reduce allocation in a few linalg functions while removing full calls

[Sacha0]

This pull request reduces allocation in a few linalg functions by replacing (allocating) full calls with (non-allocating) alternatives. Serves as another small step towards deprecation of full. Ref. #12153, #12251, #18850, and linked threads. Best!

[andreasnoack]

What about having a generic function for this operation?

[Sacha0]

What about having a generic function for this operation?

As in the present full!? I thought of extending full! from the triangular types to Symmetric/Hermitian and deploying it here, but hesitated for a few reasons:

Foremost I wanted to ponder full!'s semantics (to make certain I was not replacing one poorly defined operation with another). But full!'s semantics seem well defined: Make the parent match the child's contents and return the parent.

Next I was curious how frequently full! sees use, and whether in those cases some better approach exists. (My experience in eliminating full has been that usually a better approach exists, as e.g. in this pull request.) Outside the potential uses in this pull request, full! has only three uses (exclusively in two-argument A_mul_B[c]! methods), and one of those uses is redundant. But in those cases full!'s semantics do seem right, and as this pull request demonstrates full!'s semantics are useful beyond the existing uses.

So given the above I favor your proposition, i.e. I lean towards extending full! to Symmetric/Hermitian and deploying it here. But simultaneously I would rename full! to reflect its semantics. Some ideas: fillparent!, fixparent!, matchparent!, conformparent!, completeparent!.

In any case playing with full! seemed like something for a followup pull request, so I left off.

Thoughts? Thanks! :)

[Sacha0]

Rebased and extended to the full calls introduced in #23679. Assuming CI signs off and absent objections or requests for time, I plan to merge these changes this evening or tomorrow morning and carry through the plan outlined in #24137 (comment) in a followup pull request. Best!

[fredrikekre]

linalg/dense: Test Failed
  Expression: all((z->begin
            -π < imag(z) < π && real(z) > 0 || (0 <= imag(z) < π && abs(real(z)) < abstol || abs(imag(z) - π) < abstol && real(z) >= 0)
        end), (eigfact(acosh(A)))[:values])

[Sacha0]

(The CI failure should be fixed. Thanks @fredrikekre! :) )

[Sacha0]

Thanks all!