Matrix Math Example

Purpose

The purpose of the example is to show you the following:

• How to assign more than one MATLAB function to a component class.

• How to manually handle native memory management.

• How to access the component in a Java application (getfactor.java) by instantiating Factor and using the MWArray class library to handle data conversion.

  Note   For complete reference information about the MWArray class hierarchy, see the com.mathworks.toolbox.javabuilder package.

• How to build and run the MatrixMathDemoApp application

This example builds a Java component to perform matrix math. The example creates a program that performs Cholesky, LU, and QR factorizations on a simple tridiagonal matrix (finite difference matrix) with the following form:

A = [ 2 -1  0  0  0
     -1  2 -1  0  0
      0 -1  2 -1  0
      0  0 -1  2 -1
      0  0  0 -1  2 ]

You supply the size of the matrix on the command line, and the program constructs the matrix and performs the three factorizations. The original matrix and the results are printed to standard output. You may optionally perform the calculations using a sparse matrix by specifying the string "sparse" as the second parameter on the command line.

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MATLAB Functions to Be Encapsulated

The following code defines the MATLAB functions used in the example:

 cholesky.m

function [L] = cholesky(A)
%CHOLESKY Cholesky factorization of A.
%   L = CHOLESKY(A) returns the Cholesky factorization of A.
%   This file is used as an example for the MATLAB 
%   Builder for Java product.

%   Copyright 2001-2007 The MathWorks, Inc.

L = chol(A);

 ludecomp.m

function [L,U] = ludecomp(A)
%LUDECOMP LU factorization of A.
%   [L,U] = LUDECOMP(A) returns the LU factorization of A.
%   This file is used as an example for the MATLAB 
%   Builder for Java product.

%   Copyright 2001-2007 The MathWorks, Inc.

[L,U] = lu(A);

 qrdecomp.m

function [Q,R] = qrdecomp(A)
%QRDECOMP QR factorization of A.
%   [Q,R] = QRDECOMP(A) returns the QR factorization of A.
%   This file is used as an example for the MATLAB 
%   Builder for Java product.

%   Copyright 2001-2007 The MathWorks, Inc.

[Q,R] = qr(A);

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Understanding the getfactor Program

The getfactor program takes one or two arguments from standard input. The first argument is converted to the integer order of the test matrix. If the string sparse is passed as the second argument, a sparse matrix is created to contain the test array. The Cholesky, LU, and QR factorizations are then computed and the results are displayed to standard output.

The main method has three parts:

• The first part sets up the input matrix, creates a new factor object, and calls the cholesky, ludecomp, and qrdecomp methods. This part is executed inside of a try block. This is done so that if an exception occurs during execution, the corresponding catch block will be executed.

• The second part is the catch block. The code prints a message to standard output to let the user know about the error that has occurred.

• The third part is a finally block to manually clean up native resources before exiting.

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Procedure

Step-by-Step Procedure

1. If you have not already done so, copy the files for this example as follows:

   1. Copy the following folder that ships with MATLAB to your work folder:

      matlabroot\toolbox\javabuilder\Examples\MatrixMathExample
      

   2. At the MATLAB command prompt, cd to the new MatrixMathExample subfolder in your work folder.

2. If you have not already done so, set the environment variables that are required on a development machine. See Settings for Environment Variables (Development Machine).

3. Write the MATLAB functions as you would any MATLAB function.

   The code for the cholesky, ludecomp, and qrdecomp functions is already in your work folder in MatrixMathExample\MatrixMathDemoComp\.

4. While in MATLAB, issue the following command to open the Deployment Tool window:

   deploytool

5. You create a Java application by using the Deployment Tool GUI to build a Java class that wraps around your M-code.

   To compile or build the Java application using the Deployment Tool, use the following information as you work through this example in Building the Java Component:

   Project Name	factormatrix
   Class Name	factor
   Files to compile	cholesky.mludecomp.mqrdecomp.m

6. Write source code for an application that accesses the component.

   The sample application for this example is in MatrixMathExample\MatrixMathDemoJavaApp\getfactor.java.

