Implement forward AD for linalg.svd and improve svd_backward (#70253)
Summary:
Pull Request resolved: https://github.com/pytorch/pytorch/pull/70253
I included a derivation of the formula in the complex case, as it is
particularly tricky. As far as I know, this is the first time this formula
is derived in the literature.
I also implemented a more efficient and more accurate version of svd_backward.
More importantly, I also added a lax check in the complex case making sure the loss
function just depends on the subspaces spanned by the pairs of singular
vectors, and not their joint phase.
cc jianyuh nikitaved pearu mruberry walterddr IvanYashchuk xwang233 Lezcano
Test Plan: Imported from OSS
Reviewed By: mikaylagawarecki
Differential Revision: D33751982
Pulled By: mruberry
fbshipit-source-id: c2a4a92a921a732357e99c01ccb563813b1af512
(cherry picked from commit 391319ed8f2e0ecc1e034d8eaecfb38f5ea4615f)
