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+# -*- coding: utf-8 -*-
+"""
+==================================================
+Partial Wasserstein and Gromov-Wasserstein example
+==================================================
+
+This example is designed to show how to use the Partial (Gromov-)Wassertsein
+distance computation in POT.
+"""
+
+# Author: Laetitia Chapel <laetitia.chapel@irisa.fr>
+# License: MIT License
+
+# sphinx_gallery_thumbnail_number = 2
+
+# necessary for 3d plot even if not used
+from mpl_toolkits.mplot3d import Axes3D # noqa
+import scipy as sp
+import numpy as np
+import matplotlib.pylab as pl
+import ot
+
+
+#############################################################################
+#
+# Sample two 2D Gaussian distributions and plot them
+# --------------------------------------------------
+#
+# For demonstration purpose, we sample two Gaussian distributions in 2-d
+# spaces and add some random noise.
+
+
+n_samples = 20 # nb samples (gaussian)
+n_noise = 20 # nb of samples (noise)
+
+mu = np.array([0, 0])
+cov = np.array([[1, 0], [0, 2]])
+
+xs = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov)
+xs = np.append(xs, (np.random.rand(n_noise, 2) + 1) * 4).reshape((-1, 2))
+xt = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov)
+xt = np.append(xt, (np.random.rand(n_noise, 2) + 1) * -3).reshape((-1, 2))
+
+M = sp.spatial.distance.cdist(xs, xt)
+
+fig = pl.figure()
+ax1 = fig.add_subplot(131)
+ax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+ax2 = fig.add_subplot(132)
+ax2.scatter(xt[:, 0], xt[:, 1], color='r')
+ax3 = fig.add_subplot(133)
+ax3.imshow(M)
+pl.show()
+
+#############################################################################
+#
+# Compute partial Wasserstein plans and distance
+# ----------------------------------------------
+
+p = ot.unif(n_samples + n_noise)
+q = ot.unif(n_samples + n_noise)
+
+w0, log0 = ot.partial.partial_wasserstein(p, q, M, m=0.5, log=True)
+w, log = ot.partial.entropic_partial_wasserstein(p, q, M, reg=0.1, m=0.5,
+ log=True)
+
+print('Partial Wasserstein distance (m = 0.5): ' + str(log0['partial_w_dist']))
+print('Entropic partial Wasserstein distance (m = 0.5): ' +
+ str(log['partial_w_dist']))
+
+pl.figure(1, (10, 5))
+pl.subplot(1, 2, 1)
+pl.imshow(w0, cmap='jet')
+pl.title('Partial Wasserstein')
+pl.subplot(1, 2, 2)
+pl.imshow(w, cmap='jet')
+pl.title('Entropic partial Wasserstein')
+pl.show()
+
+
+#############################################################################
+#
+# Sample one 2D and 3D Gaussian distributions and plot them
+# ---------------------------------------------------------
+#
+# 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 = 20 # nb samples
+n_noise = 10 # nb of samples (noise)
+
+p = ot.unif(n_samples + n_noise)
+q = ot.unif(n_samples + n_noise)
+
+mu_s = np.array([0, 0])
+cov_s = np.array([[1, 0], [0, 1]])
+
+mu_t = np.array([0, 0, 0])
+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)
+xs = np.concatenate((xs, ((np.random.rand(n_noise, 2) + 1) * 4)), axis=0)
+P = sp.linalg.sqrtm(cov_t)
+xt = np.random.randn(n_samples, 3).dot(P) + mu_t
+xt = np.concatenate((xt, ((np.random.rand(n_noise, 3) + 1) * 10)), axis=0)
+
+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 partial Gromov-Wasserstein plans and distance
+# -----------------------------------------------------
+
+C1 = sp.spatial.distance.cdist(xs, xs)
+C2 = sp.spatial.distance.cdist(xt, xt)
+
+# transport 100% of the mass
+print('-----m = 1')
+m = 1
+res0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m, log=True)
+res, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q, 10,
+ m=m, log=True)
+
+print('Wasserstein distance (m = 1): ' + str(log0['partial_gw_dist']))
+print('Entropic Wasserstein distance (m = 1): ' + str(log['partial_gw_dist']))
+
+pl.figure(1, (10, 5))
+pl.title("mass to be transported m = 1")
+pl.subplot(1, 2, 1)
+pl.imshow(res0, cmap='jet')
+pl.title('Wasserstein')
+pl.subplot(1, 2, 2)
+pl.imshow(res, cmap='jet')
+pl.title('Entropic Wasserstein')
+pl.show()
+
+# transport 2/3 of the mass
+print('-----m = 2/3')
+m = 2 / 3
+res0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m, log=True)
+res, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q, 10,
+ m=m, log=True)
+
+print('Partial Wasserstein distance (m = 2/3): ' +
+ str(log0['partial_gw_dist']))
+print('Entropic partial Wasserstein distance (m = 2/3): ' +
+ str(log['partial_gw_dist']))
+
+pl.figure(1, (10, 5))
+pl.title("mass to be transported m = 2/3")
+pl.subplot(1, 2, 1)
+pl.imshow(res0, cmap='jet')
+pl.title('Partial Wasserstein')
+pl.subplot(1, 2, 2)
+pl.imshow(res, cmap='jet')
+pl.title('Entropic partial Wasserstein')
+pl.show()