def scaled_dist_test_data(self):
space = Hyperboloid(3)
point_a = space.from_coordinates(gs.array([1.0, 2.0, 3.0]),
"intrinsic")
point_b = space.from_coordinates(gs.array([4.0, 5.0, 6.0]),
"intrinsic")
smoke_data = [dict(dim=3, scale=2, point_a=point_a, point_b=point_b)]
return self.generate_tests(smoke_data)
def product_distance_extrinsic_representation_test_data(self):
point_a_intrinsic = gs.array([0.01, 0.0])
point_b_intrinsic = gs.array([0.0, 0.0])
hyperbolic_space = Hyperboloid(dim=2)
point_a_extrinsic = hyperbolic_space.from_coordinates(
point_a_intrinsic, "intrinsic")
point_b_extrinsic = hyperbolic_space.from_coordinates(
point_b_intrinsic, "intrinsic")
smoke_data = [
dict(
n_disks=1,
point_a_extrinsic=point_a_extrinsic,
point_b_extrinsic=point_b_extrinsic,
)
]
return self.generate_tests(smoke_data)
def test_distance_ball_extrinsic_from_extr_4_dim(self):
x_int = gs.array([10, 0.2, 3, 4])
y_int = gs.array([1, 6, 2.0, 1])
ball_manifold = PoincareBall(4)
extrinsic_manifold = Hyperboloid(4)
ball_metric = ball_manifold.metric
extrinsic_metric = extrinsic_manifold.metric
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)
def scaled_squared_norm_test_data(self):
space = Hyperboloid(3)
base_point = space.from_coordinates(gs.array([1.0, 1.0, 1.0]),
"intrinsic")
tangent_vec = space.to_tangent(gs.array([1.0, 2.0, 3.0, 4.0]),
base_point)
smoke_data = [
dict(dim=3,
scale=2,
tangent_vec=tangent_vec,
base_point=base_point)
]
return self.generate_tests(smoke_data)
def test_product_distance_extrinsic_representation(self):
"""Test the distance using the extrinsic representation."""
coords_type = 'extrinsic'
point_a_intrinsic = gs.array([0.01, 0.0])
point_b_intrinsic = gs.array([0.0, 0.0])
hyperbolic_space = Hyperboloid(dim=2)
point_a = hyperbolic_space.from_coordinates(
point_a_intrinsic, 'intrinsic')
point_b = hyperbolic_space.from_coordinates(
point_b_intrinsic, 'intrinsic')
duplicate_point_a = gs.stack([point_a, point_a], axis=0)
duplicate_point_b = gs.stack([point_b, point_b], axis=0)
single_disk = PoincarePolydisk(n_disks=1, coords_type=coords_type)
two_disks = PoincarePolydisk(n_disks=2, coords_type=coords_type)
distance_single_disk = single_disk.metric.dist(point_a, point_b)
distance_two_disks = two_disks.metric.dist(
duplicate_point_a, duplicate_point_b)
result = distance_two_disks
expected = 3 ** 0.5 * distance_single_disk
self.assertAllClose(result, expected)
def test_distance_ball_extrinsic_from_extr_4_dim(self):
x_int = gs.array([[10, 0.2, 3, 4]])
y_int = gs.array([[1, 6, 2., 1]])
ball_manifold = PoincareBall(4)
extrinsic_manifold = Hyperboloid(4)
ball_metric = ball_manifold.metric
extrinsic_metric = extrinsic_manifold.metric
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)
# TODO(nmiolane): Remove this when ball is properly vectorized
dst_extr = gs.to_ndarray(dst_extr, to_ndim=2, axis=1)
self.assertAllClose(dst_ball, dst_extr)
def scaled_inner_product_test_data(self):
space = Hyperboloid(3)
base_point = space.from_coordinates(gs.array([1.0, 1.0, 1.0]),
"intrinsic")
tangent_vec_a = space.to_tangent(gs.array([1.0, 2.0, 3.0, 4.0]),
base_point)
tangent_vec_b = space.to_tangent(gs.array([5.0, 6.0, 7.0, 8.0]),
base_point)
smoke_data = [
dict(
dim=3,
scale=2,
tangent_vec_a=tangent_vec_a,
tangent_vec_b=tangent_vec_b,
base_point=base_point,
)
]
return self.generate_tests(smoke_data)
class TestHyperbolic(geomstats.tests.TestCase):
def setup_method(self):
gs.random.seed(1234)
self.dimension = 3
self.space = Hyperboloid(dim=self.dimension)
self.metric = self.space.metric
self.ball_manifold = PoincareBall(dim=2)
self.n_samples = 10
def test_belongs_intrinsic(self):
self.space.coords_type = "intrinsic"
