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Using ComponentVector in ODE raises MethodError for large-ish system size #287

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jonaswickman opened this issue Dec 10, 2024 · 2 comments · Fixed by #289
Closed

Using ComponentVector in ODE raises MethodError for large-ish system size #287

jonaswickman opened this issue Dec 10, 2024 · 2 comments · Fixed by #289
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bug Something isn't working

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@jonaswickman
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Describe the bug 🐞

Solving a system of differential equations with one vector variable and one scalar variable packed into a ComponentVectorworks fine for medium system sizes but produces an error when the system size is made larger when no solver is specified in solve. I'm guessing that the default solver algorithm changes to a different solver when system size gets large enough, but that some of these solvers are not working properly with ComponentArrays. I wasn't sure whether to put this issue here or in the repo for ComponentArrays. Let me know if I should put it there instead.

Expected behavior

I expected no error to be raised when changing system size.

Minimal Reproducible Example 👇

Here is a (somewhat) minimal example that works/doesn't work depending on system size. The following code runs fine:

using DifferentialEquations
using ComponentArrays

function ode_fun!(du, u, p, t)
    x = u.x 
    y = u.y 

    du.y = p.a - sum(bi*xi for (bi, xi) in zip(p.b, x))*y
    @. du.x = (p.b*y - p.c)*x + p.d

    return nothing 
end

function run_ode(u0, p, t_end)
    ode_prob = ODEProblem{true}(ode_fun!, u0, (0.0, t_end), p)
    ode_sol = solve(ode_prob; reltol = 1e-6, abstol = 1e-6)
end

S = 151
b = 0.9*[exp( -0.5*(zi)^2 ) for zi ∈ range(-3, 3; length = S)]
p = (a = 1.0, b = b, c = 0.1, d = 0.05)

u0 = ComponentVector(x = fill(p.d/p.c, S), y = 1.0)
t_end = 1e5
ode_sol = run_ode(u0, p, t_end)

However, changing the system size S produces an error:

S = 501
b = 0.9*[exp( -0.5*(zi)^2 ) for zi ∈ range(-3, 3; length = S)]
p = (a = 1.0, b = b, c = 0.1, d = 0.05)

u0 = ComponentVector(x = fill(p.d/p.c, S), y = 1.0)
t_end = 1e5
ode_sol = run_ode(u0, p, t_end)

Error & Stacktrace ⚠️

ERROR: MethodError: no method matching nextind(::ComponentVector{Float64, Vector{Float64}, Tuple{Axis{(x = 1:501, y = 502)}}}, ::Symbol)
The function `nextind` exists, but no method is defined for this combination of argument types.

Closest candidates are:
  nextind(::AbstractArray{<:Any, N}, ::CartesianIndex{N}) where N
   @ Base multidimensional.jl:150
  nextind(::AbstractArray, ::Integer)
   @ Base abstractarray.jl:216
  nextind(::Base.JuliaSyntax.SourceFile, ::Integer)
   @ Base /cache/build/tester-amdci5-12/julialang/julia-release-1-dot-11/base/JuliaSyntax/src/source_files.jl:127
  ...

