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Analytically compute the square root of the IWP transition covariance #264

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Nov 2, 2023
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Analytically compute the square root of the IWP transition covariance #264

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d9f6de9
Analytically compute the square root of the transition covariance
nathanaelbosch Oct 30, 2023
ffe0189
Try improving the perf a bit
nathanaelbosch Oct 30, 2023
79ec25d
Make code a bit nicer and add docstring
nathanaelbosch Oct 31, 2023
2e1b1a6
JuliaFormatter.jl
nathanaelbosch Oct 31, 2023
011165b
Run benchmarks
nathanaelbosch Nov 2, 2023
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266 changes: 133 additions & 133 deletions docs/src/benchmarks/figures/lotkavolterra_2_1.svg
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208 changes: 104 additions & 104 deletions docs/src/benchmarks/figures/multi-language-wrappers_10_1.svg
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186 changes: 93 additions & 93 deletions docs/src/benchmarks/figures/multi-language-wrappers_12_1.svg
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192 changes: 96 additions & 96 deletions docs/src/benchmarks/figures/multi-language-wrappers_8_1.svg
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282 changes: 141 additions & 141 deletions docs/src/benchmarks/figures/pleiades_2_1.svg
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250 changes: 125 additions & 125 deletions docs/src/benchmarks/figures/vanderpol_2_1.svg
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486 changes: 242 additions & 244 deletions docs/src/benchmarks/figures/vanderpol_5_1.svg
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37 changes: 19 additions & 18 deletions docs/src/benchmarks/lotkavolterra.md
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Original file line number Diff line number Diff line change
Expand Up @@ -298,11 +298,11 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Project.toml`
[961ee093] ModelingToolkit v8.72.2
[54ca160b] ODEInterface v0.5.0
[09606e27] ODEInterfaceDiffEq v3.13.3
[1dea7af3] OrdinaryDiffEq v6.58.0
[1dea7af3] OrdinaryDiffEq v6.58.1
[65888b18] ParameterizedFunctions v5.16.0
[91a5bcdd] Plots v1.39.0
[bf3e78b0] ProbNumDiffEq v0.12.1 `~/.julia/dev/ProbNumDiffEq`
[0bca4576] SciMLBase v2.5.0
[bf3e78b0] ProbNumDiffEq v0.13.0 `~/.julia/dev/ProbNumDiffEq`
[0bca4576] SciMLBase v2.6.0
[505e40e9] SciPyDiffEq v0.2.1
[90137ffa] StaticArrays v1.6.5
[c3572dad] Sundials v4.20.1
Expand All @@ -328,7 +328,7 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[79e6a3ab] Adapt v3.7.1
[ec485272] ArnoldiMethod v0.2.0
[c9d4266f] ArrayAllocators v0.3.0
[4fba245c] ArrayInterface v7.5.0
[4fba245c] ArrayInterface v7.5.1
[30b0a656] ArrayInterfaceCore v0.1.29
[6e4b80f9] BenchmarkTools v1.3.2
[e2ed5e7c] Bijections v0.1.6
Expand All @@ -353,7 +353,7 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[34da2185] Compat v4.10.0
[b152e2b5] CompositeTypes v0.1.3
[2569d6c7] ConcreteStructs v0.2.3
[f0e56b4a] ConcurrentUtilities v2.2.1
[f0e56b4a] ConcurrentUtilities v2.3.0
[8f4d0f93] Conda v1.9.1
[187b0558] ConstructionBase v1.5.4
[d38c429a] Contour v0.6.2
Expand All @@ -366,7 +366,7 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[864edb3b] DataStructures v0.18.15
