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"""Tests for module bregman on OT with bregman projections """
# Author: Remi Flamary <remi.flamary@unice.fr>
# Kilian Fatras <kilian.fatras@irisa.fr>
#
# License: MIT License
import numpy as np
import ot
import pytest
def test_sinkhorn():
# test sinkhorn
n = 100
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G = ot.sinkhorn(u, u, M, 1, stopThr=1e-10)
# check constratints
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
def test_sinkhorn_empty():
# test sinkhorn
n = 100
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G, log = ot.sinkhorn([], [], M, 1, stopThr=1e-10, verbose=True, log=True)
# check constratints
np.testing.assert_allclose(u, G.sum(1), atol=1e-05)
np.testing.assert_allclose(u, G.sum(0), atol=1e-05)
G, log = ot.sinkhorn([], [], M, 1, stopThr=1e-10,
method='sinkhorn_stabilized', verbose=True, log=True)
# check constratints
np.testing.assert_allclose(u, G.sum(1), atol=1e-05)
np.testing.assert_allclose(u, G.sum(0), atol=1e-05)
G, log = ot.sinkhorn(
[], [], M, 1, stopThr=1e-10, method='sinkhorn_epsilon_scaling',
verbose=True, log=True)
# check constratints
np.testing.assert_allclose(u, G.sum(1), atol=1e-05)
np.testing.assert_allclose(u, G.sum(0), atol=1e-05)
def test_sinkhorn_variants():
# test sinkhorn
n = 100
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G0 = ot.sinkhorn(u, u, M, 1, method='sinkhorn', stopThr=1e-10)
Gs = ot.sinkhorn(u, u, M, 1, method='sinkhorn_stabilized', stopThr=1e-10)
Ges = ot.sinkhorn(
u, u, M, 1, method='sinkhorn_epsilon_scaling', stopThr=1e-10)
G_green = ot.sinkhorn(u, u, M, 1, method='greenkhorn', stopThr=1e-10)
# check values
np.testing.assert_allclose(G0, Gs, atol=1e-05)
np.testing.assert_allclose(G0, Ges, atol=1e-05)
np.testing.assert_allclose(G0, G_green, atol=1e-5)
print(G0, G_green)
def test_sinkhorn_variants_log():
# test sinkhorn
n = 100
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G0, log0 = ot.sinkhorn(u, u, M, 1, method='sinkhorn', stopThr=1e-10, log=True)
Gs, logs = ot.sinkhorn(u, u, M, 1, method='sinkhorn_stabilized', stopThr=1e-10, log=True)
Ges, loges = ot.sinkhorn(
u, u, M, 1, method='sinkhorn_epsilon_scaling', stopThr=1e-10, log=True)
G_green, loggreen = ot.sinkhorn(u, u, M, 1, method='greenkhorn', stopThr=1e-10, log=True)
# check values
np.testing.assert_allclose(G0, Gs, atol=1e-05)
np.testing.assert_allclose(G0, Ges, atol=1e-05)
np.testing.assert_allclose(G0, G_green, atol=1e-5)
print(G0, G_green)
@pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_stabilized"])
def test_barycenter(method):
n_bins = 100 # nb bins
# Gaussian distributions
a1 = ot.datasets.make_1D_gauss(n_bins, m=30, s=10) # m= mean, s= std
a2 = ot.datasets.make_1D_gauss(n_bins, m=40, s=10)
# creating matrix A containing all distributions
A = np.vstack((a1, a2)).T
# loss matrix + normalization
M = ot.utils.dist0(n_bins)
M /= M.max()
alpha = 0.5 # 0<=alpha<=1
weights = np.array([1 - alpha, alpha])
# wasserstein
reg = 1e-2
bary_wass = ot.bregman.barycenter(A, M, reg, weights, method=method)
