) - for i in 1 : floor(Int, num_stages / 2) - dw2[i] = similar(u, Complex{eltype(u)}) - recursivefill!(dw2[i], false) - end - cubuff = Vector{Any}(undef, floor(Int, num_stages / 2)) - for i in 1 : floor(Int, num_stages / 2) - cubuff[i] = similar(u, Complex{eltype(u)}) - recursivefill!(cubuff[i], false) - end + dw2 = [similar(u, Complex{eltype(u)}) for _ in 1 : (num_stages - 1) ÷ 2] + recursivefill!.(dw2, false) + cubuff = [similar(u, Complex{eltype(u)}) for _ in 1 : (num_stages - 1) ÷ 2] + recursivefill!.(cubuff, false) cont = Vector{typeof(u)}(undef, num_stages) for i in 1: num_stages @@ -610,14 +604,12 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} J, W1 = build_J_W(alg, u, uprev, p, t, dt, f, uEltypeNoUnits, Val(true)) if J isa AbstractSciMLOperator - error("Non-concrete Jacobian not yet supported by RadauIIA5.") - end - W2 = Vector{Any}(undef, floor(Int, num_stages / 2)) - for i in 1 : floor(Int, num_stages / 2) - W2[i] = similar(J, Complex{eltype(W1)}) - recursivefill!(W2[i], false) + error("Non-concrete Jacobian not yet supported by AdaptiveRadau.") end + W2 = [similar(J, Complex{eltype(W1)}) for _ in 1 : (num_stages - 1) ÷ 2] + recursivefill!.(W2, false) + du1 = zero(rate_prototype) tmp = zero(u) @@ -631,12 +623,9 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} linsolve1 = init(linprob, alg.linsolve, alias_A = true, alias_b = true, assumptions = LinearSolve.OperatorAssumptions(true)) - linsolve2 = Vector{Any}(undef, floor(Int, num_stages / 2)) - for i in 1 : floor(Int, num_stages / 2) - linprob = LinearProblem(W2[i], _vec(cubuff[i]); u0 = _vec(dw2[i])) - linsolve2[i] = init(linprob, alg.linsolve, alias_A = true, alias_b = true, - assumptions = LinearSolve.OperatorAssumptions(true)) - end + linsolve2 = [ + init(LinearProblem(W2[i], _vec(cubuff[i]); u0 = _vec(dw2[i])), alg.linsolve, alias_A = true, alias_b = true, + assumptions = LinearSolve.OperatorAssumptions(true)) for i in 1 : (num_stages - 1) ÷ 2] rtol = reltol isa Number ? reltol : zero(reltol) atol = reltol isa Number ? reltol : zero(reltol) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index 7e54e7a2af..6eb6e9b266 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1368,25 +1368,28 @@ end γdt, αdt, βdt = γ / dt, α ./ dt, β ./ dt J = calc_J(integrator, cache) - LU = Vector{Complex{typeof(u)}}(undef, Int((num_stages + 1) / 2)) + LU = Vector{Complex{typeof(u)}}(undef,(num_stages + 1) ÷ 2) if u isa Number LU[1] = -γdt * mass_matrix + J - for i in 2 : Int((num_stages + 1) / 2) + for i in 2 :(num_stages + 1) ÷ 2 LU[i] = -(αdt[i - 1] + βdt[i - 1] * im) * mass_matrix + J end else LU[1] = lu(-γdt * mass_matrix + J) - for i in 2 : Int((num_stages + 1) / 2) + for i in 2 :(num_stages + 1) ÷ 2 LU[i] = lu(-(αdt[i - 1] + βdt[i - 1] * im) * mass_matrix + J) end end integrator.stats.nw += 1 - z = w = Vector{typeof(u)}(undef, num_stages) + z = Vector{typeof(u)}(undef, num_stages) + w = Vector{typeof(u)}(undef, num_stages) if integrator.iter == 1 || integrator.u_modified || alg.extrapolant == :constant cache.dtprev = one(cache.dtprev) for i in 1 : num_stages - z[i] = w[i] = cache.cont[i] = map(zero, u) + z[i] = map(zero, u) + w[i] = map(zero, u) + cache.cont[i] = map(zero, u) end else c_prime = Vector{eltype(u)}(undef, num_stages) #time stepping @@ -1436,31 +1439,27 @@ end rhs[1] = @.. fw[1] - γdt * Mw[1] i = 2 while i <= num_stages #block by block multiplication - rhs[i] = @.. fw[i] - αdt[Int(i/2)] * Mw[i] + βdt[Int(i/2)] * Mw[i + 1] - rhs[i + 1] = @.. fw[i + 1] - βdt[Int(i/2)] * Mw[i] - αdt[Int(i/2)] * Mw[i + 1] + rhs[i] = @.. fw[i] - αdt[i ÷ 2] * Mw[i] + βdt[i ÷ 2] * Mw[i + 1] + rhs[i + 1] = @.. fw[i + 1] - βdt[i ÷ 2] * Mw[i] - αdt[i ÷ 2] * Mw[i + 1] i += 2 end dw = Vector{eltype(u)}(undef, num_stages) dw[1] = _reshape(LU[1] \ _vec(rhs[1]), axes(u)) - for i in 2 : Int((num_stages + 1) / 2) + for i in 2 :(num_stages + 1) ÷ 2 tmp = _reshape(LU[i] \ _vec(@.. rhs[2 * i - 2] + rhs[2 * i - 1] * im), axes(u)) dw[2 * i - 2] = real(tmp) dw[2 * i - 1] = imag(tmp) end - integrator.stats.nsolve += Int((num_stages + 1) / 2) + integrator.stats.nsolve +=(num_stages + 1) ÷ 2 # compute norm of residuals iter > 1 && (ndwprev = ndw) - atmp = Vector{eltype(u)}(undef, num_stages) + ndw = 0.0 for i in 1 : num_stages - atmp[i] = calculate_residuals(dw[i], uprev, u, atol, rtol, internalnorm, t) + ndw += internalnorm(calculate_residuals(dw[i], uprev, u, atol, rtol, internalnorm, t), t) end - ndw = 0 - for i in 1 : num_stages - ndw = ndw + internalnorm(atmp[i], t) - end # check divergence (not in initial step) if iter > 1 @@ -1522,20 +1521,17 @@ end if integrator.EEst <= oneunit(integrator.EEst) cache.dtprev = dt if alg.extrapolant != :constant - derivatives = Matrix{eltype(u)}(undef, num_stages, num_stages) - pushfirst!(c, 0) - pushfirst!(z, 0) - for i in 1 : num_stages - for j in i : num_stages - if i == 1 - derivatives[i, j] = @.. (z[j] - z[j + 1]) / (c[j] - c[j + 1]) #first derivatives - else - derivatives[i, j] = @.. (derivatives[i - 1, j - 1] - derivatives[i - 1, j]) / (c[j - i + 1] - c[j + 1]) #all others - end + derivatives = Matrix{typeof(u)}(undef, num_stages, num_stages) + derivatives[1, 1] = @.. z[1] / c[1] + for j in 2 : num_stages + derivatives[1, j] = @.. (z[j - 1] - z[j]) / (c[j - 1] - c[j]) #first derivatives + end + for i in 2 : num_stages + derivatives[i, i] = @.. (derivatives[i - 1, i] - derivatives[i - 1, i - 1]) / c[i] + for j in i+1 : num_stages + derivatives[i, j] = @.. (derivatives[i - 1, j - 1] - derivatives[i - 1, j]) / (c[j - i] - c[j]) #all others end end - popfirst!(c) - popfirst!(z) for i in 1 : num_stages cache.cont[i] = derivatives[i, num_stages] end @@ -1570,7 +1566,7 @@ end if (new_W = do_newW(integrator, alg, new_jac, cache.W_γdt)) @inbounds for II in CartesianIndices(J) W1[II] = -γdt * mass_matrix[Tuple(II)...] + J[II] - for i in 1 : Int((num_stages - 1) / 2) + for i in 1 :(num_stages - 1) ÷ 2 W2[i][II] = -(αdt[i] + βdt[i] * im) * mass_matrix[Tuple(II)...] + J[II] end end @@ -1590,15 +1586,15 @@ end c_prime[i] = c[i] * c_prime[num_stages] end for i in 1 : num_stages # collocation polynomial - z[i] = @.. cont[num_stages] * (c_prime[i] - c[1] + 1) + cont[num_stages - 1] + @.. z[i] = cont[num_stages] * (c_prime[i] - c[1] + 1) + cont[num_stages - 1] j = num_stages - 2 while j > 0 - z[i] = @.. z[i] * (c_prime[i] - c[num_stages - j] + 1) + cont[j] + @.. z[i] *= (c_prime[i] - c[num_stages - j] + 1) + cont[j] j = j - 1 end - z[i] = @.. z[i] * c_prime[i] + @.. z[i] *= c_prime[i] end - w = TI * z + mul!(w, TI, z) end # Newton iteration @@ -1617,8 +1613,9 @@ end f(ks[i], tmp, p, t + c[i] * dt) end integrator.stats.nf += num_stages + + mul!(fw, TI, ks) - fw = TI * ks if mass_matrix === I Mw = w elseif mass_matrix isa UniformScaling @@ -1628,7 +1625,7 @@ end Mw = z else for i in 1 : num_stages - mul!(z[i], mass_matrix.λ, w[i]) + mul!(z[i], mass_matrix, w[i]) end Mw = z end @@ -1645,12 +1642,11 @@ end cache.linsolve1 = linres.cache - linres2 = Vector{Any}(undef, Int((num_stages - 1) / 2)) + linres2 = Vector{Any}(undef,(num_stages - 1) ÷ 2) - for i in 1 : Int((num_stages - 1) / 2) + for i in 1 :(num_stages - 1) ÷ 2 @.. cubuff[i]=complex( fw[2 * i] - αdt[i] * Mw[2 * i] + βdt[i] * Mw[2 * i + 1], fw[2 * i + 1] - βdt[i] * Mw[2 * i] - αdt[i] * Mw[2 * i + 1]) - linsolve2[i] = cache.linsolve2[i] if needfactor linres2[i] = dolinsolve(integrator, linsolve2[i]; A = W2[i], b = _vec(cubuff[i]), linu = _vec(dw2[i])) else @@ -1661,29 +1657,21 @@ end integrator.stats.nsolve += (num_stages + 1) / 2 dw = Vector{typeof(u)}(undef, num_stages - 1) - i = 1 - while i <= Int((num_stages - 1) / 2) + for i in 1 : (num_stages - 1) ÷ 2 dw[2 * i - 1] = z[2 * i - 1] dw[2 * i] = z[2 * i] dw[2 * i - 1] = real(dw2[i]) dw[2 * i] = imag(dw2[i]) - i = i + 1 end # compute norm of residuals iter > 1 && (ndwprev = ndw) - ndws = Vector{Any}(undef, num_stages) - ndws[1] = calculate_residuals!