def __init__(self, L_max, d=None, L2_normalized=True):
self.L_max = L_max
self.complex_fft = SO3_FFT_SemiNaive_Complex(L_max=L_max, d=d, L2_normalized=L2_normalized)
# Compute change of basis function:
self.c2b = [change_of_basis_matrix(l,
frm=('complex', 'seismology', 'centered', 'cs'),
to=('real', 'quantum', 'centered', 'cs'))
for l in range(L_max + 1)]
def wigner_d_matrix(l,
beta,
field='real',
normalization='quantum',
order='centered',
condon_shortley='cs'):
"""
Compute the Wigner-d matrix of degree l at beta, in the basis defined by
(field, normalization, order, condon_shortley)
The Wigner-d matrix of degree l has shape (2l + 1) x (2l + 1).
:param l: the degree of the Wigner-d function. l >= 0
:param beta: the argument. 0 <= beta <= pi
:param field: 'real' or 'complex'
:param normalization: 'quantum', 'seismology', 'geodesy' or 'nfft'
:param order: 'centered' or 'block'
:param condon_shortley: 'cs' or 'nocs'
:return: d^l_mn(beta) in the chosen basis
"""
# This returns the d matrix in the (real, quantum-normalized, centered, cs) convention
d = rot_mat(alpha=0., beta=beta, gamma=0., l=l, J=Jd[l])
if (field, normalization, order, condon_shortley) != ('real', 'quantum',
'centered', 'cs'):
# TODO use change of basis function instead of matrix?
B = change_of_basis_matrix(l,
frm=('real', 'quantum', 'centered', 'cs'),
to=(field, normalization, order,
condon_shortley))
BB = change_of_basis_matrix(l,
frm=(field, normalization, order,
condon_shortley),
to=('real', 'quantum', 'centered', 'cs'))
d = B.dot(d).dot(BB)
# The Wigner-d matrices are always real, even in the complex basis
# (I tested this numerically, and have seen it in several texts)
# assert np.isclose(np.sum(np.abs(d.imag)), 0.0)
d = d.real
return d
def wigner_D_matrix(l,
alpha,
beta,
gamma,
field='real',
normalization='quantum',
order='centered',
condon_shortley='cs'):
"""
Evaluate the Wigner-d matrix D^l_mn(alpha, beta, gamma)
:param l: the degree of the Wigner-d function. l >= 0
:param alpha: the argument. 0 <= alpha <= 2 pi
:param beta: the argument. 0 <= beta <= pi
:param gamma: the argument. 0 <= gamma <= 2 pi
:param field: 'real' or 'complex'
:param normalization: 'quantum', 'seismology', 'geodesy' or 'nfft'
:param order: 'centered' or 'block'
:param condon_shortley: 'cs' or 'nocs'
:return: D^l_mn(alpha, beta, gamma) in the chosen basis
"""
D = rot_mat(alpha=alpha, beta=beta, gamma=gamma, l=l, J=Jd[l])
if (field, normalization, order, condon_shortley) != ('real', 'quantum',
'centered', 'cs'):
B = change_of_basis_matrix(l,
frm=('real', 'quantum', 'centered', 'cs'),
to=(field, normalization, order,
condon_shortley))
BB = change_of_basis_matrix(l,
frm=(field, normalization, order,
condon_shortley),
to=('real', 'quantum', 'centered', 'cs'))
D = B.dot(D).dot(BB)
if field == 'real':
# print('WIGNER D IMAG PART:', np.sum(np.abs(D.imag)))
assert np.isclose(np.sum(np.abs(D.imag)), 0.0)
D = D.real
return D