Time dependence in a non-autonomous linear ODE problem does not appear to propagate correctly to the solver

[ultimatile]

Describe the bug 🐞
To define time-dependent ODE problems for Non-autonomous Linear ODE / Lie Group Problems, MatrixOperator is used.
The update_func keyword argument of MatrixOperator specifies the time dependence of the ODE problem.

However, even when update_func is provided, the resulting numerical solution does not appear to reflect the time dependence of the ODE problem.
The computed result was the same as without update_func.

Expected behavior
The computed results should differ between cases with and without update_func specified.

Minimal Reproducible Example 👇

using OrdinaryDiffEqLinear
using Plots

alpha = 0.1; t0 = 0.0; t1 = 1.0; dt = 0.01
tspan = (t0, t1) 
u0 = ones(2) # initial condition
A0 = [0.0 1.0; 0.0 0.0] # time-independent part

function update_func(A, u, p, t)
    A[1, 2] = -alpha * t 
    A[2, 1] = alpha * t
end

# with update_func
prob = ODEProblem(MatrixOperator(A0; update_func), u0, tspan)
sol = solve(prob, MagnusGL8(); dt)
plot(sol, label=["u[1] w/ update_func" "u[2] w/ update_func"])

# without update_func
prob = ODEProblem(MatrixOperator(A0), u0, tspan)
sol = solve(prob, MagnusGL8(); dt)
plot!(sol, label=["u[1] w/o update_func" "u[2] w/o update_func"], color=[:lightblue :orange], alpha=0.8, linestyle=:dash, lw=3)

Different behavior is expected between the solid and dashed lines.

---

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

Status `/path/to/project/Project.toml`
  [521117fe] OrdinaryDiffEqLinear v1.1.0
  [91a5bcdd] Plots v1.40.11

• Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)

Status `/path/to/project/Manifest.toml`
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Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

• Output of versioninfo()

