class TestGeodesicRegression(geomstats.tests.TestCase):
_multiprocess_can_split_ = True
def setup_method(self):
gs.random.seed(1234)
self.n_samples = 20
# Set up for euclidean
self.dim_eucl = 3
self.shape_eucl = (self.dim_eucl, )
self.eucl = Euclidean(dim=self.dim_eucl)
X = gs.random.rand(self.n_samples)
self.X_eucl = X - gs.mean(X)
self.intercept_eucl_true = self.eucl.random_point()
self.coef_eucl_true = self.eucl.random_point()
self.y_eucl = (self.intercept_eucl_true +
self.X_eucl[:, None] * self.coef_eucl_true)
self.param_eucl_true = gs.vstack(
[self.intercept_eucl_true, self.coef_eucl_true])
self.param_eucl_guess = gs.vstack([
self.y_eucl[0],
self.y_eucl[0] + gs.random.normal(size=self.shape_eucl)
])
# Set up for hypersphere
self.dim_sphere = 4
self.shape_sphere = (self.dim_sphere + 1, )
self.sphere = Hypersphere(dim=self.dim_sphere)
X = gs.random.rand(self.n_samples)
self.X_sphere = X - gs.mean(X)
self.intercept_sphere_true = self.sphere.random_point()
self.coef_sphere_true = self.sphere.projection(
gs.random.rand(self.dim_sphere + 1))
self.y_sphere = self.sphere.metric.exp(
self.X_sphere[:, None] * self.coef_sphere_true,
base_point=self.intercept_sphere_true,
)
self.param_sphere_true = gs.vstack(
[self.intercept_sphere_true, self.coef_sphere_true])
self.param_sphere_guess = gs.vstack([
self.y_sphere[0],
self.sphere.to_tangent(gs.random.normal(size=self.shape_sphere),
self.y_sphere[0]),
])
# Set up for special euclidean
self.se2 = SpecialEuclidean(n=2)
self.metric_se2 = self.se2.left_canonical_metric
self.metric_se2.default_point_type = "matrix"
self.shape_se2 = (3, 3)
X = gs.random.rand(self.n_samples)
self.X_se2 = X - gs.mean(X)
self.intercept_se2_true = self.se2.random_point()
self.coef_se2_true = self.se2.to_tangent(
5.0 * gs.random.rand(*self.shape_se2), self.intercept_se2_true)
self.y_se2 = self.metric_se2.exp(
self.X_se2[:, None, None] * self.coef_se2_true[None],
self.intercept_se2_true,
)
self.param_se2_true = gs.vstack([
gs.flatten(self.intercept_se2_true),
gs.flatten(self.coef_se2_true),
])
self.param_se2_guess = gs.vstack([
gs.flatten(self.y_se2[0]),
gs.flatten(
self.se2.to_tangent(gs.random.normal(size=self.shape_se2),
self.y_se2[0])),
])
# Set up for discrete curves
n_sampling_points = 8
self.curves_2d = DiscreteCurves(R2)
self.metric_curves_2d = self.curves_2d.srv_metric
self.metric_curves_2d.default_point_type = "matrix"
self.shape_curves_2d = (n_sampling_points, 2)
X = gs.random.rand(self.n_samples)
self.X_curves_2d = X - gs.mean(X)
self.intercept_curves_2d_true = self.curves_2d.random_point(
n_sampling_points=n_sampling_points)
self.coef_curves_2d_true = self.curves_2d.to_tangent(
5.0 * gs.random.rand(*self.shape_curves_2d),
self.intercept_curves_2d_true)
# Added because of GitHub issue #1575
intercept_curves_2d_true_repeated = gs.tile(
gs.expand_dims(self.intercept_curves_2d_true, axis=0),
(self.n_samples, 1, 1),
)
self.y_curves_2d = self.metric_curves_2d.exp(
self.X_curves_2d[:, None, None] * self.coef_curves_2d_true[None],
intercept_curves_2d_true_repeated,
)
self.param_curves_2d_true = gs.vstack([
gs.flatten(self.intercept_curves_2d_true),
gs.flatten(self.coef_curves_2d_true),
])
self.param_curves_2d_guess = gs.vstack([
gs.flatten(self.y_curves_2d[0]),
gs.flatten(
self.curves_2d.to_tangent(
gs.random.normal(size=self.shape_curves_2d),
self.y_curves_2d[0])),
])
def test_loss_euclidean(self):
"""Test that the loss is 0 at the true parameters."""
gr = GeodesicRegression(
self.eucl,
metric=self.eucl.metric,
center_X=False,
method="extrinsic",
max_iter=50,
init_step_size=0.1,
verbose=True,
)
loss = gr._loss(
self.X_eucl,
self.y_eucl,
self.param_eucl_true,
self.shape_eucl,
)
self.assertAllClose(loss.shape, ())
self.assertTrue(gs.isclose(loss, 0.0))
def test_loss_hypersphere(self):
"""Test that the loss is 0 at the true parameters."""
