Feature: Support tuple and NamedTuple outputs

[bdrhill]

Problem

Functions returning tuples or NamedTuples fail with MethodError because to_array in src/trace_functions.jl doesn't handle these types.

MWE

using SparseConnectivityTracer

detector = TracerSparsityDetector()

# Tuple output fails
f_tuple(x) = (x[1]^2, x[2]^2)
jacobian_sparsity(f_tuple, [1.0, 2.0], detector)
# MethodError: no method matching to_array(::Tuple{GradientTracer...})

# NamedTuple output fails  
f_nt(x) = (a=x[1]^2, b=x[2]^2)
jacobian_sparsity(f_nt, [1.0, 2.0], detector)
# MethodError: no method matching to_array(::NamedTuple...)

Expected behavior

These should work by collecting the tuple elements into an array:

to_array(x::Tuple) = collect(x)
to_array(x::NamedTuple) = collect(values(x))

Related

This is related to #298 (Better unpacking of output types) which mentions Rational/Complex types.

[bdrhill]

Also worth noting: custom struct outputs fail with the same root cause (no to_array method). However, structs would require reflection (getfield/fieldnames) to extract values, which may be more complex than tuples.

struct MyResult{T}
    a::T
    b::T
end
f(x) = MyResult(x[1]^2, x[2]^2)
jacobian_sparsity(f, [1.0, 2.0], detector)
# MethodError: no method matching to_array(::MyResult{...})

[adrhill]

Related to #28. I personally don't have the time to implement this right now, so I'm tagging this as "not planned". A solution should be implemented with #194 in mind.