// QuadratureSum.java
//
// approximate integral f(x) from x=a to x=b by simple sum
// f(x) = 4*(x-x^2)
// a=0, b=1, n=8, h=(b-a)/n=1/8


import java.awt.*;
import java.awt.event.*;
import java.text.*;

class QuadratureSum extends Frame
{
  double a = 0.0;
  double b = 1.0;
  int n = 8; // regions, 9 points
  double h = (b-a)/n;

  QuadratureSum()
  {
    setTitle("QuadratureSum(x) 0 to 1 of 4(x-x^2)");
    setSize(450,520);
    setBackground(Color.white);
    setForeground(Color.black);
    addWindowListener(new WindowAdapter()
    {
      public void windowClosing(WindowEvent e)
      {
        System.exit(0);
      }
    });
    setVisible(true);
  }

  double f(double x) // "exact" function 
  {
    return 4.0*(x-x*x);
  }

  public void paint(Graphics g)
  {
    // set up function to be approximated
    final int ns=50;            // number of samples for plotting
    final double nf=(double)n;
    double fx[] = new double[ns]; // f(x)
    final double xmin=a;
    final double xmax=b;
    double ymin=0.0;            // for automatic scaling some day
    double ymax=1.0;
    double dx;                  // x step increment for plotting curve
    double xstart=a;            // initial value
    double x;                   // stepped value xmin to xmax
    
    dx = (xmax-xmin)/(double)(ns-1);
    // do NOT use x=x+dx, very inaccurate!
    for(int i=0; i<ns; i++) fx[i]=f(xstart+(double)i*dx); // get "exact" function
    ymin=fx[0];
    ymax=fx[0];
    for(int i=1; i<ns; i++)
    {
      ymin=Math.min(ymin,fx[i]);
      ymax=Math.max(ymax,fx[i]);
    }
    // may fudge ymin and ymax for extra room for approximation
    ymin=0.0;
    ymax=1.0;
 
    // set up plot area
    final int hw=400;   // graph area height and width
    final double xsca=hw/(xmax-xmin);  // x data scale 0 to 1
    final double ysca=hw/(ymax-ymin);  // y data scale 0 to 1
    final int f1xOff=25;  // offsets
    final int f1yOff=70;
    final int f1xC=f1xOff+hw/2; // centers
    final int f1yC=f1yOff+hw/2;
    
    g.drawRect(f1xOff, f1yOff, hw, hw);
    g.drawLine(f1xC,   f1yOff, f1xC, f1yOff+hw);
    g.drawString("1",  f1xOff-14,   f1yOff+4);
    g.drawString("0",  f1xOff-14,   f1yOff+hw+4);
    g.drawString("0", f1xOff-4,    f1yOff+hw+15);
    g.drawString("0.5",  f1xC-8,      f1yOff+hw+15);
    g.drawString("1",  f1xOff+hw-4, f1yOff+hw+15);
    g.drawString("y",  f1xOff,      f1yOff-12);
    g.drawString("x",  f1xOff+hw+6, f1yOff+hw+4);

    // plot function
    double x1new, y1new;
    double x1old=xstart;
    double y1old=fx[0];
    g.setColor(Color.black);
    for(int i=1; i<ns; i++) // n-1 lines
    {
      x1new=xstart+(double)i*dx;
      y1new=fx[i];
      g.drawLine((int)(f1xOff+x1old*xsca), (int)(f1yOff+hw-y1old*ysca),
                 (int)(f1xOff+x1new*xsca), (int)(f1yOff+hw-y1new*ysca));
      x1old=x1new;
      y1old=y1new;
    }
    
    // compute quadrature and plot areas
    // simple sum integration
    double aa[] = new double[n+1]; // quadrature points
    double area = 0.0;
    for(int i=0; i<=n; i++) // includes point n
    {
      x = xmin+(double)i*h;
      aa[i]=f(x);
      area = area + aa[i];
      g.setColor(Color.red);
      g.fillOval((int)(f1xOff+x*xsca)-3, (int)(f1yOff+hw-aa[i]*ysca)-3,6,6);
      g.setColor(Color.green);
      g.fillRect((int)(f1xOff+(x-h/2)*xsca),(int)(f1yOff+hw-aa[i]*ysca),
                 (int)(h*xsca),(int)(aa[i]*ysca));
      g.setColor(Color.blue);
      g.drawLine((int)(f1xOff+(x-h/2)*xsca), (int)(f1yOff+hw-aa[i]*ysca),
                 (int)(f1xOff+(x-h/2)*xsca), (int)(f1yOff+hw));
      g.drawLine((int)(f1xOff+(x+h/2)*xsca), (int)(f1yOff+hw-aa[i]*ysca),
                 (int)(f1xOff+(x+h/2)*xsca), (int)(f1yOff+hw));
    }      
    area = ((b-a)/(double)(n+1))*area;


    System.out.println("computed area="+area+", actual="+(4.0/6.0));

    g.setColor(Color.black);
    g.drawString((n+1)+" regions", f1xOff+20, f1yOff+hw+30);
    g.drawString("area="+area+",  error="+((4.0/6.0)-area),
                  f1xOff+100, f1yOff+hw+30);
    g.setColor(Color.red);
    Font cur18 = new Font("courier", Font.BOLD, 18); 
    g.setFont(cur18);
    g.drawString("QuadratureSum(x) -0 to 1 of 4(x-x^2)", 10, 50);
  }
  
  public static void main(String args[])
  {
    System.out.println("QuadratureSum.java running");
    new QuadratureSum();
  }
}