def test_spline_with_sph_harms(self):
"""Test spline projection the same as spherical harmonics."""
rad = IdentityRTransform().transform_grid(HortonLinear(10))
rad._points += 1
atgrid = AtomicGrid.special_init(rad, 1, scales=[], degs=[7])
sph_coor = atgrid.convert_cart_to_sph()
values = self.helper_func_power(atgrid.points)
l_max = atgrid.l_max // 2
r_sph = generate_real_sph_harms(l_max, sph_coor[:, 0], sph_coor[:, 1])
result = spline_with_sph_harms(
r_sph, values, atgrid.weights, atgrid.indices, rad.points
)
# generate ref
# for shell in range(1, 11):
for shell in range(1, 11):
sh_grid = atgrid.get_shell_grid(shell - 1, r_sq=False)
r = np.linalg.norm(sh_grid._points, axis=1)
theta = np.arctan2(sh_grid._points[:, 1], sh_grid._points[:, 0])
phi = np.arccos(sh_grid._points[:, 2] / r)
r_sph = generate_real_sph_harms(l_max, theta, phi)
r_sph_proj = np.sum(
r_sph * self.helper_func_power(sh_grid.points) * sh_grid.weights,
axis=-1,
)
assert_allclose(r_sph_proj, result(shell), atol=1e-10)
def test_spline_with_sph_harms(self):
"""Test spline projection the same as spherical harmonics."""
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])
sph_coor = atgrid.convert_cart_to_sph()
values = self.helper_func_power(atgrid.points)
l_max = atgrid.l_max // 2
r_sph = generate_real_sph_harms(l_max, sph_coor[:, 1], sph_coor[:, 2])
result = spline_with_sph_harms(r_sph, values, atgrid.weights,
atgrid.indices, rad)
# generate ref
for shell in range(1, 11):
sh_grid = atgrid.get_shell_grid(shell - 1, r_sq=False)
# Convert to spherical harmonics
r = np.linalg.norm(sh_grid._points, axis=1)
theta = np.arctan2(sh_grid._points[:, 1], sh_grid._points[:, 0])
phi = np.arccos(sh_grid._points[:, 2] / r)
# General all spherical harmonics up to l_max
r_sph = generate_real_sph_harms(l_max, theta, phi)
# Project the function 2x^2 + 3y^2 + 4z^2
r_sph_proj = np.sum(
r_sph * self.helper_func_power(sh_grid.points) *
sh_grid.weights,
axis=-1,
)
# Check the actual projection against the cubic spline interpolation.
assert_allclose(r_sph_proj, result(shell), atol=1e-10)
def test_derivative_of_interpolate_given_splines(self):
"""Test the spline interpolating derivative of function in radial coordinate."""
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])
sph_coor = atgrid.convert_cart_to_sph()
values = self.helper_func_power(atgrid.points)
l_max = atgrid.l_max // 2
r_sph = generate_real_sph_harms(l_max, sph_coor[:, 1], sph_coor[:, 2])
result = spline_with_sph_harms(r_sph, values, atgrid.weights,
atgrid.indices, rad)
semi_sph_c = sph_coor[atgrid.indices[5]:atgrid.indices[6]]
interp = interpolate_given_splines(result,
6,
semi_sph_c[:, 1],
semi_sph_c[:, 2],
deriv=1)
# same result from points and interpolation
ref_deriv = self.helper_func_power_deriv(
atgrid.points[atgrid.indices[5]:atgrid.indices[6]])
assert_allclose(interp, ref_deriv)
# test random x, y, z with fd
xyz = np.random.rand(1, 3)
xyz /= np.linalg.norm(xyz, axis=-1)[:, None]
rad = np.random.normal() * np.random.randint(1, 11)
xyz *= rad
ref_value = self.helper_func_power_deriv(xyz)
r = np.linalg.norm(xyz, axis=-1)
theta = np.arctan2(xyz[:, 1], xyz[:, 0])
phi = np.arccos(xyz[:, 2] / r)
interp = interpolate_given_splines(result,
np.abs(rad),
theta,
phi,
deriv=1)
assert_allclose(interp, ref_value)
with self.assertRaises(ValueError):
interpolate_given_splines(result,
6,
semi_sph_c[:, 1],
semi_sph_c[:, 2],
deriv=4)
with self.assertRaises(ValueError):
interpolate_given_splines(result,
6,
semi_sph_c[:, 1],
semi_sph_c[:, 2],
deriv=-1)
def test_cubicspline_and_deriv(self):
"""Test spline for derivation."""
rad = IdentityRTransform().transform_grid(HortonLinear(10))
rad._points += 1
atgrid = AtomicGrid.special_init(rad, 1, scales=[], degs=[7])
sph_coor = atgrid.convert_cart_to_sph()
values = self.helper_func_power(atgrid.points)
l_max = atgrid.l_max // 2
r_sph = generate_real_sph_harms(l_max, sph_coor[:, 0], sph_coor[:, 1])
result = spline_with_sph_harms(
r_sph, values, atgrid.weights, atgrid.indices, rad.points
)
semi_sph_c = sph_coor[atgrid.indices[5] : atgrid.indices[6]]
interp = interpolate(result, 6, semi_sph_c[:, 0], semi_sph_c[:, 1], deriv=1)
# same result from points and interpolation
ref_deriv = self.helper_func_power_deriv(
atgrid.points[atgrid.indices[5] : atgrid.indices[6]]
)
assert_allclose(interp, ref_deriv)
# test random x, y, z with fd
xyz = np.random.rand(1, 3)
xyz /= np.linalg.norm(xyz, axis=-1)[:, None]
rad = np.random.normal() * np.random.randint(1, 11)
xyz *= rad
ref_value = self.helper_func_power_deriv(xyz)
r = np.linalg.norm(xyz, axis=-1)
theta = np.arctan2(xyz[:, 1], xyz[:, 0])
phi = np.arccos(xyz[:, 2] / r)
interp = interpolate(result, np.abs(rad), theta, phi, deriv=1)
assert_allclose(interp, ref_value)
with self.assertRaises(ValueError):
interp = interpolate(result, 6, semi_sph_c[:, 0], semi_sph_c[:, 1], deriv=4)
with self.assertRaises(ValueError):
interp = interpolate(
result, 6, semi_sph_c[:, 0], semi_sph_c[:, 1], deriv=-1
)
def test_interpolate_given_splines_at_random_points(self):
"""Test interpolation given splines at random points."""
