def test_spherical_average_of_spherical_harmonic(self):
r"""Test spherical average of spherical harmonic is zero."""
# construct helper function
def func(sph_points):
# Spherical harmonic of order 6 and magnetic 0
r, phi, theta = sph_points.T
return (np.sqrt(13) / (np.sqrt(np.pi) * 32) *
(231 * np.cos(theta)**6.0 - 315 * np.cos(theta)**4.0 +
105 * np.cos(theta)**2.0 - 5.0))
# Construct Radial Grid and atomic grid with spherical harmonics of degree 10
# for all points.
oned_grid = np.arange(0.0, 5.0, 0.001)
rad = OneDGrid(oned_grid, np.ones(len(oned_grid)), (0, np.inf))
atgrid = AtomGrid(rad, degrees=[10])
spherical_pts = atgrid.convert_cartesian_to_spherical(atgrid.points)
func_values = func(spherical_pts)
spherical_avg = atgrid.spherical_average(func_values)
# Test that the spherical average of a spherical harmonic is zero.
numb_pts = 1000
random_rad_pts = np.random.uniform(0.02, np.pi, size=(numb_pts, 3))
spherical_avg2 = spherical_avg(random_rad_pts[:, 0])
assert_allclose(spherical_avg2, 0.0, atol=1e-4)
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_spherical_average_of_gaussian(self):
r"""Test spherical average of a Gaussian (radial) function is itself and its integral."""
# construct helper function
def func(sph_points):
return np.exp(-sph_points[:, 0]**2.0)
# Construct Radial Grid and atomic grid with spherical harmonics of degree 10
# for all points.
oned_grid = np.arange(0.0, 5.0, 0.001)
rad = OneDGrid(oned_grid, np.ones(len(oned_grid)), (0, np.inf))
atgrid = AtomGrid(rad, degrees=[5])
spherical_pts = atgrid.convert_cartesian_to_spherical(atgrid.points)
func_values = func(spherical_pts)
spherical_avg = atgrid.spherical_average(func_values)
# Test that the spherical average of a Gaussian is itself
numb_pts = 1000
random_rad_pts = np.random.uniform(0.0, 1.5, size=(numb_pts, 3))
spherical_avg2 = spherical_avg(random_rad_pts[:, 0])
func_vals = func(random_rad_pts)
assert_allclose(spherical_avg2, func_vals, atol=1e-4)
# Test the integral of spherical average is the integral of Gaussian e^(-x^2)e^(-y^2)...
# from -infinity to infinity which is equal to pi^(3/2)
integral = (
4.0 * np.pi *
np.trapz(y=spherical_avg(oned_grid) * oned_grid**2.0, x=oned_grid))
actual_integral = np.sqrt(np.pi)**3.0
assert_allclose(actual_integral, integral)
def test_integrating_angular_components(self):
"""Test radial points that contain zero."""
odg = OneDGrid(np.array([0.0, 1e-16, 1e-8, 1e-4, 1e-2]), np.ones(5),
(0, np.inf))
atom_grid = AtomGrid(odg, degrees=[3])
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(
3,
spherical[:, 1],
spherical[:, 2] # theta, phi points
)
# Convert to three-dimensional array (Degrees, Order, Points)
spherical_array = np.zeros((3, 2 * 3 + 1, len(atom_grid.points)))
spherical_array[0, 0, :] = spherical_harmonics[0, :] # (l,m) = (0,0)
spherical_array[1, 0, :] = spherical_harmonics[1, :] # = (1, 0)
spherical_array[1, 1, :] = spherical_harmonics[2, :] # = (1, 1)
spherical_array[1, 2, :] = spherical_harmonics[3, :] # = (1, -1)
spherical_array[2, 0, :] = spherical_harmonics[4, :] # = (2, 0)
spherical_array[2, 1, :] = spherical_harmonics[5, :] # = (2, 2)
spherical_array[2, 2, :] = spherical_harmonics[6, :] # = (2, 1)
spherical_array[2, 3, :] = spherical_harmonics[7, :] # = (2, -2)
spherical_array[2, 4, :] = spherical_harmonics[8, :] # = (2, -1)
integral = atom_grid.integrate_angular_coordinates(spherical_array)
assert integral.shape == (3, 2 * 3 + 1, 5)
# Assert that all spherical harmonics except when l=0,m=0 are all zero.
assert_almost_equal(integral[0, 0, :], np.sqrt(4.0 * np.pi))
assert_almost_equal(integral[0, 1:, :], 0.0)
assert_almost_equal(integral[1:, :, :], 0.0)
def test_convert_points_to_sph(self):
"""Test convert random points to spherical based on atomic structure."""
