def test_geodesic_and_coincides_exp_son(self):
n_geodesic_points = 10
space = SpecialOrthogonal(n=4)
initial_point = space.random_uniform(2)
vector = gs.random.rand(2, 4, 4)
initial_tangent_vec = space.to_tangent(vector=vector,
base_point=initial_point)
geodesic = space.bi_invariant_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 = points[:, -1]
expected = space.bi_invariant_metric.exp(initial_tangent_vec,
initial_point)
self.assertAllClose(result, expected)
initial_point = initial_point[0]
initial_tangent_vec = initial_tangent_vec[0]
geodesic = space.bi_invariant_metric.geodesic(
initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec)
points = geodesic(t)
result = points[-1]
expected = space.bi_invariant_metric.exp(initial_tangent_vec,
initial_point)
self.assertAllClose(expected, result)
def test_geodesic_invalid_initial_conditions(self):
space = SpecialOrthogonal(n=4)
initial_point = space.random_uniform(2)
vector = gs.random.rand(2, 4, 4)
initial_tangent_vec = space.to_tangent(vector=vector,
base_point=initial_point)
end_point = space.random_uniform(2)
self.assertRaises(
RuntimeError, lambda: space.bi_invariant_metric.geodesic(
initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec,
end_point=end_point))
class TestSpecialOrthogonal(geomstats.tests.TestCase):
def setUp(self):
self.n = 2
self.group = SpecialOrthogonal(n=self.n)
self.n_samples = 4
def test_belongs(self):
theta = gs.pi / 3
point_1 = gs.array([[gs.cos(theta), -gs.sin(theta)],
[gs.sin(theta), gs.cos(theta)]])
result = self.group.belongs(point_1)
expected = True
self.assertAllClose(result, expected)
point_2 = gs.array([[gs.cos(theta), gs.sin(theta)],
[gs.sin(theta), gs.cos(theta)]])
result = self.group.belongs(point_2)
expected = False
self.assertAllClose(result, expected)
point = gs.array([point_1, point_2])
expected = gs.array([True, False])
result = self.group.belongs(point)
self.assertAllClose(result, expected)
def test_random_uniform_and_belongs(self):
point = self.group.random_uniform()
result = self.group.belongs(point)
expected = True
self.assertAllClose(result, expected)
point = self.group.random_uniform(self.n_samples)
result = self.group.belongs(point)
expected = gs.array([True] * self.n_samples)
self.assertAllClose(result, expected)
def test_identity(self):
result = self.group.identity
expected = gs.eye(self.n)
self.assertAllClose(result, expected)
def test_is_in_lie_algebra(self):
theta = gs.pi / 3
vec_1 = gs.array([[0., -theta], [theta, 0.]])
result = self.group.is_tangent(vec_1)
expected = True
self.assertAllClose(result, expected)
vec_2 = gs.array([[0., -theta], [theta, 1.]])
result = self.group.is_tangent(vec_2)
expected = False
self.assertAllClose(result, expected)
vec = gs.array([vec_1, vec_2])
expected = gs.array([True, False])
result = self.group.is_tangent(vec)
self.assertAllClose(result, expected)
def test_is_tangent(self):
point = self.group.random_uniform()
theta = 1.
vec_1 = gs.array([[0., -theta], [theta, 0.]])
vec_1 = self.group.compose(point, vec_1)
result = self.group.is_tangent(vec_1, point)
expected = True
self.assertAllClose(result, expected)
vec_2 = gs.array([[0., -theta], [theta, 1.]])
vec_2 = self.group.compose(point, vec_2)
result = self.group.is_tangent(vec_2, point)
expected = False
self.assertAllClose(result, expected)
vec = gs.array([vec_1, vec_2])
point = gs.array([point, point])
expected = gs.array([True, False])
result = self.group.is_tangent(vec, point)
self.assertAllClose(result, expected)
def test_to_tangent(self):
theta = 1.
vec_1 = gs.array([[0., -theta], [theta, 0.]])
