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"""Tests for gromov._partial.py"""
# Author:
# Laetitia Chapel <laetitia.chapel@irisa.fr>
# Cédric Vincent-Cuat <cedvincentcuaz@gmail.com>
#
# License: MIT License
import numpy as np
import scipy as sp
import ot
import pytest
def test_raise_errors():
n_samples = 20 # nb samples (gaussian)
n_noise = 20 # nb of samples (noise)
mu = np.array([0, 0])
cov = np.array([[1, 0], [0, 2]])
rng = np.random.RandomState(42)
xs = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov, random_state=rng)
xs = np.append(xs, (rng.rand(n_noise, 2) + 1) * 4).reshape((-1, 2))
xt = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov, random_state=rng)
xt = np.append(xt, (rng.rand(n_noise, 2) + 1) * -3).reshape((-1, 2))
M = ot.dist(xs, xt)
p = ot.unif(n_samples + n_noise)
q = ot.unif(n_samples + n_noise)
with pytest.raises(ValueError):
ot.gromov.partial_gromov_wasserstein(M, M, p, q, m=2, log=True)
with pytest.raises(ValueError):
ot.gromov.partial_gromov_wasserstein(M, M, p, q, m=-1, log=True)
with pytest.raises(ValueError):
ot.gromov.entropic_partial_gromov_wasserstein(M, M, p, q, reg=1, m=2, log=True)
with pytest.raises(ValueError):
ot.gromov.entropic_partial_gromov_wasserstein(M, M, p, q, reg=1, m=-1, log=True)
def test_partial_gromov_wasserstein(nx):
rng = np.random.RandomState(42)
n_samples = 20 # nb samples
n_noise = 10 # nb of samples (noise)
p = ot.unif(n_samples + n_noise)
psub = ot.unif(n_samples - 5 + n_noise)
q = ot.unif(n_samples + n_noise)
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
mu_t = np.array([0, 0, 0])
cov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
# clean samples
xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s, random_state=rng)
P = sp.linalg.sqrtm(cov_t)
xt = rng.randn(n_samples, 3).dot(P) + mu_t
# add noise
xs = np.concatenate((xs, ((rng.rand(n_noise, 2) + 1) * 4)), axis=0)
xt = np.concatenate((xt, ((rng.rand(n_noise, 3) + 1) * 10)), axis=0)
xt2 = xs[::-1].copy()
C1 = ot.dist(xs, xs)
C1sub = ot.dist(xs[5:], xs[5:])
C2 = ot.dist(xt, xt)
C3 = ot.dist(xt2, xt2)
m = 2.0 / 3.0
C1b, C1subb, C2b, C3b, pb, psubb, qb = nx.from_numpy(C1, C1sub, C2, C3, p, psub, q)
G0 = (
np.outer(p, q) * m / (np.sum(p) * np.sum(q))
) # make sure |G0|=m, G01_m\leq p, G0.T1_n\leq q.
G0b = nx.from_numpy(G0)
# check consistency across backends and stability w.r.t loss/marginals/sym
list_sym = [True, None]
for i, loss_fun in enumerate(["square_loss", "kl_loss"]):
res, log = ot.gromov.partial_gromov_wasserstein(
C1,
C3,
p=p,
q=None,
m=m,
loss_fun=loss_fun,
n_dummies=1,
G0=G0,
log=True,
symmetric=list_sym[i],
warn=True,
verbose=True,
)
resb, logb = ot.gromov.partial_gromov_wasserstein(
C1b,
C3b,
p=None,
q=qb,
m=m,
loss_fun=loss_fun,
n_dummies=1,
G0=G0b,
log=True,
symmetric=False,
warn=True,
verbose=True,
)
resb_ = nx.to_numpy(resb)
assert np.all(res.sum(1) <= p) # cf convergence wasserstein
assert np.all(res.sum(0) <= q) # cf convergence wasserstein
try:
