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Switch RK methods to use an inf norm for eigen_est #2204

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merged 4 commits into from
May 28, 2024
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Switch RK methods to use an inf norm for eigen_est #2204

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1379b0b
switch RK methods from using internal norm to inf norm for stiffness …
oscardssmith May 20, 2024
ca2a77f
tests
oscardssmith May 20, 2024
5edf7ac
fix autodiff for krylovFBDF and fix tests
oscardssmith May 28, 2024
dbd9d84
fix autodiff
oscardssmith May 28, 2024
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4 changes: 2 additions & 2 deletions src/composite_algs.jl
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Expand Up @@ -15,7 +15,7 @@ function is_stiff(integrator, alg, ntol, stol, is_stiffalg)
stiffness = abs(eigen_est * dt / alg_stability_size(alg)) # `abs` here is just for safety
tol = is_stiffalg ? stol : ntol
os = oneunit(stiffness)
bool = stiffness > os * tol
bool = !(stiffness <= os * tol)
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why this change?

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in case eigen_est is NaN. It's a pretty good sign that things are going wrong, but since it's an estimate, if the estimate is NaN we really shouldn't be using an explicit solver.


if !bool
integrator.alg.choice_function.successive_switches += 1
Expand Down Expand Up @@ -111,7 +111,7 @@ current_nonstiff(current) = ifelse(current <= NUM_NONSTIFF, current, current - N
function DefaultODEAlgorithm(; lazy = true, stiffalgfirst = false, kwargs...)
nonstiff = (Tsit5(), Vern7(lazy = lazy))
stiff = (Rosenbrock23(; kwargs...), Rodas5P(; kwargs...), FBDF(; kwargs...),
FBDF(; linsolve = LinearSolve.KrylovJL_GMRES()))
FBDF(; linsolve = LinearSolve.KrylovJL_GMRES(), kwargs...))
AutoAlgSwitch(nonstiff, stiff; stiffalgfirst)
end

Expand Down
59 changes: 29 additions & 30 deletions src/derivative_utils.jl
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Expand Up @@ -140,7 +140,6 @@
if !(p isa DiffEqBase.NullParameters)
uf.p = p
end

jacobian!(J, uf, uprev, du1, integrator, jac_config)
end
end
Expand Down Expand Up @@ -294,7 +293,7 @@
Base.eltype(W::WOperator) = eltype(W.J)

# In WOperator update_coefficients!, accept both missing u/p/t and missing dtgamma/transform and don't update them in that case.
# This helps support partial updating logic used with Newton solvers.
# This helps support partial updating logic used with Newton solvers.
function SciMLOperators.update_coefficients!(W::WOperator,
u = nothing,
p = nothing,
Expand Down Expand Up @@ -483,16 +482,16 @@
end

function jacobian2W!(
W::AbstractMatrix, mass_matrix::MT, dtgamma::Number, J::AbstractMatrix,
W_transform::Bool)::Nothing where {MT}
W::AbstractMatrix, mass_matrix, dtgamma::Number, J::AbstractMatrix,
W_transform::Bool)::Nothing
# check size and dimension
iijj = axes(W)
@boundscheck (iijj == axes(J) && length(iijj) == 2) || _throwWJerror(W, J)
mass_matrix isa UniformScaling ||
@boundscheck axes(mass_matrix) == axes(W) || _throwWMerror(W, mass_matrix)
@inbounds if W_transform
invdtgamma = inv(dtgamma)
if MT <: UniformScaling
if mass_matrix isa UniformScaling
copyto!(W, J)
idxs = diagind(W)
λ = -mass_matrix.λ
Expand All @@ -508,28 +507,9 @@
@.. broadcast=false W=muladd(-mass_matrix, invdtgamma, J)
end
else
if MT <: UniformScaling
if mass_matrix isa UniformScaling
λ = -mass_matrix.λ
if W isa AbstractSparseMatrix && !(W isa SparseMatrixCSC)
# This is specifically to catch the GPU sparse matrix cases
# Which do not support diagonal indexing
# https://github.com/JuliaGPU/CUDA.jl/issues/1395

Wn = nonzeros(W)
Jn = nonzeros(J)

# I would hope to check this generically, but `CuSparseMatrixCSC` has `colPtr`
# and `rowVal` while SparseMatrixCSC is colptr and rowval, and there is no
# standard for checking sparsity patterns in general. So for now, write it for
# the convention of CUDA.jl and handle the case of some other convention when
# it comes up.