point = gs.random.rand(self.n_samples, self.dimension)
result = self.space.belongs(point)
self.assertTrue(gs.all(result))
def test_regularize_intrinsic(self):
self.space.coords_type = "intrinsic"
point = gs.random.rand(self.n_samples, self.dimension)
regularized = self.space.regularize(point)
self.space.coords_type = "extrinsic"
result = self.space.belongs(regularized)
self.assertTrue(gs.all(result))
def test_regularize_zero_norm(self):
point = gs.array([-1.0, 1.0, 0.0, 0.0])
with pytest.raises(ValueError):
self.space.regularize(point)
with pytest.raises(NameError):
self.space.extrinsic_to_intrinsic_coords(point)
def test_random_uniform_and_belongs(self):
point = self.space.random_point()
result = self.space.belongs(point)
expected = True
self.assertAllClose(result, expected)
def test_random_uniform(self):
result = self.space.random_point()
self.assertAllClose(gs.shape(result), (self.dimension + 1,))
def test_projection_to_tangent_space(self):
base_point = gs.array([1.0, 0.0, 0.0, 0.0])
belongs = self.space.belongs(base_point)
self.assertTrue(belongs)
tangent_vec = self.space.to_tangent(
vector=gs.array([1.0, 2.0, 1.0, 3.0]), base_point=base_point
)
result = self.metric.inner_product(tangent_vec, base_point)
expected = 0.0
self.assertAllClose(result, expected)
result = self.space.to_tangent(
vector=gs.array([1.0, 2.0, 1.0, 3.0]), base_point=base_point
)
expected = tangent_vec
self.assertAllClose(result, expected)
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
self.assertAllClose(result, expected)
point_ext = gs.array([2.0, 1.0, 1.0, 1.0])
point_int = self.space.to_coordinates(point_ext, "intrinsic")
result = self.space.from_coordinates(point_int, "intrinsic")
expected = point_ext
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(
[
[0.1, 0.0, 0.0, 0.1, 0.0, 0.0],
[0.1, 0.1, 0.1, 0.4, 0.1, 0.0],
[0.1, 0.3, 0.0, 0.1, 0.0, 0.0],
[-0.1, 0.1, -0.4, 0.1, -0.01, 0.0],
[0.0, 0.0, 0.1, 0.1, -0.08, -0.1],
[0.1, 0.1, 0.1, 0.1, 0.0, -0.5],
]
)
point_ext = self.space.from_coordinates(point_int, "intrinsic")
result = self.space.to_coordinates(point_ext, "intrinsic")
expected = point_int
expected = helper.to_vector(expected)
self.assertAllClose(result, expected)
point_ext = gs.array(
[
[2.0, 1.0, 1.0, 1.0],
[4.0, 1.0, 3.0, math.sqrt(5.0)],
[3.0, 2.0, 0.0, 2.0],
]
)
point_int = self.space.to_coordinates(point_ext, "intrinsic")
result = self.space.from_coordinates(point_int, "intrinsic")
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, 1.0, 3.0, math.sqrt(5.0)])
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 = point
self.assertAllClose(result, expected)
def test_log_and_exp_general_case_general_dim(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
dim = 5
n_samples = self.n_samples
h5 = Hyperboloid(dim=dim)
h5_metric = h5.metric
base_point = h5.random_point()
point = h5.random_point()
point = gs.cast(point, gs.float64)
base_point = gs.cast(base_point, gs.float64)
one_log = h5_metric.log(point=point, base_point=base_point)
result = h5_metric.exp(tangent_vec=one_log, base_point=base_point)
expected = point
self.assertAllClose(result, expected)
# Test vectorization of log
base_point = gs.stack([base_point] * n_samples, axis=0)
point = gs.stack([point] * n_samples, axis=0)
expected = gs.stack([one_log] * n_samples, axis=0)
log = h5_metric.log(point=point, base_point=base_point)
result = log
self.assertAllClose(gs.shape(result), (n_samples, dim + 1))
self.assertAllClose(result, expected)
result = h5_metric.exp(tangent_vec=log, base_point=base_point)
expected = point
self.assertAllClose(gs.shape(result), (n_samples, dim + 1))
self.assertAllClose(result, expected)
