def test_exp_and_belongs(self):
H2 = Hyperbolic(dimension=2)
METRIC = H2.metric
base_point = gs.array([1., 0., 0.])
with self.session():
self.assertTrue(gs.eval(H2.belongs(base_point)))
tangent_vec = H2.projection_to_tangent_space(vector=gs.array(
[1., 2., 1.]),
base_point=base_point)
exp = METRIC.exp(tangent_vec=tangent_vec, base_point=base_point)
with self.session():
self.assertTrue(gs.eval(H2.belongs(exp)))
class TestFrechetMean(geomstats.tests.TestCase):
_multiprocess_can_split_ = True
def setUp(self):
self.sphere = Hypersphere(dimension=4)
self.hyperbolic = Hyperbolic(dimension=3)
self.euclidean = Euclidean(dimension=2)
self.minkowski = Minkowski(dimension=2)
@geomstats.tests.np_only
def test_adaptive_gradient_descent_sphere(self):
n_tests = 100
result = gs.zeros(n_tests)
expected = gs.zeros(n_tests)
for i in range(n_tests):
# take 2 random points, compute their mean, and verify that
# log of each at the mean is opposite
points = self.sphere.random_uniform(n_samples=2)
mean = _adaptive_gradient_descent(points=points,
metric=self.sphere.metric)
logs = self.sphere.metric.log(point=points, base_point=mean)
result[i] = gs.linalg.norm(logs[1, :] + logs[0, :])
self.assertAllClose(expected, result, rtol=1e-10, atol=1e-10)
@geomstats.tests.np_and_pytorch_only
def test_estimate_and_belongs_sphere(self):
point_a = gs.array([1., 0., 0., 0., 0.])
point_b = gs.array([0., 1., 0., 0., 0.])
points = gs.zeros((2, point_a.shape[0]))
points[0, :] = point_a
points[1, :] = point_b
mean = FrechetMean(metric=self.sphere.metric)
mean.fit(points)
result = self.sphere.belongs(mean.estimate_)
expected = gs.array([[True]])
self.assertAllClose(result, expected)
@geomstats.tests.np_and_pytorch_only
def test_variance_sphere(self):
point = gs.array([0., 0., 0., 0., 1.])
points = gs.zeros((2, point.shape[0]))
points[0, :] = point
points[1, :] = point
result = variance(points, base_point=point, metric=self.sphere.metric)
expected = helper.to_scalar(0.)
self.assertAllClose(expected, result)
@geomstats.tests.np_and_pytorch_only
def test_estimate_sphere(self):
point = gs.array([0., 0., 0., 0., 1.])
points = gs.zeros((2, point.shape[0]))
points[0, :] = point
points[1, :] = point
mean = FrechetMean(metric=self.sphere.metric)
mean.fit(X=points)
result = mean.estimate_
expected = helper.to_vector(point)
self.assertAllClose(expected, result)
@geomstats.tests.np_and_tf_only
def test_variance_hyperbolic(self):
point = gs.array([2., 1., 1., 1.])
points = gs.array([point, point])
result = variance(points,
base_point=point,
metric=self.hyperbolic.metric)
expected = helper.to_scalar(0.)
self.assertAllClose(result, expected)
@geomstats.tests.np_and_tf_only
def test_estimate_hyperbolic(self):
point = gs.array([2., 1., 1., 1.])
points = gs.array([point, point])
mean = FrechetMean(metric=self.hyperbolic.metric)
mean.fit(X=points)
result = mean.estimate_
expected = helper.to_vector(point)
self.assertAllClose(result, expected)
@geomstats.tests.np_and_tf_only
def test_estimate_and_belongs_hyperbolic(self):
point_a = self.hyperbolic.random_uniform()
point_b = self.hyperbolic.random_uniform()
point_c = self.hyperbolic.random_uniform()
points = gs.concatenate([point_a, point_b, point_c], axis=0)
mean = FrechetMean(metric=self.hyperbolic.metric)
mean.fit(X=points)
result = self.hyperbolic.belongs(mean.estimate_)
expected = gs.array([[True]])
self.assertAllClose(result, expected)
def test_mean_euclidean(self):
point = gs.array([[1., 4.]])
mean = FrechetMean(metric=self.euclidean.metric)
points = [point, point, point]
mean.fit(points)
result = mean.estimate_
expected = point
expected = helper.to_vector(expected)
self.assertAllClose(result, expected)
points = gs.array([[1., 2.], [2., 3.], [3., 4.], [4., 5.]])
weights = gs.array([1., 2., 1., 2.])
mean = FrechetMean(metric=self.euclidean.metric)
mean.fit(points, weights=weights)
result = mean.estimate_
expected = gs.array([16. / 6., 22. / 6.])
expected = helper.to_vector(expected)
self.assertAllClose(result, expected)
def test_variance_euclidean(self):
points = gs.array([[1., 2.], [2., 3.], [3., 4.], [4., 5.]])
weights = gs.array([1., 2., 1., 2.])
