Add relative and absolute tolerance for rank.

[sam0410]

This is for issue number #3249

[StefanKarpinski]

Thanks for the PR! The standard names for this are rtol and atol, see docs for isapprox.

[sam0410]

Thanks for reviewing @StefanKarpinski. I changed the names.

[StefanKarpinski]

Requesting review from @andreasnoack for general linalg expertise and @stevengj because I know you were instrumental in the design of the isapprox behavior and we want to make sure that these APIs and behaviors are as consistent and coherent as possible.

[stevengj]

As was commented in #29793, to be consistent we should also add these keywords for pinv and nullspace.

[StefanKarpinski]

Thanks for the thorough review, @stevengj!

As was commented in #29793, to be consistent we should also add these keywords for pinv and nullspace.

It seems like it would be fine to make those changes in separate PRs if preferred after getting this one in good shape and merged.

[stevengj]

It would be easier to review them together for consistency, since it is almost the same change in all three cases, and it is good to keep the APIs for those functions consistent since they are closely related mathematically.

[StefanKarpinski]

I'd like to not overwhelm @sam0410 with too many not-strictly-necessary requests on a first PR here.

[sam0410]

Hi @StefanKarpinski, I will add the keywords to pinv and nullspace as mentioned by @stevengj in a different PR. Also, the build here is failing because of some 32bit issue- not because of the code in this PR.

[simonbyrne]

I made a few small edits (we can't deprecate the old method yet, but I've added a note that we should do that in future).

[simonbyrne]

Thanks for sticking with this!