Automatic Jacobian sparsity detection fails when concatenating interpolations

[SouthEndMusic]

Describe the bug 🐞

There is an error when trying to obtain the Jacobian sparsity of a function with Symbolics.jacobian_sparsity if that function concatenates interpolations.

Minimal Reproducible Example 👇

using Symbolics: jacobian_sparsity
using DataInterpolations

u = [1.0, 2.0]
t = [0.0, 2.0]
A = LinearInterpolation(u, t)
B = LinearInterpolation(u.^2, t; extrapolate = true)

out0 = zeros(5)
x0 = rand(5)

function f!(out, x)
    for (i, x_) in enumerate(x)
        out[i] = (B ∘ A)(x_)
    end
end

jacobian_sparsity((out, x) -> f!(out, x), out0, x0)

Error & Stacktrace ⚠️

ERROR: MethodError: no method matching (::LinearInterpolation{…})(::SymbolicUtils.BasicSymbolic{…})

Closest candidates are:
  (::DataInterpolations.AbstractInterpolation)(::Symbolics.Num)
   @ DataInterpolationsSymbolicsExt path\to\DataInterpolations\ext\DataInterpolationsSymbolicsExt.jl:15
  (::DataInterpolations.AbstractInterpolation)(::Number)
   @ DataInterpolations path\to\DataInterpolations\src\DataInterpolations.jl:25
  (::DataInterpolations.AbstractInterpolation)(::Number, ::Integer)
   @ DataInterpolations path\to\DataInterpolations\src\DataInterpolations.jl:26
  ...

Stacktrace:
 [1] f!(out::Vector{Symbolics.Num}, x::Vector{Symbolics.Num})
   @ Main path\to\runner.jl:15
 [2] (::var"#13#14")(out::Vector{Symbolics.Num}, x::Vector{Symbolics.Num})
   @ Main path\to\runner.jl:20
 [3] jacobian_sparsity(::Function, ::Vector{Float64}, ::Vector{Float64}; kwargs::@Kwargs{})
   @ Symbolics path\to\.julia\packages\Symbolics\8tggF\src\diff.jl:598
 [4] jacobian_sparsity(::Function, ::Vector{Float64}, ::Vector{Float64})
   @ Symbolics path\to\.julia\packages\Symbolics\8tggF\src\diff.jl:593
 [5] top-level scope
   @ path\to\runner.jl:20

Environment

DataInterpolations v5.3.1
Symbolics v5.30.1

[sathvikbhagavan]

With this

function f!(out, x)
    for (i, x_) in enumerate(x)
        t = A(x_)
        out[i] = B(wrap(t))
    end
end

it works,

julia> jacobian_sparsity((out, x) -> f!(out, x), out0, x0)
5×5 SparseArrays.SparseMatrixCSC{Bool, Int64} with 5 stored entries:
 1  ⋅  ⋅  ⋅  ⋅
 ⋅  1  ⋅  ⋅  ⋅
 ⋅  ⋅  1  ⋅  ⋅
 ⋅  ⋅  ⋅  1  ⋅
 ⋅  ⋅  ⋅  ⋅  1

This can be fixed with a missing dispatch or just registering interpolation. I will make the PR.