def setUp(self):
gs.random.seed(1234)
self.time_like_dim = 0
self.dimension = 2
self.space = MinkowskiSpace(self.dimension)
self.metric = self.space.metric
self.n_samples = 10
def __init__(self, dimension):
assert isinstance(dimension, int) and dimension > 0
super(HyperbolicSpace, self).__init__(
dimension=dimension,
embedding_manifold=MinkowskiSpace(dimension+1))
self.embedding_metric = self.embedding_manifold.metric
self.metric = HyperbolicMetric(self.dimension)
def __init__(self, dimension, point_type='extrinsic', scale=1):
assert isinstance(dimension, int) and dimension > 0
super(HyperbolicSpace,
self).__init__(dimension=dimension,
embedding_manifold=MinkowskiSpace(dimension + 1))
self.embedding_metric = self.embedding_manifold.metric
self.point_type = point_type
self.scale = scale
self.metric = HyperbolicMetric(self.dimension, point_type, self.scale)
self.transform_to = {
'ball-extrinsic':
HyperbolicSpace._ball_to_extrinsic_coordinates,
'extrinsic-ball':
HyperbolicSpace._extrinsic_to_ball_coordinates,
'intrinsic-extrinsic':
HyperbolicSpace._intrinsic_to_extrinsic_coordinates,
'extrinsic-intrinsic':
HyperbolicSpace._extrinsic_to_intrinsic_coordinates,
'extrinsic-half-plane':
HyperbolicSpace._extrinsic_to_half_plane_coordinates,
'half-plane-extrinsic':
HyperbolicSpace._half_plane_to_extrinsic_coordinates,
'extrinsic-extrinsic':
HyperbolicSpace._extrinsic_to_extrinsic_coordinates
}
self.belongs_to = {'ball': HyperbolicSpace._belongs_ball}
def test_inner_product(self):
"""
Test that the inner product between two tangent vectors
is the Minkowski inner product.
"""
minkowski_space = MinkowskiSpace(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)
class TestMinkowskiSpaceMethods(geomstats.tests.TestCase):
_multiprocess_can_split_ = True
def setUp(self):
gs.random.seed(1234)
self.time_like_dim = 0
self.dimension = 2
self.space = MinkowskiSpace(self.dimension)
self.metric = self.space.metric
self.n_samples = 10
def test_belongs(self):
point = gs.array([-1., 3.])
result = self.space.belongs(point)
expected = gs.array([[True]])
self.assertAllClose(result, expected)
def test_random_uniform(self):
point = self.space.random_uniform()
self.assertAllClose(gs.shape(point), (1, self.dimension))
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_inner_product_matrix(self):
result = self.metric.inner_product_matrix()
expected = gs.array([[-1., 0.], [0., 1.]])
self.assertAllClose(result, expected)
def test_inner_product(self):
point_a = gs.array([0., 1.])
point_b = gs.array([2., 10.])
result = self.metric.inner_product(point_a, point_b)
expected = helper.to_scalar(gs.dot(point_a, point_b))
expected -= (2 * point_a[self.time_like_dim] *
point_b[self.time_like_dim])
self.assertAllClose(result, expected)
def test_inner_product_vectorization(self):
n_samples = 3
one_point_a = gs.array([[-1., 0.]])
one_point_b = gs.array([[1.0, 0.]])
n_points_a = gs.array([[-1., 0.], [1., 0.], [2., math.sqrt(3)]])
n_points_b = gs.array([[2., -math.sqrt(3)], [4.0, math.sqrt(15)],
[-4.0, math.sqrt(15)]])
result = self.metric.inner_product(one_point_a, one_point_b)
expected = gs.dot(one_point_a, gs.transpose(one_point_b))
expected -= (2 * one_point_a[:, self.time_like_dim] *
one_point_b[:, self.time_like_dim])
expected = helper.to_scalar(expected)
result_no = self.metric.inner_product(n_points_a, one_point_b)
result_on = self.metric.inner_product(one_point_a, n_points_b)
result_nn = self.metric.inner_product(n_points_a, n_points_b)
self.assertAllClose(result, expected)
self.assertAllClose(gs.shape(result_no), (n_samples, 1))
self.assertAllClose(gs.shape(result_on), (n_samples, 1))
self.assertAllClose(gs.shape(result_nn), (n_samples, 1))
with self.session():
expected = np.zeros(n_samples)
for i in range(n_samples):
expected[i] = gs.eval(gs.dot(n_points_a[i], n_points_b[i]))
expected[i] -= (2 *
gs.eval(n_points_a[i, self.time_like_dim]) *
gs.eval(n_points_b[i, self.time_like_dim]))
expected = helper.to_scalar(gs.array(expected))
self.assertAllClose(result_nn, expected)
def test_squared_norm(self):
point = gs.array([-2., 4.])
