DEP: sparse.linalg: deprecate positional arguments for gcrotmk, lgmres, minres, tfqmr

[j-bowhay]

Reference issue

follow up to #18934, towards #18703

What does this implement/fix?

Agreed for adding gcrotmk, lgmres, minres, tfqmr. The artificial separation was due to Fortran removal efforts, but there is no distinction among these anymore.

Additional information

[h-vetinari]

Thanks!

[rgommers]

This and the previous PR don't look quite right to me. The * should have been either in the place where the deprecated keyword was (tol, IIRC) or otherwise at least in a place where it's an unambiguous win. Which is not the case for x0, which isn't a descriptive keyword (as I think I sketched out somewhere, but I can't find it back).

Forcing users to write gmres(A, B, x0=x0) and forbidding writing gmres(A, B, x0) does not make the code clearer, and it actually breaks a significant amount of end user code when doing so. A quick GitHub code search for "scipy gmres" finds that usage is mixed between positional and keyword usage of x0. E.g., here are two results from the first page of search results that will break:

• https://github.com/nschloe/scipyx/blob/63e78503065fd048686d263fe5feea91471b0be3/tests/test_krylov.py#L96 (@nschloe may be able to comment on this change, as he's a regular contributor)
• https://github.com/tclaudioe/Scientific-Computing/blob/51e188c9a28c5528fe4feeeb4edc7d0176d13801/SC1/10_GMRes.ipynb#L250 (first notebook

I'll note that other keywords are clearer and used as keywords in a large majority of cases (e.g., here). However, x0 is not. So I suggest adapting this and previous PRs to leave x0 alone.

[h-vetinari]

That's a good point, fine by me (which is why I had split these in separate PRs, because the placement of the * is not always 100% self-evident).

[j-bowhay]

Updated as per discussion

[h-vetinari]

Thanks!