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test_bregman.py
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"""Tests for module bregman on OT with bregman projections """
# Author: Remi Flamary <[email protected]>
# Kilian Fatras <[email protected]>
# Quang Huy Tran <[email protected]>
# Eduardo Fernandes Montesuma <[email protected]>
#
# License: MIT License
import warnings
from itertools import product
import numpy as np
import pytest
import ot
from ot.backend import tf, torch
@pytest.mark.parametrize("verbose, warn", product([True, False], [True, False]))
def test_sinkhorn(verbose, warn):
# test sinkhorn
n = 100
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G = ot.sinkhorn(u, u, M, 1, stopThr=1e-10, verbose=verbose, warn=warn)
# 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
with pytest.warns(UserWarning):
ot.sinkhorn(u, u, M, 1, stopThr=0, numItermax=1)
@pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_stabilized",
"sinkhorn_epsilon_scaling",
"greenkhorn",
"sinkhorn_log"])
def test_convergence_warning(method):
# test sinkhorn
n = 100
a1 = ot.datasets.make_1D_gauss(n, m=30, s=10)
a2 = ot.datasets.make_1D_gauss(n, m=40, s=10)
A = np.asarray([a1, a2]).T
M = ot.utils.dist0(n)
with pytest.warns(UserWarning):
ot.sinkhorn(a1, a2, M, 1., method=method, stopThr=0, numItermax=1)
if method in ["sinkhorn", "sinkhorn_stabilized", "sinkhorn_log"]:
with pytest.warns(UserWarning):
ot.barycenter(A, M, 1, method=method, stopThr=0, numItermax=1)
with pytest.warns(UserWarning):
ot.sinkhorn2(a1, a2, M, 1, method=method,
stopThr=0, numItermax=1, warn=True)
with warnings.catch_warnings():
warnings.simplefilter("error")
ot.sinkhorn2(a1, a2, M, 1, method=method,
stopThr=0, numItermax=1, warn=False)
def test_not_implemented_method():
# test sinkhorn
w = 10
n = w ** 2
rng = np.random.RandomState(42)
A_img = rng.rand(2, w, w)
A_flat = A_img.reshape(n, 2)
a1, a2 = A_flat.T
M_flat = ot.utils.dist0(n)
not_implemented = "new_method"
reg = 0.01
with pytest.raises(ValueError):
ot.sinkhorn(a1, a2, M_flat, reg, method=not_implemented)
with pytest.raises(ValueError):
ot.sinkhorn2(a1, a2, M_flat, reg, method=not_implemented)
with pytest.raises(ValueError):
ot.barycenter(A_flat, M_flat, reg, method=not_implemented)
with pytest.raises(ValueError):
ot.bregman.barycenter_debiased(A_flat, M_flat, reg,
method=not_implemented)
with pytest.raises(ValueError):
ot.bregman.convolutional_barycenter2d(A_img, reg,
method=not_implemented)
with pytest.raises(ValueError):
ot.bregman.convolutional_barycenter2d_debiased(A_img, reg,
method=not_implemented)
@pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_stabilized"])
def test_nan_warning(method):
# test sinkhorn
n = 100
a1 = ot.datasets.make_1D_gauss(n, m=30, s=10)
a2 = ot.datasets.make_1D_gauss(n, m=40, s=10)
M = ot.utils.dist0(n)
reg = 0
with pytest.warns(UserWarning):
# warn set to False to avoid catching a convergence warning instead
ot.sinkhorn(a1, a2, M, reg, method=method, warn=False)
def test_sinkhorn_stabilization():
# test sinkhorn
n = 100
a1 = ot.datasets.make_1D_gauss(n, m=30, s=10)
a2 = ot.datasets.make_1D_gauss(n, m=40, s=10)
M = ot.utils.dist0(n)
reg = 1e-5
loss1 = ot.sinkhorn2(a1, a2, M, reg, method="sinkhorn_log")
loss2 = ot.sinkhorn2(a1, a2, M, reg, tau=1, method="sinkhorn_stabilized")
np.testing.assert_allclose(
loss1, loss2, atol=1e-06) # cf convergence sinkhorn
@pytest.mark.parametrize("method, verbose, warn",
product(["sinkhorn", "sinkhorn_stabilized",
"sinkhorn_log"],
[True, False], [True, False]))
def test_sinkhorn_multi_b(method, verbose, warn):
# test sinkhorn
n = 10