# Test vectorization of exp
tangent_vec = gs.stack([one_log] * n_samples, axis=0)
exp = h5_metric.exp(tangent_vec=tangent_vec, base_point=base_point)
result = exp
expected = point
self.assertAllClose(gs.shape(result), (n_samples, dim + 1))
self.assertAllClose(result, expected)
def test_exp_and_belongs(self):
H2 = Hyperboloid(dim=2)
METRIC = H2.metric
base_point = gs.array([1.0, 0.0, 0.0])
self.assertTrue(H2.belongs(base_point))
tangent_vec = H2.to_tangent(
vector=gs.array([1.0, 2.0, 1.0]), base_point=base_point
)
exp = METRIC.exp(tangent_vec=tangent_vec, base_point=base_point)
self.assertTrue(H2.belongs(exp))
def test_exp_small_vec(self):
H2 = Hyperboloid(dim=2)
METRIC = H2.metric
base_point = H2.regularize(gs.array([1.0, 0.0, 0.0]))
self.assertTrue(H2.belongs(base_point))
tangent_vec = 1e-9 * H2.to_tangent(
vector=gs.array([1.0, 2.0, 1.0]), base_point=base_point
)
exp = METRIC.exp(tangent_vec=tangent_vec, base_point=base_point)
self.assertTrue(H2.belongs(exp))
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, 3.0, 1.0, math.sqrt(5)])
n_vecs = gs.array(
[
[2.0, 1.0, 1.0, 1.0],
[4.0, 1.0, 3.0, math.sqrt(5.0)],
[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],
]
)
one_tangent_vec = self.space.to_tangent(one_vec, base_point=one_base_point)
result = self.metric.exp(one_tangent_vec, one_base_point)
self.assertAllClose(gs.shape(result), (dim,))
n_tangent_vecs = self.space.to_tangent(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 = []
for i in range(n_samples):
expected.append(self.metric.exp(n_tangent_vecs[i], one_base_point))
expected = gs.stack(expected, axis=0)
expected = helper.to_vector(gs.array(expected))
self.assertAllClose(result, expected, atol=1e-2)
one_tangent_vec = self.space.to_tangent(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 = []
for i in range(n_samples):
expected.append(self.metric.exp(one_tangent_vec[i], n_base_points[i]))
expected = gs.stack(expected, axis=0)
expected = helper.to_vector(gs.array(expected))
self.assertAllClose(result, expected)
n_tangent_vecs = self.space.to_tangent(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 = []
for i in range(n_samples):
expected.append(self.metric.exp(n_tangent_vecs[i], n_base_points[i]))
expected = gs.stack(expected, axis=0)
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, 3.0, 1.0, math.sqrt(5)])
n_points = gs.array(
[[2.0, 1.0, 1.0, 1.0], [4.0, 1.0, 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), (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.to_tangent(
vector=gs.array([10.0, 200.0, 1.0, 1.0]), base_point=base_point
)
tangent_vec_b = self.space.to_tangent(
vector=gs.array([11.0, 20.0, -21.0, 0.0]), 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
)
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, 1.0, 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)
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, 1.0, 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)
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([1.0, 2.0, 3.0])
base_point = self.space.from_coordinates(base_point_intrinsic, "intrinsic")
point_intrinsic = base_point_intrinsic + 1e-12 * gs.array([-1.0, -2.0, 1.0])
point = self.space.from_coordinates(point_intrinsic, "intrinsic")
log = self.metric.log(point=point, base_point=base_point)
result = self.metric.exp(tangent_vec=log, base_point=base_point)
expected = point
self.assertAllClose(result, expected)
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, 1.0, 3.0, math.sqrt(5)])
vector = gs.array([2.0, 1.0, 1.0, 1.0])
vector = self.space.to_tangent(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
self.assertAllClose(result, expected)
def test_dist(self):
