def OT_sinkhorn(Xl, Xr, lambd=1e-2):
# loss matrix
C = ot.dist(Xl, Xr) + ll * ot.dist(hl, hr)
M = C / C.max()
n = len(Xl)
m = len(Xr)
print(n, m)
a, b = np.ones((n, )) / n, np.ones((m, )) / m
Gs = ot.sinkhorn(a, b, M, lambd)
plt.figure(5)
plt.imshow(Gs, interpolation='nearest')
plt.title('OT matrix sinkhorn')
plt.figure(6)
ot.plot.plot2D_samples_mat(Xl[:, :2], Xr[:, :2], Gs, color=[.5, .5, 1])
plt.plot(Xl[:, 0], Xl[:, 1], '+b', label='Source samples')
plt.plot(Xr[:, 0], Xr[:, 1], 'xr', label='Target samples')
plt.legend(loc=0)
plt.title('OT matrix Sinkhorn with samples')
return (Gs)
def OT_scores_sinkhorn(Xl, Xr, scoresl, scoresr, mu=0.5, lambd=1e-2):
# loss matrix
C = ot.dist(Xl, Xr) + mu * ot.dist(np.expand_dims(scoresl, axis=1),
np.expand_dims(scoresr, axis=1))
M = C / C.max()
n = len(Xl)
m = len(Xr)
print(n, m)
a, b = scoresl, scoresr
Gs = ot.sinkhorn(a, b, M, lambd)
plt.figure(5)
plt.imshow(Gs, interpolation='nearest')
plt.title('OT matrix sinkhorn')
plt.figure(6)
ot.plot.plot2D_samples_mat(Xl[:, :2], Xr[:, :2], Gs, color=[.5, .5, 1])
plt.plot(Xl[:, 0], Xl[:, 1], '+b', label='Source samples')
plt.plot(Xr[:, 0], Xr[:, 1], 'xr', label='Target samples')
plt.legend(loc=0)
plt.title('OT matrix Sinkhorn with samples')
return (Gs)
def OT_scores_emd(Xl, Xr, scoresl, scoresr, mu=0.5):
# loss matrix
print(scoresl)
C = ot.dist(Xl, Xr) + mu * ot.dist(np.expand_dims(scoresl, axis=1),
np.expand_dims(scoresr, axis=1))
M = C / C.max()
n = len(Xl)
m = len(Xr)
print(n, m)
a, b = scoresl, scoresr
G0 = ot.emd(a, b, M)
plt.figure(3)
plt.imshow(G0, interpolation='nearest')
plt.title('OT matrix G0')
plt.figure(4)
ot.plot.plot2D_samples_mat(Xl[:, :2], Xr[:, :2], G0, c=[.5, .5, 1])
plt.plot(Xl[:, 0], Xl[:, 1], '+b', label='Source samples')
plt.plot(Xr[:, 0], Xr[:, 1], 'xr', label='Target samples')
plt.legend(loc=0)
plt.title('OT matrix with samples')
return (G0)
def get_sim(x, sim, **kwargs):
if sim == 'gauss':
try:
rbfparam = kwargs['rbfparam']
except KeyError:
rbfparam = 1 / (2 * (np.mean(ot.dist(x, x, 'sqeuclidean')) ** 2))
S = rbf_kernel(x, x, rbfparam)
elif sim == 'gaussthr':
try:
rbfparam = kwargs['rbfparam']
except KeyError:
rbfparam = 1 / (2 * (np.mean(ot.dist(x, x, 'sqeuclidean')) ** 2))
try:
thrg = kwargs['thrg']
except KeyError:
thrg = .5
S = np.float64(rbf_kernel(x, x, rbfparam) > thrg)
elif sim == 'knn':
try:
num_neighbors = kwargs['nn']
except KeyError('sim="knn" requires the number of neighbors nn to be set'):
num_neighbors = 3
S = kn_graph(x, num_neighbors).toarray()
S = (S + S.T) / 2
return S
def test_lazy_empirical_sinkhorn():
# test sinkhorn
n = 10
a = ot.unif(n)
b = ot.unif(n)
numIterMax = 1000
X_s = np.reshape(np.arange(n), (n, 1))
X_t = np.reshape(np.arange(0, n), (n, 1))
M = ot.dist(X_s, X_t)
M_m = ot.dist(X_s, X_t, metric='minkowski')
f, g = ot.bregman.empirical_sinkhorn(X_s,
X_t,
1,
numIterMax=numIterMax,
isLazy=True,
batchSize=(1, 3),
verbose=True)
G_sqe = np.exp(f[:, None] + g[None, :] - M / 1)
sinkhorn_sqe = ot.sinkhorn(a, b, M, 1)
f, g, log_es = ot.bregman.empirical_sinkhorn(X_s,
X_t,
0.1,
numIterMax=numIterMax,
isLazy=True,
batchSize=1,
log=True)
G_log = np.exp(f[:, None] + g[None, :] - M / 0.1)
sinkhorn_log, log_s = ot.sinkhorn(a, b, M, 0.1, log=True)
f, g = ot.bregman.empirical_sinkhorn(X_s,
X_t,
1,
metric='minkowski',
numIterMax=numIterMax,
isLazy=True,
batchSize=1)
G_m = np.exp(f[:, None] + g[None, :] - M_m / 1)
sinkhorn_m = ot.sinkhorn(a, b, M_m, 1)
loss_emp_sinkhorn, log = ot.bregman.empirical_sinkhorn2(
X_s, X_t, 1, numIterMax=numIterMax, isLazy=True, batchSize=1, log=True)
loss_sinkhorn = ot.sinkhorn2(a, b, M, 1)
# check constratints
np.testing.assert_allclose(sinkhorn_sqe.sum(1), G_sqe.sum(1),
atol=1e-05) # metric sqeuclidian
np.testing.assert_allclose(sinkhorn_sqe.sum(0), G_sqe.sum(0),
atol=1e-05) # metric sqeuclidian
np.testing.assert_allclose(sinkhorn_log.sum(1), G_log.sum(1),
atol=1e-05) # log
np.testing.assert_allclose(sinkhorn_log.sum(0), G_log.sum(0),
atol=1e-05) # log
np.testing.assert_allclose(sinkhorn_m.sum(1), G_m.sum(1),
atol=1e-05) # metric euclidian
np.testing.assert_allclose(sinkhorn_m.sum(0), G_m.sum(0),
atol=1e-05) # metric euclidian
np.testing.assert_allclose(loss_emp_sinkhorn, loss_sinkhorn, atol=1e-05)
def incremental_bary_map_emd(xs, xt, a, b, m1, m2, k):
'''
Compute the incomplete minibatch barycenter mapping
between a source and a target distributions.
