def test_LMpM_range_half_integer(ell_max):
for twoell_max in range(2 * ell_max + 1):
assert np.array_equal(
sf.LMpM_range_half_integer(twoell_max / 2, twoell_max / 2),
np.array([[twoell_max / 2, twomp / 2, twom / 2]
for twomp in range(-twoell_max, twoell_max + 1, 2)
for twom in range(-twoell_max, twoell_max + 1, 2)]))
for twoell_min in range(twoell_max):
a = sf.LMpM_range_half_integer(twoell_min / 2, twoell_max / 2)
b = np.array([[twoell / 2, twomp / 2, twom / 2]
for twoell in range(twoell_min, twoell_max + 1)
for twomp in range(-twoell, twoell + 1, 2)
for twom in range(-twoell, twoell + 1, 2)])
assert np.array_equal(a, b)
def test_Wigner_D_elements_representation_property(Rs, ell_max):
# Test the representation property for special and random angles
# Try half-integers, too
ell_max = min(8, ell_max)
twoLMpM = np.round(2 * sf.LMpM_range_half_integer(0, ell_max)).astype(int)
print("")
D1 = np.empty((twoLMpM.shape[0], ), dtype=complex)
D2 = np.empty((twoLMpM.shape[0], ), dtype=complex)
D12 = np.empty((twoLMpM.shape[0], ), dtype=complex)
for i, R1 in enumerate(Rs):
print("\t{0} of {1}: R1 = {2}".format(i + 1, len(Rs), R1))
for j, R2 in enumerate(Rs):
# print("\t\t{0} of {1}: R2 = {2}".format(j+1, len(Rs), R2))
R12 = R1 * R2
sf._Wigner_D_element(R1.a, R1.b, twoLMpM, D1)
sf._Wigner_D_element(R2.a, R2.b, twoLMpM, D2)
sf._Wigner_D_element(R12.a, R12.b, twoLMpM, D12)
M12 = np.array([
np.sum([
D1[sf._Wigner_index(twoell, twomp, twompp)] *
D2[sf._Wigner_index(twoell, twompp, twom)]
for twompp in range(-twoell, twoell + 1, 2)
]) for twoell in range(2 * ell_max + 1)
for twomp in range(-twoell, twoell + 1, 2)
for twom in range(-twoell, twoell + 1, 2)
])
# if not np.allclose(M12, D12, atol=ell_max * precision_Wigner_D_element):
# for k in range(min(100, M12.size)):
# print(twoLMpM[k], "\t", abs(D12[k]-M12[k]), "\t\t", D12[k], "\t", M12[k])
# print(D12.shape, M12.shape)
assert np.allclose(M12,
D12,
atol=ell_max * precision_Wigner_D_element)
def test_Wigner_D_element_values(special_angles, ell_max):
LMpM = sf.LMpM_range_half_integer(0, ell_max // 2)
# Compare with more explicit forms given in Euler angles
print("")
for alpha in special_angles:
print("\talpha={0}".format(
alpha)) # Need to show some progress to Travis
for beta in special_angles:
print("\t\tbeta={0}".format(beta))
for gamma in special_angles:
a = np.conjugate(
np.array([
slow_Wigner_D_element(alpha, beta, gamma, ell, mp, m)
for ell, mp, m in LMpM
]))
b = sf.Wigner_D_element(
quaternion.from_euler_angles(alpha, beta, gamma), LMpM)
# if not np.allclose(a, b,
# atol=ell_max ** 6 * precision_Wigner_D_element,
# rtol=ell_max ** 6 * precision_Wigner_D_element):
# for i in range(min(a.shape[0], 100)):
# print(LMpM[i], "\t", abs(a[i]-b[i]), "\t\t", a[i], "\t", b[i])
assert np.allclose(
a,
b,
atol=ell_max**6 * precision_Wigner_D_element,
rtol=ell_max**6 * precision_Wigner_D_element)