Improve REPL printing of UmfpackLU

[goggle]

This PR addresses another issue from #24588.

Consider this code:

using LinearAlgebra
using SparseArrays
A = sparse([1, 2], [1, 2], Float64[1.0, 1.0])
F = lu(A)

Prior to this PR, the LU factorization looked like this:

julia> F
UMFPACK LU Factorization of a (2, 2) sparse matrix
Ptr{Nothing} @0x0000557483015a10

Now it is shown in the same manner as the LU factorization of a dense matrix:

julia> F
SuiteSparse.UMFPACK.UmfpackLU{Float64,Int64}
L factor:
2×2 SparseMatrixCSC{Float64,Int64} with 2 stored entries:
  [1, 1]  =  1.0
  [2, 2]  =  1.0
U factor:
2×2 SparseMatrixCSC{Float64,Int64} with 2 stored entries:
  [1, 1]  =  1.0
  [2, 2]  =  1.0

[ViralBShah]

Even the dense LU seems to show too much in my opinion. I wonder if we should show less output for the dense LU.

[goggle]

I don't see any downsides in showing some detailed information about a performed matrix factorization. It's much more visually appealing than just showing a type (or something similar) in my opinion. And it only affects REPL sessions, where the user usually wants to have some interaction. Furthermore it can easily be prevented by adding a ; at the end of the line.

[ViralBShah]

I agree with that - but this scrolls to two screenfuls! My preference would be to show fewer entries and restrict the printing to be about half a screenful.

[goggle]

To achieve this, we would need to crop the displayed matrices in a more aggressive manner, e.g. restrict the number of shown entries to 10. I would suggest to address this as a follow-up of #24588, because it's not only about LU, but also all the other factorization types.

[andreasnoack]

I think we should definitely get rid of the Ptr part of the printing. However, I'm generally not a fan of printing entries from a sparse array. I don't think it's useful information for sparse matrices so I'd rather provide some information about sparsity.

[ViralBShah]

On better printing of sparse matrices, there's also: #30587

[goggle]

@ViralBShah Thanks, this is definitely interesting!

[dkarrasch]

This PR is somewhat independent from the sparse printing, isn't it? Whatever is going on there, will be simply pasted in here, IIUC. Thus, ignoring that aspect, is this PR then acceptable? I'd say it's very much in line with what we have for other factorizations.

[andreasnoack]

Given the development in the sparse printing I also think this is fine as it is.