[e2d170a0] DataValueInterfaces v1.0.0
[8bb1440f] DelimitedFiles v1.9.1
[2b5f629d] DiffEqBase v6.135.0
[2b5f629d] DiffEqBase v6.136.0
[459566f4] DiffEqCallbacks v2.33.1
[f3b72e0c] DiffEqDevTools v2.39.0
[77a26b50] DiffEqNoiseProcess v5.19.0
Expand Down Expand Up @@ -425,26 +425,27 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[1019f520] JLFzf v0.1.6
[692b3bcd] JLLWrappers v1.5.0
[682c06a0] JSON v0.21.4
[98e50ef6] JuliaFormatter v1.0.41
[98e50ef6] JuliaFormatter v1.0.42
[ccbc3e58] JumpProcesses v9.8.0
[ef3ab10e] KLU v0.4.1
[2c470bb0] Kronecker v0.5.4
[ba0b0d4f] Krylov v0.9.4
[7f56f5a3] LSODA v0.7.5
[b964fa9f] LaTeXStrings v1.3.0
[b964fa9f] LaTeXStrings v1.3.1
[2ee39098] LabelledArrays v1.14.0
[984bce1d] LambertW v0.4.6
[23fbe1c1] Latexify v0.16.1
[10f19ff3] LayoutPointers v0.1.14
[10f19ff3] LayoutPointers v0.1.15
[50d2b5c4] Lazy v0.15.1
[1d6d02ad] LeftChildRightSiblingTrees v0.2.0
[d3d80556] LineSearches v7.2.0
[7ed4a6bd] LinearSolve v2.14.0
[7ed4a6bd] LinearSolve v2.15.0
[2ab3a3ac] LogExpFunctions v0.3.26
[e6f89c97] LoggingExtras v1.0.3
[bdcacae8] LoopVectorization v0.12.165
[10e44e05] MATLAB v0.8.4
[e2752cbe] MATLABDiffEq v1.2.0
[33e6dc65] MKL v0.6.1
[d8e11817] MLStyle v0.4.17
[1914dd2f] MacroTools v0.5.11
[d125e4d3] ManualMemory v0.1.8
Expand All @@ -454,21 +455,21 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[961ee093] ModelingToolkit v8.72.2
[46d2c3a1] MuladdMacro v0.2.4
[102ac46a] MultivariatePolynomials v0.5.2
[ffc61752] Mustache v1.0.17
[ffc61752] Mustache v1.0.18
[d8a4904e] MutableArithmetics v1.3.3
[d41bc354] NLSolversBase v7.8.3
[2774e3e8] NLsolve v4.5.1
[77ba4419] NaNMath v1.0.2
⌅ [356022a1] NamedDims v0.2.50
[8913a72c] NonlinearSolve v2.5.0
[8913a72c] NonlinearSolve v2.6.0
[54ca160b] ODEInterface v0.5.0
[09606e27] ODEInterfaceDiffEq v3.13.3
[6fd5a793] Octavian v0.3.27
[6fe1bfb0] OffsetArrays v1.12.10
[4d8831e6] OpenSSL v1.4.1
[429524aa] Optim v1.7.8
[bac558e1] OrderedCollections v1.6.2
[1dea7af3] OrdinaryDiffEq v6.58.0
[1dea7af3] OrdinaryDiffEq v6.58.1
[90014a1f] PDMats v0.11.28
[fe68d972] PSDMatrices v0.4.6
[65ce6f38] PackageExtensionCompat v1.0.2
Expand All @@ -491,7 +492,7 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[21216c6a] Preferences v1.4.1
[08abe8d2] PrettyTables v2.2.8
[27ebfcd6] Primes v0.5.4
[bf3e78b0] ProbNumDiffEq v0.12.1 `~/.julia/dev/ProbNumDiffEq`
[bf3e78b0] ProbNumDiffEq v0.13.0 `~/.julia/dev/ProbNumDiffEq`
[33c8b6b6] ProgressLogging v0.1.4
[438e738f] PyCall v1.96.1
[1fd47b50] QuadGK v2.9.1
Expand All @@ -512,8 +513,8 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[7e49a35a] RuntimeGeneratedFunctions v0.5.12
[fdea26ae] SIMD v3.4.5
[94e857df] SIMDTypes v0.1.0
[476501e8] SLEEFPirates v0.6.40
[0bca4576] SciMLBase v2.5.0
[476501e8] SLEEFPirates v0.6.42
[0bca4576] SciMLBase v2.6.0
[e9a6253c] SciMLNLSolve v0.1.9
[c0aeaf25] SciMLOperators v0.3.6
[505e40e9] SciPyDiffEq v0.2.1
Expand All @@ -529,7 +530,7 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[66db9d55] SnoopPrecompile v1.0.3
[b85f4697] SoftGlobalScope v1.1.0
[a2af1166] SortingAlgorithms v1.2.0
[47a9eef4] SparseDiffTools v2.9.1
[47a9eef4] SparseDiffTools v2.9.2
[e56a9233] Sparspak v0.3.9
[276daf66] SpecialFunctions v2.3.1
[928aab9d] SpecialMatrices v3.0.0
Expand Down Expand Up @@ -561,7 +562,7 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[0796e94c] Tokenize v0.5.25
[3bb67fe8] TranscodingStreams v0.10.1
[a2a6695c] TreeViews v0.3.0
[d5829a12] TriangularSolve v0.1.19
