def test_cubicspline_and_interp_mol(self):
"""Test cubicspline interpolation values."""
odg = OneDGrid(np.arange(10) + 1, np.ones(10), (0, np.inf))
rad = IdentityRTransform().transform_1d_grid(odg)
atgrid = AtomGrid.from_pruned(rad, 1, sectors_r=[], sectors_degree=[7])
values = self.helper_func_power(atgrid.points)
result = spline_with_atomic_grid(atgrid, values)
sph_coor = atgrid.convert_cart_to_sph()
semi_sph_c = sph_coor[atgrid.indices[5] : atgrid.indices[6]]
interp = interpolate(result, rad.points[5], semi_sph_c[:, 1], semi_sph_c[:, 2])
# same result from points and interpolation
assert_allclose(interp, values[atgrid.indices[5] : atgrid.indices[6]])
def test_interpolate_given_splines(self):
"""Test points to interpolate to is the same as original function values."""
# Construct grid
odg = OneDGrid(np.arange(10) + 1, np.ones(10), (0, np.inf))
rad = IdentityRTransform().transform_1d_grid(odg)
atgrid = AtomGrid.from_pruned(rad, 1, sectors_r=[], sectors_degree=[7])
# Construct the function values and splies.
values = self.helper_func_power(atgrid.points)
result = spline_with_atomic_grid(atgrid, values)
# Obtain the spherical coordinates and interpolate from indices[5] to indices[6]
sph_coor = atgrid.convert_cart_to_sph()
semi_sph_c = sph_coor[atgrid.indices[5]:atgrid.indices[6]]
interp = interpolate_given_splines(result, rad.points[5],
semi_sph_c[:, 1], semi_sph_c[:, 2])
# same result from points and interpolation
assert_allclose(interp, values[atgrid.indices[5]:atgrid.indices[6]])
def test_cubicspline_and_interp_gauss(self):
"""Test cubicspline interpolation values."""
oned = GaussLegendre(30)
btf = BeckeRTransform(0.0001, 1.5)
rad = btf.transform_1d_grid(oned)
atgrid = AtomGrid.from_pruned(rad, 1, sectors_r=[], sectors_degree=[7])
value_array = self.helper_func_gauss(atgrid.points)
result = spline_with_atomic_grid(atgrid, value_array)
# random test points on gauss function
for _ in range(20):
r = np.random.rand(1)[0] * 2
theta = np.random.rand(10)
phi = np.random.rand(10)
inters = interpolate_given_splines(result, r, theta, phi)
x = r * np.sin(phi) * np.cos(theta)
y = r * np.sin(phi) * np.sin(theta)
z = r * np.cos(phi)
assert_allclose(self.helper_func_gauss(np.array([x, y, z]).T),
inters,
atol=1e-4)
def test_poisson_proj(self):
"""Test the project function."""
oned = GaussChebyshev(30)
btf = BeckeRTransform(0.0001, 1.5)
rad = btf.transform_1d_grid(oned)
l_max = 7
atgrid = AtomGrid(rad, degrees=[l_max])
value_array = self.helper_func_gauss(atgrid.points)
spl_res = spline_with_atomic_grid(atgrid, value_array)
# test for random, r, theta, phi
for _ in range(20):
r = np.random.rand(1)[0] * 2
theta = np.random.rand(10) * 3.14
phi = np.random.rand(10) * 3.14
result = interpolate(spl_res, r, theta, phi)
x = r * np.sin(phi) * np.cos(theta)
y = r * np.sin(phi) * np.sin(theta)
z = r * np.cos(phi)
result_ref = self.helper_func_gauss(np.array([x, y, z]).T)
# assert similar value less than 1e-4 discrepancy
assert_allclose(result, result_ref, atol=1e-4)
sph_coor = atgrid.convert_cart_to_sph()[:, 1:3]
spls_mt = Poisson._proj_sph_value(
atgrid.rgrid,
sph_coor,
l_max // 2,
value_array,
atgrid.weights,
atgrid.indices,
)
# test each point is the same
for _ in range(20):
r = np.random.rand(1)[0] * 2
# random spherical point
int_res = np.zeros((l_max, l_max // 2 + 1), dtype=float)
for j in range(l_max // 2 + 1):
for i in range(-j, j + 1):
int_res[i, j] += spls_mt[i, j](r)
assert_allclose(spl_res(r), int_res)