gr = GeodesicRegression(
self.sphere,
metric=self.sphere.metric,
center_X=False,
method="extrinsic",
max_iter=50,
init_step_size=0.1,
verbose=True,
)
loss = gr._loss(
self.X_sphere,
self.y_sphere,
self.param_sphere_true,
self.shape_sphere,
)
self.assertAllClose(loss.shape, ())
self.assertTrue(gs.isclose(loss, 0.0))
@geomstats.tests.autograd_and_tf_only
def test_loss_se2(self):
"""Test that the loss is 0 at the true parameters."""
gr = GeodesicRegression(
self.se2,
metric=self.metric_se2,
center_X=False,
method="extrinsic",
max_iter=50,
init_step_size=0.1,
verbose=True,
)
loss = gr._loss(self.X_se2, self.y_se2, self.param_se2_true,
self.shape_se2)
self.assertAllClose(loss.shape, ())
self.assertTrue(gs.isclose(loss, 0.0))
@geomstats.tests.autograd_only
def test_loss_curves_2d(self):
"""Test that the loss is 0 at the true parameters."""
gr = GeodesicRegression(
self.curves_2d,
metric=self.metric_curves_2d,
center_X=False,
method="extrinsic",
max_iter=50,
init_step_size=0.1,
verbose=True,
)
loss = gr._loss(
self.X_curves_2d,
self.y_curves_2d,
self.param_curves_2d_true,
self.shape_curves_2d,
)
self.assertAllClose(loss.shape, ())
self.assertTrue(gs.isclose(loss, 0.0))
@geomstats.tests.autograd_tf_and_torch_only
def test_value_and_grad_loss_euclidean(self):
gr = GeodesicRegression(
self.eucl,
metric=self.eucl.metric,
center_X=False,
method="extrinsic",
max_iter=50,
init_step_size=0.1,
verbose=True,
regularization=0,
)
def loss_of_param(param):
return gr._loss(self.X_eucl, self.y_eucl, param, self.shape_eucl)
# Without numpy conversion
objective_with_grad = gs.autodiff.value_and_grad(loss_of_param)
loss_value, loss_grad = objective_with_grad(self.param_eucl_guess)
expected_grad_shape = (2, self.dim_eucl)
self.assertAllClose(loss_value.shape, ())
self.assertAllClose(loss_grad.shape, expected_grad_shape)
self.assertFalse(gs.isclose(loss_value, 0.0))
self.assertFalse(gs.isnan(loss_value))
self.assertFalse(
gs.all(gs.isclose(loss_grad, gs.zeros(expected_grad_shape))))
self.assertTrue(gs.all(~gs.isnan(loss_grad)))
# With numpy conversion
objective_with_grad = gs.autodiff.value_and_grad(loss_of_param,
to_numpy=True)
loss_value, loss_grad = objective_with_grad(self.param_eucl_guess)
# Convert back to arrays/tensors
loss_value = gs.array(loss_value)
loss_grad = gs.array(loss_grad)
expected_grad_shape = (2, self.dim_eucl)
self.assertAllClose(loss_value.shape, ())
self.assertAllClose(loss_grad.shape, expected_grad_shape)
self.assertFalse(gs.isclose(loss_value, 0.0))
self.assertFalse(gs.isnan(loss_value))
self.assertFalse(
gs.all(gs.isclose(loss_grad, gs.zeros(expected_grad_shape))))
self.assertTrue(gs.all(~gs.isnan(loss_grad)))
@geomstats.tests.autograd_tf_and_torch_only
def test_value_and_grad_loss_hypersphere(self):
gr = GeodesicRegression(
self.sphere,
metric=self.sphere.metric,
center_X=False,
method="extrinsic",
max_iter=50,
init_step_size=0.1,
verbose=True,
regularization=0,
)
def loss_of_param(param):
return gr._loss(self.X_sphere, self.y_sphere, param,
self.shape_sphere)
# Without numpy conversion
objective_with_grad = gs.autodiff.value_and_grad(loss_of_param)
loss_value, loss_grad = objective_with_grad(self.param_sphere_guess)
expected_grad_shape = (2, self.dim_sphere + 1)
self.assertAllClose(loss_value.shape, ())
self.assertAllClose(loss_grad.shape, expected_grad_shape)
self.assertFalse(gs.isclose(loss_value, 0.0))
self.assertFalse(gs.isnan(loss_value))
self.assertFalse(
gs.all(gs.isclose(loss_grad, gs.zeros(expected_grad_shape))))
self.assertTrue(gs.all(~gs.isnan(loss_grad)))
# With numpy conversion
objective_with_grad = gs.autodiff.value_and_grad(loss_of_param,
to_numpy=True)
loss_value, loss_grad = objective_with_grad(self.param_sphere_guess)
# Convert back to arrays/tensors
loss_value = gs.array(loss_value)
loss_grad = gs.array(loss_grad)
expected_grad_shape = (2, self.dim_sphere + 1)
self.assertAllClose(loss_value.shape, ())
self.assertAllClose(loss_grad.shape, expected_grad_shape)
self.assertFalse(gs.isclose(loss_value, 0.0))
self.assertFalse(gs.isnan(loss_value))
self.assertFalse(
gs.all(gs.isclose(loss_grad, gs.zeros(expected_grad_shape))))
self.assertTrue(gs.all(~gs.isnan(loss_grad)))
@geomstats.tests.autograd_and_tf_only
def test_value_and_grad_loss_se2(self):
gr = GeodesicRegression(
self.se2,
