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