class TestVisualizationMethods(unittest.TestCase):
_multiprocess_can_split_ = True
def setUp(self):
self.n_samples = 10
self.SO3_GROUP = SpecialOrthogonalGroup(n=3)
self.SE3_GROUP = SpecialEuclideanGroup(n=3)
self.S2 = Hypersphere(dimension=2)
self.H2 = HyperbolicSpace(dimension=2)
def test_plot_points_so3(self):
points = self.SO3_GROUP.random_uniform(self.n_samples)
visualization.plot(points, space='SO3_GROUP')
def test_plot_points_se3(self):
points = self.SE3_GROUP.random_uniform(self.n_samples)
visualization.plot(points, space='SE3_GROUP')
def test_plot_points_s2(self):
points = self.S2.random_uniform(self.n_samples)
visualization.plot(points, space='S2')
def test_plot_points_h2_poincare_disk(self):
points = self.H2.random_uniform(self.n_samples)
visualization.plot(points, space='H2_poincare_disk')
def test_plot_points_h2_poincare_half_plane(self):
points = self.H2.random_uniform(self.n_samples)
visualization.plot(points, space='H2_poincare_half_plane')
def test_plot_points_h2_klein_disk(self):
points = self.H2.random_uniform(self.n_samples)
visualization.plot(points, space='H2_klein_disk')
def main():
fig = plt.figure(figsize=(15, 5))
hyperbolic_plane = HyperbolicSpace(dimension=2)
data = hyperbolic_plane.random_uniform(n_samples=140)
mean = hyperbolic_plane.metric.mean(data)
tpca = TangentPCA(metric=hyperbolic_plane.metric, n_components=2)
tpca = tpca.fit(data, base_point=mean)
tangent_projected_data = tpca.transform(data)
geodesic_0 = hyperbolic_plane.metric.geodesic(
initial_point=mean, initial_tangent_vec=tpca.components_[0])
geodesic_1 = hyperbolic_plane.metric.geodesic(
initial_point=mean, initial_tangent_vec=tpca.components_[1])
n_steps = 100
t = np.linspace(-1, 1, n_steps)
geodesic_points_0 = geodesic_0(t)
geodesic_points_1 = geodesic_1(t)
print('Coordinates of the Log of the first 5 data points at the mean, '
'projected on the principal components:')
print(tangent_projected_data[:5])
ax_var = fig.add_subplot(121)
xticks = np.arange(1, 2 + 1, 1)
ax_var.xaxis.set_ticks(xticks)
ax_var.set_title('Explained variance')
ax_var.set_xlabel('Number of Principal Components')
ax_var.set_ylim((0, 1))
ax_var.plot(xticks, tpca.explained_variance_ratio_)
ax = fig.add_subplot(122)
visualization.plot(mean,
ax,
space='H2_poincare_disk',
color='darkgreen',
s=10)
visualization.plot(geodesic_points_0,
ax,
space='H2_poincare_disk',
linewidth=2)
visualization.plot(geodesic_points_1,
ax,
space='H2_poincare_disk',
linewidth=2)
visualization.plot(data,
ax,
space='H2_poincare_disk',
color='black',
alpha=0.7)
plt.show()
class TestHyperbolicSpaceMethods(geomstats.tests.TestCase):
_multiprocess_can_split_ = True
def setUp(self):
gs.random.seed(1234)
self.dimension = 3
self.space = HyperbolicSpace(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 = HyperbolicSpace(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)))
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 = np.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 = np.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 = np.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 = 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)
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)
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)
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_only
def test_variance(self):
point = gs.array([2., 1., 1., 1.])
result = self.metric.variance([point, point])
expected = 0.
