chaosmagpy.coordinate_utils.sh_analysis

chaosmagpy.coordinate_utils.sh_analysis(func, nmax)[source]

Perform a spherical harmonic expansion of a function defined on a spherical surface.

Parameters
func: callable

Function takes two inputs: colatitude in degrees and longitude in degrees. The function must accept 2-D arrays and preserve shapes.

nmax: int

Maximum spherical harmponic degree of the expansion.

Returns
coeffs: ndarray, shape (nmax*(nmax+2),)

Spherical harmonic expansion.

Examples

>>> import chaosmagpy as cp
>>> import numpy as np
>>> def func(theta, phi):
>>>     n, m = 1, 1
>>>     Pnm = cp.coordinate_utils.legendre_poly(n, theta)
>>>     return np.cos(m*np.radians(phi))*Pnm[n, m]
>>> cp.coordinate_utils.sh_analysis(func, nmax=1)
    array([0.0000000e+00, 1.0000000e+00, 1.2246468e-16])