def test_make_equiangular_grid_contains_both_poles(self, resolution):
"""Equiangular grid must contain both poles."""
_, colatitude = sphere_utils.make_equiangular_grid(resolution)
with self.subTest("North pole"):
self.assertAllClose(colatitude[0], np.zeros_like(colatitude[0]))
with self.subTest("South pole"):
self.assertAllClose(colatitude[-1], np.full_like(colatitude[-1], np.pi))
def test_spherical_harmonics_backward(self, width, ell, m):
r"""ISWSFT is Y_m^\ell when the only nonzero coeffs is 1. at (ell, m)."""
n_coeffs = (width // 2)**2
coeffs = np.zeros(n_coeffs, dtype='complex128')
coeffs[np_spin_spherical_harmonics._get_swsft_coeff_index(ell, m)] = 1
sphere = np_spin_spherical_harmonics.swsft_backward_naive(coeffs, 0)
phi_g, theta_g = sphere_utils.make_equiangular_grid(width)
sphere_gt = scipy.special.sph_harm(m, ell, phi_g, theta_g)
self.assertAllClose(sphere, sphere_gt)
def test_spin_weighted_spherical_harmonics_forward(self, width):
r"""SWSFT of sY_m^\ell has only one nonzero coefficient, at (ell, m)."""
longitude_g, colatitude_g = sphere_utils.make_equiangular_grid(width)
# We use some known expressions for spin-weighted spherical harmonics.
# spin=1, ell=1, m=0: 1Y_0^1(a, b) \propto sin(b)
Y110 = np.sin(colatitude_g) # pylint: disable=invalid-name
coeffs = np_spin_spherical_harmonics.swsft_forward_naive(Y110, 1)
self._check_nonzero_harmonic_coeffs(coeffs, 1, 0)
# spin=1, ell=1, m=1: 1Y_1^1(a, b) \propto (1-cos(b))exp(ia)
Y111 = (1 - np.cos(colatitude_g)) * np.exp(1j * longitude_g) # pylint: disable=invalid-name
coeffs = np_spin_spherical_harmonics.swsft_forward_naive(Y111, 1)
self._check_nonzero_harmonic_coeffs(coeffs, 1, 1)
# spin=1, ell=1, m=-1: 1Y_{-1}^1(a, b) \propto (1+cos(b))exp(-ia)
Y11m1 = (1 + np.cos(colatitude_g)) * np.exp(-1j * longitude_g) # pylint: disable=invalid-name
coeffs = np_spin_spherical_harmonics.swsft_forward_naive(Y11m1, 1)
self._check_nonzero_harmonic_coeffs(coeffs, 1, -1)
def test_spherical_harmonics_forward(self, width, ell, m):
r"""SWSFT of Y_m^\ell has only one nonzero coefficient, at (ell, m)."""
longitude_g, colatitude_g = sphere_utils.make_equiangular_grid(width)
sphere = scipy.special.sph_harm(m, ell, longitude_g, colatitude_g)
coeffs = np_spin_spherical_harmonics.swsft_forward_naive(sphere, 0)
self._check_nonzero_harmonic_coeffs(coeffs, ell, m)