/** Integrate a 1-D function using the Simpson Rule. **/
class SimpsonInteg implements Integrator
{
  /** Integrate the function between lo and hi with n slices. **/
  public double integrate (double lo, double hi,
                            int n, Function f)  {
    // Check data.
    if ( hi <= lo || n <= 0 || f == null) return 0.0;

    double dx =  (hi-lo)/n;
    dx = dx/2.0; // Use half widths for Simpson rule
    double area = 0.0;

    double x_lo = lo;
    double x_md = lo + dx;
    double x_hi = lo + 2.0 * dx;

    for (int i=0; i < n; i++) {
      double left_side = f.valueAt (x_lo);
      double middle    = f.valueAt (x_md);
      double rite_side = f.valueAt (x_hi);
      area += dx * (left_side + 4.0 * middle + rite_side)/3.0;
      x_lo = lo + 2.0 * i * dx;
      x_md = x_lo + dx;
      x_hi = x_lo + 2.0 * dx;
    }

    return area;
  } // integrate

} // SimpsonInteg

/**
  * This class illustrates use of Simpson's Rule for integration.
  * Compares to Rectangular and Trapezoidal methods.
  *
  *
  *   Integrator.java - interface
  *     SimpsonInteg.java   - implements Integrator
  *     TravezoidInteg.java - implements Integrator
  *     RectInteg.java      - implements Integrator
  *
  *   Function.java - interface
  *     PolyFunc.class - see below
  *
 **/
public class SimpsonApplet extends java.applet.Applet
{
  public void init () {

    SineOverX2Func sinf = new SineOverX2Func ();

    RectInteg ri = new RectInteg ();
    double integ = ri.integrate (0.01, Math.PI, 1000, sinf);
    System.out.println ("Rectangle integ = " + integ);

    TrapezoidInteg ti = new TrapezoidInteg ();
    integ = ti.integrate (0.01, Math.PI, 1000, sinf);
    System.out.println ("Trapezoid integ = " + integ);


    SimpsonInteg si = new SimpsonInteg ();
    integ = si.integrate (0.01,Math.PI,1000,sinf);
    System.out.println ("Simpson integ = " + integ);

  } // init

  /** Paint message in Applet window. **/
  public void paint (java.awt.Graphics g) {
     g.drawString ("SimpsonApplet",20,20);
  }

  /** This program can also run as an application. No graphics needed.
    * so it just runs the applet's init () function.
   **/
  public static void main (String [] args) {
    SimpsonApplet obj = new SimpsonApplet ();
    obj.init ();
  } // main

} // SimpsonApplet

/** An example 1-D function. **/
class SineOverX2Func implements Function
{
   public double valueAt (double x) {
     return Math.sin (x)/ (x*x);
   }
} // SineOverX2Func