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
b = rng.rand(n, 3)
b = b / np.sum(b, 0, keepdims=True)
M = ot.dist(x, x)
loss0, log = ot.sinkhorn(u, b, M, .1, method=method, stopThr=1e-10,
log=True)
loss = [ot.sinkhorn2(u, b[:, k], M, .1, method=method, stopThr=1e-10,
verbose=verbose, warn=warn) for k in range(3)]
# check constraints
np.testing.assert_allclose(
loss0, loss, atol=1e-4) # cf convergence sinkhorn
def test_sinkhorn_backends(nx):
n_samples = 100
n_features = 2
rng = np.random.RandomState(0)
x = rng.randn(n_samples, n_features)
y = rng.randn(n_samples, n_features)
a = ot.utils.unif(n_samples)
M = ot.dist(x, y)
G = ot.sinkhorn(a, a, M, 1)
ab, M_nx = nx.from_numpy(a, M)
Gb = ot.sinkhorn(ab, ab, M_nx, 1)
np.allclose(G, nx.to_numpy(Gb))
def test_sinkhorn2_backends(nx):
n_samples = 100
n_features = 2
rng = np.random.RandomState(0)
x = rng.randn(n_samples, n_features)
y = rng.randn(n_samples, n_features)
a = ot.utils.unif(n_samples)
M = ot.dist(x, y)
G = ot.sinkhorn(a, a, M, 1)
ab, M_nx = nx.from_numpy(a, M)
Gb = ot.sinkhorn2(ab, ab, M_nx, 1)
np.allclose(G, nx.to_numpy(Gb))
def test_sinkhorn2_gradients():
n_samples = 100
n_features = 2
rng = np.random.RandomState(0)
x = rng.randn(n_samples, n_features)
y = rng.randn(n_samples, n_features)
a = ot.utils.unif(n_samples)
M = ot.dist(x, y)
if torch:
a1 = torch.tensor(a, requires_grad=True)
b1 = torch.tensor(a, requires_grad=True)
M1 = torch.tensor(M, requires_grad=True)
val = ot.sinkhorn2(a1, b1, M1, 1)
val.backward()
assert a1.shape == a1.grad.shape
assert b1.shape == b1.grad.shape
assert M1.shape == M1.grad.shape
def test_sinkhorn_empty():
# test sinkhorn
n = 100
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G, log = ot.sinkhorn([], [], M, 1, stopThr=1e-10, method="sinkhorn_log",
verbose=True, log=True)
# check constraints
np.testing.assert_allclose(u, G.sum(1), atol=1e-05)
np.testing.assert_allclose(u, G.sum(0), atol=1e-05)
G, log = ot.sinkhorn([], [], M, 1, stopThr=1e-10, verbose=True, log=True)
# check constraints
np.testing.assert_allclose(u, G.sum(1), atol=1e-05)
np.testing.assert_allclose(u, G.sum(0), atol=1e-05)
G, log = ot.sinkhorn([], [], M, 1, stopThr=1e-10,
method='sinkhorn_stabilized', verbose=True, log=True)
# check constraints
np.testing.assert_allclose(u, G.sum(1), atol=1e-05)
np.testing.assert_allclose(u, G.sum(0), atol=1e-05)
G, log = ot.sinkhorn(
[], [], M, 1, stopThr=1e-10, method='sinkhorn_epsilon_scaling',
verbose=True, log=True)
# check constraints
np.testing.assert_allclose(u, G.sum(1), atol=1e-05)
np.testing.assert_allclose(u, G.sum(0), atol=1e-05)
# test empty weights greenkhorn
ot.sinkhorn([], [], M, 1, method='greenkhorn', stopThr=1e-10, log=True)
@pytest.skip_backend('tf')
@pytest.skip_backend("jax")
def test_sinkhorn_variants(nx):
# test sinkhorn
n = 100
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
ub, M_nx = nx.from_numpy(u, M)
G = ot.sinkhorn(u, u, M, 1, method='sinkhorn', stopThr=1e-10)
Gl = nx.to_numpy(ot.sinkhorn(
ub, ub, M_nx, 1, method='sinkhorn_log', stopThr=1e-10))
G0 = nx.to_numpy(ot.sinkhorn(
ub, ub, M_nx, 1, method='sinkhorn', stopThr=1e-10))
Gs = nx.to_numpy(ot.sinkhorn(
ub, ub, M_nx, 1, method='sinkhorn_stabilized', stopThr=1e-10))
Ges = nx.to_numpy(ot.sinkhorn(
ub, ub, M_nx, 1, method='sinkhorn_epsilon_scaling', stopThr=1e-10))
G_green = nx.to_numpy(ot.sinkhorn(
ub, ub, M_nx, 1, method='greenkhorn', stopThr=1e-10))
# check values
np.testing.assert_allclose(G, G0, atol=1e-05)
np.testing.assert_allclose(G, Gl, atol=1e-05)
np.testing.assert_allclose(G0, Gs, atol=1e-05)
np.testing.assert_allclose(G0, Ges, atol=1e-05)