# Distance between a point and itself is 0.
point_a = gs.array([4.0, 1.0, 3.0, math.sqrt(5)])
point_b = point_a
result = self.metric.dist(point_a, point_b)
expected = 0
self.assertAllClose(result, expected)
def test_exp_and_dist_and_projection_to_tangent_space(self):
base_point = gs.array([4.0, 1.0, 3.0, math.sqrt(5)])
vector = gs.array([0.001, 0.0, -0.00001, -0.00003])
tangent_vec = self.space.to_tangent(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
self.assertAllClose(result, expected, atol=1e-2)
def test_geodesic_and_belongs(self):
initial_point = gs.array([4.0, 1.0, 3.0, math.sqrt(5)])
n_geodesic_points = 100
vector = gs.array([1.0, 0.0, 0.0, 0.0])
initial_tangent_vec = self.space.to_tangent(
vector=vector, base_point=initial_point
)
geodesic = self.metric.geodesic(
initial_point=initial_point, initial_tangent_vec=initial_tangent_vec
)
t = gs.linspace(start=0.0, stop=1.0, num=n_geodesic_points)
points = geodesic(t)
result = gs.all(self.space.belongs(points))
self.assertTrue(result)
def test_geodesic_and_belongs_large_initial_velocity(self):
initial_point = gs.array([4.0, 1.0, 3.0, math.sqrt(5)])
n_geodesic_points = 100
vector = gs.array([2.0, 0.0, 0.0, 0.0])
initial_tangent_vec = self.space.to_tangent(
vector=vector, base_point=initial_point
)
geodesic = self.metric.geodesic(
initial_point=initial_point, initial_tangent_vec=initial_tangent_vec
)
t = gs.linspace(start=0.0, stop=1.0, num=n_geodesic_points)
points = geodesic(t)
result = gs.all(self.space.belongs(points, atol=gs.atol * 1e4))
self.assertTrue(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([2.0, 1.0, 1.0, 1.0])
vector = 1e-10 * gs.array([0.06, -51.0, 6.0, 5.0])
exp = self.metric.exp(tangent_vec=vector, base_point=base_point)
result = self.metric.log(point=exp, base_point=base_point)
expected = self.space.to_tangent(vector=vector, base_point=base_point)
self.assertAllClose(result, expected)
def test_scaled_inner_product(self):
base_point_intrinsic = gs.array([1.0, 1.0, 1.0])
base_point = self.space.from_coordinates(base_point_intrinsic, "intrinsic")
tangent_vec_a = gs.array([1.0, 2.0, 3.0, 4.0])
tangent_vec_b = gs.array([5.0, 6.0, 7.0, 8.0])
tangent_vec_a = self.space.to_tangent(tangent_vec_a, base_point)
tangent_vec_b = self.space.to_tangent(tangent_vec_b, base_point)
scale = 2
default_space = Hyperboloid(dim=self.dimension)
scaled_space = Hyperboloid(dim=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)
def test_scaled_squared_norm(self):
base_point_intrinsic = gs.array([1.0, 1.0, 1.0])
base_point = self.space.from_coordinates(base_point_intrinsic, "intrinsic")
tangent_vec = gs.array([1.0, 2.0, 3.0, 4.0])
tangent_vec = self.space.to_tangent(tangent_vec, base_point)
scale = 2
default_space = Hyperboloid(dim=self.dimension)
scaled_space = Hyperboloid(dim=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)
def test_scaled_distance(self):
point_a_intrinsic = gs.array([1.0, 2.0, 3.0])
point_b_intrinsic = gs.array([4.0, 5.0, 6.0])
point_a = self.space.from_coordinates(point_a_intrinsic, "intrinsic")
point_b = self.space.from_coordinates(point_b_intrinsic, "intrinsic")