@assert J.colPtr == W.colPtr
@assert J.rowVal == W.rowVal

@.. broadcast=false Wn=dtgamma * Jn
W .= W + λ * I
elseif W isa SparseMatrixCSC
if W isa SparseMatrixCSC
#=
using LinearAlgebra, SparseArrays, FastBroadcast
J = sparse(Diagonal(ones(4)))
Expand All @@ -553,6 +533,25 @@
@.. broadcast=false W.nzval=dtgamma * J.nzval
idxs = diagind(W)
@.. broadcast=false @view(W[idxs])=@view(W[idxs]) + λ
elseif W isa AbstractSparseMatrix

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# This is specifically to catch the GPU sparse matrix cases
# Which do not support diagonal indexing
# https://github.com/JuliaGPU/CUDA.jl/issues/1395

Wn = nonzeros(W)
Jn = nonzeros(J)

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# I would hope to check this generically, but `CuSparseMatrixCSC` has `colPtr`
# and `rowVal` while SparseMatrixCSC is colptr and rowval, and there is no
# standard for checking sparsity patterns in general. So for now, write it for
# the convention of CUDA.jl and handle the case of some other convention when
# it comes up.

@assert J.colPtr == W.colPtr
@assert J.rowVal == W.rowVal

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@.. broadcast=false Wn=dtgamma * Jn
W .= W + λ * I

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else # Anything not a sparse matrix
@.. broadcast=false W=dtgamma * J
idxs = diagind(W)
Expand All @@ -565,16 +564,16 @@
return nothing
end

function jacobian2W!(W::Matrix, mass_matrix::MT, dtgamma::Number, J::Matrix,
W_transform::Bool)::Nothing where {MT}
function jacobian2W!(W::Matrix, mass_matrix, dtgamma::Number, J::Matrix,
W_transform::Bool)::Nothing
# check size and dimension
iijj = axes(W)
@boundscheck (iijj == axes(J) && length(iijj) == 2) || _throwWJerror(W, J)
mass_matrix isa UniformScaling ||
@boundscheck axes(mass_matrix) == axes(W) || _throwWMerror(W, mass_matrix)
@inbounds if W_transform
invdtgamma = inv(dtgamma)
if MT <: UniformScaling
if mass_matrix isa UniformScaling
copyto!(W, J)
idxs = diagind(W)
λ = -mass_matrix.λ
Expand All @@ -587,7 +586,7 @@
end
end
else
if MT <: UniformScaling
if mass_matrix isa UniformScaling
idxs = diagind(W)
@inbounds @simd ivdep for i in eachindex(W)
W[i] = dtgamma * J[i]
Expand Down
16 changes: 6 additions & 10 deletions src/perform_step/explicit_rk_perform_step.jl
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Expand Up @@ -48,10 +48,9 @@
u = uprev + dt * accum

if integrator.alg isa CompositeAlgorithm
# Hairer II, page 22
ϱu = integrator.opts.internalnorm(kk[end] - kk[end - 1], t)
ϱd = integrator.opts.internalnorm(u - u_beforefinal, t)
integrator.eigen_est = ϱu / ϱd
# Hairer II, page 22 modified to use Inf norm
n = maximum(abs.((kk[end] .- kk[end - 1]) / (u .- u_beforefinal)))
integrator.eigen_est = integrator.opts.internalnorm(n, t)

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end

if integrator.opts.adaptive
Expand Down Expand Up @@ -221,12 +220,9 @@
end

if integrator.alg isa CompositeAlgorithm
# Hairer II, page 22
@.. broadcast=false utilde=kk[end] - kk[end - 1]
ϱu = integrator.opts.internalnorm(utilde, t)
@.. broadcast=false utilde=u - tmp
ϱd = integrator.opts.internalnorm(utilde, t)
integrator.eigen_est = ϱu / ϱd
# Hairer II, page 22 modified to use Inf norm
@.. broadcast=false utilde=abs((kk[end] - kk[end - 1]) / (u - tmp))
integrator.eigen_est = integrator.opts.internalnorm(maximum(utilde), t)

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end

if integrator.opts.adaptive
Expand Down
93 changes: 10 additions & 83 deletions src/perform_step/low_order_rk_perform_step.jl
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Expand Up @@ -761,9 +761,8 @@
integrator.stats.nf += 6
if integrator.alg isa CompositeAlgorithm
g7 = u
# Hairer II, page 22
integrator.eigen_est = integrator.opts.internalnorm(k7 - k6, t) /
integrator.opts.internalnorm(g7 - g6, t)
# Hairer II, page 22 modified to use the Inf norm
integrator.eigen_est = integrator.opts.internalnorm(maximum(abs.(k7 .- k6) ./ (g7 .- g6)), t)