(faster for small batch size)
Parameters
----------
- xs : ndarray(ns, d)
source data
- xt : ndarray(nt, d)
target data
- a : ndarray(ns)
source distribution weights
- b : ndarray(nt)
target distribution weights
- m1 : int
source batch size
- m2 : int
target batch size
- k : int
number of batch couples
Returns
-------
- new_xs : ndarray(ns, d)
Transported source measure
- new_xt : ndarray(nt, d)
Transported target measure
'''
new_xs = np.zeros(xs.shape)
new_xt = np.zeros(xt.shape)
Ns = np.shape(xs)[0]
Nt = np.shape(xt)[0]
if m1 < 101:
for i in range(k):
#Test mini batch
sub_xs, sub_weights_a, id_a = small_mini_batch(xs, a, m1, Ns)
sub_xt, sub_weights_b, id_b = small_mini_batch(xt, b, m2, Nt)
sub_M = ot.dist(sub_xs, sub_xt, "sqeuclidean").copy()
G0 = ot.emd(sub_weights_a, sub_weights_b, sub_M)
new_xs[id_a] += G0.dot(xt[id_b])
new_xt[id_b] += G0.T.dot(xs[id_a])
else:
for i in range(k):
#Test mini batch
sub_xs, sub_weights_a, id_a = mini_batch(xs, a, m1, Ns)
sub_xt, sub_weights_b, id_b = mini_batch(xt, b, m2, Nt)
sub_M = ot.dist(sub_xs, sub_xt, "sqeuclidean").copy()
G0 = ot.emd(sub_weights_a, sub_weights_b, sub_M)
new_xs[id_a] += G0.dot(xt[id_b])
new_xt[id_b] += G0.T.dot(xs[id_a])
return 1. / k * Ns * new_xs, 1. / k * Nt * new_xt
def graph_d(self, graph1, graph2):
""" Compute the Wasserstein distance between two graphs. Uniform weights are used.
Parameters
----------
graph1 : a Graph object
graph2 : a Graph object
Returns
-------
The Wasserstein distance between the features of graph1 and graph2
"""
nodes1 = graph1.nodes()
nodes2 = graph2.nodes()
t1masses = np.ones(len(nodes1)) / len(nodes1)
t2masses = np.ones(len(nodes2)) / len(nodes2)
x1 = self.reshaper(graph1.all_matrix_attr())
x2 = self.reshaper(graph2.all_matrix_attr())
if self.features_metric == 'dirac':
f = lambda x, y: x != y
M = ot.dist(x1, x2, metric=f)
else:
M = ot.dist(x1, x2, metric=self.features_metric)
if np.max(M) != 0:
M = M / np.max(M)
self.M = M
transp = ot.emd(t1masses, t2masses, M)
self.transp = transp
return np.sum(transp * M)
def test_gromov_entropic_barycenter():
ns = 50
nt = 60
Xs, ys = ot.datasets.get_data_classif('3gauss', ns)
Xt, yt = ot.datasets.get_data_classif('3gauss2', nt)
C1 = ot.dist(Xs)
C2 = ot.dist(Xt)
n_samples = 3
Cb = ot.gromov.entropic_gromov_barycenters(
n_samples, [C1, C2], [ot.unif(ns), ot.unif(nt)],
ot.unif(n_samples), [.5, .5],
'square_loss',
1e-3,
max_iter=100,
tol=1e-3)
np.testing.assert_allclose(Cb.shape, (n_samples, n_samples))
Cb2 = ot.gromov.entropic_gromov_barycenters(
n_samples, [C1, C2], [ot.unif(ns), ot.unif(nt)],
ot.unif(n_samples), [.5, .5],
'kl_loss',
1e-3,
max_iter=100,
tol=1e-3)
np.testing.assert_allclose(Cb2.shape, (n_samples, n_samples))
def test_gromov_entropic_barycenter():
ns = 20
nt = 30
Xs, ys = ot.datasets.make_data_classif('3gauss', ns, random_state=42)
Xt, yt = ot.datasets.make_data_classif('3gauss2', nt, random_state=42)
C1 = ot.dist(Xs)
C2 = ot.dist(Xt)
n_samples = 2
Cb = ot.gromov.entropic_gromov_barycenters(
n_samples, [C1, C2], [ot.unif(ns), ot.unif(nt)],
ot.unif(n_samples), [.5, .5],
'square_loss',
1e-3,
max_iter=50,
tol=1e-5,
verbose=True)
np.testing.assert_allclose(Cb.shape, (n_samples, n_samples))
Cb2 = ot.gromov.entropic_gromov_barycenters(
n_samples, [C1, C2], [ot.unif(ns), ot.unif(nt)],
ot.unif(n_samples), [.5, .5],
'kl_loss',
1e-3,
max_iter=100,
tol=1e-3)
np.testing.assert_allclose(Cb2.shape, (n_samples, n_samples))
def test_gromov():
n_samples = 50 # nb samples
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
xs = ot.datasets.get_2D_samples_gauss(n_samples, mu_s, cov_s)
xt = xs[::-1].copy()
p = ot.unif(n_samples)
q = ot.unif(n_samples)
C1 = ot.dist(xs, xs)
C2 = ot.dist(xt, xt)
C1 /= C1.max()
C2 /= C2.max()
G = ot.gromov_wasserstein(C1, C2, p, q, 'square_loss', epsilon=5e-4)
# check constratints
np.testing.assert_allclose(p, G.sum(1),
atol=1e-04) # cf convergence gromov
np.testing.assert_allclose(q, G.sum(0),
atol=1e-04) # cf convergence gromov
def test_fgw_barycenter():
np.random.seed(42)
ns = 50
nt = 60
Xs, ys = ot.datasets.make_data_classif('3gauss', ns, random_state=42)
Xt, yt = ot.datasets.make_data_classif('3gauss2', nt, random_state=42)
ys = np.random.randn(Xs.shape[0], 2)
yt = np.random.randn(Xt.shape[0], 2)
C1 = ot.dist(Xs)
C2 = ot.dist(Xt)
n_samples = 3
X, C = ot.gromov.fgw_barycenters(n_samples, [ys, yt], [C1, C2],
[ot.unif(ns), ot.unif(nt)], [.5, .5],
0.5,
fixed_structure=False,
fixed_features=False,
p=ot.unif(n_samples),
loss_fun='square_loss',
max_iter=100,
tol=1e-3)
np.testing.assert_allclose(C.shape, (n_samples, n_samples))
