add: [CartesianIndex...] sparse method

[kunzaatko]

A method for specifying the indexes to fill with values directly as
CartesianIndices.

For example:

julia> sparse([CartesianIndex(1,1), CartesianIndex(2,2), CartesianIndex(3,3)], [1.0, 2.0, 3.0], 3, 3)

is now possible.

• documentation?
• Additional tests?

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 84.11%. Comparing base (ce852af) to head (0021a71).
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Additional details and impacted files

@@            Coverage Diff             @@
##             main     #600      +/-   ##
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+ Coverage   84.08%   84.11%   +0.02%     
==========================================
  Files          12       12              
  Lines        9192     9195       +3     
==========================================
+ Hits         7729     7734       +5     
+ Misses       1463     1461       -2     

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[kunzaatko]

Another method that should be considered are ones that are created by using a range on instances of CartesianIndex

julia> CartesianIndex(3,4):CartesianIndex(4,9)
CartesianIndices((3:4, 4:9))

julia> CartesianIndex(3,4):CartesianIndex(4,9) |> typeof |> supertypes
(CartesianIndices{2, Tuple{UnitRange{Int64}, UnitRange{Int64}}}, AbstractMatrix{CartesianIndex{2}}, Any)

[jishnub]

Note that the CartesianIndices block above is dense (although it might be useful as the indices of a block matrix). A sparse range along a 1D axis may be created as a StepRangeLen of CartesianIndexes.

[kunzaatko]

Perhaps what you are describing is a more realistic use of the dense block. That was what I had in mind although the sparse function does not give an ideal interface for this use, am I correct? Something like this does not have much overhead thought (and maybe any overhead is even compiled out?)

julia> sparse(CartesianIndex(12:14):CartesianIndex(15:17), ones(3*3), 20, 20) + sparse(CartesianIndex(2:4):CartesianIndex(5:7), ones(3*3), 20, 20)

Which would create a sparse matrix with dense blocks inside. The structure of the type does not give the best memory usage for this case...

[jishnub]

I think you require 2D CartesianIndexes here ?

[kunzaatko]

Absolutely correct. Fixed this.