[MRG] Domain adaptation and unbalanced solvers with backend support (#343)

* First draft

* Add matrix inverse and square root to backend

* Eigen decomposition for older versions of pytorch (1.8.1 and older)

* Corrected eigen decomposition for pytorch 1.8.1 and older

* Spectral theorem is a thing

* Optimization

* small optimization

* More functions converted

* pep8

* remove a warning and prepare torch meshgrid for future torch release (which will change default indexing)

* dots and pep8

* Meshgrid corrected for older version and prepared for future versions changes

* New backend functions

* Base transport

* LinearTransport

* All transport classes + pep8

* PR added to release file

* Jcpot barycenter test

* unbalanced with backend

* pep8

* bug solve

* test of domain adaptation with backends

* solve bug for tic toc & macos

* solving scipy deprecation warning

* solving scipy deprecation warning attempt2

* solving scipy deprecation warning attempt3

* A warning is triggered when a float->int conversion is detected

* bug solve

* docs

* release file updated

* Better handling of float->int conversion in EMD

* Corrected test for is_floating_point

* docs

* release file updated

* cupy does not allow implicit cast

* fromnumpy

* added test

* test da tf jax

* test unbalanced with no provided histogram

* using type_as argument in unif function correctly

* pep8

* transport plan cast in emd changed behaviour, now trying to cast as histogram's dtype, defaulting to cost matrix

Co-authored-by: Rémi Flamary <remi.flamary@gmail.com>

Author: ncassereau

RELEASES.md

@@ -11,6 +11,7 @@
   of the regularization parameter (PR #336).
 - Backend implementation for `ot.lp.free_support_barycenter` (PR #340).
 - Add weak OT solver + example  (PR #341).
+- Add backend support for Domain Adaptation and Unbalanced solvers (PR #343).
 - Add (F)GW linear dictionary learning solvers + example  (PR #319)
 - Add links to related PR and Issues in the doc release page (PR #350)
 
@@ -19,6 +20,7 @@
 - Fix bug in instantiating an `autograd` function `ValFunction` (Issue #337, 
   PR #338)
 - Fix POT ABI compatibility with old and new numpy (Issue #346, PR #349)
+- Warning when feeding integer cost matrix to EMD solver resulting in an integer transport plan (Issue #345, PR #343)
 - Fix bug where gromov_wasserstein2 does not perform backpropagation with CUDA
   tensors (Issue #351, PR #352)