/*
*  Exmaples Sheet 3 example problem
*
*    Integrate:
*      I = \int_{0}^{\infty}  \frac{1}{\sqrt{2\pi(1+x)}} e^{-\frac{x^2}{4\kappa}} dx
*    with classes
*
*/
#include <cstdlib>
#include <iostream>
#include <cmath>

const double Pi=4.*atan(1.);

// integrand function
class Integrand
{

  public:
    // parameter kappa
    double kappa;
    // function operator
    double operator()(double x)
    {
      return exp(-(x*x)/(4.*kappa))/sqrt(2.*Pi*(1+x));
    }
};

// integrate function, just need to specify no of steps and kappa
double integrate(int n,Integrand& f)
{
  // stepsize, x_max
  double h,x_max;
  // choose x_max = 10*kappa
  x_max = 10*f.kappa;
  h = x_max/n;
  // initialise x
  double x=0.;
  // store running sum
  double sum=f(x)/2.;
  for(int i=1;i<n;i++)
  {
    x=i*h;
    sum = sum + f(x);
  }
  sum = sum + f(x_max)/2.;
  return sum*h;
}
 

int main()
{
  // declare instance of the integrand function
  Integrand f;
  int n;
  std::cout << " Input number of steps\n";
  std::cin >> n;
  // output results to the screen
  for(int kappa=1;kappa<=10;kappa++)
  {
    f.kappa = kappa;
    std::cout << " kappa = " << kappa << " I = " << integrate(n,f) << " \n";
  }
  return 0;
}