base_point = gs.zeros(2)
result = variance(points,
weights=weights,
base_point=base_point,
metric=self.euclidean.metric)
# we expect the average of the points' sq norms.
expected = (1 * 5. + 2 * 13. + 1 * 25. + 2 * 41.) / 6.
expected = helper.to_scalar(expected)
self.assertAllClose(result, expected)
def test_mean_minkowski(self):
point = gs.array([[2., -math.sqrt(3)]])
points = [point, point, point]
mean = FrechetMean(metric=self.minkowski.metric)
mean.fit(points)
result = mean.estimate_
expected = point
expected = helper.to_vector(expected)
self.assertAllClose(result, expected)
points = gs.array([[1., 0.], [2., math.sqrt(3)], [3., math.sqrt(8)],
[4., math.sqrt(24)]])
weights = gs.array([1., 2., 1., 2.])
mean = FrechetMean(metric=self.minkowski.metric)
mean.fit(points, weights=weights)
result = mean.estimate_
result = self.minkowski.belongs(result)
expected = gs.array([[True]])
self.assertAllClose(result, expected)
def test_variance_minkowski(self):
points = gs.array([[1., 0.], [2., math.sqrt(3)], [3., math.sqrt(8)],
[4., math.sqrt(24)]])
weights = gs.array([1., 2., 1., 2.])
base_point = gs.array([-1., 0.])
var = variance(points,
weights=weights,
base_point=base_point,
metric=self.minkowski.metric)
result = helper.to_scalar(var != 0)
# we expect the average of the points' Minkowski sq norms.
expected = helper.to_scalar(gs.array([True]))
self.assertAllClose(result, expected)
class TestHyperbolicMethods(geomstats.tests.TestCase):
def setUp(self):
gs.random.seed(1234)
self.dimension = 2
self.extrinsic_manifold = Hyperbolic(dimension=self.dimension)
self.ball_manifold = Hyperbolic(dimension=self.dimension,
point_type='ball')
self.intrinsic_manifold = Hyperbolic(dimension=self.dimension,
point_type='intrinsic')
self.half_plane_manifold = Hyperbolic(dimension=self.dimension,
point_type='half-plane')
self.ball_metric = HyperbolicMetric(dimension=self.dimension,
point_type='ball')
self.extrinsic_metric = HyperbolicMetric(dimension=self.dimension,
point_type='extrinsic')
self.n_samples = 10
@geomstats.tests.np_and_pytorch_only
def test_extrinsic_ball_extrinsic(self):
x_in = gs.array([[0.5, 7]])
x = self.intrinsic_manifold.to_coordinates(x_in,
to_point_type='extrinsic')
x_b = self.extrinsic_manifold.to_coordinates(x, to_point_type='ball')
x2 = self.ball_manifold.to_coordinates(x_b, to_point_type='extrinsic')
self.assertAllClose(x, x2, atol=1e-8)
@geomstats.tests.np_and_pytorch_only
def test_extrinsic_half_plane_extrinsic(self):
x_in = gs.array([[0.5, 7]])
x = self.intrinsic_manifold.to_coordinates(x_in,
to_point_type='extrinsic')
x_up = self.extrinsic_manifold.to_coordinates(
x, to_point_type='half-plane')
x2 = self.half_plane_manifold.to_coordinates(x_up,
to_point_type='extrinsic')
self.assertAllClose(x, x2, atol=1e-8)
@geomstats.tests.np_and_pytorch_only
def test_intrinsic_extrinsic_intrinsic(self):
x_intr = gs.array([[0.5, 7]])
x_extr = self.intrinsic_manifold.to_coordinates(
x_intr, to_point_type='extrinsic')
x_intr2 = self.extrinsic_manifold.to_coordinates(
x_extr, to_point_type='intrinsic')
self.assertAllClose(x_intr, x_intr2, atol=1e-8)
@geomstats.tests.np_and_pytorch_only
def test_ball_extrinsic_ball(self):
x = gs.array([[0.5, 0.2]])
x_e = self.ball_manifold.to_coordinates(x, to_point_type='extrinsic')
x2 = self.extrinsic_manifold.to_coordinates(x_e, to_point_type='ball')
self.assertAllClose(x, x2, atol=1e-10)
@geomstats.tests.np_and_pytorch_only
def test_belongs_ball(self):
x = gs.array([[0.5, 0.2]])
belong = self.ball_manifold.belongs(x)
assert (belong[0])
@geomstats.tests.np_and_pytorch_only
def test_distance_ball_extrinsic_from_ball(self):
x_ball = gs.array([[0.7, 0.2]])
y_ball = gs.array([[0.2, 0.2]])
x_extr = self.ball_manifold.to_coordinates(x_ball,
to_point_type='extrinsic')
y_extr = self.ball_manifold.to_coordinates(y_ball,
to_point_type='extrinsic')
dst_ball = self.ball_metric.dist(x_ball, y_ball)
dst_extr = self.extrinsic_metric.dist(x_extr, y_extr)
self.assertAllClose(dst_ball, dst_extr)
@geomstats.tests.np_and_pytorch_only
def test_distance_ball_extrinsic_from_extr(self):
x_int = gs.array([[10, 0.2]])
y_int = gs.array([[1, 6.]])