np.testing.assert_allclose(G0, G_green, atol=1e-5)
@pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_stabilized",
"sinkhorn_epsilon_scaling",
"greenkhorn",
"sinkhorn_log"])
@pytest.skip_arg(("nx", "method"), ("tf", "sinkhorn_epsilon_scaling"), reason="tf does not support sinkhorn_epsilon_scaling", getter=str)
@pytest.skip_arg(("nx", "method"), ("tf", "greenkhorn"), reason="tf does not support greenkhorn", getter=str)
@pytest.skip_arg(("nx", "method"), ("jax", "sinkhorn_epsilon_scaling"), reason="jax does not support sinkhorn_epsilon_scaling", getter=str)
@pytest.skip_arg(("nx", "method"), ("jax", "greenkhorn"), reason="jax does not support greenkhorn", getter=str)
def test_sinkhorn_variants_dtype_device(nx, method):
n = 100
rng = np.random.RandomState(42)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
for tp in nx.__type_list__:
print(nx.dtype_device(tp))
ub, Mb = nx.from_numpy(u, M, type_as=tp)
Gb = ot.sinkhorn(ub, ub, Mb, 1, method=method, stopThr=1e-10)
nx.assert_same_dtype_device(Mb, Gb)
@pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_stabilized", "sinkhorn_log"])
def test_sinkhorn2_variants_dtype_device(nx, method):
n = 100
rng = np.random.RandomState(42)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
for tp in nx.__type_list__:
print(nx.dtype_device(tp))
ub, Mb = nx.from_numpy(u, M, type_as=tp)
lossb = ot.sinkhorn2(ub, ub, Mb, 1, method=method, stopThr=1e-10)
nx.assert_same_dtype_device(Mb, lossb)
@pytest.mark.skipif(not tf, reason="tf not installed")
@pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_stabilized", "sinkhorn_log"])
def test_sinkhorn2_variants_device_tf(method):
nx = ot.backend.TensorflowBackend()
n = 100
rng = np.random.RandomState(42)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
# Check that everything stays on the CPU
with tf.device("/CPU:0"):
ub, Mb = nx.from_numpy(u, M)
Gb = ot.sinkhorn(ub, ub, Mb, 1, method=method, stopThr=1e-10)
lossb = ot.sinkhorn2(ub, ub, Mb, 1, method=method, stopThr=1e-10)
nx.assert_same_dtype_device(Mb, Gb)
nx.assert_same_dtype_device(Mb, lossb)
# Check that everything happens on the GPU
ub, Mb = nx.from_numpy(u, M)
Gb = ot.sinkhorn(ub, ub, Mb, 1, method=method, stopThr=1e-10)
lossb = ot.sinkhorn2(ub, ub, Mb, 1, method=method, stopThr=1e-10)
nx.assert_same_dtype_device(Mb, Gb)
nx.assert_same_dtype_device(Mb, lossb)
# Check this only if GPU is available
if len(tf.config.list_physical_devices('GPU')) > 0:
assert nx.dtype_device(Gb)[1].startswith("GPU")
@pytest.skip_backend('tf')
@pytest.skip_backend("jax")
def test_sinkhorn_variants_multi_b(nx):
# test sinkhorn
n = 50
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
b = rng.rand(n, 3)
b = b / np.sum(b, 0, keepdims=True)
M = ot.dist(x, x)
ub, bb, M_nx = nx.from_numpy(u, b, M)
G = ot.sinkhorn(u, b, M, 1, method='sinkhorn', stopThr=1e-10)
Gl = nx.to_numpy(ot.sinkhorn(
ub, bb, M_nx, 1, method='sinkhorn_log', stopThr=1e-10))
G0 = nx.to_numpy(ot.sinkhorn(
ub, bb, M_nx, 1, method='sinkhorn', stopThr=1e-10))
Gs = nx.to_numpy(ot.sinkhorn(
ub, bb, M_nx, 1, method='sinkhorn_stabilized', stopThr=1e-10))
# check values
np.testing.assert_allclose(G, G0, atol=1e-05)
np.testing.assert_allclose(G, Gl, atol=1e-05)
np.testing.assert_allclose(G0, Gs, atol=1e-05)
@pytest.skip_backend('tf')
@pytest.skip_backend("jax")
def test_sinkhorn2_variants_multi_b(nx):
# test sinkhorn
n = 50
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
b = rng.rand(n, 3)
b = b / np.sum(b, 0, keepdims=True)
M = ot.dist(x, x)
ub, bb, M_nx = nx.from_numpy(u, b, M)
G = ot.sinkhorn2(u, b, M, 1, method='sinkhorn', stopThr=1e-10)
