pytorch Allow linalg.lstsq to use svd to compute the result for rank deficient matrices.

Fixes #117122

This PR adds the logic so that in the case of rank deficient matrices, it can fallback to an SVD backend for batched mode. A big thank you to @tvercaut for the well written issue and suggestion on how to approach the problem.

Summary:

At the time of writing this I haven't touched non-batched yet. I am hoping to get some feedback before proceeding.
I believe there should be eyes on how specifically we want to fallback to SVD as the implementation when we run into rank deficient matrices.

Please keep in mind this is my 2nd PR to pytorch, and I've never really used pytorch. I'm learning independently through digging deep in the internals so I may make some obvious mistakes. Please forgive!

cc @gujinghui @PenghuiCheng @XiaobingSuper @jianyuh @jgong5 @mingfeima @sanchitintel @ashokei @jingxu10 @min-jean-cho @yanbing-j @Guobing-Chen @Xia-Weiwen @snadampal

Apr 28 '24 00:04 ZelboK

:link: Helpful Links

:test_tube: See artifacts and rendered test results at hud.pytorch.org/pr/125110

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As of commit 454d0d4b147057b3483aa0af71494b47634cb7e2 with merge base 4d063c8e8aa6be1b0b249ffedc3fd24f2aed2113 (): :green_heart: Looks good so far! There are no failures yet. :green_heart:

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Apr 28 '24 00:04 pytorch-bot[bot]

@janeyx99 @ptrblck

2nd PR! 🎉 Sorry it took me some days. I'm learning Pytorch internals independently so I'm still learning the codebase.

Also I'm curious to know if there's a community like slack or discord for Pytorch?

Apr 28 '24 01:04 ZelboK

mind cleaning up all the spurious new lines and the PR in general?

Apr 28 '24 04:04 lezcano

@lezcano

My apologies! I've cleaned it up. I missed some new lines from when I was cleaning up my debugging/experimenting code so I could understand the codebase.

Apr 28 '24 09:04 ZelboK

@lezcano

So when it comes to the tests, what kind of test did you think would be appropriate, aside from checking that it no longer throws? I can add gelss as a driver to be used in test_linalg_lstsq_batch_broadcasting for example and assure its results are as expected. I'm not too familiar with the test suites yet so hoping for guidance here.

Edit: Workflow runs exposed two failing tests for CPU and complex lstsq computations. I didn't notice I didn't build with LAPACK, so these tests were skipped. Will look into it now.

Apr 28 '24 16:04 ZelboK

@cpuhrsch @lezcano Could one of you please run the pipeline / tests workflow to see if perhaps these tests are flaky on my environment for whatever reason?

May 01 '24 12:05 ZelboK

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May 19 '24 19:05 linux-foundation-easycla[bot]

bad rebase. Too many people are tagged now. Open a new PR.

May 19 '24 19:05 lezcano

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Allow linalg.lstsq to use svd to compute the result for rank deficient matrices.

:link: Helpful Links

:test_tube: See artifacts and rendered test results at hud.pytorch.org/pr/125110

:white_check_mark: No Failures

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