Symbolics.jacobian_sparsity detection errors with PreallocationTools

Specific Domains Numerics
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1

When I try to do jacobian sparsity detection, I get error that ERROR: MethodError: no method matching zero(::Type{Any}).
The array returned from PreallocationsTools.jl for array of Symbolics.Num datatype, is of type Vector{Any}. So when I do some mathematical operations on it, it errors. Here is a MWE

using Symbolics, PreallocationTools, SparseArrays
import LinearAlgebra as LA

function f!(du::AbstractArray{T}, u::AbstractArray{T}, p) where {T}
    ∇, vbd, intp, Γd, tmp, v = p
    v = get_tmp(v, first(u))
    tmp = get_tmp(tmp, first(u))
    v[Γd] .= vbd
    v[intp] .= u
    @show typeof(v)
    LA.mul!(tmp, ∇, v)
    tmp - sin.(v)
    du .= tmp[intp]
    return
end

function main()
    n = 1000
    Γd = rand(1:n, 10)
    v = rand(n)
    vcache = DiffCache(v[:])
    tmp = DiffCache(v[:])
    vbd = v[Γd]
    intp = setdiff(1:n, Γd)
    ∇ = sprand(n, n, 0.3)
    p = (∇, vbd, intp, Γd, tmp, vcache)
    u = v[intp]
    du = similar(u)
    f1!(du, u) = f!(du, u, p)
    jac_sp = Symbolics.jacobian_sparsity(f1!, du, u)
    jac_sp = Float64.(jac_sp)
    return jac_sp
end

jac_sp = main()

It seems I’m missing something and there should be an easy fix for this. Thanks in advance.

2

You might need special handling of it, like v = v isa Vector{Any} ? typeof(first(v)).(v) : v to concretize it. Since that would only allocate in the symbolics run, it won’t really impact performance in what you need but should fix the symbolics tracing.

3

That doesn’t quite for this example, after this change it says

ERROR: UndefRefError: access to undefined reference

It seems, preallocationtools hasn’t yet allocated memory for this datatype.
But this idea works if we manually allocate the memory for vector for type T.

    v = v isa Vector{Any} ? Vector{T}(undef, length(v)) : v

Thanks a lot Chris.