Gl = nx.to_numpy(ot.sinkhorn2(
ub, bb, M_nx, 1, method='sinkhorn_log', stopThr=1e-10))
G0 = nx.to_numpy(ot.sinkhorn2(
ub, bb, M_nx, 1, method='sinkhorn', stopThr=1e-10))
Gs = nx.to_numpy(ot.sinkhorn2(
ub, bb, M_nx, 1, method='sinkhorn_stabilized', stopThr=1e-10))
# check values
np.testing.assert_allclose(G, G0, atol=1e-05)
np.testing.assert_allclose(G, Gl, atol=1e-05)
np.testing.assert_allclose(G0, Gs, atol=1e-05)
def test_sinkhorn_variants_log():
# test sinkhorn
n = 50
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G0, log0 = ot.sinkhorn(u, u, M, 1, method='sinkhorn',
stopThr=1e-10, log=True)
Gl, logl = ot.sinkhorn(
u, u, M, 1, method='sinkhorn_log', stopThr=1e-10, log=True)
Gs, logs = ot.sinkhorn(
u, u, M, 1, method='sinkhorn_stabilized', stopThr=1e-10, log=True)
Ges, loges = ot.sinkhorn(
u, u, M, 1, method='sinkhorn_epsilon_scaling', stopThr=1e-10, log=True,)
G_green, loggreen = ot.sinkhorn(
u, u, M, 1, method='greenkhorn', stopThr=1e-10, log=True)
# check values
np.testing.assert_allclose(G0, Gs, atol=1e-05)
np.testing.assert_allclose(G0, Gl, atol=1e-05)
np.testing.assert_allclose(G0, Ges, atol=1e-05)
np.testing.assert_allclose(G0, G_green, atol=1e-5)
@pytest.mark.parametrize("verbose, warn", product([True, False], [True, False]))
def test_sinkhorn_variants_log_multib(verbose, warn):
# test sinkhorn
n = 50
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
b = rng.rand(n, 3)
b = b / np.sum(b, 0, keepdims=True)
M = ot.dist(x, x)
G0, log0 = ot.sinkhorn(u, b, M, 1, method='sinkhorn',
stopThr=1e-10, log=True)
Gl, logl = ot.sinkhorn(u, b, M, 1, method='sinkhorn_log', stopThr=1e-10, log=True,
verbose=verbose, warn=warn)
Gs, logs = ot.sinkhorn(u, b, M, 1, method='sinkhorn_stabilized', stopThr=1e-10, log=True,
verbose=verbose, warn=warn)
# check values
np.testing.assert_allclose(G0, Gs, atol=1e-05)
np.testing.assert_allclose(G0, Gl, atol=1e-05)
@pytest.mark.parametrize("method, verbose, warn",
product(["sinkhorn", "sinkhorn_stabilized", "sinkhorn_log"],
[True, False], [True, False]))
def test_barycenter(nx, method, verbose, warn):
n_bins = 100 # nb bins
# Gaussian distributions
a1 = ot.datasets.make_1D_gauss(n_bins, m=30, s=10) # m= mean, s= std
a2 = ot.datasets.make_1D_gauss(n_bins, m=40, s=10)
# creating matrix A containing all distributions
A = np.vstack((a1, a2)).T
# loss matrix + normalization
M = ot.utils.dist0(n_bins)
M /= M.max()
alpha = 0.5 # 0<=alpha<=1
weights = np.array([1 - alpha, alpha])
A_nx, M_nx, weights_nx = nx.from_numpy(A, M, weights)
reg = 1e-2
if nx.__name__ in ("jax", "tf") and method == "sinkhorn_log":
with pytest.raises(NotImplementedError):
ot.bregman.barycenter(A_nx, M_nx, reg, weights, method=method)
else:
# wasserstein
bary_wass_np = ot.bregman.barycenter(
A, M, reg, weights, method=method, verbose=verbose, warn=warn)
bary_wass, _ = ot.bregman.barycenter(
A_nx, M_nx, reg, weights_nx, method=method, log=True)
bary_wass = nx.to_numpy(bary_wass)
np.testing.assert_allclose(1, np.sum(bary_wass))
np.testing.assert_allclose(bary_wass, bary_wass_np)
ot.bregman.barycenter(A_nx, M_nx, reg, log=True)
def test_free_support_sinkhorn_barycenter():
measures_locations = [
np.array([-1.]).reshape((1, 1)), # First dirac support
np.array([1.]).reshape((1, 1)) # Second dirac support
]
measures_weights = [
np.array([1.]), # First dirac sample weights
np.array([1.]) # Second dirac sample weights
]
# Barycenter initialization
X_init = np.array([-12.]).reshape((1, 1))
# Obvious barycenter locations. Take a look on test_ot.py, test_free_support_barycenter
bar_locations = np.array([0.]).reshape((1, 1))