   The program listing is shown here.

    getfactor.java

   /* getfactor.java
    * This file is used as an example for the MATLAB
    * Builder for Java product.
    *
    * Copyright 2001-2007 The MathWorks, Inc.
    */
   
   /* Necessary package imports */
   import com.mathworks.toolbox.javabuilder.*;
   import factormatrix.*;
   
   /*
    * getfactor class computes cholesky, LU, and QR 
    * factorizations of a finite difference matrix
    * of order N. The value of N is passed on the
    * command line. If a second command line arg
    * is passed with the value of "sparse", then
    * a sparse matrix is used.
    */
   class getfactor
   {
      public static void main(String[] args)
      {
         MWNumericArray a = null;   /* Stores matrix to factor */
         Object[] result = null;    /* Stores the result */
         factor theFactor = null;   /* Stores factor class instance */
   
         try
         {
            /* If no input, exit */
            if (args.length == 0)
            {
               System.out.println("Error: must input a positive integer");
               return;
            }
   
            /* Convert input value */
            int n = Integer.valueOf(args[0]).intValue();
   
            if (n <= 0)
            {
               System.out.println("Error: must input a positive integer");
               return;
            }
   
            /*
             * Allocate matrix. If second input is "sparse"
             * allocate a sparse array 
             */
            int[] dims = {n, n};
   
            if (args.length > 1 && args[1].equals("sparse"))
               a = MWNumericArray.newSparse(dims[0], dims[1],n+2*(n-1), 
                                     MWClassID.DOUBLE, MWComplexity.REAL);
            else
               a = MWNumericArray.newInstance(dims,MWClassID.DOUBLE, MWComplexity.REAL);
   
            /* Set matrix values */
            int[] index = {1, 1};
   
            for (index[0] = 1; index[0] <= dims[0]; index[0]++)
            {
               for (index[1] = 1; index[1] <= dims[1]; index[1]++)
               {
                  if (index[1] == index[0])
                     a.set(index, 2.0);
                  else if (index[1] == index[0]+1 || index[1] == index[0]-1)
                     a.set(index, -1.0);
               }
            }
   
            /* Create new factor object */
            theFactor = new factor();
   
            /* Print original matrix */
            System.out.println("Original matrix:");
            System.out.println(a);
   
            /* Compute cholesky factorization and print results. */
            result = theFactor.cholesky(1, a);
            System.out.println("Cholesky factorization:");
            System.out.println(result[0]);
            MWArray.disposeArray(result);
   
            /* Compute LU factorization and print results. */
            result = theFactor.ludecomp(2, a);
            System.out.println("LU factorization:");
            System.out.println("L matrix:");
            System.out.println(result[0]);
            System.out.println("U matrix:");
            System.out.println(result[1]);
            MWArray.disposeArray(result);
   
            /* Compute QR factorization and print results. */
            result = theFactor.qrdecomp(2, a);
            System.out.println("QR factorization:");
            System.out.println("Q matrix:");
            System.out.println(result[0]);
            System.out.println("R matrix:");
            System.out.println(result[1]);
         }
   
         catch (Exception e)
         {
            System.out.println("Exception: " + e.toString());
         }
   
         finally
         {
            /* Free native resources */
            MWArray.disposeArray(a);
            MWArray.disposeArray(result);
            if (theFactor != null)
               theFactor.dispose();
         }
      }
   }

   The statement:

   theFactor = new factor();
   

   creates an instance of the class factor.

   The following statements call the methods that encapsulate the MATLAB functions:

   result = theFactor.cholesky(1, a);
   ...
   result = theFactor.ludecomp(2, a);
   ...
   result = theFactor.qrdecomp(2, a);
   ...

7. Compile the getfactor application using javac. When entering this command, ensure there are no spaces between path names in the matlabroot argument. For example, there should be no space between javabuilder.jar; and .\distrib\factormatrix.jar in the following example.

   cd to the matlabroot\factormatrix folder. Ensure getfactor.java is in this folder.

