Error with jac_prototype in Mass Matrix Form of ODEFunction (svd! on Sparse Matrix)

[SanjeevKhare]

Describe the bug 🐞

I’m solving a DAE system mass matrix form. The system works correctly when I define the ODEFunction without the jac_prototype. However, when I include the jac_prototype (which is a SparseMatrixCSC), I encounter an error during the call to solve.

Expected behavior

I expect the solver to solve DAE.

Minimal Reproducible Example 👇

using LinearAlgebra
using SparseArrays
using ADTypes, SparseConnectivityTracer
using DifferentialEquations

function laplacian(n)
    main_diag = -2.0 * ones(n)
    off_diag = ones(n - 1)
    return spdiagm(0 => main_diag, -1 => off_diag, 1 => off_diag)
end

function landau_khalatnikov_debug!(du, u, p)
    poisson_residue_debug!(du, u, p)
    return nothing
end

function poisson_residue_debug!(du, u, p)
    l1, l2 = laplacian.(p)
    lap = kron(l2, I(p[1])) + kron(I(p[2]), l1)
    du, u = view(du, :), view(u, :)
    mul!(du, lap, u)
    return nothing
end

function system_residue_debug!(du, u, p, t)
    Ny, Nx, Nyfed = p
    num_nodes = Ny * Nx
    num_edges = Nyfed * Nx
    fill!(du, zero(eltype(u)))
    Py = view(u, 1:num_edges)
    dPy = view(du, 1:num_edges)
    ϕ = view(u, 1+num_edges:num_edges+num_nodes)
    dϕ = view(du, 1+num_edges:num_edges+num_nodes)

    Py = reshape(Py, Nyfed, Nx)
    dPy = reshape(dPy, Nyfed, Nx)
    ϕ = reshape(ϕ, Ny, Nx)
    dϕ = reshape(dϕ, Ny, Nx)

    landau_khalatnikov_debug!(dPy, Py, (Nyfed, Nx))
    poisson_residue_debug!(dϕ, ϕ, (Ny, Nx))
    return nothing
end

Nx, Ny, Nyfe = 32, 32, 13
params = Ny, Nx, Nyfe + 1

ϕ = zeros(Ny, Nx)
Py = rand(Nyfe + 1, Nx)
u0 = rand(length(Py) + length(ϕ))
du = similar(u0)

# Jacobian sparsity
system_residue_debug!(du, u0, params, 0.0)
jac_sparsity_system = ADTypes.jacobian_sparsity((du, u) -> system_residue_debug!(du, u, params, 0.0), similar(u0), copy(u0), TracerSparsityDetector())
jac_prototype = float.(jac_sparsity_system)

mass_matrix = Diagonal(vcat(ones(length(Py)), zeros(length(ϕ))))
ode_func = ODEFunction(system_residue_debug!, jac_prototype=jac_prototype, mass_matrix=mass_matrix)
ode_prob = ODEProblem(ode_func, u0, (0.0, 1e-19), params)
sol = solve(ode_prob, Rodas5(), reltol=1e-8, abstol=1e-8)

Error & Stacktrace ⚠️

ERROR: MethodError: no method matching svd!(::SparseMatrixCSC{Float64, Int64}; full::Bool, alg::LinearAlgebra.DivideAndConquer)
The function `svd!` exists, but no method is defined for this combination of argument types.

Closest candidates are:
  svd!(::LinearAlgebra.AbstractTriangular; kwargs...)
   @ LinearAlgebra ~/.julia/juliaup/julia-1.11.4+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/LinearAlgebra/src/triangular.jl:2746
  svd!(::SciMLOperators.ScaledOperator, Any...) got unsupported keyword arguments "full", "alg"
   @ SciMLOperators ~/.julia/packages/SciMLOperators/2UPBq/src/basic.jl:285
  svd!(::SciMLOperators.ComposedOperator, Any...) got unsupported keyword arguments "full", "alg"
   @ SciMLOperators ~/.julia/packages/SciMLOperators/2UPBq/src/basic.jl:663
  ...