metric=self.metric_se2,
center_X=False,
method="extrinsic",
max_iter=50,
init_step_size=0.1,
verbose=True,
)
def loss_of_param(param):
return gr._loss(self.X_se2, self.y_se2, param, self.shape_se2)
objective_with_grad = gs.autodiff.value_and_grad(loss_of_param)
loss_value, loss_grad = objective_with_grad(self.param_se2_true)
expected_grad_shape = (
2,
self.shape_se2[0] * self.shape_se2[1],
)
self.assertTrue(gs.isclose(loss_value, 0.0))
loss_value, loss_grad = objective_with_grad(self.param_se2_guess)
self.assertAllClose(loss_value.shape, ())
self.assertAllClose(loss_grad.shape, expected_grad_shape)
self.assertFalse(gs.isclose(loss_value, 0.0))
self.assertFalse(
gs.all(gs.isclose(loss_grad, gs.zeros(expected_grad_shape))))
self.assertTrue(gs.all(~gs.isnan(loss_grad)))
objective_with_grad = gs.autodiff.value_and_grad(loss_of_param,
to_numpy=True)
loss_value, loss_grad = objective_with_grad(self.param_se2_guess)
expected_grad_shape = (
2,
self.shape_se2[0] * self.shape_se2[1],
)
self.assertAllClose(loss_value.shape, ())
self.assertAllClose(loss_grad.shape, expected_grad_shape)
self.assertFalse(gs.isclose(loss_value, 0.0))
self.assertFalse(gs.isnan(loss_value))
self.assertFalse(
gs.all(gs.isclose(loss_grad, gs.zeros(expected_grad_shape))))
self.assertTrue(gs.all(~gs.isnan(loss_grad)))
@geomstats.tests.autograd_tf_and_torch_only
def test_loss_minimization_extrinsic_euclidean(self):
"""Minimize loss from noiseless data."""
gr = GeodesicRegression(self.eucl, regularization=0)
def loss_of_param(param):
return gr._loss(self.X_eucl, self.y_eucl, param, self.shape_eucl)
objective_with_grad = gs.autodiff.value_and_grad(loss_of_param,
to_numpy=True)
initial_guess = gs.flatten(self.param_eucl_guess)
res = minimize(
objective_with_grad,
initial_guess,
method="CG",
jac=True,
tol=10 * gs.atol,
options={
"disp": True,
"maxiter": 50
},
)
self.assertAllClose(gs.array(res.x).shape, (self.dim_eucl * 2, ))
self.assertAllClose(res.fun, 0.0, atol=1000 * gs.atol)
# Cast required because minimization happens in scipy in float64
param_hat = gs.cast(gs.array(res.x), self.param_eucl_true.dtype)
intercept_hat, coef_hat = gs.split(param_hat, 2)
coef_hat = self.eucl.to_tangent(coef_hat, intercept_hat)
self.assertAllClose(intercept_hat, self.intercept_eucl_true)
tangent_vec_of_transport = self.eucl.metric.log(
self.intercept_eucl_true, base_point=intercept_hat)
transported_coef_hat = self.eucl.metric.parallel_transport(
tangent_vec=coef_hat,
base_point=intercept_hat,
direction=tangent_vec_of_transport,
)
self.assertAllClose(transported_coef_hat,
self.coef_eucl_true,
atol=10 * gs.atol)
@geomstats.tests.autograd_tf_and_torch_only
def test_loss_minimization_extrinsic_hypersphere(self):
"""Minimize loss from noiseless data."""
gr = GeodesicRegression(self.sphere, regularization=0)
def loss_of_param(param):
return gr._loss(self.X_sphere, self.y_sphere, param,
self.shape_sphere)
objective_with_grad = gs.autodiff.value_and_grad(loss_of_param,
to_numpy=True)
initial_guess = gs.flatten(self.param_sphere_guess)
res = minimize(
objective_with_grad,
initial_guess,
method="CG",
jac=True,
tol=10 * gs.atol,
options={
"disp": True,
"maxiter": 50
},
)
self.assertAllClose(
gs.array(res.x).shape, ((self.dim_sphere + 1) * 2, ))
self.assertAllClose(res.fun, 0.0, atol=5e-3)
# Cast required because minimization happens in scipy in float64
param_hat = gs.cast(gs.array(res.x), self.param_sphere_true.dtype)
intercept_hat, coef_hat = gs.split(param_hat, 2)
intercept_hat = self.sphere.projection(intercept_hat)
coef_hat = self.sphere.to_tangent(coef_hat, intercept_hat)
self.assertAllClose(intercept_hat,
self.intercept_sphere_true,
atol=5e-2)
tangent_vec_of_transport = self.sphere.metric.log(
self.intercept_sphere_true, base_point=intercept_hat)
transported_coef_hat = self.sphere.metric.parallel_transport(
tangent_vec=coef_hat,
base_point=intercept_hat,
direction=tangent_vec_of_transport,
)
self.assertAllClose(transported_coef_hat,
self.coef_sphere_true,
atol=0.6)
@geomstats.tests.autograd_and_tf_only
def test_loss_minimization_extrinsic_se2(self):
gr = GeodesicRegression(
self.se2,
metric=self.metric_se2,
center_X=False,
method="extrinsic",
max_iter=50,
init_step_size=0.1,
verbose=True,
)
def loss_of_param(param):
return gr._loss(self.X_se2, self.y_se2, param, self.shape_se2)
