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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()