scale = 2
scaled_space = Hyperboloid(dim=self.dimension, scale=2)
distance_default_metric = self.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)
def test_is_tangent(self):
base_point = gs.array([4.0, 1.0, 3.0, math.sqrt(5.0)])
point = gs.array([2.0, 1.0, 1.0, 1.0])
log = self.metric.log(point=point, base_point=base_point)
result = self.space.is_tangent(log, base_point)
self.assertTrue(result)
@geomstats.tests.np_autograd_and_tf_only
def test_parallel_transport_vectorization(self):
space = self.space
shape = (4, space.dim + 1)
metric = space.metric
results = helper.test_parallel_transport(space, metric, shape)
for res in results:
self.assertTrue(res)
def test_projection_and_belongs(self):
shape = (self.n_samples, self.dimension + 1)
result = helper.test_projection_and_belongs(
self.space, shape, atol=gs.atol * 100
)
for res in result:
self.assertTrue(res)
point = gs.array([0.0, 1.0, 0.0, 0.0])
projected = self.space.projection(point)
result = self.space.belongs(projected)
self.assertTrue(result)
class TestHyperbolicCoords(geomstats.tests.TestCase):
def setUp(self):
gs.random.seed(1234)
self.dimension = 2
self.extrinsic_manifold = Hyperboloid(dim=self.dimension)
self.extrinsic_metric = self.extrinsic_manifold.metric
self.ball_manifold = PoincareBall(dim=self.dimension)
self.ball_metric = self.ball_manifold.metric
self.intrinsic_manifold = Hyperboloid(dim=self.dimension,
coords_type="intrinsic")
self.intrinsic_metric = self.intrinsic_manifold.metric
self.n_samples = 10
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)
def test_belongs_intrinsic(self):
x_in = gs.array([0.5, 7])
is_in = self.intrinsic_manifold.belongs(x_in)
self.assertTrue(is_in)
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, 3.0])
is_in = self.extrinsic_manifold.belongs(x_true)
self.assertTrue(is_in)
is_out = self.extrinsic_manifold.belongs(x_false)
self.assertFalse(is_out)
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)
def test_extrinsic_half_plane_extrinsic(self):
x_in = gs.array([0.5, 7], dtype=gs.float64)
x = self.intrinsic_manifold.to_coordinates(x_in,
to_coords_type="extrinsic")
x_up = self.extrinsic_manifold.to_coordinates(
x, to_coords_type="half-space")
x2 = Hyperbolic.change_coordinates_system(x_up, "half-space",
"extrinsic")
self.assertAllClose(x, x2)
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)
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)
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)
def test_distance_ball_extrinsic_from_extr(self):
x_int = gs.array([10, 0.2])
y_int = gs.array([1, 6.0])
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)
def test_distance_ball_extrinsic_from_extr_4_dim(self):
x_int = gs.array([10, 0.2, 3, 4])
y_int = gs.array([1, 6, 2.0, 1])
ball_manifold = PoincareBall(4)
extrinsic_manifold = Hyperboloid(4)
ball_metric = ball_manifold.metric
extrinsic_metric = extrinsic_manifold.metric
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)
def test_log_exp_ball_extrinsic_from_extr(self):
"""Compare log exp in different parameterizations."""