objective_with_grad = gs.autodiff.value_and_grad(loss_of_param,
to_numpy=True)
res = minimize(
objective_with_grad,
gs.flatten(self.param_se2_guess),
method="CG",
jac=True,
options={
"disp": True,
"maxiter": 50
},
)
self.assertAllClose(gs.array(res.x).shape, (18, ))
self.assertAllClose(res.fun, 0.0, atol=1e-6)
# Cast required because minimization happens in scipy in float64
param_hat = gs.cast(gs.array(res.x), self.param_se2_true.dtype)
intercept_hat, coef_hat = gs.split(param_hat, 2)
intercept_hat = gs.reshape(intercept_hat, self.shape_se2)
coef_hat = gs.reshape(coef_hat, self.shape_se2)
intercept_hat = self.se2.projection(intercept_hat)
coef_hat = self.se2.to_tangent(coef_hat, intercept_hat)
self.assertAllClose(intercept_hat, self.intercept_se2_true, atol=1e-4)
tangent_vec_of_transport = self.se2.metric.log(
self.intercept_se2_true, base_point=intercept_hat)
transported_coef_hat = self.se2.metric.parallel_transport(
tangent_vec=coef_hat,
base_point=intercept_hat,
direction=tangent_vec_of_transport,
)
self.assertAllClose(transported_coef_hat, self.coef_se2_true, atol=0.6)
@geomstats.tests.autograd_tf_and_torch_only
def test_fit_extrinsic_euclidean(self):
gr = GeodesicRegression(
self.eucl,
metric=self.eucl.metric,
center_X=False,
method="extrinsic",
max_iter=50,
init_step_size=0.1,
verbose=True,
initialization="random",
regularization=0.9,
)
gr.fit(self.X_eucl, self.y_eucl, compute_training_score=True)
training_score = gr.training_score_
intercept_hat, coef_hat = gr.intercept_, gr.coef_
self.assertAllClose(intercept_hat.shape, self.shape_eucl)
self.assertAllClose(coef_hat.shape, self.shape_eucl)
self.assertAllClose(training_score, 1.0, atol=500 * gs.atol)
self.assertAllClose(intercept_hat, self.intercept_eucl_true)
tangent_vec_of_transport = self.eucl.metric.log(
self.intercept_eucl_true, base_point=intercept_hat)
transported_coef_hat = self.eucl.metric.parallel_transport(
tangent_vec=coef_hat,
base_point=intercept_hat,
direction=tangent_vec_of_transport,
)
self.assertAllClose(transported_coef_hat, self.coef_eucl_true)
@geomstats.tests.autograd_tf_and_torch_only
def test_fit_extrinsic_hypersphere(self):
gr = GeodesicRegression(
self.sphere,
metric=self.sphere.metric,
center_X=False,
method="extrinsic",
max_iter=50,
init_step_size=0.1,
verbose=True,
initialization="random",
regularization=0.9,
)
gr.fit(self.X_sphere, self.y_sphere, compute_training_score=True)
training_score = gr.training_score_
intercept_hat, coef_hat = gr.intercept_, gr.coef_
self.assertAllClose(intercept_hat.shape, self.shape_sphere)
self.assertAllClose(coef_hat.shape, self.shape_sphere)
self.assertAllClose(training_score, 1.0, atol=500 * gs.atol)
self.assertAllClose(intercept_hat,
self.intercept_sphere_true,
atol=5e-3)
tangent_vec_of_transport = self.sphere.metric.log(
self.intercept_sphere_true, base_point=intercept_hat)
transported_coef_hat = self.sphere.metric.parallel_transport(
tangent_vec=coef_hat,
base_point=intercept_hat,
direction=tangent_vec_of_transport,
)
self.assertAllClose(transported_coef_hat,
self.coef_sphere_true,
atol=0.6)
@geomstats.tests.autograd_and_tf_only
def test_fit_extrinsic_se2(self):
gr = GeodesicRegression(
self.se2,
metric=self.metric_se2,
center_X=False,
method="extrinsic",
max_iter=50,
init_step_size=0.1,
verbose=True,
initialization="warm_start",
)
gr.fit(self.X_se2, self.y_se2, compute_training_score=True)
intercept_hat, coef_hat = gr.intercept_, gr.coef_
training_score = gr.training_score_
self.assertAllClose(intercept_hat.shape, self.shape_se2)
self.assertAllClose(coef_hat.shape, self.shape_se2)
self.assertTrue(gs.isclose(training_score, 1.0))
self.assertAllClose(intercept_hat, self.intercept_se2_true, atol=1e-4)
tangent_vec_of_transport = self.se2.metric.log(
self.intercept_se2_true, base_point=intercept_hat)
transported_coef_hat = self.se2.metric.parallel_transport(
tangent_vec=coef_hat,
base_point=intercept_hat,
direction=tangent_vec_of_transport,
)
self.assertAllClose(transported_coef_hat, self.coef_se2_true, atol=0.6)
@geomstats.tests.autograd_tf_and_torch_only
def test_fit_riemannian_euclidean(self):
gr = GeodesicRegression(
self.eucl,
metric=self.eucl.metric,
center_X=False,
method="riemannian",
max_iter=50,
init_step_size=0.1,
verbose=True,
)
gr.fit(self.X_eucl, self.y_eucl, compute_training_score=True)
