/* 
Jonathan Hauenstein - University of Notre Dame
Center for Applied Mathematics Minicourse on Parallel Computing
April 24, May 1, May 8, 2008
Sample programs are designed for educational use 
*/

#include "trapezoid.h"
#include <mpi.h>

double f(double x)
{ // function to evaluate
  if (-1 <= x && x <= 1) return sqrt(1 - x*x); else return 0;
}

double trapApprox(double a, double b)
{ // computes and returns the trapezoid integral approximation
  return 0.5*(b - a)*(f(a) + f(b));
}

double composite_trapApprox(trapInfo *info)
{ // computes and returns the composite trapezoid integral approximation
  // Note: this is not the most efficient implementation since it is designed for educational purposes.
  int i; double stepSize, approx = 0;

  if (info->n > 0)
  { // compute the step size
    stepSize = (info->b - info->a) / info->n;

    // compute the approximation
    for (i = 0; i < info->n; i++)
      approx += trapApprox(info->a + i*stepSize, info->a + (i+1)*stepSize);
  }

  return approx;
}