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
|
# -*- coding: utf-8 -*-
"""
Created on Fri Oct 21 09:51:45 2016
@author: rflamary
"""
import numpy as np
import matplotlib.pylab as pl
from matplotlib import gridspec
import ot
#%% parameters
n=100 # nb bins
ma=20 # mean of a
mb=60 # mean of b
sa=20 # std of a
sb=60 # std of b
# bin positions
x=np.arange(n,dtype=np.float64)
# Gaussian distributions
a=np.exp(-(x-ma)**2/(2*sa^2))
b=np.exp(-(x-mb)**2/(2*sb^2))
# normalization
a/=a.sum()
b/=b.sum()
# 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)
gs = gridspec.GridSpec(3, 3)
ax1=pl.subplot(gs[0,1:])
pl.plot(x,b,'r',label='Target distribution')
pl.yticks(())
#pl.axis('off')
ax2=pl.subplot(gs[1:,0])
pl.plot(a,x,'b',label='Source distribution')
pl.gca().invert_xaxis()
pl.gca().invert_yaxis()
pl.xticks(())
#pl.ylim((0,n))
#pl.axis('off')
pl.subplot(gs[1:,1:],sharex=ax1,sharey=ax2)
pl.imshow(M,interpolation='nearest')
pl.xlim((0,n))
#pl.ylim((0,n))
#pl.axis('off')
#%% EMD
G0=ot.emd(a,b,M)
#%% plot EMD optimal tranport matrix
pl.figure(3)
gs = gridspec.GridSpec(3, 3)
ax1=pl.subplot(gs[0,1:])
pl.plot(x,b,'r',label='Target distribution')
pl.yticks(())
#pl.axis('off')
ax2=pl.subplot(gs[1:,0])
pl.plot(a,x,'b',label='Source distribution')
pl.gca().invert_xaxis()
pl.gca().invert_yaxis()
pl.xticks(())
#pl.ylim((0,n))
#pl.axis('off')
pl.subplot(gs[1:,1:],sharex=ax1,sharey=ax2)
pl.imshow(G0,interpolation='nearest')
pl.xlim((0,n))
#pl.ylim((0,n))
#pl.axis('off')
|