# precision error while doubling numbers of computations with symmetric=False
# some instability can occur with kl. to investigate further.
# changing log offset in _transform_matrix was a way to solve it
# but it also negatively affects some other solvers in the API
np.testing.assert_allclose(res, resb_, rtol=1e-4)
except AssertionError:
pass
# tests with different number of samples across spaces
m = 2.0 / 3.0
res, log = ot.gromov.partial_gromov_wasserstein(
C1, C1sub, p=p, q=psub, m=m, log=True
)
resb, logb = ot.gromov.partial_gromov_wasserstein(
C1b, C1subb, p=pb, q=psubb, m=m, log=True
)
resb_ = nx.to_numpy(resb)
np.testing.assert_allclose(res, resb_, rtol=1e-4)
assert np.all(res.sum(1) <= p) # cf convergence wasserstein
assert np.all(res.sum(0) <= psub) # cf convergence wasserstein
np.testing.assert_allclose(np.sum(res), m, atol=1e-15)
# Edge cases - tests with m=1 set by default (coincide with gw)
m = 1
res0 = ot.gromov.partial_gromov_wasserstein(C1, C2, p, q, m=m, log=False)
res0b, log0b = ot.gromov.partial_gromov_wasserstein(
C1b, C2b, pb, qb, m=None, log=True
)
G = ot.gromov.gromov_wasserstein(C1, C2, p, q, "square_loss")
np.testing.assert_allclose(G, res0, rtol=1e-4)
np.testing.assert_allclose(res0b, res0, rtol=1e-4)
# tests for pGW2
for loss_fun in ["square_loss", "kl_loss"]:
w0, log0 = ot.gromov.partial_gromov_wasserstein2(
C1, C2, p=None, q=q, m=m, loss_fun=loss_fun, log=True
)
w0_val = ot.gromov.partial_gromov_wasserstein2(
C1b, C2b, p=pb, q=None, m=m, loss_fun=loss_fun, log=False
)
np.testing.assert_allclose(w0, w0_val, rtol=1e-4)
# tests integers
C1_int = C1.astype(int)
C1b_int = nx.from_numpy(C1_int)
C2_int = C2.astype(int)
C2b_int = nx.from_numpy(C2_int)
res0b, log0b = ot.gromov.partial_gromov_wasserstein(
C1b_int, C2b_int, pb, qb, m=m, log=True
)
assert nx.to_numpy(res0b).dtype == C1_int.dtype
def test_partial_partial_gromov_linesearch(nx):
rng = np.random.RandomState(42)
n_samples = 20 # nb samples
n_noise = 10 # nb of samples (noise)
p = ot.unif(n_samples + n_noise)
q = ot.unif(n_samples + n_noise)
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
mu_t = np.array([0, 0, 0])
cov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s, random_state=rng)
xs = np.concatenate((xs, ((rng.rand(n_noise, 2) + 1) * 4)), axis=0)
P = sp.linalg.sqrtm(cov_t)
xt = rng.randn(n_samples, 3).dot(P) + mu_t
xt = np.concatenate((xt, ((rng.rand(n_noise, 3) + 1) * 10)), axis=0)
xt2 = xs[::-1].copy()
C1 = ot.dist(xs, xs)
C2 = ot.dist(xt, xt)
C3 = ot.dist(xt2, xt2)
m = 2.0 / 3.0
C1b, C2b, C3b, pb, qb = nx.from_numpy(C1, C2, C3, p, q)
G0 = (
np.outer(p, q) * m / (np.sum(p) * np.sum(q))
) # make sure |G0|=m, G01_m\leq p, G0.T1_n\leq q.
G0b = nx.from_numpy(G0)
# computing necessary inputs to the line-search
Gb, _ = ot.gromov.partial_gromov_wasserstein(C1b, C2b, pb, qb, m=m, log=True)
deltaGb = Gb - G0b
fC1, fC2, hC1, hC2 = ot.gromov._utils._transform_matrix(C1b, C2b, "square_loss")
fC2t = fC2.T
ones_p = nx.ones(p.shape[0], type_as=pb)
ones_q = nx.ones(p.shape[0], type_as=pb)
constC1 = nx.outer(nx.dot(fC1, pb), ones_q)
constC2 = nx.outer(ones_p, nx.dot(qb, fC2t))
cost_G0b = ot.gromov.gwloss(constC1 + constC2, hC1, hC2, G0b)
df_G0b = ot.gromov.gwggrad(constC1 + constC2, hC1, hC2, G0b)
df_Gb = ot.gromov.gwggrad(constC1 + constC2, hC1, hC2, Gb)
# perform line-search
alpha, _, cost_Gb, _ = ot.gromov.solve_partial_gromov_linesearch(
G0b, deltaGb, cost_G0b, df_G0b, df_Gb, 0.0, 1.0, alpha_min=0.0, alpha_max=1.0