intercept_hat, coef_hat = gr.intercept_, gr.coef_
training_score = gr.training_score_
self.assertAllClose(intercept_hat.shape, self.shape_eucl)
self.assertAllClose(coef_hat.shape, self.shape_eucl)
self.assertAllClose(training_score, 1.0, atol=0.1)
self.assertAllClose(intercept_hat, self.intercept_eucl_true)
tangent_vec_of_transport = self.eucl.metric.log(
self.intercept_eucl_true, base_point=intercept_hat)
transported_coef_hat = self.eucl.metric.parallel_transport(
tangent_vec=coef_hat,
base_point=intercept_hat,
direction=tangent_vec_of_transport,
)
self.assertAllClose(transported_coef_hat,
self.coef_eucl_true,
atol=1e-2)
@geomstats.tests.autograd_tf_and_torch_only
def test_fit_riemannian_hypersphere(self):
gr = GeodesicRegression(
self.sphere,
metric=self.sphere.metric,
center_X=False,
method="riemannian",
max_iter=50,
init_step_size=0.1,
verbose=True,
)
gr.fit(self.X_sphere, self.y_sphere, compute_training_score=True)
intercept_hat, coef_hat = gr.intercept_, gr.coef_
training_score = gr.training_score_
self.assertAllClose(intercept_hat.shape, self.shape_sphere)
self.assertAllClose(coef_hat.shape, self.shape_sphere)
self.assertAllClose(training_score, 1.0, atol=0.1)
self.assertAllClose(intercept_hat,
self.intercept_sphere_true,
atol=1e-2)
tangent_vec_of_transport = self.sphere.metric.log(
self.intercept_sphere_true, base_point=intercept_hat)
transported_coef_hat = self.sphere.metric.parallel_transport(
tangent_vec=coef_hat,
base_point=intercept_hat,
direction=tangent_vec_of_transport,
)
self.assertAllClose(transported_coef_hat,
self.coef_sphere_true,
atol=0.6)
@geomstats.tests.autograd_and_tf_only
def test_fit_riemannian_se2(self):
init = (self.y_se2[0], gs.zeros_like(self.y_se2[0]))
gr = GeodesicRegression(
self.se2,
metric=self.metric_se2,
center_X=False,
method="riemannian",
max_iter=50,
init_step_size=0.1,
verbose=True,
initialization=init,
)
gr.fit(self.X_se2, self.y_se2, compute_training_score=True)
intercept_hat, coef_hat = gr.intercept_, gr.coef_
training_score = gr.training_score_
self.assertAllClose(intercept_hat.shape, self.shape_se2)
self.assertAllClose(coef_hat.shape, self.shape_se2)
self.assertAllClose(training_score, 1.0, atol=1e-4)
self.assertAllClose(intercept_hat, self.intercept_se2_true, atol=1e-4)
tangent_vec_of_transport = self.se2.metric.log(
self.intercept_se2_true, base_point=intercept_hat)
transported_coef_hat = self.se2.metric.parallel_transport(
tangent_vec=coef_hat,
base_point=intercept_hat,
direction=tangent_vec_of_transport,
)
self.assertAllClose(transported_coef_hat, self.coef_se2_true, atol=0.6)
class TestSpecialEuclidean(geomstats.tests.TestCase):
def setUp(self):
gs.random.seed(12)
self.n = 2
self.group = SpecialEuclidean(n=self.n)
self.n_samples = 3
self.point = self.group.random_point(self.n_samples)
self.tangent_vec = self.group.to_tangent(
gs.random.rand(self.n_samples, self.group.n + 1, self.group.n + 1),
self.point)
def test_belongs(self):
theta = gs.pi / 3
point_1 = gs.array([[gs.cos(theta), -gs.sin(theta), 2.],
[gs.sin(theta), gs.cos(theta), 3.], [0., 0., 1.]])
result = self.group.belongs(point_1)
self.assertTrue(result)
point_2 = gs.array([[gs.cos(theta), -gs.sin(theta), 2.],
[gs.sin(theta), gs.cos(theta), 3.], [0., 0., 0.]])
result = self.group.belongs(point_2)
self.assertFalse(result)
point = gs.array([point_1, point_2])
expected = gs.array([True, False])
result = self.group.belongs(point)
self.assertAllClose(result, expected)
point = point_1[0]
result = self.group.belongs(point)
self.assertFalse(result)
point = gs.zeros((2, 3))
result = self.group.belongs(point)
self.assertFalse(result)
point = gs.zeros((2, 2, 3))
result = self.group.belongs(point)
self.assertFalse(gs.all(result))
self.assertAllClose(result.shape, (2, ))
def test_random_point_and_belongs(self):
point = self.group.random_point()
result = self.group.belongs(point)
self.assertTrue(result)
point = self.group.random_point(self.n_samples)
result = self.group.belongs(point)
expected = gs.array([True] * self.n_samples)
self.assertAllClose(result, expected)
def test_identity(self):
result = self.group.identity
expected = gs.eye(self.n + 1)
self.assertAllClose(result, expected)
def test_is_tangent(self):
theta = gs.pi / 3
vec_1 = gs.array([[0., -theta, 2.], [theta, 0., 3.], [0., 0., 0.]])