x_extr = self.intrinsic_manifold.to_coordinates(
x_int, to_point_type='extrinsic')
y_extr = self.intrinsic_manifold.to_coordinates(
y_int, to_point_type='extrinsic')
x_ball = self.extrinsic_manifold.to_coordinates(x_extr,
to_point_type='ball')
y_ball = self.extrinsic_manifold.to_coordinates(y_extr,
to_point_type='ball')
dst_ball = self.ball_metric.dist(x_ball, y_ball)
dst_extr = self.extrinsic_metric.dist(x_extr, y_extr)
self.assertAllClose(dst_ball, dst_extr)
@geomstats.tests.np_and_pytorch_only
def test_distance_ball_extrinsic_from_extr_5_dim(self):
x_int = gs.array([[10, 0.2, 3, 4]])
y_int = gs.array([[1, 6, 2., 1]])
extrinsic_manifold = Hyperbolic(4, point_type='extrinsic')
ball_metric = HyperbolicMetric(4, point_type='ball')
extrinsic_metric = HyperbolicMetric(4, point_type='extrinsic')
x_extr = extrinsic_manifold.from_coordinates(
x_int, from_point_type='intrinsic')
y_extr = extrinsic_manifold.from_coordinates(
y_int, from_point_type='intrinsic')
x_ball = extrinsic_manifold.to_coordinates(x_extr,
to_point_type='ball')
y_ball = extrinsic_manifold.to_coordinates(y_extr,
to_point_type='ball')
dst_ball = ball_metric.dist(x_ball, y_ball)
dst_extr = extrinsic_metric.dist(x_extr, y_extr)
self.assertAllClose(dst_ball, dst_extr)
@geomstats.tests.np_and_pytorch_only
def test_log_exp_ball_extrinsic_from_extr(self):
x_int = gs.array([[4., 0.2]])
y_int = gs.array([[3., 3]])
x_extr = self.intrinsic_manifold.to_coordinates(
x_int, to_point_type='extrinsic')
y_extr = self.intrinsic_manifold.to_coordinates(
y_int, to_point_type='extrinsic')
x_ball = self.extrinsic_manifold.to_coordinates(x_extr,
to_point_type='ball')
y_ball = self.extrinsic_manifold.to_coordinates(y_extr,
to_point_type='ball')
x_ball_log_exp = self.ball_metric.exp(
self.ball_metric.log(y_ball, x_ball), x_ball)
x_extr_a = self.extrinsic_metric.exp(
self.extrinsic_metric.log(y_extr, x_extr), x_extr)
x_extr_b = self.extrinsic_manifold.from_coordinates(
x_ball_log_exp, from_point_type='ball')
self.assertAllClose(x_extr_a, x_extr_b, atol=1e-4)
@geomstats.tests.np_and_pytorch_only
def test_log_exp_ball(self):
x = gs.array([[0.1, 0.2]])
y = gs.array([[0.2, 0.5]])
log = self.ball_metric.log(y, x)
exp = self.ball_metric.exp(log, x)
self.assertAllClose(exp, y)
@geomstats.tests.np_and_pytorch_only
def test_log_exp_ball_batch(self):
x = gs.array([[0.1, 0.2]])
y = gs.array([[0.2, 0.5], [0.1, 0.7]])
log = self.ball_metric.log(y, x)
exp = self.ball_metric.exp(log, x)
self.assertAllClose(exp, y)
class TestHyperbolicMethods(geomstats.tests.TestCase):
def setUp(self):
gs.random.seed(1234)
self.dimension = 3
self.space = Hyperbolic(dimension=self.dimension)
self.metric = self.space.metric
self.n_samples = 10
def test_random_uniform_and_belongs(self):
point = self.space.random_uniform()
result = self.space.belongs(point)
expected = gs.array([[True]])
self.assertAllClose(result, expected)
def test_random_uniform(self):
result = self.space.random_uniform()
self.assertAllClose(gs.shape(result), (1, self.dimension + 1))
def test_intrinsic_and_extrinsic_coords(self):
"""
Test that the composition of
intrinsic_to_extrinsic_coords and
extrinsic_to_intrinsic_coords
gives the identity.
"""
point_int = gs.ones(self.dimension)
point_ext = self.space.intrinsic_to_extrinsic_coords(point_int)
result = self.space.extrinsic_to_intrinsic_coords(point_ext)
expected = point_int
expected = helper.to_vector(expected)
self.assertAllClose(result, expected)
point_ext = gs.array([2.0, 1.0, 1.0, 1.0])
point_int = self.space.extrinsic_to_intrinsic_coords(point_ext)
result = self.space.intrinsic_to_extrinsic_coords(point_int)
expected = point_ext
expected = helper.to_vector(expected)
self.assertAllClose(result, expected)
def test_intrinsic_and_extrinsic_coords_vectorization(self):
"""
Test that the composition of
intrinsic_to_extrinsic_coords and
extrinsic_to_intrinsic_coords
gives the identity.
