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+# -*- coding: utf-8 -*-
+"""
+====================================================
+2D Optimal transport between empirical distributions
+====================================================
+
+Illustration of 2D optimal transport between discributions that are weighted
+sum of diracs. The OT matrix is plotted with the samples.
+
+"""
+
+# Author: Remi Flamary <remi.flamary@unice.fr>
+# Kilian Fatras <kilian.fatras@irisa.fr>
+#
+# License: MIT License
+
+import numpy as np
+import matplotlib.pylab as pl
+import ot
+import ot.plot
+
+##############################################################################
+# Generate data
+# -------------
+
+#%% parameters and data generation
+
+n = 50 # nb samples
+
+mu_s = np.array([0, 0])
+cov_s = np.array([[1, 0], [0, 1]])
+
+mu_t = np.array([4, 4])
+cov_t = np.array([[1, -.8], [-.8, 1]])
+
+xs = ot.datasets.make_2D_samples_gauss(n, mu_s, cov_s)
+xt = ot.datasets.make_2D_samples_gauss(n, mu_t, cov_t)
+
+a, b = np.ones((n,)) / n, np.ones((n,)) / n # uniform distribution on samples
+
+# loss matrix
+M = ot.dist(xs, xt)
+M /= M.max()
+
+##############################################################################
+# Plot data
+# ---------
+
+#%% plot samples
+
+pl.figure(1)
+pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+pl.legend(loc=0)
+pl.title('Source and target distributions')
+
+pl.figure(2)
+pl.imshow(M, interpolation='nearest')
+pl.title('Cost matrix M')
+
+##############################################################################
+# Compute EMD
+# -----------
+
+#%% EMD
+
+G0 = ot.emd(a, b, M)
+
+pl.figure(3)
+pl.imshow(G0, interpolation='nearest')
+pl.title('OT matrix G0')
+
+pl.figure(4)
+ot.plot.plot2D_samples_mat(xs, xt, G0, c=[.5, .5, 1])
+pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+pl.legend(loc=0)
+pl.title('OT matrix with samples')
+
+
+##############################################################################
+# Compute Sinkhorn
+# ----------------
+
+#%% sinkhorn
+
+# reg term
+lambd = 1e-3
+
+Gs = ot.sinkhorn(a, b, M, lambd)
+
+pl.figure(5)
+pl.imshow(Gs, interpolation='nearest')
+pl.title('OT matrix sinkhorn')
+
+pl.figure(6)
+ot.plot.plot2D_samples_mat(xs, xt, Gs, color=[.5, .5, 1])
+pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+pl.legend(loc=0)
+pl.title('OT matrix Sinkhorn with samples')
+
+pl.show()
+
+
+##############################################################################
+# Emprirical Sinkhorn
+# ----------------
+
+#%% sinkhorn
+
+# reg term
+lambd = 1e-3
+
+Ges = ot.bregman.empirical_sinkhorn(xs, xt, lambd)
+
+pl.figure(7)
+pl.imshow(Ges, interpolation='nearest')
+pl.title('OT matrix empirical sinkhorn')
+
+pl.figure(8)
+ot.plot.plot2D_samples_mat(xs, xt, Ges, color=[.5, .5, 1])
+pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+pl.legend(loc=0)
+pl.title('OT matrix Sinkhorn from samples')
+
+pl.show()