point = self.group.random_point()
tangent_vec = self.group.compose(point, vec_1)
result = self.group.is_tangent(tangent_vec, point)
self.assertTrue(result)
vec_2 = gs.array([[0., -theta, 2.], [theta, 0., 3.], [0., 0., 1.]])
tangent_vec = self.group.compose(point, vec_2)
result = self.group.is_tangent(tangent_vec, point)
self.assertFalse(result)
vec = gs.array([vec_1, vec_2])
expected = gs.array([True, False])
result = self.group.is_tangent(vec)
self.assertAllClose(result, expected)
def test_to_tangent_vec_vectorization(self):
n = self.group.n
tangent_vecs = gs.arange(self.n_samples * (n + 1)**2)
tangent_vecs = gs.cast(tangent_vecs, gs.float32)
tangent_vecs = gs.reshape(tangent_vecs,
(self.n_samples, ) + (n + 1, ) * 2)
point = self.group.random_point(self.n_samples)
tangent_vecs = Matrices.mul(point, tangent_vecs)
regularized = self.group.to_tangent(tangent_vecs, point)
result = Matrices.mul(
Matrices.transpose(point), regularized) + \
Matrices.mul(Matrices.transpose(regularized), point)
result = result[:, :n, :n]
expected = gs.zeros_like(result)
self.assertAllClose(result, expected)
def test_compose_and_inverse_matrix_form(self):
point = self.group.random_point()
inv_point = self.group.inverse(point)
result = self.group.compose(point, inv_point)
expected = self.group.identity
self.assertAllClose(result, expected)
if not geomstats.tests.tf_backend():
result = self.group.compose(inv_point, point)
expected = self.group.identity
self.assertAllClose(result, expected)
def test_compose_vectorization(self):
n_samples = self.n_samples
n_points_a = self.group.random_point(n_samples=n_samples)
n_points_b = self.group.random_point(n_samples=n_samples)
one_point = self.group.random_point(n_samples=1)
result = self.group.compose(one_point, n_points_a)
self.assertAllClose(gs.shape(result),
(n_samples, ) + (self.group.n + 1, ) * 2)
result = self.group.compose(n_points_a, one_point)
if not geomstats.tests.tf_backend():
self.assertAllClose(gs.shape(result),
(n_samples, ) + (self.group.n + 1, ) * 2)
result = self.group.compose(n_points_a, n_points_b)
self.assertAllClose(gs.shape(result),
(n_samples, ) + (self.group.n + 1, ) * 2)
def test_inverse_vectorization(self):
n_samples = self.n_samples
points = self.group.random_point(n_samples=n_samples)
result = self.group.inverse(points)
self.assertAllClose(gs.shape(result),
(n_samples, ) + (self.group.n + 1, ) * 2)
def test_compose_matrix_form(self):
point = self.group.random_point()
result = self.group.compose(point, self.group.identity)
expected = point
self.assertAllClose(result, expected)
if not geomstats.tests.tf_backend():
# Composition by identity, on the left
# Expect the original transformation
result = self.group.compose(self.group.identity, point)
expected = point
self.assertAllClose(result, expected)
# Composition of translations (no rotational part)
# Expect the sum of the translations
point_a = gs.array([[1., 0., 1.], [0., 1., 1.5], [0., 0., 1.]])
point_b = gs.array([[1., 0., 2.], [0., 1., 2.5], [0., 0., 1.]])
result = self.group.compose(point_a, point_b)
last_line_0 = gs.array_from_sparse([(0, 2), (1, 2)], [1., 1.],
(3, 3))
expected = point_a + point_b * last_line_0
self.assertAllClose(result, expected)
def test_left_exp_coincides(self):
vector_group = SpecialEuclidean(n=2, point_type='vector')
theta = gs.pi / 3
initial_vec = gs.array([theta, 2., 2.])
initial_matrix_vec = self.group.lie_algebra.matrix_representation(
initial_vec)
vector_exp = vector_group.left_canonical_metric.exp(initial_vec)
result = self.group.left_canonical_metric.exp(initial_matrix_vec)
expected = vector_group.matrix_from_vector(vector_exp)
self.assertAllClose(result, expected)
def test_right_exp_coincides(self):
vector_group = SpecialEuclidean(n=2, point_type='vector')
theta = gs.pi / 2
initial_vec = gs.array([theta, 1., 1.])
