def test_quaternion_multiplication(self):
"""Quaternion and matrix multiplication are equivalent."""
a = random_quaternions(15, torch.float64).reshape((3, 5, 4))
b = random_quaternions(21, torch.float64).reshape((7, 3, 1, 4))
ab = quaternion_multiply(a, b)
self.assertEqual(ab.shape, (7, 3, 5, 4))
a_matrix = quaternion_to_matrix(a)
b_matrix = quaternion_to_matrix(b)
ab_matrix = torch.matmul(a_matrix, b_matrix)
ab_from_matrix = matrix_to_quaternion(ab_matrix)
self._assert_quaternions_close(ab, ab_from_matrix)
def test_quaternion_application(self):
"""Applying a quaternion is the same as applying the matrix."""
quaternions = random_quaternions(3, torch.float64, requires_grad=True)
matrices = quaternion_to_matrix(quaternions)
points = torch.randn(3, 3, dtype=torch.float64, requires_grad=True)
transform1 = quaternion_apply(quaternions, points)
transform2 = torch.matmul(matrices, points[..., None])[..., 0]
self.assertTrue(torch.allclose(transform1, transform2))
[p, q] = torch.autograd.grad(transform1.sum(), [points, quaternions])
self.assertTrue(torch.isfinite(p).all())
self.assertTrue(torch.isfinite(q).all())
def test_from_quat(self):
"""quat -> mtx -> quat"""
data = random_quaternions(13, dtype=torch.float64)
mdata = matrix_to_quaternion(quaternion_to_matrix(data))
self.assertTrue(torch.allclose(data, mdata))