Julia Version 1.11.4
Commit 8561cc3d68d (2025-03-10 11:36 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin24.0.0)
  CPU: 10 × Apple M1 Max
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, apple-m1)
Threads: 1 default, 0 interactive, 1 GC (on 8 virtual cores)
Environment:
  DYLD_FALLBACK_LIBRARY_PATH = /Users/USERNAME/.julia/artifacts/c1600fa286afe4bf3616780a19b65285c63968ca/lib:/Users/USERNAME/.julia/artifacts/b820a0a437e8501d06a17439abd84feaa5b6cca3/lib:/Users/USERNAME/.julia/artifacts/5b90ad21b4b1af3a9446241fb5afe3e3b3eda941/lib:/Users/USERNAME/.julia/juliaup/julia-1.11.4+0.aarch64.apple.darwin14/lib/julia:/Users/USERNAME/.julia/artifacts/c99c0e2b61a41b4b2294b30e9f7f26e50c2e38eb/lib:/Users/USERNAME/.julia/artifacts/9410bad2635eda2239b4a72ba4316c4aa8f5b76e/lib:/Users/USERNAME/.julia/artifacts/3b568c51fbf75bfe59ac69d26b176034fdd63ebb/lib:/Users/USERNAME/.julia/artifacts/21209a2ac399ce693d73daf1aa8d670fbc84d70f/lib:/Users/USERNAME/.julia/artifacts/c59059ef20910985e15a497e3f3f9f5a01df2645/lib:/Users/USERNAME/.julia/artifacts/38c2ea0f23a62cc587d9939b8338d89cc961ea34/lib:/Users/USERNAME/.julia/artifacts/365365262519d2f165f6ca9bdc0f104718889a88/lib:/Users/USERNAME/.julia/artifacts/becfd6f89f1a272ace2375b067f1153515ca70b3/lib:/Users/USERNAME/.julia/artifacts/f00ec04851ced5895bd99297d49916ba59ca783d/lib:/Users/USERNAME/.julia/artifacts/6ebc40d37ee48f23c8a0edb94c2f1a8622edba3a/lib:/Users/USERNAME/.julia/artifacts/1994697285dfe8747ff7ec6927666edc88750202/lib:/Users/USERNAME/.julia/artifacts/c5d5b7c7e77b04af2eabde40ebbf379932d8bfd7/lib:/Users/USERNAME/.julia/artifacts/81e1d2f3a1459f121eaae539b9549e9e740a6c62/lib:/Users/USERNAME/.julia/artifacts/a3e73ecf5d803bb3792a23f0382a2b5573383647/lib:/Users/USERNAME/.julia/artifacts/67723a86975c82b43f01cda306999b382d3435f0/lib:/Users/USERNAME/.julia/artifacts/115f3a18328d7b88e31c9e3f095aeb12eb381710/lib:/Users/USERNAME/.julia/artifacts/ca2831bf6edc5088aec5b329ea98364951d6cad0/lib:/Users/USERNAME/.julia/artifacts/477447566a69a531a7a3f8e0130cbfe460b37eec/lib:/Users/USERNAME/.julia/artifacts/b58891667c46c467bd51be0e963c1ef1f0314934/lib:/Users/USERNAME/.julia/artifacts/0db9c3f6cf936a0da49e2ba954ba3e10bed6ad72/lib:/Users/USERNAME/.julia/artifacts/1a7e22e66b523d9cb884cf85c3ec065b5fb3e5c3/lib:/Users/USERNAME/.julia/artifacts/638182c11b24bfb41187d67770f2bee17fb08c74/lib:/Users/USERNAME/.julia/artifacts/83ff444c229f9dd64a13999123a4eb14e632d67a/lib:/Users/USERNAME/.julia/artifacts/6095fcd268ea712c0f786f5ff1a45bf0eb7b005e/lib:/Users/USERNAME/.julia/artifacts/7ead0a440ba045155db235bff6602a984f08a651/lib:/Users/USERNAME/.julia/artifacts/9d8a957aa3387b17b8639251016c87710db1a175/lib:/Users/USERNAME/.julia/artifacts/63d48e4aab8721470f588bdeb1e2b462ee3b6a68/lib:/Users/USERNAME/.julia/artifacts/b7801db3b1dfdd7e22586e15fd2fcd146c1ad1d9/lib:/Users/USERNAME/.julia/artifacts/8da603395acfbdbef8c5de3b7223aeb9276ecbdb/lib:/Users/USERNAME/.julia/artifacts/

Additional context
This is forwarded from this post. Please refer to the original post for more details on the ODE problem presented in this issue.

[ultimatile]

Replacing update_func with update_func! appears to yield the expected behavior.

9c9
< function update_func(A, u, p, t)
---
> function update_func!(A, u, p, t)
15c15
< prob = ODEProblem(MatrixOperator(A0; update_func), u0, tspan)
---
> prob = ODEProblem(MatrixOperator(A0; update_func!), u0, tspan)

Could this be a documentation issue rather than a bug?

---

I don't know how it affects the results, but the order of solves has changed the results without update_func (dashed lines).
By first executing without update_func, the following figure was obtained and the behavior was completely as expected

[ChrisRackauckas]

Oh I see. Yeah... well we should check to make sure the right update func is defined and give a better error message, since that's a bit tricky. But yes, it seems like OrdinaryDiffEq is working in the sense that if you give it the right function it will do it, but what we should do is that if update_func is defined and update_func! is not, but you're using an in-place solve, we should error saying that we need update_func!. That would just be a better user experience. So let's keep this open to add that erroring.

[angerpointnerd]

Could it be that there is still something wrong with the out-of-place update_func though?

