/* From: "COMPUTATIONAL PHYSICS, 2nd Ed" 
   by RH Landau, MJ Paez, and CC Bordeianu 
   Copyright Wiley-VCH, 2007.
   Electronic Materials copyright: R Landau, Oregon State Univ, 2007;
   MJ Paez, Univ Antioquia, 2007; & CC Bordeianu, Univ Bucharest, 2007
   Support by National Science Foundation
*/
//  qmc.c:  Feynman path integral for ground state wave function 

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
// if you don't have drand48 uncomment the following two lines 
    #define drand48 1.0/RAND_MAX*rand 
    #define srand48 srand                
      
#define max 250000                               // number of trials
#define seed 68111                      // seed for number generator

main()  {
	
  double change, newE, oldE, path [101];
  int i, j, element, prop [101];
  double energy( double array[]);            // finds energy of path
  FILE *output;                              // save data in qmc.dat
  output = fopen("qmc.dat","w");
  srand48(seed);                            // seed number generator
  for (j = 0; j<= 100; j++) path[j] = 0.0;           // initial path
  for (j = 0; j<= 100; j++) prop[j] = 0;      // initial probability
  oldE= energy(path);                         // find energy of path
  for (i = 0; i<max; i++)  {
		                                       // pick one random element
    element = drand48()*101;               
    change = (int)((drand48()-0.5)*20)/10.0;     // change -0.9..0.9
		                                       // change path, find new E
    path[element] += change;    
    newE = energy(path);   
		                                          // Metropolis Algorithm
    if ((newE>oldE) && (exp(-newE+oldE) <=  drand48()))
      { path[element] -= change;  }                        // reject
		                                          // add up probabilities
    for (j = 0; j<= 100; j++)  {             
      element = path[j]*10+50;
      prop[element]++; 
    }
    oldE= newE;
  }
  for (i = 0; i<= 100; i++) 
	        { fprintf(output, "%d\t%f\n", i-50, (double) prop[i]/max);}
  printf("data stored in qmc.dat\n");
  fclose(output);
}                                                     // end of main

double energy (double array[]) {    
	                                    // energy of path configuration
  int i;
  double sum = 0.;
  for (i = 0; i<100; i++)
	      { sum += pow(array[i+1]-array[i], 2.0) + array[i]*array[i]; }
  return (sum);
}