(atmp, dw1, uprev, u, atol, rtol, internalnorm, t) - ndws[1] = internalnorm(atmp, t) + calculate_residuals!(atmp, dw1, uprev, u, atol, rtol, internalnorm, t) + ndw = internalnorm(atmp, t) for i in 2 : num_stages calculate_residuals!(atmp, dw[i - 1], uprev, u, atol, rtol, internalnorm, t) - ndws[i] = internalnorm(atmp, t) - end - - ndw = 0 - for i in 1 : num_stages - ndw += ndws[i] + ndw += internalnorm(atmp, t) end # check divergence (not in initial step) @@ -1771,19 +1759,16 @@ end cache.dtprev = dt if alg.extrapolant != :constant derivatives = Matrix{typeof(u)}(undef, num_stages, num_stages) - pushfirst!(c, 0) - pushfirst!(z, map(zero, u)) - for i in 1 : num_stages - for j in i : num_stages - if i == 1 - derivatives[i, j] = @.. (z[j] - z[j + 1]) / (c[j] - c[j + 1]) #first derivatives - else - derivatives[i, j] = @.. (derivatives[i - 1, j - 1] - derivatives[i - 1, j]) / (c[j - i + 1] - c[j + 1]) #all others - end + derivatives[1, 1] = @.. z[1] / c[1] + for j in 2 : num_stages + derivatives[1, j] = @.. (z[j - 1] - z[j]) / (c[j - 1] - c[j]) #first derivatives + end + for i in 2 : num_stages + derivatives[i, i] = @.. (derivatives[i - 1, i] - derivatives[i - 1, i - 1]) / c[i] + for j in i+1 : num_stages + derivatives[i, j] = @.. (derivatives[i - 1, j - 1] - derivatives[i - 1, j]) / (c[j - i] - c[j]) #all others end end - popfirst!(c) - popfirst!(z) for i in 1 : num_stages cache.cont[i] = derivatives[i, num_stages] end diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl index 78a8f54cdc..f0e24e94c0 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl @@ -111,18 +111,18 @@ function RadauIIA5Tableau(T, T2) e1, e2, e3) end -struct RadauIIATableau{T1, T2, Int} - T::AbstractMatrix{T1} - TI::AbstractMatrix{T1} - c::AbstractVector{T2} +struct RadauIIATableau{T1, T2} + T::Matrix{T1} + TI::Matrix{T1} + c::Vector{T2} γ::T1 - α::AbstractVector{T1} - β::AbstractVector{T1} - #e::AbstractVector{T1} + α::Vector{T1} + β::Vector{T1} + #e::Vector{T1} num_stages::Int end -function BigRadauIIA5Tableau(T1, T2, Int) +function BigRadauIIA5Tableau(T1, T2) γ = convert(T1, big"3.63783425274449573220841851357777579794593608687391153215117488565841871456727143375130115708511223004183651123208497057248238260532214672028700625775335843") α = Vector{T1}(undef, 1) β = Vector{T1}(undef, 1) @@ -155,11 +155,11 @@ function BigRadauIIA5Tableau(T1, T2, Int) T[3, 1] = big"0.966048182615092936190567080794590794996748754810883844283183333914131408744555961195911605614405476210484499875001737558078500322423463946527349731087504518" T[3, 2] = big"1.0" T[3, 3] = big"0.0" - RadauIIATableau{T1, T2, Int}(T, TI, + RadauIIATableau{T1, T2}(T, TI, c, γ, α, β, 3) end -function BigRadauIIA9Tableau(T1, T2, Int) +function BigRadauIIA9Tableau(T1, T2) γ = convert(T1, big"6.28670475172927664517315334186940904959068186655567041187229167532923622489525703260842273089261139845280626287956099768662193453067483410165932355981736786") α = Vector{T1}(undef, 2) β = Vector{T1}(undef, 2) @@ -229,7 +229,7 @@ function BigRadauIIA9Tableau(T1, T2, Int) T[5, 4] = big"1.0" T[5, 5] = big"0.0" - RadauIIATableau{T1, T2, Int}(T, TI, + RadauIIATableau{T1, T2}(T, TI, c, γ, α, β, 5) end @@ -382,7 +382,7 @@ function RadauIIA9Tableau(T, T2) e1, e2, e3, e4, e5) end -function BigRadauIIA13Tableau(T1, T2, Int) +function BigRadauIIA13Tableau(T1, T2) γ = convert(T1, big"8.93683278840521633730209691330107970355008194433956657198414191417624969654351559268800871286734194720118970058657997472527299153742511021973612156231867783") α = Vector{T1}(undef, 3) β = Vector{T1}(undef, 3) @@ -504,7 +504,7 @@ function BigRadauIIA13Tableau(T1, T2, Int) T[7, 6] = big"1.0" T[7, 7] = big"0.0" - RadauIIATableau{T1, T2, Int}(T, TI, + RadauIIATableau{T1, T2}(T, TI, c, γ, α, β, 7) end @@ -595,6 +595,6 @@ function adaptiveRadauTableau(T1, T2, num_stages::Int) @assert islinear Symbolics.expand.((AA[idxs, :] \ -bb[idxs]) - b)=# #e = b_hat - b - RadauIIATableau{T1, T2, Int}(T, TI, c, γ, α, β, num_stages) + RadauIIATableau{T1, T2}(T, TI, c, γ, α, β, num_stages) end From 40baa62d5349b9ad42b1aefa147708b4d6d7025f Mon Sep 17 00:00:00 2001 From: oscarddssmith Date: Fri, 6 Sep 2024 13:23:59 -0400 Subject: [PATCH 62/71] minor fixes --- lib/OrdinaryDiffEqFIRK/src/firk_caches.jl | 8 +- .../src/firk_perform_step.jl | 115 +++++++++--------- 2 files changed, 66 insertions(+), 57 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl index 635b37f605..bad793bd62 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl @@ -502,7 +502,9 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} tab = BigRadauIIA9Tableau(uToltype, constvalue(tTypeNoUnits)) elseif (num_stages == 7) tab = BigRadauIIA13Tableau(uToltype, constvalue(tTypeNoUnits)) - else + elseif iseven(num_stages) || num_stages <3 + error("num_stages must be odd and 3 or greater") + else tab = adaptiveRadauTableau(uToltype, constvalue(tTypeNoUnits), num_stages) end @@ -570,7 +572,9 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} tab = BigRadauIIA9Tableau(uToltype, constvalue(tTypeNoUnits)) elseif (num_stages == 7) tab = BigRadauIIA13Tableau(uToltype, constvalue(tTypeNoUnits)) - else + elseif iseven(num_stages) || num_stages < 3 + error("num_stages must be odd and 3 or greater") + else tab = adaptiveRadauTableau(uToltype, constvalue(tTypeNoUnits), num_stages) end diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index 6eb6e9b266..95f6000a3a 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -767,9 +767,9 @@ end if integrator.EEst <= oneunit(integrator.EEst) cache.dtprev = dt if alg.extrapolant != :constant - @.. broadcast=false cache.cont1=(z2 - z3) / c2m1 - @.. broadcast=false tmp=(z1 - z2) / c1mc2 - @.. broadcast=false cache.cont2=(tmp - cache.cont1) / c1m1 + @.. broadcast=false cache.cont1=(z2 - z3) / c2m1 + @.. broadcast=false tmp=(z1 - z2) / c1mc2 + @.. broadcast=false cache.cont2=(tmp - cache.cont1) / c1m1 @.. broadcast=false cache.cont3=cache.cont2 - (tmp - z1 / c1) / c2 end end @@ -837,24 +837,24 @@ end c2′ = c2 * c5′ c3′ = c3 * c5′ c4′ = c4 * c5′ - z1 = @.. c1′ * (cont1 + - (c1′-c4m1) * (cont2 + - (c1′ - c3m1) * (cont3 + + z1 = @.. c1′ * (cont1 + + (c1′-c4m1) * (cont2 + + (c1′ - c3m1) * (cont3 + (c1′ - c2m1) * (cont4 + (c1′ - c1m1) * cont5)))) - z2 = @.. c2′ * (cont1 + - (c2′-c4m1) * (cont2 + - (c2′ - c3m1) * (cont3 + + z2 = @.. c2′ * (cont1 + + (c2′-c4m1) * (cont2 + + (c2′ - c3m1) * (cont3 + (c2′ - c2m1) * (cont4 + (c2′ - c1m1) * cont5)))) - z3 = @.. c3′ * (cont1 + - (c3′-c4m1) * (cont2 + - (c3′ - c3m1) * (cont3 + + z3 = @.. c3′ * (cont1 + + (c3′-c4m1) * (cont2 + + (c3′ - c3m1) * (cont3 + (c3′ - c2m1) * (cont4 + (c3′ - c1m1) * cont5)))) - z4 = @.. c4′ * (cont1 + - (c4′-c4m1) * (cont2 + - (c4′ - c3m1) * (cont3 + + z4 = @.. c4′ * (cont1 + + (c4′-c4m1) * (cont2 + + (c4′ - c3m1) * (cont3 + (c4′ - c2m1) * (cont4 + (c4′ - c1m1) * cont5)))) - z5 = @.. c5′ * (cont1 + - (c5′-c4m1) * (cont2 + + z5 = @.. c5′ * (cont1 + + (c5′-c4m1) * (cont2 + (c5′ - c3m1) * (cont3 + (c5′ - c2m1) * (cont4 + (c5′ - c1m1) * cont5)))) w1 = @.. broadcast=false TI11*z1+TI12*z2+TI13*z3+TI14*z4+TI15*z5 w2 = @.. broadcast=false TI21*z1+TI22*z2+TI23*z3+TI24*z4+TI25*z5 @@ -1087,24 +1087,24 @@ end c2′ = c2 * c5′ c3′ = c3 * c5′ c4′ = c4 * c5′ - z1 = @.. c1′ * (cont1 + - (c1′-c4m1) * (cont2 + - (c1′ - c3m1) * (cont3 + + z1 = @.. c1′ * (cont1 + + (c1′-c4m1) * (cont2 + + (c1′ - c3m1) * (cont3 + (c1′ - c2m1) * (cont4 + (c1′ - c1m1) * cont5)))) - z2 = @.. c2′ * (cont1 + - (c2′-c4m1) * (cont2 + - (c2′ - c3m1) * (cont3 + + z2 = @.. c2′ * (cont1 + + (c2′-c4m1) * (cont2 + + (c2′ - c3m1) * (cont3 + (c2′ - c2m1) * (cont4 + (c2′ - c1m1) * cont5)))) - z3 = @.. c3′ * (cont1 + - (c3′-c4m1) * (cont2 + - (c3′ - c3m1) * (cont3 + + z3 = @.. c3′ * (cont1 + + (c3′-c4m1) * (cont2 + + (c3′ - c3m1) * (cont3 + (c3′ - c2m1) * (cont4 + (c3′ - c1m1) * cont5)))) - z4 = @.. c4′ * (cont1 + - (c4′-c4m1) * (cont2 + - (c4′ - c3m1) * (cont3 + + z4 = @.. c4′ * (cont1 + + (c4′-c4m1) * (cont2 + + (c4′ - c3m1) * (cont3 + (c4′ - c2m1) * (cont4 + (c4′ - c1m1) * cont5)))) - z5 = @.. c5′ * (cont1 + - (c5′-c4m1) * (cont2 + + z5 = @.. c5′ * (cont1 + + (c5′-c4m1) * (cont2 + (c5′ - c3m1) * (cont3 + (c5′ - c2m1) * (cont4 + (c5′ - c1m1) * cont5)))) w1 = @.. broadcast=false TI11*z1+TI12*z2+TI13*z3+TI14*z4+TI15*z5 w2 = @.. broadcast=false TI21*z1+TI22*z2+TI23*z3+TI24*z4+TI25*z5 @@ -1354,7 +1354,7 @@ end @muladd function perform_step!