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
|
.. _sphx_glr_auto_examples_demo_OT_1D_test.py:
Demo for 1D optimal transport
@author: rflamary
.. code-block:: python
import numpy as np
import matplotlib.pylab as pl
import ot
from ot.datasets import get_1D_gauss as gauss
#%% parameters
n=100 # nb bins
# bin positions
x=np.arange(n,dtype=np.float64)
# Gaussian distributions
a=gauss(n,m=n*.2,s=5) # m= mean, s= std
b=gauss(n,m=n*.6,s=10)
# loss matrix
M=ot.dist(x.reshape((n,1)),x.reshape((n,1)))
M/=M.max()
#%% plot the distributions
pl.figure(1)
pl.plot(x,a,'b',label='Source distribution')
pl.plot(x,b,'r',label='Target distribution')
pl.legend()
#%% plot distributions and loss matrix
pl.figure(2)
ot.plot.plot1D_mat(a,b,M,'Cost matrix M')
#%% EMD
G0=ot.emd(a,b,M)
pl.figure(3)
ot.plot.plot1D_mat(a,b,G0,'OT matrix G0')
#%% Sinkhorn
lambd=1e-3
Gs=ot.sinkhorn(a,b,M,lambd,verbose=True)
pl.figure(4)
ot.plot.plot1D_mat(a,b,Gs,'OT matrix Sinkhorn')
#%% Sinkhorn
lambd=1e-4
Gss,log=ot.bregman.sinkhorn_stabilized(a,b,M,lambd,verbose=True,log=True)
Gss2,log2=ot.bregman.sinkhorn_stabilized(a,b,M,lambd,verbose=True,log=True,warmstart=log['warmstart'])
pl.figure(5)
ot.plot.plot1D_mat(a,b,Gss,'OT matrix Sinkhorn stabilized')
#%% Sinkhorn
lambd=1e-11
Gss=ot.bregman.sinkhorn_epsilon_scaling(a,b,M,lambd,verbose=True)
pl.figure(5)
ot.plot.plot1D_mat(a,b,Gss,'OT matrix Sinkhorn stabilized')
**Total running time of the script:** ( 0 minutes 0.000 seconds)
.. container:: sphx-glr-footer
.. container:: sphx-glr-download
:download:`Download Python source code: demo_OT_1D_test.py <demo_OT_1D_test.py>`
.. container:: sphx-glr-download
:download:`Download Jupyter notebook: demo_OT_1D_test.ipynb <demo_OT_1D_test.ipynb>`
.. rst-class:: sphx-glr-signature
`Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_
|
