#! /usr/bin/env python
"""
 madelung.py is program which calculates the Madelung constant M
 of molecular structures in condensed matter physics is related
 to the attomic electric potential V_total = e/(4pi epsilon_o a) * M 

 The program takes as input L, number of atoms per dimension of a symmetric NaCl  lattice

 For  an L of 200, the program takes a little over one minute to calculate
 and returns a value of M = -1.745. the true value for  sodium chloride is -1.748

 hpc-login-24 294% time madelung.py
 Enter number of atoms per dimension: 200
 Madelung constant: -1.74468504217
 48.447u 0.021s 0:50.56 95.8%	0+0k 0+0io 0pf+0w


 Paul Eugenio 
 PHZ4151C
 Feb 6, 2019
"""


# program header code
from __future__ import division, print_function
import timeit

mysetup = '''
from math import sqrt
# initalize variables
M = 0.0  

L = int(raw_input("Enter number of atoms per dimension: "))
'''
mycode = '''
#
# Madelung constant for an atom in the center of a cubic lattice of
# alternating +e and -e atoms
for i in range(-L, L+1):
    for j in range(-L, L+1):
        for k in range(-L, L+1):
            if not( i==0 and j==0 and k==0):
                if(i+j+k)%2==0: 
                    # it's a positive ion
                    M += 1/sqrt(i*i + j*j + k*k)
                else: 
                    # it's a negative ion
                    M -= 1/sqrt(i*i + j*j + k*k)

print("Madelung constant:",M)
'''

print( "run time: {0:3.3} seconds".format( timeit.timeit(setup=mysetup,
                                                         stmt=mycode, number=1) ) )