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"""Tests for ot.smooth model """
# Author: Remi Flamary <remi.flamary@unice.fr>
#
# License: MIT License
import numpy as np
import ot
import pytest
from scipy.optimize import check_grad
def test_smooth_ot_dual():
# get data
n = 100
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
with pytest.raises(NotImplementedError):
Gl2, log = ot.smooth.smooth_ot_dual(u, u, M, 1, reg_type='none')
# squared l2 regularisation
Gl2, log = ot.smooth.smooth_ot_dual(u, u, M, 1, reg_type='l2', log=True, stopThr=1e-10)
# check constraints
np.testing.assert_allclose(
u, Gl2.sum(1), atol=1e-05) # cf convergence sinkhorn
np.testing.assert_allclose(
u, Gl2.sum(0), atol=1e-05) # cf convergence sinkhorn
# kl regularisation
G = ot.smooth.smooth_ot_dual(u, u, M, 1, reg_type='kl', stopThr=1e-10)
# check constraints
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
G2 = ot.sinkhorn(u, u, M, 1, stopThr=1e-10)
np.testing.assert_allclose(G, G2, atol=1e-05)
# sparsity-constrained regularisation
max_nz = 2
Gsc, log = ot.smooth.smooth_ot_dual(
u, u, M, 1,
max_nz=max_nz,
log=True,
reg_type='sparsity_constrained',
stopThr=1e-10)
# check marginal constraints
np.testing.assert_allclose(u, Gsc.sum(1), atol=1e-03)
np.testing.assert_allclose(u, Gsc.sum(0), atol=1e-03)
# check sparsity constraints
np.testing.assert_array_less(
np.sum(Gsc > 0, axis=0),
np.ones(n) * max_nz + 1)
def test_smooth_ot_semi_dual():
# get data
n = 100
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
with pytest.raises(NotImplementedError):
Gl2, log = ot.smooth.smooth_ot_semi_dual(u, u, M, 1, reg_type='none')
# squared l2 regularisation
Gl2, log = ot.smooth.smooth_ot_semi_dual(u, u, M, 1, reg_type='l2', log=True, stopThr=1e-10)
# check constraints
np.testing.assert_allclose(
u, Gl2.sum(1), atol=1e-05) # cf convergence sinkhorn
np.testing.assert_allclose(
u, Gl2.sum(0), atol=1e-05) # cf convergence sinkhorn
# kl regularisation
G = ot.smooth.smooth_ot_semi_dual(u, u, M, 1, reg_type='kl', stopThr=1e-10)
# check constraints
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
G2 = ot.sinkhorn(u, u, M, 1, stopThr=1e-10)
np.testing.assert_allclose(G, G2, atol=1e-05)
# sparsity-constrained regularisation
max_nz = 2
Gsc = ot.smooth.smooth_ot_semi_dual(
u, u, M, 1, reg_type='sparsity_constrained',
max_nz=max_nz, stopThr=1e-10)
# check marginal constraints
np.testing.assert_allclose(u, Gsc.sum(1), atol=1e-03)
np.testing.assert_allclose(u, Gsc.sum(0), atol=1e-03)
# check sparsity constraints
np.testing.assert_array_less(np.sum(Gsc > 0, axis=0),
np.ones(n) * max_nz + 1)
def test_sparsity_constrained_gradient():
max_nz = 5
regularizer = ot.smooth.SparsityConstrained(max_nz=max_nz)
rng = np.random.RandomState(0)
X = rng.randn(10,)
b = 0.5
def delta_omega_func(X):
return regularizer.delta_Omega(X)[0]
def delta_omega_grad(X):
return regularizer.delta_Omega(X)[1]
dual_grad_err = check_grad(delta_omega_func, delta_omega_grad, X)
np.testing.assert_allclose(dual_grad_err, 0.0, atol=1e-07)
def max_omega_func(X, b):
return regularizer.max_Omega(X, b)[0]
def max_omega_grad(X, b):
return regularizer.max_Omega(X, b)[1]
semi_dual_grad_err = check_grad(max_omega_func, max_omega_grad, X, b)
np.testing.assert_allclose(semi_dual_grad_err, 0.0, atol=1e-07)
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