"""
point_int = gs.array([[.1, 0., 0., .1, 0., 0.],
[.1, .1, .1, .4, .1, 0.],
[.1, .3, 0., .1, 0., 0.],
[-0.1, .1, -.4, .1, -.01, 0.],
[0., 0., .1, .1, -0.08, -0.1],
[.1, .1, .1, .1, 0., -0.5]])
point_ext = self.space.intrinsic_to_extrinsic_coords(point_int)
result = self.space.extrinsic_to_intrinsic_coords(point_ext)
expected = point_int
expected = helper.to_vector(expected)
self.assertAllClose(result, expected)
point_ext = gs.array([[2., 1., 1., 1.],
[4., 1., 3., math.sqrt(5.)],
[3., 2., 0., 2.]])
point_int = self.space.extrinsic_to_intrinsic_coords(point_ext)
result = self.space.intrinsic_to_extrinsic_coords(point_int)
expected = point_ext
expected = helper.to_vector(expected)
self.assertAllClose(result, expected)
def test_log_and_exp_general_case(self):
"""
Test that the riemannian exponential
and the riemannian logarithm are inverse.
Expect their composition to give the identity function.
"""
# Riemannian Log then Riemannian Exp
# General case
base_point = gs.array([4.0, 1., 3.0, math.sqrt(5.)])
point = gs.array([2.0, 1.0, 1.0, 1.0])
log = self.metric.log(point=point, base_point=base_point)
result = self.metric.exp(tangent_vec=log, base_point=base_point)
expected = helper.to_vector(point)
self.assertAllClose(result, expected)
def test_exp_and_belongs(self):
H2 = Hyperbolic(dimension=2)
METRIC = H2.metric
base_point = gs.array([1., 0., 0.])
with self.session():
self.assertTrue(gs.eval(H2.belongs(base_point)))
tangent_vec = H2.projection_to_tangent_space(
vector=gs.array([1., 2., 1.]),
base_point=base_point)
exp = METRIC.exp(tangent_vec=tangent_vec,
base_point=base_point)
with self.session():
self.assertTrue(gs.eval(H2.belongs(exp)))
@geomstats.tests.np_and_pytorch_only
def test_exp_vectorization(self):
n_samples = 3
dim = self.dimension + 1
one_vec = gs.array([2.0, 1.0, 1.0, 1.0])
one_base_point = gs.array([4.0, 3., 1.0, math.sqrt(5)])
n_vecs = gs.array([[2., 1., 1., 1.],
[4., 1., 3., math.sqrt(5.)],
[3., 2., 0., 2.]])
n_base_points = gs.array([
[2.0, 0.0, 1.0, math.sqrt(2)],
[5.0, math.sqrt(8), math.sqrt(8), math.sqrt(8)],
[1.0, 0.0, 0.0, 0.0]])
one_tangent_vec = self.space.projection_to_tangent_space(
one_vec, base_point=one_base_point)
result = self.metric.exp(one_tangent_vec, one_base_point)
self.assertAllClose(gs.shape(result), (1, dim))
n_tangent_vecs = self.space.projection_to_tangent_space(
n_vecs, base_point=one_base_point)
result = self.metric.exp(n_tangent_vecs, one_base_point)
self.assertAllClose(gs.shape(result), (n_samples, dim))
expected = gs.zeros((n_samples, dim))
with self.session():
for i in range(n_samples):
expected[i] = gs.eval(
self.metric.exp(n_tangent_vecs[i], one_base_point))
expected = helper.to_vector(gs.array(expected))
self.assertAllClose(result, expected)
one_tangent_vec = self.space.projection_to_tangent_space(
one_vec, base_point=n_base_points)
result = self.metric.exp(one_tangent_vec, n_base_points)
self.assertAllClose(gs.shape(result), (n_samples, dim))
expected = gs.zeros((n_samples, dim))
with self.session():
for i in range(n_samples):
expected[i] = gs.eval(self.metric.exp(one_tangent_vec[i],
n_base_points[i]))
expected = helper.to_vector(gs.array(expected))
self.assertAllClose(result, expected)
n_tangent_vecs = self.space.projection_to_tangent_space(
n_vecs, base_point=n_base_points)
result = self.metric.exp(n_tangent_vecs, n_base_points)
self.assertAllClose(gs.shape(result), (n_samples, dim))
expected = gs.zeros((n_samples, dim))
with self.session():
for i in range(n_samples):
expected[i] = gs.eval(self.metric.exp(n_tangent_vecs[i],
n_base_points[i]))
expected = helper.to_vector(gs.array(expected))
self.assertAllClose(result, expected)
def test_log_vectorization(self):
n_samples = 3
dim = self.dimension + 1
one_point = gs.array([2.0, 1.0, 1.0, 1.0])
one_base_point = gs.array([4.0, 3., 1.0, math.sqrt(5)])
n_points = gs.array([[2.0, 1.0, 1.0, 1.0],
[4.0, 1., 3.0, math.sqrt(5)],
[3.0, 2.0, 0.0, 2.0]])
n_base_points = gs.array([
[2.0, 0.0, 1.0, math.sqrt(2)],
[5.0, math.sqrt(8), math.sqrt(8), math.sqrt(8)],
[1.0, 0.0, 0.0, 0.0]])
result = self.metric.log(one_point, one_base_point)
self.assertAllClose(gs.shape(result), (1, dim))
result = self.metric.log(n_points, one_base_point)
self.assertAllClose(gs.shape(result), (n_samples, dim))
result = self.metric.log(one_point, n_base_points)
self.assertAllClose(gs.shape(result), (n_samples, dim))
result = self.metric.log(n_points, n_base_points)
self.assertAllClose(gs.shape(result), (n_samples, dim))
def test_inner_product(self):
"""
Test that the inner product between two tangent vectors
is the Minkowski inner product.
