//  This function computes the autocorrelation function for 
//  the standard c++ random number generator

#include <fstream>
#include <iomanip>
#include <iostream>
#include <cmath>
using namespace std;
// output file as global variable
ofstream ofile;  

//     Main function begins here     
int main(int argc, char* argv[])
{
     int n;
     char *outfilename;

     cin >> n;
     double MCint = 0.;      double MCintsqr2=0.;
     double invers_period = 1./RAND_MAX; // initialise the random number generator
     srand(time(NULL));  // This produces the so-called seed in MC jargon
     // Compute the variance and the mean value of the uniform distribution
     // Compute also the specific values x for each cycle in order to be able to
     // the covariance and the correlation function  
     // Read in output file, abort if there are too few command-line arguments
     if( argc <= 2 ){
       cout << "Bad Usage: " << argv[0] << 
	 " read also output file and number of cycles on same line" << endl;
       exit(1);
     }
     else{
       outfilename=argv[1];
     }
     ofile.open(outfilename); 
     // Get  the number of Monte-Carlo samples
     n = atoi(argv[2]);
     double *X;  
     X = new double[n];
     for (int i = 0;  i < n; i++){
           double x = double(rand())*invers_period; 
           X[i] = x;
           MCint += x;
           MCintsqr2 += x*x;
     }
     double Mean = MCint/((double) n );
     MCintsqr2 = MCintsqr2/((double) n );
     double STDev = sqrt(MCintsqr2-Mean*Mean);
     double Variance = MCintsqr2-Mean*Mean;
//   Write mean value and standard deviation 
     cout << " Standard deviation= " << STDev << " Integral = " << Mean << endl;

     // Now we compute the autocorrelation function
     double *autocor;  autocor = new double[n];
     for (int j = 0; j < n; j++){
       double sum = 0.0;
       for (int k = 0; k < (n-j); k++){
	 sum  += (X[k]-Mean)*(X[k+j]-Mean); 
       }
       autocor[j] = sum/Variance/((double) n );
       ofile << setiosflags(ios::showpoint | ios::uppercase);
       ofile << setw(15) << setprecision(8) << j;
       ofile << setw(15) << setprecision(8) << autocor[j] << endl;
     }
     ofile.close();  // close output file
     return 0;
}  // end of main program