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end
if integrator.opts.adaptive
utilde = dt *
Expand Down Expand Up @@ -836,12 +835,9 @@
if integrator.alg isa CompositeAlgorithm
g7 = u
g6 = tmp
# Hairer II, page 22
@.. broadcast=false thread=thread utilde=k7 - k6
ϱu = integrator.opts.internalnorm(utilde, t)
@.. broadcast=false thread=thread utilde=g7 - g6
ϱd = integrator.opts.internalnorm(utilde, t)
integrator.eigen_est = ϱu / ϱd
# Hairer II, page 22 modified to use Inf norm
@.. broadcast=false thread=thread utilde=abs((k7 - k6) / (g7 - g6))
integrator.eigen_est = integrator.opts.internalnorm(maximum(utilde), t)
end
if integrator.opts.adaptive
@.. broadcast=false thread=thread utilde=dt * (btilde1 * k1 + btilde2 * k2 +
Expand Down Expand Up @@ -889,9 +885,8 @@
integrator.stats.nf += 6
if integrator.alg isa CompositeAlgorithm
g7 = u
# Hairer II, page 22
integrator.eigen_est = integrator.opts.internalnorm(k7 - k6, t) /
integrator.opts.internalnorm(g7 - g6, t)
# Hairer II, page 22 modified to use the Inf norm
integrator.eigen_est = integrator.opts.internalnorm(maximum(abs.(k7 .- k6) ./ (g7 .- g6)), t)

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end
if integrator.opts.adaptive
utilde = dt *
Expand Down Expand Up @@ -957,12 +952,9 @@
if integrator.alg isa CompositeAlgorithm
g6 = tmp
g7 = u
# Hairer II, page 22
@.. broadcast=false thread=thread g6=g7 - g6
ϱd = integrator.opts.internalnorm(g6, t)
@.. broadcast=false thread=thread tmp=k7 - k6
ϱu = integrator.opts.internalnorm(tmp, t)
integrator.eigen_est = (ϱu / ϱd) * oneunit(t)
# Hairer II, page 22 modified to use Inf norm
@.. broadcast=false thread=thread utilde=abs((k7 - k6) / (g7 - g6))
integrator.eigen_est = integrator.opts.internalnorm(maximum(utilde) * oneunit(t), t)

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end
if integrator.opts.adaptive
@.. broadcast=false thread=thread utilde=dt * (btilde1 * k1 + btilde3 * k3 +
Expand All @@ -987,71 +979,6 @@
return nothing
end

#=
@muladd function perform_step!(integrator, cache::DP5Cache, repeat_step=false)
@unpack t,dt,uprev,u,f,p = integrator
uidx = eachindex(integrator.uprev)
@unpack a21,a31,a32,a41,a42,a43,a51,a52,a53,a54,a61,a62,a63,a64,a65,a71,a73,a74,a75,a76,btilde1,btilde3,btilde4,btilde5,btilde6,btilde7,c1,c2,c3,c4,c5,c6 = cache.tab
@unpack k1,k2,k3,k4,k5,k6,k7,dense_tmp3,dense_tmp4,update,bspl,utilde,tmp,atmp = cache
@unpack d1,d3,d4,d5,d6,d7 = cache.tab
a = dt*a21
@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*(a31*k1[i]+a32*k2[i])
end
f(k3, tmp, p, t+c2*dt)
@tight_loop_macros for i in uidx
@inbounds tmp[i] = uprev[i]+dt*(a41*k1[i]+a42*k2[i]+a43*k3[i])
end
f(k4, tmp, p, t+c3*dt)
@tight_loop_macros for i in uidx
@inbounds tmp[i] = uprev[i]+dt*(a51*k1[i]+a52*k2[i]+a53*k3[i]+a54*k4[i])
end
f(k5, tmp, p, t+c4*dt)
@tight_loop_macros for i in uidx
@inbounds tmp[i] = uprev[i]+dt*(a61*k1[i]+a62*k2[i]+a63*k3[i]+a64*k4[i]+a65*k5[i])
end
f(k6, tmp, p, t+dt)
@tight_loop_macros for i in uidx
@inbounds update[i] = a71*k1[i]+a73*k3[i]+a74*k4[i]+a75*k5[i]+a76*k6[i]
@inbounds u[i] = uprev[i]+dt*update[i]
end
f(k7, u, p, t+dt)
integrator.stats.nf += 6
if integrator.alg isa CompositeAlgorithm
g6 = tmp
g7 = u
# Hairer II, page 22
ϱu, ϱd = zero(eltype(k7))^2, zero(eltype(g7))^2
@inbounds for i in eachindex(k7)
ϱu += (k7[i] - k6[i])^2
ϱd += (g7[i] - g6[i])^2
end
integrator.eigen_est = sqrt(ϱu/ϱd)*oneunit(t)
end
if integrator.opts.adaptive
@tight_loop_macros for i in uidx
@inbounds utilde[i] = dt*(btilde1*k1[i] + btilde3*k3[i] + btilde4*k4[i] + btilde5*k5[i] + btilde6*k6[i] + btilde7*k7[i])
end
calculate_residuals!(atmp, utilde, uprev, u, integrator.opts.abstol, integrator.opts.reltol,integrator.opts.internalnorm,t)
integrator.EEst = integrator.opts.internalnorm(atmp,t)
end
if integrator.opts.calck
@tight_loop_macros for i in uidx
#integrator.k[4] == k5
@inbounds integrator.k[4][i] = d1*k1[i]+d3*k3[i]+d4*k4[i]+d5*k5[i]+d6*k6[i]+d7*k7[i]
#bspl == k3
@inbounds bspl[i] = k1[i] - update[i]
# k6 === integrator.k[3] === k2
@inbounds integrator.k[3][i] = update[i] - k7[i] - bspl[i]
end
end
end
=#

