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Java example source code file (MagicSquareExample.java)
The MagicSquareExample.java Java example source codepackage 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: |
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