[MRG] Tiny fix in SSNB (#535)

* added functions to a new mapping module

* simplify ssnb function structure

* SSNB example

* removed numpy saves from example for prod

* tests apart from the import exception catch

* tests apart from the import exception catch

* da class and tests

* guessed PR number

* removed unused import

* PEP8 tab errors fix

* skip ssnb test if no cvxpy

* test and doc fixes

* doc dependency + minor comment in ot __init__.py

* PEP8 fixes

* test typo fix

* ssnb da backend test fix

* moved joint ot mappings to the mapping module

* better ssnb example + ssnb initilisation + small joint_ot_mapping tests

* better ssnb example + ssnb initilisation + small joint_ot_mapping tests

* removed unused dependency in example

* no longer import mapping in __init__ + example thumbnail fix + made qcqp_constants function private

* merge with POT main

* fix barycentric projection factor omission in SSNB solver init

* added modif in RELEASES.md

* fix PR number in RELEASES.md

* broadcast fix

Author: eloitanguy

RELEASES.md

@@ -3,7 +3,7 @@
 ## 0.9.2dev
 
 #### New features
-+ Added support for [Nearest Brenier Potentials (SSNB)](http://proceedings.mlr.press/v108/paty20a/paty20a.pdf) (PR #526)
++ Added support for [Nearest Brenier Potentials (SSNB)](http://proceedings.mlr.press/v108/paty20a/paty20a.pdf) (PR #526) + minor fix (PR #535)
 + Tweaked `get_backend` to ignore `None` inputs (PR #525)
 + Callbacks for generalized conditional gradient in `ot.da.sinkhorn_l1l2_gl` are now vectorized to improve performance (PR #507)
 + The `linspace` method of the backends now has the `type_as` argument to convert to the same dtype and device. (PR #533)

examples/others/plot_SSNB.py

@@ -41,7 +41,7 @@
 # Author: Eloi Tanguy <eloi.tanguy@u-paris.fr>
 # License: MIT License
 
-# sphinx_gallery_thumbnail_number = 4
+# sphinx_gallery_thumbnail_number = 3
 
 import matplotlib.pyplot as plt
 import numpy as np
@@ -63,20 +63,6 @@
 plt.legend(loc='upper right')
 plt.show()
 
-# %%
-# Plotting image of barycentric projection (SSNB initialisation values)
-plt.clf()
-pi = ot.emd(ot.unif(n_fitting_samples), ot.unif(n_fitting_samples), ot.dist(Xs, Xt))
-plt.scatter(Xs[:, 0], Xs[:, 1], c='dodgerblue', label='source')
-plt.scatter(Xt[:, 0], Xt[:, 1], c='red', label='target')
-bar_img = pi @ Xt
-for i in range(n_fitting_samples):
-    plt.plot([Xs[i, 0], bar_img[i, 0]], [Xs[i, 1], bar_img[i, 1]], color='black', alpha=.5)
-plt.title('Images of in-data source samples by the barycentric map')
-plt.legend(loc='upper right')
-plt.axis('equal')
-plt.show()
-
 # %%
 # Fitting the Nearest Brenier Potential
 L = 3  # need L > 2 to allow the 2*y term, default is 1.4

ot/mapping.py

@@ -124,7 +124,7 @@ def nearest_brenier_potential_fit(X, V, X_classes=None, a=None, b=None, strongly
     if init_method == 'target':
         G_val = V
     else:  # Init G_val with barycentric projection
-        G_val = emd(a, b, dist(X, V)) @ V
+        G_val = emd(a, b, dist(X, V)) @ V / a.reshape(n, 1)
     phi_val = None
     log_dict = {
         'G_list': [],