np.testing.assert_allclose(1, np.sum(bary_wass))
ot.bregman.barycenter(A, M, reg, log=True, verbose=True)
def test_barycenter_stabilization():
n_bins = 100 # nb bins
# Gaussian distributions
a1 = ot.datasets.make_1D_gauss(n_bins, m=30, s=10) # m= mean, s= std
a2 = ot.datasets.make_1D_gauss(n_bins, m=40, s=10)
# creating matrix A containing all distributions
A = np.vstack((a1, a2)).T
# loss matrix + normalization
M = ot.utils.dist0(n_bins)
M /= M.max()
alpha = 0.5 # 0<=alpha<=1
weights = np.array([1 - alpha, alpha])
# wasserstein
reg = 1e-2
bar_stable = ot.bregman.barycenter(A, M, reg, weights,
method="sinkhorn_stabilized",
stopThr=1e-8)
bar = ot.bregman.barycenter(A, M, reg, weights, method="sinkhorn",
stopThr=1e-8)
np.testing.assert_allclose(bar, bar_stable)
def test_wasserstein_bary_2d():
size = 100 # size of a square image
a1 = np.random.randn(size, size)
a1 += a1.min()
a1 = a1 / np.sum(a1)
a2 = np.random.randn(size, size)
a2 += a2.min()
a2 = a2 / np.sum(a2)
# creating matrix A containing all distributions
A = np.zeros((2, size, size))
A[0, :, :] = a1
A[1, :, :] = a2
# wasserstein
reg = 1e-2
bary_wass = ot.bregman.convolutional_barycenter2d(A, reg)
np.testing.assert_allclose(1, np.sum(bary_wass))
# help in checking if log and verbose do not bug the function
ot.bregman.convolutional_barycenter2d(A, reg, log=True, verbose=True)
def test_unmix():
n_bins = 50 # nb bins
# Gaussian distributions
a1 = ot.datasets.make_1D_gauss(n_bins, m=20, s=10) # m= mean, s= std
a2 = ot.datasets.make_1D_gauss(n_bins, m=40, s=10)
a = ot.datasets.make_1D_gauss(n_bins, m=30, s=10)
# creating matrix A containing all distributions
D = np.vstack((a1, a2)).T
# loss matrix + normalization
M = ot.utils.dist0(n_bins)
M /= M.max()
M0 = ot.utils.dist0(2)
M0 /= M0.max()
h0 = ot.unif(2)
# wasserstein
reg = 1e-3
um = ot.bregman.unmix(a, D, M, M0, h0, reg, 1, alpha=0.01,)
np.testing.assert_allclose(1, np.sum(um), rtol=1e-03, atol=1e-03)
np.testing.assert_allclose([0.5, 0.5], um, rtol=1e-03, atol=1e-03)
ot.bregman.unmix(a, D, M, M0, h0, reg,
1, alpha=0.01, log=True, verbose=True)
def test_empirical_sinkhorn():
# test sinkhorn
n = 100
a = ot.unif(n)
b = ot.unif(n)
X_s = np.reshape(np.arange(n), (n, 1))
X_t = np.reshape(np.arange(0, n), (n, 1))
M = ot.dist(X_s, X_t)
M_m = ot.dist(X_s, X_t, metric='minkowski')
G_sqe = ot.bregman.empirical_sinkhorn(X_s, X_t, 1)
sinkhorn_sqe = ot.sinkhorn(a, b, M, 1)
G_log, log_es = ot.bregman.empirical_sinkhorn(X_s, X_t, 0.1, log=True)
sinkhorn_log, log_s = ot.sinkhorn(a, b, M, 0.1, log=True)
G_m = ot.bregman.empirical_sinkhorn(X_s, X_t, 1, metric='minkowski')
sinkhorn_m = ot.sinkhorn(a, b, M_m, 1)
loss_emp_sinkhorn = ot.bregman.empirical_sinkhorn2(X_s, X_t, 1)
loss_sinkhorn = ot.sinkhorn2(a, b, M, 1)
# check constratints
np.testing.assert_allclose(
sinkhorn_sqe.sum(1), G_sqe.sum(1), atol=1e-05) # metric sqeuclidian
np.testing.assert_allclose(
sinkhorn_sqe.sum(0), G_sqe.sum(0), atol=1e-05) # metric sqeuclidian
np.testing.assert_allclose(
sinkhorn_log.sum(1), G_log.sum(1), atol=1e-05) # log
