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"""Test for low rank sinkhorn solvers"""
# Author: Laurène DAVID <laurene.david@ip-paris.fr>
#
# License: MIT License
import ot
import numpy as np
import pytest
from ot.lowrank import sklearn_import # check sklearn installation
def test_compute_lr_sqeuclidean_matrix():
# test computation of low rank cost matrices M1 and M2
n = 100
X_s = np.reshape(1.0 * np.arange(2 * n), (n, 2))
X_t = np.reshape(1.0 * np.arange(2 * n), (n, 2))
M1, M2 = ot.lowrank.compute_lr_sqeuclidean_matrix(X_s, X_t, rescale_cost=False)
M = ot.dist(X_s, X_t, metric="sqeuclidean") # original cost matrix
np.testing.assert_allclose(np.dot(M1, M2.T), M, atol=1e-05)
def test_lowrank_sinkhorn():
# test low rank sinkhorn
n = 100
a = ot.unif(n)
b = ot.unif(n)
X_s = np.reshape(1.0 * np.arange(n), (n, 1))
X_t = np.reshape(1.0 * np.arange(n), (n, 1))
Q, R, g, log = ot.lowrank.lowrank_sinkhorn(
X_s, X_t, a, b, reg=0.1, log=True, rescale_cost=False
)
P = log["lazy_plan"][:]
value_linear = log["value_linear"]
# check constraints for P
np.testing.assert_allclose(a, P.sum(1), atol=1e-05)
np.testing.assert_allclose(b, P.sum(0), atol=1e-05)
# check if lazy_plan is equal to the fully computed plan
P_true = np.dot(Q, np.dot(np.diag(1 / g), R.T))
np.testing.assert_allclose(P, P_true, atol=1e-05)
# check if value_linear is correct with its original formula
M = ot.dist(X_s, X_t, metric="sqeuclidean")
value_linear_true = np.sum(M * P_true)
np.testing.assert_allclose(value_linear, value_linear_true, atol=1e-05)
# check warn parameter when Dykstra algorithm doesn't converge
with pytest.warns(UserWarning):
ot.lowrank.lowrank_sinkhorn(X_s, X_t, a, b, reg=0.1, stopThr=0, numItermax=1)
@pytest.mark.parametrize(("init"), ("random", "deterministic", "kmeans"))
def test_lowrank_sinkhorn_init(init):
# test lowrank inits
n = 100
a = ot.unif(n)
b = ot.unif(n)
X_s = np.reshape(1.0 * np.arange(n), (n, 1))
X_t = np.reshape(1.0 * np.arange(n), (n, 1))
# test ImportError if init="kmeans" and sklearn not imported
if init in ["random", "deterministic"] or (
(init == "kmeans") and (sklearn_import is True)
):
Q, R, g, log = ot.lowrank.lowrank_sinkhorn(
X_s, X_t, a, b, reg=0.1, init=init, log=True
)
P = log["lazy_plan"][:]
# check constraints for P
np.testing.assert_allclose(a, P.sum(1), atol=1e-05)
np.testing.assert_allclose(b, P.sum(0), atol=1e-05)
else:
with pytest.raises(ImportError):
Q, R, g = ot.lowrank.lowrank_sinkhorn(X_s, X_t, a, b, reg=0.1, init=init)
@pytest.mark.parametrize(("alpha, rank"), ((0.8, 2), (0.5, 3), (0.2, 6)))
def test_lowrank_sinkhorn_alpha_error(alpha, rank):
# Test warning for value of alpha
n = 100
a = ot.unif(n)
b = ot.unif(n)
X_s = np.reshape(1.0 * np.arange(n), (n, 1))
X_t = np.reshape(1.0 * np.arange(0, n), (n, 1))
with pytest.raises(ValueError):
ot.lowrank.lowrank_sinkhorn(
X_s, X_t, a, b, reg=0.1, rank=rank, alpha=alpha, warn=False
)
@pytest.mark.parametrize(("gamma_init"), ("rescale", "theory"))
def test_lowrank_sinkhorn_gamma_init(gamma_init):
# Test lr sinkhorn with different init strategies
n = 100
a = ot.unif(n)
b = ot.unif(n)
X_s = np.reshape(1.0 * np.arange(n), (n, 1))
X_t = np.reshape(1.0 * np.arange(n), (n, 1))
Q, R, g, log = ot.lowrank.lowrank_sinkhorn(
X_s, X_t, a, b, reg=0.1, gamma_init=gamma_init, log=True
)
P = log["lazy_plan"][:]
# check constraints for P
np.testing.assert_allclose(a, P.sum(1), atol=1e-05)
np.testing.assert_allclose(b, P.sum(0), atol=1e-05)
@pytest.skip_backend("tf")
def test_lowrank_sinkhorn_backends(nx):
# Test low rank sinkhorn for different backends
n = 100
a = ot.unif(n)
b = ot.unif(n)
X_s = np.reshape(1.0 * np.arange(n), (n, 1))
X_t = np.reshape(1.0 * np.arange(0, n), (n, 1))
ab, bb, X_sb, X_tb = nx.from_numpy(a, b, X_s, X_t)
Q, R, g, log = ot.lowrank.lowrank_sinkhorn(X_sb, X_tb, ab, bb, reg=0.1, log=True)
lazy_plan = log["lazy_plan"]
P = lazy_plan[:]
np.testing.assert_allclose(ab, P.sum(1), atol=1e-05)
np.testing.assert_allclose(bb, P.sum(0), atol=1e-05)
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