np.testing.assert_allclose(X.shape, (n_samples, ys.shape[1]))
xalea = np.random.randn(n_samples, 2)
init_C = ot.dist(xalea, xalea)
X, C = ot.gromov.fgw_barycenters(n_samples, [ys, yt], [C1, C2],
ps=[ot.unif(ns), ot.unif(nt)],
lambdas=[.5, .5],
alpha=0.5,
fixed_structure=True,
init_C=init_C,
fixed_features=False,
p=ot.unif(n_samples),
loss_fun='square_loss',
max_iter=100,
tol=1e-3)
np.testing.assert_allclose(C.shape, (n_samples, n_samples))
np.testing.assert_allclose(X.shape, (n_samples, ys.shape[1]))
init_X = np.random.randn(n_samples, ys.shape[1])
X, C, log = ot.gromov.fgw_barycenters(
n_samples, [ys, yt], [C1, C2], [ot.unif(ns), ot.unif(nt)], [.5, .5],
0.5,
fixed_structure=False,
fixed_features=True,
init_X=init_X,
p=ot.unif(n_samples),
loss_fun='square_loss',
max_iter=100,
tol=1e-3,
log=True)
np.testing.assert_allclose(C.shape, (n_samples, n_samples))
np.testing.assert_allclose(X.shape, (n_samples, ys.shape[1]))
def _compute_copula_ot_dependence(empirical: np.array, target: np.array,
forget: np.array, n_obs: int) -> float:
"""
Calculates optimal copula transport dependence measure.
:param empirical: (np.array) Empirical copula.
:param target: (np.array) Target copula.
:param forget: (np.array) Forget copula.
:param nb_obs: (int) Number of observations.
:return: (float) Optimal copula transport dependence.
"""
# Uniform distribution on samples
t_measure, f_measure, e_measure = (np.ones(
(n_obs, )) / n_obs, np.ones((n_obs, )) / n_obs, np.ones(
(n_obs, )) / n_obs)
# Compute the ground distance matrix between locations
gdist_e2t = ot.dist(empirical, target)
gdist_e2f = ot.dist(empirical, forget)
# Compute the optimal transport matrix
e2t_ot = ot.emd(t_measure, e_measure, gdist_e2t)
e2f_ot = ot.emd(f_measure, e_measure, gdist_e2f)
# Compute the optimal transport distance:
# <optimal transport matrix, ground distance matrix>_F
e2t_dist = np.trace(np.dot(np.transpose(e2t_ot), gdist_e2t))
e2f_dist = np.trace(np.dot(np.transpose(e2f_ot), gdist_e2f))
# Compute the copula ot dependence measure
ot_measure = 1 - e2t_dist / (e2f_dist + e2t_dist)
return ot_measure
def test_gromov_barycenter():
ns = 50
nt = 60
Xs, ys = ot.datasets.get_data_classif('3gauss', ns)
Xt, yt = ot.datasets.get_data_classif('3gauss2', nt)
C1 = ot.dist(Xs)
C2 = ot.dist(Xt)
n_samples = 3
Cb = ot.gromov.gromov_barycenters(n_samples, [C1, C2],
[ot.unif(ns), ot.unif(nt)
], ot.unif(n_samples), [.5, .5],
'square_loss', # 5e-4,
max_iter=100, tol=1e-3)
np.testing.assert_allclose(Cb.shape, (n_samples, n_samples))
Cb2 = ot.gromov.gromov_barycenters(n_samples, [C1, C2],
[ot.unif(ns), ot.unif(nt)
], ot.unif(n_samples), [.5, .5],
'kl_loss', # 5e-4,
max_iter=100, tol=1e-3)
np.testing.assert_allclose(Cb2.shape, (n_samples, n_samples))
def test_empirical_sinkhorn_divergence():
#Test sinkhorn divergence
n = 10
a = ot.unif(n)
b = ot.unif(n)
X_s = np.reshape(np.arange(n), (n, 1))
X_t = np.reshape(np.arange(0, n * 2, 2), (n, 1))
M = ot.dist(X_s, X_t)
M_s = ot.dist(X_s, X_s)
M_t = ot.dist(X_t, X_t)
emp_sinkhorn_div = ot.bregman.empirical_sinkhorn_divergence(X_s, X_t, 1)
sinkhorn_div = (ot.sinkhorn2(a, b, M, 1) -
1 / 2 * ot.sinkhorn2(a, a, M_s, 1) -
1 / 2 * ot.sinkhorn2(b, b, M_t, 1))
emp_sinkhorn_div_log, log_es = ot.bregman.empirical_sinkhorn_divergence(
X_s, X_t, 1, log=True)
sink_div_log_ab, log_s_ab = ot.sinkhorn2(a, b, M, 1, log=True)
sink_div_log_a, log_s_a = ot.sinkhorn2(a, a, M_s, 1, log=True)
sink_div_log_b, log_s_b = ot.sinkhorn2(b, b, M_t, 1, log=True)
sink_div_log = sink_div_log_ab - 1 / 2 * (sink_div_log_a + sink_div_log_b)
# check constratints
np.testing.assert_allclose(emp_sinkhorn_div, sinkhorn_div,
atol=1e-05) # cf conv emp sinkhorn
np.testing.assert_allclose(emp_sinkhorn_div_log, sink_div_log,
atol=1e-05) # cf conv emp sinkhorn
def forward_seq(self, x_train, x_test):
N = self.Nmasses
(Pl_train, P_train) = particleApproximation_v0(x_train, N)
(Pl_test, P_test) = particleApproximation_v0(x_test, N)
Pl_tem = 0
for a in range(2): #x_train.shape[0]):
t = Pl_train[a]
Pl_tem = Pl_tem + t
Pl_tem = Pl_tem / 2 #x_train.shape[0]
P_tem = np.ones((N, )) / float(N)
#Pl_tem_vec=np.reshape(Pl_tem,(Pl_tem.shape[0]*Pl_tem.shape[1],),order='F')
V = list()
M = x_train.shape[0]
for ind in range(M):
Ni = Pl_train[ind].shape[0]
C = ot.dist(Pl_train[ind], Pl_tem)
b = P_tem # b=np.ones((N,))/float(N)
a = P_train[ind] # a=np.ones((Ni,))/float(Ni)
p = ot.emd(a, b, C) # exact linear program
#V.append(np.matmul((N*p).T,Pl_train[ind])-Pl_tem)
V.append(np.matmul((N * p).T, Pl_train[ind]) +
Pl_tem) # already giving transport displacement?
