def testOrderZeroDegreeZero(self):
"""Tests the spherical harmonics of order zero and degree zero."""
num_theta = 6
num_phi = 4
expected = (1.0 / jnp.sqrt(4.0 * math.pi) * jnp.ones(
(1, 1, num_theta, num_phi)))
theta = jnp.linspace(0, math.pi, num_theta)
phi = jnp.linspace(0, 2.0 * math.pi, num_phi)
sph_harm = spherical_harmonics.SphericalHarmonics(l_max=0,
theta=theta,
phi=phi)
actual = jnp.real(sph_harm.harmonics_nonnegative_order())
np.testing.assert_allclose(actual, expected, rtol=1.1e-7, atol=3e-8)
def testOrderOneDegreeZero(self):
"""Tests the spherical harmonics of order one and degree zero."""
num_theta = 4
num_phi = 6
theta = jnp.linspace(0, math.pi, num_theta)
phi = jnp.linspace(0, 2.0 * math.pi, num_phi)
expected = jnp.sqrt(3.0 / (4.0 * math.pi)) * jnp.outer(
jnp.cos(theta), jnp.ones_like(phi))
sph_harm = spherical_harmonics.SphericalHarmonics(l_max=1,
theta=theta,
phi=phi)
actual = jnp.real(sph_harm.harmonics_nonnegative_order()[1, 0, :, :])
np.testing.assert_allclose(actual, expected, rtol=7e-8, atol=1.5e-8)
def testOrderOneDegreeOne(self):
"""Tests the spherical harmonics of order one and degree one."""
num_theta = 7
num_phi = 8
theta = jnp.linspace(0, math.pi, num_theta)
phi = jnp.linspace(0, 2.0 * math.pi, num_phi)
expected = -1.0 / 2.0 * jnp.sqrt(3.0 / (2.0 * math.pi)) * jnp.outer(
jnp.sin(theta), jnp.exp(1j * phi))
sph_harm = spherical_harmonics.SphericalHarmonics(l_max=1,
theta=theta,
phi=phi)
actual = sph_harm.harmonics_nonnegative_order()[1, 1, :, :]
np.testing.assert_allclose(jnp.abs(actual),
jnp.abs(expected),
rtol=1e-8,
atol=6e-8)
def testAgainstScipySpecialSphHarmNonnegativeOrder(self):
"""Tests the accuracy against scipy.special.sph_harm."""
l_max = 64
num_theta = 128
num_phi = 128
theta = jnp.linspace(0, math.pi, num_theta)
phi = jnp.linspace(0, 2.0 * math.pi, num_phi)
expected = _compute_spherical_harmonics(l_max=l_max,
theta=theta,
phi=phi)
sph_harm = spherical_harmonics.SphericalHarmonics(l_max=l_max,
theta=theta,
phi=phi)
actual = sph_harm.harmonics_nonnegative_order()
np.testing.assert_allclose(jnp.abs(actual),
jnp.abs(expected),
rtol=1e-8,
atol=9e-5)