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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.backend import tf
from ot.lp import wasserstein_1d
from scipy.stats import wasserstein_distance
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(0.0, 1.0, n)
w_u = w_u / w_u.sum()
w_v = rng.uniform(0.0, 1.0, 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))
# check that an error is raised if the metric is not a Minkowski one
np.testing.assert_raises(ValueError, ot.emd_1d, u, v, w_u, w_v, metric="cosine")
np.testing.assert_raises(ValueError, ot.emd2_1d, u, v, w_u, w_v, metric="cosine")
def test_wasserstein_1d(nx):
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, rho_ub, rho_vb = nx.from_numpy(x, rho_u, 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), 1.0)
# 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, rho_ub, rho_vb = nx.from_numpy(x, rho_u, rho_v, type_as=tp)
res = wasserstein_1d(xb, xb, rho_ub, rho_vb, p=1)
nx.assert_same_dtype_device(xb, res)
@pytest.mark.skipif(not tf, reason="tf not installed")
def test_wasserstein_1d_device_tf():
nx = ot.backend.TensorflowBackend()
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()
# Check that everything stays on the CPU
with tf.device("/CPU:0"):
xb, rho_ub, rho_vb = nx.from_numpy(x, rho_u, rho_v)
res = wasserstein_1d(xb, xb, rho_ub, rho_vb, p=1)
nx.assert_same_dtype_device(xb, res)
if len(tf.config.list_physical_devices("GPU")) > 0:
# Check that everything happens on the GPU
xb, rho_ub, rho_vb = nx.from_numpy(x, rho_u, rho_v)
res = wasserstein_1d(xb, xb, rho_ub, rho_vb, p=1)
nx.assert_same_dtype_device(xb, res)
assert nx.dtype_device(res)[1].startswith("GPU")
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 = rng.randn(n, 2)
v = rng.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, rho_ub, rho_vb = nx.from_numpy(x, rho_u, 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)
@pytest.mark.skipif(not tf, reason="tf not installed")
def test_emd1d_device_tf():
nx = ot.backend.TensorflowBackend()
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()
# Check that everything stays on the CPU
with tf.device("/CPU:0"):
xb, rho_ub, rho_vb = nx.from_numpy(x, rho_u, rho_v)
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)
if len(tf.config.list_physical_devices("GPU")) > 0:
# Check that everything happens on the GPU
xb, rho_ub, rho_vb = nx.from_numpy(x, rho_u, rho_v)
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)
assert nx.dtype_device(emd)[1].startswith("GPU")
def test_wasserstein_1d_circle():
# test binary_search_circle and wasserstein_circle give similar results as emd
n = 20
m = 30
rng = np.random.RandomState(0)
u = rng.rand(
n,
)
v = rng.rand(
m,
)
w_u = rng.uniform(0.0, 1.0, n)
w_u = w_u / w_u.sum()
w_v = rng.uniform(0.0, 1.0, m)
w_v = w_v / w_v.sum()
M1 = np.minimum(np.abs(u[:, None] - v[None]), 1 - np.abs(u[:, None] - v[None]))
wass1 = ot.emd2(w_u, w_v, M1)
wass1_bsc = ot.binary_search_circle(u, v, w_u, w_v, p=1)
w1_circle = ot.wasserstein_circle(u, v, w_u, w_v, p=1)
M2 = M1**2
wass2 = ot.emd2(w_u, w_v, M2)
wass2_bsc = ot.binary_search_circle(u, v, w_u, w_v, p=2)
w2_circle = ot.wasserstein_circle(u, v, w_u, w_v, p=2)
# check loss is similar
np.testing.assert_allclose(wass1, wass1_bsc)
np.testing.assert_allclose(wass1, w1_circle, rtol=1e-2)
np.testing.assert_allclose(wass2, wass2_bsc)
np.testing.assert_allclose(wass2, w2_circle)
@pytest.skip_backend("tf")
def test_wasserstein1d_circle_devices(nx):
rng = np.random.RandomState(0)
n = 10
x = np.linspace(0, 1, 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, rho_ub, rho_vb = nx.from_numpy(x, rho_u, rho_v, type_as=tp)
w1 = ot.wasserstein_circle(xb, xb, rho_ub, rho_vb, p=1)
w2_bsc = ot.wasserstein_circle(xb, xb, rho_ub, rho_vb, p=2)
nx.assert_same_dtype_device(xb, w1)
nx.assert_same_dtype_device(xb, w2_bsc)
def test_wasserstein_1d_unif_circle():
# test semidiscrete_wasserstein2_unif_circle versus wasserstein_circle
n = 20
m = 1000
rng = np.random.RandomState(0)
u = rng.rand(
n,
)
v = rng.rand(
m,
)
# w_u = rng.uniform(0., 1., n)
# w_u = w_u / w_u.sum()
w_u = ot.utils.unif(n)
w_v = ot.utils.unif(m)
M1 = np.minimum(np.abs(u[:, None] - v[None]), 1 - np.abs(u[:, None] - v[None]))
wass2 = ot.emd2(w_u, w_v, M1**2)
wass2_circle = ot.wasserstein_circle(u, v, w_u, w_v, p=2, eps=1e-15)
wass2_unif_circle = ot.semidiscrete_wasserstein2_unif_circle(u, w_u)
# check loss is similar
np.testing.assert_allclose(wass2, wass2_unif_circle, atol=1e-2)
np.testing.assert_allclose(wass2_circle, wass2_unif_circle, atol=1e-2)
def test_wasserstein1d_unif_circle_devices(nx):
rng = np.random.RandomState(0)
n = 10
x = np.linspace(0, 1, n)
rho_u = np.abs(rng.randn(n))
rho_u /= rho_u.sum()
for tp in nx.__type_list__:
print(nx.dtype_device(tp))
xb, rho_ub = nx.from_numpy(x, rho_u, type_as=tp)
w2 = ot.semidiscrete_wasserstein2_unif_circle(xb, rho_ub)
nx.assert_same_dtype_device(xb, w2)
def test_binary_search_circle_log():
n = 20
m = 30
rng = np.random.RandomState(0)
u = rng.rand(
n,
)
v = rng.rand(
m,
)
wass2_bsc, log = ot.binary_search_circle(u, v, p=2, log=True)
optimal_thetas = log["optimal_theta"]
assert optimal_thetas.shape[0] == 1
def test_wasserstein_circle_bad_shape():
n = 20
m = 30
rng = np.random.RandomState(0)
u = rng.rand(n, 2)
v = rng.rand(m, 1)
with pytest.raises(ValueError):
_ = ot.wasserstein_circle(u, v, p=2)
with pytest.raises(ValueError):
_ = ot.wasserstein_circle(u, v, p=1)
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