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
|
# -*- coding: utf-8 -*-
"""
================================
Smooth and sparse OT example
================================
This example illustrates the computation of
Smooth and Sparse (KL an L2 reg.) OT and
sparsity-constrained OT, together with their visualizations.
"""
# Author: Remi Flamary <remi.flamary@unice.fr>
#
# License: MIT License
# sphinx_gallery_thumbnail_number = 5
import numpy as np
import matplotlib.pylab as pl
import ot
import ot.plot
from ot.datasets import make_1D_gauss as gauss
##############################################################################
# Generate data
# -------------
# %% 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
# ----------------------------------
# %% 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 Smooth OT
# ---------------
# %% Smooth OT with KL regularization
lambd = 2e-3
Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type="kl")
pl.figure(3, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, Gsm, "OT matrix Smooth OT KL reg.")
pl.show()
# %% Smooth OT with squared l2 regularization
lambd = 1e-1
Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type="l2")
pl.figure(4, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, Gsm, "OT matrix Smooth OT l2 reg.")
pl.show()
# %% Sparsity-constrained OT
lambd = 1e-1
max_nz = 2 # two non-zero entries are permitted per column of the OT plan
Gsc = ot.smooth.smooth_ot_dual(
a, b, M, lambd, reg_type="sparsity_constrained", max_nz=max_nz
)
pl.figure(5, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, Gsc, "Sparsity constrained OT matrix; k=2.")
pl.show()
|