Stacktrace:
  [1] findnext(testf::typeof(iszero), A::ComponentVector{Float64, Vector{Float64}, Tuple{Axis{…}}}, start::Symbol)
    @ Base ./array.jl:2355
  [2] findfirst
    @ ./array.jl:2403 [inlined]
  [3] ldiv!(B::Vector{Float64}, D::LinearAlgebra.Diagonal{Float64, ComponentVector{…}}, A::Vector{Float64})
    @ LinearAlgebra ~/.julia/juliaup/julia-1.11.2+0.x64.linux.gnu/share/julia/stdlib/v1.11/LinearAlgebra/src/diagonal.jl:490
  [4] mulorldiv!
    @ ~/.julia/packages/Krylov/FdZzQ/src/krylov_utils.jl:306 [inlined]
  [5] gmres!(solver::Krylov.GmresSolver{…}, A::OrdinaryDiffEqDifferentiation.WOperator{…}, b::ComponentVector{…}; M::LinearSolve.InvPreconditioner{…}, N::LinearAlgebra.Diagonal{…}, ldiv::Bool, restart::Bool, reorthogonalization::Bool, atol::Float64, rtol::Float64, itmax::Int64, timemax::Float64, verbose::Int64, history::Bool, callback::Krylov.var"#976#984", iostream::Core.CoreSTDOUT)
    @ Krylov ~/.julia/packages/Krylov/FdZzQ/src/gmres.jl:240
  [6] gmres!
    @ ~/.julia/packages/Krylov/FdZzQ/src/gmres.jl:108 [inlined]
  [7] solve!
    @ ~/.julia/packages/Krylov/FdZzQ/src/krylov_solve.jl:140 [inlined]
  [8] solve!(cache::LinearSolve.LinearCache{…}, alg::KrylovJL{…}; kwargs::@Kwargs{…})
    @ LinearSolve ~/.julia/packages/LinearSolve/WDeMC/src/iterative_wrappers.jl:289
  [9] solve!
    @ ~/.julia/packages/LinearSolve/WDeMC/src/iterative_wrappers.jl:240 [inlined]
 [10] #solve!#8
    @ ~/.julia/packages/LinearSolve/WDeMC/src/common.jl:269 [inlined]
 [11] solve!
    @ ~/.julia/packages/LinearSolve/WDeMC/src/common.jl:268 [inlined]
 [12] dolinsolve(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, linsolve::LinearSolve.LinearCache{…}; A::OrdinaryDiffEqDifferentiation.WOperator{…}, linu::ComponentVector{…}, b::ComponentVector{…}, du::Nothing, u::Nothing, p::Nothing, t::Nothing, weight::Nothing, solverdata::Nothing, reltol::Float64)
    @ OrdinaryDiffEqDifferentiation ~/.julia/packages/OrdinaryDiffEqDifferentiation/OR1Bv/src/linsolve_utils.jl:29
 [13] dolinsolve
    @ ~/.julia/packages/OrdinaryDiffEqDifferentiation/OR1Bv/src/linsolve_utils.jl:5 [inlined]
 [14] compute_step!(nlsolver::OrdinaryDiffEqNonlinearSolve.NLSolver{…}, integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, γW::Float64)
    @ OrdinaryDiffEqNonlinearSolve ~/.julia/packages/OrdinaryDiffEqNonlinearSolve/4nSEo/src/newton.jl:224
 [15] nlsolve!(nlsolver::OrdinaryDiffEqNonlinearSolve.NLSolver{…}, integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, cache::OrdinaryDiffEqBDF.FBDFCache{…}, repeat_step::Bool)
    @ OrdinaryDiffEqNonlinearSolve ~/.julia/packages/OrdinaryDiffEqNonlinearSolve/4nSEo/src/nlsolve.jl:52
 [16] perform_step!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, cache::OrdinaryDiffEqBDF.FBDFCache{…}, repeat_step::Bool)
    @ OrdinaryDiffEqBDF ~/.julia/packages/OrdinaryDiffEqBDF/J0IGS/src/bdf_perform_step.jl:1270
 [17] perform_step!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, cache::OrdinaryDiffEqCore.DefaultCache{…}, repeat_step::Bool)
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/H25Bn/src/perform_step/composite_perform_step.jl:151
 [18] perform_step!
    @ ~/.julia/packages/OrdinaryDiffEqCore/H25Bn/src/perform_step/composite_perform_step.jl:138 [inlined]
 [19] solve!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/H25Bn/src/solve.jl:569
 [20] #__solve#62
    @ ~/.julia/packages/OrdinaryDiffEqCore/H25Bn/src/solve.jl:7 [inlined]
 [21] __solve
    @ ~/.julia/packages/OrdinaryDiffEqCore/H25Bn/src/solve.jl:1 [inlined]
 [22] solve_call(_prob::ODEProblem{…}, args::CompositeAlgorithm{…}; merge_callbacks::Bool, kwargshandle::Nothing, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:632
 [23] solve_call
    @ ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:589 [inlined]
 [24] #solve_up#53
    @ ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1120 [inlined]
 [25] solve_up
    @ ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1099 [inlined]
 [26] #solve#51
    @ ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1036 [inlined]
 [27] solve
    @ ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1026 [inlined]
 [28] #__solve#3
    @ ~/.julia/packages/OrdinaryDiffEqDefault/2qVWT/src/default_alg.jl:46 [inlined]
 [29] __solve
    @ ~/.julia/packages/OrdinaryDiffEqDefault/2qVWT/src/default_alg.jl:45 [inlined]
 [30] #__solve#72
    @ ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1436 [inlined]
 [31] __solve
    @ ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1427 [inlined]
 [32] solve_call(::ODEProblem{…}; merge_callbacks::Bool, kwargshandle::Nothing, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:632
 [33] solve_up(::ODEProblem{…}, ::Nothing, ::ComponentVector{…}, ::@NamedTuple{…}; kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1105
 [34] solve_up
    @ ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1099 [inlined]
 [35] solve(::ODEProblem{…}; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1036
 [36] solve
    @ ~/.julia/packages/DiffEqBase/HW4ge/src/solve.jl:1026 [inlined]
 [37] run_ode(u0::ComponentVector{…}, p::@NamedTuple{…}, t_end::Float64)
    @ Main ~/Files/Documents/Dropbox/Meanderings/2024/Nasser SAD/Julia/diff_eq_error.jl:18
 [38] top-level scope
    @ REPL[2]:1
Some type information was truncated. Use `show(err)` to see complete types.