rad_pts = np.array([0.1, 0.5, 1])
rad_wts = np.array([0.3, 0.4, 0.3])
rad_grid = OneDGrid(rad_pts, rad_wts)
center = np.random.rand(3)
atgrid = AtomGrid(rad_grid, degrees=[7], center=center)
points = np.random.rand(100, 3)
calc_sph = atgrid.convert_cart_to_sph(points)
# compute ref result
ref_coor = points - center
# radius
r = np.linalg.norm(ref_coor, axis=-1)
# azimuthal
theta = np.arctan2(ref_coor[:, 1], ref_coor[:, 0])
# polar
phi = np.arccos(ref_coor[:, 2] / r)
assert_allclose(np.stack([r, theta, phi]).T, calc_sph)
assert_equal(calc_sph.shape, (100, 3))
# test single point
point = np.random.rand(3)
calc_sph = atgrid.convert_cart_to_sph(point)
ref_coor = point - center
r = np.linalg.norm(ref_coor)
theta = np.arctan2(ref_coor[1], ref_coor[0])
phi = np.arccos(ref_coor[2] / r)
assert_allclose(np.array([r, theta, phi]).reshape(-1, 3), calc_sph)
def test_generate_spherical(self):
"""Test generated real spherical harmonics values."""
atgrid = AngularGrid(degree=7)
pts = atgrid.points
wts = atgrid.weights
r = np.linalg.norm(pts, axis=1)
# polar
phi = np.arccos(pts[:, 2] / r)
# azimuthal
theta = np.arctan2(pts[:, 1], pts[:, 0])
# generate spherical harmonics
sph_h = AtomGrid._generate_real_sph_harm(3, theta, phi) # l_max = 3
assert sph_h.shape == (16, 26)
for _ in range(100):
n1, n2 = np.random.randint(0, 16, 2)
re = sum(sph_h[n1] * sph_h[n2] * wts)
if n1 != n2:
print(n1, n2, re)
assert_almost_equal(re, 0)
else:
print(n1, n2, re)
assert_almost_equal(re, 1)
for i in range(10):
sph_h = AtomGrid._generate_real_sph_harm(i, theta, phi)
assert sph_h.shape == ((i + 1)**2, 26)
def test_spherical_complete(self):
"""Test atomitc grid consistence for spherical integral."""
num_pts = len(LEBEDEV_DEGREES)
pts = HortonLinear(num_pts)
for _ in range(10):
start = np.random.rand() * 1e-5
end = np.random.rand() * 10 + 10
tf = PowerRTransform(start, end)
rad_grid = tf.transform_1d_grid(pts)
atgrid = AtomGrid(rad_grid, degrees=list(LEBEDEV_DEGREES.keys()))
values = np.random.rand(len(LEBEDEV_DEGREES))
pt_val = np.zeros(atgrid.size)
for index, value in enumerate(values):
pt_val[atgrid._indices[index]:atgrid._indices[index +
1]] = value
rad_int_val = (value * rad_grid.weights[index] * 4 * np.pi *
rad_grid.points[index]**2)
atgrid_int_val = np.sum(
pt_val[atgrid._indices[index]:atgrid._indices[index + 1]] *
atgrid.weights[atgrid._indices[index]:atgrid.
