def test_single_nj_rotation_to_wigner_rotation():
R_in_2 = np.asarray(
[0 + 0.5j, 0, 0 + 0.1j, 0, 0 - 0.5j],
dtype=np.complex128,
)
R_in_4 = np.asarray(
[0 - 0.2j, 0, 0 + 0.5j, 0, 0 + 0.1j, 0, 0 - 0.5j, 0, 0 + 0.2j],
dtype=np.complex128,
)
for ang_l, R_in in zip([2, 4], [R_in_2, R_in_4]):
n_ = ang_l + 1
for _ in range(10):
euler_angle = np.random.rand(
3) * np.pi / 2 # positive quadrant only.
euler_angle[-1] = 0.0
cos_angle = np.cos(euler_angle)
cos_alpha = np.asarray([cos_angle[0]])
cos_beta = np.asarray([cos_angle[1]])
# single rotation
R_out = clib.single_wigner_rotation(ang_l, euler_angle, R_in)
R_out_2 = clib.__wigner_rotation_2(ang_l, cos_alpha, cos_beta,
R_in).ravel()
np.testing.assert_almost_equal(
R_out[:n_],
R_out_2,
decimal=8,
err_msg=f"Error l={ang_l}, index={_}")
def test_single_2j_rotation_00():
ang_momentum_l = 2
R_in = np.asarray([0 + 0.5j, 0, 0 + 0.1j, 0, 0 - 0.5j], dtype=np.complex128)
indexes = np.arange(5) - 2.0
for _ in range(10):
euler_angle = np.random.rand(3) * 2.0 * np.pi
# single rotation
R_out = clib.single_wigner_rotation(ang_momentum_l, euler_angle, R_in)
exp_im_alpha = np.exp(-1j * indexes * euler_angle[0])
R_out_p = R_in * exp_im_alpha
wigner = clib.wigner_d_matrices(ang_momentum_l, np.asarray([euler_angle[1]]))
R_out_p = np.dot(wigner.reshape(5, 5), R_out_p)
exp_im_gamma = np.exp(-1j * indexes * euler_angle[2])
R_out_p *= exp_im_gamma
np.testing.assert_almost_equal(R_out, R_out_p, decimal=8)