V = np.asarray(V)
x_train_hat = np.zeros((len(V), V[0].shape[0] * V[0].shape[1]))
for a in range(len(V)):
x_train_hat[a, :] = np.reshape(V[a],
(V[0].shape[0] * V[0].shape[1], ),
order='F')
V = list()
M = x_test.shape[0]
for ind in range(M):
Ni = Pl_test[ind].shape[0]
C = ot.dist(Pl_test[ind], Pl_tem)
b = P_tem # b=np.ones((N,))/float(N)
a = P_test[ind] # a=np.ones((Ni,))/float(Ni)
p = ot.emd(a, b, C) # exact linear program
#V.append(np.matmul((N*p).T,Pl_test[ind])-Pl_tem)
V.append(np.matmul((N * p).T, Pl_test[ind]) + Pl_tem)
V = np.asarray(V)
x_test_hat = np.zeros((len(V), V[0].shape[0] * V[0].shape[1]))
for a in range(len(V)):
x_test_hat[a, :] = np.reshape(V[a],
(V[0].shape[0] * V[0].shape[1], ),
order='F')
return x_train_hat, x_test_hat, Pl_tem, P_tem
def graph_d(self, graph1, graph2):
""" Compute the Fused Gromov-Wasserstein distance between two graphs. Uniform weights are used.
Parameters
----------
graph1 : a Graph object
graph2 : a Graph object
Returns
-------
The Fused Gromov-Wasserstein distance between the features of graph1 and graph2
"""
gofeature = True
nodes1 = graph1.nodes()
nodes2 = graph2.nodes()
startstruct = time.time()
C1 = graph1.distance_matrix(method=self.method)
C2 = graph2.distance_matrix(method=self.method)
end2 = time.time()
t1masses = np.ones(len(nodes1)) / len(nodes1)
t2masses = np.ones(len(nodes2)) / len(nodes2)
try:
x1 = self.reshaper(graph1.all_matrix_attr())
x2 = self.reshaper(graph2.all_matrix_attr())
except NoAttrMatrix:
x1 = None
x2 = None
gofeature = False
if gofeature:
if self.features_metric == 'dirac':
def f(x, y):
return x != y
M = ot.dist(x1, x2, metric=f)
elif self.features_metric == 'hamming_dist': # see experimental setup in the original paper
def f(x, y):
return hamming_dist(x, y)
M = ot.dist(x1, x2, metric=f)
else:
M = ot.dist(x1, x2, metric=self.features_metric)
self.M = M
else:
M = np.zeros((C1.shape[0], C2.shape[0]))
startdist = time.time()
transpwgw, log = self.calc_fgw(M, C1, C2, t1masses, t2masses)
enddist = time.time()
enddist = time.time()
log['struct_time'] = (end2 - startstruct)
log['dist_time'] = (enddist - startdist)
self.transp = transpwgw
self.log = log
return log['loss'][::-1][0]
def test_dual_sgd_sinkhorn():
# test all dual algorithms
n = 10
reg = 1
nb_iter = 15000
batch_size = 10
rng = np.random.RandomState(0)
# Test uniform
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G_sgd = ot.stochastic.solve_dual_entropic(u,
u,
M,
reg,
batch_size,
numItermax=nb_iter)
G_sinkhorn = ot.sinkhorn(u, u, M, reg)
# check constratints
np.testing.assert_allclose(G_sgd.sum(1), G_sinkhorn.sum(1), atol=1e-03)
np.testing.assert_allclose(G_sgd.sum(0), G_sinkhorn.sum(0), atol=1e-03)
np.testing.assert_allclose(G_sgd, G_sinkhorn,
atol=1e-03) # cf convergence sgd
# Test gaussian
n = 30
reg = 1
batch_size = 30
a = ot.datasets.make_1D_gauss(n, 15, 5) # m= mean, s= std
b = ot.datasets.make_1D_gauss(n, 15, 5)
X_source = np.arange(n, dtype=np.float64)
Y_target = np.arange(n, dtype=np.float64)
M = ot.dist(X_source.reshape((n, 1)), Y_target.reshape((n, 1)))
M /= M.max()
G_sgd = ot.stochastic.solve_dual_entropic(a,
b,
M,
reg,
batch_size,
numItermax=nb_iter)
G_sinkhorn = ot.sinkhorn(a, b, M, reg)
# check constratints
np.testing.assert_allclose(G_sgd.sum(1), G_sinkhorn.sum(1), atol=1e-03)
np.testing.assert_allclose(G_sgd.sum(0), G_sinkhorn.sum(0), atol=1e-03)
np.testing.assert_allclose(G_sgd, G_sinkhorn,
atol=1e-03) # cf convergence sgd
def barycenter_free(b1,
b2,
xs1,
xs2,
w1,
w2,
entr_reg,
k,
tol=1e-5,
max_iter=100,
verbose=False):
d = xs1.shape[1]
ys = np.random.normal(size=(k, d))
cost_old = np.float("Inf")
its = 0
converged = False
while not converged and its < max_iter:
its += 1
if verbose:
print("Barycenter points iteration: {}".format(its))
if its > 1:
ys = (w1 * np.matmul(gamma1, xs1) +
w2 * np.matmul(gamma2, xs2)) / (np.dot(
(w1 * np.sum(gamma1, axis=1) +
w2 * np.sum(gamma2, axis=1)).reshape(
(k, 1)), np.ones((1, d))))
M1 = ot.dist(ys, xs1)
M2 = ot.dist(ys, xs2)
(gamma1, gamma2) = barycenter_bregman(b1,
b2,
M1,
M2,
w1,
w2,
entr_reg,
max_iter=500)
cost = (w1 * np.sum(gamma1 * M1) + w2 * np.sum(gamma2 * M2)
) + entr_reg * (w1 * stats.entropy(gamma1.reshape(
(-1, 1))) + w2 * stats.entropy(gamma2.reshape((-1, 1))))
# TODO: Calculate the entropy safely
# cost = w1 * np.sum(gamma1 * M1) + w2 * np.sum(gamma2 * M2)
err = abs(cost - cost_old) / max(abs(cost), 1e-12)
cost_old = cost.copy()
if verbose:
print("Relative change in points iteration: {}".format(err))
if err < tol:
converged = True
return (ys, np.dot(gamma1, np.ones(gamma1.shape[1])), cost, gamma1, gamma2)