Here is an example, slightly modified from the one above, where the two versions (update_func vs update_func!) give different results (unless I've missed something):

using Pkg; Pkg.activate(@__DIR__)
using OrdinaryDiffEq
using Plots

α = 0.1
t0 = 0.0
t1 = 10.0
dt = 0.01

p = (; α)
tspan = (t0, t1) 
u0 = ones(2)
A0 = zeros(2, 2)

function update_func!(A, u, p, t)
    A[1, 2] = - p.α * t
    A[2, 1] = p.α * t
    return nothing
end

function update_func(A, u, p, t)
    newA = zero(2,2)
    update_func!(newA, u, p, t)
    return newA
end

F(p, t, t0) =  p.α * (t^2 - t0^2) / 2
function analytic_solution(u0, p, t, t0)
    u1 = cos(F(p, t, t0)) * u0[1] - sin(F(p, t, t0)) * u0[2]
    u2 = sin(F(p, t, t0)) * u0[1] + cos(F(p, t, t0)) * u0[2]
    return [u1, u2]
end

analytic_solution_matrix(times, u0, p, t0) =  reduce(hcat, (t -> analytic_solution(u0, p, t, t0)).(times)) |> permutedims

function solve_and_plot(matrixOp, u0, tspan, p; plotKwargs...)
    prob = ODEProblem(matrixOp, u0, tspan, p)
    sol = solve(prob, MagnusGL8(); dt)

    plot(sol; label=["u[1] (magnus)" "u[2] (magnus)"], seriestype=:line, lw=7, opacity=0.3, plotKwargs...)
    plot!(sol.t, analytic_solution_matrix(sol.t, u0, p, t0); label=["u[1] (exact)" "u[2] (exact)"])
end

# In-place
A! = MatrixOperator(A0; update_func!)
p1 = solve_and_plot(A!, u0, tspan, p; title="in-place")

# Out-of-place
A = MatrixOperator(A0; update_func)
p2 = solve_and_plot(A, u0, tspan, p; title="out-of-place")

plot(p1, p2; size=(900, 400))
savefig("inplace_vs_outofplace.png")