Stacktrace:
  [1] svd(A::SparseMatrixCSC{Float64, Int64}; full::Bool, alg::LinearAlgebra.DivideAndConquer)
    @ LinearAlgebra ~/.julia/juliaup/julia-1.11.4+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/LinearAlgebra/src/svd.jl:179
  [2] svd(A::SparseMatrixCSC{Float64, Int64})
    @ LinearAlgebra ~/.julia/juliaup/julia-1.11.4+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/LinearAlgebra/src/svd.jl:178
  [3] pinv(A::SparseMatrixCSC{Float64, Int64}; atol::Float64, rtol::Float64)
    @ LinearAlgebra ~/.julia/juliaup/julia-1.11.4+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/LinearAlgebra/src/dense.jl:1562
  [4] pinv
    @ ~/.julia/juliaup/julia-1.11.4+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/LinearAlgebra/src/dense.jl:1546 [inlined]
  [5] maybe_pinv!!
    @ ~/.julia/packages/NonlinearSolveBase/5ckRl/src/utils.jl:206 [inlined]
  [6] step!(cache::NonlinearSolveQuasiNewton.QuasiNewtonCache{…}; recompute_jacobian::Nothing)
    @ NonlinearSolveQuasiNewton ~/.julia/packages/NonlinearSolveQuasiNewton/aC2cy/src/solve.jl:247
  [7] step!
    @ ~/.julia/packages/NonlinearSolveQuasiNewton/aC2cy/src/solve.jl:232 [inlined]
  [8] #step!#163
    @ ~/.julia/packages/NonlinearSolveBase/5ckRl/src/solve.jl:253 [inlined]
  [9] step!
    @ ~/.julia/packages/NonlinearSolveBase/5ckRl/src/solve.jl:247 [inlined]
 [10] solve!(cache::NonlinearSolveQuasiNewton.QuasiNewtonCache{…})
    @ NonlinearSolveBase ~/.julia/packages/NonlinearSolveBase/5ckRl/src/solve.jl:18
 [11] __solve(::NonlinearProblem{…}, ::NonlinearSolveQuasiNewton.QuasiNewtonAlgorithm{…}; kwargs::@Kwargs{…})
    @ NonlinearSolveBase ~/.julia/packages/NonlinearSolveBase/5ckRl/src/solve.jl:6
 [12] macro expansion
    @ ~/.julia/packages/NonlinearSolveBase/5ckRl/src/solve.jl:173 [inlined]
 [13] __generated_polysolve(::NonlinearProblem{…}, ::NonlinearSolveBase.NonlinearSolvePolyAlgorithm{…}; stats::SciMLBase.NLStats, alias_u0::Bool, verbose::Bool, initializealg::NonlinearSolveBase.NonlinearSolveDefaultInit, kwargs::@Kwargs{…})
    @ NonlinearSolveBase ~/.julia/packages/NonlinearSolveBase/5ckRl/src/solve.jl:130
 [14] __generated_polysolve
    @ ~/.julia/packages/NonlinearSolveBase/5ckRl/src/solve.jl:130 [inlined]
 [15] #__solve#154
    @ ~/.julia/packages/NonlinearSolveBase/5ckRl/src/solve.jl:127 [inlined]
 [16] __solve
    @ ~/.julia/packages/NonlinearSolveBase/5ckRl/src/solve.jl:124 [inlined]
 [17] #solve_call#35
    @ ~/.julia/packages/DiffEqBase/zYZst/src/solve.jl:635 [inlined]
 [18] solve_call
    @ ~/.julia/packages/DiffEqBase/zYZst/src/solve.jl:592 [inlined]
 [19] #solve_up#44
    @ ~/.julia/packages/DiffEqBase/zYZst/src/solve.jl:1126 [inlined]
 [20] solve_up
    @ ~/.julia/packages/DiffEqBase/zYZst/src/solve.jl:1120 [inlined]
 [21] #solve#43
    @ ~/.julia/packages/DiffEqBase/zYZst/src/solve.jl:1114 [inlined]
 [22] _initialize_dae!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, prob::ODEProblem{…}, alg::BrownFullBasicInit{…}, isinplace::Val{…})
    @ OrdinaryDiffEqNonlinearSolve ~/.julia/packages/OrdinaryDiffEqNonlinearSolve/e4hoO/src/initialize_dae.jl:434
 [23] _initialize_dae!
    @ ~/.julia/packages/OrdinaryDiffEqCore/bMOsj/src/initialize_dae.jl:56 [inlined]
 [24] initialize_dae!
    @ ~/.julia/packages/OrdinaryDiffEqCore/bMOsj/src/initialize_dae.jl:40 [inlined]
 [25] initialize_dae!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/bMOsj/src/initialize_dae.jl:40
 [26] __init(prob::ODEProblem{…}, alg::Rodas5{…}, timeseries_init::Tuple{}, ts_init::Tuple{}, ks_init::Tuple{}, recompile::Type{…}; saveat::Tuple{}, tstops::Tuple{}, d_discontinuities::Tuple{}, save_idxs::Nothing, save_everystep::Bool, save_on::Bool, save_start::Bool, save_end::Nothing, callback::Nothing, dense::Bool, calck::Bool, dt::Float64, dtmin::Float64, dtmax::Float64, force_dtmin::Bool, adaptive::Bool, gamma::Rational{…}, abstol::Float64, reltol::Float64, qmin::Rational{…}, qmax::Int64, qsteady_min::Int64, qsteady_max::Rational{…}, beta1::Nothing, beta2::Nothing, qoldinit::Rational{…}, controller::Nothing, fullnormalize::Bool, failfactor::Int64, maxiters::Int64, internalnorm::typeof(DiffEqBase.ODE_DEFAULT_NORM), internalopnorm::typeof(opnorm), isoutofdomain::typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), unstable_check::typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), verbose::Bool, timeseries_errors::Bool, dense_errors::Bool, advance_to_tstop::Bool, stop_at_next_tstop::Bool, initialize_save::Bool, progress::Bool, progress_steps::Int64, progress_name::String, progress_message::typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), progress_id::Symbol, userdata::Nothing, allow_extrapolation::Bool, initialize_integrator::Bool, alias::ODEAliasSpecifier, initializealg::OrdinaryDiffEqCore.DefaultInit, kwargs::@Kwargs{})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/bMOsj/src/solve.jl:565
 [27] __init (repeats 5 times)
    @ ~/.julia/packages/OrdinaryDiffEqCore/bMOsj/src/solve.jl:11 [inlined]
 [28] __solve(::ODEProblem{…}, ::Rodas5{…}; kwargs::@Kwargs{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/bMOsj/src/solve.jl:6
 [29] __solve
    @ ~/.julia/packages/OrdinaryDiffEqCore/bMOsj/src/solve.jl:1 [inlined]
 [30] #solve_call#35
    @ ~/.julia/packages/DiffEqBase/zYZst/src/solve.jl:635 [inlined]
 [31] solve_call
    @ ~/.julia/packages/DiffEqBase/zYZst/src/solve.jl:592 [inlined]
 [32] solve_up(prob::ODEProblem{…}, sensealg::Nothing, u0::Vector{…}, p::Tuple{…}, args::Rodas5{…}; kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/zYZst/src/solve.jl:1142
 [33] solve_up
    @ ~/.julia/packages/DiffEqBase/zYZst/src/solve.jl:1120 [inlined]
 [34] solve(prob::ODEProblem{…}, args::Rodas5{…}; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/zYZst/src/solve.jl:1057
 [35] top-level scope
    @ REPL[23]: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()

