38 lines
1.1 KiB
Python
38 lines
1.1 KiB
Python
|
import numpy as np
|
||
|
|
from numpy.testing import assert_allclose
|
||
|
|
import scipy.special as sc
|
||
|
|
|
||
|
|
|
||
|
|
def test_first_harmonics():
|
||
|
|
# Test against explicit representations of the first four
|
||
|
|
# spherical harmonics which use `theta` as the azimuthal angle,
|
||
|
|
# `phi` as the polar angle, and include the Condon-Shortley
|
||
|
|
# phase.
|
||
|
|
|
||
|
|
# Notation is Ymn
|
||
|
|
def Y00(theta, phi):
|
||
|
|
return 0.5*np.sqrt(1/np.pi)
|
||
|
|
|
||
|
|
def Yn11(theta, phi):
|
||
|
|
return 0.5*np.sqrt(3/(2*np.pi))*np.exp(-1j*theta)*np.sin(phi)
|
||
|
|
|
||
|
|
def Y01(theta, phi):
|
||
|
|
return 0.5*np.sqrt(3/np.pi)*np.cos(phi)
|
||
|
|
|
||
|
|
def Y11(theta, phi):
|
||
|
|
return -0.5*np.sqrt(3/(2*np.pi))*np.exp(1j*theta)*np.sin(phi)
|
||
|
|
|
||
|
|
harms = [Y00, Yn11, Y01, Y11]
|
||
|
|
m = [0, -1, 0, 1]
|
||
|
|
n = [0, 1, 1, 1]
|
||
|
|
|
||
|
|
theta = np.linspace(0, 2*np.pi)
|
||
|
|
phi = np.linspace(0, np.pi)
|
||
|
|
theta, phi = np.meshgrid(theta, phi)
|
||
|
|
|
||
|
|
for harm, m, n in zip(harms, m, n):
|
||
|
|
assert_allclose(sc.sph_harm(m, n, theta, phi),
|
||
|
|
harm(theta, phi),
|
||
|
|
rtol=1e-15, atol=1e-15,
|
||
|
|
err_msg="Y^{}_{} incorrect".format(m, n))
|