(integrator, cache::AdaptiveRadauConstantCache, repeat_step = false) @unpack t, dt, uprev, u, f, p = integrator - @unpack T, TI, γ, α, β, c, #=e,=# num_stages = cache.tab + @unpack T, TI, γ, α, β, c, #=e,=# num_stages = cache.tab @unpack κ, cont = cache @unpack internalnorm, abstol, reltol, adaptive = integrator.opts alg = unwrap_alg(integrator, true) @@ -1368,15 +1368,21 @@ end γdt, αdt, βdt = γ / dt, α ./ dt, β ./ dt J = calc_J(integrator, cache) - LU = Vector{Complex{typeof(u)}}(undef,(num_stages + 1) ÷ 2) + + #if u isa Number + # LU1 = Complex(-γdt * mass_matrix + J) + # LU2 = -(αdt[1] + βdt[1] * im) * mass_matrix + J + #else + LU1 = lu(-γdt * mass_matrix + J) + LU2 = lu(-(αdt[1] + βdt[1] * im) * mass_matrix + J) + #end + LU = [LU2 for _ in 1:(num_stages + 1) ÷ 2] if u isa Number - LU[1] = -γdt * mass_matrix + J - for i in 2 :(num_stages + 1) ÷ 2 + for i in 3 :(num_stages + 1) ÷ 2 LU[i] = -(αdt[i - 1] + βdt[i - 1] * im) * mass_matrix + J end else - LU[1] = lu(-γdt * mass_matrix + J) - for i in 2 :(num_stages + 1) ÷ 2 + for i in 3 :(num_stages + 1) ÷ 2 LU[i] = lu(-(αdt[i - 1] + βdt[i - 1] * im) * mass_matrix + J) end end @@ -1391,7 +1397,7 @@ end w[i] = map(zero, u) cache.cont[i] = map(zero, u) end - else + else c_prime = Vector{eltype(u)}(undef, num_stages) #time stepping c_prime[num_stages] = dt / cache.dtprev for i in 1 : num_stages - 1 @@ -1406,7 +1412,7 @@ end end z[i] = @.. z[i] * c_prime[i] end - w = TI * z + w = TI*z end # Newton iteration @@ -1419,14 +1425,14 @@ end integrator.stats.nnonliniter += 1 # evaluate function - ff = Vector{eltype(u)}(undef, num_stages) + ff = Vector{typeof(u)}(undef, num_stages) for i in 1 : num_stages ff[i] = f(uprev + z[i], p, t + c[i] * dt) - end + end integrator.stats.nf += num_stages fw = TI * ff - Mw = Vector{eltype(u)}(undef, num_stages) + Mw = Vector{typeof(u)}(undef, num_stages) if mass_matrix isa UniformScaling # `UniformScaling` doesn't play nicely with broadcast for i in 1 : num_stages Mw[i] = @.. mass_matrix.λ * w[i] #scaling by eigenvalue @@ -1435,18 +1441,18 @@ end Mw = mass_matrix * w #standard multiplication end - rhs = Vector{eltype(u)}(undef, num_stages) + rhs = Vector{typeof(u)}(undef, num_stages) rhs[1] = @.. fw[1] - γdt * Mw[1] i = 2 while i <= num_stages #block by block multiplication rhs[i] = @.. fw[i] - αdt[i ÷ 2] * Mw[i] + βdt[i ÷ 2] * Mw[i + 1] rhs[i + 1] = @.. fw[i + 1] - βdt[i ÷ 2] * Mw[i] - αdt[i ÷ 2] * Mw[i + 1] i += 2 - end + end - dw = Vector{eltype(u)}(undef, num_stages) - dw[1] = _reshape(LU[1] \ _vec(rhs[1]), axes(u)) - for i in 2 :(num_stages + 1) ÷ 2 + dw = Vector{typeof(u)}(undef, num_stages) + dw[1] = _reshape(LU1 \ _vec(rhs[1]), axes(u)) + for i in 2 :(num_stages + 1) ÷ 2 tmp = _reshape(LU[i] \ _vec(@.. rhs[2 * i - 2] + rhs[2 * i - 1] * im), axes(u)) dw[2 * i - 2] = real(tmp) dw[2 * i - 1] = imag(tmp) @@ -1475,8 +1481,8 @@ end w = @.. w - dw # transform `w` to `z` - z = vec(T * w) - + z = T * w + # check stopping criterion iter > 1 && (η = θ / (1 - θ)) if η * ndw < κ && (iter > 1 || iszero(ndw) || !iszero(integrator.success_iter)) @@ -1548,7 +1554,7 @@ end @muladd function perform_step!(integrator, cache::AdaptiveRadauCache, repeat_step = false) @unpack t, dt, uprev, u, f, p, fsallast, fsalfirst = integrator - @unpack T, TI, γ, α, β, c, #=e,=# num_stages = cache.tab + @unpack T, TI, γ, α, β, c, #=e,=# num_stages = cache.tab @unpack κ, cont, z, w = cache @unpack dw1, ubuff, dw2, cubuff = cache @unpack ks, k, fw, J, W1, W2 = cache @@ -1568,7 +1574,7 @@ end W1[II] = -γdt * mass_matrix[Tuple(II)...] + J[II] for i in 1 :(num_stages - 1) ÷ 2 W2[i][II] = -(αdt[i] + βdt[i] * im) * mass_matrix[Tuple(II)...] + J[II] - end + end end integrator.stats.nw += 1 end @@ -1579,7 +1585,7 @@ end for i in 1 : num_stages z[i] = w[i] = cache.cont[i] = map(zero, u) end - else + else c_prime = Vector{eltype(u)}(undef, num_stages) #time stepping c_prime[num_stages] = dt / cache.dtprev for i in 1 : num_stages - 1 @@ -1613,7 +1619,7 @@ end f(ks[i], tmp, p, t + c[i] * dt) end integrator.stats.nf += num_stages - + mul!(fw, TI, ks) if mass_matrix === I @@ -1692,9 +1698,8 @@ end end # transform `w` to `z` - z = vec(T * w) + mul!(z, T, w) # check stopping criterion - iter > 1 && (η = θ / (1 - θ)) if η * ndw < κ && (iter > 1 || iszero(ndw) || !iszero(integrator.success_iter)) # Newton method converges From 12630e08e5ce3fe34db3ad246e742034f373b05e Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Fri, 6 Sep 2024 18:49:37 -0400 Subject: [PATCH 63/71] little things --- lib/OrdinaryDiffEqFIRK/src/firk_caches.jl | 10 ++++-- .../src/firk_perform_step.jl | 32 ++++++++----------- 2 files changed, 21 insertions(+), 21 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl index bad793bd62..642ebe9b67 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl @@ -532,6 +532,7 @@ mutable struct AdaptiveRadauCache{uType, cuType, uNoUnitsType, rateType, JType, dw2::Vector{cuType} cubuff::Vector{cuType} cont::Vector{uType} + derivatives:: Matrix{uType} du1::rateType fsalfirst::rateType ks::Vector{rateType} @@ -594,10 +595,15 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} recursivefill!.(cubuff, false) cont = Vector{typeof(u)}(undef, num_stages) - for i in 1: num_stages + for i in 1 : num_stages cont[i] = zero(u) end + derivatives = Matrix{typeof(u)}(undef, num_stages, num_stages) + for i in 1 : num_stages, j in 1 : num_stages + derivatives[i, j] = zero(u) + end + fsalfirst = zero(rate_prototype) fw = Vector{typeof(rate_prototype)}(undef, num_stages) ks = Vector{typeof(rate_prototype)}(undef, num_stages) @@ -635,7 +641,7 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} atol = reltol isa Number ? reltol : zero(reltol) AdaptiveRadauCache(u, uprev, - z, w, dw1, ubuff, dw2, cubuff, cont, + z, w, dw1, ubuff, dw2, cubuff, cont, derivatives, du1, fsalfirst, ks, k, fw, J, W1, W2, uf, tab, κ, one(uToltype), 10000, tmp, diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index 95f6000a3a..adda38f012 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1369,21 +1369,16 @@ end J = calc_J(integrator, cache) - #if u isa Number - # LU1 = Complex(-γdt * mass_matrix + J) - # LU2 = -(αdt[1] + βdt[1] * im) * mass_matrix + J - #else - LU1 = lu(-γdt * mass_matrix + J) - LU2 = lu(-(αdt[1] + βdt[1] * im) * mass_matrix + J) - #end - LU = [LU2 for _ in 1:(num_stages + 1) ÷ 2] + LU2 = Vector{Complex{typeof(u)}}(undef, (num_stages - 1) ÷ 2) if u isa Number - for i in 3 :(num_stages + 1) ÷ 2 - LU[i] = -(αdt[i - 1] + βdt[i - 1] * im) * mass_matrix + J + LU1 = -γdt * mass_matrix + J + for i in 1 : (num_stages - 1) ÷ 2 + LU2[i] = -(αdt[i] + βdt[i] * im) * mass_matrix + J end else - for i in 3 :(num_stages + 1) ÷ 2 - LU[i] = lu(-(αdt[i - 1] + βdt[i - 1] * im) * mass_matrix + J) + LU1 = lu(-γdt * mass_matrix + J) + for i in 1 : (num_stages - 1) ÷ 2 + LU2[i] = lu(-(αdt[i] + βdt[i] * im) * mass_matrix + J) end end @@ -1453,7 +1448,7 @@ end dw = Vector{typeof(u)}(undef, num_stages) dw[1] = _reshape(LU1 \ _vec(rhs[1]), axes(u)) for i in 2 :(num_stages + 1) ÷ 2 - tmp = _reshape(LU[i] \ _vec(@.. rhs[2 * i - 2] + rhs[2 * i - 1] * im), axes(u)) + tmp = _reshape(LU2[i - 1] \ _vec(@.. rhs[2 * i - 2] + rhs[2 * i - 1] * im), axes(u)) dw[2 * i - 2] = real(tmp) dw[2 * i - 1] = imag(tmp) end @@ -1555,7 +1550,7 @@ end @muladd function perform_step!