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+# -*- coding: utf-8 -*-
+"""
+==========================
+Gromov-Wasserstein example
+==========================
+
+This example is designed to show how to use the Gromov-Wassertsein distance
+computation in POT.
+"""
+
+# Author: Erwan Vautier <erwan.vautier@gmail.com>
+# Nicolas Courty <ncourty@irisa.fr>
+#
+# License: MIT License
+
+import scipy as sp
+import numpy as np
+import matplotlib.pylab as pl
+from mpl_toolkits.mplot3d import Axes3D # noqa
+import ot
+
+#############################################################################
+#
+# Sample two Gaussian distributions (2D and 3D)
+# ---------------------------------------------
+#
+# The Gromov-Wasserstein distance allows to compute distances with samples that
+# do not belong to the same metric space. For demonstration purpose, we sample
+# two Gaussian distributions in 2- and 3-dimensional spaces.
+
+
+n_samples = 30 # nb samples
+
+mu_s = np.array([0, 0])
+cov_s = np.array([[1, 0], [0, 1]])
+
+mu_t = np.array([4, 4, 4])
+cov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
+
+
+xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s)
+P = sp.linalg.sqrtm(cov_t)
+xt = np.random.randn(n_samples, 3).dot(P) + mu_t
+
+#############################################################################
+#
+# Plotting the distributions
+# --------------------------
+
+
+fig = pl.figure()
+ax1 = fig.add_subplot(121)
+ax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+ax2 = fig.add_subplot(122, projection='3d')
+ax2.scatter(xt[:, 0], xt[:, 1], xt[:, 2], color='r')
+pl.show()
+
+#############################################################################
+#
+# Compute distance kernels, normalize them and then display
+# ---------------------------------------------------------
+
+
+C1 = sp.spatial.distance.cdist(xs, xs)
+C2 = sp.spatial.distance.cdist(xt, xt)
+
+C1 /= C1.max()
+C2 /= C2.max()
+
+pl.figure()
+pl.subplot(121)
+pl.imshow(C1)
+pl.subplot(122)
+pl.imshow(C2)
+pl.show()
+
+#############################################################################
+#
+# Compute Gromov-Wasserstein plans and distance
+# ---------------------------------------------
+
+p = ot.unif(n_samples)
+q = ot.unif(n_samples)
+
+gw0, log0 = ot.gromov.gromov_wasserstein(
+ C1, C2, p, q, 'square_loss', verbose=True, log=True)
+
+gw, log = ot.gromov.entropic_gromov_wasserstein(
+ C1, C2, p, q, 'square_loss', epsilon=5e-4, log=True, verbose=True)
+
+
+print('Gromov-Wasserstein distances: ' + str(log0['gw_dist']))
+print('Entropic Gromov-Wasserstein distances: ' + str(log['gw_dist']))
+
+
+pl.figure(1, (10, 5))
+
+pl.subplot(1, 2, 1)
+pl.imshow(gw0, cmap='jet')
+pl.title('Gromov Wasserstein')
+
+pl.subplot(1, 2, 2)
+pl.imshow(gw, cmap='jet')
+pl.title('Entropic Gromov Wasserstein')
+
+pl.show()