"""
minkowski_space = Minkowski(self.dimension + 1)
base_point = gs.array(
[1.16563816, 0.36381045, -0.47000603, 0.07381469])
tangent_vec_a = self.space.projection_to_tangent_space(
vector=gs.array([10., 200., 1., 1.]),
base_point=base_point)
tangent_vec_b = self.space.projection_to_tangent_space(
vector=gs.array([11., 20., -21., 0.]),
base_point=base_point)
result = self.metric.inner_product(
tangent_vec_a, tangent_vec_b, base_point)
expected = minkowski_space.metric.inner_product(
tangent_vec_a, tangent_vec_b, base_point)
with self.session():
self.assertAllClose(result, expected)
def test_squared_norm_and_squared_dist(self):
"""
Test that the squared distance between two points is
the squared norm of their logarithm.
"""
point_a = gs.array([2.0, 1.0, 1.0, 1.0])
point_b = gs.array([4.0, 1., 3.0, math.sqrt(5)])
log = self.metric.log(point=point_a, base_point=point_b)
result = self.metric.squared_norm(vector=log)
expected = self.metric.squared_dist(point_a, point_b)
with self.session():
self.assertAllClose(result, expected)
def test_norm_and_dist(self):
"""
Test that the distance between two points is
the norm of their logarithm.
"""
point_a = gs.array([2.0, 1.0, 1.0, 1.0])
point_b = gs.array([4.0, 1., 3.0, math.sqrt(5)])
log = self.metric.log(point=point_a, base_point=point_b)
result = self.metric.norm(vector=log)
expected = self.metric.dist(point_a, point_b)
with self.session():
self.assertAllClose(result, expected)
def test_log_and_exp_edge_case(self):
"""
Test that the riemannian exponential
and the riemannian logarithm are inverse.
Expect their composition to give the identity function.
"""
# Riemannian Log then Riemannian Exp
# Edge case: two very close points, base_point_2 and point_2,
# form an angle < epsilon
base_point_intrinsic = gs.array([1., 2., 3.])
base_point = self.space.intrinsic_to_extrinsic_coords(
base_point_intrinsic)
point_intrinsic = (base_point_intrinsic +
1e-12 * gs.array([-1., -2., 1.]))
point = self.space.intrinsic_to_extrinsic_coords(
point_intrinsic)
log = self.metric.log(point=point, base_point=base_point)
result = self.metric.exp(tangent_vec=log, base_point=base_point)
expected = point
with self.session():
self.assertAllClose(result, expected)
@geomstats.tests.np_and_tf_only
def test_exp_and_log_and_projection_to_tangent_space_general_case(self):
"""
Test that the riemannian exponential
and the riemannian logarithm are inverse.
Expect their composition to give the identity function.
"""
# Riemannian Exp then Riemannian Log
# General case
base_point = gs.array([4.0, 1., 3.0, math.sqrt(5)])
vector = gs.array([2.0, 1.0, 1.0, 1.0])
vector = self.space.projection_to_tangent_space(
vector=vector,
base_point=base_point)
exp = self.metric.exp(tangent_vec=vector, base_point=base_point)
result = self.metric.log(point=exp, base_point=base_point)
expected = vector
with self.session():
self.assertAllClose(result, expected)
def test_dist(self):
