Diagonal-sandwiched triple product for SparseMatrixCSC

[jishnub]

After this,

julia> using SparseArrays, LinearAlgebra

julia> D = Diagonal(1:4)
4×4 Diagonal{Int64, UnitRange{Int64}}:
 1  ⋅  ⋅  ⋅
 ⋅  2  ⋅  ⋅
 ⋅  ⋅  3  ⋅
 ⋅  ⋅  ⋅  4

julia> S = sprand(4, 4, 0.2)
4×4 SparseMatrixCSC{Float64, Int64} with 6 stored entries:
 0.8632  0.206049   ⋅        0.921636
  ⋅       ⋅        0.49266    ⋅ 
  ⋅       ⋅        0.329707   ⋅ 
  ⋅       ⋅         ⋅        0.69844

julia> D * S * D
4×4 SparseMatrixCSC{Float64, Int64} with 6 stored entries:
 0.8632  0.412098   ⋅        3.68655
  ⋅       ⋅        2.95596    ⋅ 
  ⋅       ⋅        2.96736    ⋅ 
  ⋅       ⋅         ⋅       11.175

This operation of pre- and post-multiplication by Diagonals is not uncommon, as it scales the rows and columns of the sandwiched matrix. After this PR, the result is a sparse matrix as well.

The new implementation changes the following behavior:

julia> D = Diagonal(StepRangeLen(NaN, 0, 4));

julia> D * S * D
4×4 SparseMatrixCSC{Float64, Int64} with 3 stored entries:
    ⋅    ⋅      ⋅    ⋅ 
    ⋅    ⋅   NaN     ⋅ 
    ⋅    ⋅   NaN     ⋅ 
 NaN     ⋅      ⋅    ⋅ 

whereas, previously, this would have been a dense matrix of NaNs. This new behavior is consistent with sparse matrices having a strong zero.

The implementation isn't optimal from a performance perspective, as it uses a sequence of multiplications instead of doing it all in one go. However, the performance may be improved iteratively.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 84.12%. Comparing base (313a04f) to head (dbe4321).

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #562      +/-   ##
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+ Coverage   84.09%   84.12%   +0.03%     
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  Lines        9102     9120      +18     
==========================================
+ Hits         7654     7672      +18     
  Misses       1448     1448              

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[dkarrasch]

I'd suggest to write it all out in one pass through the nzvals.

[jishnub]

I've updated the method for a SparseMatrixCSC. The fallback method handles views and adjoint/transpose.