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+# -*- coding: utf-8 -*-
+"""
+==========================================
+2D Optimal transport for different metrics
+==========================================
+
+2D OT on empirical distributio with different gound metric.
+
+Stole the figure idea from Fig. 1 and 2 in
+https://arxiv.org/pdf/1706.07650.pdf
+
+
+"""
+
+# Author: Remi Flamary <remi.flamary@unice.fr>
+#
+# License: MIT License
+
+import numpy as np
+import matplotlib.pylab as pl
+import ot
+import ot.plot
+
+##############################################################################
+# Dataset 1 : uniform sampling
+# ----------------------------
+
+n = 20 # nb samples
+xs = np.zeros((n, 2))
+xs[:, 0] = np.arange(n) + 1
+xs[:, 1] = (np.arange(n) + 1) * -0.001 # to make it strictly convex...
+
+xt = np.zeros((n, 2))
+xt[:, 1] = np.arange(n) + 1
+
+a, b = ot.unif(n), ot.unif(n) # uniform distribution on samples
+
+# loss matrix
+M1 = ot.dist(xs, xt, metric='euclidean')
+M1 /= M1.max()
+
+# loss matrix
+M2 = ot.dist(xs, xt, metric='sqeuclidean')
+M2 /= M2.max()
+
+# loss matrix
+Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean'))
+Mp /= Mp.max()
+
+# Data
+pl.figure(1, figsize=(7, 3))
+pl.clf()
+pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+pl.axis('equal')
+pl.title('Source and target distributions')
+
+
+# Cost matrices
+pl.figure(2, figsize=(7, 3))
+
+pl.subplot(1, 3, 1)
+pl.imshow(M1, interpolation='nearest')
+pl.title('Euclidean cost')
+
+pl.subplot(1, 3, 2)
+pl.imshow(M2, interpolation='nearest')
+pl.title('Squared Euclidean cost')
+
+pl.subplot(1, 3, 3)
+pl.imshow(Mp, interpolation='nearest')
+pl.title('Sqrt Euclidean cost')
+pl.tight_layout()
+
+##############################################################################
+# Dataset 1 : Plot OT Matrices
+# ----------------------------
+
+
+#%% EMD
+G1 = ot.emd(a, b, M1)
+G2 = ot.emd(a, b, M2)
+Gp = ot.emd(a, b, Mp)
+
+# OT matrices
+pl.figure(3, figsize=(7, 3))
+
+pl.subplot(1, 3, 1)
+ot.plot.plot2D_samples_mat(xs, xt, G1, 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.axis('equal')
+# pl.legend(loc=0)
+pl.title('OT Euclidean')
+
+pl.subplot(1, 3, 2)
+ot.plot.plot2D_samples_mat(xs, xt, G2, 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.axis('equal')
+# pl.legend(loc=0)
+pl.title('OT squared Euclidean')
+
+pl.subplot(1, 3, 3)
+ot.plot.plot2D_samples_mat(xs, xt, Gp, 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.axis('equal')
+# pl.legend(loc=0)
+pl.title('OT sqrt Euclidean')
+pl.tight_layout()
+
+pl.show()
+
+
+##############################################################################
+# Dataset 2 : Partial circle
+# --------------------------
+
+n = 50 # nb samples
+xtot = np.zeros((n + 1, 2))
+xtot[:, 0] = np.cos(
+ (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)
+xtot[:, 1] = np.sin(
+ (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)
+
+xs = xtot[:n, :]
+xt = xtot[1:, :]
+
+a, b = ot.unif(n), ot.unif(n) # uniform distribution on samples
+
+# loss matrix
+M1 = ot.dist(xs, xt, metric='euclidean')
+M1 /= M1.max()
+
+# loss matrix
+M2 = ot.dist(xs, xt, metric='sqeuclidean')
+M2 /= M2.max()
+
+# loss matrix
+Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean'))
+Mp /= Mp.max()
+
+
+# Data
+pl.figure(4, figsize=(7, 3))
+pl.clf()
+pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+pl.axis('equal')
+pl.title('Source and traget distributions')
+
+
+# Cost matrices
+pl.figure(5, figsize=(7, 3))
+
+pl.subplot(1, 3, 1)
+pl.imshow(M1, interpolation='nearest')
+pl.title('Euclidean cost')
+
+pl.subplot(1, 3, 2)
+pl.imshow(M2, interpolation='nearest')
+pl.title('Squared Euclidean cost')
+
+pl.subplot(1, 3, 3)
+pl.imshow(Mp, interpolation='nearest')
+pl.title('Sqrt Euclidean cost')
+pl.tight_layout()
+
+##############################################################################
+# Dataset 2 : Plot OT Matrices
+# -----------------------------
+
+
+#%% EMD
+G1 = ot.emd(a, b, M1)
+G2 = ot.emd(a, b, M2)
+Gp = ot.emd(a, b, Mp)
+
+# OT matrices
+pl.figure(6, figsize=(7, 3))
+
+pl.subplot(1, 3, 1)
+ot.plot.plot2D_samples_mat(xs, xt, G1, 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.axis('equal')
+# pl.legend(loc=0)
+pl.title('OT Euclidean')
+
+pl.subplot(1, 3, 2)
+ot.plot.plot2D_samples_mat(xs, xt, G2, 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.axis('equal')
+# pl.legend(loc=0)
+pl.title('OT squared Euclidean')
+
+pl.subplot(1, 3, 3)
+ot.plot.plot2D_samples_mat(xs, xt, Gp, 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.axis('equal')
+# pl.legend(loc=0)
+pl.title('OT sqrt Euclidean')
+pl.tight_layout()
+
+pl.show()