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_mean(self):
point = gs.array([2., 1., 1., 1.])
result = self.metric.mean([point, point])
expected = point
self.assertAllClose(result, expected)
@geomstats.tests.np_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()
mean = self.metric.mean([point_a, point_b, point_c])
result = self.space.belongs(mean)
expected = gs.array([[True]])
self.assertAllClose(result, expected)
class TestHyperbolicSpaceTensorFlow(tf.test.TestCase):
_multiprocess_can_split_ = True
def setUp(self):
gs.random.seed(1234)
self.dimension = 3
self.space = HyperbolicSpace(dimension=self.dimension)
self.metric = self.space.metric
self.n_samples = 10
@classmethod
def setUpClass(cls):
os.environ['GEOMSTATS_BACKEND'] = 'tensorflow'
importlib.reload(gs)
@classmethod
def tearDownClass(cls):
os.environ['GEOMSTATS_BACKEND'] = 'numpy'
importlib.reload(gs)
def test_belongs(self):
point = self.space.random_uniform()
bool_belongs = self.space.belongs(point)
expected = helper.to_scalar(tf.convert_to_tensor([[True]]))
with self.test_session():
self.assertAllClose(gs.eval(expected), gs.eval(bool_belongs))
def test_random_uniform(self):
point = self.space.random_uniform()
with self.test_session():
self.assertAllClose(gs.eval(point).shape, (1, self.dimension + 1))
def test_random_uniform_and_belongs(self):
point = self.space.random_uniform()
with self.test_session():
self.assertTrue(gs.eval(self.space.belongs(point)))
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)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
point_ext = tf.convert_to_tensor([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)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(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)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
point_ext = tf.convert_to_tensor([[2.0, 1.0, 1.0, 1.0],
[4.0, 1., 3.0,
math.sqrt(5)], [3.0, 2.0, 0.0,
2.0]])
point_int = self.space.extrinsic_to_intrinsic_coords(point_ext)
result = self.space.intrinsic_to_extrinsic_coords(point_int)
# TODO(nina): Make sure this holds for (x, y, z, ..) AND (-x, y,z)
expected = point_ext
expected = helper.to_vector(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(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 = tf.convert_to_tensor([4.0, 1., 3.0, math.sqrt(5)])
point = tf.convert_to_tensor([2.0, 1.0, 1.0, 1.0])
with self.test_session():
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(gs.eval(result), gs.eval(expected))
def test_exp_and_belongs(self):
H2 = HyperbolicSpace(dimension=2)
METRIC = H2.metric
base_point = tf.convert_to_tensor([1., 0., 0.])
with self.test_session():
self.assertTrue(gs.eval(H2.belongs(base_point)))
tangent_vec = H2.projection_to_tangent_space(
vector=tf.convert_to_tensor([1., 2., 1.]), base_point=base_point)
exp = METRIC.exp(tangent_vec=tangent_vec, base_point=base_point)
with self.test_session():
self.assertTrue(gs.eval(H2.belongs(exp)))
def test_exp_vectorization(self):
n_samples = 3
dim = self.dimension + 1
one_vec = tf.convert_to_tensor([2.0, 1.0, 1.0, 1.0])
one_base_point = tf.convert_to_tensor([4.0, 3., 1.0, math.sqrt(5)])
n_vecs = tf.convert_to_tensor([[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 = tf.convert_to_tensor(
[[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)
with self.test_session():
self.assertAllClose(gs.eval(result).shape, (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)
with self.test_session():
self.assertAllClose(gs.eval(result).shape, (n_samples, dim))
expected = np.zeros((n_samples, dim))
with self.test_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(tf.convert_to_tensor(expected))
self.assertAllClose(gs.eval(result), gs.eval(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)
with self.test_session():
self.assertAllClose(gs.eval(result).shape, (n_samples, dim))
expected = np.zeros((n_samples, dim))
with self.test_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(tf.convert_to_tensor(expected))
self.assertAllClose(gs.eval(result), gs.eval(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)
with self.test_session():
self.assertAllClose(gs.eval(result).shape, (n_samples, dim))
expected = np.zeros((n_samples, dim))
with self.test_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(tf.convert_to_tensor(expected))
self.assertAllClose(gs.eval(result), gs.eval(expected))
def test_log_vectorization(self):
n_samples = 3
dim = self.dimension + 1
one_point = tf.convert_to_tensor([2.0, 1.0, 1.0, 1.0])
one_base_point = tf.convert_to_tensor([4.0, 3., 1.0, math.sqrt(5)])
n_points = tf.convert_to_tensor([[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 = tf.convert_to_tensor(
[[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)
with self.test_session():
self.assertAllClose(gs.eval(result).shape, (1, dim))
result = self.metric.log(n_points, one_base_point)
with self.test_session():
self.assertAllClose(gs.eval(result).shape, (n_samples, dim))
result = self.metric.log(one_point, n_base_points)
with self.test_session():
self.assertAllClose(gs.eval(result).shape, (n_samples, dim))
result = self.metric.log(n_points, n_base_points)
with self.test_session():
self.assertAllClose(gs.eval(result).shape, (n_samples, dim))
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 = tf.convert_to_tensor([2.0, 1.0, 1.0, 1.0])
point_b = tf.convert_to_tensor([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.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
def test_norm_and_dist(self):
"""
Test that the distance between two points is
the norm of their logarithm.
