def test_fitting_product_of_spherical_harmonic(self):
r"""Test fitting the radial components of r**2 times spherical harmonic."""
max_degree = 7 # Maximum degree
rad = OneDGrid(np.linspace(0.0, 1.0, num=10), np.ones(10), (0, np.inf))
atom_grid = AtomGrid(rad, degrees=[max_degree])
max_degree = atom_grid.l_max
spherical = atom_grid.convert_cartesian_to_spherical()
spherical_harmonic = generate_real_spherical_harmonics(
4,
spherical[:, 1],
spherical[:, 2] # theta, phi points
)
# Test on the function r^2 * Y^1_3
func_vals = spherical[:,
0]**2.0 * spherical_harmonic[(3 + 1)**2 + 1, :]
# Fit radial components
fit = atom_grid.radial_component_splines(func_vals)
radial_pts = np.arange(0.0, 1.0, 0.01)
i = 0
for l_value in range(0, max_degree // 2):
for m in ([0] + [x for x in range(1, l_value + 1)] +
[x for x in range(-l_value, 0)]):
if i != (3 + 1)**2 + 1:
assert_almost_equal(fit[i](radial_pts), 0.0, decimal=8)
else:
# Test that on the right spherical harmonic the function r* Y^1_3 projects
# to \rho^{1,3}(r) = r
assert_almost_equal(fit[i](radial_pts), radial_pts**2.0)
i += 1
def test_fitting_spherical_harmonics(self):
r"""Test fitting the radial components of spherical harmonics is just a one, rest zeros."""
max_degree = 10 # Maximum degree
rad = OneDGrid(np.linspace(0.0, 1.0, num=10), np.ones(10), (0, np.inf))
atom_grid = AtomGrid(rad, degrees=[max_degree])
max_degree = atom_grid.l_max
spherical = atom_grid.convert_cartesian_to_spherical()
# Evaluate all spherical harmonics on the atomic grid points (r_i, theta_j, phi_j).
spherical_harmonics = generate_real_spherical_harmonics(
max_degree,
spherical[:, 1],
spherical[:, 2] # theta, phi points
)
i = 0
# Go through each spherical harmonic up to max_degree // 2 and check if projection
# for its radial component is one and the rest are all zeros.
for l_value in range(0, max_degree // 2):
for m in ([0] + [x for x in range(1, l_value + 1)] +
[x for x in range(-l_value, 0)]):
spherical_harm = spherical_harmonics[i, :]
radial_components = atom_grid.radial_component_splines(
spherical_harm)
assert len(radial_components) == (atom_grid.l_max // 2 +
1)**2.0
radial_pts = np.arange(0.0, 1.0, 0.01)
# Go Through each (l, m)
for j, radial_comp in enumerate(radial_components):
# If the current index is j, then projection of spherical harmonic
# onto itself should be all ones, else they are all zero.
if i == j:
assert_almost_equal(radial_comp(radial_pts), 1.0)
else:
assert_almost_equal(radial_comp(radial_pts),
0.0,
decimal=8)
i += 1
