def _dmat_to_real(l, d, reorder_p=False):
''' Transform the input D-matrix to make it compatible with the real
spherical harmonic functions.
'''
# The input D matrix works for pure spherical harmonics. The real
# representation should be U^\dagger * D * U, where U is the unitary
# matrix that transform the complex harmonics to the real harmonics.
u = sph.sph_pure2real(l, reorder_p)
return reduce(numpy.dot, (u.conj().T, d, u)).real
def angular_moment_matrix(l):
'''Matrix of angular moment operator l*1j on the real spherical harmonic
basis'''
lz = numpy.diag(numpy.arange(-l, l + 1, dtype=numpy.complex128))
lx = numpy.zeros_like(lz)
ly = numpy.zeros_like(lz)
for mi in range(-l, l + 1):
mj = mi + 1
if mj <= l:
lx[l + mi, l + mj] = .5 * ((l + mj) * (l - mj + 1))**.5
ly[l + mi, l + mj] = .5j * ((l + mj) * (l - mj + 1))**.5
mj = mi - 1
if mj >= -l:
lx[l + mi, l + mj] = .5 * ((l - mj) * (l + mj + 1))**.5
ly[l + mi, l + mj] = -.5j * ((l - mj) * (l + mj + 1))**.5
u = sph.sph_pure2real(l)
lx = u.conj().T.dot(lx).dot(u)
ly = u.conj().T.dot(ly).dot(u)
lz = u.conj().T.dot(lz).dot(u)
return numpy.array((lx, ly, lz))