/*
* (C) Copyright 2005 Arnaud Bailly (arnaud.oqube@gmail.com),
* Yves Roos (yroos@lifl.fr) and others.
*
* Licensed under the Apache License, Version 2.0 (the License);
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an AS IS BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package rationals.algebra;
import java.util.Arrays;
/**
* Matrix representation of an automaton.
* <p>
* The elements of a the matrix are {@see SemiRing}objects.
*
* @author nono
* @version $Id: Matrix.java 6 2006-08-30 08:56:44Z oqube $
*/
public final class Matrix implements SemiRing {
/* matrices for transitions, initial and terminal states */
protected final SemiRing[][] matrix;
private int line;
private int col;
public Matrix(int ns) {
this.line = this.col = ns;
this.matrix = new SemiRing[ns][ns];
}
/**
* @param matrix
*/
public Matrix(Matrix matrix) {
this(matrix.line);
for (int i = 0; i < line; i++)
for (int j = 0; j < col; j++)
this.matrix[i][j] = matrix.matrix[i][j];
}
/**
* @param l
* @param c
*/
public Matrix(int l, int c) {
this.line = l;
this.col = c;
matrix = new SemiRing[l][c];
}
/**
* Returns the n <sup>th </sup> power of this matrix.
*
* @param n
* the power. Must be positive or null.
* @param res
* matrix where the result should be stored. Must be same size as
* this matrix with all elements initialized with null.
* @return the result Matrix object with transition matrix equals the n
* <sup>th </sup> power of this matrix's transition.
*/
public Matrix power(int n, Matrix res) {
int l = line;
if(line != col)
throw new IllegalStateException("Cannot compute power of a non square matrix");
SemiRing[][] tmp = new SemiRing[l][l];
for (int i = 0; i < l; i++)
Arrays.fill(tmp[i], matrix[0][0].zero());
for (int k = 0; k <n; k++) {
for (int i = 0; i < l; i++) {
for (int j = 0; j < l; j++) {
for (int m = 0; m < l; m++) {
if (k==0)
tmp[i][j] = tmp[i][j].plus(matrix[i][m]
.mult(matrix[m][j]));
else
tmp[i][j] = tmp[i][j].plus(res.matrix[i][m]
.mult(matrix[m][j]));
}
}
}
/* copy to res */
for (int i = 0; i < l; i++)
System.arraycopy(tmp[i],0,res.matrix[i],0,l);
}
return res;
}
/**
* Returns the star of this matrix.
*
* @return
*/
public Matrix star() {
return null;
}
public int getLine() {
return line;
}
public String toString() {
final String ln = System.getProperty("line.separator");
StringBuffer sb = new StringBuffer();
int n = matrix.length;
for (int i = 0; i < line; i++) {
sb.append("[ ");
for (int j = 0; j < col; j++) {
String s = matrix[i][j].toString();
sb.append(s).append(' ');
}
sb.append("]").append(ln);
}
return sb.toString();
}
/* (non-Javadoc)
* @see rationals.algebra.SemiRing#plus(rationals.algebra.SemiRing)
*/
public SemiRing plus(SemiRing s2) {
if(s2 == null)
throw new IllegalArgumentException("Null argument");
Matrix o = (Matrix)s2; // maybe ClassCastException
if(col != o.col || line != o.line)
throw new IllegalArgumentException("Incompatible matrices dimensions : cannot add non square matrices");
int l = line;
int c = col;
Matrix res = Matrix.zero(l,c,matrix[0][0]);
for(int i=0;i<l;i++)
for(int j=0;j<c;j++)
res.matrix[i][j] = matrix[i][j].plus(o.matrix[i][j]);
return res;
}
/* (non-Javadoc)
* @see rationals.algebra.SemiRing#mult(rationals.algebra.SemiRing)
*/
public SemiRing mult(SemiRing s2) {
if(s2 == null)
throw new IllegalArgumentException("Null argument");
Matrix o = (Matrix)s2; // maybe ClassCastException
if(col != o.line)
throw new IllegalArgumentException("Incompatible matrices dimensions");
int l = line; // lines
int c = o.col; // cols
int m = col;
Matrix res = Matrix.zero(l,c,matrix[0][0]);
for(int i=0;i<l;i++) {
for(int j=0;j<c;j++)
for(int k=0;k<m;k++){
if(k ==0)
res.matrix[i][j] = matrix[i][k].mult(o.matrix[k][j]);
else
res.matrix[i][j] = res.matrix[i][j].plus(matrix[i][k].mult(o.matrix[k][j]));
}
}
return res;
}
/* (non-Javadoc)
* @see rationals.algebra.SemiRing#one()
*/
public SemiRing one() {
if(line != col)
throw new IllegalStateException("Cannot get unit matrix on non-square matrices");
return one(line,matrix[0][0]);
}
/* (non-Javadoc)
* @see rationals.algebra.SemiRing#zero()
*/
public SemiRing zero() {
return zero(line,col,matrix[0][0]);
}
public int getCol() {
return col;
}
/**
* Factory method for creating Matrix instances with coefficients
* in a certain SemiRing.
*
* @param sr a SemiRing instance. Used to get one and zero.
* @return a new zero matrix.
*/
public static Matrix zero(int line,int col,SemiRing sr) {
Matrix m = new Matrix(line,col);
for(int i=0;i<line;i++)
for(int j=0;j<col;j++)
m.matrix[i][j] = sr.zero();
return m;
}
/**
* Factory method for creating unit Matrix instances with coefficients
* in a certain SemiRing.
*
* @param sr a SemiRing instance. Used to get one and zero.
* @return a new unit square matrix.
*/
public static Matrix one(int dim,SemiRing sr) {
Matrix m = new Matrix(dim);
for(int i=0;i<dim;i++)
for(int j=0;j<dim;j++)
m.matrix[i][j] = (i == j) ? sr.one() : sr.zero();
return m;
}
}