Differentiate general eigen and eigvals
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Currently, ForwardDiff.jl only supports differentiating through
eigenandeigvalsofSymmetricorHermitianmatrices, but not for a generalStridedMatrix. In JuliaManifolds/Manifolds.jl#27 (comment), there is a working version for differentiating througheigenandeigvalsfor general matrices, which also works for complex eigenvalues (e.g., DifferentiableEigen.jl does not support complex eigenvalues). I just copied that version here for higher visibility, more convenient usage, and to avoid type piracy in my (and maybe other's) code. So credit goes to @mateuszbaran. The algorithm is from https://people.maths.ox.ac.uk/gilesm/files/NA-08-01.pdf.I open this as a draft PR because I am not sure if there is something additional that needs to be considered. If this PR is wanted, I can add tests and do a bit of cleanup.
cc @dlfivefifty since he added support for
eigenfor symmetric and Hermitian matrices.Closes #111.