expv does not work when used in NonlinearSolve.jl equations

[homocomputeris]

Describe the bug 🐞

Solver fails when expv is in the function. exponential! kinda works.

Expected behavior

Optimize. See https://discourse.julialang.org/t/how-can-i-use-nonlinearsolve-jl-with-matrix-functions/112379

Minimal Reproducible Example 👇

using NonlinearSolve
using LinearAlgebra
using ExponentialUtilities

dim = 2
function f(u, p)
    v = rand(2)
    return expv(1, u, v) - v*2
end

u0 = rand(dim, dim) * 0.01
p = nothing
prob = NonlinearProblem(f, u0, p)
sol = solve(prob)
display(sol)
err = sol - zeros(dim, dim)
display(err)

Error & Stacktrace ⚠️

ERROR: MethodError: no method matching exponential!(::Matrix{ForwardDiff.Dual{ForwardDiff.Tag{…}, Float64, 4}}, ::ExpMethodHigham2005Base)

Closest candidates are:
  exponential!(::StridedMatrix{T}, ::ExpMethodHigham2005Base, ::Any) where T<:Union{Float32, Float64, ComplexF64, ComplexF32}
   @ ExponentialUtilities ~/.julia/packages/ExponentialUtilities/xLH9y/src/exp_baseexp.jl:23
  exponential!(::StridedMatrix{T}, ::ExpMethodHigham2005Base) where T<:Union{Float32, Float64, ComplexF64, ComplexF32}
   @ ExponentialUtilities ~/.julia/packages/ExponentialUtilities/xLH9y/src/exp_baseexp.jl:23
  exponential!(::Any, ::ExpMethodNative, ::Any)
   @ ExponentialUtilities ~/.julia/packages/ExponentialUtilities/xLH9y/src/exp.jl:70
  ...

