def test_compose_and_inverse(self):
# 1. Compose transformation by its inverse on the right
# Expect the group identity
rot_vec = tf.convert_to_tensor([0.2, 0.1, 0.1])
mat = self.so3_group.matrix_from_rotation_vector(rot_vec)
inv_mat = self.group.inverse(mat)
result = self.group.compose(mat, inv_mat)
expected = self.group.identity
expected = helper.to_matrix(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
# 2. Compose transformation by its inverse on the left
# Expect the group identity
rot_vec = tf.convert_to_tensor([0.7, 0.1, 0.1])
mat = self.so3_group.matrix_from_rotation_vector(rot_vec)
inv_mat = self.group.inverse(mat)
result = self.group.compose(inv_mat, mat)
expected = self.group.identity
expected = helper.to_matrix(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
def test_retractation_and_lifting(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.point_a
point = self.point_b
tangent_vec = self.tangent_vector_1
lifted = self.metric.lifting(point=point, base_point=base_point)
result = self.metric.retraction(tangent_vec=lifted,
base_point=base_point)
expected = helper.to_matrix(point)
self.assertAllClose(result, expected, atol=ATOL)
retract = self.metric.retraction(tangent_vec=tangent_vec,
base_point=base_point)
result = self.metric.lifting(point=retract, base_point=base_point)
expected = helper.to_matrix(tangent_vec)
self.assertAllClose(result, expected, atol=ATOL)
def test_inner_product_matrix(self):
result = self.metric.inner_product_matrix()
expected = gs.eye(self.dimension)
expected = helper.to_matrix(expected)
self.assertAllClose(result, expected)
def test_inverse(self):
mat = gs.array([[1., 2., 3.], [4., 5., 6.], [7., 8., 10.]])
result = self.group.inverse(mat)
expected = 1. / 3. * gs.array([[-2., -4., 3.], [-2., 11., -6.],
[3., -6., 3.]])
expected = helper.to_matrix(expected)
self.assertTrue(gs.allclose(result, expected))
def test_inner_product_matrix(self):
result = self.metric.inner_product_matrix()
expected = gs.eye(self.dimension)
expected = helper.to_matrix(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
def test_group_log_and_exp(self):
point = 5 * gs.eye(self.n)
group_log = self.group.group_log(point)
result = self.group.group_exp(group_log)
expected = point
expected = helper.to_matrix(expected)
self.assertAllClose(result, expected)
def test_log_and_exp(self):
base_point = gs.array([[5., 0., 0.], [0., 7., 2.], [0., 2., 8.]])
point = gs.array([[9., 0., 0.], [0., 5., 0.], [0., 0., 1.]])
log = self.metric.log(point=point, base_point=base_point)
result = self.metric.exp(tangent_vec=log, base_point=base_point)
expected = helper.to_matrix(point)
self.assertAllClose(result, expected)
def test_inverse(self):
mat = tf.convert_to_tensor([[1., 2., 3.], [4., 5., 6.], [7., 8., 10.]])
result = self.group.inverse(mat)
expected = 1. / 3. * tf.convert_to_tensor(
[[-2., -4., 3.], [-2., 11., -6.], [3., -6., 3.]])
expected = helper.to_matrix(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
def test_compose_and_inverse(self):
# 1. Compose transformation by its inverse on the right
# Expect the group identity
rot_vec = gs.array([0.2, 0.1, 0.1])
mat = self.so3_group.matrix_from_rotation_vector(rot_vec)
inv_mat = self.group.inverse(mat)
result = self.group.compose(mat, inv_mat)
expected = self.group.identity
expected = helper.to_matrix(expected)
self.assertAllClose(result, expected)
# 2. Compose transformation by its inverse on the left
# Expect the group identity
rot_vec = gs.array([0.7, 0.1, 0.1])
mat = self.so3_group.matrix_from_rotation_vector(rot_vec)
inv_mat = self.group.inverse(mat)
result = self.group.compose(inv_mat, mat)
expected = self.group.identity
expected = helper.to_matrix(expected)
self.assertAllClose(result, expected)
def test_log_and_exp(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.point_a
point = self.point_b
log = self.metric.log(point=point, base_point=base_point)
result = self.metric.exp(tangent_vec=log, base_point=base_point)
expected = helper.to_matrix(point)
self.assertAllClose(result, expected, atol=ATOL)
def test_make_symmetric(self):
sym_mat = gs.array([[1., 2.], [2., 1.]])
result = self.space.make_symmetric(sym_mat)
expected = helper.to_matrix(sym_mat)
self.assertAllClose(result, expected)
mat = gs.array([[1., 2., 3.], [0., 0., 0.], [3., 1., 1.]])
result = self.space.make_symmetric(mat)
expected = gs.array([[[1., 1., 3.], [1., 0., 0.5], [3., 0.5, 1.]]])
self.assertAllClose(result, expected)
mat = gs.array([[[1e100, 1e-100, 1e100], [1e100, 1e-100, 1e100],
[1e-100, 1e-100, 1e100]]])
result = self.space.make_symmetric(mat)
res = 0.5 * (1e100 + 1e-100)
expected = gs.array([[[1e100, res, res], [res, 1e-100, res],
[res, res, 1e100]]])
self.assertAllClose(result, expected)
def test_compose(self):
# 1. Composition by identity, on the right
# Expect the original transformation
rot_vec = gs.array([0.2, -0.1, 0.1])
mat = self.so3_group.matrix_from_rotation_vector(rot_vec)
result = self.group.compose(mat, self.group.identity)
expected = mat
expected = helper.to_matrix(mat)
self.assertAllClose(result, expected)
# 2. Composition by identity, on the left
# Expect the original transformation
rot_vec = gs.array([0.2, 0.1, -0.1])
mat = self.so3_group.matrix_from_rotation_vector(rot_vec)
result = self.group.compose(self.group.identity, mat)
expected = mat
self.assertAllClose(result, expected)
def test_compose(self):
# 1. Composition by identity, on the right
# Expect the original transformation
rot_vec = tf.convert_to_tensor([0.2, -0.1, 0.1])
mat = self.so3_group.matrix_from_rotation_vector(rot_vec)
result = self.group.compose(mat, self.group.identity)
expected = mat
expected = helper.to_matrix(mat)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
# 2. Composition by identity, on the left
# Expect the original transformation
rot_vec = tf.convert_to_tensor([0.2, 0.1, -0.1])
mat = self.so3_group.matrix_from_rotation_vector(rot_vec)
result = self.group.compose(self.group.identity, mat)
expected = mat
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