# Calculate free support barycenter w/ Sinkhorn algorithm. We set the entropic regularization
# term to 1, but this should be, in general, fine-tuned to the problem.
X = ot.bregman.free_support_sinkhorn_barycenter(
measures_locations, measures_weights, X_init, reg=1)
# Verifies if calculated barycenter matches ground-truth
np.testing.assert_allclose(X, bar_locations, rtol=1e-5, atol=1e-7)
@pytest.mark.parametrize("method, verbose, warn",
product(["sinkhorn", "sinkhorn_stabilized", "sinkhorn_log"],
[True, False], [True, False]))
def test_barycenter_assymetric_cost(nx, method, verbose, warn):
n_bins = 20 # nb bins
# Gaussian distributions
A = ot.datasets.make_1D_gauss(n_bins, m=30, s=10) # m= mean, s= std
# creating matrix A containing all distributions
A = A[:, None]
# assymetric loss matrix + normalization
rng = np.random.RandomState(42)
M = rng.randn(n_bins, n_bins) ** 2
M /= M.max()
A_nx, M_nx = nx.from_numpy(A, M)
reg = 1e-2
if nx.__name__ in ("jax", "tf") and method == "sinkhorn_log":
with pytest.raises(NotImplementedError):
ot.bregman.barycenter(A_nx, M_nx, reg, method=method)
else:
# wasserstein
bary_wass_np = ot.bregman.barycenter(
A, M, reg, method=method, verbose=verbose, warn=warn)
bary_wass, _ = ot.bregman.barycenter(
A_nx, M_nx, reg, method=method, log=True)
bary_wass = nx.to_numpy(bary_wass)
np.testing.assert_allclose(1, np.sum(bary_wass))
np.testing.assert_allclose(bary_wass, bary_wass_np)
ot.bregman.barycenter(A_nx, M_nx, reg, log=True)
@pytest.mark.parametrize("method, verbose, warn",
product(["sinkhorn", "sinkhorn_log"],
[True, False], [True, False]))
def test_barycenter_debiased(nx, method, verbose, warn):
n_bins = 100 # nb bins
# Gaussian distributions
a1 = ot.datasets.make_1D_gauss(n_bins, m=30, s=10) # m= mean, s= std
a2 = ot.datasets.make_1D_gauss(n_bins, m=40, s=10)
# creating matrix A containing all distributions
A = np.vstack((a1, a2)).T
# loss matrix + normalization
M = ot.utils.dist0(n_bins)
M /= M.max()
alpha = 0.5 # 0<=alpha<=1
weights = np.array([1 - alpha, alpha])
A_nx, M_nx, weights_nx = nx.from_numpy(A, M, weights)
# wasserstein
reg = 1e-2
if nx.__name__ in ("jax", "tf") and method == "sinkhorn_log":
with pytest.raises(NotImplementedError):
ot.bregman.barycenter_debiased(
A_nx, M_nx, reg, weights, method=method)
else:
bary_wass_np = ot.bregman.barycenter_debiased(A, M, reg, weights, method=method,
verbose=verbose, warn=warn)
bary_wass, _ = ot.bregman.barycenter_debiased(
A_nx, M_nx, reg, weights_nx, method=method, log=True)
bary_wass = nx.to_numpy(bary_wass)
np.testing.assert_allclose(1, np.sum(bary_wass), atol=1e-3)
np.testing.assert_allclose(bary_wass, bary_wass_np, atol=1e-5)
ot.bregman.barycenter_debiased(
A_nx, M_nx, reg, log=True, verbose=False)
@pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_log"])
def test_convergence_warning_barycenters(method):
w = 10
n_bins = w ** 2 # nb bins
# Gaussian distributions
a1 = ot.datasets.make_1D_gauss(n_bins, m=30, s=10) # m= mean, s= std
a2 = ot.datasets.make_1D_gauss(n_bins, m=40, s=10)
# creating matrix A containing all distributions
A = np.vstack((a1, a2)).T
A_img = A.reshape(2, w, w)
A_img /= A_img.sum((1, 2))[:, None, None]
# loss matrix + normalization
M = ot.utils.dist0(n_bins)
M /= M.max()
alpha = 0.5 # 0<=alpha<=1
weights = np.array([1 - alpha, alpha])
reg = 0.1
with pytest.warns(UserWarning):
ot.bregman.barycenter_debiased(
A, M, reg, weights, method=method, numItermax=1)
with pytest.warns(UserWarning):
ot.bregman.barycenter(A, M, reg, weights, method=method, numItermax=1)
with pytest.warns(UserWarning):
ot.bregman.convolutional_barycenter2d(A_img, reg, weights,