initial_matrix_vec = self.group.lie_algebra.matrix_representation(
initial_vec)
vector_exp = vector_group.right_canonical_metric.exp(initial_vec)
result = self.group.right_canonical_metric.exp(initial_matrix_vec,
n_steps=25)
expected = vector_group.matrix_from_vector(vector_exp)
self.assertAllClose(result, expected, atol=1e-6)
def test_basis_belongs(self):
lie_algebra = self.group.lie_algebra
result = lie_algebra.belongs(lie_algebra.basis)
self.assertTrue(gs.all(result))
def test_basis_has_the_right_dimension(self):
for n in range(2, 5):
algebra = SpecialEuclideanMatrixLieAlgebra(n)
self.assertEqual(int(n * (n + 1) / 2), algebra.dim)
def test_belongs_lie_algebra(self):
theta = gs.pi / 3
vec_1 = gs.array([[0., -theta, 2.], [theta, 0., 3.], [0., 0., 0.]])
result = self.group.lie_algebra.belongs(vec_1)
expected = True
self.assertAllClose(result, expected)
vec_2 = gs.array([[0., -theta, 2.], [theta, 0., 3.], [0., 0., 1.]])
result = self.group.lie_algebra.belongs(vec_2)
expected = False
self.assertAllClose(result, expected)
vec = gs.array([vec_1, vec_2])
expected = gs.array([True, False])
result = self.group.lie_algebra.belongs(vec)
self.assertAllClose(result, expected)
def test_basis_representation_is_correctly_vectorized(self):
for n in range(2, 5):
algebra = SpecialEuclideanMatrixLieAlgebra(n)
shape = gs.shape(algebra.basis_representation(algebra.basis))
dim = int(n * (n + 1) / 2)
self.assertAllClose(shape, (dim, dim))
def test_left_metric_wrong_group(self):
group = self.group.rotations
self.assertRaises(
ValueError,
lambda: SpecialEuclideanMatrixCannonicalLeftMetric(group))
group = SpecialEuclidean(3, point_type='vector')
self.assertRaises(
ValueError,
lambda: SpecialEuclideanMatrixCannonicalLeftMetric(group))
def test_exp_and_belongs(self):
exp = self.group.left_canonical_metric.exp(self.tangent_vec,
self.point)
result = self.group.belongs(exp)
self.assertTrue(gs.all(result))
exp = self.group.left_canonical_metric.exp(self.tangent_vec[0],
self.point[0])
result = self.group.belongs(exp)
self.assertTrue(result)
@geomstats.tests.np_and_tf_only
def test_log_and_is_tan(self):
exp = self.group.left_canonical_metric.exp(self.tangent_vec,
self.point)
log = self.group.left_canonical_metric.log(exp, self.point)
result = self.group.is_tangent(log, self.point)
self.assertTrue(gs.all(result))
exp = self.group.left_canonical_metric.exp(self.tangent_vec[0],
self.point[0])
log = self.group.left_canonical_metric.log(exp, self.point)
result = self.group.is_tangent(log, self.point)
self.assertTrue(gs.all(result))
log = self.group.left_canonical_metric.log(exp, self.point[0])
result = self.group.is_tangent(log, self.point[0])
self.assertTrue(result)
@geomstats.tests.np_and_tf_only
def test_exp_log(self):
exp = self.group.left_canonical_metric.exp(self.tangent_vec,
self.point)
result = self.group.left_canonical_metric.log(exp, self.point)
self.assertAllClose(result, self.tangent_vec)
exp = self.group.left_canonical_metric.exp(self.tangent_vec[0],
self.point[0])
result = self.group.left_canonical_metric.log(exp, self.point[0])
self.assertAllClose(result, self.tangent_vec[0])
def test_parallel_transport(self):
metric = self.group.left_canonical_metric
shape = (self.n_samples, self.group.n + 1, self.group.n + 1)
results = helper.test_parallel_transport(self.group, metric, shape)
for res in results:
self.assertTrue(res)
def test_lie_algebra_basis_belongs(self):
basis = self.group.lie_algebra.basis
result = self.group.lie_algebra.belongs(basis)
self.assertTrue(gs.all(result))
def test_lie_algebra_projection_and_belongs(self):
vec = gs.random.rand(self.n_samples, self.group.n + 1,
self.group.n + 1)
tangent_vec = self.group.lie_algebra.projection(vec)
result = self.group.lie_algebra.belongs(tangent_vec)
self.assertTrue(gs.all(result))
def test_basis_representation(self):
vec = gs.random.rand(self.n_samples, self.group.dim)
tangent_vec = self.group.lie_algebra.matrix_representation(vec)
result = self.group.lie_algebra.basis_representation(tangent_vec)
self.assertAllClose(result, vec)
result = self.group.lie_algebra.basis_representation(tangent_vec[0])
self.assertAllClose(result, vec[0])
def test_metrics_expected_point_type(self):
left = self.group.left_canonical_metric
right = self.group.right_canonical_metric
metric = self.group.metric
for m in [left, right, metric]:
self.assertTrue(m.default_point_type == 'matrix')
def test_metric_left_invariant(self):
group = self.group
point = group.random_point()
expected = group.left_canonical_metric.norm(self.tangent_vec)
translated = group.tangent_translation_map(point)(self.tangent_vec)
result = group.left_canonical_metric.norm(translated)
self.assertAllClose(result, expected)
def test_projection_and_belongs(self):
shape = (self.n_samples, self.n + 1, self.n + 1)
result = helper.test_projection_and_belongs(self.group, shape)
for res in result:
self.assertTrue(res)
class TestSpecialEuclidean(geomstats.tests.TestCase):
def setUp(self):
self.n = 2
self.group = SpecialEuclidean(n=self.n)
self.n_samples = 4
def test_belongs(self):
theta = gs.pi / 3
point_1 = gs.array([[gs.cos(theta), -gs.sin(theta), 2.],
[gs.sin(theta), gs.cos(theta), 3.], [0., 0., 1.]])
