ai-content-maker/.venv/Lib/site-packages/scipy/special/tests/test_sph_harm.py

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=f"Y^{m}_{n} incorrect")