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plot_OT_2D_samples.py
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plot_OT_2D_samples.py
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# -*- coding: utf-8 -*-
"""
====================================================
Optimal Transport between 2D 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
# sphinx_gallery_thumbnail_number = 4
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)
##############################################################################
# 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-1
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-1
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()