[d5829a12] TriangularSolve v0.1.20
[410a4b4d] Tricks v0.1.8
[781d530d] TruncatedStacktraces v1.4.0
[5c2747f8] URIs v1.5.1
Expand Down
50 changes: 26 additions & 24 deletions docs/src/benchmarks/multi-language-wrappers.md
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Expand Up @@ -392,6 +392,7 @@ Platform Info:
Environment:
JULIA_NUM_THREADS = auto
JULIA_STACKTRACE_MINIMAL = true
JULIA_IMAGE_THREADS = 1
```


Expand All @@ -414,14 +415,14 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Project.toml`
[961ee093] ModelingToolkit v8.72.2
[54ca160b] ODEInterface v0.5.0
[09606e27] ODEInterfaceDiffEq v3.13.3
[1dea7af3] OrdinaryDiffEq v6.58.0
[1dea7af3] OrdinaryDiffEq v6.58.1
[65888b18] ParameterizedFunctions v5.16.0
[91a5bcdd] Plots v1.39.0
[bf3e78b0] ProbNumDiffEq v0.12.1 `~/.julia/dev/ProbNumDiffEq`
[0bca4576] SciMLBase v2.4.3
[bf3e78b0] ProbNumDiffEq v0.13.0 `~/.julia/dev/ProbNumDiffEq`
[0bca4576] SciMLBase v2.6.0
[505e40e9] SciPyDiffEq v0.2.1
[90137ffa] StaticArrays v1.6.5
[c3572dad] Sundials v4.20.0
[c3572dad] Sundials v4.20.1
[44d3d7a6] Weave v0.10.12
[0518478a] deSolveDiffEq v0.1.1
```
Expand All @@ -441,16 +442,16 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
⌅ [c3fe647b] AbstractAlgebra v0.32.5
[621f4979] AbstractFFTs v1.5.0
[1520ce14] AbstractTrees v0.4.4
[79e6a3ab] Adapt v3.7.0
[79e6a3ab] Adapt v3.7.1
[ec485272] ArnoldiMethod v0.2.0
[c9d4266f] ArrayAllocators v0.3.0
[4fba245c] ArrayInterface v7.4.11
[4fba245c] ArrayInterface v7.5.1
[30b0a656] ArrayInterfaceCore v0.1.29
[6e4b80f9] BenchmarkTools v1.3.2
[e2ed5e7c] Bijections v0.1.6
[d1d4a3ce] BitFlags v0.1.7
[62783981] BitTwiddlingConvenienceFunctions v0.1.5
⌅ [fa961155] CEnum v0.4.2
[fa961155] CEnum v0.5.0
[2a0fbf3d] CPUSummary v0.2.4
[00ebfdb7] CSTParser v3.3.6
[49dc2e85] Calculus v0.5.1
Expand All @@ -469,7 +470,7 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[34da2185] Compat v4.10.0
[b152e2b5] CompositeTypes v0.1.3
[2569d6c7] ConcreteStructs v0.2.3
[f0e56b4a] ConcurrentUtilities v2.2.1
[f0e56b4a] ConcurrentUtilities v2.3.0
[8f4d0f93] Conda v1.9.1
[187b0558] ConstructionBase v1.5.4
[d38c429a] Contour v0.6.2
Expand All @@ -482,7 +483,7 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[864edb3b] DataStructures v0.18.15
[e2d170a0] DataValueInterfaces v1.0.0
[8bb1440f] DelimitedFiles v1.9.1
[2b5f629d] DiffEqBase v6.134.0
[2b5f629d] DiffEqBase v6.136.0
[459566f4] DiffEqCallbacks v2.33.1
[f3b72e0c] DiffEqDevTools v2.39.0
[77a26b50] DiffEqNoiseProcess v5.19.0
Expand All @@ -496,7 +497,7 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[7c1d4256] DynamicPolynomials v0.5.3
[b305315f] Elliptic v1.0.1
[4e289a0a] EnumX v1.0.4
[f151be2c] EnzymeCore v0.6.2
[f151be2c] EnzymeCore v0.6.3
[6912e4f1] Espresso v0.6.1
[460bff9d] ExceptionUnwrapping v0.1.9
[d4d017d3] ExponentialUtilities v1.25.0
Expand All @@ -522,7 +523,7 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[c27321d9] Glob v1.3.1
[86223c79] Graphs v1.9.0
[42e2da0e] Grisu v1.0.2
[0b43b601] Groebner v0.4.4
⌅ [0b43b601] Groebner v0.4.4
[d5909c97] GroupsCore v0.4.0
[cd3eb016] HTTP v1.10.0
[eafb193a] Highlights v0.5.2
Expand All @@ -541,26 +542,27 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[1019f520] JLFzf v0.1.6
[692b3bcd] JLLWrappers v1.5.0
[682c06a0] JSON v0.21.4
[98e50ef6] JuliaFormatter v1.0.40
[98e50ef6] JuliaFormatter v1.0.42
[ccbc3e58] JumpProcesses v9.8.0
[ef3ab10e] KLU v0.4.1