def test_entropic_gromov():
n_samples = 50 # nb samples
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
xs = ot.datasets.make_2D_samples_gauss(n_samples,
mu_s,
cov_s,
random_state=42)
xt = xs[::-1].copy()
p = ot.unif(n_samples)
q = ot.unif(n_samples)
C1 = ot.dist(xs, xs)
C2 = ot.dist(xt, xt)
C1 /= C1.max()
C2 /= C2.max()
G = ot.gromov.entropic_gromov_wasserstein(C1,
C2,
p,
q,
'square_loss',
epsilon=5e-4,
verbose=True)
# check constratints
np.testing.assert_allclose(p, G.sum(1),
atol=1e-04) # cf convergence gromov
np.testing.assert_allclose(q, G.sum(0),
atol=1e-04) # cf convergence gromov
gw, log = ot.gromov.entropic_gromov_wasserstein2(C1,
C2,
p,
q,
'kl_loss',
epsilon=1e-2,
log=True)
G = log['T']
np.testing.assert_allclose(gw, 0, atol=1e-1, rtol=1e-1)
# check constratints
np.testing.assert_allclose(p, G.sum(1),
atol=1e-04) # cf convergence gromov
np.testing.assert_allclose(q, G.sum(0),
atol=1e-04) # cf convergence gromov
def test_gromov():
n_samples = 50 # nb samples
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
xs = ot.datasets.make_2D_samples_gauss(n_samples,
mu_s,
cov_s,
random_state=4)
xt = xs[::-1].copy()
p = ot.unif(n_samples)
q = ot.unif(n_samples)
C1 = ot.dist(xs, xs)
C2 = ot.dist(xt, xt)
C1 /= C1.max()
C2 /= C2.max()
G = ot.gromov.gromov_wasserstein(C1, C2, p, q, 'square_loss', verbose=True)
# check constratints
np.testing.assert_allclose(p, G.sum(1),
atol=1e-04) # cf convergence gromov
np.testing.assert_allclose(q, G.sum(0),
atol=1e-04) # cf convergence gromov
Id = (1 / (1.0 * n_samples)) * np.eye(n_samples, n_samples)
np.testing.assert_allclose(G, np.flipud(Id), atol=1e-04)
gw, log = ot.gromov.gromov_wasserstein2(C1, C2, p, q, 'kl_loss', log=True)
gw_val = ot.gromov.gromov_wasserstein2(C1, C2, p, q, 'kl_loss', log=False)
G = log['T']
np.testing.assert_allclose(gw, 0, atol=1e-1, rtol=1e-1)
np.testing.assert_allclose(gw, gw_val, atol=1e-1,
rtol=1e-1) # cf log=False
# check constratints
np.testing.assert_allclose(p, G.sum(1),
atol=1e-04) # cf convergence gromov
np.testing.assert_allclose(q, G.sum(0),
atol=1e-04) # cf convergence gromov
def calculate_gw_cpu(Xs, Xt, numItermax=500):
st = time.time()
C1 = ot.dist(Xs, Xs, 'sqeuclidean')
C2 = ot.dist(Xt, Xt, 'sqeuclidean')
p = np.ones(Xs.shape[0]) / Xs.shape[0]
q = np.ones(Xt.shape[0]) / Xt.shape[0]
T, log = gw(C1, C2, p, q, 'square_loss', log=True, numItermax=numItermax)
d_gw = log['loss'][::-1][0]
converge_gw_pot = abs(log['loss'][::-1][0] - log['loss'][::-1][1]) <= 1e-5
ed = time.time()
time_gw = ed - st
return d_gw, time_gw, converge_gw_pot
def test_fgw():
n_samples = 50 # nb samples
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s, random_state=42)
xt = xs[::-1].copy()
ys = np.random.randn(xs.shape[0], 2)
yt = ys[::-1].copy()
p = ot.unif(n_samples)
q = ot.unif(n_samples)
C1 = ot.dist(xs, xs)
C2 = ot.dist(xt, xt)
C1 /= C1.max()
C2 /= C2.max()
M = ot.dist(ys, yt)
M /= M.max()
G, log = ot.gromov.fused_gromov_wasserstein(M, C1, C2, p, q, 'square_loss', alpha=0.5, log=True)
# check constratints
np.testing.assert_allclose(
p, G.sum(1), atol=1e-04) # cf convergence fgw
np.testing.assert_allclose(
q, G.sum(0), atol=1e-04) # cf convergence fgw
Id = (1 / (1.0 * n_samples)) * np.eye(n_samples, n_samples)
np.testing.assert_allclose(
G, np.flipud(Id), atol=1e-04) # cf convergence gromov
fgw, log = ot.gromov.fused_gromov_wasserstein2(M, C1, C2, p, q, 'square_loss', alpha=0.5, log=True)
G = log['T']
np.testing.assert_allclose(fgw, 0, atol=1e-1, rtol=1e-1)
# check constratints
np.testing.assert_allclose(
p, G.sum(1), atol=1e-04) # cf convergence gromov
np.testing.assert_allclose(
q, G.sum(0), atol=1e-04) # cf convergence gromov
def test_generalized_conditional_gradient():
n_bins = 100 # nb bins
np.random.seed(0)
# bin positions
x = np.arange(n_bins, dtype=np.float64)
# Gaussian distributions
a = ot.datasets.get_1D_gauss(n_bins, m=20, s=5) # m= mean, s= std
b = ot.datasets.get_1D_gauss(n_bins, m=60, s=10)
# loss matrix
M = ot.dist(x.reshape((n_bins, 1)), x.reshape((n_bins, 1)))
M /= M.max()
def f(G):
return 0.5 * np.sum(G**2)
def df(G):
return G
reg1 = 1e-3
reg2 = 1e-1
G, log = ot.optim.gcg(a, b, M, reg1, reg2, f, df, verbose=True, log=True)
np.testing.assert_allclose(a, G.sum(1), atol=1e-05)
np.testing.assert_allclose(b, G.sum(0), atol=1e-05)
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, verbose=True, log=True)
# check constratints
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 constratints
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 constratints
np.testing.assert_allclose(u, G.sum(1), atol=1e-05)
