error when function may return both real and complex results

[simeonschaub]

Minimal example:

julia> using FiniteDifferences

julia> using ChainRulesTestUtils: _fdm

julia> j′vp(_fdm, x -> sum(x) > 1 ? zeros(10) : zeros(ComplexF64, 10), rand(10), zeros(10))
ERROR: DimensionMismatch("second dimension of A, 20, does not match length of x, 10")
Stacktrace:
 [1] gemv!(y::Vector{Float64}, tA::Char, A::Matrix{Float64}, x::Vector{Float64}, α::Bool, β::Bool)
   @ LinearAlgebra /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.8/LinearAlgebra/src/matmul.jl:530
 [2] mul!
   @ /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.8/LinearAlgebra/src/matmul.jl:97 [inlined]
 [3] mul!
   @ /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.8/LinearAlgebra/src/matmul.jl:275 [inlined]
 [4] *(transA::LinearAlgebra.Transpose{Float64, Matrix{Float64}}, x::Vector{Float64})
   @ LinearAlgebra /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.8/LinearAlgebra/src/matmul.jl:87
 [5] _j′vp(fdm::FiniteDifferences.AdaptedFiniteDifferenceMethod{5, 1, FiniteDifferences.UnadaptedFiniteDifferenceMethod{7, 5}}, f::Function, ȳ::Vector{Float64}, x::Vector{Float64})
   @ FiniteDifferences ~/.julia/dev/FiniteDifferences/src/grad.jl:80
 [6] j′vp(fdm::FiniteDifferences.AdaptedFiniteDifferenceMethod{5, 1, FiniteDifferences.UnadaptedFiniteDifferenceMethod{7, 5}}, f::Function, ȳ::Vector{Float64}, x::Vector{Float64})
   @ FiniteDifferences ~/.julia/dev/FiniteDifferences/src/grad.jl:73
 [7] top-level scope
   @ REPL[10]:1

The issue here is that jacobian assumes that to_vec(f(x)) is always the same size if x is perturbed, which fails if f(x) can sometimes be real and sometimes complex. This does occur in the real world, in my case it was with eigen(M).vectors (ref https://github.com/JuliaDiff/ChainRules.jl/blob/8ce21af2c8f8fa5dad4b1d5aaac32c7847ed1b9f/test/rulesets/LinearAlgebra/factorization.jl#L214). It might be enough to just throw a better error message here suggesting to convert the output of f to complex numbers.