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"""Tests for module bregman on OT with bregman projections """
# Author: Remi Flamary <remi.flamary@unice.fr>
#
# License: MIT License
import numpy as np
import ot
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)
Gerr = ot.sinkhorn(u, u, M, 1, method='do_not_exists', 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, Gerr)
def test_bary():
n_bins = 100 # nb bins
# Gaussian distributions
a1 = ot.datasets.get_1D_gauss(n_bins, m=30, s=10) # m= mean, s= std
a2 = ot.datasets.get_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-3
bary_wass = ot.bregman.barycenter(A, M, reg, weights)
np.testing.assert_allclose(1, np.sum(bary_wass))
ot.bregman.barycenter(A, M, reg, log=True, verbose=True)
def test_unmix():
n_bins = 50 # nb bins
# Gaussian distributions
a1 = ot.datasets.get_1D_gauss(n_bins, m=20, s=10) # m= mean, s= std
a2 = ot.datasets.get_1D_gauss(n_bins, m=40, s=10)
a = ot.datasets.get_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)
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