Environment (please complete the following information):

  • Output of using Pkg; Pkg.status()
[7d9f7c33] Accessors v0.1.39
  [6e4b80f9] BenchmarkTools v1.5.0
  [13f3f980] CairoMakie v0.12.17
  [b0b7db55] ComponentArrays v0.15.19
  [0c46a032] DifferentialEquations v7.15.0
  [e9467ef8] GLMakie v0.10.17
⌅ [8913a72c] NonlinearSolve v3.15.1
  [90137ffa] StaticArrays v1.9.8
  • Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
[47edcb42] ADTypes v1.11.0
  [621f4979] AbstractFFTs v1.5.0
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.39
  [79e6a3ab] Adapt v4.1.1
  [35492f91] AdaptivePredicates v1.2.0
  [66dad0bd] AliasTables v1.1.3
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  [6e4b80f9] BenchmarkTools v1.5.0
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [764a87c0] BoundaryValueDiffEq v5.12.0
  [56b672f2] BoundaryValueDiffEqCore v1.2.0
  [85d9eb09] BoundaryValueDiffEqFIRK v1.2.0
  [1a22d4ce] BoundaryValueDiffEqMIRK v1.2.0
  [ed55bfe0] BoundaryValueDiffEqShooting v1.2.0
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⌅ [3da002f7] ColorTypes v0.11.5
⌃ [c3611d14] ColorVectorSpace v0.10.0
⌅ [5ae59095] Colors v0.12.11
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  [34da2185] Compat v4.16.0
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  [2569d6c7] ConcreteStructs v0.2.3
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  [459566f4] DiffEqCallbacks v4.2.2
  [77a26b50] DiffEqNoiseProcess v5.24.0
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  [0c46a032] DifferentialEquations v7.15.0
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  [6c6a2e73] Scratch v1.2.1
  [efcf1570] Setfield v1.1.1
⌅ [65257c39] ShaderAbstractions v0.4.1
  [992d4aef] Showoff v1.0.3
  [73760f76] SignedDistanceFields v0.4.0
⌅ [727e6d20] SimpleNonlinearSolve v1.12.3
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [45858cf5] Sixel v0.1.3
  [a2af1166] SortingAlgorithms v1.2.1
  [9f842d2f] SparseConnectivityTracer v0.6.9
  [47a9eef4] SparseDiffTools v2.23.0
  [0a514795] SparseMatrixColorings v0.4.10
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.4.0
  [860ef19b] StableRNGs v1.0.2
  [cae243ae] StackViews v0.1.1
  [aedffcd0] Static v1.1.1
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.8
  [1e83bf80] StaticArraysCore v1.4.3
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.3
  [4c63d2b9] StatsFuns v1.3.2
  [9672c7b4] SteadyStateDiffEq v2.4.1
  [789caeaf] StochasticDiffEq v6.71.1
  [7792a7ef] StrideArraysCore v0.5.7
⌅ [09ab397b] StructArrays v0.6.21
  [c3572dad] Sundials v4.26.1
  [2efcf032] SymbolicIndexingInterface v0.3.36
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [62fd8b95] TensorCore v0.1.1
  [8290d209] ThreadingUtilities v0.5.2
  [731e570b] TiffImages v0.11.1
