SparseMatrixCSC constructors for structured matrices - Diagonal, Tridiagonal, etc.

[dkarrasch]

This keeps identical functionality, but makes the specialized constructors for structured matrices such as Diagonal, Bidiagonal etc. available to the broadcast machinery.

Fixes #31770.

[ViralBShah]

Looks good. It would be good to get some tests in and merge.

[dkarrasch]

There exist these:

julia/stdlib/SparseArrays/test/sparse.jl

Lines 1463 to 1479 in 4b6ab68

	@testset "issue #10837, sparse constructors from special matrices" begin
	T = Tridiagonal(randn(4),randn(5),randn(4))
	S = sparse(T)
	@test norm(Array(T) - Array(S)) == 0.0
	T = SymTridiagonal(randn(5),rand(4))
	S = sparse(T)
	@test norm(Array(T) - Array(S)) == 0.0
	B = Bidiagonal(randn(5),randn(4),:U)
	S = sparse(B)
	@test norm(Array(B) - Array(S)) == 0.0
	B = Bidiagonal(randn(5),randn(4),:L)
	S = sparse(B)
	@test norm(Array(B) - Array(S)) == 0.0
	D = Diagonal(randn(5))
	S = sparse(D)
	@test norm(Array(D) - Array(S)) == 0.0
	end

Since sparse calls SparseMatrixCSC they are tested already. Should I simply duplicate these tests and replace each sparse by SparseMatrixCSC or is it enough what we have.

On a different note, I have code that does what was asked for in #10843 (comment). I could add it here and leave the individual commits for review, or open another PR.

Edit: It may make sense to merge this as is and then have another PR in which the SparseMatrixCSC constructors are changed. The speed-up is about a factor of 10, so worth it, I'd say.

[ViralBShah]

I agree. Merged this one in - but we can have further optimizations if you already have them in a separate PR.

[Roger-luo]

Will this be backported?

[ViralBShah]

Triage should decide whether this goes into 1.2.

[StefanKarpinski]

This is a feature, so no.