Creating of `OptimizationSystem` with registered function traces

[avinashresearch1]

MWE:

using Symbolics, ModelingToolkit
using LinearAlgebra
import LinearAlgebra: eigvals

p_free = @variables begin
    p1, [bounds = (0, 1)]
    p2, [bounds = (0, 1)]
    p3, [bounds = (0, 1)]
    p4, [bounds = (0, 1)]
end

m = diagm(p_free)

function myeigvals_1(A::AbstractMatrix)
    eigvals(A)[1]
end

@register_symbolic myeigvals_1(A::AbstractMatrix)

obj = myeigvals_1(m)
@named opt_sys = OptimizationSystem(obj, p_free, [])

This line in the OptimizationSystemconstructor calls substitute with fold = true by default and no way to change it:

ModelingToolkit.jl/src/systems/optimization/optimizationsystem.jl

Line 117 in 5691fa3

op′ = substitute(op′, irreducible_subs)

and this ends up tracing.

Error & Stacktrace ⚠️

ERROR: MethodError: no method matching zero(::Type{Any})
This error has been manually thrown, explicitly, so the method may exist but be intentionally marked as unimplemented.

Closest candidates are:
  zero(::Type{Union{Missing, T}}) where T
   @ Base missing.jl:105
  zero(::Type{Union{}}, Any...)
   @ Base number.jl:310
  zero(::Type{Dates.DateTime})
   @ Dates ~/.julia/juliaup/julia-1.11.3+0.x64.linux.gnu/share/julia/stdlib/v1.11/Dates/src/types.jl:458
  ...

Stacktrace:
 [1] zero(::Type{Any})
   @ Base ./missing.jl:106
 [2] eigtype(T::Type)
   @ LinearAlgebra ~/.julia/juliaup/julia-1.11.3+0.x64.linux.gnu/share/julia/stdlib/v1.11/LinearAlgebra/src/eigen.jl:319
 [3] eigvals(A::Matrix{Any}; kws::@Kwargs{})
   @ LinearAlgebra ~/.julia/juliaup/julia-1.11.3+0.x64.linux.gnu/share/julia/stdlib/v1.11/LinearAlgebra/src/eigen.jl:343
 [4] eigvals(A::Matrix{Any})
   @ LinearAlgebra ~/.julia/juliaup/julia-1.11.3+0.x64.linux.gnu/share/julia/stdlib/v1.11/LinearAlgebra/src/eigen.jl:343
 [5] myeigvals_1(A::Matrix{Any})
   @ Main ~/JULIAHUB/AFRL/SymbolicRegisterTest.jl/much_simpler_MWE.jl:17
 [6] substitute(expr::SymbolicUtils.BasicSymbolic{Real}, dict::Dict{Any, Any}; fold::Bool)
   @ SymbolicUtils ~/.julia/packages/SymbolicUtils/QUEf3/src/substitute.jl:28
 [7] substitute(expr::SymbolicUtils.BasicSymbolic{Real}, dict::Dict{Any, Any})
   @ SymbolicUtils ~/.julia/packages/SymbolicUtils/QUEf3/src/substitute.jl:16
 [8] OptimizationSystem(op::Num, unknowns::Vector{…}, ps::Vector{…}; observed::Vector{…}, constraints::Vector{…}, default_u0::Dict{…}, default_p::Dict{…}, defaults::Dict{…}, name::Symbol, description::String, systems::Vector{…}, checks::Bool, metadata::Nothing, gui_metadata::Nothing)
   @ ModelingToolkit ~/.julia/packages/ModelingToolkit/8S2W1/src/systems/optimization/optimizationsystem.jl:117
 [9] top-level scope
   @ ~/.julia/packages/ModelingToolkit/8S2W1/src/systems/abstractsystem.jl:1958
Some type information was truncated. Use `show(err)` to see complete types.

Note that this traced into the eigvals call.

One can also look at:

julia> substitute(myeigvals_1(m), Dict())
ERROR: MethodError: no method matching zero(::Type{Any})
This error has been manually thrown, explicitly, so the method may exist but be intentionally marked as unimplemented.

Closest candidates are:
  zero(::Type{Union{Missing, T}}) where T
   @ Base missing.jl:105
  zero(::Type{Union{}}, Any...)
   @ Base number.jl:310
  zero(::Type{Dates.DateTime})
   @ Dates ~/.julia/juliaup/julia-1.11.3+0.x64.linux.gnu/share/julia/stdlib/v1.11/Dates/src/types.jl:458
  ...

Stacktrace:
  [1] zero(::Type{Any})
    @ Base ./missing.jl:106
  [2] eigtype(T::Type)
    @ LinearAlgebra ~/.julia/juliaup/julia-1.11.3+0.x64.linux.gnu/share/julia/stdlib/v1.11/LinearAlgebra/src/eigen.jl:319
  [3] eigvals(A::Matrix{Any}; kws::@Kwargs{})
    @ LinearAlgebra ~/.julia/juliaup/julia-1.11.3+0.x64.linux.gnu/share/julia/stdlib/v1.11/LinearAlgebra/src/eigen.jl:343
  [4] eigvals(A::Matrix{Any})
    @ LinearAlgebra ~/.julia/juliaup/julia-1.11.3+0.x64.linux.gnu/share/julia/stdlib/v1.11/LinearAlgebra/src/eigen.jl:343
  [5] myeigvals_1(A::Matrix{Any})
    @ Main ~/JULIAHUB/AFRL/SymbolicRegisterTest.jl/much_simpler_MWE.jl:17
  [6] substitute(expr::SymbolicUtils.BasicSymbolic{Real}, dict::Dict{Any, Any}; fold::Bool)

yet, if fold = false it doesn't trace as expected:

A proposed fix is for OptimizationSystem to expose the fold kwarg?

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

⌃ [961ee093] ModelingToolkit v9.64.3
  [7f7a1694] Optimization v4.1.1
  [d1185830] SymbolicUtils v3.19.0
  [0c5d862f] Symbolics v6.29.2