"""
point_a = tf.convert_to_tensor([2.0, 1.0, 1.0, 1.0])
point_b = tf.convert_to_tensor([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.test_session():
self.assertAllClose(gs.eval(result), gs.eval(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 = tf.convert_to_tensor([1., 2., 3.])
base_point = self.space.intrinsic_to_extrinsic_coords(
base_point_intrinsic)
point_intrinsic = (base_point_intrinsic +
1e-12 * tf.convert_to_tensor([-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.test_session():
self.assertAllClose(gs.eval(result), gs.eval(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 = tf.convert_to_tensor([4.0, 1., 3.0, math.sqrt(5)])
# TODO(nina): this fails for high euclidean norms of vector_1
vector = tf.convert_to_tensor([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
norm = gs.linalg.norm(expected)
atol = RTOL
if norm != 0:
atol = RTOL * norm
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(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 = tf.convert_to_tensor([4.0, 1., 3.0, math.sqrt(5)])
vector = 1e-10 * tf.convert_to_tensor([.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)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected), atol=1e-8)
def test_dist(self):
# Distance between a point and itself is 0.
point_a = tf.convert_to_tensor([4.0, 1., 3.0, math.sqrt(5)])
point_b = point_a
result = self.metric.dist(point_a, point_b)
expected = tf.convert_to_tensor([[0]])
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
def test_exp_and_dist_and_projection_to_tangent_space(self):
# TODO(nina): this fails for high norms of vector
base_point = tf.convert_to_tensor([4.0, 1., 3.0, math.sqrt(5)])
vector = tf.convert_to_tensor([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.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected), atol=1e-2)
def test_geodesic_and_belongs(self):
# TODO(nina): this tests fails when geodesic goes "too far"
initial_point = tf.convert_to_tensor([4.0, 1., 3.0, math.sqrt(5)])
n_geodesic_points = 100
vector = tf.convert_to_tensor([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)
bool_belongs = self.space.belongs(points)
expected = tf.convert_to_tensor(n_geodesic_points * [[True]])
with self.test_session():
self.assertAllClose(gs.eval(expected), gs.eval(bool_belongs))
class TestHyperbolicSpaceMethods(unittest.TestCase):
_multiprocess_can_split_ = True
def setUp(self):
gs.random.seed(1234)
self.dimension = 6
self.space = HyperbolicSpace(dimension=self.dimension)
self.metric = self.space.metric
self.n_samples = 10
def test_belongs(self):
point = self.space.random_uniform()
belongs = self.space.belongs(point)
gs.testing.assert_allclose(belongs.shape, (1, 1))
def test_random_uniform(self):
point = self.space.random_uniform()
gs.testing.assert_allclose(point.shape, (1, self.dimension + 1))
def test_random_uniform_and_belongs(self):
point = self.space.random_uniform()
self.assertTrue(self.space.belongs(point))
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)
gs.testing.assert_allclose(result, expected)
point_ext = self.space.random_uniform()
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)
gs.testing.assert_allclose(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)
gs.testing.assert_allclose(result, expected)
n_samples = self.n_samples
point_ext = self.space.random_uniform(n_samples=n_samples)
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)
gs.testing.assert_allclose(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 = self.space.random_uniform()
point = self.space.random_uniform()
log = self.metric.log(point=point, base_point=base_point)
result = self.metric.exp(tangent_vec=log, base_point=base_point)
expected = point
gs.testing.assert_allclose(result, expected)
def test_exp_and_belongs(self):
H2 = HyperbolicSpace(dimension=2)
METRIC = H2.metric
base_point = gs.array([1., 0., 0.])
