85 lines
2.9 KiB
Python
85 lines
2.9 KiB
Python
import numpy as np
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import pytest
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from numpy.testing import assert_allclose
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import scipy.special as sc
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class TestSphHarm:
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@pytest.mark.slow
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def test_p(self):
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m_max = 20
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n_max = 10
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theta = np.linspace(0, np.pi)
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phi = np.linspace(0, 2*np.pi)
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theta, phi = np.meshgrid(theta, phi)
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y, y_jac, y_hess = sc.sph_harm_y_all(n_max, m_max, theta, phi, diff_n=2)
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p, p_jac, p_hess = sc.sph_legendre_p_all(n_max, m_max, theta, diff_n=2)
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m = np.concatenate([np.arange(m_max + 1), np.arange(-m_max, 0)])
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m = np.expand_dims(m, axis=(0,)+tuple(range(2,theta.ndim+2)))
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assert_allclose(y, p * np.exp(1j * m * phi))
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assert_allclose(y_jac[..., 0], p_jac * np.exp(1j * m * phi))
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assert_allclose(y_jac[..., 1], 1j * m * p * np.exp(1j * m * phi))
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assert_allclose(y_hess[..., 0, 0], p_hess * np.exp(1j * m * phi))
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assert_allclose(y_hess[..., 0, 1], 1j * m * p_jac * np.exp(1j * m * phi))
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assert_allclose(y_hess[..., 1, 0], y_hess[..., 0, 1])
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assert_allclose(y_hess[..., 1, 1], -m * m * p * np.exp(1j * m * phi))
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@pytest.mark.parametrize("n_max", [7, 10, 50])
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@pytest.mark.parametrize("m_max", [1, 4, 5, 9, 14])
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def test_all(self, n_max, m_max):
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theta = np.linspace(0, np.pi)
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phi = np.linspace(0, 2 * np.pi)
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n = np.arange(n_max + 1)
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n = np.expand_dims(n, axis=tuple(range(1,theta.ndim+2)))
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m = np.concatenate([np.arange(m_max + 1), np.arange(-m_max, 0)])
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m = np.expand_dims(m, axis=(0,)+tuple(range(2,theta.ndim+2)))
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y_actual = sc.sph_harm_y_all(n_max, m_max, theta, phi)
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y_desired = sc.sph_harm_y(n, m, theta, phi)
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np.testing.assert_allclose(y_actual, y_desired, rtol=1e-05)
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@pytest.mark.filterwarnings("ignore::DeprecationWarning")
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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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# sph_harm is deprecated and is implemented as a shim around sph_harm_y.
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# This test is maintained to verify the correctness of the shim.
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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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