function initialize!(integrator, cache::KYK2014DGSSPRK_3S2_ConstantCache)
integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal
integrator.stats.nf += 1
Expand Down
44 changes: 12 additions & 32 deletions src/perform_step/verner_rk_perform_step.jl
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Expand Up @@ -40,9 +40,7 @@
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
integrator.eigen_est = integrator.opts.internalnorm(maximum(abs.((k9 .- k8) ./ (g9 .- g8))), t)

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end
if integrator.opts.adaptive
utilde = dt *
Expand Down Expand Up @@ -163,11 +161,8 @@
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
@.. broadcast=false thread=thread rtmp=abs((k9 - k8) / (g9 - g8))
integrator.eigen_est = integrator.opts.internalnorm(maximum(rtmp), t)

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end
if integrator.opts.adaptive
@.. broadcast=false thread=thread utilde=dt * (btilde1 * k1 + btilde4 * k4 +
Expand Down Expand Up @@ -252,9 +247,7 @@
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
integrator.eigen_est = integrator.opts.internalnorm(maximum(abs.((k10 .- k9) ./ (g10 .- g9))), t)

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end
if integrator.opts.adaptive
utilde = dt *
Expand Down Expand Up @@ -415,11 +408,8 @@
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
@.. broadcast=false thread=thread rtmp=abs((k10 - k9) / (g10 - g9))
integrator.eigen_est = integrator.opts.internalnorm(maximum(rtmp), t)

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end
if integrator.opts.adaptive
@.. broadcast=false thread=thread utilde=dt * (btilde1 * k1 + btilde4 * k4 +
Expand Down Expand Up @@ -547,9 +537,7 @@
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
integrator.eigen_est = integrator.opts.internalnorm(maximum(abs.((k13 .- k12) ./ (g13 .- g12))), t)

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end
if integrator.opts.adaptive
utilde = dt *
Expand Down Expand Up @@ -739,11 +727,8 @@
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
@.. broadcast=false thread=thread rtmp = abs((k13 - k12) / (g13 - g12))
integrator.eigen_est = integrator.opts.internalnorm(maximum(rtmp), t)

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end
@.. broadcast=false thread=thread u=uprev +
dt *
Expand Down Expand Up @@ -918,9 +903,7 @@
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
integrator.eigen_est = integrator.opts.internalnorm(maximum(abs.((k16 .- k15) ./ (g16 .- g15))), t)

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end
if integrator.opts.adaptive
utilde = dt * (btilde1 * k1 + btilde8 * k8 + btilde9 * k9 + btilde10 * k10 +
Expand Down Expand Up @@ -1148,11 +1131,8 @@
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
@.. broadcast=false thread=thread rtmp=abs((k16 - k15) / (g16 - g15))
integrator.eigen_est = integrator.opts.internalnorm(maximum(rtmp), t)

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end
@.. broadcast=false thread=thread u=uprev +
dt *
Expand Down
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