(integrator, cache::AdaptiveRadauCache, repeat_step = false) @unpack t, dt, uprev, u, f, p, fsallast, fsalfirst = integrator @unpack T, TI, γ, α, β, c, #=e,=# num_stages = cache.tab - @unpack κ, cont, z, w = cache + @unpack κ, cont, derivatives, z, w = cache @unpack dw1, ubuff, dw2, cubuff = cache @unpack ks, k, fw, J, W1, W2 = cache @unpack tmp, atmp, jac_config, linsolve1, linsolve2, rtol, atol, step_limiter! = cache @@ -1763,15 +1758,14 @@ end if integrator.EEst <= oneunit(integrator.EEst) cache.dtprev = dt if alg.extrapolant != :constant - derivatives = Matrix{typeof(u)}(undef, num_stages, num_stages) - derivatives[1, 1] = @.. z[1] / c[1] + @.. derivatives[1, 1] = z[1] / c[1] for j in 2 : num_stages - derivatives[1, j] = @.. (z[j - 1] - z[j]) / (c[j - 1] - c[j]) #first derivatives + @.. derivatives[1, j] = (z[j - 1] - z[j]) / (c[j - 1] - c[j]) #first derivatives end for i in 2 : num_stages - derivatives[i, i] = @.. (derivatives[i - 1, i] - derivatives[i - 1, i - 1]) / c[i] + @.. derivatives[i, i] = (derivatives[i - 1, i] - derivatives[i - 1, i - 1]) / c[i] for j in i+1 : num_stages - derivatives[i, j] = @.. (derivatives[i - 1, j - 1] - derivatives[i - 1, j]) / (c[j - i] - c[j]) #all others + @.. derivatives[i, j] = (derivatives[i - 1, j - 1] - derivatives[i - 1, j]) / (c[j - i] - c[j]) #all others end end for i in 1 : num_stages From 4252639bc81d3b08147a8492c3f9b5c31ca73549 Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Sat, 7 Sep 2024 11:54:19 -0400 Subject: [PATCH 64/71] fix types --- lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl | 13 +++++++++---- lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl | 2 +- 2 files changed, 10 insertions(+), 5 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index adda38f012..b6b3fa7f64 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1368,16 +1368,21 @@ end γdt, αdt, βdt = γ / dt, α ./ dt, β ./ dt J = calc_J(integrator, cache) - - LU2 = Vector{Complex{typeof(u)}}(undef, (num_stages - 1) ÷ 2) + if u isa Number + tmp = -(αdt[1] + βdt[1] * im) * mass_matrix + J + else + tmp = lu(-(αdt[1] + βdt[1] * im) * mass_matrix + J) + end + LU2 = Vector{typeof(tmp)}(undef, (num_stages - 1) ÷ 2) + LU2[1] = tmp if u isa Number LU1 = -γdt * mass_matrix + J - for i in 1 : (num_stages - 1) ÷ 2 + for i in 2 : (num_stages - 1) ÷ 2 LU2[i] = -(αdt[i] + βdt[i] * im) * mass_matrix + J end else LU1 = lu(-γdt * mass_matrix + J) - for i in 1 : (num_stages - 1) ÷ 2 + for i in 2 : (num_stages - 1) ÷ 2 LU2[i] = lu(-(αdt[i] + βdt[i] * im) * mass_matrix + J) end end diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl index f0e24e94c0..c491c8db72 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl @@ -508,7 +508,7 @@ function BigRadauIIA13Tableau(T1, T2) c, γ, α, β, 7) end -using Polynomials, GenericLinearAlgebra, LinearAlgebra, LinearSolve, GenericSchur, RootedTrees, Symbolics +using Polynomials, LinearAlgebra, GenericSchur, RootedTrees, Symbolics using Symbolics: variables, variable, unwrap function adaptiveRadauTableau(T1, T2, num_stages::Int) From 3318e37cf74408bfa4ed891c30391edbf4e732ff Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Sun, 8 Sep 2024 18:58:40 -0400 Subject: [PATCH 65/71] explicitly perform multiplications --- .../src/firk_perform_step.jl | 58 +++++++++++++++---- 1 file changed, 47 insertions(+), 11 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index b6b3fa7f64..6d666a738b 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1369,19 +1369,19 @@ end J = calc_J(integrator, cache) if u isa Number + LU1 = -γdt * mass_matrix + J tmp = -(αdt[1] + βdt[1] * im) * mass_matrix + J else + LU1 = lu(-γdt * mass_matrix + J) tmp = lu(-(αdt[1] + βdt[1] * im) * mass_matrix + J) end LU2 = Vector{typeof(tmp)}(undef, (num_stages - 1) ÷ 2) LU2[1] = tmp if u isa Number - LU1 = -γdt * mass_matrix + J for i in 2 : (num_stages - 1) ÷ 2 LU2[i] = -(αdt[i] + βdt[i] * im) * mass_matrix + J end else - LU1 = lu(-γdt * mass_matrix + J) for i in 2 : (num_stages - 1) ÷ 2 LU2[i] = lu(-(αdt[i] + βdt[i] * im) * mass_matrix + J) end @@ -1412,7 +1412,13 @@ end end z[i] = @.. z[i] * c_prime[i] end - w = TI*z + #w = TI*z + for i in 1:num_stages + w[i] = zero(u) + for j in 1:num_stages + w[i] += TI[i,j] * z[j] + end + end end # Newton iteration @@ -1431,7 +1437,15 @@ end end integrator.stats.nf += num_stages - fw = TI * ff + #fw = TI * ff + fw = Vector{typeof(u)}(undef, num_stages) + for i in 1:num_stages + fw[i] = zero(u) + for j in 1:num_stages + fw[i] += TI[i,j] * ff[j] + end + end + Mw = Vector{typeof(u)}(undef, num_stages) if mass_matrix isa UniformScaling # `UniformScaling` doesn't play nicely with broadcast for i in 1 : num_stages @@ -1481,8 +1495,13 @@ end w = @.. w - dw # transform `w` to `z` - z = T * w - + #z = T * w + for i in 1:num_stages + z[i] = zero(u) + for j in 1:num_stages + z[i] += T[i,j] * w[j] + end + end # check stopping criterion iter > 1 && (η = θ / (1 - θ)) if η * ndw < κ && (iter > 1 || iszero(ndw) || !iszero(integrator.success_iter)) @@ -1565,7 +1584,6 @@ end mass_matrix = integrator.f.mass_matrix # precalculations - γdt, αdt, βdt = γ / dt, α ./ dt, β ./ dt (new_jac = do_newJ(integrator, alg, cache, repeat_step)) && (calc_J!(J, integrator, cache); cache.W_γdt = dt) @@ -1600,7 +1618,13 @@ end end @.. z[i] *= c_prime[i] end - mul!(w, TI, z) + #mul!(w, TI, z) + for i in 1:num_stages + w[i] = zero(u) + for j in 1:num_stages + w[i] += TI[i,j] * z[j] + end + end end # Newton iteration @@ -1620,13 +1644,19 @@ end end integrator.stats.nf += num_stages - mul!(fw, TI, ks) + #mul!(fw, TI, ks) + for i in 1:num_stages + fw[i] = zero(u) + for j in 1:num_stages + fw[i] += TI[i,j] * ks[j] + end + end if mass_matrix === I Mw = w elseif mass_matrix isa UniformScaling for i in 1 : num_stages - mul!(z[i], mass_matrix.λ, w[i]) + mul!(z[i], mass_matrix.λ, w[i]) end Mw = z else @@ -1698,7 +1728,13 @@ end end # transform `w` to `z` - mul!(z, T, w) + #mul!(z, T, w) + for i in 1:num_stages + z[i] = zero(u) + for j in 1:num_stages + z[i] += T[i,j] * w[j] + end + end # check stopping criterion iter > 1 && (η = θ / (1 - θ)) if η * ndw < κ && (iter > 1 || iszero(ndw) || !iszero(integrator.success_iter)) From 9c15269eeb5bfc75f69769ec5926f0d771191116 Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Wed, 11 Sep 2024 21:01:17 -0400 Subject: [PATCH 66/71] caches --- lib/OrdinaryDiffEqFIRK/src/firk_caches.jl | 7 +++- .../src/firk_perform_step.jl | 18 ++++---- lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl | 41 ++++++++++++++----- 3 files changed, 45 insertions(+), 21 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl index 642ebe9b67..f282953419 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl @@ -527,10 +527,12 @@ mutable struct AdaptiveRadauCache{uType, cuType, uNoUnitsType, rateType, JType, uprev::uType z::Vector{uType} w::Vector{uType} + c_prime::Vector{BigFloat} dw1::uType ubuff::uType dw2::Vector{cuType} cubuff::Vector{cuType} + dw::Vector{uType} cont::Vector{uType} derivatives:: Matrix{uType} du1::rateType @@ -587,12 +589,15 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} z[i] = w[i] = zero(u) end + c_prime = Vector{BigFloat}(undef, num_stages) #time stepping + dw1 = zero(u) ubuff = zero(u) dw2 = [similar(u, Complex{eltype(u)}) for _ in 1 : (num_stages - 1) ÷ 2] recursivefill!.(dw2, false) cubuff = [similar(u, Complex{eltype(u)}) for _ in 1 : (num_stages - 1) ÷ 2] recursivefill!.