def testSphHarmCornerCaseWithWrongNmax(self):
"""Tests the corner case where `n_max` is not the maximum value of `n`."""
m = jnp.array([2])
n = jnp.array([10])
n_clipped = jnp.array([6])
n_max = 6
theta = jnp.array([0.9])
phi = jnp.array([0.2])
expected = lsp_special.sph_harm(m, n, theta, phi, n_max)
actual = lsp_special.sph_harm(m, n_clipped, theta, phi, n_max)
self.assertAllClose(actual, expected, rtol=1e-8, atol=9e-5)
def testSphHarmOrderZeroDegreeOne(self):
"""Tests the spherical harmonics of order one and degree zero."""
theta = jnp.array([2.0])
phi = jnp.array([3.1])
n_max = 1
expected = jnp.sqrt(3.0 / (4.0 * np.pi)) * jnp.cos(phi)
actual = jnp.real(
lsp_special.sph_harm(jnp.array([0]), jnp.array([1]), theta, phi, n_max))
self.assertAllClose(actual, expected, rtol=2e-7, atol=6e-8)
def testSphHarmOrderZeroDegreeZero(self):
"""Tests the spherical harmonics of order zero and degree zero."""
theta = jnp.array([0.3])
phi = jnp.array([2.3])
n_max = 0
expected = jnp.array([1.0 / jnp.sqrt(4.0 * np.pi)])
actual = jnp.real(
lsp_special.sph_harm(jnp.array([0]), jnp.array([0]), theta, phi, n_max))
self.assertAllClose(actual, expected, rtol=1.1e-7, atol=3e-8)
def testSphHarmOrderOneDegreeOne(self):
"""Tests the spherical harmonics of order one and degree one."""
theta = jnp.array([2.0])
phi = jnp.array([2.5])
n_max = 1
expected = (-1.0 / 2.0 * jnp.sqrt(3.0 / (2.0 * np.pi)) * jnp.sin(phi) *
jnp.exp(1j * theta))
actual = lsp_special.sph_harm(jnp.array([1]), jnp.array([1]), theta,
phi, n_max)
self.assertAllClose(actual, expected, rtol=1e-8, atol=6e-8)
def testSphHarmAccuracy(self):
m = jnp.arange(-3, 3)[:, None]
n = jnp.arange(3, 6)
n_max = 5
theta = 0.0
phi = jnp.pi
expected = lsp_special.sph_harm(m, n, theta, phi, n_max)
actual = osp_special.sph_harm(m, n, theta, phi)
self.assertAllClose(actual, expected, rtol=1e-8, atol=9e-5)