// Author: Mark Lingle
//   Modified: Volker Crede
//
// Project 11
// 4-1-08

#include<iostream>
#include<math.h>

using namespace std;


class IntegralCalculator // main integration class
{
  public:

  IntegralCalculator (double aIntegrandFunction(double)) { 
    iIntegrandFunction = aIntegrandFunction; }
  void setNumberOfIntervals(const int aNumberOfIntervals)p;
  int numberOfIntervals();

  // This function calculates the integrals using rectangles
  void integrate(double aLeftLimit, double aRightLimit,
		 int aNumberOfIntervals, double integrand(double)) {
    double dx = (aRightLimit - aLeftLimit) / aNumberOfIntervals;
    double x = 0;
    double sum = 0;

    for (int loop = 0; loop < aNumberOfIntervals; loop++) {
      sum += integrand(x);
      x+= dx;
    }
  }

  // input data
  void readInputData() {
    cout << "This program will integrate the function f(x) = x*x 
             for any limits you choose." << endl;
    cout << "Input the lower and upper limits of your integral: ";
    cin >> aLeftLimit >> aRightLimit;
    cout << "Input the number of intervals: ";
    cin >> aNumberOfIntervals;
  }

  // Displays results
  void print() {
    cout << "The answer is " << aResult << endl << endl;
  }


  void SimpsonRule() // calculates integral using Simpson 3-point rule
  {
    double w = (aRightLimit - aLeftLimit) / aNumberOfIntervals;
    double sum = 0;

    for (int i = 0; i < aNumberOfIntervals - 1; i++) {
       sum += iIntegrandFunction(aLeftLimit + i*w) + 
                    4*iIntegrandFunction(aLeftLimit+ w*(i+0.5)) +
	                     iIntegrandFunction(aLeftLimit + (i + 1)*w);
    }
    aResult = (w/6.0)*sum;
  }

  private:
  int aNumberOfIntervals; // Number of intervals
  double aLeftLimit, aRightLimit, aResult; // declares variables
  double (*iIntegrandFunction) (double); // function to be integrated
};


//Function that is being integrated. f(x)=x^2
double square(double aX) {
  return aX*aX;
}
 

int main(){
  char ch = 'y';

  while (ch == 'y' || ch == 'Y') // Program stays in loop till user 
                                 // terminates by inputing "n/N."
  {
    IntegralCalculator IC1(square); // create the calculator
    IC1.readInputData(); // get user input
    IC1.SimpsonRule(); // INTEGRATE!
    IC1.print(); // output result
 
    cout << "This program was written and compiled by 
             Mark Lingle for PHZ4151C." << endl;
    cout << "Would you like to run it again?" << endl; 
    cout << "Please enter y/Y for yes or n/N for no." << endl;
    cin >> ch;
  }
}