def test_cubicspline_and_deriv(self):
"""Test spline for derivation."""
odg = OneDGrid(np.arange(10) + 1, np.ones(10), (0, np.inf))
rad = IdentityRTransform().transform_1d_grid(odg)
atgrid = AtomGrid.from_pruned(rad, 1, r_sectors=[], 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[:, 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(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(result, np.abs(rad), theta, phi, deriv=1)
assert_allclose(interp, ref_value)
with self.assertRaises(ValueError):
interp = interpolate(result,
6,
semi_sph_c[:, 1],
semi_sph_c[:, 2],
deriv=4)
with self.assertRaises(ValueError):
interp = interpolate(result,
6,
semi_sph_c[:, 1],
semi_sph_c[:, 2],
deriv=-1)
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_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_cubicspline_and_interp_gauss(self):
"""Test cubicspline interpolation values."""
oned = GaussLegendre(30)
btf = BeckeTF(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(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)