// metropolis yöntemi ile random sayı üretir, monte darlo integrasyon
// compile: gcc random.c -lm
// usage: ./a.out trial#

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <limits.h>


// w is gaussian weight function
double w(double x, double y)
{
   double sigma ;
// sigma is standard deviation
   sigma = 0.05 ;

   return exp(-(x *x + y*y) / (2 * sigma * sigma) ) ;

}



void generator(double * x, double * y)
{
   double xt, yt, ratio, tmp ;
   double delta = 0.2 ;


   tmp = (double)rand() / (double)RAND_MAX  ;
// update x by adding a multiples of delta , (2 * tmp - 1) creates a number between -1.0 and 1.0
   xt = (*x) + delta * (2 * tmp - 1) ; 

   tmp = (double)rand() / (double)RAND_MAX  ;
// update y by adding a multiples of delta , (2 * tmp - 1) creates a number between -1.0 and 1.0
   yt = (*y) + delta * (2 * tmp - 1) ; 


// compare updated x,y values with old x,y values, accept or reject updated values as new values according to weight function
   ratio = w(xt, yt ) / w(*x, *y) ;
   tmp = (double)rand() / (double)RAND_MAX  ;

   if(ratio > tmp )
   {

      *x = xt ;
      *y = yt ;
   }


}


int main(int argc, char* argv[])
{

   int i;
   double x,y ;

// how many random number will generated 
   int  count = atoi(argv[1]);

//assign initial random numbers between 0-1 to x,y

   x = (double) rand() / RAND_MAX ;
   y = (double) rand() / RAND_MAX ;

   for(i=0 ; i < count ; i++)
   {

      printf("%f %f\n", x, y) ;
      generator(&x,&y);
   }


   return 0;

}