)
np.testing.assert_allclose(alpha, 1.0, rtol=1e-4)
@pytest.skip_backend("jax", reason="test very slow with jax backend")
@pytest.skip_backend("tf", reason="test very slow with tf backend")
def test_entropic_partial_gromov_wasserstein(nx):
rng = np.random.RandomState(42)
n_samples = 20 # nb samples
n_noise = 10 # nb of samples (noise)
p = ot.unif(n_samples + n_noise)
psub = ot.unif(n_samples - 5 + n_noise)
q = ot.unif(n_samples + n_noise)
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
mu_t = np.array([0, 0, 0])
cov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
# clean samples
xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s, random_state=rng)
P = sp.linalg.sqrtm(cov_t)
xt = rng.randn(n_samples, 3).dot(P) + mu_t
# add noise
xs = np.concatenate((xs, ((rng.rand(n_noise, 2) + 1) * 4)), axis=0)
xt = np.concatenate((xt, ((rng.rand(n_noise, 3) + 1) * 10)), axis=0)
xt2 = xs[::-1].copy()
C1 = ot.dist(xs, xs)
C1sub = ot.dist(xs[5:], xs[5:])
C2 = ot.dist(xt, xt)
C3 = ot.dist(xt2, xt2)
m = 2.0 / 3.0
C1b, C1subb, C2b, C3b, pb, psubb, qb = nx.from_numpy(C1, C1sub, C2, C3, p, psub, q)
G0 = (
np.outer(p, q) * m / (np.sum(p) * np.sum(q))
) # make sure |G0|=m, G01_m\leq p, G0.T1_n\leq q.
G0b = nx.from_numpy(G0)
# check consistency across backends and stability w.r.t loss/marginals/sym
list_sym = [True, None]
for i, loss_fun in enumerate(["square_loss", "kl_loss"]):
res, log = ot.gromov.entropic_partial_gromov_wasserstein(
C1,
C3,
p=p,
q=None,
reg=1e4,
m=m,
loss_fun=loss_fun,
G0=None,
log=True,
symmetric=list_sym[i],
verbose=True,
)
resb, logb = ot.gromov.entropic_partial_gromov_wasserstein(
C1b,
C3b,
p=None,
q=qb,
reg=1e4,
m=m,
loss_fun=loss_fun,
G0=G0b,
log=True,
symmetric=False,
verbose=True,
)
resb_ = nx.to_numpy(resb)
try: # some instability can occur with kl. to investigate further.
np.testing.assert_allclose(res, resb_, rtol=1e-4)
except AssertionError:
pass
assert np.all(res.sum(1) <= p) # cf convergence wasserstein
assert np.all(res.sum(0) <= q) # cf convergence wasserstein
# tests with m is None
res = ot.gromov.entropic_partial_gromov_wasserstein(
C1,
C3,
p=p,
q=None,
reg=1e4,
G0=None,
log=False,
symmetric=list_sym[i],
verbose=True,
)
resb = ot.gromov.entropic_partial_gromov_wasserstein(
C1b,
C3b,
p=None,
q=qb,
reg=1e4,
G0=None,
log=False,
symmetric=False,
verbose=True,
)
resb_ = nx.to_numpy(resb)
np.testing.assert_allclose(res, resb_, rtol=1e-4)
np.testing.assert_allclose(np.sum(res), 1.0, rtol=1e-4)
# tests with different number of samples across spaces
m = 0.5
res, log = ot.gromov.entropic_partial_gromov_wasserstein(
C1, C1sub, p=p, q=psub, reg=1e4, m=m, log=True
)
resb, logb = ot.gromov.entropic_partial_gromov_wasserstein(
C1b, C1subb, p=pb, q=psubb, reg=1e4, m=m, log=True
)
resb_ = nx.to_numpy(resb)
np.testing.assert_allclose(res, resb_, rtol=1e-4)
assert np.all(res.sum(1) <= p) # cf convergence wasserstein
assert np.all(res.sum(0) <= psub) # cf convergence wasserstein
np.testing.assert_allclose(np.sum(res), m, rtol=1e-4)
# tests for pGW2
for loss_fun in ["square_loss", "kl_loss"]:
w0, log0 = ot.gromov.entropic_partial_gromov_wasserstein2(
C1, C2, p=None, q=q, reg=1e4, m=m, loss_fun=loss_fun, log=True
)
w0_val = ot.gromov.entropic_partial_gromov_wasserstein2(
C1b, C2b, p=pb, q=None, reg=1e4, m=m, loss_fun=loss_fun, log=False
)
np.testing.assert_allclose(w0, w0_val, rtol=1e-8)
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