x_int = gs.array([4.0, 0.2])
y_int = gs.array([3.0, 3])
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")
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_coords_type="ball")
self.assertAllClose(x_extr_a, x_extr_b, atol=3e-4)
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)
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)
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)
class TestPoincareHalfSpace(geomstats.tests.TestCase):
def setup_method(self):
self.manifold = PoincareHalfSpace(2)
self.metric = self.manifold.metric
self.hyperboloid_manifold = Hyperboloid(2)
self.hyperboloid_metric = self.hyperboloid_manifold.metric
def test_belongs(self):
point = gs.array([1.5, 2.3])
result = self.manifold.belongs(point)
self.assertTrue(result)
points = gs.array([[1.5, 2.0], [2.5, -0.3]])
result = self.manifold.belongs(points)
expected = gs.array([True, False])
self.assertAllClose(result, expected)
def test_inner_product_vectorization(self):
tangent_vec = gs.array([[1.0, 2.0], [3.0, 4.0]])
base_point = gs.array([[0.0, 1.0], [0.0, 5.0]])
result = self.metric.inner_product(tangent_vec, tangent_vec, base_point)
expected = gs.array([5.0, 1.0])
self.assertAllClose(result, expected)
def test_half_space_to_ball_coordinates(self):
point_half_space = gs.array([0.0, 1.0])
result = self.manifold.half_space_to_ball_coordinates(point_half_space)
expected = gs.zeros(2)
self.assertAllClose(result, expected)
def test_half_space_to_ball_coordinates_vectorization(self):
point_half_space = gs.array([[0.0, 1.0], [0.0, 2.0]])
point_ball = self.manifold.half_space_to_ball_coordinates(point_half_space)
expected = gs.array([[0.0, 0.0], [0.0, 1.0 / 3.0]])
self.assertAllClose(point_ball, expected)
def test_ball_to_half_space_coordinates(self):
point_ball = gs.array([-0.3, 0.7])
point_half_space = self.manifold.ball_to_half_space_coordinates(point_ball)
point_ext = self.hyperboloid_manifold.from_coordinates(point_ball, "ball")
point_half_space_expected = self.hyperboloid_manifold.to_coordinates(
point_ext, "half-space"
)
self.assertAllClose(point_half_space, point_half_space_expected)
def test_coordinates(self):
point_half_space = gs.array([1.5, 2.3])
point_ball = self.manifold.half_space_to_ball_coordinates(point_half_space)
result = self.manifold.ball_to_half_space_coordinates(point_ball)
self.assertAllClose(result, point_half_space)
def test_exp_and_coordinates_tangent(self):
base_point = gs.array([1.5, 2.3])
tangent_vec = gs.array([0.0, 1.0])
end_point = self.metric.exp(tangent_vec, base_point)
self.assertAllClose(base_point[0], end_point[0])
def test_ball_half_plane_are_inverse(self):
base_point = gs.array([1.5, 2.3])
base_point_ball = self.manifold.half_space_to_ball_coordinates(base_point)
result = self.manifold.ball_to_half_space_coordinates(base_point_ball)
self.assertAllClose(result, base_point)
def test_ball_half_plane_tangent_are_inverse(self):
base_point = gs.array([1.5, 2.3])
tangent_vec = gs.array([0.5, 1.0])
tangent_vec_ball = self.manifold.half_space_to_ball_tangent(
tangent_vec, base_point
)
base_point_ball = self.manifold.half_space_to_ball_coordinates(base_point)
result = self.manifold.ball_to_half_space_tangent(
tangent_vec_ball, base_point_ball
)
self.assertAllClose(result, tangent_vec)
@geomstats.tests.np_and_autograd_only
def test_exp(self):
point = gs.array([1.0, 1.0])
tangent_vec = gs.array([2.0, 1.0])
end_point = self.metric.exp(tangent_vec, point)
