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
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
|
"""Tests for module partial """
# Author:
# Laetitia Chapel <laetitia.chapel@irisa.fr>
#
# License: MIT License
import numpy as np
import scipy as sp
import ot
def test_partial_wasserstein():
n_samples = 20 # nb samples (gaussian)
n_noise = 20 # nb of samples (noise)
mu = np.array([0, 0])
cov = np.array([[1, 0], [0, 2]])
xs = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov)
xs = np.append(xs, (np.random.rand(n_noise, 2) + 1) * 4).reshape((-1, 2))
xt = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov)
xt = np.append(xt, (np.random.rand(n_noise, 2) + 1) * -3).reshape((-1, 2))
M = ot.dist(xs, xt)
p = ot.unif(n_samples + n_noise)
q = ot.unif(n_samples + n_noise)
m = 0.5
w0, log0 = ot.partial.partial_wasserstein(p, q, M, m=m, log=True)
w, log = ot.partial.entropic_partial_wasserstein(p, q, M, reg=1, m=m,
log=True)
# check constratints
np.testing.assert_equal(
w0.sum(1) - p <= 1e-5, [True] * len(p)) # cf convergence wasserstein
np.testing.assert_equal(
w0.sum(0) - q <= 1e-5, [True] * len(q)) # cf convergence wasserstein
np.testing.assert_equal(
w.sum(1) - p <= 1e-5, [True] * len(p)) # cf convergence wasserstein
np.testing.assert_equal(
w.sum(0) - q <= 1e-5, [True] * len(q)) # cf convergence wasserstein
# check transported mass
np.testing.assert_allclose(
np.sum(w0), m, atol=1e-04)
np.testing.assert_allclose(
np.sum(w), m, atol=1e-04)
w0, log0 = ot.partial.partial_wasserstein2(p, q, M, m=m, log=True)
w0_val = ot.partial.partial_wasserstein2(p, q, M, m=m, log=False)
G = log0['T']
np.testing.assert_allclose(w0, w0_val, atol=1e-1, rtol=1e-1)
# check constratints
np.testing.assert_equal(
G.sum(1) <= p, [True] * len(p)) # cf convergence wasserstein
np.testing.assert_equal(
G.sum(0) <= q, [True] * len(q)) # cf convergence wasserstein
np.testing.assert_allclose(
np.sum(G), m, atol=1e-04)
def test_partial_gromov_wasserstein():
n_samples = 20 # nb samples
n_noise = 10 # nb of samples (noise)
p = ot.unif(n_samples + n_noise)
q = ot.unif(n_samples + n_noise)
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
mu_t = np.array([0, 0, 0])
cov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s)
xs = np.concatenate((xs, ((np.random.rand(n_noise, 2) + 1) * 4)), axis=0)
P = sp.linalg.sqrtm(cov_t)
xt = np.random.randn(n_samples, 3).dot(P) + mu_t
xt = np.concatenate((xt, ((np.random.rand(n_noise, 3) + 1) * 10)), axis=0)
xt2 = xs[::-1].copy()
C1 = ot.dist(xs, xs)
C2 = ot.dist(xt, xt)
C3 = ot.dist(xt2, xt2)
m = 2 / 3
res0, log0 = ot.partial.partial_gromov_wasserstein(C1, C3, p, q, m=m,
log=True)
np.testing.assert_allclose(res0, 0, atol=1e-1, rtol=1e-1)
C1 = sp.spatial.distance.cdist(xs, xs)
C2 = sp.spatial.distance.cdist(xt, xt)
m = 1
res0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m,
log=True)
G = ot.gromov.gromov_wasserstein(C1, C2, p, q, 'square_loss')
np.testing.assert_allclose(G, res0, atol=1e-04)
res, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q, 10,
m=m, log=True)
G = ot.gromov.entropic_gromov_wasserstein(
C1, C2, p, q, 'square_loss', epsilon=10)
np.testing.assert_allclose(G, res, atol=1e-02)
w0, log0 = ot.partial.partial_gromov_wasserstein2(C1, C2, p, q, m=m,
log=True)
w0_val = ot.partial.partial_gromov_wasserstein2(C1, C2, p, q, m=m,
log=False)
G = log0['T']
np.testing.assert_allclose(w0, w0_val, atol=1e-1, rtol=1e-1)
m = 2 / 3
res0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m,
log=True)
res, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q,
100, m=m,
log=True)
# check constratints
np.testing.assert_equal(
res0.sum(1) <= p, [True] * len(p)) # cf convergence wasserstein
np.testing.assert_equal(
res0.sum(0) <= q, [True] * len(q)) # cf convergence wasserstein
np.testing.assert_allclose(
np.sum(res0), m, atol=1e-04)
np.testing.assert_equal(
res.sum(1) <= p, [True] * len(p)) # cf convergence wasserstein
np.testing.assert_equal(
res.sum(0) <= q, [True] * len(q)) # cf convergence wasserstein
np.testing.assert_allclose(
np.sum(res), m, atol=1e-04)
|