np.testing.assert_allclose(
sinkhorn_log.sum(0), G_log.sum(0), atol=1e-05) # log
np.testing.assert_allclose(
sinkhorn_m.sum(1), G_m.sum(1), atol=1e-05) # metric euclidian
np.testing.assert_allclose(
sinkhorn_m.sum(0), G_m.sum(0), atol=1e-05) # metric euclidian
np.testing.assert_allclose(loss_emp_sinkhorn, loss_sinkhorn, atol=1e-05)
def test_empirical_sinkhorn_divergence():
#Test sinkhorn divergence
n = 10
a = ot.unif(n)
b = ot.unif(n)
X_s = np.reshape(np.arange(n), (n, 1))
X_t = np.reshape(np.arange(0, n * 2, 2), (n, 1))
M = ot.dist(X_s, X_t)
M_s = ot.dist(X_s, X_s)
M_t = ot.dist(X_t, X_t)
emp_sinkhorn_div = ot.bregman.empirical_sinkhorn_divergence(X_s, X_t, 1)
sinkhorn_div = (ot.sinkhorn2(a, b, M, 1) - 1 / 2 * ot.sinkhorn2(a, a, M_s, 1) - 1 / 2 * ot.sinkhorn2(b, b, M_t, 1))
emp_sinkhorn_div_log, log_es = ot.bregman.empirical_sinkhorn_divergence(X_s, X_t, 1, log=True)
sink_div_log_ab, log_s_ab = ot.sinkhorn2(a, b, M, 1, log=True)
sink_div_log_a, log_s_a = ot.sinkhorn2(a, a, M_s, 1, log=True)
sink_div_log_b, log_s_b = ot.sinkhorn2(b, b, M_t, 1, log=True)
sink_div_log = sink_div_log_ab - 1 / 2 * (sink_div_log_a + sink_div_log_b)
# check constratints
np.testing.assert_allclose(
emp_sinkhorn_div, sinkhorn_div, atol=1e-05) # cf conv emp sinkhorn
np.testing.assert_allclose(
emp_sinkhorn_div_log, sink_div_log, atol=1e-05) # cf conv emp sinkhorn
def test_stabilized_vs_sinkhorn_multidim():
# test if stable version matches sinkhorn
# for multidimensional inputs
n = 100
# Gaussian distributions
a = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std
b1 = ot.datasets.make_1D_gauss(n, m=60, s=8)
b2 = ot.datasets.make_1D_gauss(n, m=30, s=4)
# creating matrix A containing all distributions
b = np.vstack((b1, b2)).T
M = ot.utils.dist0(n)
M /= np.median(M)
epsilon = 0.1
G, log = ot.bregman.sinkhorn(a, b, M, reg=epsilon,
method="sinkhorn_stabilized",
log=True)
G2, log2 = ot.bregman.sinkhorn(a, b, M, epsilon,
method="sinkhorn", log=True)
np.testing.assert_allclose(G, G2)
def test_implemented_methods():
IMPLEMENTED_METHODS = ['sinkhorn', 'sinkhorn_stabilized']
ONLY_1D_methods = ['greenkhorn', 'sinkhorn_epsilon_scaling']
NOT_VALID_TOKENS = ['foo']
# test generalized sinkhorn for unbalanced OT barycenter
n = 3
rng = np.random.RandomState(42)
x = rng.randn(n, 2)
a = ot.utils.unif(n)
# make dists unbalanced
b = ot.utils.unif(n)
A = rng.rand(n, 2)
M = ot.dist(x, x)
epsilon = 1.
for method in IMPLEMENTED_METHODS:
ot.bregman.sinkhorn(a, b, M, epsilon, method=method)
ot.bregman.sinkhorn2(a, b, M, epsilon, method=method)
ot.bregman.barycenter(A, M, reg=epsilon, method=method)
with pytest.raises(ValueError):
for method in set(NOT_VALID_TOKENS):
ot.bregman.sinkhorn(a, b, M, epsilon, method=method)
ot.bregman.sinkhorn2(a, b, M, epsilon, method=method)
ot.bregman.barycenter(A, M, reg=epsilon, method=method)
for method in ONLY_1D_methods:
ot.bregman.sinkhorn(a, b, M, epsilon, method=method)
with pytest.raises(ValueError):
ot.bregman.sinkhorn2(a, b, M, epsilon, method=method)
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