def test_to_euler(self):
"""mtx -> euler -> mtx"""
data = random_rotations(13, dtype=torch.float64)
for convention in self._all_euler_angle_conventions():
euler_angles = matrix_to_euler_angles(data, convention)
mdata = euler_angles_to_matrix(euler_angles, convention)
self.assertTrue(torch.allclose(data, mdata))
def test_euler_grad_exists(self):
"""Euler angle calculations are differentiable."""
rotation = random_rotation(dtype=torch.float64, requires_grad=True)
for convention in self._all_euler_angle_conventions():
euler_angles = matrix_to_euler_angles(rotation, convention)
mdata = euler_angles_to_matrix(euler_angles, convention)
[g] = torch.autograd.grad(mdata.sum(), rotation)
self.assertTrue(torch.isfinite(g).all())
def test_from_euler(self):
"""euler -> mtx -> euler"""
n_repetitions = 10
# tolerance is how much we keep the middle angle away from the extreme
# allowed values which make the calculation unstable (Gimbal lock).
tolerance = 0.04
half_pi = math.pi / 2
data = torch.zeros(n_repetitions, 3)
data.uniform_(-math.pi, math.pi)
data[:, 1].uniform_(-half_pi + tolerance, half_pi - tolerance)
for convention in self._tait_bryan_conventions():
matrices = euler_angles_to_matrix(data, convention)
mdata = matrix_to_euler_angles(matrices, convention)
self.assertTrue(torch.allclose(data, mdata))
data[:, 1] += half_pi
for convention in self._proper_euler_conventions():
matrices = euler_angles_to_matrix(data, convention)
mdata = matrix_to_euler_angles(matrices, convention)
self.assertTrue(torch.allclose(data, mdata))