np.testing.assert_allclose(u, G.sum(0), atol=1e-05)
def test_sinkhorn_variants():
# test sinkhorn
n = 100
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G0 = ot.sinkhorn(u, u, M, 1, method='sinkhorn', stopThr=1e-10)
Gs = ot.sinkhorn(u, u, M, 1, method='sinkhorn_stabilized', stopThr=1e-10)
Ges = ot.sinkhorn(u,
u,
M,
1,
method='sinkhorn_epsilon_scaling',
stopThr=1e-10)
Gerr = ot.sinkhorn(u, u, M, 1, method='do_not_exists', stopThr=1e-10)
G_green = ot.sinkhorn(u, u, M, 1, method='greenkhorn', stopThr=1e-10)
# check values
np.testing.assert_allclose(G0, Gs, atol=1e-05)
np.testing.assert_allclose(G0, Ges, atol=1e-05)
np.testing.assert_allclose(G0, Gerr)
np.testing.assert_allclose(G0, G_green, atol=1e-5)
print(G0, G_green)
def test_warnings():
n = 100 # nb bins
m = 100 # nb bins
mean1 = 30
mean2 = 50
# bin positions
x = np.arange(n, dtype=np.float64)
y = np.arange(m, dtype=np.float64)
# Gaussian distributions
a = gauss(n, m=mean1, s=5) # m= mean, s= std
b = gauss(m, m=mean2, s=10)
# loss matrix
M = ot.dist(x.reshape((-1, 1)), y.reshape((-1, 1)))**(1. / 2)
print('Computing {} EMD '.format(1))
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always")
print('Computing {} EMD '.format(1))
ot.emd(a, b, M, numItermax=1)
assert "numItermax" in str(w[-1].message)
def double_wasserstein1(X_train_smote):
n, m, r, _ = X_train_smote.shape
# uniform measures at points clouds of card m
a2 = np.ones(m) / m
b2 = np.ones(m) / m
# uniform measures at points of card r
a1 = np.ones(r) / r
b1 = np.ones(r) / r
# 1st level distance matrix of size m x m
M1 = np.zeros((m, m))
# M1 loop
for i in range(m):
for j in range(i + 1, m):
# pairwise squared Euclidean distances as the ground metric
M0_ij = ot.dist(X_train_smote[0, i],
X_train_smote[1, j],
metric="sqeuclidean")
# 2-Wasserstein distance btw point clouds, take square root
M1[i, j] = ot.emd2(a1, b1, M0_ij)**0.5
# 1st level symmetrize
M1 = M1 + M1.T
np.fill_diagonal(M1, 1e9)
# 1-Wasserstein distance btw collections of point clouds
W1 = ot.emd2(a2, b2, M1)
return W1
def test_emd_emd2_devices_tf():
if not tf:
return
nx = ot.backend.TensorflowBackend()
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)
# Check that everything stays on the CPU
with tf.device("/CPU:0"):
ab, Mb = nx.from_numpy(a, M)
Gb = ot.emd(ab, ab, Mb)
w = ot.emd2(ab, ab, Mb)
nx.assert_same_dtype_device(Mb, Gb)
nx.assert_same_dtype_device(Mb, w)
if len(tf.config.list_physical_devices('GPU')) > 0:
# Check that everything happens on the GPU
ab, Mb = nx.from_numpy(a, M)
Gb = ot.emd(ab, ab, Mb)
w = ot.emd2(ab, ab, Mb)
nx.assert_same_dtype_device(Mb, Gb)
nx.assert_same_dtype_device(Mb, w)
assert nx.dtype_device(Gb)[1].startswith("GPU")
def test_conditional_gradient(nx):
n_bins = 100 # nb bins
np.random.seed(0)
# bin positions
x = np.arange(n_bins, dtype=np.float64)
# Gaussian distributions
a = ot.datasets.make_1D_gauss(n_bins, m=20, s=5) # m= mean, s= std
b = ot.datasets.make_1D_gauss(n_bins, m=60, s=10)
# loss matrix
M = ot.dist(x.reshape((n_bins, 1)), x.reshape((n_bins, 1)))
M /= M.max()
def f(G):
return 0.5 * np.sum(G**2)
def df(G):
return G
def fb(G):
return 0.5 * nx.sum(G ** 2)
ab, bb, Mb = nx.from_numpy(a, b, M)
reg = 1e-1
G, log = ot.optim.cg(a, b, M, reg, f, df, verbose=True, log=True)
Gb, log = ot.optim.cg(ab, bb, Mb, reg, fb, df, verbose=True, log=True)
Gb = nx.to_numpy(Gb)
np.testing.assert_allclose(Gb, G)
np.testing.assert_allclose(a, Gb.sum(1))
np.testing.assert_allclose(b, Gb.sum(0))
def test_gpu_sinkhorn_lpl1():
rng = np.random.RandomState(0)
for n_samples in [50, 100, 500]:
print(n_samples)
a = rng.rand(n_samples // 4, 100)
labels_a = np.random.randint(10, size=(n_samples // 4))
b = rng.rand(n_samples, 100)
wa = ot.unif(n_samples // 4)
wb = ot.unif(n_samples)
M = ot.dist(a.copy(), b.copy())
M2 = ot.gpu.dist(a.copy(), b.copy(), to_numpy=False)
reg = 1
G = ot.da.sinkhorn_lpl1_mm(wa, labels_a, wb, M, reg)
G1 = ot.gpu.da.sinkhorn_lpl1_mm(wa, labels_a, wb, M, reg)
np.testing.assert_allclose(G1, G, rtol=1e-10)
ot.gpu.da.sinkhorn_lpl1_mm(wa,
labels_a,
wb,
M2,
reg,
to_numpy=False,
log=True)
def test_gpu_sinkhorn():
rng = np.random.RandomState(0)
for n_samples in [50, 100, 500, 1000]:
a = rng.rand(n_samples // 4, 100)
b = rng.rand(n_samples, 100)
wa = ot.unif(n_samples // 4)
wb = ot.unif(n_samples)
wb2 = np.random.rand(n_samples, 20)
wb2 /= wb2.sum(0, keepdims=True)
M = ot.dist(a.copy(), b.copy())
M2 = ot.gpu.dist(a.copy(), b.copy(), to_numpy=False)
reg = 1
G = ot.sinkhorn(wa, wb, M, reg)
G1 = ot.gpu.sinkhorn(wa, wb, M, reg)
np.testing.assert_allclose(G1, G, rtol=1e-10)
# run all on gpu
ot.gpu.sinkhorn(wa, wb, M2, reg, to_numpy=False, log=True)
