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import math
import numpy as np
from numpy.linalg import eig
def lj_matrix(mol_data,
nc_data,
max_len=25,
as_eig=False,
bohr_radius_units=False):
"""
Creates the coulomb matrix from the molecule data given.
mol_data: molecule data, matrix of atom coordinates.
nc_data: nuclear charge data, array of atom data.
max_len: maximum amount of atoms in molecule.
as_eig: if data should be returned as matrix or array of eigenvalues.
bohr_radius_units: if units should be in bohr's radius units.
"""
if bohr_radius_units:
conversion_rate = 0.52917721067
else:
conversion_rate = 1
mol_n = len(mol_data)
mol_nr = range(mol_n)
if not mol_n == len(nc_data):
print(''.join(['Error. Molecule matrix dimension is different ',
'than the nuclear charge array dimension.']))
else:
if max_len < mol_n:
print(''.join(['Error. Molecule matrix dimension (mol_n) is ',
'greater than max_len. Using mol_n.']))
max_len = None
if max_len:
lj = np.zeros((max_len, max_len))
ml_r = range(max_len)
# Actual calculation of the coulomb matrix.
for i in ml_r:
if i < mol_n:
x_i = mol_data[i, 0]
y_i = mol_data[i, 1]
z_i = mol_data[i, 2]
Z_i = nc_data[i]
else:
break
for j in ml_r:
if j < mol_n:
x_j = mol_data[j, 0]
y_j = mol_data[j, 1]
z_j = mol_data[j, 2]
x = (x_i-x_j)**2
y = (y_i-y_j)**2
z = (z_i-z_j)**2
if i == j:
lj[i, j] = (0.5*Z_i**2.4)
else:
# Calculations are done after i==j is checked
# so no division by zero is done.
# A little play with r exponents
# so no square root is calculated.
# Conversion factor is included in r^2.
# 1/r^2
r_2 = 1/(conversion_rate**2*(x + y + z))
r_6 = math.pow(r_2, 3)
r_12 = math.pow(r_6, 2)
lj[i, j] = (4*(r_12 - r_6))
else:
break
# Now the value will be returned.
if as_eig:
lj_sorted = np.sort(eig(lj)[0])[::-1]
# Thanks to SO for the following lines of code.
# https://stackoverflow.com/a/43011036
# Keep zeros at the end.
mask = lj_sorted != 0.
f_mask = mask.sum(0, keepdims=1) >\
np.arange(lj_sorted.shape[0]-1, -1, -1)
f_mask = f_mask[::-1]
lj_sorted[f_mask] = lj_sorted[mask]
lj_sorted[~f_mask] = 0.
return lj_sorted
else:
return lj
else:
lj_temp = []
# Actual calculation of the coulomb matrix.
for i in mol_nr:
x_i = mol_data[i, 0]
y_i = mol_data[i, 1]
z_i = mol_data[i, 2]
Z_i = nc_data[i]
lj_row = []
for j in mol_nr:
x_j = mol_data[j, 0]
y_j = mol_data[j, 1]
z_j = mol_data[j, 2]
x = (x_i-x_j)**2
y = (y_i-y_j)**2
z = (z_i-z_j)**2
if i == j:
lj_row.append(0.5*Z_i**2.4)
else:
# Calculations are done after i==j is checked
# so no division by zero is done.
# A little play with r exponents
# so no square root is calculated.
# Conversion factor is included in r^2.
# 1/r^2
r_2 = 1/(conversion_rate**2*(x + y + z))
r_6 = math.pow(r_2, 3)
r_12 = math.pow(r_6, 2)
lj_row.append(4*(r_12 - r_6))
lj_temp.append(np.array(lj_row))
lj = np.array(lj_temp)
# Now the value will be returned.
if as_eig:
return np.sort(eig(lj)[0])[::-1]
else:
return lj
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