result = self.group.to_tangent(vec_1)
expected = vec_1
self.assertAllClose(result, expected)
n_samples = self.n_samples
base_points = self.group.random_uniform(n_samples=n_samples)
tangent_vecs = self.group.compose(base_points, vec_1)
result = self.group.to_tangent(tangent_vecs, base_points)
expected = tangent_vecs
self.assertAllClose(result, expected)
def test_projection_and_belongs(self):
gs.random.seed(3)
group = SpecialOrthogonal(n=4)
mat = gs.random.rand(4, 4)
point = group.projection(mat)
result = group.belongs(point)
self.assertTrue(result)
mat = gs.random.rand(2, 4, 4)
point = group.projection(mat)
result = group.belongs(point, atol=1e-4)
self.assertTrue(gs.all(result))
def test_skew_to_vec_and_back(self):
group = SpecialOrthogonal(n=4)
vec = gs.random.rand(group.dim)
mat = group.skew_matrix_from_vector(vec)
result = group.vector_from_skew_matrix(mat)
self.assertAllClose(result, vec)
class TestSpecialOrthogonal(geomstats.tests.TestCase):
def setUp(self):
self.n = 2
self.group = SpecialOrthogonal(n=self.n)
self.n_samples = 4
def test_dim(self):
for n in [2, 3, 4, 5, 6]:
group = SpecialOrthogonal(n=n)
result = group.dim
expected = n * (n - 1) / 2
self.assertAllClose(result, expected)
def test_belongs(self):
theta = gs.pi / 3
point_1 = gs.array([[gs.cos(theta), - gs.sin(theta)],
[gs.sin(theta), gs.cos(theta)]])
result = self.group.belongs(point_1)
self.assertTrue(result)
point_2 = gs.array([[gs.cos(theta), gs.sin(theta)],
[gs.sin(theta), gs.cos(theta)]])
result = self.group.belongs(point_2)
self.assertFalse(result)
point = gs.array([point_1, point_2])
expected = gs.array([True, False])
result = self.group.belongs(point)
self.assertAllClose(result, expected)
point = point_1[0]
result = self.group.belongs(point)
self.assertFalse(result)
point = gs.zeros((2, 3))
result = self.group.belongs(point)
self.assertFalse(result)
point = gs.zeros((2, 2, 3))
result = self.group.belongs(point)
self.assertFalse(gs.all(result))
def test_random_uniform_and_belongs(self):
point = self.group.random_uniform()
result = self.group.belongs(point)
expected = True
self.assertAllClose(result, expected)
point = self.group.random_uniform(self.n_samples)
result = self.group.belongs(point)
expected = gs.array([True] * self.n_samples)
self.assertAllClose(result, expected)
def test_identity(self):
result = self.group.identity
expected = gs.eye(self.n)
self.assertAllClose(result, expected)
def test_is_in_lie_algebra(self):
theta = gs.pi / 3
vec_1 = gs.array([[0., - theta],
[theta, 0.]])
result = self.group.is_tangent(vec_1)
self.assertTrue(result)
vec_2 = gs.array([[0., - theta],
[theta, 1.]])
result = self.group.is_tangent(vec_2)
self.assertFalse(result)
vec = gs.array([vec_1, vec_2])
result = self.group.is_tangent(vec)
expected = gs.array([True, False])
self.assertAllClose(result, expected)
def test_is_tangent(self):
point = self.group.random_uniform()
theta = 1.
vec_1 = gs.array([[0., - theta],
[theta, 0.]])
vec_1 = self.group.compose(point, vec_1)
result = self.group.is_tangent(vec_1, point)
self.assertTrue(result)
vec_2 = gs.array([[0., - theta],
[theta, 1.]])
vec_2 = self.group.compose(point, vec_2)
result = self.group.is_tangent(vec_2, point)
self.assertFalse(result)
vec = gs.array([vec_1, vec_2])
point = gs.array([point, point])
expected = gs.array([True, False])
result = self.group.is_tangent(vec, point)
self.assertAllClose(result, expected)
def test_to_tangent(self):
theta = 1.
vec_1 = gs.array([[0., - theta],
[theta, 0.]])