  [a759f4b9] TimerOutputs v0.5.26
  [3bb67fe8] TranscodingStreams v0.11.3
  [d5829a12] TriangularSolve v0.2.1
  [981d1d27] TriplotBase v0.1.0
  [781d530d] TruncatedStacktraces v1.4.0
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [1986cc42] Unitful v1.21.1
  [3d5dd08c] VectorizationBase v0.21.71
  [19fa3120] VertexSafeGraphs v0.2.0
  [e3aaa7dc] WebP v0.1.3
  [efce3f68] WoodburyMatrices v1.0.0
  [6e34b625] Bzip2_jll v1.0.8+2
  [4e9b3aee] CRlibm_jll v1.0.1+0
  [83423d85] Cairo_jll v1.18.2+1
  [ee1fde0b] Dbus_jll v1.14.10+0
  [5ae413db] EarCut_jll v2.2.4+0
  [2702e6a9] EpollShim_jll v0.0.20230411+1
  [2e619515] Expat_jll v2.6.4+1
  [b22a6f82] FFMPEG_jll v6.1.2+0
  [f5851436] FFTW_jll v3.3.10+1
  [a3f928ae] Fontconfig_jll v2.15.0+0
  [d7e528f0] FreeType2_jll v2.13.3+1
  [559328eb] FriBidi_jll v1.0.14+0
  [0656b61e] GLFW_jll v3.4.0+1
  [78b55507] Gettext_jll v0.21.0+0
  [59f7168a] Giflib_jll v5.2.2+0
  [7746bdde] Glib_jll v2.82.2+1
  [3b182d85] Graphite2_jll v1.3.14+1
  [2e76f6c2] HarfBuzz_jll v8.5.0+0
  [905a6f67] Imath_jll v3.1.11+0
  [1d5cc7b8] IntelOpenMP_jll v2024.2.1+0
  [aacddb02] JpegTurbo_jll v3.0.4+0
  [c1c5ebd0] LAME_jll v3.100.2+0
  [88015f11] LERC_jll v4.0.0+0
  [1d63c593] LLVMOpenMP_jll v18.1.7+0
  [dd4b983a] LZO_jll v2.10.2+1
⌅ [e9f186c6] Libffi_jll v3.2.2+1
  [d4300ac3] Libgcrypt_jll v1.11.0+0
  [7e76a0d4] Libglvnd_jll v1.7.0+0
  [7add5ba3] Libgpg_error_jll v1.50.0+0
  [94ce4f54] Libiconv_jll v1.17.0+1
  [4b2f31a3] Libmount_jll v2.40.2+0
  [89763e89] Libtiff_jll v4.7.0+0
  [38a345b3] Libuuid_jll v2.40.2+0
  [856f044c] MKL_jll v2024.2.0+0
  [e7412a2a] Ogg_jll v1.3.5+1
  [18a262bb] OpenEXR_jll v3.2.4+0
  [458c3c95] OpenSSL_jll v3.0.15+1
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.3+0
  [36c8627f] Pango_jll v1.54.1+0
⌅ [30392449] Pixman_jll v0.43.4+0
  [f50d1b31] Rmath_jll v0.5.1+0
⌅ [fb77eaff] Sundials_jll v5.2.3+0
  [a2964d1f] Wayland_jll v1.21.0+1
  [2381bf8a] Wayland_protocols_jll v1.31.0+0
  [02c8fc9c] XML2_jll v2.13.5+0
  [aed1982a] XSLT_jll v1.1.42+0
  [ffd25f8a] XZ_jll v5.6.3+0
  [4f6342f7] Xorg_libX11_jll v1.8.6+1
  [0c0b7dd1] Xorg_libXau_jll v1.0.11+1
  [935fb764] Xorg_libXcursor_jll v1.2.0+4
  [a3789734] Xorg_libXdmcp_jll v1.1.4+1
  [1082639a] Xorg_libXext_jll v1.3.6+1
  [d091e8ba] Xorg_libXfixes_jll v5.0.3+4
  [a51aa0fd] Xorg_libXi_jll v1.7.10+4
  [d1454406] Xorg_libXinerama_jll v1.1.4+4
  [ec84b674] Xorg_libXrandr_jll v1.5.2+4
  [ea2f1a96] Xorg_libXrender_jll v0.9.11+0
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.1+1
  [c7cfdc94] Xorg_libxcb_jll v1.17.0+1
  [cc61e674] Xorg_libxkbfile_jll v1.1.2+0
  [35661453] Xorg_xkbcomp_jll v1.4.6+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
  [c5fb5394] Xorg_xtrans_jll v1.5.0+1
  [3161d3a3] Zstd_jll v1.5.6+1
  [9a68df92] isoband_jll v0.2.3+0