  [47edcb42] ADTypes v1.14.0
  [0c46a032] DifferentialEquations v7.16.1
  [9f842d2f] SparseConnectivityTracer v0.6.16
  [2f01184e] SparseArrays v1.11.0

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

  [47edcb42] ADTypes v1.14.0
  [7d9f7c33] Accessors v0.1.42
  [79e6a3ab] Adapt v4.3.0
  [66dad0bd] AliasTables v1.1.3
  [a95523ee] AlmostBlockDiagonals v0.1.10
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.18.0
  [4c555306] ArrayLayouts v1.11.1
  [aae01518] BandedMatrices v1.9.3
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [764a87c0] BoundaryValueDiffEq v5.16.0
  [7227322d] BoundaryValueDiffEqAscher v1.5.0
  [56b672f2] BoundaryValueDiffEqCore v1.8.0
  [85d9eb09] BoundaryValueDiffEqFIRK v1.6.0
  [1a22d4ce] BoundaryValueDiffEqMIRK v1.6.0
  [9255f1d6] BoundaryValueDiffEqMIRKN v1.5.0
  [ed55bfe0] BoundaryValueDiffEqShooting v1.6.0
  [70df07ce] BracketingNonlinearSolve v1.1.3
  [fa961155] CEnum v0.5.0
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  [d360d2e6] ChainRulesCore v1.25.1
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  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.22
  [e2d170a0] DataValueInterfaces v1.0.0
  [bcd4f6db] DelayDiffEq v5.52.0
  [2b5f629d] DiffEqBase v6.167.2
  [459566f4] DiffEqCallbacks v4.4.0
  [77a26b50] DiffEqNoiseProcess v5.24.1
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [0c46a032] DifferentialEquations v7.16.1
  [a0c0ee7d] DifferentiationInterface v0.6.51
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  [6a86dc24] FiniteDiff v2.27.0
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  [2774e3e8] NLsolve v4.5.1
  [77ba4419] NaNMath v1.1.3
  [8913a72c] NonlinearSolve v4.5.1
  [be0214bd] NonlinearSolveBase v1.5.2
  [5959db7a] NonlinearSolveFirstOrder v1.3.1
  [9a2c21bd] NonlinearSolveQuasiNewton v1.2.1
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  [429524aa] Optim v1.12.0
  [bac558e1] OrderedCollections v1.8.0
  [1dea7af3] OrdinaryDiffEq v6.93.0
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  [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 v1.9.0
  [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
  [90014a1f] PDMats v0.11.34
  [65ce6f38] PackageExtensionCompat v1.0.2
  [d96e819e] Parameters v0.12.3
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  [b27032c2] LibCURL v0.6.4
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  [1a1011a3] SharedArrays v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [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+4
  [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 1.11.4
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: 11 × Apple M3 Pro
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, apple-m2)
Threads: 1 default, 0 interactive, 1 GC (on 5 virtual cores)

Additional context
I have posted this on discourse as well over here. The error is related to NonlinearSolve step.

[oscardssmith]

This will be fixed by SciML/NonlinearSolve.jl#577

[ChrisRackauckas]

Solved in the latest NonlinearSolve v4.6 release.