_indices[index + 1]])
assert_almost_equal(rad_int_val, atgrid_int_val)
ref_int_at = atgrid.integrate(pt_val)
ref_int_rad = rad_grid.integrate(4 * np.pi * rad_grid.points**2 *
values)
assert_almost_equal(ref_int_at, ref_int_rad)
def test_from_size(self):
"""Test horton style grid."""
nums = np.array([1, 1])
coors = np.array([[0, 0, -0.5], [0, 0, 0.5]])
becke = BeckeWeights(order=3)
mol_grid = MolGrid.from_size(nums,
coors,
self.rgrid,
110,
becke,
rotate=False)
atg1 = AtomGrid.from_pruned(
self.rgrid,
0.5,
sectors_r=np.array([]),
sectors_degree=np.array([17]),
center=coors[0],
)
atg2 = AtomGrid.from_pruned(
self.rgrid,
0.5,
sectors_r=np.array([]),
sectors_degree=np.array([17]),
center=coors[1],
)
ref_grid = MolGrid(nums, [atg1, atg2], becke, store=True)
assert_allclose(ref_grid.points, mol_grid.points)
assert_allclose(ref_grid.weights, mol_grid.weights)
def test_total_atomic_grid(self):
"""Normal initialization test."""
radial_pts = np.arange(0.1, 1.1, 0.1)
radial_wts = np.ones(10) * 0.1
rgrid = OneDGrid(radial_pts, radial_wts)
rad = 0.5
r_sectors = np.array([0.5, 1, 1.5])
degs = np.array([6, 14, 14, 6])
# generate a proper instance without failing.
ag_ob = AtomGrid.from_pruned(rgrid,
radius=rad,
sectors_r=r_sectors,
sectors_degree=degs)
assert isinstance(ag_ob, AtomGrid)
assert len(ag_ob.indices) == 11
assert ag_ob.l_max == 15
ag_ob = AtomGrid.from_pruned(rgrid,
radius=rad,
sectors_r=np.array([]),
sectors_degree=np.array([6]))
assert isinstance(ag_ob, AtomGrid)
assert len(ag_ob.indices) == 11
ag_ob = AtomGrid(rgrid, sizes=[110])
assert ag_ob.l_max == 17
assert_array_equal(ag_ob._degs, np.ones(10) * 17)
assert ag_ob.size == 110 * 10
# new init AtomGrid
ag_ob2 = AtomGrid(rgrid, degrees=[17])
assert ag_ob2.l_max == 17
assert_array_equal(ag_ob2._degs, np.ones(10) * 17)
assert ag_ob2.size == 110 * 10
assert isinstance(ag_ob.rgrid, OneDGrid)
assert_allclose(ag_ob.rgrid.points, rgrid.points)
assert_allclose(ag_ob.rgrid.weights, rgrid.weights)
def test_integrate_hydrogen_trimer_1s(self):
"""Test molecular integral in H3."""
coordinates = np.array(
[[0.0, 0.0, -0.5], [0.0, 0.0, 0.5], [0.0, 0.5, 0.0]], float)
atg1 = AtomGrid.from_pruned(
self.rgrid,
0.5,
r_sectors=np.array([]),
degs=np.array([17]),
center=coordinates[0],
)
atg2 = AtomGrid.from_pruned(
self.rgrid,
0.5,
r_sectors=np.array([]),
degs=np.array([17]),
center=coordinates[1],
)
atg3 = AtomGrid.from_pruned(
self.rgrid,
0.5,
r_sectors=np.array([]),
degs=np.array([17]),
center=coordinates[2],
)
becke = BeckeWeights(order=3)
mg = MolGrid([atg1, atg2, atg3], becke, np.array([1, 1, 1]))
dist0 = np.sqrt(((coordinates[0] - mg.points)**2).sum(axis=1))
dist1 = np.sqrt(((coordinates[1] - mg.points)**2).sum(axis=1))
dist2 = np.sqrt(((coordinates[2] - mg.points)**2).sum(axis=1))
fn = (np.exp(-2 * dist0) / np.pi + np.exp(-2 * dist1) / np.pi +
np.exp(-2 * dist2) / np.pi)
occupation = mg.integrate(fn)
assert_almost_equal(occupation, 3.0, decimal=4)
def test_poisson_solve_mtr_cmpl(self):
"""Test solve poisson equation and interpolate the result."""
