ENH: Add uarray support for scipy.linalg

[Smit-create]

• Reference issue: uarray based backend compatibility tracker scipy/scipy#14353

[Smit-create]

@rgommers
I have a suggestion for the design:

1. We can move all the _*_replacer functions to a new file _multimethods_replacers.py and document in each replacer that which functions in _multimethods.py uses it for dispatching since there isn't much to look into these replacer functions for bugs and moreover it reduces the effort to write some common replacer functions like _x_replacer which can be used across multiple submodules.
2. So, _multimethods.py will purely contain the function definitions which will reduce its size too and easy to maintain.

[rgommers]

This and _a_b_replacer further down seem identical, as does _A_E_replacer. Why do we need multiple of these, just with a different name to match parameter names? It looks to me like this could be simplified.

[Smit-create]

Why do we need multiple of these, just with a different name to match parameter names?

Yes, see scipy#14407 (comment)

[rgommers]

That will reduce it a little; I suspect we may be able to get rid of some of those replacers completely to make it a small issue. The definitions could also be grouped together at the top of the file, right under _create_linalg = ....

Let's see what @AnirudhDagar and @czgdp1807 think as well.

[rgommers]

As we discussed, this:

• overrides functions which use asanyarray internally, and
• breaks for sparse matrix inputs

The asanyarray should be looked into per function (and possibly removed, as I think is likely a good idea for clarkson_woodruff), the sparse matrices need handling with an explicit check here and don't need to be coerced.

[czgdp1807]

The definitions could also be grouped together at the top of the file, right under _create_linalg = ....

Yes. Putting together all the replacers might also help in discovering patterns which we can utilise in future. And yes, some replacers are exactly similar with just different function names.

[Smit-create]

Linalg looks complete now and ready for higher-level review. Just some refactoring can make it look better. Also, we need to figure out the circular import issue in order to run the whole test suite with scipy backend (i.e. actually using _multimethods functions wherever possible).