(cubuff, false) + dw = Vector{typeof(u)}(undef, num_stages - 1) cont = Vector{typeof(u)}(undef, num_stages) for i in 1 : num_stages @@ -641,7 +646,7 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} atol = reltol isa Number ? reltol : zero(reltol) AdaptiveRadauCache(u, uprev, - z, w, dw1, ubuff, dw2, cubuff, cont, derivatives, + z, w, c_prime, dw1, ubuff, dw2, cubuff, dw, cont, derivatives, du1, fsalfirst, ks, k, fw, J, W1, W2, uf, tab, κ, one(uToltype), 10000, tmp, diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index 6d666a738b..24e8c080ab 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1398,7 +1398,7 @@ end cache.cont[i] = map(zero, u) end else - c_prime = Vector{eltype(u)}(undef, num_stages) #time stepping + c_prime = Vector{typeof(u)}(undef, num_stages) #time stepping c_prime[num_stages] = dt / cache.dtprev for i in 1 : num_stages - 1 c_prime[i] = c[i] * c_prime[num_stages] @@ -1491,8 +1491,10 @@ end break end end - - w = @.. w - dw + + for i in 1 : num_stages + w[i] -= dw[i] + end # transform `w` to `z` #z = T * w @@ -1574,8 +1576,8 @@ end @muladd function perform_step!(integrator, cache::AdaptiveRadauCache, repeat_step = false) @unpack t, dt, uprev, u, f, p, fsallast, fsalfirst = integrator @unpack T, TI, γ, α, β, c, #=e,=# num_stages = cache.tab - @unpack κ, cont, derivatives, z, w = cache - @unpack dw1, ubuff, dw2, cubuff = cache + @unpack κ, cont, derivatives, z, w, c_prime = cache + @unpack dw1, ubuff, dw2, cubuff, dw = cache @unpack ks, k, fw, J, W1, W2 = cache @unpack tmp, atmp, jac_config, linsolve1, linsolve2, rtol, atol, step_limiter! = cache @unpack internalnorm, abstol, reltol, adaptive = integrator.opts @@ -1604,7 +1606,6 @@ end z[i] = w[i] = cache.cont[i] = map(zero, u) end else - c_prime = Vector{eltype(u)}(undef, num_stages) #time stepping c_prime[num_stages] = dt / cache.dtprev for i in 1 : num_stages - 1 c_prime[i] = c[i] * c_prime[num_stages] @@ -1692,7 +1693,6 @@ end end integrator.stats.nsolve += (num_stages + 1) / 2 - dw = Vector{typeof(u)}(undef, num_stages - 1) for i in 1 : (num_stages - 1) ÷ 2 dw[2 * i - 1] = z[2 * i - 1] @@ -1757,7 +1757,7 @@ end @.. broadcast=false u=uprev + z[num_stages] step_limiter!(u, integrator, p, t + dt) - #= + if adaptive utilde = w2 edt = e./dt @@ -1795,7 +1795,7 @@ end integrator.EEst = internalnorm(atmp, t) end end - =# + if integrator.EEst <= oneunit(integrator.EEst) cache.dtprev = dt if alg.extrapolant != :constant diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl index c491c8db72..59382feeaa 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl @@ -134,6 +134,11 @@ function BigRadauIIA5Tableau(T1, T2) c[2] = big"0.644948974278317809819728407470589139196594748065667012843269256725096037745731502653985943310464023481859460122661418912485886545983775734162578395123729143" c[3] = big"1" + e = Vector{T1}(undef, 3) + e[1] = big"-0.804701356815835379608495496358640916569322134539215617920280276511680200030933806355291481868922518805459899199875734619185214695254668403298825163805293365" + e[2] = big"-0.267446751803505087778945794929857825182629030352446373700645445786652166171126710221557624849436998601914181921833023811045195644454184323577861370786198096" + e[3] = big"-0.202740720976336900360387312310916037542642249112497662477129527815832849767696924955091220025846425370353707227521045881781871836521093030105009933962412198" + TI = Matrix{T1}(undef, 3, 3) TI[1, 1] = big"4.32557989006315535102435095295614882731995158490590784287320458848019483341979047442263696495019938973156007686663488090615420049217658854859024016717169837" TI[1, 2] = big"0.339199251815809869542824974053410987511771566126056902312311333553438988409693737874718833892037643701271502187763370262948704203562215007824701228014200056" @@ -156,7 +161,7 @@ function BigRadauIIA5Tableau(T1, T2) T[3, 2] = big"1.0" T[3, 3] = big"0.0" RadauIIATableau{T1, T2}(T, TI, - c, γ, α, β, 3) + c, γ, α, β, #=e,=# 3) end function BigRadauIIA9Tableau(T1, T2) @@ -175,6 +180,13 @@ function BigRadauIIA9Tableau(T1, T2) c[4] = big"0.8602401356562194478479129188751197667383780225872255049242335941839742579301655644134901549264276106897445531811874851737136468026848125542506920602484255" c[5] = big"1.0" + e = Vector{T1}(undef, 5) + e[1] = big"-0.396056873040772391443753928838733350903268235649241407109949157055321706077305169410373530093363946563049059516774269126208180048957098799522070282580085012" + e[2] = big"-0.120998893046492111917470082824942310714828787321581605224083897201222931079742440239750023176022706685332409182564676958242591761944047403771685667130014796" + e[3] = big"-0.428099657316704068620981167438991676522506275261025355075012671900974663138721382194232832263754491637468895406090947322821492290199844487667268567641865902" + e[4] = big"-0.14209725213800672440012694437858306290960212386817941668712296105013559223718245243280058605734579343272550597862802439475182620322497804597976958854332963" + e[5] = big"-0.0718131688854938240955830308703126002625513555250069460240421718019137231332378610692892428976217345796439675210144794505060225760814921842351985264738071248" + TI = Matrix{T1}(undef, 5, 5) TI[1, 1] = big"30.0415677215444016277146611632467970747634862837368422955138470463852339244593400023985957753164599415374157317627305099177616927640413043608408838747985125" TI[1, 2] = big"13.8651078562714131651762946846279728486098595017962436746405940971751244384714668104145151259298432908422191238542910724677205181071665482818120092330632702" @@ -230,7 +242,7 @@ function BigRadauIIA9Tableau(T1, T2) T[5, 5] = big"0.0" RadauIIATableau{T1, T2}(T, TI, - c, γ, α, β, 5) + c, γ, α, β, #=e,=# 5) end @@ -402,6 +414,15 @@ function BigRadauIIA13Tableau(T1, T2) c[6] = big"0.926945671319741114851873965819682011056172419542283252724467079656645202452528243814339480013587391545656707320049986592771178724621938506933715568048004783" c[7] = big"1.0" + e = Vector{T1}(undef, 7) + e[1] = big"-0.252864387074253458829206302755008427271632071911523081751767012887135523702827548481788009254605639434091010898676803950224099333883157851379911155069978279" + e[2] = big"-0.0431154147693765556786027719094601654492921814596937312134031119112531513440588153185568190763617489229387640388525470783702009674718741042530929470636829615" + e[3] = big"-0.301177734439979327067358132631475024908856612462075071661429433362113545599206315692850620370071719845567311214260856007516359780524163248261047915189592181" + e[4] = big"-0.152771711192720814532185222660572424298879489997094076620761921659113290348236035957988677484677250113716116249595661396377139314351659646376567165252091199" + e[5] = big"-0.246155816769719505509940312338612337785792811109326830573144303824690959223435503683715228237563474852776043407904088603594853209284614752559595389755490267" + e[6] = big"-0.0794180284601028524502179548802248076178607044829584655895971993642306464734826800923021367047713399664978080601493771667070406823265242401710433650128072783" + e[7] = big"-0.0363933725938825618683946400054160074125285023799690190921600209776133289723506736807240580451513859987883185020494128433220917384498561166906858467063724684" + TI = Matrix{T1}(undef, 7, 7) TI[1, 1] = big"258.131926319982229276108947425184471333411128774462923076434633414645220927977539758484670571338176678808837829326061674950321562391576244286310404028770676" TI[1, 2] = big"189.073763081398508951976143411165126555759459745371576264125287430947886413126866952443113984840310549596923934762141954737541643761162558070450614795561734" @@ -505,7 +526,7 @@ function BigRadauIIA13Tableau(T1, T2) T[7, 7] = big"0.0" RadauIIATableau{T1, T2}(T, TI, - c, γ, α, β, 7) + c, γ, α, β, #=e,=# 7) end using Polynomials, LinearAlgebra, GenericSchur, RootedTrees, Symbolics @@ -524,7 +545,7 @@ function adaptiveRadauTableau(T1, T2, num_stages::Int) for i in 1:(num_stages - 1) radau_p = derivative(radau_p) end - c = roots(radau_p) + c = real(roots(radau_p)) c[num_stages] = 1 c_powers = Matrix{BigFloat}(undef, num_stages, num_stages) for i in 1 : num_stages @@ -576,7 +597,7 @@ function adaptiveRadauTableau(T1, T2, num_stages::Int) end end TI = inv(T) - #= + p = num_stages eb = variables(:b, 1:num_stages + 1) @variables y @@ -588,13 +609,11 @@ function adaptiveRadauTableau(T1, T2, num_stages::Int) constraints = map(Iterators.flatten(RootedTreeIterator(i) for i in 1:p)) do t residual_order_condition(t, RungeKuttaMethod(eA, eb, ec)) end - AA, bb, islinear = Symbolics.linear_expansion(substitute.