Implement torch.linalg.svd (#45562)
Summary:
This is related to https://github.com/pytorch/pytorch/issues/42666 .
I am opening this PR to have the opportunity to discuss things.
First, we need to consider the differences between `torch.svd` and `numpy.linalg.svd`:
1. `torch.svd` takes `some=True`, while `numpy.linalg.svd` takes `full_matrices=True`, which is effectively the opposite (and with the opposite default, too!)
2. `torch.svd` returns `(U, S, V)`, while `numpy.linalg.svd` returns `(U, S, VT)` (i.e., V transposed).
3. `torch.svd` always returns a 3-tuple; `numpy.linalg.svd` returns only `S` in case `compute_uv==False`
4. `numpy.linalg.svd` also takes an optional `hermitian=False` argument.
I think that the plan is to eventually deprecate `torch.svd` in favor of `torch.linalg.svd`, so this PR does the following:
1. Rename/adapt the old `svd` C++ functions into `linalg_svd`: in particular, now `linalg_svd` takes `full_matrices` and returns `VT`
2. Re-implement the old C++ interface on top of the new (by negating `full_matrices` and transposing `VT`).
3. The C++ version of `linalg_svd` *always* returns a 3-tuple (we can't do anything else). So, there is a python wrapper which manually calls `torch._C._linalg.linalg_svd` to tweak the return value in case `compute_uv==False`.
Currently, `linalg_svd_backward` is broken because it has not been adapted yet after the `V ==> VT` change, but before continuing and spending more time on it I wanted to make sure that the general approach is fine.
Pull Request resolved: https://github.com/pytorch/pytorch/pull/45562
Reviewed By: H-Huang
Differential Revision: D25803557
Pulled By: mruberry
fbshipit-source-id: 4966f314a0ba2ee391bab5cda4563e16275ce91f
