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
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
|
"""Tests for main module ot """
# Author: Remi Flamary <remi.flamary@unice.fr>
#
# License: MIT License
import numpy as np
import ot
from ot.datasets import get_1D_gauss as gauss
def test_doctest():
import doctest
# test lp solver
doctest.testmod(ot.lp, verbose=True)
# test bregman solver
doctest.testmod(ot.bregman, verbose=True)
def test_emd_emd2():
# test emd and emd2 for simple identity
n = 100
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G = ot.emd(u, u, M)
# check G is identity
np.testing.assert_allclose(G, np.eye(n) / n)
# check constratints
np.testing.assert_allclose(u, G.sum(1)) # cf convergence sinkhorn
np.testing.assert_allclose(u, G.sum(0)) # cf convergence sinkhorn
w = ot.emd2(u, u, M)
# check loss=0
np.testing.assert_allclose(w, 0)
def test_emd_empty():
# test emd and emd2 for simple identity
n = 100
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G = ot.emd([], [], M)
# check G is identity
np.testing.assert_allclose(G, np.eye(n) / n)
# check constratints
np.testing.assert_allclose(u, G.sum(1)) # cf convergence sinkhorn
np.testing.assert_allclose(u, G.sum(0)) # cf convergence sinkhorn
w = ot.emd2([], [], M)
# check loss=0
np.testing.assert_allclose(w, 0)
def test_emd2_multi():
n = 1000 # nb bins
# bin positions
x = np.arange(n, dtype=np.float64)
# Gaussian distributions
a = gauss(n, m=20, s=5) # m= mean, s= std
ls = np.arange(20, 1000, 20)
nb = len(ls)
b = np.zeros((n, nb))
for i in range(nb):
b[:, i] = gauss(n, m=ls[i], s=10)
# loss matrix
M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
# M/=M.max()
print('Computing {} EMD '.format(nb))
# emd loss 1 proc
ot.tic()
emd1 = ot.emd2(a, b, M, 1)
ot.toc('1 proc : {} s')
# emd loss multipro proc
ot.tic()
emdn = ot.emd2(a, b, M)
ot.toc('multi proc : {} s')
np.testing.assert_allclose(emd1, emdn)
def test_dual_variables():
# %% parameters
n = 5000 # nb bins
m = 6000 # nb bins
mean1 = 1000
mean2 = 1100
# bin positions
x = np.arange(n, dtype=np.float64)
y = np.arange(m, dtype=np.float64)
# Gaussian distributions
a = gauss(n, m=mean1, s=5) # m= mean, s= std
b = gauss(m, m=mean2, s=10)
# loss matrix
M = ot.dist(x.reshape((-1, 1)), y.reshape((-1, 1))) ** (1. / 2)
# M/=M.max()
# %%
print('Computing {} EMD '.format(1))
# emd loss 1 proc
ot.tic()
G, alpha, beta = ot.emd(a, b, M, dual_variables=True)
ot.toc('1 proc : {} s')
cost1 = (G * M).sum()
cost_dual = np.vdot(a, alpha) + np.vdot(b, beta)
# emd loss 1 proc
ot.tic()
cost_emd2 = ot.emd2(a, b, M)
ot.toc('1 proc : {} s')
ot.tic()
G2 = ot.emd(b, a, np.ascontiguousarray(M.T))
ot.toc('1 proc : {} s')
cost2 = (G2 * M.T).sum()
# Check that both cost computations are equivalent
np.testing.assert_almost_equal(cost1, cost_emd2)
# Check that dual and primal cost are equal
np.testing.assert_almost_equal(cost1, cost_dual)
# Check symmetry
np.testing.assert_almost_equal(cost1, cost2)
# Check with closed-form solution for gaussians
np.testing.assert_almost_equal(cost1, np.abs(mean1 - mean2))
[ind1, ind2] = np.nonzero(G)
# Check that reduced cost is zero on transport arcs
np.testing.assert_array_almost_equal((M - alpha.reshape(-1, 1) - beta.reshape(1, -1))[ind1, ind2],
np.zeros(ind1.size))
|