method=method, numItermax=1)
with pytest.warns(UserWarning):
ot.bregman.convolutional_barycenter2d_debiased(A_img, reg, weights,
method=method, numItermax=1)
def test_barycenter_stabilization(nx):
n_bins = 100 # nb bins
# Gaussian distributions
a1 = ot.datasets.make_1D_gauss(n_bins, m=30, s=10) # m= mean, s= std
a2 = ot.datasets.make_1D_gauss(n_bins, m=40, s=10)
# creating matrix A containing all distributions
A = np.vstack((a1, a2)).T
# loss matrix + normalization
M = ot.utils.dist0(n_bins)
M /= M.max()
alpha = 0.5 # 0<=alpha<=1
weights = np.array([1 - alpha, alpha])
A_nx, M_nx, weights_b = nx.from_numpy(A, M, weights)
# wasserstein
reg = 1e-2
bar_np = ot.bregman.barycenter(
A, M, reg, weights, method="sinkhorn", stopThr=1e-8, verbose=True)
bar_stable = nx.to_numpy(ot.bregman.barycenter(
A_nx, M_nx, reg, weights_b, method="sinkhorn_stabilized",
stopThr=1e-8, verbose=True
))
bar = nx.to_numpy(ot.bregman.barycenter(
A_nx, M_nx, reg, weights_b, method="sinkhorn",
stopThr=1e-8, verbose=True
))
np.testing.assert_allclose(bar, bar_stable)
np.testing.assert_allclose(bar, bar_np)
def create_random_images_dist(seed, size=20):
"""Creates an array of two random images of size (size, size). Returns an array of shape (2, size, size)."""
rng = np.random.RandomState(seed)
# First image
a1 = rng.rand(size, size)
a1 += a1.min()
a1 = a1 / np.sum(a1) # Ensure that it is a probability distribution
# Second image
a2 = rng.rand(size, size)
a2 += a2.min()
a2 = a2 / np.sum(a2)
# Creating matrix A containing all distributions
A = np.zeros((2, size, size))
A[0, :, :] = a1
A[1, :, :] = a2
return A
@pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_log"])
def test_wasserstein_bary_2d(nx, method):
# Create the array of images to test
A = create_random_images_dist(42, size=20)
A_nx = nx.from_numpy(A)
# wasserstein
reg = 1e-2
if nx.__name__ in ("jax", "tf") and method == "sinkhorn_log":
with pytest.raises(NotImplementedError):
ot.bregman.convolutional_barycenter2d(A_nx, reg, method=method)
else:
bary_wass_np, log_np = ot.bregman.convolutional_barycenter2d(
A, reg, method=method, verbose=True, log=True
)
bary_wass = nx.to_numpy(
ot.bregman.convolutional_barycenter2d(A_nx, reg, method=method)
)
np.testing.assert_allclose(1, np.sum(bary_wass), rtol=1e-3)
np.testing.assert_allclose(bary_wass, bary_wass_np, atol=1e-3)
# help in checking if log and verbose do not bug the function
ot.bregman.convolutional_barycenter2d(A, reg, log=True, verbose=True)
@pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_log"])
def test_wasserstein_bary_2d_dtype_device(nx, method):
# Create the array of images to test
A = create_random_images_dist(42, size=20)
for tp in nx.__type_list__:
print(nx.dtype_device(tp))
Ab = nx.from_numpy(A, type_as=tp)
# wasserstein
reg = 1e-2
if nx.__name__ in ("jax", "tf") and method == "sinkhorn_log":
with pytest.raises(NotImplementedError):
ot.bregman.convolutional_barycenter2d(Ab, reg, method=method)
else:
# Compute the barycenter with numpy
bary_wass_np, log_np = ot.bregman.convolutional_barycenter2d(
A, reg, method=method, verbose=True, log=True
)
# Compute the barycenter with the backend
bary_wass_b = ot.bregman.convolutional_barycenter2d(Ab, reg, method=method)
# Convert the backend result to numpy, to compare with the numpy result
bary_wass = nx.to_numpy(bary_wass_b)
np.testing.assert_allclose(1, np.sum(bary_wass), rtol=1e-3)
np.testing.assert_allclose(bary_wass, bary_wass_np, atol=1e-3)
# help in checking if log and verbose do not bug the function
ot.bregman.convolutional_barycenter2d(A, reg, log=True, verbose=True)