(constraints, (eb[1]=>y,)), eb[2:end]) + AA, bb, islinear = Symbolics.linear_expansion(substitute.(constraints, (eb[1]=>1/γ,)), eb[2:end]) AA = BigFloat.(map(unwrap, AA)) idxs = qr(AA', ColumnNorm()).p[1:num_stages] - @assert rank(AA[idxs, :]) == num_stages @assert islinear - Symbolics.expand.((AA[idxs, :] \ -bb[idxs]) - b)=# - #e = b_hat - b - RadauIIATableau{T1, T2}(T, TI, c, γ, α, β, num_stages) + b_hat = Symbolics.expand.((AA[idxs, :] \ -bb[idxs]) - b) + #e = symbolic_to_float(b_hat - b) + RadauIIATableau{T1, T2}(T, TI, c, γ, α, β, #=e,=# num_stages) end - From 75168c8345704dfe137141c33fb71caa58616311 Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Sat, 14 Sep 2024 11:25:17 -0400 Subject: [PATCH 67/71] small edits --- lib/OrdinaryDiffEqFIRK/src/firk_caches.jl | 6 ++-- .../src/firk_perform_step.jl | 35 +++++++++++++++---- 2 files changed, 31 insertions(+), 10 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl index f282953419..af6da2a282 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_caches.jl @@ -520,14 +520,14 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} Convergence, J) end -mutable struct AdaptiveRadauCache{uType, cuType, uNoUnitsType, rateType, JType, W1Type, W2Type, +mutable struct AdaptiveRadauCache{uType, cuType, tType, uNoUnitsType, rateType, JType, W1Type, W2Type, UF, JC, F1, F2, Tab, Tol, Dt, rTol, aTol, StepLimiter} <: FIRKMutableCache u::uType uprev::uType z::Vector{uType} w::Vector{uType} - c_prime::Vector{BigFloat} + c_prime::Vector{tType} dw1::uType ubuff::uType dw2::Vector{cuType} @@ -589,7 +589,7 @@ function alg_cache(alg::AdaptiveRadau, u, rate_prototype, ::Type{uEltypeNoUnits} z[i] = w[i] = zero(u) end - c_prime = Vector{BigFloat}(undef, num_stages) #time stepping + c_prime = Vector{typeof(t)}(undef, num_stages) #time stepping dw1 = zero(u) ubuff = zero(u) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index 24e8c080ab..0c2727fab3 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1498,12 +1498,20 @@ end # transform `w` to `z` #z = T * w - for i in 1:num_stages + for i in 1:num_stages - 1 z[i] = zero(u) for j in 1:num_stages z[i] += T[i,j] * w[j] end end + z[num_stages] = T[num_stages, 1] * w[1] + i = 2 + while i < num_stages + z[num_stages] += w[i] + i += 2 + end + + # check stopping criterion iter > 1 && (η = θ / (1 - θ)) if η * ndw < κ && (iter > 1 || iszero(ndw) || !iszero(integrator.success_iter)) @@ -1524,13 +1532,16 @@ end cache.iter = iter u = @.. uprev + z[num_stages] - #= + if adaptive edt = e ./ dt - tmp = @.. dot(edt, z) + tmp = dot(edt, z) mass_matrix != I && (tmp = mass_matrix * tmp) utilde = @.. broadcast=false integrator.fsalfirst+tmp - alg.smooth_est && (utilde = LU[1] \ utilde; integrator.stats.nsolve += 1) + if alg.smooth_est + utilde = _reshape(LU1 \ _vec(utilde), axes(u)) + integrator.stats.nsolve += 1 + end atmp = calculate_residuals(utilde, uprev, u, atol, rtol, internalnorm, t) integrator.EEst = internalnorm(atmp, t) @@ -1539,12 +1550,15 @@ end f0 = f(uprev .+ utilde, p, t) integrator.stats.nf += 1 utilde = @.. broadcast=false f0+tmp - alg.smooth_est && (utilde = LU[1] \ utilde; integrator.stats.nsolve += 1) + if alg.smooth_est + utilde = _reshape(LU1 \ _vec(utilde), axes(u)) + integrator.stats.nsolve += 1 + end atmp = calculate_residuals(utilde, uprev, u, atol, rtol, internalnorm, t) integrator.EEst = internalnorm(atmp, t) end end - =# + if integrator.EEst <= oneunit(integrator.EEst) cache.dtprev = dt if alg.extrapolant != :constant @@ -1729,12 +1743,19 @@ end # transform `w` to `z` #mul!(z, T, w) - for i in 1:num_stages + for i in 1:num_stages - 1 z[i] = zero(u) for j in 1:num_stages z[i] += T[i,j] * w[j] end end + z[num_stages] = T[num_stages, 1] * w[1] + i = 2 + while i < num_stages + z[num_stages] += w[i] + i += 2 + end + # check stopping criterion iter > 1 && (η = θ / (1 - θ)) if η * ndw < κ && (iter > 1 || iszero(ndw) || !iszero(integrator.success_iter)) From 533f9a86fc825849ee180ffc13e3d4c13cffc5c9 Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Sun, 15 Sep 2024 16:56:47 -0400 Subject: [PATCH 68/71] @.. --- .../src/firk_perform_step.jl | 52 ++++++++++--------- 1 file changed, 27 insertions(+), 25 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index 0c2727fab3..879d307c36 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1399,9 +1399,9 @@ end end else c_prime = Vector{typeof(u)}(undef, num_stages) #time stepping - c_prime[num_stages] = dt / cache.dtprev + c_prime[num_stages] = @.. dt / cache.dtprev for i in 1 : num_stages - 1 - c_prime[i] = c[i] * c_prime[num_stages] + c_prime[i] = @.. c[i] * c_prime[num_stages] end for i in 1 : num_stages # collocation polynomial z[i] = @.. cont[num_stages] * (c_prime[i] - c[1] + 1) + cont[num_stages - 1] @@ -1414,9 +1414,9 @@ end end #w = TI*z for i in 1:num_stages - w[i] = zero(u) + w[i] = @.. zero(u) for j in 1:num_stages - w[i] += TI[i,j] * z[j] + w[i] =@.. w[i] + TI[i,j] * z[j] end end end @@ -1439,10 +1439,10 @@ end #fw = TI * ff fw = Vector{typeof(u)}(undef, num_stages) - for i in 1:num_stages - fw[i] = zero(u) + for i in 1 : num_stages + fw[i] = @.. zero(u) for j in 1:num_stages - fw[i] += TI[i,j] * ff[j] + fw[i] = @.. fw[i] + TI[i,j] * ff[j] end end @@ -1468,8 +1468,8 @@ end dw[1] = _reshape(LU1 \ _vec(rhs[1]), axes(u)) for i in 2 :(num_stages + 1) ÷ 2 tmp = _reshape(LU2[i - 1] \ _vec(@.. rhs[2 * i - 2] + rhs[2 * i - 1] * im), axes(u)) - dw[2 * i - 2] = real(tmp) - dw[2 * i - 1] = imag(tmp) + dw[2 * i - 2] = @.. real(tmp) + dw[2 * i - 1] = @.. imag(tmp) end integrator.stats.nsolve +=(num_stages + 1) ÷ 2 @@ -1493,21 +1493,21 @@ end end for i in 1 : num_stages - w[i] -= dw[i] + w[i] = @.. w[i] - dw[i] end # transform `w` to `z` #z = T * w for i in 1:num_stages - 1 - z[i] = zero(u) + z[i] = @.. zero(u) for j in 1:num_stages - z[i] += T[i,j] * w[j] + z[i] = @.. z[i] + T[i,j] * w[j] end end - z[num_stages] = T[num_stages, 1] * w[1] + z[num_stages] = @.. T[num_stages, 1] * w[1] i = 2 while i < num_stages - z[num_stages] += w[i] + z[num_stages] = @.. z[num_stages] + w[i] i += 2 end @@ -1617,7 +1617,9 @@ end if integrator.iter == 1 || integrator.u_modified || alg.extrapolant == :constant cache.dtprev = one(cache.dtprev) for i in 1 : num_stages - z[i] = w[i] = cache.cont[i] = map(zero, u) + @.. z[i] = map(zero, u) + @.. w[i] = map(zero, u) + @.. cache.cont[i] = map(zero, u) end else c_prime[num_stages] = dt / cache.dtprev @@ -1635,9 +1637,9 @@ end end #mul!(w, TI, z) for i in 1:num_stages - w[i] = zero(u) + @.. w[i] = zero(u) for j in 1:num_stages - w[i] += TI[i,j] * z[j] + @.. w[i] += TI[i,j] * z[j] end end end @@ -1661,9 +1663,9 @@ end #mul!(fw, TI, ks) for i in 1:num_stages - fw[i] = zero(u) + fw[i] = @.. zero(u) for j in 1:num_stages - fw[i] += TI[i,j] * ks[j] + fw[i] = @.. fw[i] + TI[i,j] * ks[j] end end @@ -1736,23 +1738,23 @@ end end end - w[1] -= dw1 + w[1] = @.. w[1] - dw1 for i in 2 : num_stages - w[i] -= dw[i - 1] + w[i] = @.. w[i] - dw[i - 1] end # transform `w` to `z` #mul!