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
|
.. _sphx_glr_auto_examples_plot_compute_emd.py:
====================
1D optimal transport
====================
@author: rflamary
.. rst-class:: sphx-glr-horizontal
*
.. image:: /auto_examples/images/sphx_glr_plot_compute_emd_001.png
:scale: 47
*
.. image:: /auto_examples/images/sphx_glr_plot_compute_emd_002.png
:scale: 47
.. 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
n_target=50 # nb target distributions
# bin positions
x=np.arange(n,dtype=np.float64)
lst_m=np.linspace(20,90,n_target)
# Gaussian distributions
a=gauss(n,m=20,s=5) # m= mean, s= std
B=np.zeros((n,n_target))
for i,m in enumerate(lst_m):
B[:,i]=gauss(n,m=m,s=5)
# loss matrix and normalization
M=ot.dist(x.reshape((n,1)),x.reshape((n,1)),'euclidean')
M/=M.max()
M2=ot.dist(x.reshape((n,1)),x.reshape((n,1)),'sqeuclidean')
M2/=M2.max()
#%% plot the distributions
pl.figure(1)
pl.subplot(2,1,1)
pl.plot(x,a,'b',label='Source distribution')
pl.title('Source distribution')
pl.subplot(2,1,2)
pl.plot(x,B,label='Target distributions')
pl.title('Target distributions')
#%% Compute and plot distributions and loss matrix
d_emd=ot.emd2(a,B,M) # direct computation of EMD
d_emd2=ot.emd2(a,B,M2) # direct computation of EMD with loss M3
pl.figure(2)
pl.plot(d_emd,label='Euclidean EMD')
pl.plot(d_emd2,label='Squared Euclidean EMD')
pl.title('EMD distances')
pl.legend()
#%%
reg=1e-2
d_sinkhorn=ot.sinkhorn(a,B,M,reg)
d_sinkhorn2=ot.sinkhorn(a,B,M2,reg)
pl.figure(2)
pl.clf()
pl.plot(d_emd,label='Euclidean EMD')
pl.plot(d_emd2,label='Squared Euclidean EMD')
pl.plot(d_sinkhorn,'+',label='Euclidean Sinkhorn')
pl.plot(d_sinkhorn2,'+',label='Squared Euclidean Sinkhorn')
pl.title('EMD distances')
pl.legend()
**Total running time of the script:** ( 0 minutes 0.521 seconds)
.. container:: sphx-glr-footer
.. container:: sphx-glr-download
:download:`Download Python source code: plot_compute_emd.py <plot_compute_emd.py>`
.. container:: sphx-glr-download
:download:`Download Jupyter notebook: plot_compute_emd.ipynb <plot_compute_emd.ipynb>`
.. rst-class:: sphx-glr-signature
`Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_
|
