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"""Tests for module 1d Wasserstein solver"""
# Author: Adrien Corenflos <adrien.corenflos@aalto.fi>
# Nicolas Courty <ncourty@irisa.fr>
#
# License: MIT License
import numpy as np
import pytest
import ot
from ot.lp import wasserstein_1d
from ot.backend import get_backend_list
from scipy.stats import wasserstein_distance
backend_list = get_backend_list()
def test_emd_1d_emd2_1d_with_weights():
# test emd1d gives similar results as emd
n = 20
m = 30
rng = np.random.RandomState(0)
u = rng.randn(n, 1)
v = rng.randn(m, 1)
w_u = rng.uniform(0., 1., n)
w_u = w_u / w_u.sum()
w_v = rng.uniform(0., 1., m)
w_v = w_v / w_v.sum()
M = ot.dist(u, v, metric='sqeuclidean')
G, log = ot.emd(w_u, w_v, M, log=True)
wass = log["cost"]
G_1d, log = ot.emd_1d(u, v, w_u, w_v, metric='sqeuclidean', log=True)
wass1d = log["cost"]
wass1d_emd2 = ot.emd2_1d(u, v, w_u, w_v, metric='sqeuclidean', log=False)
wass1d_euc = ot.emd2_1d(u, v, w_u, w_v, metric='euclidean', log=False)
# check loss is similar
np.testing.assert_allclose(wass, wass1d)
np.testing.assert_allclose(wass, wass1d_emd2)
# check loss is similar to scipy's implementation for Euclidean metric
wass_sp = wasserstein_distance(u.reshape((-1,)), v.reshape((-1,)), w_u, w_v)
np.testing.assert_allclose(wass_sp, wass1d_euc)
# check constraints
np.testing.assert_allclose(w_u, G.sum(1))
np.testing.assert_allclose(w_v, G.sum(0))
@pytest.mark.parametrize('nx', backend_list)
def test_wasserstein_1d(nx):
from scipy.stats import wasserstein_distance
rng = np.random.RandomState(0)
n = 100
x = np.linspace(0, 5, n)
rho_u = np.abs(rng.randn(n))
rho_u /= rho_u.sum()
rho_v = np.abs(rng.randn(n))
rho_v /= rho_v.sum()
xb = nx.from_numpy(x)
rho_ub = nx.from_numpy(rho_u)
rho_vb = nx.from_numpy(rho_v)
# test 1 : wasserstein_1d should be close to scipy W_1 implementation
np.testing.assert_almost_equal(wasserstein_1d(xb, xb, rho_ub, rho_vb, p=1),
wasserstein_distance(x, x, rho_u, rho_v))
# test 2 : wasserstein_1d should be close to one when only translating the support
np.testing.assert_almost_equal(wasserstein_1d(xb, xb + 1, p=2),
1.)
# test 3 : arrays test
X = np.stack((np.linspace(0, 5, n), np.linspace(0, 5, n) * 10), -1)
Xb = nx.from_numpy(X)
res = wasserstein_1d(Xb, Xb, rho_ub, rho_vb, p=2)
np.testing.assert_almost_equal(100 * res[0], res[1], decimal=4)
def test_wasserstein_1d_type_devices(nx):
rng = np.random.RandomState(0)
n = 10
x = np.linspace(0, 5, n)
rho_u = np.abs(rng.randn(n))
rho_u /= rho_u.sum()
rho_v = np.abs(rng.randn(n))
rho_v /= rho_v.sum()
for tp in nx.__type_list__:
print(nx.dtype_device(tp))
xb = nx.from_numpy(x, type_as=tp)
rho_ub = nx.from_numpy(rho_u, type_as=tp)
rho_vb = nx.from_numpy(rho_v, type_as=tp)
res = wasserstein_1d(xb, xb, rho_ub, rho_vb, p=1)
nx.assert_same_dtype_device(xb, res)
def test_emd_1d_emd2_1d():
# test emd1d gives similar results as emd
n = 20
m = 30
rng = np.random.RandomState(0)
u = rng.randn(n, 1)
v = rng.randn(m, 1)
M = ot.dist(u, v, metric='sqeuclidean')
G, log = ot.emd([], [], M, log=True)
wass = log["cost"]
G_1d, log = ot.emd_1d(u, v, [], [], metric='sqeuclidean', log=True)
wass1d = log["cost"]
wass1d_emd2 = ot.emd2_1d(u, v, [], [], metric='sqeuclidean', log=False)
wass1d_euc = ot.emd2_1d(u, v, [], [], metric='euclidean', log=False)
# check loss is similar
np.testing.assert_allclose(wass, wass1d)
np.testing.assert_allclose(wass, wass1d_emd2)
# check loss is similar to scipy's implementation for Euclidean metric
wass_sp = wasserstein_distance(u.reshape((-1,)), v.reshape((-1,)))
np.testing.assert_allclose(wass_sp, wass1d_euc)
# check constraints
np.testing.assert_allclose(np.ones((n,)) / n, G.sum(1))
np.testing.assert_allclose(np.ones((m,)) / m, G.sum(0))
# check G is similar
np.testing.assert_allclose(G, G_1d, atol=1e-15)
# check AssertionError is raised if called on non 1d arrays
u = np.random.randn(n, 2)
v = np.random.randn(m, 2)
with pytest.raises(AssertionError):
ot.emd_1d(u, v, [], [])
def test_emd1d_type_devices(nx):
rng = np.random.RandomState(0)
n = 10
x = np.linspace(0, 5, n)
rho_u = np.abs(rng.randn(n))
rho_u /= rho_u.sum()
rho_v = np.abs(rng.randn(n))
rho_v /= rho_v.sum()
for tp in nx.__type_list__:
print(nx.dtype_device(tp))
xb = nx.from_numpy(x, type_as=tp)
rho_ub = nx.from_numpy(rho_u, type_as=tp)
rho_vb = nx.from_numpy(rho_v, type_as=tp)
emd = ot.emd_1d(xb, xb, rho_ub, rho_vb)
emd2 = ot.emd2_1d(xb, xb, rho_ub, rho_vb)
nx.assert_same_dtype_device(xb, emd)
nx.assert_same_dtype_device(xb, emd2)
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