# Distance between a point and itself is 0.
point_a = gs.array([4.0, 1., 3.0, math.sqrt(5)])
point_b = point_a
result = self.metric.dist(point_a, point_b)
expected = gs.array([[0]])
with self.session():
self.assertAllClose(result, expected)
@geomstats.tests.np_and_pytorch_only
def test_dist_poincare(self):
point_a = gs.array([0.5, 0.5])
point_b = gs.array([0.5, -0.5])
self.space.metric.point_type = 'ball'
dist_a_b = self.metric.dist(point_a, point_b)
self.space.metric.point_type = 'extrinsic'
result = dist_a_b
expected = gs.array([[2.887270927429199]])
with self.session():
self.assertAllClose(result, expected)
def test_exp_poincare(self):
self.space.metric.point_type = 'ball'
result = 0
expected = 0
self.space.metric.point_type = 'extrinsic'
with self.session():
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_log_poincare(self):
point = gs.array([0.3, 0.5])
base_point = gs.array([0.3, 0.3])
self.space.metric.point_type = 'ball'
result = self.space.metric.log(point, base_point)
expected = gs.array([-0.01733576, 0.21958634])
self.space.metric.point_type = 'extrinsic'
with self.session():
self.assertAllClose(result, expected)
def test_exp_and_dist_and_projection_to_tangent_space(self):
base_point = gs.array([4.0, 1., 3.0, math.sqrt(5)])
vector = gs.array([0.001, 0., -.00001, -.00003])
tangent_vec = self.space.projection_to_tangent_space(
vector=vector,
base_point=base_point)
exp = self.metric.exp(tangent_vec=tangent_vec,
base_point=base_point)
result = self.metric.dist(base_point, exp)
sq_norm = self.metric.embedding_metric.squared_norm(
tangent_vec)
expected = sq_norm
with self.session():
self.assertAllClose(result, expected, atol=1e-2)
def test_geodesic_and_belongs(self):
# TODO(nina): Fix this tests, as it fails when geodesic goes "too far"
initial_point = gs.array([4.0, 1., 3.0, math.sqrt(5)])
n_geodesic_points = 100
vector = gs.array([1., 0., 0., 0.])
initial_tangent_vec = self.space.projection_to_tangent_space(
vector=vector,
base_point=initial_point)
geodesic = self.metric.geodesic(
initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec)
t = gs.linspace(start=0., stop=1., num=n_geodesic_points)
points = geodesic(t)
result = self.space.belongs(points)
expected = gs.array(n_geodesic_points * [[True]])
with self.session():
self.assertAllClose(expected, result)
def test_exp_and_log_and_projection_to_tangent_space_edge_case(self):
"""
Test that the riemannian exponential and
the riemannian logarithm are inverse.
Expect their composition to give the identity function.
"""
# Riemannian Exp then Riemannian Log
# Edge case: tangent vector has norm < epsilon
base_point = gs.array([2., 1., 1., 1.])
vector = 1e-10 * gs.array([.06, -51., 6., 5.])
exp = self.metric.exp(tangent_vec=vector, base_point=base_point)
result = self.metric.log(point=exp, base_point=base_point)
expected = self.space.projection_to_tangent_space(
vector=vector,
base_point=base_point)
self.assertAllClose(result, expected, atol=1e-8)
@geomstats.tests.np_and_tf_only
def test_variance(self):
point = gs.array([2., 1., 1., 1.])
points = gs.array([point, point])
result = self.metric.variance(points)
expected = helper.to_scalar(0.)
self.assertAllClose(result, expected)
@geomstats.tests.np_and_tf_only
def test_mean(self):
point = gs.array([2., 1., 1., 1.])
points = gs.array([point, point])
result = self.metric.mean(points)
expected = helper.to_vector(point)
self.assertAllClose(result, expected)
@geomstats.tests.np_and_tf_only
def test_mean_and_belongs(self):
point_a = self.space.random_uniform()
point_b = self.space.random_uniform()
point_c = self.space.random_uniform()
points = gs.concatenate([point_a, point_b, point_c], axis=0)
mean = self.metric.mean(points)
result = self.space.belongs(mean)
expected = gs.array([[True]])
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_scaled_inner_product(self):
base_point_intrinsic = gs.array([1, 1, 1])
base_point = self.space.intrinsic_to_extrinsic_coords(
base_point_intrinsic)
tangent_vec_a = gs.array([1, 2, 3, 4])
tangent_vec_b = gs.array([5, 6, 7, 8])
tangent_vec_a = self.space.projection_to_tangent_space(
tangent_vec_a,
base_point)
tangent_vec_b = self.space.projection_to_tangent_space(
tangent_vec_b,
base_point)
scale = 2
default_space = Hyperbolic(dimension=self.dimension)
scaled_space = Hyperbolic(dimension=self.dimension, scale=2)
inner_product_default_metric = \
default_space.metric.inner_product(
tangent_vec_a,
tangent_vec_b,
base_point)
inner_product_scaled_metric = \
scaled_space.metric.inner_product(
tangent_vec_a,
tangent_vec_b,
base_point)
result = inner_product_scaled_metric
expected = scale ** 2 * inner_product_default_metric
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_scaled_squared_norm(self):
base_point_intrinsic = gs.array([1, 1, 1])
base_point = self.space.intrinsic_to_extrinsic_coords(
base_point_intrinsic)
