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
|
"""Tests for ot.smooth model"""
# Author: Remi Flamary <remi.flamary@unice.fr>
#
# License: MIT License
import numpy as np
import ot
import pytest
from scipy.optimize import check_grad
def test_smooth_ot_dual():
# get data
n = 100
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
with pytest.raises(NotImplementedError):
Gl2, log = ot.smooth.smooth_ot_dual(u, u, M, 1, reg_type="none")
# squared l2 regularisation
Gl2, log = ot.smooth.smooth_ot_dual(
u, u, M, 1, reg_type="l2", log=True, stopThr=1e-10
)
# check constraints
np.testing.assert_allclose(u, Gl2.sum(1), atol=1e-05) # cf convergence sinkhorn
np.testing.assert_allclose(u, Gl2.sum(0), atol=1e-05) # cf convergence sinkhorn
# kl regularisation
G = ot.smooth.smooth_ot_dual(u, u, M, 1, reg_type="kl", stopThr=1e-10)
# check constraints
np.testing.assert_allclose(u, G.sum(1), atol=1e-05) # cf convergence sinkhorn
np.testing.assert_allclose(u, G.sum(0), atol=1e-05) # cf convergence sinkhorn
G2 = ot.sinkhorn(u, u, M, 1, stopThr=1e-10)
np.testing.assert_allclose(G, G2, atol=1e-05)
# sparsity-constrained regularisation
max_nz = 2
Gsc, log = ot.smooth.smooth_ot_dual(
u,
u,
M,
1,
max_nz=max_nz,
log=True,
reg_type="sparsity_constrained",
stopThr=1e-10,
)
# check marginal constraints
np.testing.assert_allclose(u, Gsc.sum(1), atol=1e-03)
np.testing.assert_allclose(u, Gsc.sum(0), atol=1e-03)
# check sparsity constraints
np.testing.assert_array_less(np.sum(Gsc > 0, axis=0), np.ones(n) * max_nz + 1)
def test_smooth_ot_semi_dual():
# get data
n = 100
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
with pytest.raises(NotImplementedError):
Gl2, log = ot.smooth.smooth_ot_semi_dual(u, u, M, 1, reg_type="none")
# squared l2 regularisation
Gl2, log = ot.smooth.smooth_ot_semi_dual(
u, u, M, 1, reg_type="l2", log=True, stopThr=1e-10
)
# check constraints
np.testing.assert_allclose(u, Gl2.sum(1), atol=1e-05) # cf convergence sinkhorn
np.testing.assert_allclose(u, Gl2.sum(0), atol=1e-05) # cf convergence sinkhorn
# kl regularisation
G = ot.smooth.smooth_ot_semi_dual(u, u, M, 1, reg_type="kl", stopThr=1e-10)
# check constraints
np.testing.assert_allclose(u, G.sum(1), atol=1e-05) # cf convergence sinkhorn
np.testing.assert_allclose(u, G.sum(0), atol=1e-05) # cf convergence sinkhorn
G2 = ot.sinkhorn(u, u, M, 1, stopThr=1e-10)
np.testing.assert_allclose(G, G2, atol=1e-05)
# sparsity-constrained regularisation
max_nz = 2
Gsc = ot.smooth.smooth_ot_semi_dual(
u, u, M, 1, reg_type="sparsity_constrained", max_nz=max_nz, stopThr=1e-10
)
# check marginal constraints
np.testing.assert_allclose(u, Gsc.sum(1), atol=1e-03)
np.testing.assert_allclose(u, Gsc.sum(0), atol=1e-03)
# check sparsity constraints
np.testing.assert_array_less(np.sum(Gsc > 0, axis=0), np.ones(n) * max_nz + 1)
def test_sparsity_constrained_gradient():
max_nz = 5
regularizer = ot.smooth.SparsityConstrained(max_nz=max_nz)
rng = np.random.RandomState(0)
X = rng.randn(
10,
)
b = 0.5
def delta_omega_func(X):
return regularizer.delta_Omega(X)[0]
def delta_omega_grad(X):
return regularizer.delta_Omega(X)[1]
dual_grad_err = check_grad(delta_omega_func, delta_omega_grad, X)
np.testing.assert_allclose(dual_grad_err, 0.0, atol=1e-07)
def max_omega_func(X, b):
return regularizer.max_Omega(X, b)[0]
def max_omega_grad(X, b):
return regularizer.max_Omega(X, b)[1]
semi_dual_grad_err = check_grad(max_omega_func, max_omega_grad, X, b)
np.testing.assert_allclose(semi_dual_grad_err, 0.0, atol=1e-07)
|
