/* 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; and CC Bordeianu, Univ Bucharest, 2007.
   Support by National Science Foundation                              
*/
// QMC.java: Quantum MonteCarlo Feynman path integration

import java.io.*;                          // Location of PrintWriter
import java.util.*;                             // Location of Random
import java.lang.*;                               // Location of Math

public class QMC  {
	
  public static void main(String[] argv) 
                         throws IOException, FileNotFoundException {
													 
    PrintWriter q = new PrintWriter(                   // File output
                             new FileOutputStream("QMC.DAT"), true);
    int N = 100, M = 101, Trials = 25000, seedTrials = 200;   
    double path[] = new double[N], xscale = 10.;
    long prop[]   = new long[M],   seed = 10199435; 
		                                                  // Begin Trials
    for ( int count = 0; count < seedTrials*10; count +=  10) {
      Random randnum = new Random(seed + count); 
      double change = 0., newE = 0., oldE = 0. ; 
			                                                // Initial path
      for ( int i=0; i < N; i++ )  path[i] = 0. ;            
      oldE = energy(path);                          // Find E of path
			                                         // Pick random element
      for ( int i=0; i < Trials; i++ )  {             
        int element = randnum.nextInt(N); 
        change = 1.8*(0.5 - randnum.nextDouble()); 
        path[element] += change;                       // Change path
        newE = energy(path);                            // Find new E
				         // Metroplis algorithm
        if ( newE > oldE && Math.exp(-newE + oldE)
					                                                 // Reject
          <= randnum.nextDouble() ) path[element]-=change;  
																								// Add probabilities
        for ( int j=0; j < N; j++ )  {           
          element = (int)Math.round( (M-1)*(path[j]/xscale + .5) ); 
          if (element < M && element>=0)  prop[element]++ ; 
       }
       oldE = newE; 
      }                                                     // t loop
    }                                                    // Seed loop
    for ( int i=0; i < M; i++ )  q.println(xscale*(i-(M-1)/2) 
        + " " + (double)prop[i]/((double)Trials*(double)seedTrials));
    System.out.println(" "); 
    System.out.println("QMC Program Complete."); 
    System.out.println("Data stored in QMC.DAT"); 
    System.out.println(" "); 
  }
 
  public static double energy(double path[])  {
		
    int i = 0; 
    double sum = 0. ; 
		
    for ( i=0; i < path.length-2; i++ ) 
      { sum +=  (path[i+1] - path[i])*(path[i+1] - path[i]) ;  } 
    sum +=  path[i+1]*path[i+1]; 
    return sum; 
} }                                                      // End class