Jacobi Method example

I wrote this code a while back. Apparently, this post is getting a few hits. I refined it a bit. Also wanted to make sure it was looked right.

What is the Jacobi method? It's an iterative way of solving a system of equations. Ax = b. This is learned in Numerical Analysis classes.

Generally, you decompose a matrix into its diagonal and lower and upper triangles. Such that,

A = D + L + U

x0 is the initial guess.

Now you want to solve for x. x_approx = inverse of D * (b - (L+U)x0)

Get x_approx from this formula, then plug it into x0 and do it all over again until you reach the desired error.

% Code is for matlab / octave
format long e;
A = [ 2 -1; -1 2];
b = [ 2; 1];
k = 20;
xi = [0;0]; % initial guess

%we want
%x' = Dinv(b - (L+U)x)

% just take the diagonal of A
D=[A(1,1) 0;0 A(2,2)]; 

Di=inv(D);

%lower and upper triangles of A
L=[0 0; -A(2,1) 0];
U=[0 -A(1, 2); 0 0];

% this part doesn't change, so calc now
C=Di*b;
% this is the main term of the algo
M=Di*(L+U);

x = [5/3; 4/3]; % solution

abs_err = [ 100 ; 100];
abs_err = abs_err - x;
i=0;

%stop until error is <= 1e-6
while abs_err(1) >= 1e-6 && abs_err(2) >= 1e-6
 xi=M*xi+C
 abs_err = abs(xi - x);
 fprintf('i = %f abs-err = %f %f \n',i,abs_err(1),abs_err(2));
 i=i+1;
end

matlab : polynomial fitting

octave-3.2.3:4> for i = 1 : 51
> x(i) = .2*(i - 1);
> end


octave-3.2.3:6> for i = 1: 51
> y(i) = 1 - x(i);
> end

octave-3.2.3:8> polyfit(x,y,4)
ans =

   1.1249e-17  -2.3654e-16   1.7285e-15  -1.0000e+00   1.0000e+00

Java : sample applet

 
 import java.applet.*;
 import java.awt.*;
 
 public class A extends Applet
 {
        private int w, h;
        public void init( )
        {
         w = 45;
         h = 50;
        }
    
        public void paint(Graphics g)
        {
         g.drawRect(w, h, 20, 80);
        }
 }

Sample J2Me Midlet for sound recording

import java.io.*;
import javax.microedition.midlet.*;
import javax.microedition.lcdui.*;
import javax.microedition.media.*;
import javax.microedition.media.control.*;

public class VoiceRecordMidlet extends MIDlet {
      private Display display;

      public void startApp() {
            display = Display.getDisplay(this);
            display.setCurrent(new VoiceRecordForm());
      }

      public void pauseApp() {
      }

      public void destroyApp(boolean unconditional) {
            notifyDestroyed();
      }
}

class VoiceRecordForm extends Form implements CommandListener {
      private StringItem message;
      private StringItem errormessage;
      private final Command record, play;
      private Player player;
      private byte[] recordedAudioArray = null;
      public VoiceRecordForm() {
            super("Recording Audio");
            message = new StringItem("", "Select Record to start recording.");
            this.append(message);
            errormessage = new StringItem("", "");
            this.append(errormessage);
            record = new Command("Record", Command.OK, 0);
            this.addCommand(record);
            play = new Command("Play", Command.BACK, 0);
            this.addCommand(play);
            this.setCommandListener(this);
      }
      public void commandAction(Command comm, Displayable disp) {
            if (comm == record) {
                  Thread t = new Thread() {
                        public void run() {
                              try {
                                    player = Manager.createPlayer("capture://audio?encoding=pcm");
                                    player.realize();
                                    RecordControl rc = (RecordControl) player.getControl("RecordControl");
                                    ByteArrayOutputStream output = new ByteArrayOutputStream();
                                    rc.setRecordStream(output);
                                    rc.startRecord();
                                    player.start();
                                    message.setText("Recording...");
                                    Thread.sleep(5000);
                                    message.setText("Recording Done!");
                                    rc.commit();
                                    recordedAudioArray = output.toByteArray();
                                    player.close();
                              } catch (Exception e) {
                                    errormessage.setLabel("Error");
                                    errormessage.setText(e.toString());
                              }
                        }
                  };
                  t.start();

            }
            else if (comm == play) {
                  try {
                        ByteArrayInputStream recordedInputStream = new ByteArrayInputStream(recordedAudioArray);
                        Player p2 = Manager.createPlayer(recordedInputStream, "audio/basic");
                        p2.prefetch();
                        p2.start();
                  } catch (Exception e) {
                        errormessage.setLabel("Error");
                        errormessage.setText(e.toString());
                  }
            }
      }
}