tangent_vec = gs.array([1, 2, 3, 4])
tangent_vec = self.space.projection_to_tangent_space(
tangent_vec, base_point)
scale = 2
default_space = Hyperbolic(dimension=self.dimension)
scaled_space = Hyperbolic(dimension=self.dimension, scale=2)
squared_norm_default_metric = default_space.metric.squared_norm(
tangent_vec, base_point)
squared_norm_scaled_metric = scaled_space.metric.squared_norm(
tangent_vec, base_point)
result = squared_norm_scaled_metric
expected = scale ** 2 * squared_norm_default_metric
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_scaled_distance(self):
point_a_intrinsic = gs.array([1, 2, 3])
point_b_intrinsic = gs.array([4, 5, 6])
point_a = self.space.intrinsic_to_extrinsic_coords(point_a_intrinsic)
point_b = self.space.intrinsic_to_extrinsic_coords(point_b_intrinsic)
scale = 2
default_space = Hyperbolic(dimension=self.dimension)
scaled_space = Hyperbolic(dimension=self.dimension, scale=2)
distance_default_metric = default_space.metric.dist(point_a, point_b)
distance_scaled_metric = scaled_space.metric.dist(point_a, point_b)
result = distance_scaled_metric
expected = scale * distance_default_metric
self.assertAllClose(result, expected)
class TestHyperbolicMethods(geomstats.tests.TestCase):
def setUp(self):
gs.random.seed(1234)
self.dimension = 2
self.extrinsic_manifold = Hyperbolic(
dimension=self.dimension)
self.ball_manifold = Hyperbolic(
dimension=self.dimension, coords_type='ball')
self.intrinsic_manifold = Hyperbolic(
dimension=self.dimension, coords_type='intrinsic')
self.half_plane_manifold = Hyperbolic(
dimension=self.dimension, coords_type='half-plane')
self.ball_metric = HyperbolicMetric(
dimension=self.dimension, coords_type='ball')
self.extrinsic_metric = HyperbolicMetric(
dimension=self.dimension, coords_type='extrinsic')
self.n_samples = 10
@geomstats.tests.np_and_pytorch_only
def test_extrinsic_ball_extrinsic(self):
x_in = gs.array([[0.5, 7]])
x = self.intrinsic_manifold.to_coordinates(
x_in, to_coords_type='extrinsic')
x_b = self.extrinsic_manifold.to_coordinates(x, to_coords_type='ball')
x2 = self.ball_manifold.to_coordinates(x_b, to_coords_type='extrinsic')
self.assertAllClose(x, x2, atol=1e-8)
@geomstats.tests.np_and_pytorch_only
def test_belongs_intrinsic(self):
x_in = gs.array([[0.5, 7]])
is_in = self.intrinsic_manifold.belongs(x_in)
self.assertTrue(is_in)
@geomstats.tests.np_and_pytorch_only
def test_belongs_extrinsic(self):
x_true = self.intrinsic_manifold.to_coordinates(gs.array([[0.5, 7]]),
'extrinsic')
x_false = gs.array([[0.5, 7, 3.]])
is_in = self.extrinsic_manifold.belongs(x_true)
self.assertTrue(is_in)
is_out = self.extrinsic_manifold.belongs(x_false)
self.assertFalse(is_out)
@geomstats.tests.np_and_pytorch_only
def test_belongs_ball(self):
x_true = gs.array([[0.5, 0.5]])
x_false = gs.array([[0.8, 0.8]])
is_in = self.ball_manifold.belongs(x_true)
self.assertTrue(is_in)
is_out = self.ball_manifold.belongs(x_false)
self.assertFalse(is_out)
@geomstats.tests.np_and_pytorch_only
def test_belongs_half_plane(self):
x_true = gs.array([[0.5, 0.5]])
x_false = gs.array([[0.8, -0.8]])
is_in = self.half_plane_manifold.belongs(x_true)
self.assertTrue(is_in)
is_out = self.half_plane_manifold.belongs(x_false)
self.assertFalse(is_out)
@geomstats.tests.np_and_pytorch_only
def test_extrinsic_half_plane_extrinsic(self):
x_in = gs.array([[0.5, 7]])
x = self.intrinsic_manifold.to_coordinates(
x_in, to_coords_type='extrinsic')
x_up = self.extrinsic_manifold.to_coordinates(
x, to_coords_type='half-plane')
x2 = self.half_plane_manifold.to_coordinates(
x_up, to_coords_type='extrinsic')
self.assertAllClose(x, x2, atol=1e-8)
@geomstats.tests.np_and_pytorch_only
def test_intrinsic_extrinsic_intrinsic(self):
x_intr = gs.array([[0.5, 7]])
x_extr = self.intrinsic_manifold.to_coordinates(
x_intr, to_coords_type='extrinsic')
x_intr2 = self.extrinsic_manifold.to_coordinates(
x_extr, to_coords_type='intrinsic')
self.assertAllClose(x_intr, x_intr2, atol=1e-8)
@geomstats.tests.np_and_pytorch_only
def test_ball_extrinsic_ball(self):
x = gs.array([[0.5, 0.2]])
x_e = self.ball_manifold.to_coordinates(x, to_coords_type='extrinsic')
x2 = self.extrinsic_manifold.to_coordinates(x_e, to_coords_type='ball')
self.assertAllClose(x, x2, atol=1e-10)
@geomstats.tests.np_and_pytorch_only
def test_distance_ball_extrinsic_from_ball(self):
x_ball = gs.array([[0.7, 0.2]])
y_ball = gs.array([[0.2, 0.2]])
x_extr = self.ball_manifold.to_coordinates(
x_ball, to_coords_type='extrinsic')
y_extr = self.ball_manifold.to_coordinates(
y_ball, to_coords_type='extrinsic')
dst_ball = self.ball_metric.dist(x_ball, y_ball)
dst_extr = self.extrinsic_metric.dist(x_extr, y_extr)
self.assertAllClose(dst_ball, dst_extr)
@geomstats.tests.np_and_pytorch_only
def test_distance_ball_extrinsic_from_extr(self):
x_int = gs.array([[10, 0.2]])
y_int = gs.array([[1, 6.]])