result = self.metric.squared_norm(point)
expected = gs.array([[12.]])
self.assertAllClose(result, expected)
def test_squared_norm_vectorization(self):
n_samples = 3
n_points = gs.array([[-1., 0.], [1., 0.], [2., math.sqrt(3)]])
result = self.metric.squared_norm(n_points)
self.assertAllClose(gs.shape(result), (n_samples, 1))
def test_exp(self):
base_point = gs.array([1.0, 0.])
vector = gs.array([2., math.sqrt(3)])
result = self.metric.exp(tangent_vec=vector, base_point=base_point)
expected = base_point + vector
expected = helper.to_vector(expected)
self.assertAllClose(result, expected)
def test_exp_vectorization(self):
dim = self.dimension
n_samples = 3
one_tangent_vec = gs.array([[-1., 0.]])
one_base_point = gs.array([[1.0, 0.]])
n_tangent_vecs = gs.array([[-1., 0.], [1., 0.], [2., math.sqrt(3)]])
n_base_points = gs.array([[2., -math.sqrt(3)], [4.0,
math.sqrt(15)],
[-4.0, math.sqrt(15)]])
result = self.metric.exp(one_tangent_vec, one_base_point)
expected = one_tangent_vec + one_base_point
expected = helper.to_vector(expected)
self.assertAllClose(result, expected)
result = self.metric.exp(n_tangent_vecs, one_base_point)
self.assertAllClose(gs.shape(result), (n_samples, dim))
result = self.metric.exp(one_tangent_vec, n_base_points)
self.assertAllClose(gs.shape(result), (n_samples, dim))
result = self.metric.exp(n_tangent_vecs, n_base_points)
self.assertAllClose(gs.shape(result), (n_samples, dim))
def test_log(self):
base_point = gs.array([-1., 0.])
point = gs.array([2., math.sqrt(3)])
result = self.metric.log(point=point, base_point=base_point)
expected = point - base_point
expected = helper.to_vector(expected)
self.assertAllClose(result, expected)
def test_log_vectorization(self):
dim = self.dimension
n_samples = 3
one_point = gs.array([[-1., 0.]])
one_base_point = gs.array([[1.0, 0.]])
n_points = gs.array([[-1., 0.], [1., 0.], [2., math.sqrt(3)]])
n_base_points = gs.array([[2., -math.sqrt(3)], [4.0,
math.sqrt(15)],
[-4.0, math.sqrt(15)]])
result = self.metric.log(one_point, one_base_point)
expected = one_point - one_base_point
expected = helper.to_vector(expected)
self.assertAllClose(result, expected)
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_squared_dist(self):
point_a = gs.array([2., -math.sqrt(3)])
point_b = gs.array([4.0, math.sqrt(15)])
result = self.metric.squared_dist(point_a, point_b)
vec = point_b - point_a
expected = gs.dot(vec, vec)
expected -= 2 * vec[self.time_like_dim] * vec[self.time_like_dim]
expected = helper.to_scalar(expected)
self.assertAllClose(result, expected)
def test_geodesic_and_belongs(self):
n_geodesic_points = 100
initial_point = gs.array([2., -math.sqrt(3)])
initial_tangent_vec = gs.array([2., 0.])
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]])
self.assertAllClose(result, expected)
def test_mean(self):
point = gs.array([[2., -math.sqrt(3)]])
result = self.metric.mean(points=[point, point, point])
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.])
result = self.metric.mean(points, weights)
result = self.space.belongs(result)
expected = gs.array([[True]])
self.assertAllClose(result, expected)
def test_variance(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.])
variance = self.metric.variance(points, weights, base_point)
result = helper.to_scalar(variance != 0)
# we expect the average of the points' Minkowski sq norms.
expected = helper.to_scalar(gs.array([True]))
self.assertAllClose(result, expected)