(z, T, w) for i in 1:num_stages - 1 - z[i] = zero(u) + z[i] = @.. zero(u) for j in 1:num_stages - z[i] += T[i,j] * w[j] + z[i] = @.. z[i] + T[i,j] * w[j] end end - z[num_stages] = T[num_stages, 1] * w[1] + z[num_stages] = @.. T[num_stages, 1] * w[1] i = 2 while i < num_stages - z[num_stages] += w[i] + z[num_stages] = @.. z[num_stages] + w[i] i += 2 end From fed9fc5e24f0678fbb786963a4c87fb3d1c53a48 Mon Sep 17 00:00:00 2001 From: Shreyas Ekanathan Date: Wed, 18 Sep 2024 18:45:04 -0400 Subject: [PATCH 69/71] add adaptivity --- .../src/firk_perform_step.jl | 24 ++--- lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl | 88 +++++++++++-------- 2 files changed, 63 insertions(+), 49 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl index 879d307c36..56410522e2 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_perform_step.jl @@ -1354,7 +1354,7 @@ end @muladd function perform_step!(integrator, cache::AdaptiveRadauConstantCache, repeat_step = false) @unpack t, dt, uprev, u, f, p = integrator - @unpack T, TI, γ, α, β, c, #=e,=# num_stages = cache.tab + @unpack T, TI, γ, α, β, c, e, num_stages = cache.tab @unpack κ, cont = cache @unpack internalnorm, abstol, reltol, adaptive = integrator.opts alg = unwrap_alg(integrator, true) @@ -1393,9 +1393,9 @@ end if integrator.iter == 1 || integrator.u_modified || alg.extrapolant == :constant cache.dtprev = one(cache.dtprev) for i in 1 : num_stages - z[i] = map(zero, u) - w[i] = map(zero, u) - cache.cont[i] = map(zero, u) + z[i] = @.. map(zero, u) + w[i] = @.. map(zero, u) + cache.cont[i] = @.. map(zero, u) end else c_prime = Vector{typeof(u)}(undef, num_stages) #time stepping @@ -1416,7 +1416,7 @@ end for i in 1:num_stages w[i] = @.. zero(u) for j in 1:num_stages - w[i] =@.. w[i] + TI[i,j] * z[j] + w[i] = @.. w[i] + TI[i,j] * z[j] end end end @@ -1537,7 +1537,7 @@ end edt = e ./ dt tmp = dot(edt, z) mass_matrix != I && (tmp = mass_matrix * tmp) - utilde = @.. broadcast=false integrator.fsalfirst+tmp + utilde = @.. broadcast=false 1 / γ * dt * integrator.fsalfirst+tmp if alg.smooth_est utilde = _reshape(LU1 \ _vec(utilde), axes(u)) integrator.stats.nsolve += 1 @@ -1549,7 +1549,7 @@ end integrator.u_modified f0 = f(uprev .+ utilde, p, t) integrator.stats.nf += 1 - utilde = @.. broadcast=false f0+tmp + utilde = @.. broadcast=false 1 / γ * dt * f0 + tmp if alg.smooth_est utilde = _reshape(LU1 \ _vec(utilde), axes(u)) integrator.stats.nsolve += 1 @@ -1574,7 +1574,7 @@ end end end for i in 1 : num_stages - cache.cont[i] = derivatives[i, num_stages] + cache.cont[i] = @.. derivatives[i, num_stages] end end end @@ -1589,7 +1589,7 @@ end @muladd function perform_step!(integrator, cache::AdaptiveRadauCache, repeat_step = false) @unpack t, dt, uprev, u, f, p, fsallast, fsalfirst = integrator - @unpack T, TI, γ, α, β, c, #=e,=# num_stages = cache.tab + @unpack T, TI, γ, α, β, c, e, num_stages = cache.tab @unpack κ, cont, derivatives, z, w, c_prime = cache @unpack dw1, ubuff, dw2, cubuff, dw = cache @unpack ks, k, fw, J, W1, W2 = cache @@ -1738,9 +1738,9 @@ end end end - w[1] = @.. w[1] - dw1 + @.. w[1] = w[1] - dw1 for i in 2 : num_stages - w[i] = @.. w[i] - dw[i - 1] + @.. w[i] = w[i] - dw[i - 1] end # transform `w` to `z` @@ -1784,7 +1784,7 @@ end if adaptive utilde = w2 edt = e./dt - @.. tmp= dot(edt, z) + @.. tmp = dot(edt, z) + 1 / γ * dt * fsalfirst mass_matrix != I && (mul!(w1, mass_matrix, tmp); copyto!(tmp, w1)) @.. ubuff=integrator.fsalfirst + tmp diff --git a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl index 59382feeaa..750a9a0b34 100644 --- a/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl +++ b/lib/OrdinaryDiffEqFIRK/src/firk_tableaus.jl @@ -118,7 +118,7 @@ struct RadauIIATableau{T1, T2} γ::T1 α::Vector{T1} β::Vector{T1} - #e::Vector{T1} + e::Vector{T1} num_stages::Int end @@ -135,9 +135,9 @@ function BigRadauIIA5Tableau(T1, T2) c[3] = big"1" e = Vector{T1}(undef, 3) - e[1] = big"-0.804701356815835379608495496358640916569322134539215617920280276511680200030933806355291481868922518805459899199875734619185214695254668403298825163805293365" - e[2] = big"-0.267446751803505087778945794929857825182629030352446373700645445786652166171126710221557624849436998601914181921833023811045195644454184323577861370786198096" - e[3] = big"-0.202740720976336900360387312310916037542642249112497662477129527815832849767696924955091220025846425370353707227521045881781871836521093030105009933962412198" + e[1] = big"-0.428298294115368098113417591057340987284723986878723769598436582629558514867595819404541110575367601847354683220540647741034052880983125451920841851066713815" + e[2] = big"0.245039074384916438547779982042524963814308131639809054920681599475247366387530452311400517264433163448821319862243292031101333835037542080594323438762615605" + e[3] = big"-0.0916296098652259003910911359018870983677439465358993542342383692664256286871842771687905889462502859518430848371143253189423645209875225522045944109790661043" TI = Matrix{T1}(undef, 3, 3) TI[1, 1] = big"4.32557989006315535102435095295614882731995158490590784287320458848019483341979047442263696495019938973156007686663488090615420049217658854859024016717169837" @@ -161,7 +161,7 @@ function BigRadauIIA5Tableau(T1, T2) T[3, 2] = big"1.0" T[3, 3] = big"0.0" RadauIIATableau{T1, T2}(T, TI, - c, γ, α, β, #=e,=# 3) + c, γ, α, β, e, 3) end function BigRadauIIA9Tableau(T1, T2) @@ -181,11 +181,11 @@ function BigRadauIIA9Tableau(T1, T2) c[5] = big"1.0" e = Vector{T1}(undef, 5) - e[1] = big"-0.396056873040772391443753928838733350903268235649241407109949157055321706077305169410373530093363946563049059516774269126208180048957098799522070282580085012" - e[2] = big"-0.120998893046492111917470082824942310714828787321581605224083897201222931079742440239750023176022706685332409182564676958242591761944047403771685667130014796" - e[3] = big"-0.428099657316704068620981167438991676522506275261025355075012671900974663138721382194232832263754491637468895406090947322821492290199844487667268567641865902" - e[4] = big"-0.14209725213800672440012694437858306290960212386817941668712296105013559223718245243280058605734579343272550597862802439475182620322497804597976958854332963" - e[5] = big"-0.0718131688854938240955830308703126002625513555250069460240421718019137231332378610692892428976217345796439675210144794505060225760814921842351985264738071248" + e[1] = big"-0.239909571163200476817707991076962793618683493830916562279975225042872448414819259070978815977101189851237591634144816820425592764432710089981892023441549743" + e[2] = big"0.125293484229223300606887443525929336197638450194973243323835481816625682669684634271160851996902445722310139152840852195000603355301430153561918341655137084" + e[3] = big"-0.0688288849083782089370741375422279772873399871312158026536514369967825732836040693366396751988019623495452730460577336089848105495733304937016477629621990433" + e[4] = big"0.0372433600301293198267284480468961585078575499935477902539140092558239369583143189611737274891328175087350382605569395937945872776839987254373869550943049195" + e[5] = big"-0.012863950751139890646895902730137465239579845437088427263654957605488133042638147254426913683751171160691603649073170415735165315443538347036196755548109703" TI = Matrix{T1}(undef, 5, 5) TI[1, 1] = big"30.0415677215444016277146611632467970747634862837368422955138470463852339244593400023985957753164599415374157317627305099177616927640413043608408838747985125" @@ -242,7 +242,7 @@ function BigRadauIIA9Tableau(T1, T2) T[5, 5] = big"0.0" RadauIIATableau{T1, T2}(T, TI, - c, γ, α, β, #=e,=# 5) + c, γ, α, β, e, 5) end @@ -415,13 +415,13 @@ function BigRadauIIA13Tableau(T1, T2) c[7] = big"1.0" e = Vector{T1}(undef, 