diff --git a/docs/src/benchmarks/figures/vanderpol_2_1.svg b/docs/src/benchmarks/figures/vanderpol_2_1.svg
index 8c6033f49..f075bb00f 100644
--- a/docs/src/benchmarks/figures/vanderpol_2_1.svg
+++ b/docs/src/benchmarks/figures/vanderpol_2_1.svg
@@ -1,140 +1,140 @@
diff --git a/docs/src/benchmarks/figures/vanderpol_3_1.svg b/docs/src/benchmarks/figures/vanderpol_3_1.svg
index e178b22bf..bd9f0e096 100644
--- a/docs/src/benchmarks/figures/vanderpol_3_1.svg
+++ b/docs/src/benchmarks/figures/vanderpol_3_1.svg
@@ -1,229 +1,227 @@
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diff --git a/docs/src/benchmarks/figures/vanderpol_5_1.svg b/docs/src/benchmarks/figures/vanderpol_5_1.svg
index e6f8321e7..ee0aec004 100644
--- a/docs/src/benchmarks/figures/vanderpol_5_1.svg
+++ b/docs/src/benchmarks/figures/vanderpol_5_1.svg
@@ -1,258 +1,140 @@
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diff --git a/docs/src/benchmarks/vanderpol.md b/docs/src/benchmarks/vanderpol.md
index d864cc063..a9b690b29 100644
--- a/docs/src/benchmarks/vanderpol.md
+++ b/docs/src/benchmarks/vanderpol.md
@@ -75,6 +75,61 @@ plot(wp, palette=Plots.palette([:blue, :red], length(_setups)), xticks = 10.0 .^
+## Comparison of the different initialization schemes
+
+```julia
+DENSE = false;
+SAVE_EVERYSTEP = false;
+
+abstols = 1.0 ./ 10.0 .^ (6:13)
+reltols = 1.0 ./ 10.0 .^ (3:10)
+
+orders = (2, 3, 5, 8)
+ps = []
+for o in orders
+ _setups = [
+ "EK1($o) TaylorInit" => Dict(:alg => EK1(order=o, smooth=DENSE, initialization=TaylorModeInit(o)))
+ "EK1($o) ForwardDiffInit" => Dict(:alg => EK1(order=o, smooth=DENSE, initialization=ForwardDiffInit(o)))
+ "EK1($o) SimpleInit" => Dict(:alg => EK1(order=o, smooth=DENSE, initialization=SimpleInit()))
+ "EK1($o) ClassicSolverInit" => Dict(:alg => EK1(order=o, smooth=DENSE, initialization=ClassicSolverInit()))
+ ]
+
+ labels = first.(_setups)
+ setups = last.(_setups)
+
+ wp = WorkPrecisionSet(
+ prob, abstols, reltols, setups;
+ names = labels,
+ #print_names = true,
+ appxsol = test_sol,
+ dense = DENSE,
+ save_everystep = SAVE_EVERYSTEP,
+ numruns = 10,
+ maxiters = Int(1e7),
+ timeseries_errors = false,
+ verbose = false,
+ )
+
+ p = plot(wp, color=[2 4 5 6], xticks = 10.0 .^ (-16:1:5))
+ push!(ps, p)
+end
+plot(
+ ps...,
+ layout=(length(orders), 1),
+ size = (1000, length(orders)*300),
+ xlabel=["" "" "" "Error"],
+)
+```
+
+```
+Error: PosDefException: matrix is not Hermitian; Cholesky factorization fai
+led.
+```
+
+
+
+
+
## Solving the first- vs second-order ODE
```julia
@@ -91,7 +146,7 @@ test_sol2 = solve(prob2, RadauIIA5(), abstol=1/10^14, reltol=1/10^14, dense=fals
plot(test_sol2, title="Van der Pol Solution (2nd order)", legend=false, ylims=(-2.5, 2.5))
```
-
+
```julia
DENSE = false;
@@ -130,7 +185,7 @@ wp = WorkPrecisionSet(
plot(wp, color=[1 1 1 1 2 2 2 2], xticks = 10.0 .^ (-16:1:5))
```
-
+
@@ -164,6 +219,7 @@ Platform Info:
Environment:
JULIA_NUM_THREADS = auto
JULIA_STACKTRACE_MINIMAL = true
+ JULIA_IMAGE_THREADS = 1
```
@@ -186,14 +242,14 @@ 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 v2.7.3
[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
```
@@ -213,16 +269,15 @@ 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
- [30b0a656] ArrayInterfaceCore v0.1.29
+ [4fba245c] ArrayInterface v7.5.1
[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
@@ -241,7 +296,7 @@ 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
@@ -254,21 +309,21 @@ 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 v6.138.0
[459566f4] DiffEqCallbacks v2.33.1
[f3b72e0c] DiffEqDevTools v2.39.0
[77a26b50] DiffEqNoiseProcess v5.19.0
[163ba53b] DiffResults v1.1.0
[b552c78f] DiffRules v1.15.1
[b4f34e82] Distances v0.10.10
- [31c24e10] Distributions v0.25.102
+ [31c24e10] Distributions v0.25.103
[ffbed154] DocStringExtensions v0.9.3
⌅ [5b8099bc] DomainSets v0.6.7
[fa6b7ba4] DualNumbers v0.6.8
[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
@@ -294,7 +349,7 @@ 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
@@ -313,26 +368,27 @@ 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
+ [bdcacae8] LoopVectorization v0.12.166
[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
@@ -342,13 +398,13 @@ 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 v2.6.1
[54ca160b] ODEInterface v0.5.0
[09606e27] ODEInterfaceDiffEq v3.13.3
[6fd5a793] Octavian v0.3.27
@@ -356,7 +412,7 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[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
@@ -379,7 +435,7 @@ 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
@@ -400,12 +456,12 @@ 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 v2.7.3
[e9a6253c] SciMLNLSolve v0.1.9
[c0aeaf25] SciMLOperators v0.3.6
[505e40e9] SciPyDiffEq v0.2.1
- [6c6a2e73] Scratch v1.2.0
+ [6c6a2e73] Scratch v1.2.1
[91c51154] SentinelArrays v1.4.0
[efcf1570] Setfield v1.1.1
[1277b4bf] ShiftedArrays v2.0.0
@@ -417,7 +473,7 @@ 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
@@ -433,7 +489,7 @@ 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
@@ -447,9 +503,9 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[a759f4b9] TimerOutputs v0.5.23
[c751599d] ToeplitzMatrices v0.8.2
[0796e94c] Tokenize v0.5.25
- [3bb67fe8] TranscodingStreams v0.10.1
+ [3bb67fe8] TranscodingStreams v0.10.2
[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
@@ -466,7 +522,6 @@ Status `~/.julia/dev/ProbNumDiffEq/benchmarks/Manifest.toml`
[1b915085] WinReg v1.0.0
[ddb6d928] YAML v0.4.9
[c2297ded] ZMQ v1.2.2
- [700de1a5] ZygoteRules v0.2.4
[0518478a] deSolveDiffEq v0.1.1
[6e34b625] Bzip2_jll v1.0.8+0
[83423d85] Cairo_jll v1.16.1+1