def test_right_exp_coincides(self, n, initial_vec):
group = SpecialEuclidean(n=n)
vector_group = SpecialEuclidean(n=n, point_type="vector")
initial_matrix_vec = group.lie_algebra.matrix_representation(initial_vec)
vector_exp = vector_group.right_canonical_metric.exp(initial_vec)
result = group.right_canonical_metric.exp(initial_matrix_vec, n_steps=25)
expected = vector_group.matrix_from_vector(vector_exp)
self.assertAllClose(result, expected, atol=1e-6)
def test_right_exp_coincides(self):
vector_group = SpecialEuclidean(n=2, point_type="vector")
theta = gs.pi / 2
initial_vec = gs.array([theta, 1.0, 1.0])
initial_matrix_vec = self.group.lie_algebra.matrix_representation(initial_vec)
vector_exp = vector_group.right_canonical_metric.exp(initial_vec)
result = self.group.right_canonical_metric.exp(initial_matrix_vec, n_steps=25)
expected = vector_group.matrix_from_vector(vector_exp)
self.assertAllClose(result, expected, atol=1e-6)
def test_left_exp_coincides(self):
vector_group = SpecialEuclidean(n=2, point_type='vector')
theta = gs.pi / 3
initial_vec = gs.array([theta, 2., 2.])
initial_matrix_vec = self.group.lie_algebra.matrix_representation(
initial_vec)
vector_exp = vector_group.left_canonical_metric.exp(initial_vec)
result = self.group.left_canonical_metric.exp(initial_matrix_vec)
expected = vector_group.matrix_from_vector(vector_exp)
self.assertAllClose(result, expected)
def setUp(self):
warnings.simplefilter("ignore", category=ImportWarning)
gs.random.seed(1234)
group = SpecialEuclidean(n=2, point_type="vector")
point_1 = gs.array([0.1, 0.2, 0.3])
point_2 = gs.array([0.5, 5.0, 60.0])
translation_large = gs.array([0.0, 5.0, 6.0])
translation_small = gs.array([0.0, 0.6, 0.7])
elements_all = {
"translation_large": translation_large,
"translation_small": translation_small,
"point_1": point_1,
"point_2": point_2,
}
elements = elements_all
if geomstats.tests.tf_backend():
# Tf is extremely slow
elements = {"point_1": point_1, "point_2": point_2}
elements_matrices_all = {
key: group.matrix_from_vector(elements_all[key])
for key in elements_all
}
elements_matrices = elements_matrices_all
self.group = group
self.elements_all = elements_all
self.elements = elements
self.elements_matrices_all = elements_matrices_all
self.elements_matrices = elements_matrices
self.n_samples = 4
def setUp(self):
warnings.simplefilter('ignore', category=ImportWarning)
gs.random.seed(1234)
group = SpecialEuclidean(n=2, point_type='vector')
point_1 = gs.array([0.1, 0.2, 0.3])
point_2 = gs.array([0.5, 5., 60.])
translation_large = gs.array([0., 5., 6.])
translation_small = gs.array([0., 0.6, 0.7])
elements_all = {
'translation_large': translation_large,
'translation_small': translation_small,
'point_1': point_1,
'point_2': point_2
}
elements = elements_all
if geomstats.tests.tf_backend():
# Tf is extremely slow
elements = {'point_1': point_1, 'point_2': point_2}
elements_matrices_all = {
key: group.matrix_from_vector(elements_all[key])
for key in elements_all
}
elements_matrices = elements_matrices_all
self.group = group
self.elements_all = elements_all
self.elements = elements
self.elements_matrices_all = elements_matrices_all
self.elements_matrices = elements_matrices
self.n_samples = 4