The program here computes the correlation function for one of the Mersenne RNG included with the c++ compiler.
// This function computes the autocorrelation function for
// the Mersenne random number generator
#include <fstream>
#include <iomanip>
#include <iostream>
#include <cmath>
#include <random>
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.;
// Initialize the seed and call the Mersienne algo
std::random_device rd;
std::mt19937_64 gen(rd());
// Set up the uniform distribution for x \in [[0, 1]
std::uniform_real_distribution<double> RandomNumberGenerator(0.0,1.0);
// 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 = RandomNumberGenerator(gen);
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
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