  [a4ae2306] libaom_jll v3.9.0+0
  [0ac62f75] libass_jll v0.15.2+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [f638f0a6] libfdk_aac_jll v2.0.3+0
  [b53b4c65] libpng_jll v1.6.44+0
  [075b6546] libsixel_jll v1.10.3+1
  [f27f6e37] libvorbis_jll v1.3.7+2
  [c5f90fcd] libwebp_jll v1.4.0+0
  [1317d2d5] oneTBB_jll v2021.12.0+0
  [1270edf5] x264_jll v10164.0.0+0
⌅ [dfaa095f] x265_jll v3.6.0+0
  [d8fb68d0] xkbcommon_jll v1.4.1+1
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [8bf52ea8] CRC32c v1.11.0
  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.11.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [9abbd945] Profile v1.11.0
  [3fa0cd96] REPL v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [1a1011a3] SharedArrays v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.11.0
  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.6.0+0
  [e37daf67] LibGit2_jll v1.7.2+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.6+0
  [14a3606d] MozillaCACerts_jll v2023.12.12
  [4536629a] OpenBLAS_jll v0.3.27+1
  [05823500] OpenLibm_jll v0.8.1+2
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.7.0+0
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.59.0+0
  [3f19e933] p7zip_jll v17.4.0+2
  • Output of versioninfo()
Julia Version 1.11.2
Commit 5e9a32e7af2 (2024-12-01 20:02 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 12 × Intel(R) Core(TM) i7-10750H CPU @ 2.60GHz
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, skylake)
Threads: 1 default, 0 interactive, 1 GC (on 12 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS =

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@jonaswickman jonaswickman added the bug Something isn't working label Dec 10, 2024
@ChrisRackauckas ChrisRackauckas transferred this issue from SciML/DifferentialEquations.jl Dec 14, 2024
@ChrisRackauckas
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The underlying issue here is that ComponentArrays seems to be incompatible with Krylov.jl. Probably the right thing to do is to add a specialization on ldiv!(B::Vector{Float64}, D::LinearAlgebra.Diagonal{Float64, ComponentVector{…}}, A::Vector{Float64}).

@ChrisRackauckas
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Note that the easy workaround is to just choose a method like FBDF(). The issue is that when it gets too large, it switches to FBDF(linsolve=KrylovJL_GMRES()) and it's the GMRES that's failing.

@ChrisRackauckas ChrisRackauckas mentioned this issue Dec 22, 2024
Merged
@ChrisRackauckas ChrisRackauckas mentioned this issue Dec 22, 2024
Merged
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Add specialized ldiv! handling SciML/ComponentArrays.jl
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@ChrisRackauckas @jonaswickman