Stacktrace:
  [1] expv!(w::Vector{…}, t::Int64, Ks::KrylovSubspace{…}; cache::Nothing, expmethod::ExpMethodHigham2005Base)
    @ ExponentialUtilities ~/.julia/packages/ExponentialUtilities/xLH9y/src/krylov_phiv.jl:95
  [2] _expv_hb(t::Int64, A::Matrix{…}, b::Vector{…}; expmethod::ExpMethodHigham2005Base, cache::Nothing, kwargs_arnoldi::@Kwargs{})
    @ ExponentialUtilities ~/.julia/packages/ExponentialUtilities/xLH9y/src/krylov_phiv.jl:51
  [3] _expv_hb(t::Int64, A::Matrix{ForwardDiff.Dual{ForwardDiff.Tag{…}, Float64, 4}}, b::Vector{Float64})
    @ ExponentialUtilities ~/.julia/packages/ExponentialUtilities/xLH9y/src/krylov_phiv.jl:45
  [4] expv(t::Int64, A::Matrix{ForwardDiff.Dual{…}}, b::Vector{Float64}; mode::Symbol, kwargs::@Kwargs{})
    @ ExponentialUtilities ~/.julia/packages/ExponentialUtilities/xLH9y/src/krylov_phiv.jl:38
  [5] expv(t::Int64, A::Matrix{ForwardDiff.Dual{ForwardDiff.Tag{…}, Float64, 4}}, b::Vector{Float64})
    @ ExponentialUtilities ~/.julia/packages/ExponentialUtilities/xLH9y/src/krylov_phiv.jl:35
  [6] f(u::Matrix{ForwardDiff.Dual{ForwardDiff.Tag{NonlinearSolve.NonlinearSolveTag, Float64}, Float64, 4}}, p::Nothing)
    @ Main ./Untitled-1:8
  [7] (::NonlinearFunction{…})(::Matrix{…}, ::Vararg{…})
    @ SciMLBase ~/.julia/packages/SciMLBase/QSc1r/src/scimlfunctions.jl:2197
  [8] (::SciMLBase.JacobianWrapper{false, NonlinearFunction{…}, Nothing})(u::Matrix{ForwardDiff.Dual{…}})
    @ SciMLBase ~/.julia/packages/SciMLBase/QSc1r/src/function_wrappers.jl:97
  [9] vector_mode_dual_eval!(f::SciMLBase.JacobianWrapper{…}, cfg::ForwardDiff.JacobianConfig{…}, x::Matrix{…})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/apiutils.jl:24
 [10] vector_mode_jacobian!(result::Matrix{…}, f::SciMLBase.JacobianWrapper{…}, x::Matrix{…}, cfg::ForwardDiff.JacobianConfig{…})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/jacobian.jl:145
 [11] jacobian!(result::Matrix{…}, f::Function, x::Matrix{…}, cfg::ForwardDiff.JacobianConfig{…}, ::Val{…})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/jacobian.jl:58
 [12] jacobian!(result::Matrix{…}, f::Function, x::Matrix{…}, cfg::ForwardDiff.JacobianConfig{…})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/jacobian.jl:56
 [13] sparse_jacobian!(J::Matrix{…}, ::AutoForwardDiff{…}, cache::SparseDiffTools.ForwardDiffJacobianCache{…}, f::SciMLBase.JacobianWrapper{…}, x::Matrix{…})
    @ SparseDiffTools ~/.julia/packages/SparseDiffTools/qxnHN/src/highlevel/forward_mode.jl:60
 [14] (::NonlinearSolve.JacobianCache{…})(J::Matrix{…}, u::Matrix{…}, p::Nothing)
    @ NonlinearSolve ~/.julia/packages/NonlinearSolve/5yLII/src/internal/jacobian.jl:136
 [15] JacobianCache
    @ ~/.julia/packages/NonlinearSolve/5yLII/src/internal/jacobian.jl:106 [inlined]
 [16] __step!(cache::NonlinearSolve.GeneralizedFirstOrderAlgorithmCache{…}; recompute_jacobian::Nothing, kwargs::@Kwargs{})
    @ NonlinearSolve ~/.julia/packages/NonlinearSolve/5yLII/src/core/generalized_first_order.jl:207
 [17] __step!
    @ ~/.julia/packages/NonlinearSolve/5yLII/src/core/generalized_first_order.jl:203 [inlined]
 [18] #step!#210
    @ ~/.julia/packages/NonlinearSolve/5yLII/src/core/generic.jl:55 [inlined]
 [19] step!
    @ ~/.julia/packages/NonlinearSolve/5yLII/src/core/generic.jl:50 [inlined]
 [20] solve!(cache::NonlinearSolve.GeneralizedFirstOrderAlgorithmCache{…})
    @ NonlinearSolve ~/.julia/packages/NonlinearSolve/5yLII/src/core/generic.jl:13
 [21] __solve(::NonlinearProblem{…}, ::GeneralizedFirstOrderAlgorithm{…}; kwargs::@Kwargs{…})
    @ NonlinearSolve ~/.julia/packages/NonlinearSolve/5yLII/src/core/generic.jl:4
 [22] __solve
    @ ~/.julia/packages/NonlinearSolve/5yLII/src/core/generic.jl:1 [inlined]
 [23] macro expansion
    @ ~/.julia/packages/NonlinearSolve/5yLII/src/default.jl:278 [inlined]
 [24] __solve(::NonlinearProblem{…}, ::NonlinearSolvePolyAlgorithm{…}; alias_u0::Bool, verbose::Bool, kwargs::@Kwargs{…})
    @ NonlinearSolve ~/.julia/packages/NonlinearSolve/5yLII/src/default.jl:248
 [25] __solve
    @ ~/.julia/packages/NonlinearSolve/5yLII/src/default.jl:248 [inlined]
 [26] #__solve#329
    @ ~/.julia/packages/NonlinearSolve/5yLII/src/default.jl:511 [inlined]
 [27] __solve
    @ ~/.julia/packages/NonlinearSolve/5yLII/src/default.jl:508 [inlined]
 [28] #__solve#61
    @ ~/.julia/packages/DiffEqBase/nc5nE/src/solve.jl:1371 [inlined]
 [29] __solve
    @ ~/.julia/packages/DiffEqBase/nc5nE/src/solve.jl:1364 [inlined]
 [30] #solve_call#34
    @ ~/.julia/packages/DiffEqBase/nc5nE/src/solve.jl:609 [inlined]
 [31] solve_call
    @ ~/.julia/packages/DiffEqBase/nc5nE/src/solve.jl:567 [inlined]
 [32] #solve_up#42
    @ ~/.julia/packages/DiffEqBase/nc5nE/src/solve.jl:1050 [inlined]
 [33] solve_up
    @ ~/.julia/packages/DiffEqBase/nc5nE/src/solve.jl:1044 [inlined]
 [34] #solve#41
    @ ~/.julia/packages/DiffEqBase/nc5nE/src/solve.jl:1038 [inlined]
 [35] solve(::NonlinearProblem{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/nc5nE/src/solve.jl:1028
 [36] top-level scope
    @ Untitled-1:14
Some type information was truncated. Use `show(err)` to see complete types.

