1 files changed, 69 insertions, 0 deletions
diff --git a/examples/barycenters/plot_free_support_barycenter.py b/examples/barycenters/plot_free_support_barycenter.py
new file mode 100644
index 0000000..27ddc8e
--- /dev/null
+++ b/examples/barycenters/plot_free_support_barycenter.py
@@ -0,0 +1,69 @@
+# -*- coding: utf-8 -*-
+"""
+====================================================
+2D free support Wasserstein barycenters of distributions
+====================================================
+
+Illustration of 2D Wasserstein barycenters if distributions are weighted
+sum of diracs.
+
+"""
+
+# Author: Vivien Seguy <vivien.seguy@iip.ist.i.kyoto-u.ac.jp>
+#
+# License: MIT License
+
+import numpy as np
+import matplotlib.pylab as pl
+import ot
+
+
+##############################################################################
+# Generate data
+# -------------
+
+N = 3
+d = 2
+measures_locations = []
+measures_weights = []
+
+for i in range(N):
+
+    n_i = np.random.randint(low=1, high=20)  # nb samples
+
+    mu_i = np.random.normal(0., 4., (d,))  # Gaussian mean
+
+    A_i = np.random.rand(d, d)
+    cov_i = np.dot(A_i, A_i.transpose())  # Gaussian covariance matrix
+
+    x_i = ot.datasets.make_2D_samples_gauss(n_i, mu_i, cov_i)  # Dirac locations
+    b_i = np.random.uniform(0., 1., (n_i,))
+    b_i = b_i / np.sum(b_i)  # Dirac weights
+
+    measures_locations.append(x_i)
+    measures_weights.append(b_i)
+
+
+##############################################################################
+# Compute free support barycenter
+# -------------------------------
+
+k = 10  # number of Diracs of the barycenter
+X_init = np.random.normal(0., 1., (k, d))  # initial Dirac locations
+b = np.ones((k,)) / k  # weights of the barycenter (it will not be optimized, only the locations are optimized)
+
+X = ot.lp.free_support_barycenter(measures_locations, measures_weights, X_init, b)
+
+
+##############################################################################
+# Plot data
+# ---------
+
+pl.figure(1)
+for (x_i, b_i) in zip(measures_locations, measures_weights):
+    color = np.random.randint(low=1, high=10 * N)
+    pl.scatter(x_i[:, 0], x_i[:, 1], s=b_i * 1000, label='input measure')
+pl.scatter(X[:, 0], X[:, 1], s=b * 1000, c='black', marker='^', label='2-Wasserstein barycenter')
+pl.title('Data measures and their barycenter')
+pl.legend(loc=0)
+pl.show()