Allow pushing to vector after 3-arg ldiv!

[simonbyrne]

Fixes #43507. Fixes #29852.

[oscardssmith]

This doesn't seem like a good fix. It fixes the specific problem, but doesn't do anything to address the more general problem which is that you can't resize a Vector if it ever has been viewed, even if none of those views exist.

[simonbyrne]

Sure, but that's a much more general issue. This solves a specific concrete issue that causes problems elsewhere (SciML/LinearSolve.jl#81)

[oscardssmith]

In that case, can you add a TODO to this to say it's safe to remove once the general issue is solved?

[simonbyrne]

Is there a big problem to having separate methods? It does make it simpler, and avoids intermediate views

[dkarrasch]

In the failing test (which fails for Julia v1.6+), the untouched matrix-method in the m <= n branch copies to the wrong place: Y is 3x3, B is 2x3 and copyto! (in the new line 136) copies along linear indices. It should perhaps read as:

function ldiv!(Y::AbstractMatrix, A::Factorization, B::AbstractMatrix)
    require_one_based_indexing(Y, B)
    m, n = size(A, 1), size(A, 2)
    if m > n
        Bc = copy(B)
        ldiv!(A, Bc)
        return copyto!(Y, view(Bc, 1:n, :))
    else
        copyto!(view(Y, 1:m, :), view(B, 1:m, :))
        return ldiv!(A, Y)
    end
end

At least with this change the failing test fails no more. Not sure if we need more size checks here, actually.

[dkarrasch]

Backporting to v1.6 requires special care due to the ColumnNorm() argument...

[simonbyrne]

Thanks @dkarrasch!

Backporting to v1.6 requires special care due to the ColumnNorm() argument...

I think changing it to Val(true) should work.

[dkarrasch]

Shall we just merge or rebase before merging?