This PR adds `linalg.vander`, the linalg version of `torch.vander`.
We add autograd support and support for batched inputs.
We also take this chance to improve the docs (TODO: Check that they
render correctly!) and add an OpInfo.
**Discussion**: The current default for the `increasing` kwargs is extremely
odd as it is the opposite of the classical definition (see
[wiki](https://en.wikipedia.org/wiki/Vandermonde_matrix)). This is
reflected in the docs, where I explicit both the odd defaults that we
use and the classical definition. See also [this stackoverflow
post](https://stackoverflow.com/a/71758047/5280578), which shows how
people are confused by this defaults.
My take on this would be to correct the default to be `increasing=True`
and document the divergence with NumPy (as we do for other `linalg`
functions) as:
- It is what people expect
- It gives the correct determinant called "the Vandermonde determinant" rather than (-1)^{n-1} times the Vandermonde det (ugh).
- [Minor] It is more efficient (no `flip` needed)
- Since it's under `linalg.vander`, it's strictly not a drop-in replacement for `np.vander`.
We will deprecate `torch.vander` in a PR after this one in this stack
(once we settle on what's the correct default).
Thoughts? mruberry
cc kgryte rgommers as they might have some context for the defaults of
NumPy.
Fixes https://github.com/pytorch/pytorch/issues/60197
Pull Request resolved: https://github.com/pytorch/pytorch/pull/76303
Approved by: https://github.com/albanD, https://github.com/mruberry
621ff0f973