# run sinkhorn for multiple targets
ot.gpu.sinkhorn(wa, wb2, M2, reg, to_numpy=False, log=True)
def test_gpu_dist():
rng = np.random.RandomState(0)
for n_samples in [50, 100, 500, 1000]:
print(n_samples)
a = rng.rand(n_samples // 4, 100)
b = rng.rand(n_samples, 100)
M = ot.dist(a.copy(), b.copy())
M2 = ot.gpu.dist(a.copy(), b.copy())
np.testing.assert_allclose(M, M2, rtol=1e-10)
M2 = ot.gpu.dist(a.copy(),
b.copy(),
metric='euclidean',
to_numpy=False)
# check raise not implemented wrong metric
with pytest.raises(NotImplementedError):
M2 = ot.gpu.dist(a.copy(),
b.copy(),
metric='cityblock',
to_numpy=False)
def makeTransportPlan(self):
if self.source_data and self.target_data:
if self.source_data_size == self.target_data_size:
loss_matrix = ot.dist(self.source_data, self.target_data)
loss_matrix = loss_matrix / loss_matrix.max()
if not self.source_weight:
self.source_weight = np.ones(
(self.source_data_size, )) / self.source_data_size
print(
"The Source weights are intiialized to one. If custome weight please load weight."
)
if not self.target_weight:
self.target_weight = np.ones(
(self.target_data_size, )) / self.target_data_size
print(
"The Target weights are intiialized to one. If custome weight please load weight."
)
transport = ot.emd(self.source_weight,
self.target_weight,
loss_matrix,
log=True)
print("Transport Plan Complete")
print("The cost is: {}".format(transport[1]['cost']))
self.transport_plan = transport[0]
return transport
else:
print(
"Optimal Transport Plan not complete due to mismatch in Source and Target Size."
)
return
else:
print(
"Optimal Transport Plan not complete. Please add Source & Target data and rerun."
)
return
def test_dist():
n = 100
x = np.random.randn(n, 2)
D = np.zeros((n, n))
for i in range(n):
for j in range(n):
D[i, j] = np.sum(np.square(x[i, :] - x[j, :]))
D2 = ot.dist(x, x)
D3 = ot.dist(x)
# dist shoul return squared euclidean
np.testing.assert_allclose(D, D2)
np.testing.assert_allclose(D, D3)
def test_entropic_gromov():
n_samples = 50 # nb samples
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
xs = ot.datasets.get_2D_samples_gauss(n_samples, mu_s, cov_s)
xt = xs[::-1].copy()
p = ot.unif(n_samples)
q = ot.unif(n_samples)
C1 = ot.dist(xs, xs)
C2 = ot.dist(xt, xt)
C1 /= C1.max()
C2 /= C2.max()
G = ot.gromov.entropic_gromov_wasserstein(
C1, C2, p, q, 'square_loss', epsilon=5e-4)
# check constratints
np.testing.assert_allclose(
p, G.sum(1), atol=1e-04) # cf convergence gromov
np.testing.assert_allclose(
q, G.sum(0), atol=1e-04) # cf convergence gromov
gw, log = ot.gromov.entropic_gromov_wasserstein2(
C1, C2, p, q, 'kl_loss', epsilon=1e-2, log=True)
G = log['T']
np.testing.assert_allclose(gw, 0, atol=1e-1, rtol=1e-1)
# check constratints
np.testing.assert_allclose(
p, G.sum(1), atol=1e-04) # cf convergence gromov
np.testing.assert_allclose(
q, G.sum(0), atol=1e-04) # cf convergence gromov
def test_emd2_multi():
n = 1000 # nb bins
# bin positions
x = np.arange(n, dtype=np.float64)
# Gaussian distributions
a = gauss(n, m=20, s=5) # m= mean, s= std
ls = np.arange(20, 1000, 20)
nb = len(ls)
b = np.zeros((n, nb))
for i in range(nb):
b[:, i] = gauss(n, m=ls[i], s=10)
# loss matrix
M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
# M/=M.max()
print('Computing {} EMD '.format(nb))
# emd loss 1 proc
ot.tic()
emd1 = ot.emd2(a, b, M, 1)
ot.toc('1 proc : {} s')
# emd loss multipro proc
ot.tic()
emdn = ot.emd2(a, b, M)
ot.toc('multi proc : {} s')
np.testing.assert_allclose(emd1, emdn)
# emd loss multipro proc with log
ot.tic()
emdn = ot.emd2(a, b, M, log=True, return_matrix=True)
ot.toc('multi proc : {} s')
for i in range(len(emdn)):
emd = emdn[i]
log = emd[1]
cost = emd[0]
check_duality_gap(a, b[:, i], M, log['G'], log['u'], log['v'], cost)
emdn[i] = cost
emdn = np.array(emdn)
np.testing.assert_allclose(emd1, emdn)
def test_sinkhorn():
# 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)
# check constratints
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
def test_plot1D_mat():
import ot
import ot.plot
n_bins = 100 # nb bins
# bin positions
x = np.arange(n_bins, dtype=np.float64)
# Gaussian distributions
a = ot.datasets.get_1D_gauss(n_bins, m=20, s=5) # m= mean, s= std
b = ot.datasets.get_1D_gauss(n_bins, m=60, s=10)
# loss matrix
M = ot.dist(x.reshape((n_bins, 1)), x.reshape((n_bins, 1)))
M /= M.max()
ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')
def test_sinkhorn_variants():
# test sinkhorn
n = 100
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G0 = ot.sinkhorn(u, u, M, 1, method='sinkhorn', stopThr=1e-10)
