1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
|
# -*- coding: utf-8 -*-
"""
====================================================
Weak Optimal Transport VS exact Optimal Transport
====================================================
Illustration of 2D optimal transport between distributions that are weighted
sum of Diracs. The OT matrix is plotted with the samples.
"""
# Author: Remi Flamary <remi.flamary@polytechnique.edu>
#
# License: MIT License
# sphinx_gallery_thumbnail_number = 4
import numpy as np
import matplotlib.pylab as pl
import ot
import ot.plot
##############################################################################
# Generate data an plot it
# ------------------------
# %% 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, -0.8], [-0.8, 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 = ot.unif(n), ot.unif(n) # uniform distribution on samples
# loss matrix
M = ot.dist(xs, xt)
M /= M.max()
# %% 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 Weak OT and exact OT solutions
# --------------------------------------
# %% EMD
G0 = ot.emd(a, b, M)
# %% Weak OT
Gweak = ot.weak_optimal_transport(xs, xt, a, b)
##############################################################################
# Plot weak OT and exact OT solutions
# --------------------------------------
pl.figure(3, (8, 5))
pl.subplot(1, 2, 1)
pl.imshow(G0, interpolation="nearest")
pl.title("OT matrix")
pl.subplot(1, 2, 2)
pl.imshow(Gweak, interpolation="nearest")
pl.title("Weak OT matrix")
pl.figure(4, (8, 5))
pl.subplot(1, 2, 1)
ot.plot.plot2D_samples_mat(xs, xt, G0, c=[0.5, 0.5, 1])
pl.plot(xs[:, 0], xs[:, 1], "+b", label="Source samples")
pl.plot(xt[:, 0], xt[:, 1], "xr", label="Target samples")
pl.title("OT matrix with samples")
pl.subplot(1, 2, 2)
ot.plot.plot2D_samples_mat(xs, xt, Gweak, c=[0.5, 0.5, 1])
pl.plot(xs[:, 0], xs[:, 1], "+b", label="Source samples")
pl.plot(xt[:, 0], xt[:, 1], "xr", label="Target samples")
pl.title("Weak OT matrix with samples")
|
