/*
================================================================
 example: Non- uniform distribution
 use of the random number generator - rand
 from standard C++ library
 the code generates: 
 double random numbers between xmin and xmax
 distributed with some probability w(x)
 AG 
================================================================
*/
#include <iostream>
#include <fstream>
#include <iomanip>
#include <cstdlib>
#include <cmath>
#include <ctime>
using namespace std;

double w(double);

int main ()
{
  int nmax = 10000;     /* define how many random numbers to generate */
  double xmin=0.0, xmax=2.0, ymin, ymax;
  double x, y;
  int count = 0;
  
  cout.precision(6);
  cout.setf(ios::fixed | ios::showpoint); 
  
/* for writing random numbers to a file */
 ofstream file_3;
 file_3.open ("table04.dat");
 file_3.precision(5);
 file_3.setf(ios::fixed | ios::showpoint);
 
 ymax = w(xmin);     /* may need to be redifined for other distribution */
 ymin = w(xmax);     /* may need to be redifined for other distribution */
 cout << "ymin = " << ymin << "  ymax = " << ymax << endl;
 
 srand(time(NULL)); 
 
  for (double i=1; i <= nmax; i=i+1)
  {
      x = xmin + (xmax-xmin)*rand()/(RAND_MAX-1);  
      y = ymin + (ymax-ymin)*rand()/(RAND_MAX-1); 
      if (y > w(x)) continue;
      count = count + 1;
      file_3  << " " << x << endl;   /* output to a file */
  }
  cout << "count = " << count << endl;

  return 0;
}

/*
 Probability distribution w(x)
*/
    double w(double x)
{
    return exp(0.0-1.0*x*x);
}