Introduce coloring results

[gdalle]

Warning

Breaking change: bumping version to v0.4.0

Source

• Introduce a new "detailed" interface with three functions: column_coloring_detailed, row_coloring_detailed and symmetric_coloring_detailed. Make the ADTypes interface fall back on those (we'll see once this stabilizes if it is worth upstreaming).
• Let the detailed coloring functions return an AbstractColoringResult, which must then be used in decompression routines. A minima, this object contains the color vector and the group vector. There is also one specific implementation for SparseMatrixCSC, where decompression indices are stored.
• Anticipate generalizations of coloring results to 1) bidirectional coloring and 2) indirect recovery with linear systems, thanks to a flexible set of type parameters on AbstractColoringResult{partition,symmetric,decompression}.
• Merge decompress_columns, decompress_row and decompress_symmetric into a single symbol decompress, using dispatch on the result type to figure out the right algorithm.
• Relax tests on same sparsity pattern, which added significant overhead.

Docs

• Update docstrings and public symbols

Tests

• Adjust to new framework
• Test in-place decompression too

---

@amontoison this should be very easy to adapt to sparse GPU matrices

[amontoison]

Should we add ncolors in SimpleColoringResult by default?
I don't remember if we already have it during the coloring.

[gdalle]

You can get it as length(get_groups(coloring_result)). I chose to precompute the groups by default because we frequently need them for differentiation or decompression and it's not very expensive.

Don't mind the CI, I'm currently debugging something that only occurs on LTS

[gdalle]

@amontoison any idea how this could ever happen for A::SparseMatrixCSC? It's the reason why CI fails, apparently only on 1.6

[gdalle]

Okay apparently it's caused by JuliaSparse/SparseArrays.jl#44 and fixed in JuliaLang/julia#40523

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.16%. Comparing base (e8d5f2f) to head (f5098f9).

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #38      +/-   ##
==========================================
+ Coverage   97.81%   99.16%   +1.35%     
==========================================
  Files           9        9              
  Lines         366      360       -6     
==========================================
- Hits          358      357       -1     
+ Misses          8        3       -5     

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[gdalle]

@amontoison I made a few more changes and updated the PR description accordingly, care to take a second look?
Still missing the StarSet handling but otherwise we're nearly good

[amontoison]

LGTM!