result = self.group.to_tangent(vec_1)
expected = vec_1
self.assertAllClose(result, expected)
n_samples = self.n_samples
base_points = self.group.random_uniform(n_samples=n_samples)
tangent_vecs = self.group.compose(base_points, vec_1)
result = self.group.to_tangent(tangent_vecs, base_points)
expected = tangent_vecs
self.assertAllClose(result, expected)
def test_projection_and_belongs(self):
gs.random.seed(4)
shape = (self.n_samples, self.n, self.n)
result = helper.test_projection_and_belongs(
self.group, shape, gs.atol * 100)
for res in result:
self.assertTrue(res)
def test_skew_to_vec_and_back(self):
group = SpecialOrthogonal(n=4)
vec = gs.random.rand(group.dim)
mat = group.skew_matrix_from_vector(vec)
result = group.vector_from_skew_matrix(mat)
self.assertAllClose(result, vec)
def test_parallel_transport(self):
metric = self.group.bi_invariant_metric
shape = (self.n_samples, self.group.n, self.group.n)
results = helper.test_parallel_transport(self.group, metric, shape)
for res in results:
self.assertTrue(res)
def test_metric_left_invariant(self):
group = self.group
point = group.random_point()
tangent_vec = self.group.lie_algebra.basis[0]
expected = group.bi_invariant_metric.norm(
tangent_vec)
translated = group.tangent_translation_map(point)(tangent_vec)
result = group.bi_invariant_metric.norm(translated)
self.assertAllClose(result, expected)
@geomstats.tests.np_and_tf_only
def test_distance_broadcast(self):
group = self.group
point = group.random_point(5)
result = group.bi_invariant_metric.dist_broadcast(point[:3], point)
expected = []
for a in point[:3]:
expected.append(group.bi_invariant_metric.dist(a, point))
expected = gs.stack(expected)
self.assertAllClose(result, expected)
class TestSpecialOrthogonal(geomstats.tests.TestCase):
def setUp(self):
self.n = 2
self.group = SpecialOrthogonal(n=self.n)
self.n_samples = 4
def test_belongs(self):
theta = gs.pi / 3
point_1 = gs.array([[gs.cos(theta), -gs.sin(theta)],
[gs.sin(theta), gs.cos(theta)]])
result = self.group.belongs(point_1)
expected = True
self.assertAllClose(result, expected)
point_2 = gs.array([[gs.cos(theta), gs.sin(theta)],
[gs.sin(theta), gs.cos(theta)]])
result = self.group.belongs(point_2)
expected = False
self.assertAllClose(result, expected)
point = gs.array([point_1, point_2])
expected = gs.array([True, False])
result = self.group.belongs(point)
self.assertAllClose(result, expected)
def test_random_uniform_and_belongs(self):
point = self.group.random_uniform()
result = self.group.belongs(point)
expected = True
self.assertAllClose(result, expected)
point = self.group.random_uniform(self.n_samples)
result = self.group.belongs(point)
expected = gs.array([True] * self.n_samples)
self.assertAllClose(result, expected)
def test_identity(self):
result = self.group.identity
expected = gs.eye(self.n)
self.assertAllClose(result, expected)
def test_is_in_lie_algebra(self):
theta = gs.pi / 3
vec_1 = gs.array([[0., -theta], [theta, 0.]])
result = self.group.is_tangent(vec_1)
expected = True
self.assertAllClose(result, expected)
vec_2 = gs.array([[0., -theta], [theta, 1.]])
result = self.group.is_tangent(vec_2)
expected = False
self.assertAllClose(result, expected)
vec = gs.array([vec_1, vec_2])
expected = gs.array([True, False])
result = self.group.is_tangent(vec)
self.assertAllClose(result, expected)
def test_is_tangent(self):
point = self.group.random_uniform()
theta = 1.
vec_1 = gs.array([[0., -theta], [theta, 0.]])
vec_1 = self.group.compose(point, vec_1)
result = self.group.is_tangent(vec_1, point, atol=1e-6)
expected = True
self.assertAllClose(result, expected)
vec_2 = gs.array([[0., -theta], [theta, 1.]])
vec_2 = self.group.compose(point, vec_2)
result = self.group.is_tangent(vec_2, point, atol=1e-6)
expected = False
self.assertAllClose(result, expected)
vec = gs.array([vec_1, vec_2])
point = gs.array([point, point])
expected = gs.array([True, False])
result = self.group.is_tangent(vec, point, atol=1e-6)
self.assertAllClose(result, expected)
def test_to_tangent(self):
theta = 1.
vec_1 = gs.array([[0., -theta], [theta, 0.]])
result = self.group.to_tangent(vec_1)
expected = vec_1
self.assertAllClose(result, expected)
n_samples = self.n_samples
base_points = self.group.random_uniform(n_samples=n_samples)
tangent_vecs = self.group.compose(base_points, vec_1)
result = self.group.to_tangent(tangent_vecs, base_points)
expected = tangent_vecs
self.assertAllClose(result, expected)
