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
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
|
.. _sphx_glr_auto_examples_plot_OT_2D_samples.py:
====================================================
2D Optimal transport between empirical distributions
====================================================
.. rst-class:: sphx-glr-horizontal
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_001.png
:scale: 47
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_002.png
:scale: 47
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_003.png
:scale: 47
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_004.png
:scale: 47
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_005.png
:scale: 47
*
.. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_006.png
:scale: 47
.. code-block:: python
# Author: Remi Flamary <remi.flamary@unice.fr>
#
# License: MIT License
import numpy as np
import matplotlib.pylab as pl
import ot
#%% 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.get_2D_samples_gauss(n, mu_s, cov_s)
xt = ot.datasets.get_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 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')
#%% 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')
#%% 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()
**Total running time of the script:** ( 0 minutes 2.908 seconds)
.. container:: sphx-glr-footer
.. container:: sphx-glr-download
:download:`Download Python source code: plot_OT_2D_samples.py <plot_OT_2D_samples.py>`
.. container:: sphx-glr-download
:download:`Download Jupyter notebook: plot_OT_2D_samples.ipynb <plot_OT_2D_samples.ipynb>`
.. rst-class:: sphx-glr-signature
`Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_
|
