1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
|
/* GaussElimination.java
* =========================================================================
* This file is part of the GrInvIn project - http://www.grinvin.org
*
* Copyright (C) 2005-2008 Universiteit Gent
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* A copy of the GNU General Public License can be found in the file
* LICENSE.txt provided with the source distribution of this program (see
* the META-INF directory in the source jar). This license can also be
* found on the GNU website at http://www.gnu.org/licenses/gpl.html.
*
* If you did not receive a copy of the GNU General Public License along
* with this program, contact the lead developer, or write to the Free
* Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
* 02110-1301, USA.
*/
package org.grinvin.util;
import java.math.BigInteger;
import java.util.Arrays;
/**
*
*/
public class GaussElimination {
private BigInteger[][] matrix;
private int rank = -1;
/**
* Creates a new instance of GaussElimination
*/
public GaussElimination(int[][] matrix) {
try {
this.matrix = new BigInteger[matrix.length][matrix[0].length];
} catch (ArrayIndexOutOfBoundsException ex) {
this.matrix = new BigInteger[matrix.length][0];
}
for(int i = 0; i < matrix.length; i++)
for(int j = 0; j < matrix[i].length; j++)
this.matrix[i][j] = BigInteger.valueOf(matrix[i][j]);
}
public void doElimination() {
doElimination(0);
}
private void doElimination(int currentRow) {
//make sure first element is non-zero
int columnsMoved = 0;
while(matrix[currentRow][currentRow].equals(BigInteger.ZERO) && columnsMoved <= matrix[0].length - currentRow){
int position = currentRow;
while(position < matrix.length && matrix[position][currentRow].equals(BigInteger.ZERO))
position++;
if(position==matrix.length) { //only zeroes in this column
moveColumnToEnd(currentRow);
columnsMoved++;
} else
switchRows(currentRow, position);
}
if(matrix[currentRow][currentRow].equals(BigInteger.ZERO)){ //there are only zeroes left: elimination is done
rank = currentRow;
return;
}
for(int i = currentRow+1; i<matrix.length; i++){
//find lcm
BigInteger gcd = matrix[i][currentRow].gcd(matrix[currentRow][currentRow]);
BigInteger factor1 = matrix[i][currentRow].divide(gcd);
BigInteger factor2 = matrix[currentRow][currentRow].divide(gcd);
substractRows(currentRow, currentRow, factor1, i, factor2);
simplifyRow(i);
}
if(currentRow<matrix.length-1 && currentRow<matrix[0].length-1)
doElimination(currentRow+1);
else
rank = currentRow;
}
private void switchRows (int row1, int row2){
BigInteger[] temp = matrix[row1];
matrix[row1] = matrix[row2];
matrix[row2] = temp;
}
private void switchColumns (int col1, int col2){
BigInteger temp;
for(BigInteger[] integer : matrix){
temp = integer[col1];
integer[col1] = integer[col2];
integer[col2] = temp;
}
}
private void moveColumnToEnd (int col){
for(int i = col; i < matrix[0].length - 1; i++)
switchColumns(i, i+1);
}
private void multiplyRow(int row, BigInteger factor){
for(int i = 0; i<matrix[row].length; i++)
matrix[row][i] = matrix[row][i].multiply(factor);
}
private void simplifyRow(int row){
//find gcd
BigInteger gcd;
int i = 0;
while(i<matrix[row].length && matrix[row][i].equals(BigInteger.ZERO))
i++;
if(i==matrix[row].length)
return; //row only contains zeroes
else
gcd = matrix[row][i];
for(int j = i; j<matrix[row].length; j++)
if(!matrix[row][j].equals(BigInteger.ZERO))
gcd = gcd.gcd(matrix[row][j]);
//divide all elements by gcd
for(int j = 0; j<matrix[row].length; j++)
matrix[row][j] = matrix[row][j].divide(gcd);
}
private void substractRows(int start, int row1, BigInteger factor1, int row2, BigInteger factor2){
for(int i = start; i<matrix[row1].length; i++)
matrix[row2][i] = matrix[row2][i].multiply(factor2).subtract(matrix[row1][i].multiply(factor1));
}
//todo: this may be removed after debugging???
public void print(){
for(BigInteger[] integer2 : matrix)
System.out.println(Arrays.toString(integer2));
System.out.println();
}
public int getRank(){
if(rank==-1)
doElimination();
return rank;
}
public static void main(String[] a){
int[][] m = new int[5][5];
for(int i = 0; i<5; i++)
for(int j = i; j<5; j++)
m[i][j] = (i+1)*(j+1) + 1;
GaussElimination g = new GaussElimination(m);
g.print();
g.switchRows(1,3);
g.print();
g.doElimination();
g.print();
}
}
|
