// weight function kullanarak monte carlo integrasyon

/*

COMPILATION: gcc integral1d.c -lm
USAGE: ./a.out trial#

This program computes integral of ( 1 / (1 + x*x) ) in x=[0,1] by using importance sampling Monte Carlo 


*/



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


// f() is the function to be integrated
double f(double x)
{

   return (1.0 / (1.0 + x*x) ) ;

}


// random x values are generated according to probability distribution function w() 
double w(double x)
{


   return ((1.0/3.0) * (4 - 2 * x)) ;
}


// my_rand() function generates random numbers according to p.d.f w()
// this function uses inverse of the p.d.f w() 
double my_rand()
{

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

   return (2.0 - sqrt(4.0 - 3.0*y) ) ;
}


int main(int argc, char* argv[])
{
   int trials;  // number of random points
   int i;
   double sum = 0.0;
   double x;


   trials = atoi(argv[1]); // read number of random point from command line argument


   for(i=0 ; i < trials ; i++ )
   {
      x = my_rand()  ;
    
      sum += ( f(x) / w(x)) ;

   }

   double integral = sum / trials ;

   printf("computed value of the integral= %f \n", integral);
   printf("true value of the integral=     %f \n", atan(1.0));
   printf("error=                          %f  \n", fabs( integral - atan(1.0)));


return 0;

}