def test_issue_15654():
if not scipy:
skip("scipy not installed")
from sympy.abc import n, l, r, Z
from sympy.physics import hydrogen
nv, lv, rv, Zv = 1, 0, 3, 1
sympy_value = hydrogen.R_nl(nv, lv, rv, Zv).evalf()
f = lambdify((n, l, r, Z), hydrogen.R_nl(n, l, r, Z))
scipy_value = f(nv, lv, rv, Zv)
assert abs(sympy_value - scipy_value) < 1e-15
def generate_lookup_tables(num_grid_points,
n_max,
charge,
unique_nl_values,
R_c=None):
# Exponential grid construction with trapezoidal integration strips
if R_c is None:
R_c = 10 + (
2.5
) * n_max**2 # automatically calculated cutoff that seems to work well
print(
'Using %d grid points with a cutoff of %.3f Bohr. Nuclear charge Z = %.3f'
% (num_grid_points, R_c, charge))
#grid_points_exp = [ ( 1e-6 * (radial_cutoff/1e-6)**(n/(num_grid_points)) - 1e-6 ) for n in range(0,num_grid_points) ] # Adapted exponential grid from: https://math.nist.gov/DFTdata/atomdata/node6.html
grid_points_exp = [
(R_c**(n / num_grid_points) - 1) for n in range(0, num_grid_points)
] # But this seems to work better
grid_points_exp_spacing = [
(grid_points_exp[n + 1] - grid_points_exp[n - 1]) / 2
for n in range(1, num_grid_points - 1)
] # spacing for nth grid point, excluding n=0 and n=num_grid_points-1 (done on next line)
grid_points_exp_spacing.insert(
0, (grid_points_exp[1] - grid_points_exp[0]) / 2) # n=0 spacing
grid_points_exp_spacing.append((grid_points_exp[num_grid_points - 1] -
grid_points_exp[num_grid_points - 2]) /
2) # n=num_grid_points-1 spacing
radial_grid = grid_points_exp
# Construct radial lookup table for the hydrogenic R_nl
print('Initialising radial lookup tables...')
radial_lookup_table = np.zeros(
[n_max, n_max, len(radial_grid)]
) # n_cutoff * n_cutoff arrays each consisting of len(radial_grid) zeros. Obviously, this table is `triangular' (l_max<n).
for n in range(1, n_max + 1):
for l in range(n):
if (n, l) in unique_nl_values:
for r_i, r in enumerate(radial_grid):
radial_lookup_table[n - 1][l][r_i] = hydrogenic.R_nl(
n, l, r, charge)
print('Finished initialising radial lookup tables.')
return (radial_grid, radial_lookup_table, grid_points_exp_spacing)
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
import matplotlib.pyplot as plt
import numpy as np
from sympy.abc import n, l, r, Z
from sympy.physics import hydrogen
from sympy.utilities.lambdify import lambdify
R_nl = lambdify((n, l, r, Z), hydrogen.R_nl(n, l, r, Z),
('numpy', 'math', 'sympy'))
Z = 1
n, l = 2, 0
r = np.linspace(0, 10, 1000)
plt.plot(r, R_nl(n, l, r, Z))
plt.show()
