gradient! writes to the wrong entries for structured inputs #838

extract_gradient! and extract_gradient_chunk! take their target positions from structural_eachindex(result), i.e. from the result container, while the seeds are laid out according to structural_eachindex(x). When the two disagree, the derivatives land in the wrong entries.

julia> using ForwardDiff, LinearAlgebra, DiffResults

julia> x = UpperTriangular([1.0 2.0 3.0; 0.0 4.0 5.0; 0.0 0.0 6.0]);

julia> f(z) = sum(abs2, z) / 2;   # df/dz[i,j] == z[i,j] on the structural entries

julia> ForwardDiff.gradient(f, x)   # correct -- the result is allocated as `similar(x)`
3×3 UpperTriangular{Float64, Matrix{Float64}}:
 1.0  2.0  3.0
  ⋅   4.0  5.0
  ⋅    ⋅   6.0

julia> out = fill(NaN, 3, 3); ForwardDiff.gradient!(out, f, x); out
3×3 Matrix{Float64}:
 1.0  3.0  NaN
 2.0  5.0  NaN
 4.0  6.0  NaN

The six derivatives are written to linear positions 1:6 of the dense result instead of to the upper triangle. No error, no warning, and it happens at every chunk size including vector mode.

With a DiffResult it errors instead, because DiffResults.gradient! does a linear copyto! into the UpperTriangular buffer that GradientResult allocated:

julia> ForwardDiff.gradient!(DiffResults.GradientResult(x), f, x)
ERROR: ArgumentError: cannot set index (2, 1) in the lower triangular part of an UpperTriangular matrix to a nonzero value (2.0)

Same for LowerTriangular and Diagonal. Introduced in #739.

The fix is presumably to derive the positions from x rather than from result — gradient! has x right there. That is what I ended up doing for the Hessian in #837, where the same delegation would otherwise have mis-scattered the gradient stored in a HessianResult (whose gradient buffer is dense even when x is not).

ForwardDiff v1.4.5, Julia 1.12.6.