# Test that the dtype and device are the same after the computation
nx.assert_same_dtype_device(Ab, bary_wass_b)
@pytest.mark.skipif(not tf, reason="tf not installed")
@pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_log"])
def test_wasserstein_bary_2d_device_tf(method):
# Using the Tensorflow backend
nx = ot.backend.TensorflowBackend()
# Create the array of images to test
A = create_random_images_dist(42, size=20)
# Check that everything stays on the CPU
with tf.device("/CPU:0"):
Ab = nx.from_numpy(A)
# wasserstein
reg = 1e-2
if method == "sinkhorn_log":
with pytest.raises(NotImplementedError):
ot.bregman.convolutional_barycenter2d(Ab, reg, method=method)
else:
# Compute the barycenter with numpy
bary_wass_np, log_np = ot.bregman.convolutional_barycenter2d(
A, reg, method=method, verbose=True, log=True
)
# Compute the barycenter with the backend
bary_wass_b = ot.bregman.convolutional_barycenter2d(Ab, reg, method=method)
# Convert the backend result to numpy, to compare with the numpy result
bary_wass = nx.to_numpy(bary_wass_b)
np.testing.assert_allclose(1, np.sum(bary_wass), rtol=1e-3)
np.testing.assert_allclose(bary_wass, bary_wass_np, atol=1e-3)
# help in checking if log and verbose do not bug the function
ot.bregman.convolutional_barycenter2d(A, reg, log=True, verbose=True)
# Test that the dtype and device are the same after the computation
nx.assert_same_dtype_device(Ab, bary_wass_b)
# Check that everything happens on the GPU
Ab = nx.from_numpy(A)
# wasserstein
reg = 1e-2
if method == "sinkhorn_log":
with pytest.raises(NotImplementedError):
ot.bregman.convolutional_barycenter2d(Ab, reg, method=method)
else:
# Compute the barycenter with numpy
bary_wass_np, log_np = ot.bregman.convolutional_barycenter2d(
A, reg, method=method, verbose=True, log=True
)
# Compute the barycenter with the backend
bary_wass_b = ot.bregman.convolutional_barycenter2d(Ab, reg, method=method)
# Convert the backend result to numpy, to compare with the numpy result
bary_wass = nx.to_numpy(bary_wass_b)
np.testing.assert_allclose(1, np.sum(bary_wass), rtol=1e-3)
np.testing.assert_allclose(bary_wass, bary_wass_np, atol=1e-3)
# help in checking if log and verbose do not bug the function
ot.bregman.convolutional_barycenter2d(A, reg, log=True, verbose=True)
# Test that the dtype and device are the same after the computation
nx.assert_same_dtype_device(Ab, bary_wass_b)
# Check this only if GPU is available
if len(tf.config.list_physical_devices("GPU")) > 0:
assert nx.dtype_device(bary_wass_b)[1].startswith("GPU")
@pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_log"])
def test_wasserstein_bary_2d_debiased(nx, method):
# Create the array of images to test
A = create_random_images_dist(42, size=20)
A_nx = nx.from_numpy(A)
# wasserstein
reg = 1e-2
if nx.__name__ in ("jax", "tf") and method == "sinkhorn_log":
with pytest.raises(NotImplementedError):
ot.bregman.convolutional_barycenter2d_debiased(A_nx, reg, method=method)
else:
bary_wass_np, log_np = ot.bregman.convolutional_barycenter2d_debiased(
A, reg, method=method, verbose=True, log=True
)
bary_wass = nx.to_numpy(
ot.bregman.convolutional_barycenter2d_debiased(A_nx, reg, method=method)
)
np.testing.assert_allclose(1, np.sum(bary_wass), rtol=1e-3)
np.testing.assert_allclose(bary_wass, bary_wass_np, atol=1e-3)
# help in checking if log and verbose do not bug the function
ot.bregman.convolutional_barycenter2d_debiased(A, reg, log=True, verbose=True)
@pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_log"])
def test_wasserstein_bary_2d_debiased_dtype_device(nx, method):
# Create the array of images to test
A = create_random_images_dist(42, size=20)
