alvinalexander.com | career | drupal | java | mac | mysql | perl | scala | uml | unix  

Java example source code file (MagicSquareExample.java)

This example Java source code file (MagicSquareExample.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

adios\n, class, date, eigenvaluedecomposition, inf, ludecomposition, magicsquareexample, matrix, qrdecomposition, see, string, test, time, util

The MagicSquareExample.java Java example source code

package Jama.examples;
import Jama.*; 
import java.util.Date;

/** Example of use of Matrix Class, featuring magic squares. **/

public class MagicSquareExample {

   /** Generate magic square test matrix. **/

   public static Matrix magic (int n) {

      double[][] M = new double[n][n];

      // Odd order

      if ((n % 2) == 1) {
         int a = (n+1)/2;
         int b = (n+1);
         for (int j = 0; j < n; j++) {
            for (int i = 0; i < n; i++) {
               M[i][j] = n*((i+j+a) % n) + ((i+2*j+b) % n) + 1;
            }
         }

      // Doubly Even Order

      } else if ((n % 4) == 0) {
         for (int j = 0; j < n; j++) {
            for (int i = 0; i < n; i++) {
               if (((i+1)/2)%2 == ((j+1)/2)%2) {
                  M[i][j] = n*n-n*i-j;
               } else {
                  M[i][j] = n*i+j+1;
               }
            }
         }

      // Singly Even Order

      } else {
         int p = n/2;
         int k = (n-2)/4;
         Matrix A = magic(p);
         for (int j = 0; j < p; j++) {
            for (int i = 0; i < p; i++) {
               double aij = A.get(i,j);
               M[i][j] = aij;
               M[i][j+p] = aij + 2*p*p;
               M[i+p][j] = aij + 3*p*p;
               M[i+p][j+p] = aij + p*p;
            }
         }
         for (int i = 0; i < p; i++) {
            for (int j = 0; j < k; j++) {
               double t = M[i][j]; M[i][j] = M[i+p][j]; M[i+p][j] = t;
            }
            for (int j = n-k+1; j < n; j++) {
               double t = M[i][j]; M[i][j] = M[i+p][j]; M[i+p][j] = t;
            }
         }
         double t = M[k][0]; M[k][0] = M[k+p][0]; M[k+p][0] = t;
         t = M[k][k]; M[k][k] = M[k+p][k]; M[k+p][k] = t;
      }
      return new Matrix(M);
   }

   /** Shorten spelling of print. **/

   private static void print (String s) {
      System.out.print(s);
   }
   
   /** Format double with Fw.d. **/

   public static String fixedWidthDoubletoString (double x, int w, int d) {
      java.text.DecimalFormat fmt = new java.text.DecimalFormat();
      fmt.setMaximumFractionDigits(d);
      fmt.setMinimumFractionDigits(d);
      fmt.setGroupingUsed(false);
      String s = fmt.format(x);
      while (s.length() < w) {
         s = " " + s;
      }
      return s;
   }

   /** Format integer with Iw. **/

   public static String fixedWidthIntegertoString (int n, int w) {
      String s = Integer.toString(n);
      while (s.length() < w) {
         s = " " + s;
      }
      return s;
   }


   public static void main (String argv[]) {

   /* 
    | Tests LU, QR, SVD and symmetric Eig decompositions.
    |
    |   n       = order of magic square.
    |   trace   = diagonal sum, should be the magic sum, (n^3 + n)/2.
    |   max_eig = maximum eigenvalue of (A + A')/2, should equal trace.
    |   rank    = linear algebraic rank,
    |             should equal n if n is odd, be less than n if n is even.
    |   cond    = L_2 condition number, ratio of singular values.
    |   lu_res  = test of LU factorization, norm1(L*U-A(p,:))/(n*eps).
    |   qr_res  = test of QR factorization, norm1(Q*R-A)/(n*eps).
    */

      print("\n    Test of Matrix Class, using magic squares.\n");
      print("    See MagicSquareExample.main() for an explanation.\n");
      print("\n      n     trace       max_eig   rank        cond      lu_res      qr_res\n\n");
 
      Date start_time = new Date();
      double eps = Math.pow(2.0,-52.0);
      for (int n = 3; n <= 32; n++) {
         print(fixedWidthIntegertoString(n,7));

         Matrix M = magic(n);

         int t = (int) M.trace();
         print(fixedWidthIntegertoString(t,10));

         EigenvalueDecomposition E =
            new EigenvalueDecomposition(M.plus(M.transpose()).times(0.5));
         double[] d = E.getRealEigenvalues();
         print(fixedWidthDoubletoString(d[n-1],14,3));

         int r = M.rank();
         print(fixedWidthIntegertoString(r,7));

         double c = M.cond();
         print(c < 1/eps ? fixedWidthDoubletoString(c,12,3) :
            "         Inf");

         LUDecomposition LU = new LUDecomposition(M);
         Matrix L = LU.getL();
         Matrix U = LU.getU();
         int[] p = LU.getPivot();
         Matrix R = L.times(U).minus(M.getMatrix(p,0,n-1));
         double res = R.norm1()/(n*eps);
         print(fixedWidthDoubletoString(res,12,3));

         QRDecomposition QR = new QRDecomposition(M);
         Matrix Q = QR.getQ();
         R = QR.getR();
         R = Q.times(R).minus(M);
         res = R.norm1()/(n*eps);
         print(fixedWidthDoubletoString(res,12,3));

         print("\n");
      }
      Date stop_time = new Date();
      double etime = (stop_time.getTime() - start_time.getTime())/1000.;
      print("\nElapsed Time = " + 
         fixedWidthDoubletoString(etime,12,3) + " seconds\n");
      print("Adios\n");
   }
}

Other Java examples (source code examples)

Here is a short list of links related to this Java MagicSquareExample.java source code file:

... this post is sponsored by my books ...

#1 New Release!

FP Best Seller

 

new blog posts

 

Copyright 1998-2024 Alvin Alexander, alvinalexander.com
All Rights Reserved.

A percentage of advertising revenue from
pages under the /java/jwarehouse URI on this website is
paid back to open source projects.