oned = GaussChebyshev(50)
btf = BeckeRTransform(1e-7, 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)
p_0 = atgrid.integrate(value_array)
# test density sum up to np.pi**(3 / 2)
assert_allclose(p_0, np.pi**1.5, 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,
)
ibtf = InverseRTransform(btf)
linsp = np.linspace(-1, 0.99, 50)
bound = p_0 * np.sqrt(4 * np.pi)
pois_mtr = Poisson.solve_poisson(spls_mt, linsp, bound, tfm=ibtf)
assert pois_mtr.shape == (7, 4)
near_rg_pts = np.array([1e-2, 0.1, 0.2, 0.3, 0.5, 0.7, 1.0, 1.2])
near_tf_pts = ibtf.transform(near_rg_pts)
ref_short_res = [
6.28286, # 0.01
6.26219, # 0.1
6.20029, # 0.2
6.09956, # 0.3
5.79652, # 0.5
5.3916, # 0.7
4.69236, # 1.0
4.22403, # 1.2
]
for i, j in enumerate(near_tf_pts):
assert_almost_equal(
Poisson.interpolate_radial(pois_mtr, j, 0, True) /
near_rg_pts[i],
ref_short_res[i] * np.sqrt(4 * np.pi),
decimal=3,
)
matrix_result = Poisson.interpolate_radial(pois_mtr, j)
assert_almost_equal(
matrix_result[0, 0] / near_rg_pts[i],
ref_short_res[i] * np.sqrt(4 * np.pi),
decimal=3,
)
# test interpolate with sph
result = Poisson.interpolate(pois_mtr, j, np.random.rand(5),
np.random.rand(5))
assert_allclose(result / near_rg_pts[i] - ref_short_res[i],
np.zeros(5),
atol=1e-3)
def test_atomic_grid(self):
"""Test atomic grid center transilation."""
rad_pts = np.array([0.1, 0.5, 1])
rad_wts = np.array([0.3, 0.4, 0.3])
rad_grid = OneDGrid(rad_pts, rad_wts)
degs = np.array([3, 5, 7])
# origin center
# randome center
pts, wts, ind = AtomGrid._generate_atomic_grid(rad_grid, degs)
ref_pts, ref_wts, ref_ind = AtomGrid._generate_atomic_grid(rad_grid, degs)
# diff grid points diff by center and same weights
assert_allclose(pts, ref_pts)
assert_allclose(wts, ref_wts)
def test_interpolation_of_laplacian_with_spherical_harmonic(self):
r"""Test the interpolation of Laplacian of spherical harmonic is eigenvector."""
odg = OneDGrid(np.linspace(0.0, 10, num=2000), np.ones(2000),
(0, np.inf))
rad = IdentityRTransform().transform_1d_grid(odg)
degree = 6 * 2 + 2
atgrid = AtomGrid.from_pruned(rad,
1,
sectors_r=[],
sectors_degree=[degree])
def func(sph_points):
# Spherical harmonic of order 6 and magnetic 0
r, phi, theta = sph_points.T
return (np.sqrt(2.0) * np.sqrt(13) / (np.sqrt(np.pi) * 32) *
(231 * np.cos(theta)**6.0 - 315 * np.cos(theta)**4.0 +
105 * np.cos(theta)**2.0 - 5.0))
# Get spherical points from atomic grid
spherical_pts = atgrid.convert_cartesian_to_spherical(atgrid.points)
func_values = func(spherical_pts)
laplacian = atgrid.interpolate_laplacian(func_values)
# Test on the same points used for interpolation and random points.
for grid in [atgrid.points, np.random.uniform(-0.75, 0.75, (250, 3))]:
actual = laplacian(grid)
spherical_pts = atgrid.convert_cartesian_to_spherical(grid)
# Eigenvector spherical harmonic times l(l + 1) / r^2
with np.errstate(divide="ignore", invalid="ignore"):
desired = (-func(spherical_pts) * 6 * (6 + 1) /
spherical_pts[:, 0]**2.0)
desired[spherical_pts[:, 0]**2.0 < 1e-10] = 0.0
assert_almost_equal(actual, desired, decimal=3)
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_interpolation_of_laplacian_of_exponential(self):
r"""Test the interpolation of Laplacian of exponential."""
