Positive Semidefinite FDM

[Roger-luo]

central_fdm will cause problem when one wants the input always being positive semidefinite, e.g the real value logdet function. It cause the gradcheck of logdet in Zygote fails occasionally, any idea how to preserve this property while doing FDM?

Update: I workaround it by doing

gradcheck(x->logdet(x * x'), rand(4, 4))

[willtebbutt]

Ah, yes, this is generally problematic. I always do something similar to what you've done (I'll usually add the identity to x * x' to ensure it's reasonably well conditioned though), but it's not a particularly satisfying solution.

[wesselb]

Perhaps a bit of an old issue, but just wanted to remark that there is also the solution of using forward_fdm instead of central_fdm:

julia> x = randn(2, 2); x = x'x;

julia> v = randn(2, 2); v = v'v;

julia> forward_fdm(5, 1)(ε -> logdet(x + ε .* v), 0)
38.547460846816136