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])
sph_coor = atgrid.convert_cart_to_sph()
values = self.helper_func_power(atgrid.points)
l_max = atgrid.l_max // 2
r_sph = generate_real_sph_harms(l_max, sph_coor[:, 1], sph_coor[:, 2])
result = spline_with_sph_harms(r_sph, values, atgrid.weights,
atgrid.indices, rad)
semi_sph_c = sph_coor[atgrid.indices[5]:atgrid.indices[6]]
interp = interpolate_given_splines(result, 6, semi_sph_c[:, 1],
semi_sph_c[:, 2])
# same result from points and interpolation
assert_allclose(interp, values[atgrid.indices[5]:atgrid.indices[6]])
# random multiple interpolation test
for _ in range(100):
indices = np.random.randint(1, 11, np.random.randint(1, 10))
interp = interpolate_given_splines(result, indices,
semi_sph_c[:, 1], semi_sph_c[:,
2])
for i, j in enumerate(indices):
assert_allclose(
interp[i], values[atgrid.indices[j - 1]:atgrid.indices[j]])
# test random x, y, z
xyz = np.random.rand(10, 3)
xyz /= np.linalg.norm(xyz, axis=-1)[:, None]
rad = np.random.normal() * np.random.randint(1, 11)
xyz *= rad
ref_value = self.helper_func_power(xyz)
r = np.linalg.norm(xyz, axis=-1)
theta = np.arctan2(xyz[:, 1], xyz[:, 0])
phi = np.arccos(xyz[:, 2] / r)
interp = interpolate_given_splines(result, np.abs(rad), theta, phi)
assert_allclose(interp, ref_value)
def test_cubicspline_and_interp(self):
"""Test cubicspline interpolation values."""
rad = IdentityRTransform().transform_grid(HortonLinear(10))
rad._points += 1
atgrid = AtomicGrid.special_init(rad, 1, scales=[], degs=[7])
sph_coor = atgrid.convert_cart_to_sph()
values = self.helper_func_power(atgrid.points)
l_max = atgrid.l_max // 2
r_sph = generate_real_sph_harms(l_max, sph_coor[:, 0], sph_coor[:, 1])
result = spline_with_sph_harms(
r_sph, values, atgrid.weights, atgrid.indices, rad.points
)
semi_sph_c = sph_coor[atgrid.indices[5] : atgrid.indices[6]]
interp = interpolate(result, 6, semi_sph_c[:, 0], semi_sph_c[:, 1])
# same result from points and interpolation
assert_allclose(interp, values[atgrid.indices[5] : atgrid.indices[6]])
# random multiple interpolation test
for _ in range(100):
indices = np.random.randint(1, 11, np.random.randint(1, 10))
interp = interpolate(result, indices, semi_sph_c[:, 0], semi_sph_c[:, 1])
for i, j in enumerate(indices):
assert_allclose(
interp[i], values[atgrid.indices[j - 1] : atgrid.indices[j]]
)
# test random x, y, z
xyz = np.random.rand(10, 3)
xyz /= np.linalg.norm(xyz, axis=-1)[:, None]
rad = np.random.normal() * np.random.randint(1, 11)
xyz *= rad
ref_value = self.helper_func_power(xyz)
r = np.linalg.norm(xyz, axis=-1)
theta = np.arctan2(xyz[:, 1], xyz[:, 0])
phi = np.arccos(xyz[:, 2] / r)
interp = interpolate(result, np.abs(rad), theta, phi)
assert_allclose(interp, ref_value)
def test_cubicpline_and_interp(self):
"""Test cubicspline interpolation values."""
rad = HortonLinear(10)
rad._points += 1
atgrid = AtomicGrid(rad, 1, scales=[], degs=[7])
sph_coor = atgrid.convert_cart_to_sph()
values = self.helper_func_power(atgrid.points)
l_max = atgrid.l_max // 2
r_sph = generate_real_sph_harms(l_max, sph_coor[:, 0], sph_coor[:, 1])
result = spline_with_sph_harms(r_sph, values, atgrid.weights,
atgrid.indices, rad.points)
semi_sph_c = sph_coor[atgrid.indices[5]:atgrid.indices[6]]
interp = interpelate(result, 6, semi_sph_c[:, 0], semi_sph_c[:, 1])
# same result from points and interpolation
assert_allclose(interp, values[atgrid.indices[5]:atgrid.indices[6]])
# random multiple interpolation test
for _ in range(100):
indices = np.random.randint(1, 11, np.random.randint(1, 10))
interp = interpelate(result, indices, semi_sph_c[:, 0],
semi_sph_c[:, 1])
for i, j in enumerate(indices):
assert_allclose(
interp[i], values[atgrid.indices[j - 1]:atgrid.indices[j]])