odg = OneDGrid(np.linspace(0.01, 1, num=1000), np.ones(1000),
(0, np.inf))
degree = 10
atgrid = AtomGrid.from_pruned(odg,
1,
sectors_r=[],
sectors_degree=[degree])
def func(cart_pts):
radius = np.linalg.norm(cart_pts, axis=1)
return np.exp(-radius)
func_values = func(atgrid.points)
laplacian = atgrid.interpolate_laplacian(func_values)
# Test on the same points used for interpolation and random points.
for grid in [atgrid.points, np.random.uniform(-0.5, 0.5, (250, 3))]:
actual = laplacian(grid)
spherical_pts = atgrid.convert_cartesian_to_spherical(grid)
# Laplacian of exponential is e^-x (x - 2) / x
desired = (np.exp(-spherical_pts[:, 0]) *
(spherical_pts[:, 0] - 2.0) / spherical_pts[:, 0])
assert_almost_equal(actual, desired, decimal=3)
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)
for _ in range(10):
degree = np.random.randint(5, 20)
atgrid = AtomGrid.from_pruned(rad,
1,
sectors_r=[],
sectors_degree=[degree])
values = self.helper_func_power(atgrid.points)
# spls = atgrid.fit_values(values)
for i in range(10):
interp = atgrid.interpolate(
atgrid.points[atgrid.indices[i]:atgrid.indices[i + 1]],
values,
deriv=1,
)
# same result from points and interpolation
ref_deriv = self.helper_func_power_deriv(
atgrid.points[atgrid.indices[i]:atgrid.indices[i + 1]])
assert_allclose(interp, ref_deriv)
# test random x, y, z with fd
for _ in range(10):
xyz = np.random.rand(10, 3) * np.random.uniform(1, 6)
ref_value = self.helper_func_power_deriv(xyz)
interp = atgrid.interpolate(xyz, values, deriv=1)
assert_allclose(interp, ref_value)
def test_cubicspline_and_interp(self):
"""Test cubicspline interpolation values."""
odg = OneDGrid(np.arange(10) + 1, np.ones(10), (0, np.inf))
rad_grid = IdentityRTransform().transform_1d_grid(odg)
for _ in range(10):
degree = np.random.randint(5, 20)
atgrid = AtomGrid.from_pruned(rad_grid,
1,
sectors_r=[],
sectors_degree=[degree])
values = self.helper_func_power(atgrid.points)
# spls = atgrid.fit_values(values)
for i in range(10):
interp = atgrid.interpolate(
atgrid.points[atgrid.indices[i]:atgrid.indices[i + 1]],
values)
# same result from points and interpolation
assert_allclose(
interp, values[atgrid.indices[i]:atgrid.indices[i + 1]])
# test random x, y, z
for _ in range(10):
xyz = np.random.rand(10, 3) * np.random.uniform(1, 6)
# 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)
interp = atgrid.interpolate(xyz, values)
assert_allclose(interp, ref_value)
def test_molgrid_attrs(self):
"""Test MolGrid attributes."""
# numbers = np.array([6, 8], int)
coordinates = np.array([[0.0, 0.2, -0.5], [0.1, 0.0, 0.5]], float)
atg1 = AtomGrid.from_pruned(
self.rgrid,
1.228,
r_sectors=np.array([]),
degs=np.array([17]),
center=coordinates[0],
)
atg2 = AtomGrid.from_pruned(
self.rgrid,
0.945,
r_sectors=np.array([]),
degs=np.array([17]),
center=coordinates[1],
)
becke = BeckeWeights(order=3)
mg = MolGrid([atg1, atg2], becke, np.array([6, 8]), store=True)
assert mg.size == 2 * 110 * 100
assert mg.points.shape == (mg.size, 3)
assert mg.weights.shape == (mg.size, )
assert mg.aim_weights.shape == (mg.size, )
assert mg.get_atomic_grid(0) is atg1
assert mg.get_atomic_grid(1) is atg2
simple_ag1 = mg.get_atomic_grid(0)
simple_ag2 = mg.get_atomic_grid(1)
assert_allclose(simple_ag1.points, atg1.points)
assert_allclose(simple_ag1.weights, atg1.weights)
assert_allclose(simple_ag2.weights, atg2.weights)
# test molgrid is not stored
mg2 = MolGrid([atg1, atg2], becke, np.array([6, 8]), store=False)
assert mg2._atomic_grids is None
simple2_ag1 = mg2.get_atomic_grid(0)
simple2_ag2 = mg2.get_atomic_grid(1)
assert isinstance(simple2_ag1, LocalGrid)
assert isinstance(simple2_ag2, LocalGrid)
assert_allclose(simple2_ag1.points, atg1.points)
assert_allclose(simple2_ag1.weights, atg1.weights)
assert_allclose(simple2_ag2.weights, atg2.weights)
def test_molgrid_attrs_subgrid(self):
"""Test sub atomic grid attributes."""