[2c470bb0] Kronecker v0.5.4
[ba0b0d4f] Krylov v0.9.4
[7f56f5a3] LSODA v0.7.5
[b964fa9f] LaTeXStrings v1.3.0
[b964fa9f] LaTeXStrings v1.3.1
[2ee39098] LabelledArrays v1.14.0
[984bce1d] LambertW v0.4.6
[23fbe1c1] Latexify v0.16.1
[10f19ff3] LayoutPointers v0.1.14
[10f19ff3] LayoutPointers v0.1.15
[50d2b5c4] Lazy v0.15.1
[1d6d02ad] LeftChildRightSiblingTrees v0.2.0
[d3d80556] LineSearches v7.2.0
[7ed4a6bd] LinearSolve v2.12.1
[7ed4a6bd] LinearSolve v2.15.0
[2ab3a3ac] LogExpFunctions v0.3.26
[e6f89c97] LoggingExtras v1.0.3
[bdcacae8] LoopVectorization v0.12.165
[10e44e05] MATLAB v0.8.4
[e2752cbe] MATLABDiffEq v1.2.0
[33e6dc65] MKL v0.6.1
[d8e11817] MLStyle v0.4.17
[1914dd2f] MacroTools v0.5.11
[d125e4d3] ManualMemory v0.1.8
Expand All @@ -570,21 +572,21 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[961ee093] ModelingToolkit v8.72.2
[46d2c3a1] MuladdMacro v0.2.4
[102ac46a] MultivariatePolynomials v0.5.2
[ffc61752] Mustache v1.0.17
[ffc61752] Mustache v1.0.18
[d8a4904e] MutableArithmetics v1.3.3
[d41bc354] NLSolversBase v7.8.3
[2774e3e8] NLsolve v4.5.1
[77ba4419] NaNMath v1.0.2
⌅ [356022a1] NamedDims v0.2.50
[8913a72c] NonlinearSolve v2.4.0
[8913a72c] NonlinearSolve v2.6.0
[54ca160b] ODEInterface v0.5.0
[09606e27] ODEInterfaceDiffEq v3.13.3
[6fd5a793] Octavian v0.3.27
[6fe1bfb0] OffsetArrays v1.12.10
[4d8831e6] OpenSSL v1.4.1
[429524aa] Optim v1.7.8
[bac558e1] OrderedCollections v1.6.2
[1dea7af3] OrdinaryDiffEq v6.58.0
[1dea7af3] OrdinaryDiffEq v6.58.1
[90014a1f] PDMats v0.11.28
[fe68d972] PSDMatrices v0.4.6
[65ce6f38] PackageExtensionCompat v1.0.2
Expand All @@ -607,7 +609,7 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[21216c6a] Preferences v1.4.1
[08abe8d2] PrettyTables v2.2.8
[27ebfcd6] Primes v0.5.4
[bf3e78b0] ProbNumDiffEq v0.12.1 `~/.julia/dev/ProbNumDiffEq`
[bf3e78b0] ProbNumDiffEq v0.13.0 `~/.julia/dev/ProbNumDiffEq`
[33c8b6b6] ProgressLogging v0.1.4
[438e738f] PyCall v1.96.1
[1fd47b50] QuadGK v2.9.1
Expand All @@ -628,8 +630,8 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[7e49a35a] RuntimeGeneratedFunctions v0.5.12
[fdea26ae] SIMD v3.4.5
[94e857df] SIMDTypes v0.1.0
[476501e8] SLEEFPirates v0.6.39
[0bca4576] SciMLBase v2.4.3
[476501e8] SLEEFPirates v0.6.42
[0bca4576] SciMLBase v2.6.0
[e9a6253c] SciMLNLSolve v0.1.9
[c0aeaf25] SciMLOperators v0.3.6
[505e40e9] SciPyDiffEq v0.2.1
Expand All @@ -645,7 +647,7 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[66db9d55] SnoopPrecompile v1.0.3
[b85f4697] SoftGlobalScope v1.1.0
[a2af1166] SortingAlgorithms v1.2.0
[47a9eef4] SparseDiffTools v2.8.0
[47a9eef4] SparseDiffTools v2.9.2
[e56a9233] Sparspak v0.3.9
[276daf66] SpecialFunctions v2.3.1
[928aab9d] SpecialMatrices v3.0.0
Expand All @@ -661,7 +663,7 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[69024149] StringEncodings v0.3.7
[892a3eda] StringManipulation v0.3.4
[09ab397b] StructArrays v0.6.16
[c3572dad] Sundials v4.20.0
[c3572dad] Sundials v4.20.1
[2efcf032] SymbolicIndexingInterface v0.2.2
[d1185830] SymbolicUtils v1.4.0
[0c5d862f] Symbolics v5.10.0
Expand All @@ -677,7 +679,7 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[0796e94c] Tokenize v0.5.25
[3bb67fe8] TranscodingStreams v0.10.1
[a2a6695c] TreeViews v0.3.0
[d5829a12] TriangularSolve v0.1.19
[d5829a12] TriangularSolve v0.1.20
[410a4b4d] Tricks v0.1.8
[781d530d] TruncatedStacktraces v1.4.0
[5c2747f8] URIs v1.5.1
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