001 /* 002 * Copyright (C) 2008-2010 by Holger Arndt 003 * 004 * This file is part of the Universal Java Matrix Package (UJMP). 005 * See the NOTICE file distributed with this work for additional 006 * information regarding copyright ownership and licensing. 007 * 008 * UJMP is free software; you can redistribute it and/or modify 009 * it under the terms of the GNU Lesser General Public License as 010 * published by the Free Software Foundation; either version 2 011 * of the License, or (at your option) any later version. 012 * 013 * UJMP is distributed in the hope that it will be useful, 014 * but WITHOUT ANY WARRANTY; without even the implied warranty of 015 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 016 * GNU Lesser General Public License for more details. 017 * 018 * You should have received a copy of the GNU Lesser General Public 019 * License along with UJMP; if not, write to the 020 * Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, 021 * Boston, MA 02110-1301 USA 022 */ 023 024 package org.ujmp.core.intmatrix.calculation; 025 026 import org.ujmp.core.Matrix; 027 import org.ujmp.core.MatrixFactory; 028 import org.ujmp.core.exceptions.MatrixException; 029 030 /** 031 * Creates a magic square matrix. The sums of all rows and columns are equal. 032 * This code is taken from JAMA. 033 */ 034 public class Magic extends AbstractIntCalculation { 035 private static final long serialVersionUID = -2372321035531662110L; 036 037 private final Matrix magic; 038 039 public Magic(Matrix matrix, int size) { 040 super(matrix); 041 this.magic = magic(size); 042 } 043 044 public int getInt(long... coordinates) throws MatrixException { 045 return magic.getAsInt(coordinates); 046 } 047 048 public static Matrix magic(int n) { 049 final int[][] M = new int[n][n]; 050 051 // Odd order 052 if ((n % 2) == 1) { 053 int a = (n + 1) / 2; 054 int b = (n + 1); 055 056 for (int j = 0; j < n; j++) { 057 for (int i = 0; i < n; i++) { 058 M[i][j] = n * ((i + j + a) % n) + ((i + 2 * j + b) % n) + 1; 059 } 060 } 061 062 // Doubly Even Order 063 } else if ((n % 4) == 0) { 064 for (int j = 0; j < n; j++) { 065 for (int i = 0; i < n; i++) { 066 if (((i + 1) / 2) % 2 == ((j + 1) / 2) % 2) { 067 M[i][j] = n * n - n * i - j; 068 } else { 069 M[i][j] = n * i + j + 1; 070 } 071 } 072 } 073 074 // Singly Even Order 075 } else { 076 int p = n / 2; 077 int k = (n - 2) / 4; 078 079 Matrix A = magic(p); 080 081 for (int j = 0; j < p; j++) { 082 for (int i = 0; i < p; i++) { 083 int aij = A.getAsInt(i, j); 084 M[i][j] = aij; 085 M[i][j + p] = aij + 2 * p * p; 086 M[i + p][j] = aij + 3 * p * p; 087 M[i + p][j + p] = aij + p * p; 088 } 089 } 090 091 for (int i = 0; i < p; i++) { 092 for (int j = 0; j < k; j++) { 093 int t = M[i][j]; 094 M[i][j] = M[i + p][j]; 095 M[i + p][j] = t; 096 } 097 098 for (int j = n - k + 1; j < n; j++) { 099 int t = M[i][j]; 100 M[i][j] = M[i + p][j]; 101 M[i + p][j] = t; 102 } 103 } 104 int t = M[k][0]; 105 M[k][0] = M[k + p][0]; 106 M[k + p][0] = t; 107 t = M[k][k]; 108 M[k][k] = M[k + p][k]; 109 M[k + p][k] = t; 110 } 111 return MatrixFactory.linkToArray(M); 112 } 113 114 }