def test_Wigner_D_matrices_representation_property(Rs, ell_max):
# Test the representation property for special and random angles
# Can't try half-integers because Wigner_D_matrices doesn't accept them
ell_max = min(8, ell_max)
LMpM = sf.LMpM_range(0, ell_max)
print("")
D1 = np.empty((LMpM.shape[0], ), dtype=complex)
D2 = np.empty((LMpM.shape[0], ), dtype=complex)
D12 = np.empty((LMpM.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[i:]):
# print("\t\t{0} of {1}: R2 = {2}".format(j+1, len(Rs), R2))
R12 = R1 * R2
sf._Wigner_D_matrices(R1.a, R1.b, 0, ell_max, D1)
sf._Wigner_D_matrices(R2.a, R2.b, 0, ell_max, D2)
sf._Wigner_D_matrices(R12.a, R12.b, 0, ell_max, D12)
M12 = np.array([
np.sum([
D1[sf.LMpM_index(ell, mp, mpp, 0)] *
D2[sf.LMpM_index(ell, mpp, m, 0)]
for mpp in range(-ell, ell + 1)
]) for ell in range(ell_max + 1)
for mp in range(-ell, ell + 1) for m in range(-ell, ell + 1)
])
assert np.allclose(M12,
D12,
atol=ell_max * precision_Wigner_D_element)
def test_rotations_of_each_mode_individually(Rs):
ell_min = 0
ell_max = 8 # sf.ell_max is just too much; this test is too slow, and ell=8 should be fine
R_basis = Rs
Ds = np.empty((len(Rs), sf.LMpM_total_size(ell_min, ell_max)),
dtype=complex)
for i, R in enumerate(Rs):
Ds[i, :] = sf.Wigner_D_matrices(R, ell_min, ell_max)
for ell in range(ell_max + 1):
first_zeros = np.zeros((len(Rs), sf.LM_total_size(ell_min, ell - 1)),
dtype=complex)
later_zeros = np.zeros((len(Rs), sf.LM_total_size(ell + 1, ell_max)),
dtype=complex)
for Mp in range(-ell, ell):
W_in = delta_waveform(ell,
Mp,
begin=-10.0,
end=100.0,
n_times=len(Rs),
ell_min=ell_min,
ell_max=ell_max)
# Now, the modes are f^{\ell,m[} = \delta^{\ell,mp}_{L,Mp}
assert W_in.ensure_validity(alter=False)
W_out = scri.WaveformModes(W_in)
W_out.rotate_decomposition_basis(Rs)
assert W_out.ensure_validity(alter=False)
assert np.array_equal(W_out.t, W_in.t)
assert np.max(np.abs(W_out.frame - R_basis)) == 0.0
i_D0 = sf.LMpM_index(ell, Mp, -ell, ell_min)
assert np.array_equal(
W_out.data[:, :sf.LM_total_size(ell_min, ell - 1)],
first_zeros)
if ell < ell_max:
assert np.array_equal(
W_out.data[:,
sf.LM_total_size(ell_min, ell - 1):-sf.
LM_total_size(ell + 1, ell_max)],
Ds[:, i_D0:i_D0 + (2 * ell + 1)],
)
assert np.array_equal(
W_out.data[:, -sf.LM_total_size(ell + 1, ell_max):],
later_zeros)
else:
assert np.array_equal(
W_out.data[:, sf.LM_total_size(ell_min, ell - 1):],
Ds[:, i_D0:i_D0 + (2 * ell + 1)])
assert W_out.ell_min == W_in.ell_min
assert W_out.ell_max == W_in.ell_max
assert np.array_equal(W_out.LM, W_in.LM)
for h_in, h_out in zip(W_in.history, W_out.history[:-1]):
assert h_in == h_out.replace(
type(W_out).__name__ + str(W_out.num),
type(W_in).__name__ + str(W_in.num))
assert W_out.frameType == W_in.frameType
assert W_out.dataType == W_in.dataType
assert W_out.r_is_scaled_out == W_in.r_is_scaled_out
assert W_out.m_is_scaled_out == W_in.m_is_scaled_out
assert W_out.num != W_in.num
def test_LMpM_index(ell_max):
for ell_min in range(ell_max + 1):
LMpM = sf.LMpM_range(ell_min, ell_max)
for ell in range(ell_min, ell_max + 1):
for mp in range(-ell, ell + 1):
for m in range(-ell, ell + 1):
assert np.array_equal(
np.array([ell, mp, m]),
LMpM[sf.LMpM_index(ell, mp, m, ell_min)])
def test_LMpM_total_size(ell_max):
for l_min in range(ell_max + 1):
for l_max in range(l_min, ell_max + 1):
assert sf.LMpM_index(l_max + 1, -(l_max + 1), -(l_max + 1),
l_min) == sf.LMpM_total_size(l_min, l_max)