environment/versioninfo

julia> using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
Status `~/Projects/test_matrix_operators/Manifest.toml`
  [47edcb42] ADTypes v1.14.0
  [7d9f7c33] Accessors v0.1.42
  [79e6a3ab] Adapt v4.3.0
  [66dad0bd] AliasTables v1.1.3
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.18.0
  [4c555306] ArrayLayouts v1.11.1
  [d1d4a3ce] BitFlags v0.1.9
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [70df07ce] BracketingNonlinearSolve v1.1.2
  [2a0fbf3d] CPUSummary v0.2.6
  [d360d2e6] ChainRulesCore v1.25.1
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [944b1d66] CodecZlib v0.7.8
  [35d6a980] ColorSchemes v3.29.0
  [3da002f7] ColorTypes v0.12.1
  [c3611d14] ColorVectorSpace v0.11.0
  [5ae59095] Colors v0.13.0
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.16.0
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [f0e56b4a] ConcurrentUtilities v2.5.0
  [187b0558] ConstructionBase v1.5.8
  [d38c429a] Contour v0.6.3
  [adafc99b] CpuId v0.3.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.22
  [e2d170a0] DataValueInterfaces v1.0.0
  [8bb1440f] DelimitedFiles v1.9.1
  [2b5f629d] DiffEqBase v6.167.2
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.6.50
  [ffbed154] DocStringExtensions v0.9.4
  [4e289a0a] EnumX v1.0.5
  [f151be2c] EnzymeCore v0.8.8
  [460bff9d] ExceptionUnwrapping v0.1.11
  [d4d017d3] ExponentialUtilities v1.27.0
  [e2ba6199] ExprTools v0.1.10
  [55351af7] ExproniconLite v0.10.14
  [c87230d0] FFMPEG v0.4.2
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [442a2c76] FastGaussQuadrature v1.0.2
  [a4df4552] FastPower v1.1.2
  [1a297f60] FillArrays v1.13.0
  [6a86dc24] FiniteDiff v2.27.0
  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
⌅ [f6369f11] ForwardDiff v0.10.38
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [46192b85] GPUArraysCore v0.2.0
  [28b8d3ca] GR v0.73.13
  [c145ed77] GenericSchur v0.5.4
  [86223c79] Graphs v1.12.1
  [42e2da0e] Grisu v1.0.2
  [cd3eb016] HTTP v1.10.15
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.5
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.4
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.10
  [692b3bcd] JLLWrappers v1.7.0
  [682c06a0] JSON v0.21.4
  [ae98c720] Jieko v0.2.1
  [ba0b0d4f] Krylov v0.9.10
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.6
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.6.1
  [87fe0de2] LineSearch v0.1.4
  [d3d80556] LineSearches v7.3.0
  [7ed4a6bd] LinearSolve v3.7.2
  [2ab3a3ac] LogExpFunctions v0.3.29
  [e6f89c97] LoggingExtras v1.1.0
  [1914dd2f] MacroTools v0.5.15
  [d125e4d3] ManualMemory v0.1.8
  [bb5d69b7] MaybeInplace v0.1.4
  [739be429] MbedTLS v1.1.9
  [442fdcdd] Measures v0.3.2
  [e1d29d7a] Missings v1.2.0
  [2e0e35c7] Moshi v0.3.5
  [46d2c3a1] MuladdMacro v0.2.4
  [d41bc354] NLSolversBase v7.9.1
  [77ba4419] NaNMath v1.1.3
  [8913a72c] NonlinearSolve v4.5.0
  [be0214bd] NonlinearSolveBase v1.5.1
  [5959db7a] NonlinearSolveFirstOrder v1.3.0
  [9a2c21bd] NonlinearSolveQuasiNewton v1.2.0
  [26075421] NonlinearSolveSpectralMethods v1.1.0
  [4d8831e6] OpenSSL v1.4.3
  [bac558e1] OrderedCollections v1.8.0
  [1dea7af3] OrdinaryDiffEq v6.93.0
  [89bda076] OrdinaryDiffEqAdamsBashforthMoulton v1.2.0
⌃ [6ad6398a] OrdinaryDiffEqBDF v1.3.0
  [bbf590c4] OrdinaryDiffEqCore v1.22.0
  [50262376] OrdinaryDiffEqDefault v1.3.0
  [4302a76b] OrdinaryDiffEqDifferentiation v1.4.0
  [9286f039] OrdinaryDiffEqExplicitRK v1.1.0
  [e0540318] OrdinaryDiffEqExponentialRK v1.4.0
  [becaefa8] OrdinaryDiffEqExtrapolation v1.5.0
⌃ [5960d6e9] OrdinaryDiffEqFIRK v1.9.0
  [101fe9f7] OrdinaryDiffEqFeagin v1.1.0
  [d3585ca7] OrdinaryDiffEqFunctionMap v1.1.1
  [d28bc4f8] OrdinaryDiffEqHighOrderRK v1.1.0
  [9f002381] OrdinaryDiffEqIMEXMultistep v1.3.0
  [521117fe] OrdinaryDiffEqLinear v1.1.0
  [1344f307] OrdinaryDiffEqLowOrderRK v1.2.0
  [b0944070] OrdinaryDiffEqLowStorageRK v1.3.0
⌃ [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.5.0
  [c9986a66] OrdinaryDiffEqNordsieck v1.1.0
  [5dd0a6cf] OrdinaryDiffEqPDIRK v1.3.0
  [5b33eab2] OrdinaryDiffEqPRK v1.1.0
  [04162be5] OrdinaryDiffEqQPRK v1.1.0
  [af6ede74] OrdinaryDiffEqRKN v1.1.0
⌃ [43230ef6] OrdinaryDiffEqRosenbrock v1.8.0
  [2d112036] OrdinaryDiffEqSDIRK v1.3.0
  [669c94d9] OrdinaryDiffEqSSPRK v1.2.1
  [e3e12d00] OrdinaryDiffEqStabilizedIRK v1.3.0
  [358294b1] OrdinaryDiffEqStabilizedRK v1.1.0
  [fa646aed] OrdinaryDiffEqSymplecticRK v1.3.0
