rrule for QR-decomposition

[oschulz]

Would be nice to have an rrule for QR-decomposition.

According to https://rkube.github.io/jekyll/update/2021/07/06/backpropagating-through-qr.html, Pytorch uses the method described in https://arxiv.org/abs/1710.08717 .

[oschulz]

CC @cscherrer

[sethaxen]

We already have #516, #306, and #469. 2 of these are by the author of the linked blog post.

QR rules in Julia are trickier than in PyTorch, jax, etc for reasons summarized in #469 (comment). I'll allocate some time in the coming month to dig into these proposals and push this forward.

[oschulz]

Oh, right - thanks @sethaxen ! I'll close this issue, then.

[oschulz]

Sorry, I somehow overlooked the existing PRs.

[wangleiphy]

@GiggleLiu anything you can help with here ?

[GiggleLiu]

@GiggleLiu anything you can help with here ?

I probably can help with testing complex valued backward rule, and thin qr. The general purposed qr backward with pivot is a bit tricky. Since I do not have time to dive into all of these issues at the moment, I would suggest copy-paste the part that you need?