circle_center = point[0] + point[1] * tangent_vec[1] / tangent_vec[0]
circle_radius = gs.sqrt((circle_center - point[0]) ** 2 + point[1] ** 2)
moebius_d = 1
moebius_c = 1 / (2 * circle_radius)
moebius_b = circle_center - circle_radius
moebius_a = (circle_center + circle_radius) * moebius_c
point_complex = point[0] + 1j * point[1]
tangent_vec_complex = tangent_vec[0] + 1j * tangent_vec[1]
point_moebius = (
1j
* (moebius_d * point_complex - moebius_b)
/ (moebius_c * point_complex - moebius_a)
)
tangent_vec_moebius = (
-1j
* tangent_vec_complex
* (1j * moebius_c * point_moebius + moebius_d) ** 2
)
end_point_moebius = point_moebius * gs.exp(tangent_vec_moebius / point_moebius)
end_point_complex = (moebius_a * 1j * end_point_moebius + moebius_b) / (
moebius_c * 1j * end_point_moebius + moebius_d
)
end_point_expected = gs.hstack(
[np.real(end_point_complex), np.imag(end_point_complex)]
)
self.assertAllClose(end_point, end_point_expected)
@geomstats.tests.np_and_autograd_only
def test_exp_vectorization(self):
point = gs.array([[1.0, 1.0], [1.0, 1.0]])
tangent_vec = gs.array([[2.0, 1.0], [2.0, 1.0]])
result = self.metric.exp(tangent_vec, point)
point = point[0]
tangent_vec = tangent_vec[0]
circle_center = point[0] + point[1] * tangent_vec[1] / tangent_vec[0]
circle_radius = gs.sqrt((circle_center - point[0]) ** 2 + point[1] ** 2)
moebius_d = 1
moebius_c = 1 / (2 * circle_radius)
moebius_b = circle_center - circle_radius
moebius_a = (circle_center + circle_radius) * moebius_c
point_complex = point[0] + 1j * point[1]
tangent_vec_complex = tangent_vec[0] + 1j * tangent_vec[1]
point_moebius = (
1j
* (moebius_d * point_complex - moebius_b)
/ (moebius_c * point_complex - moebius_a)
)
tangent_vec_moebius = (
-1j
* tangent_vec_complex
* (1j * moebius_c * point_moebius + moebius_d) ** 2
)
end_point_moebius = point_moebius * gs.exp(tangent_vec_moebius / point_moebius)
end_point_complex = (moebius_a * 1j * end_point_moebius + moebius_b) / (
moebius_c * 1j * end_point_moebius + moebius_d
)
end_point_expected = gs.hstack(
[np.real(end_point_complex), np.imag(end_point_complex)]
)
expected = gs.stack([end_point_expected, end_point_expected])
self.assertAllClose(result, expected)
def test_exp_and_log_are_inverse(self):
points = gs.array([[1.0, 1.0], [1.0, 1.0]])
tangent_vecs = gs.array([[2.0, 1.0], [2.0, 1.0]])
end_points = self.metric.exp(tangent_vecs, points)
result = self.metric.log(end_points, points)
expected = tangent_vecs
self.assertAllClose(result, expected)
def test_projection(self):
point = gs.array([[1.0, -1.0], [0.0, 1.0]])
projected = self.manifold.projection(point)
result = self.manifold.belongs(projected)
self.assertTrue(gs.all(result))
projected = self.manifold.projection(point[0])
result = self.manifold.belongs(projected)
self.assertTrue(result)
class TestHyperbolicMethods(geomstats.tests.TestCase):
def setUp(self):
gs.random.seed(1234)
self.dimension = 3
self.space = Hyperboloid(dim=self.dimension)
self.metric = self.space.metric
self.ball_manifold = PoincareBall(dim=2)
self.n_samples = 10
def test_random_uniform_and_belongs(self):
point = self.space.random_uniform()
result = self.space.belongs(point)
expected = True
self.assertAllClose(result, expected)
def test_random_uniform(self):
result = self.space.random_uniform()
self.assertAllClose(gs.shape(result), (self.dimension + 1,))
def test_projection_to_tangent_space(self):
base_point = gs.array([1., 0., 0., 0.])
