add free support barycenter algorithm

Author: Vivien Seguy

examples/plot_free_support_barycenter.py

@@ -21,7 +21,7 @@
 # Generate data
 # -------------
 #%% parameters and data generation
-N = 4
+N = 6
 d = 2
 measures_locations = []
 measures_weights = []
@@ -30,11 +30,13 @@
 
     n = np.random.randint(low=1, high=20)  # nb samples
 
-    mu = np.random.normal(0., 1., (d,))
-    cov = np.random.uniform(0., 1., (d,d))
+    mu = np.random.normal(0., 4., (d,))
+
+    A = np.random.rand(d, d)
+    cov = np.dot(A,A.transpose())
 
     xs = ot.datasets.make_2D_samples_gauss(n, mu, cov)
-    b = np.random.uniform(0., 1., n)
+    b = np.random.uniform(0., 1., (n,))
     b = b/np.sum(b)
 
     measures_locations.append(xs)
@@ -59,7 +61,9 @@
 
 pl.figure(1)
 for (xs, b) in zip(measures_locations, measures_weights):
-    pl.scatter(xs[:, 0], xs[:, 1], s=b, c=np.tile(np.random.uniform(0. ,255., size=(3,)), (1,b.size(0))) , label='Data measures')
-pl.scatter(xs[:, 0], xs[:, 1], s=b, c='black' , label='2-Wasserstein barycenter')
-pl.legend(loc=0)
+    color = np.random.randint(low=1, high=10*N)
+    pl.scatter(xs[:, 0], xs[:, 1], s=b*1000, label='input measure')
+pl.scatter(X[:, 0], X[:, 1], s=b_init*1000, c='black' , marker='^', label='2-Wasserstein barycenter')
 pl.title('Data measures and their barycenter')
+pl.legend(loc=0)
+pl.show()