  [b1df2697] OrdinaryDiffEqTsit5 v1.1.0
  [79d7bb75] OrdinaryDiffEqVerner v1.1.1
  [65ce6f38] PackageExtensionCompat v1.0.2
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.1
  [ccf2f8ad] PlotThemes v3.3.0
  [995b91a9] PlotUtils v1.4.3
  [91a5bcdd] Plots v1.40.11
  [f517fe37] Polyester v0.7.16
  [1d0040c9] PolyesterWeave v0.2.2
  [d236fae5] PreallocationTools v0.4.26
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [43287f4e] PtrArrays v1.3.0
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
  [731186ca] RecursiveArrayTools v3.31.2
  [189a3867] Reexport v1.2.2
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [94e857df] SIMDTypes v0.1.0
  [0bca4576] SciMLBase v2.82.0
  [19f34311] SciMLJacobianOperators v0.1.1
  [c0aeaf25] SciMLOperators v0.3.13
  [53ae85a6] SciMLStructures v1.7.0
  [6c6a2e73] Scratch v1.2.1
  [efcf1570] Setfield v1.1.2
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.2.0
  [727e6d20] SimpleNonlinearSolve v2.2.0
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  [47a9eef4] SparseDiffTools v2.24.0
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  [276daf66] SpecialFunctions v2.5.0
  [860ef19b] StableRNGs v1.0.2
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  [90137ffa] StaticArrays v1.9.13
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  [3783bdb8] TableTraits v1.0.1
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  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.5.2
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [1986cc42] Unitful v1.22.0
  [45397f5d] UnitfulLatexify v1.6.4
  [41fe7b60] Unzip v0.2.0
  [19fa3120] VertexSafeGraphs v0.2.0
  [6e34b625] Bzip2_jll v1.0.9+0
  [83423d85] Cairo_jll v1.18.4+0
  [ee1fde0b] Dbus_jll v1.14.10+0
  [2702e6a9] EpollShim_jll v0.0.20230411+1
  [2e619515] Expat_jll v2.6.5+0
⌅ [b22a6f82] FFMPEG_jll v4.4.4+1
  [a3f928ae] Fontconfig_jll v2.16.0+0
  [d7e528f0] FreeType2_jll v2.13.4+0
  [559328eb] FriBidi_jll v1.0.17+0
  [0656b61e] GLFW_jll v3.4.0+2
  [d2c73de3] GR_jll v0.73.13+0
  [78b55507] Gettext_jll v0.21.0+0
⌃ [7746bdde] Glib_jll v2.82.4+0
  [3b182d85] Graphite2_jll v1.3.15+0
  [2e76f6c2] HarfBuzz_jll v8.5.0+0
  [1d5cc7b8] IntelOpenMP_jll v2025.0.4+0
  [aacddb02] JpegTurbo_jll v3.1.1+0
  [c1c5ebd0] LAME_jll v3.100.2+0
  [88015f11] LERC_jll v4.0.1+0
  [1d63c593] LLVMOpenMP_jll v18.1.7+0
  [dd4b983a] LZO_jll v2.10.3+0
⌅ [e9f186c6] Libffi_jll v3.2.2+2
  [d4300ac3] Libgcrypt_jll v1.11.1+0
  [7e76a0d4] Libglvnd_jll v1.7.0+0
  [7add5ba3] Libgpg_error_jll v1.51.1+0
  [94ce4f54] Libiconv_jll v1.18.0+0
  [4b2f31a3] Libmount_jll v2.41.0+0
  [89763e89] Libtiff_jll v4.7.1+0
  [38a345b3] Libuuid_jll v2.41.0+0
  [856f044c] MKL_jll v2025.0.1+1
  [e7412a2a] Ogg_jll v1.3.5+1
  [458c3c95] OpenSSL_jll v3.0.16+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [91d4177d] Opus_jll v1.3.3+0
  [36c8627f] Pango_jll v1.56.1+0
  [30392449] Pixman_jll v0.44.2+0
⌅ [c0090381] Qt6Base_jll v6.7.1+1
⌅ [629bc702] Qt6Declarative_jll v6.7.1+2
⌅ [ce943373] Qt6ShaderTools_jll v6.7.1+1
⌃ [e99dba38] Qt6Wayland_jll v6.7.1+1
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
⌃ [a2964d1f] Wayland_jll v1.21.0+2
  [2381bf8a] Wayland_protocols_jll v1.36.0+0
  [02c8fc9c] XML2_jll v2.13.6+1
  [aed1982a] XSLT_jll v1.1.43+0
  [ffd25f8a] XZ_jll v5.8.1+0
  [f67eecfb] Xorg_libICE_jll v1.1.2+0
  [c834827a] Xorg_libSM_jll v1.2.4+0
  [4f6342f7] Xorg_libX11_jll v1.8.6+3
  [0c0b7dd1] Xorg_libXau_jll v1.0.12+0
  [935fb764] Xorg_libXcursor_jll v1.2.3+0
  [a3789734] Xorg_libXdmcp_jll v1.1.5+0
  [1082639a] Xorg_libXext_jll v1.3.6+3
  [d091e8ba] Xorg_libXfixes_jll v6.0.0+0
  [a51aa0fd] Xorg_libXi_jll v1.8.2+0
  [d1454406] Xorg_libXinerama_jll v1.1.5+0
  [ec84b674] Xorg_libXrandr_jll v1.5.4+0
  [ea2f1a96] Xorg_libXrender_jll v0.9.11+1
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.2+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.0+3
  [cc61e674] Xorg_libxkbfile_jll v1.1.2+1
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.4+0
  [12413925] Xorg_xcb_util_image_jll v0.4.0+1
  [2def613f] Xorg_xcb_util_jll v0.4.0+1
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
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⌅ [1270edf5] x264_jll v2021.5.5+0
⌅ [dfaa095f] x265_jll v3.5.0+0
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  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
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Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