self.assertTrue(self.space.belongs(base_point))
tangent_vec = self.space.projection_to_tangent_space(
vector=gs.array([1., 2., 1., 3.]),
base_point=base_point)
result = self.metric.inner_product(tangent_vec, base_point)
expected = 0.
self.assertAllClose(result, expected)
result = self.space.projection_to_tangent_space(
vector=gs.array([1., 2., 1., 3.]),
base_point=base_point)
expected = tangent_vec
self.assertAllClose(result, expected)
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.from_coordinates(point_int, 'intrinsic')
result = self.space.to_coordinates(point_ext, 'intrinsic')
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.to_coordinates(point_ext, 'intrinsic')
result = self.space.from_coordinates(point_int, 'intrinsic')
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.from_coordinates(point_int, 'intrinsic')
result = self.space.to_coordinates(point_ext, 'intrinsic')
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.to_coordinates(point_ext, 'intrinsic')
result = self.space.from_coordinates(point_int, 'intrinsic')
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 = point
self.assertAllClose(result, expected)
def test_log_and_exp_general_case_general_dim(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
dim = 5
n_samples = self.n_samples
h5 = Hyperboloid(dim=dim)
h5_metric = h5.metric
base_point = h5.random_uniform()
point = h5.random_uniform()
one_log = h5_metric.log(point=point, base_point=base_point)
result = h5_metric.exp(tangent_vec=one_log, base_point=base_point)
expected = point
self.assertAllClose(result, expected)
# Test vectorization of log
base_point = gs.stack([base_point] * n_samples, axis=0)
point = gs.stack([point] * n_samples, axis=0)
expected = gs.stack([one_log] * n_samples, axis=0)
log = h5_metric.log(point=point, base_point=base_point)
result = log
self.assertAllClose(gs.shape(result), (n_samples, dim + 1))
self.assertAllClose(result, expected)
result = h5_metric.exp(tangent_vec=log, base_point=base_point)
expected = point
self.assertAllClose(gs.shape(result), (n_samples, dim + 1))
self.assertAllClose(result, expected)
# Test vectorization of exp
tangent_vec = gs.stack([one_log] * n_samples, axis=0)
exp = h5_metric.exp(tangent_vec=tangent_vec, base_point=base_point)
result = exp
expected = point
self.assertAllClose(gs.shape(result), (n_samples, dim + 1))
self.assertAllClose(result, expected)
def test_exp_and_belongs(self):
H2 = Hyperboloid(dim=2)
METRIC = H2.metric
base_point = gs.array([1., 0., 0.])
self.assertTrue(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)
self.assertTrue(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), (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))
for i in range(n_samples):
expected[i] = 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))
for i in range(n_samples):
expected[i] = 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))
for i in range(n_samples):
expected[i] = 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), (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)
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)
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)
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.from_coordinates(base_point_intrinsic, 'intrinsic')
point_intrinsic = (base_point_intrinsic +
1e-12 * gs.array([-1., -2., 1.]))
point =\
self.space.from_coordinates(point_intrinsic, 'intrinsic')
log = self.metric.log(point=point, base_point=base_point)
result = self.metric.exp(tangent_vec=log, base_point=base_point)
expected = point
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
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 = 0
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
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 = n_geodesic_points * [True]
self.assertAllClose(result, expected)
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_only
def test_scaled_inner_product(self):
base_point_intrinsic = gs.array([1, 1, 1])
base_point = self.space.from_coordinates(
base_point_intrinsic, "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 = Hyperboloid(dim=self.dimension)
scaled_space = Hyperboloid(dim=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.from_coordinates(base_point_intrinsic,
'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 = Hyperboloid(dim=self.dimension)
scaled_space = Hyperboloid(dim=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.from_coordinates(point_a_intrinsic, 'intrinsic')
point_b = self.space.from_coordinates(point_b_intrinsic, 'intrinsic')
scale = 2
scaled_space = Hyperboloid(dim=self.dimension, scale=2)
distance_default_metric = self.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)
