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
|
#!/usr/bin/env python
# coding: utf-8
# In[ ]:
from ot.bregman import screenkhorn
from ot.datasets import make_1D_gauss as gauss
import ot.plot
import ot
import matplotlib.pylab as pl
import numpy as np
get_ipython().run_line_magic('matplotlib', 'inline')
#
# # 1D Screened optimal transport
#
#
# This example illustrates the computation of Screenkhorn: Screening Sinkhorn Algorithm for Optimal transport.
#
#
# In[13]:
# Author: Mokhtar Z. Alaya <mokhtarzahdi.alaya@gmail.com>
#
# License: MIT License
# Generate data
# -------------
#
#
# In[14]:
#%% parameters
n = 100 # nb bins
# bin positions
x = np.arange(n, dtype=np.float64)
# Gaussian distributions
a = gauss(n, m=20, s=5) # m= mean, s= std
b = gauss(n, m=60, s=10)
# loss matrix
M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
M /= M.max()
# Plot distributions and loss matrix
# ----------------------------------
#
#
# In[15]:
#%% plot the distributions
pl.figure(1, figsize=(6.4, 3))
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, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')
# Solve Screened Sinkhorn
# --------------
#
#
# In[21]:
# Screenkhorn
lambd = 1e-2 # entropy parameter
ns_budget = 30 # budget number of points to be keeped in the source distribution
nt_budget = 30 # budget number of points to be keeped in the target distribution
Gsc = screenkhorn(a, b, M, lambd, ns_budget, nt_budget, uniform=False, restricted=True, verbose=True)
pl.figure(4, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, Gs, 'OT matrix Screenkhorn')
pl.show()
# In[ ]:
|