   • On Windows, execute the following command:

     javac -classpath
     .;matlabroot\toolbox\javabuilder\jar\javabuilder.jar;
     .\distrib\factormatrix.jar getfactor.java
     

   • On UNIX, execute the following command:

     javac -classpath
     .:matlabroot/toolbox/javabuilder/jar/javabuilder.jar:
     ./distrib/factormatrix.jar getfactor.java
     

8. Run the application.

   Run getfactor using a nonsparse matrix

   • On Windows, execute the getfactor class file as follows:

     java -classpath
     .;matlabroot\toolbox\javabuilder\jar\javabuilder.jar;
     .\distrib\factormatrix.jar 
     getfactor 4
     

   • On UNIX, execute the getfactor class file as follows:

     java -classpath
     .:matlabroot/toolbox/javabuilder/jar/javabuilder.jar:
     ./distrib/factormatrix.jar 
     getfactor 4
     

Note   The supported JRE version is 1.6.0. To find out what JRE you are using, refer to the output of 'version -java' in MATLAB or refer to the jre.cfg file in matlabroot/sys/java/jre/<arch> or mcrroot/sys/java/jre/<arch>.

Note   If you are running on Mac or Solaris 64-bit platforms, you must add the -d64 flag in the Java command. See Limitations and Restrictions for more specific information.

 Output for the Matrix Math Example

Original matrix:
     2    -1     0     0
    -1     2    -1     0
     0    -1     2    -1
     0     0    -1     2
Cholesky factorization:
    1.4142   -0.7071         0         0
         0    1.2247   -0.8165         0
         0         0    1.1547   -0.8660
         0         0         0    1.1180


LU factorization:
L matrix:
    1.0000         0         0         0
   -0.5000    1.0000         0         0
         0   -0.6667    1.0000         0
         0         0   -0.7500    1.0000


U matrix:
    2.0000   -1.0000         0         0
         0    1.5000   -1.0000         0
         0         0    1.3333   -1.0000
         0         0         0    1.2500


QR factorization:
Q matrix:
   -0.8944   -0.3586   -0.1952    0.1826
    0.4472   -0.7171   -0.3904    0.3651
         0    0.5976   -0.5855    0.5477
         0         0    0.6831    0.7303


R matrix:
   -2.2361    1.7889   -0.4472         0
         0   -1.6733    1.9124   -0.5976
         0         0   -1.4639    1.9518
         0         0         0    0.9129

To run the same program for a sparse matrix, use the same command and add the string sparse to the command line:

java (... same arguments) getfactor 4 sparse

 Output for a Sparse Matrix

Original matrix:
   (1,1)        2
   (2,1)       -1
   (1,2)       -1
   (2,2)        2
   (3,2)       -1
   (2,3)       -1
   (3,3)        2
   (4,3)       -1
   (3,4)       -1
   (4,4)        2


Cholesky factorization:
   (1,1)       1.4142
   (1,2)      -0.7071
   (2,2)       1.2247
   (2,3)      -0.8165
   (3,3)       1.1547
   (3,4)      -0.8660
   (4,4)       1.1180


LU factorization:
L matrix:
   (1,1)       1.0000
   (2,1)      -0.5000
   (2,2)       1.0000
   (3,2)      -0.6667
   (3,3)       1.0000
   (4,3)      -0.7500
   (4,4)       1.0000


U matrix:
   (1,1)       2.0000
   (1,2)      -1.0000
   (2,2)       1.5000
   (2,3)      -1.0000
   (3,3)       1.3333
   (3,4)      -1.0000
   (4,4)       1.2500


QR factorization:
Q matrix:
   (1,1)       0.8944
   (2,1)      -0.4472
   (1,2)       0.3586
   (2,2)       0.7171
   (3,2)      -0.5976
   (1,3)       0.1952
   (2,3)       0.3904
   (3,3)       0.5855
   (4,3)      -0.6831
   (1,4)       0.1826
   (2,4)       0.3651
   (3,4)       0.5477
   (4,4)       0.7303


R matrix:
   (1,1)       2.2361
   (1,2)      -1.7889
   (2,2)       1.6733
   (1,3)       0.4472
   (2,3)      -1.9124
   (3,3)       1.4639
   (2,4)       0.5976
   (3,4)      -1.9518
   (4,4)       0.9129

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