def test_atomic_rotate(self):
"""Test random rotation for atomic grid."""
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)
# make sure True and 1 is not the same result
atgrid1 = AtomGrid(rad_grid, degrees=degs, rotate=True)
atgrid2 = AtomGrid(rad_grid, degrees=degs, rotate=1)
# test diff points, same weights
assert not np.allclose(atgrid.points, atgrid1.points)
assert not np.allclose(atgrid.points, atgrid2.points)
assert not np.allclose(atgrid1.points, atgrid2.points)
assert_allclose(atgrid.weights, atgrid1.weights)
assert_allclose(atgrid.weights, atgrid2.weights)
assert_allclose(atgrid1.weights, atgrid2.weights)
# test same integral
value = np.prod(atgrid.points**2, axis=-1)
value1 = np.prod(atgrid.points**2, axis=-1)
value2 = np.prod(atgrid.points**2, axis=-1)
res = atgrid.integrate(value)
res1 = atgrid1.integrate(value1)
res2 = atgrid2.integrate(value2)
assert_almost_equal(res, res1)
assert_almost_equal(res1, res2)
# test rotated shells
for i in range(len(degs)):
non_rot_shell = atgrid.get_shell_grid(i).points
rot_shell = atgrid2.get_shell_grid(i).points
rot_mt = R.random(random_state=1 + i).as_matrix()
assert_allclose(rot_shell, non_rot_shell @ rot_mt)
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_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_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_poisson_solve(self):
"""Test the poisson solve function."""
oned = GaussChebyshev(30)
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,
)
# test splines project fit gauss function well
def gauss(r):
return np.exp(-(r**2))
for _ in range(20):
coors = np.random.rand(10, 3)
r = np.linalg.norm(coors, axis=-1)
spl_0_0 = spls_mt[0, 0]
interp_v = spl_0_0(r)
ref_v = gauss(r) * np.sqrt(4 * np.pi)
# 0.28209479 is the value in spherical harmonic Z_0_0
assert_allclose(interp_v, ref_v, atol=1e-3)
ibtf = InverseRTransform(btf)
linsp = np.linspace(-1, 0.99, 50)
bound = p_0 * np.sqrt(4 * np.pi)
res_bv = Poisson.solve_poisson_bv(spls_mt[0, 0],
linsp,
bound,
tfm=ibtf)
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)
long_rg_pts = np.array([2, 3, 4, 5, 6, 7, 8, 9, 10])
long_tf_pts = ibtf.transform(long_rg_pts)
short_res = res_bv(near_tf_pts)[0] / near_rg_pts / (2 * np.sqrt(np.pi))
long_res = res_bv(long_tf_pts)[0] / long_rg_pts / (2 * np.sqrt(np.pi))
# ref are calculated with mathemetical
# integrate[exp[-x^2 - y^2 - z^2] / sqrt[(x - a)^2 + y^2 +z^2], range]
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
]
ref_long_res = [
2.77108, # 2
1.85601, # 3
1.39203, # 4
1.11362, # 5
0.92802, # 6
0.79544, # 7
0.69601, # 8
0.61867, # 9
0.55680, # 10
]
assert_allclose(short_res, ref_short_res, atol=5e-4)
assert_allclose(long_res, ref_long_res, atol=5e-4)
# solve same poisson equation with gauss directly
gauss_pts = btf.transform(linsp)
res_gs = Poisson.solve_poisson_bv(gauss, gauss_pts, p_0)
gs_int_short = res_gs(near_rg_pts)[0] / near_rg_pts
gs_int_long = res_gs(long_rg_pts)[0] / long_rg_pts
assert_allclose(gs_int_short, ref_short_res, 5e-4)
assert_allclose(gs_int_long, ref_long_res, 5e-4)