# numbers = np.array([6, 8], int)
coordinates = np.array([[0.0, 0.2, -0.5], [0.1, 0.0, 0.5]], float)
atg1 = AtomGrid.from_pruned(
self.rgrid,
1.228,
r_sectors=np.array([]),
degs=np.array([17]),
center=coordinates[0],
)
atg2 = AtomGrid.from_pruned(
self.rgrid,
0.945,
r_sectors=np.array([]),
degs=np.array([17]),
center=coordinates[1],
)
becke = BeckeWeights(order=3)
mg = MolGrid([atg1, atg2], becke, np.array([6, 8]), store=True)
# mg = BeckeMolGrid(coordinates, numbers, None, (rgrid, 110), mode='keep')
assert mg.size == 2 * 110 * 100
assert mg.points.shape == (mg.size, 3)
assert mg.weights.shape == (mg.size, )
assert mg.aim_weights.shape == (mg.size, )
assert len(mg._indices) == 2 + 1
# assert mg.k == 3
# assert mg.random_rotate
for i in range(2):
atgrid = mg[i]
assert isinstance(atgrid, AtomGrid)
assert atgrid.size == 100 * 110
assert atgrid.points.shape == (100 * 110, 3)
assert atgrid.weights.shape == (100 * 110, )
assert (atgrid.center == coordinates[i]).all()
mg = MolGrid([atg1, atg2], becke, np.array([6, 8]))
for i in range(2):
atgrid = mg[i]
assert isinstance(atgrid, LocalGrid)
assert_allclose(atgrid.center, mg._coors[i])
def test_find_l_for_rad_list(self):
"""Test private method find_l_for_rad_list."""
radial_pts = np.arange(0.1, 1.1, 0.1)
radial_wts = np.ones(10) * 0.1
rgrid = OneDGrid(radial_pts, radial_wts)
rad = 1
r_sectors = np.array([0.2, 0.4, 0.8])
degs = np.array([3, 5, 7, 3])
atomic_grid_degree = AtomGrid._find_l_for_rad_list(
rgrid.points, rad * r_sectors, degs)
assert_equal(atomic_grid_degree, [3, 3, 5, 5, 7, 7, 7, 7, 3, 3])
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_from_pruned_with_degs_and_size(self):
"""Test different initilize method."""
radial_pts = np.arange(0.1, 1.1, 0.1)
radial_wts = np.ones(10) * 0.1
rgrid = OneDGrid(radial_pts, radial_wts)
rad = 0.5
r_sectors = np.array([0.5, 1, 1.5])
degs = np.array([3, 5, 7, 5])
size = np.array([6, 14, 26, 14])
# construct atomic grid with degs
atgrid1 = AtomGrid.from_pruned(
rgrid, radius=rad, sectors_r=r_sectors, sectors_degree=degs
)
# construct atomic grid with size
atgrid2 = AtomGrid.from_pruned(
rgrid, radius=rad, sectors_r=r_sectors, sectors_size=size
)
# test two grids are the same
assert_equal(atgrid1.size, atgrid2.size)
assert_allclose(atgrid1.points, atgrid2.points)
assert_allclose(atgrid1.weights, atgrid2.weights)
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)
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)
# spls = atgrid.fit_values(values)
for i in range(10):
interp = atgrid.interpolate(
atgrid.points[atgrid.indices[i]:atgrid.indices[i + 1]], values)
# same result from points and interpolation
assert_allclose(interp,
values[atgrid.indices[i]:atgrid.indices[i + 1]])
def test_raises_errors(self):
"""Test proper error raises."""
