sph.py 文件源码

def sph_harm(m, n, az, el, type='complex'):
    '''Compute sphercial harmonics

    Parameters
    ----------
    m : (int)
        Order of the spherical harmonic. abs(m) <= n

    n : (int)
        Degree of the harmonic, sometimes called l. n >= 0

    az: (float)
        Azimuthal (longitudinal) coordinate [0, 2pi], also called Theta.

    el : (float)
        Elevation (colatitudinal) coordinate [0, pi], also called Phi.

    Returns
    -------
    y_mn : (complex float)
        Complex spherical harmonic of order m and degree n,
        sampled at theta = az, phi = el
    '''
    if type == 'legacy':
        return scy.sph_harm(m, n, az, el)
    elif type == 'real':
        Lnm = scy.lpmv(_np.abs(m), n, _np.cos(el))

        factor_1 = (2 * n + 1) / (4 * _np.pi)
        factor_2 = scy.factorial(n - _np.abs(m)) / scy.factorial(n + abs(m))

        if m != 0:
            factor_1 = 2 * factor_1

        if m < 0:
            return (-1) ** m * _np.sqrt(factor_1 * factor_2) * Lnm * _np.sin(m * az)
        else:
            return (-1) ** m * _np.sqrt(factor_1 * factor_2) * Lnm * _np.cos(m * az)
    else:
        # For the correct Condon–Shortley phase, all m>0 need to be increased by 1
        return (-1) ** _np.float_(m - (m < 0) * (m % 2)) * scy.sph_harm(m, n, az, el)