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"""Tests for module Unbalanced OT with entropy regularization"""
# Author: Hicham Janati <hicham.janati@inria.fr>
#
# License: MIT License
import numpy as np
import ot
import pytest
@pytest.mark.parametrize("method", ["sinkhorn"])
def test_unbalanced_convergence(method):
# test generalized sinkhorn for unbalanced OT
n = 100
rng = np.random.RandomState(42)
x = rng.randn(n, 2)
a = ot.utils.unif(n)
# make dists unbalanced
b = ot.utils.unif(n) * 1.5
M = ot.dist(x, x)
epsilon = 1.
alpha = 1.
K = np.exp(- M / epsilon)
G, log = ot.unbalanced.sinkhorn_unbalanced(a, b, M, reg=epsilon, alpha=alpha,
stopThr=1e-10, method=method,
log=True)
loss = ot.unbalanced.sinkhorn_unbalanced2(a, b, M, epsilon, alpha,
method=method)
# check fixed point equations
fi = alpha / (alpha + epsilon)
v_final = (b / K.T.dot(log["u"])) ** fi
u_final = (a / K.dot(log["v"])) ** fi
np.testing.assert_allclose(
u_final, log["u"], atol=1e-05)
np.testing.assert_allclose(
v_final, log["v"], atol=1e-05)
# check if sinkhorn_unbalanced2 returns the correct loss
np.testing.assert_allclose((G * M).sum(), loss, atol=1e-5)
@pytest.mark.parametrize("method", ["sinkhorn"])
def test_unbalanced_multiple_inputs(method):
# test generalized sinkhorn for unbalanced OT
n = 100
rng = np.random.RandomState(42)
x = rng.randn(n, 2)
a = ot.utils.unif(n)
# make dists unbalanced
b = rng.rand(n, 2)
M = ot.dist(x, x)
epsilon = 1.
alpha = 1.
K = np.exp(- M / epsilon)
loss, log = ot.unbalanced.sinkhorn_unbalanced(a, b, M, reg=epsilon,
alpha=alpha,
stopThr=1e-10, method=method,
log=True)
# check fixed point equations
fi = alpha / (alpha + epsilon)
v_final = (b / K.T.dot(log["u"])) ** fi
u_final = (a[:, None] / K.dot(log["v"])) ** fi
np.testing.assert_allclose(
u_final, log["u"], atol=1e-05)
np.testing.assert_allclose(
v_final, log["v"], atol=1e-05)
assert len(loss) == b.shape[1]
def test_unbalanced_barycenter():
# test generalized sinkhorn for unbalanced OT barycenter
n = 100
rng = np.random.RandomState(42)
x = rng.randn(n, 2)
A = rng.rand(n, 2)
# make dists unbalanced
A = A * np.array([1, 2])[None, :]
M = ot.dist(x, x)
epsilon = 1.
alpha = 1.
K = np.exp(- M / epsilon)
q, log = ot.unbalanced.barycenter_unbalanced(A, M, reg=epsilon, alpha=alpha,
stopThr=1e-10,
log=True)
# check fixed point equations
fi = alpha / (alpha + epsilon)
v_final = (q[:, None] / K.T.dot(log["u"])) ** fi
u_final = (A / K.dot(log["v"])) ** fi
np.testing.assert_allclose(
u_final, log["u"], atol=1e-05)
np.testing.assert_allclose(
v_final, log["v"], atol=1e-05)
def test_implemented_methods():
IMPLEMENTED_METHODS = ['sinkhorn']
TO_BE_IMPLEMENTED_METHODS = ['sinkhorn_stabilized',
'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) * 1.5
M = ot.dist(x, x)
epsilon = 1.
alpha = 1.
for method in IMPLEMENTED_METHODS:
ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha,
method=method)
ot.unbalanced.sinkhorn_unbalanced2(a, b, M, epsilon, alpha,
method=method)
with pytest.warns(UserWarning, match='not implemented'):
for method in set(TO_BE_IMPLEMENTED_METHODS):
ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha,
method=method)
ot.unbalanced.sinkhorn_unbalanced2(a, b, M, epsilon, alpha,
method=method)
with pytest.raises(ValueError):
for method in set(NOT_VALID_TOKENS):
ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha,
method=method)
ot.unbalanced.sinkhorn_unbalanced2(a, b, M, epsilon, alpha,
method=method)
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