result = self.group.belongs(point_1)
expected = True
self.assertAllClose(result, expected)
point_2 = gs.array([[gs.cos(theta), -gs.sin(theta), 2.],
[gs.sin(theta), gs.cos(theta), 3.], [0., 0., 0.]])
result = self.group.belongs(point_2)
expected = False
self.assertAllClose(result, expected)
point = gs.array([point_1, point_2])
expected = gs.array([True, False])
result = self.group.belongs(point)
self.assertAllClose(result, expected)
def test_random_uniform_and_belongs(self):
point = self.group.random_uniform()
result = self.group.belongs(point)
expected = True
self.assertAllClose(result, expected)
point = self.group.random_uniform(self.n_samples)
result = self.group.belongs(point)
expected = gs.array([True] * self.n_samples)
self.assertAllClose(result, expected)
def test_identity(self):
result = self.group.identity
expected = gs.eye(self.n + 1)
self.assertAllClose(result, expected)
def test_is_in_lie_algebra(self):
theta = gs.pi / 3
vec_1 = gs.array([[0., -theta, 2.], [theta, 0., 3.], [0., 0., 0.]])
result = self.group.is_tangent(vec_1)
expected = True
self.assertAllClose(result, expected)
vec_2 = gs.array([[0., -theta, 2.], [theta, 0., 3.], [0., 0., 1.]])
result = self.group.is_tangent(vec_2)
expected = False
self.assertAllClose(result, expected)
vec = gs.array([vec_1, vec_2])
expected = gs.array([True, False])
result = self.group.is_tangent(vec)
self.assertAllClose(result, expected)
def test_to_tangent_vec_vectorization(self):
n = self.group.n
tangent_vecs = gs.arange(self.n_samples * (n + 1)**2)
tangent_vecs = gs.cast(tangent_vecs, gs.float32)
tangent_vecs = gs.reshape(tangent_vecs,
(self.n_samples, ) + (n + 1, ) * 2)
point = self.group.random_uniform(self.n_samples)
tangent_vecs = self.group.compose(point, tangent_vecs)
regularized = self.group.to_tangent(tangent_vecs, point)
result = self.group.compose(
self.group.transpose(point), regularized) + \
self.group.compose(self.group.transpose(regularized), point)
result = result[:, :n, :n]
expected = gs.zeros_like(result)
self.assertAllClose(result, expected)
def test_compose_and_inverse_matrix_form(self):
point = self.group.random_uniform()
inv_point = self.group.inverse(point)
result = self.group.compose(point, inv_point)
expected = self.group.identity
self.assertAllClose(result, expected)
if not geomstats.tests.tf_backend():
result = self.group.compose(inv_point, point)
expected = self.group.identity
self.assertAllClose(result, expected)
def test_compose_vectorization(self):
n_samples = self.n_samples
n_points_a = self.group.random_uniform(n_samples=n_samples)
n_points_b = self.group.random_uniform(n_samples=n_samples)
one_point = self.group.random_uniform(n_samples=1)
result = self.group.compose(one_point, n_points_a)
self.assertAllClose(gs.shape(result),
(n_samples, ) + (self.group.n + 1, ) * 2)
result = self.group.compose(n_points_a, one_point)
if not geomstats.tests.tf_backend():
self.assertAllClose(gs.shape(result),
(n_samples, ) + (self.group.n + 1, ) * 2)
result = self.group.compose(n_points_a, n_points_b)
self.assertAllClose(gs.shape(result),
(n_samples, ) + (self.group.n + 1, ) * 2)
def test_inverse_vectorization(self):
n_samples = self.n_samples
points = self.group.random_uniform(n_samples=n_samples)
result = self.group.inverse(points)
self.assertAllClose(gs.shape(result),
(n_samples, ) + (self.group.n + 1, ) * 2)
def test_compose_matrix_form(self):
point = self.group.random_uniform()
result = self.group.compose(point, self.group.identity)
expected = point
self.assertAllClose(result, expected)
if not geomstats.tests.tf_backend():
# Composition by identity, on the left
# Expect the original transformation
result = self.group.compose(self.group.identity, point)
expected = point
self.assertAllClose(result, expected)
# Composition of translations (no rotational part)
# Expect the sum of the translations
point_a = gs.array([[1., 0., 1.], [0., 1., 1.5], [0., 0., 1.]])
point_b = gs.array([[1., 0., 2.], [0., 1., 2.5], [0., 0., 1.]])
result = self.group.compose(point_a, point_b)
last_line_0 = gs.array_from_sparse([(0, 2), (1, 2)], [1., 1.],
(3, 3))
expected = point_a + point_b * last_line_0
self.assertAllClose(result, expected)