julia> versioninfo()
Julia Version 1.10.8
Commit 4c16ff44be8 (2025-01-22 10:06 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 64 × AMD Ryzen Threadripper PRO 3975WX 32-Cores
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
Threads: 1 default, 0 interactive, 1 GC (on 64 virtual cores)
Environment:
  JULIA_PKG_USE_CLI_GIT = true
  JULIA_EDITOR = code
  JULIA_NUM_THREADS = 

(The Julia version is still 1.10.8, but I also tried fresh environments with 1.11.4 and the 1.12 beta with the same results)

[ChrisRackauckas]

Yeah something seems funky in the out of place one.

[angerpointnerd]

I tried to figure out what's going on and so far I think the out-of-place update_func is not actually used in the Magnus solvers.

Putting a

@show newA

in update_func from the above MWE indicates that the function is never actually called. Instead it will use the (constant) A0 with whatever values it had after running the solver with in-place update_func!. If I turn around the two solves, I get a different plot, because A0 was never updated by the in-place solver and we just get a constant solution (A0 = zeros(2,2), so the right-hand-side is just zero).

At least from what I could see here
https://github.com/SciML/OrdinaryDiffEq.jl/blob/15007385d68ee0256ddb69a451cda083d75ad26b/lib/OrdinaryDiffEqLinear/src/linear_perform_step.jl
it seems that almost all solvers call an in-place update_coefficients!, which in turn calls update_func! in the MatrixOperator:
https://github.com/SciML/SciMLOperators.jl/blob/29ea228be466d841159c90bacfec89d686f51fdc/src/matrix.jl#L158-L166

There seems to be no "re-routing" of the function call between the in-place and out-of-place versions depending on which one was given. My idea would be to do some inspection on the provided update_func and update_func! in the constructor of MatrixOperator, such that update_coefficients! and update_coefficients always pick the one that is actually defined by the user, e.g.

• if update_func is passed, an internal update_func! gets defined such that it updates the given cache by just writing the values from update_func to it (so it would still allocate, but have the right behavior)
• if update_func! is passed, we define update_func to create a new array each time and call the passed update_func! on it
• if both are passed by the user it should throw an error (which one should be picked?)
• if neither are passed, we could either throw an error and suggest to define an "empty" update_func! (which I would prefer to be more explicit about what the user wants), or we keep the current behavior and assume A should stay constant, so both update_func[!] versions do nothing
• all downstream code could then be left as is as (hopefully) both versions of update_func[!] should work and be consistent

I'd be happy to give it a try implementing a solution, but I'm not sure the idea above is the right way to go.