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// 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;
}