[WIP] Wrapper for OT barycenter solvers with free support

[cedricvincentcuaz]

Types of changes

• creation of the class ot.utils.BaryResult extending OTResult

• Long term objectives: Wrap all barycenter solvers available in POT and more, ideally establishing links between these wrappers and those for inner OT solvers ot.solve_sample, ot.solve, and ot.solve_gromov - respectively associated with their barycenter solver ot.solve_bary_sample (free support); ot.solve_bary (free masses); ot.solve_bary_gromov (free joint support)

• a) ot.solvers.solve_bary_sample systematically optimizes the support of the barycenter using BCD with closed forms if the parameter metric is in ('sqeuclidean', 'euclidean') calling an hidden function _bary_sample_bcd which works with most OT problems in ot.solve_sample. metric can also be a callable or a list of callable function following the API of lp.free_support_barycenter_generic_costs for balanced OT only.

• b) handle variations in masses across OT problems only for unbalanced problems - keeping masses unchanged for exact and inexact sinkhorn like solvers - via parameter update_masses in ot.solvers._bary_sample_bcd.

• c) Handle given initialization of transport plans & potentials + warmstart strategies : added parameter warmstart to solve_bary_sample, and based on the requested inner OT solver, we pick the adequate strategy warmstart_plan or warmstart_potentials passed to _bary_sample_bcd .

• d) Options for stopping criterion between losses and barycenter variations: added parameter stopping_criterion in ('loss', 'bary') passed to _bary_sample_bcd.

Extensions let for future works:

• a) include lazy inner OT solvers referenced in the list lst_method_lazy (in ot.solvers)

How has this been tested (if it applies)

• a) test.test_solvers.assert_allclose_bary_sol method to compare solutions as BaryResult objects.
• b) test_solve_bary_sample grid across all available barycenter solvers depending on those available in ot.solvers.solve_sample.
• c) test_solve_bary_sample_NotImplemented test error messages for methods not implemented yet.
• d) test_solve_bary_sample_ValueError Test ValueError cases including stopping_criterion and X_b_init shape.
• e) test_solve_bary_sample_callable_metric test barycenter solvers for balanced OT with callable metrics.

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

❌ Patch coverage is 94.05594% with 17 lines in your changes missing coverage. Please review.
✅ Project coverage is 96.78%. Comparing base (aed0120) to head (82d2ff8).

Additional details and impacted files

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- Coverage   96.81%   96.78%   -0.04%     
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  Files         124      124              
  Lines       24263    24546     +283     
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+ Hits        23490    23756     +266     
- Misses        773      790      +17     

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