assert H2.belongs(base_point)
tangent_vec = H2.projection_to_tangent_space(
vector=gs.array([10., 200., 1.]),
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 = self.n_samples
dim = self.dimension + 1
one_vec = self.space.random_uniform()
one_base_point = self.space.random_uniform()
n_vecs = self.space.random_uniform(n_samples=n_samples)
n_base_points = self.space.random_uniform(n_samples=n_samples)
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)
gs.testing.assert_allclose(result.shape, (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)
gs.testing.assert_allclose(result.shape, (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(expected)
gs.testing.assert_allclose(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)
gs.testing.assert_allclose(result.shape, (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(expected)
gs.testing.assert_allclose(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)
gs.testing.assert_allclose(result.shape, (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(expected)
gs.testing.assert_allclose(result, expected)
def test_log_vectorization(self):
n_samples = self.n_samples
dim = self.dimension + 1
one_point = self.space.random_uniform()
one_base_point = self.space.random_uniform()
n_points = self.space.random_uniform(n_samples=n_samples)
n_base_points = self.space.random_uniform(n_samples=n_samples)
result = self.metric.log(one_point, one_base_point)
gs.testing.assert_allclose(result.shape, (1, dim))
result = self.metric.log(n_points, one_base_point)
gs.testing.assert_allclose(result.shape, (n_samples, dim))
result = self.metric.log(one_point, n_base_points)
gs.testing.assert_allclose(result.shape, (n_samples, dim))
result = self.metric.log(n_points, n_base_points)
gs.testing.assert_allclose(result.shape, (n_samples, dim))
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 = self.space.random_uniform()
point_b = self.space.random_uniform()
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)
gs.testing.assert_allclose(result, expected)
def test_norm_and_dist(self):
"""
Test that the distance between two points is
the norm of their logarithm.
"""
point_a = self.space.random_uniform()
point_b = self.space.random_uniform()
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)
gs.testing.assert_allclose(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., 4., 5., 6.])
base_point = self.space.intrinsic_to_extrinsic_coords(
base_point_intrinsic)
point_intrinsic = (base_point_intrinsic
+ 1e-12 * gs.array([-1., -2., 1., 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
gs.testing.assert_allclose(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 = self.space.random_uniform()
# TODO(xxx): this fails for high euclidean norms of vector_1
vector = gs.array([9., 4., 0., 0., -1., -3., 2.])
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
norm = gs.linalg.norm(expected)
atol = RTOL
if norm != 0:
atol = RTOL * norm
self.assertTrue(gs.allclose(result, expected, atol=atol))
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 = self.space.random_uniform()
vector = 1e-10 * gs.array([.06, -51., 6., 5., 6., 6., 6.])
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)
gs.testing.assert_allclose(result, expected, atol=1e-8)
def test_dist(self):
# Distance between a point and itself is 0.
point_a = self.space.random_uniform()
point_b = point_a
result = self.metric.dist(point_a, point_b)
expected = 0.
gs.testing.assert_allclose(result, expected)
def test_exp_and_dist_and_projection_to_tangent_space(self):
# TODO(xxx): this fails for high norms of vector
base_point = self.space.random_uniform()
vector = gs.array([2., 0., -1., -2., 7., 4., 1.])
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 = math.sqrt(sq_norm)
gs.testing.assert_allclose(result, expected)
def test_geodesic_and_belongs(self):
# TODO(xxx): this tests fails when geodesic goes "too far"
initial_point = self.space.random_uniform()
vector = gs.array([2., 0., -1., -2., 7., 4., 1.])
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=100)
points = geodesic(t)
self.assertTrue(gs.all(self.space.belongs(points)))
def test_variance(self):
point = self.space.random_uniform()
result = self.metric.variance([point, point])
expected = 0
gs.testing.assert_allclose(result, expected)
def test_mean(self):
point = self.space.random_uniform()
result = self.metric.mean([point, point])
expected = point
gs.testing.assert_allclose(result, expected)
def test_mean_and_belongs(self):
point_a = self.space.random_uniform()
point_b = self.space.random_uniform()
point_c = self.space.random_uniform()
result = self.metric.mean([point_a, point_b, point_c])
self.assertTrue(self.space.belongs(result))