oned = GaussChebyshev(50)
btf = BeckeRTransform(1e-7, 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)
p_0 = atgrid.integrate(value_array)
# test density sum up to np.pi**(3 / 2)
assert_allclose(p_0, np.pi**1.5, atol=1e-4)
sph_coor = atgrid.convert_cart_to_sph()
with self.assertRaises(ValueError):
Poisson._proj_sph_value(
atgrid.rgrid,
sph_coor,
l_max // 2,
value_array,
atgrid.weights,
atgrid.indices,
)
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_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
def test_get_shell_grid(self):
"""Test angular grid get from get_shell_grid function."""
rad_pts = np.array([0.1, 0.5, 1])
rad_wts = np.array([0.3, 0.4, 0.3])
rad_grid = OneDGrid(rad_pts, rad_wts)
degs = [3, 5, 7]
atgrid = AtomGrid(rad_grid, degrees=degs)
assert atgrid.n_shells == 3
# grep shell with r^2
for i in range(atgrid.n_shells):
sh_grid = atgrid.get_shell_grid(i)
assert isinstance(sh_grid, AngularGrid)
ref_grid = AngularGrid(degree=degs[i])
assert np.allclose(sh_grid.points, ref_grid.points * rad_pts[i])
assert np.allclose(sh_grid.weights,
ref_grid.weights * rad_wts[i] * rad_pts[i]**2)
# grep shell without r^2
for i in range(atgrid.n_shells):
sh_grid = atgrid.get_shell_grid(i, r_sq=False)
assert isinstance(sh_grid, AngularGrid)
ref_grid = AngularGrid(degree=degs[i])
assert np.allclose(sh_grid.points, ref_grid.points * rad_pts[i])
assert np.allclose(sh_grid.weights, ref_grid.weights * rad_wts[i])
def test_integrate_hirshfeld_weights_pair_1s(self):
"""Test molecular integral in H2."""
coordinates = np.array([[0.0, 0.0, -0.5], [0.0, 0.0, 0.5]])
atg1 = AtomGrid.from_pruned(
self.rgrid,
0.5,
r_sectors=np.array([]),
degs=np.array([17]),
center=coordinates[0],
)
atg2 = AtomGrid.from_pruned(
self.rgrid,
0.5,
r_sectors=np.array([]),
degs=np.array([17]),
center=coordinates[1],
)
mg = MolGrid([atg1, atg2], HirshfeldWeights(), np.array([1, 1]))
dist0 = np.sqrt(((coordinates[0] - mg.points)**2).sum(axis=1))
dist1 = np.sqrt(((coordinates[1] - mg.points)**2).sum(axis=1))
fn = np.exp(-2 * dist0) / np.pi + 1.5 * np.exp(-2 * dist1) / np.pi
occupation = mg.integrate(fn)
assert_almost_equal(occupation, 2.5, decimal=5)
def test_horton_molgrid(self):
"""Test horton style grid."""
nums = np.array([1, 1])
coors = np.array([[0, 0, -0.5], [0, 0, 0.5]])
becke = BeckeWeights(order=3)
mol_grid = MolGrid.horton_molgrid(coors, nums, self.rgrid, 110, becke)
atg1 = AtomGrid.from_pruned(
self.rgrid,
0.5,
r_sectors=np.array([]),
degs=np.array([17]),
center=coors[0],
)
atg2 = AtomGrid.from_pruned(
self.rgrid,
0.5,
r_sectors=np.array([]),
degs=np.array([17]),
center=coors[1],
)
ref_grid = MolGrid([atg1, atg2], becke, nums, store=True)
assert_allclose(ref_grid.points, mol_grid.points)
assert_allclose(ref_grid.weights, mol_grid.weights)