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

[667455a9] Cubature v1.5.1
  [31c24e10] Distributions v0.25.107
  [d4d017d3] ExponentialUtilities v1.26.1
  [f6369f11] ForwardDiff v0.10.36
⌃ [de52edbc] Integrals v4.3.0
⌃ [8913a72c] NonlinearSolve v3.8.3
⌃ [1dea7af3] OrdinaryDiffEq v6.70.1
⌃ [91a5bcdd] Plots v1.40.1
  [44d3d7a6] Weave v0.10.12

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

⌃ [47edcb42] ADTypes v0.2.6
⌃ [7d9f7c33] Accessors v0.1.35
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  [944b1d66] CodecZlib v0.7.4
  [35d6a980] ColorSchemes v3.24.0
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⌃ [34da2185] Compat v4.12.0
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⌃ [864edb3b] DataStructures v0.18.16
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  [8bb1440f] DelimitedFiles v1.9.1
⌃ [2b5f629d] DiffEqBase v6.146.2
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⌃ [bdcacae8] LoopVectorization v0.12.166
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⌃ [bb5d69b7] MaybeInplace v0.1.1
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⌃ [8913a72c] NonlinearSolve v3.8.3
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⌃ [727e6d20] SimpleNonlinearSolve v1.4.1
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  [2db6ffa8] libevdev_jll v1.11.0+0
  [f638f0a6] libfdk_aac_jll v2.0.2+0
  [36db933b] libinput_jll v1.18.0+0
⌃ [b53b4c65] libpng_jll v1.6.40+0
  [f27f6e37] libvorbis_jll v1.3.7+1
  [009596ad] mtdev_jll v1.1.6+0
  [1270edf5] x264_jll v2021.5.5+0
  [dfaa095f] x265_jll v3.5.0+0
  [d8fb68d0] xkbcommon_jll v1.4.1+1
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.10.0
  [de0858da] Printf
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays v1.10.0
  [10745b16] Statistics v1.10.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.1.0+0
  [deac9b47] LibCURL_jll v8.4.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.2+1
  [14a3606d] MozillaCACerts_jll v2023.1.10
  [4536629a] OpenBLAS_jll v0.3.23+4
  [05823500] OpenLibm_jll v0.8.1+2
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.8.0+1
  [8e850ede] nghttp2_jll v1.52.0+1
  [3f19e933] p7zip_jll v17.4.0+2
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 1.10.2
Commit bd47eca2c8a (2024-03-01 10:14 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (x86_64-apple-darwin22.4.0)
  CPU: 8 × Intel(R) Core(TM) i5-8279U CPU @ 2.40GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, skylake)
Threads: 8 default, 0 interactive, 4 GC (on 8 virtual cores)
Environment:
  JULIA_EDITOR = code

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