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- 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))
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