Mario Lezcano Casado

The MPS tests were failing when I dispatched the function to the simple implementation. I left the current implementation (which just supports `k=0`) and left a comment.

Summary of the current errors: - [XLA](https://github.com/pytorch/pytorch/actions/runs/3096234035/jobs/5011756688) and [ONNX](https://github.com/pytorch/pytorch/actions/runs/3096234035/jobs/5011727486): Should be easy to fix - [NNC](https://github.com/pytorch/pytorch/actions/runs/3096235185/jobs/5011710134) / [nvFuser](https://github.com/pytorch/pytorch/actions/runs/3096235185/jobs/5012128949): These tests parse `torch.eye(1, k=0)` as `torch.eye(1, 0)` disregarding the kwarg. I...

@eellison this PR is stuck on some JIT failures. In particular, [NNC](https://github.com/pytorch/pytorch/actions/runs/3096235185/jobs/5011710134) / [nvFuser](https://github.com/pytorch/pytorch/actions/runs/3096235185/jobs/5012128949) fail because here https://github.com/pytorch/pytorch/blob/b13b10a8fab83c9c260e16a8cfb4d99140e9352b/torch/jit/_trace.py#L344-L351 even though `func` is bound as `torch.eye(n, k=k)`, with `k` a kwarg,...

I asked for access to the collab with the benchmarks. It would be good to put some example benchmark in the open, so that it can be reviewed by OSS...

At risk of stating the obvious, that message happens when you try to run `backward` on an element that does not have a `requires_grad=True` or comes from a computation with...

Ok, so I think what's happening here is that you are removing the whole backward function, while in the other PR, they are removing only the backward function for the...

FWIW, if you want to check that a matrix is SPD, as you're doing in that test, you should check that `A = A.mT` and then that `linalg.eigvalsh(A)` (perhaps with...

Also, note that `linalg.eigvalsh` supports batches (as all the `linalg` functions do) so you can remove the for loop, which should make this function *much* more efficient.

Would this PR fix https://github.com/pytorch/pytorch/issues/80252?

And if so, please throw in some relevant benchmarks once @peterbell10's concerns are addressed