Gs = ot.sinkhorn(u, u, M, 1, method='sinkhorn_stabilized', stopThr=1e-10)
Ges = ot.sinkhorn(
u, u, M, 1, method='sinkhorn_epsilon_scaling', stopThr=1e-10)
Gerr = ot.sinkhorn(u, u, M, 1, method='do_not_exists', stopThr=1e-10)
# check values
np.testing.assert_allclose(G0, Gs, atol=1e-05)
np.testing.assert_allclose(G0, Ges, atol=1e-05)
np.testing.assert_allclose(G0, Gerr)
def test_emd_empty():
# test emd and emd2 for simple identity
n = 100
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G = ot.emd([], [], M)
# check G is identity
np.testing.assert_allclose(G, np.eye(n) / n)
# check constratints
np.testing.assert_allclose(u, G.sum(1)) # cf convergence sinkhorn
np.testing.assert_allclose(u, G.sum(0)) # cf convergence sinkhorn
w = ot.emd2([], [], M)
# check loss=0
np.testing.assert_allclose(w, 0)
def test_dual_variables():
n = 5000 # nb bins
m = 6000 # nb bins
mean1 = 1000
mean2 = 1100
# bin positions
x = np.arange(n, dtype=np.float64)
y = np.arange(m, dtype=np.float64)
# Gaussian distributions
a = gauss(n, m=mean1, s=5) # m= mean, s= std
b = gauss(m, m=mean2, s=10)
# loss matrix
M = ot.dist(x.reshape((-1, 1)), y.reshape((-1, 1))) ** (1. / 2)
print('Computing {} EMD '.format(1))
# emd loss 1 proc
ot.tic()
G, log = ot.emd(a, b, M, log=True)
ot.toc('1 proc : {} s')
ot.tic()
G2 = ot.emd(b, a, np.ascontiguousarray(M.T))
ot.toc('1 proc : {} s')
cost1 = (G * M).sum()
# Check symmetry
np.testing.assert_array_almost_equal(cost1, (M * G2.T).sum())
# Check with closed-form solution for gaussians
np.testing.assert_almost_equal(cost1, np.abs(mean1 - mean2))
# Check that both cost computations are equivalent
np.testing.assert_almost_equal(cost1, log['cost'])
check_duality_gap(a, b, M, G, log['u'], log['v'], log['cost'])
def test_warnings():
n = 100 # nb bins
m = 100 # nb bins
mean1 = 30
mean2 = 50
# bin positions
x = np.arange(n, dtype=np.float64)
y = np.arange(m, dtype=np.float64)
# Gaussian distributions
a = gauss(n, m=mean1, s=5) # m= mean, s= std
b = gauss(m, m=mean2, s=10)
# loss matrix
M = ot.dist(x.reshape((-1, 1)), y.reshape((-1, 1))) ** (1. / 2)
print('Computing {} EMD '.format(1))
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always")
print('Computing {} EMD '.format(1))
ot.emd(a, b, M, numItermax=1)
assert "numItermax" in str(w[-1].message)
assert len(w) == 1
a[0] = 100
print('Computing {} EMD '.format(2))
ot.emd(a, b, M)
assert "infeasible" in str(w[-1].message)
assert len(w) == 2
a[0] = -1
print('Computing {} EMD '.format(2))
ot.emd(a, b, M)
assert "infeasible" in str(w[-1].message)
assert len(w) == 3
# Generate data # ------------- #%% parameters n = 100 # nb bins # bin positions x = np.arange(n, dtype=np.float64) # Gaussian distributions a = ot.datasets.get_1D_gauss(n, m=20, s=5) # m= mean, s= std b = ot.datasets.get_1D_gauss(n, m=60, s=10) # loss matrix M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1))) M /= M.max() ############################################################################## # Solve EMD # --------- #%% EMD G0 = ot.emd(a, b, M) pl.figure(3, figsize=(5, 5)) ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0') ############################################################################## # Solve EMD with Frobenius norm regularization
############################################################################## # Dataset 1 : uniform sampling # ---------------------------- n = 20 # nb samples xs = np.zeros((n, 2)) xs[:, 0] = np.arange(n) + 1 xs[:, 1] = (np.arange(n) + 1) * -0.001 # to make it strictly convex... xt = np.zeros((n, 2)) xt[:, 1] = np.arange(n) + 1 a, b = ot.unif(n), ot.unif(n) # uniform distribution on samples # loss matrix M1 = ot.dist(xs, xt, metric='euclidean') M1 /= M1.max() # loss matrix M2 = ot.dist(xs, xt, metric='sqeuclidean') M2 /= M2.max() # loss matrix Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean')) Mp /= Mp.max() # Data pl.figure(1, figsize=(7, 3)) pl.clf() pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
n = 50 # nb samples
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
mu_t = np.array([4, 4])
cov_t = np.array([[1, -.8], [-.8, 1]])
xs = ot.datasets.get_2D_samples_gauss(n, mu_s, cov_s)
xt = ot.datasets.get_2D_samples_gauss(n, mu_t, cov_t)
a, b = np.ones((n,)) / n, np.ones((n,)) / n # uniform distribution on samples
# loss matrix
M = ot.dist(xs, xt)
M /= M.max()
##############################################################################
# Plot data
# ---------
#%% plot samples
pl.figure(1)
pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
pl.legend(loc=0)
pl.title('Source and target distributions')
pl.figure(2)