def test_from_matrix(self):
r = Rotation([[1, 0, 0, 0], [3, 0, 0, 0], [0, 1, 0, 0], [0, 2, 0, 0]])
om = np.array(
[np.eye(3), np.eye(3), np.diag([1, -1, -1]), np.diag([1, -1, -1])]
)
assert np.allclose(Rotation.from_matrix(om).data, r.data)
assert np.allclose(
Rotation.from_matrix(om.reshape((2, 2, 3, 3))).data, r.reshape(2, 2).data
)
def test_to_matrix(self):
r = Rotation([[1, 0, 0, 0], [3, 0, 0, 0], [0, 1, 0, 0], [0, 2, 0, 0]])
om = np.array(
[np.eye(3), np.eye(3), np.diag([1, -1, -1]), np.diag([1, -1, -1])]
)
# Shapes are handled correctly
assert np.allclose(r.reshape(2, 2).to_matrix(), om.reshape(2, 2, 3, 3))
r2 = Rotation(
[
[0.1, 0.2, 0.3, 0.4],
[0.5, 0.6, 0.7, 0.8],
[0.9, 0.91, 0.92, 0.93],
[1, 2, 3, 4],
]
)
om_from_r2 = r2.to_matrix()
# Inverse equal to transpose
assert all(np.allclose(np.linalg.inv(i), i.T) for i in om_from_r2)
# Cross product of any two rows gives the third
assert all(np.allclose(np.cross(i[:, 0], i[:, 1]), i[:, 2]) for i in om_from_r2)
# Sum of squares of any column or row equals unity
assert np.allclose(np.sum(np.square(om_from_r2), axis=1), 1) # Rows
assert np.allclose(np.sum(np.square(om_from_r2), axis=2), 1) # Columns