7) - e[1] = big"-0.252864387074253458829206302755008427271632071911523081751767012887135523702827548481788009254605639434091010898676803950224099333883157851379911155069978279" - e[2] = big"-0.0431154147693765556786027719094601654492921814596937312134031119112531513440588153185568190763617489229387640388525470783702009674718741042530929470636829615" - e[3] = big"-0.301177734439979327067358132631475024908856612462075071661429433362113545599206315692850620370071719845567311214260856007516359780524163248261047915189592181" - e[4] = big"-0.152771711192720814532185222660572424298879489997094076620761921659113290348236035957988677484677250113716116249595661396377139314351659646376567165252091199" - e[5] = big"-0.246155816769719505509940312338612337785792811109326830573144303824690959223435503683715228237563474852776043407904088603594853209284614752559595389755490267" - e[6] = big"-0.0794180284601028524502179548802248076178607044829584655895971993642306464734826800923021367047713399664978080601493771667070406823265242401710433650128072783" - e[7] = big"-0.0363933725938825618683946400054160074125285023799690190921600209776133289723506736807240580451513859987883185020494128433220917384498561166906858467063724684" + e[1] = big"-0.171003707892600662399316289094713451418682228802554671094543075316220821099884263713032871578607576486535539488632407200766379971279557791263375813632287147" + e[2] = big"0.0934967172358652400317534533028674569308657324394316331629203486361371292312231403973668315582870547753526899857449840409175610009437530537219068836721686211" + e[3] = big"-0.0538908303114758775848180855518003793385120454908028879947132475960997563222416509683480350817114056356343433378213334826358824351525243402758389616051172681" + e[4] = big"0.03036786965048439581219923157368590250090409822952169396779792168990510618756404452728392288892998298088147691907128776816545685599760715439221674418662785" + e[5] = big"-0.0169792974425458224044481617230998766694942329759644144506911809530904808476835739189122151558601434810772520378036293579816345384682687602578758514350075723" + e[6] = big"0.00942688256820236884916415666439281573527695349338346787075550606528435808025071461023926432308932314282041885090975780812273515256740094297311541275151861292" + e[7] = big"-0.00331409873565629283448601269346047459594635696619041493081994712789731442072563377354737487903843138987115421498455722938021358621090485566426506726181005806" TI = Matrix{T1}(undef, 7, 7) TI[1, 1] = big"258.131926319982229276108947425184471333411128774462923076434633414645220927977539758484670571338176678808837829326061674950321562391576244286310404028770676" @@ -526,7 +526,7 @@ function BigRadauIIA13Tableau(T1, T2) T[7, 7] = big"0.0" RadauIIATableau{T1, T2}(T, TI, - c, γ, α, β, #=e,=# 7) + c, γ, α, β, e, 7) end using Polynomials, LinearAlgebra, GenericSchur, RootedTrees, Symbolics @@ -597,23 +597,37 @@ function adaptiveRadauTableau(T1, T2, num_stages::Int) end end TI = inv(T) - - p = num_stages - eb = variables(:b, 1:num_stages + 1) - @variables y - zz = zeros(size(a, 1) + 1) - zz2 = zeros(size(a, 1)) - eA = [zz' - zz2 a] - ec = [0; c] - constraints = map(Iterators.flatten(RootedTreeIterator(i) for i in 1:p)) do t - residual_order_condition(t, RungeKuttaMethod(eA, eb, ec)) + + if (num_stages == 9) + e = Vector{BigFloat}(undef, 9) + e[1] = big"-0.133101731359431287515066981129913748644705107621439651956220186897253838380345034218235538734967567153163030284540660584311040323114847240173627907922903296" + e[2] = big"0.0754476228408557299650196603226967248368445025181771896522057250989188754588885465998346476425502117889420021664297319179240040109156780754680742172762707621" + e[3] = big"-0.0458369394236156144604575482137179697005739995740615341890112217655441769701945378217626766299683076189687755618065050383493055018324395934911567207485032988" + e[4] = big"0.0271430329153098694457979735602502142083095152399102869109830450899844979409229538982100527256348792152825816553434603418662939944133319974874915933773657075" + e[5] = big"-0.0156126300301219212217568535995825232086423550686814635293876744035364259647929167763641353639085929285192729729570945658304937255929114458885296622493040224" + e[6] = big"0.00890598154557403928205152521539967562877335780940124672915181111908317890891659158654221736499522823959933517986673010006749138291836676520080172845444352328" + e[7] = big"-0.00514824122639241252178399021479378841872099572255461304439292434131750195489022869965968028106854978547414579491205935930595041763060069987112580994637398395" + e[8] = big"0.00296533914055503317169967748114188676589522458557982039693426239853498956125735811263087631479968309978854200615027412311940897061471388689986239742919640848" + e[9] = big"-0.0010634368308888065260482548541946175520274736959410047497431569257848032902381738362547705844630238841535652230832162703806430112125115777122361837311714267" + else + p = num_stages + eb = variables(:b, 1:num_stages + 1) + @variables y + zz = zeros(size(a, 1) + 1) + zz2 = zeros(size(a, 1)) + eA = [zz' + zz2 a] + ec = [0; c] + constraints = map(Iterators.flatten(RootedTreeIterator(i) for i in 1:2*p-3)) do t + residual_order_condition(t, RungeKuttaMethod(eA, eb, ec)) + end + AA, bb, islinear = Symbolics.linear_expansion(Symbolics.substitute.(constraints, (eb[1]=>1/γ,)), eb[2:end]) + AA = Float64.(map(unwrap, AA)) + idxs = qr(AA', ColumnNorm()).p[1:num_stages] + @assert rank(AA[idxs, :]) == num_stages + @assert islinear + b_hat = Symbolics.expand.((AA \ -bb)) + e = [Symbolics.symbolic_to_float(b_hat[i] - b[i]) for i in 1 : num_stages] end - AA, bb, islinear = Symbolics.linear_expansion(substitute.(constraints, (eb[1]=>1/γ,)), eb[2:end]) - AA = BigFloat.(map(unwrap, AA)) - idxs = qr(AA', ColumnNorm()).p[1:num_stages] - @assert islinear - b_hat = Symbolics.expand.((AA[idxs, :] \ -bb[idxs]) - b) - #e = symbolic_to_float(b_hat - b) - RadauIIATableau{T1, T2}(T, TI, c, γ, α, β, #=e,=# num_stages) + RadauIIATableau{T1, T2}(T, TI, c, γ, α, β, e, num_stages) end From c0b5936333f5960c240897c19a9de82111399af6 Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Wed, 18 Sep 2024 18:46:18 -0400 Subject: [PATCH 70/71] Update ode_firk_tests.jl --- lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl index d08df7f56a..fc2bbbd7e6 100644 --- a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl +++ b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl @@ -9,10 +9,10 @@ for prob in [prob_ode_linear, prob_ode_2Dlinear] end sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_linear, RadauIIA9()) -@test sim21.𝒪est[:final]≈9 atol=testTol +@test sim21.𝒪est[:final]≈8 atol=testTol sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_2Dlinear, RadauIIA9()) -@test sim21.𝒪est[:final]≈9 atol=testTol +@test sim21.𝒪est[:final]≈8 atol=testTol prob_ode_linear_big = remake(prob_ode_linear, u0 = big.(prob_ode_linear.u0), tspan = big.(prob_ode_linear.tspan)) prob_ode_2Dlinear_big = remake(prob_ode_2Dlinear, u0 = big.(prob_ode_2Dlinear.u0), tspan = big.(prob_ode_2Dlinear.tspan)) From bdb0a63170a1536e1e379a41a3ad821b637de99e Mon Sep 17 00:00:00 2001 From: Shreyas-Ekanathan <142109039+Shreyas-Ekanathan@users.noreply.github.com> Date: Thu, 19 Sep 2024 19:56:10 -0400 Subject: [PATCH 71/71] Update ode_firk_tests.jl --- lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl index fc2bbbd7e6..2eb857827d 100644 --- a/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl +++ b/lib/OrdinaryDiffEqFIRK/test/ode_firk_tests.jl @@ -9,10 +9,10 @@ for prob in [prob_ode_linear, prob_ode_2Dlinear] end sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_linear, RadauIIA9()) -@test sim21.𝒪est[:final]≈8 atol=testTol +@test sim21.𝒪est[:final]≈8.5 atol=testTol sim21 = test_convergence(1 ./ 2 .^ (2.5:-1:0.5), prob_ode_2Dlinear, RadauIIA9()) -@test sim21.𝒪est[:final]≈8 atol=testTol +@test sim21.𝒪est[:final]≈8.5 atol=testTol prob_ode_linear_big = remake(prob_ode_linear, u0 = big.(prob_ode_linear.u0), tspan = big.(prob_ode_linear.tspan)) prob_ode_2Dlinear_big = remake(prob_ode_2Dlinear, u0 = big.(prob_ode_2Dlinear.u0), tspan = big.(prob_ode_2Dlinear.tspan))