updating book

doc/LectureNotes/DataFiles/autocorrelation.cpp

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+//  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, setting the distance d between two
+     // to a most 1/4 of the total number of cycles
+     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