x_extr = self.intrinsic_manifold.to_coordinates(
x_int, to_coords_type='extrinsic')
y_extr = self.intrinsic_manifold.to_coordinates(
y_int, to_coords_type='extrinsic')
x_ball = self.extrinsic_manifold.to_coordinates(
x_extr, to_coords_type='ball')
y_ball = self.extrinsic_manifold.to_coordinates(
y_extr, to_coords_type='ball')
dst_ball = self.ball_metric.dist(x_ball, y_ball)
dst_extr = self.extrinsic_metric.dist(x_extr, y_extr)
self.assertAllClose(dst_ball, dst_extr)
@geomstats.tests.np_and_pytorch_only
def test_distance_ball_extrinsic_from_extr_5_dim(self):
x_int = gs.array([[10, 0.2, 3, 4]])
y_int = gs.array([[1, 6, 2., 1]])
extrinsic_manifold = Hyperbolic(4, coords_type='extrinsic')
ball_metric = HyperbolicMetric(4, coords_type='ball')
extrinsic_metric = HyperbolicMetric(4, coords_type='extrinsic')
x_extr = extrinsic_manifold.from_coordinates(
x_int, from_coords_type='intrinsic')
y_extr = extrinsic_manifold.from_coordinates(
y_int, from_coords_type='intrinsic')
x_ball = extrinsic_manifold.to_coordinates(
x_extr, to_coords_type='ball')
y_ball = extrinsic_manifold.to_coordinates(
y_extr, to_coords_type='ball')
dst_ball = ball_metric.dist(x_ball, y_ball)
dst_extr = extrinsic_metric.dist(x_extr, y_extr)
self.assertAllClose(dst_ball, dst_extr)
@geomstats.tests.np_and_pytorch_only
def test_log_exp_ball_extrinsic_from_extr(self):
"""Compare log exp in different parameterizations."""
# TODO(Hazaatiti): Fix this test
# x_int = gs.array([[4., 0.2]])
# y_int = gs.array([[3., 3]])
# x_extr = self.intrinsic_manifold.to_coordinates(
# x_int, to_point_type='extrinsic')
# y_extr = self.intrinsic_manifold.to_coordinates(
# y_int, to_point_type='extrinsic')
# x_ball = self.extrinsic_manifold.to_coordinates(
# x_extr, to_point_type='ball')
# y_ball = self.extrinsic_manifold.to_coordinates(
# y_extr, to_point_type='ball')
# x_ball_log_exp = self.ball_metric.exp(
# self.ball_metric.log(y_ball, x_ball), x_ball)
# x_extr_a = self.extrinsic_metric.exp(
# self.extrinsic_metric.log(y_extr, x_extr), x_extr)
# x_extr_b = self.extrinsic_manifold.from_coordinates(
# x_ball_log_exp, from_point_type='ball')
# self.assertAllClose(x_extr_a, x_extr_b, atol=1e-4)
@geomstats.tests.np_only
def test_log_exp_ball(self):
x = gs.array([[0.1, 0.2]])
y = gs.array([[0.2, 0.5]])
log = self.ball_metric.log(point=y, base_point=x)
exp = self.ball_metric.exp(tangent_vec=log, base_point=x)
self.assertAllClose(exp, y, atol=1e-1)
@geomstats.tests.np_only
def test_log_exp_ball_vectorization(self):
x = gs.array([[0.1, 0.2]])
y = gs.array([[0.2, 0.5], [0.1, 0.7]])
log = self.ball_metric.log(y, x)
exp = self.ball_metric.exp(log, x)
self.assertAllClose(exp, y, atol=1e-1)
@geomstats.tests.np_only
def test_log_exp_ball_null_tangent(self):
x = gs.array([[0.1, 0.2], [0.1, 0.2]])
tangent_vec = gs.array([[0.0, 0.0], [0.0, 0.0]])
exp = self.ball_metric.exp(tangent_vec, x)
self.assertAllClose(exp, x, atol=1e-10)