for tp in nx.__type_list__:
print(nx.dtype_device(tp))
Ab = nx.from_numpy(A, type_as=tp)
# wasserstein
reg = 1e-2
if nx.__name__ in ("jax", "tf") and method == "sinkhorn_log":
with pytest.raises(NotImplementedError):
ot.bregman.convolutional_barycenter2d_debiased(Ab, reg, method=method)
else:
# Compute the barycenter with numpy
bary_wass_np, log_np = ot.bregman.convolutional_barycenter2d_debiased(
A, reg, method=method, verbose=True, log=True
)
# Compute the barycenter with the backend
bary_wass_b = ot.bregman.convolutional_barycenter2d_debiased(
Ab, reg, method=method
)
# Convert the backend result to numpy, to compare with the numpy result
bary_wass = nx.to_numpy(bary_wass_b)
np.testing.assert_allclose(1, np.sum(bary_wass), rtol=1e-3)
np.testing.assert_allclose(bary_wass, bary_wass_np, atol=1e-3)
# help in checking if log and verbose do not bug the function
ot.bregman.convolutional_barycenter2d_debiased(
A, reg, log=True, verbose=True
)
# Test that the dtype and device are the same after the computation
nx.assert_same_dtype_device(Ab, bary_wass_b)
@pytest.mark.skipif(not tf, reason="tf not installed")
@pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_log"])
def test_wasserstein_bary_2d_debiased_device_tf(method):
# Using the Tensorflow backend
nx = ot.backend.TensorflowBackend()
# Create the array of images to test
A = create_random_images_dist(42, size=20)
# Check that everything stays on the CPU
with tf.device("/CPU:0"):
Ab = nx.from_numpy(A)
# wasserstein
reg = 1e-2
if method == "sinkhorn_log":
with pytest.raises(NotImplementedError):
ot.bregman.convolutional_barycenter2d_debiased(Ab, reg, method=method)
else:
# Compute the barycenter with numpy
bary_wass_np, log_np = ot.bregman.convolutional_barycenter2d_debiased(
A, reg, method=method, verbose=True, log=True
)
# Compute the barycenter with the backend
bary_wass_b = ot.bregman.convolutional_barycenter2d_debiased(
Ab, reg, method=method
)
# Convert the backend result to numpy, to compare with the numpy result
bary_wass = nx.to_numpy(bary_wass_b)
np.testing.assert_allclose(1, np.sum(bary_wass), rtol=1e-3)
np.testing.assert_allclose(bary_wass, bary_wass_np, atol=1e-3)
# help in checking if log and verbose do not bug the function
ot.bregman.convolutional_barycenter2d_debiased(
A, reg, log=True, verbose=True
)
# Test that the dtype and device are the same after the computation
nx.assert_same_dtype_device(Ab, bary_wass_b)
# Check that everything happens on the GPU
Ab = nx.from_numpy(A)
# wasserstein
reg = 1e-2
if method == "sinkhorn_log":
with pytest.raises(NotImplementedError):
ot.bregman.convolutional_barycenter2d_debiased(Ab, reg, method=method)
else:
# Compute the barycenter with numpy
bary_wass_np, log_np = ot.bregman.convolutional_barycenter2d_debiased(
A, reg, method=method, verbose=True, log=True
)
# Compute the barycenter with the backend
bary_wass_b = ot.bregman.convolutional_barycenter2d_debiased(
Ab, reg, method=method
)
# Convert the backend result to numpy, to compare with the numpy result
bary_wass = nx.to_numpy(bary_wass_b)
np.testing.assert_allclose(1, np.sum(bary_wass), rtol=1e-3)
def test_unmix(nx):
n_bins = 50 # nb bins
# Gaussian distributions
a1 = ot.datasets.make_1D_gauss(n_bins, m=20, s=10) # m= mean, s= std
a2 = ot.datasets.make_1D_gauss(n_bins, m=40, s=10)
a = ot.datasets.make_1D_gauss(n_bins, m=30, s=10)
# creating matrix A containing all distributions
D = np.vstack((a1, a2)).T
# loss matrix + normalization
M = ot.utils.dist0(n_bins)
M /= M.max()
M0 = ot.utils.dist0(2)
M0 /= M0.max()
h0 = ot.unif(2)
ab, Db, M_nx, M0b, h0b = nx.from_numpy(a, D, M, M0, h0)