[WIP] implementation of low rank ot via factor relaxation paper

[fegounna]

Types of changes

Added implementation of the paper Low-Rank Optimal Transport through Factor Relaxation with Latent Coupling
https://arxiv.org/abs/2411.10555

How has this been tested (if it applies)

Tested it on optimal transport problems and compared it with sinkhorn solver.
Tested using numpy and torch.

PR checklist

• I have read the CONTRIBUTING document.
• The documentation is up-to-date with the changes I made (check build artifacts).
• All tests passed,
• and additional code has been covered with new tests.
• I have added the PR and Issue fix to the RELEASES.md file.

[codecov]

Codecov Report

Attention: Patch coverage is 19.35484% with 50 lines in your changes missing coverage. Please review.

Project coverage is 96.84%. Comparing base (c128104) to head (4a44da2).
Report is 1 commits behind head on master.

Additional details and impacted files

@@ Coverage Diff @@## master #719 +/- ##
==========================================
- Coverage 97.08% 96.84% -0.25% 
==========================================
Files 100 102 +2 Lines 19947 20009 +62 ==========================================
+ Hits 19365 19377 +12 - Misses 582 632 +50 

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[rflamary]

Hello,
Thanks for your PR. Things that need to be done before we do a full coder review:

• Add tests for a functions with a good coverage.
• Add examples in /examples/ folder for the documentation
• Merge your contribution wit /ot/lowrank.py en potentially factorize code/unify API

[fegounna]

Thanks you for your message.
I will do it next week.

[cedricvincentcuaz]

Hello @fegounna ,
Thank you for the implementation of this new feature. Did you have the chance to look into edits @rflamary requested ? Feel free to ask if you have any question.
Best,
Cédric