householderqrdecomposer.java

一个关于java 的常用工具包

package org.jutil.math.matrix;

/**
 * <p>A class of objects that compute the QR factorization of a matrix using
 * the Householder Algorithm.</p>
 *
 * @path    $Source: /cvsroot/org-jutil/jutil.org/src/org/jutil/math/matrix/HouseholderQRDecomposer.java,v $
 * @version $Revision: 1.3 $
 * @date    $Date: 2002/05/20 15:01:37 $
 * @state   $State: Exp $
 * @author  Marko van Dooren
 * @release $Name:  $
 */
public class HouseholderQRDecomposer implements QRDecomposer {

	/* The revision of this class */
	public final static String CVS_REVISION ="$Revision: 1.3 $";

	/**
	 * <p>The decomposition is done using the Householder algorithm.</p>
	 * <p>The algorithmic complexity is <b>O(2mn^2 - (2/3)n^3)</b>.</p>
	 */
	public QRDecomposition decompose(Matrix matrix) {
		Matrix R = (Matrix) matrix.clone();
		int columns = matrix.getNbColumns();
		int rows = matrix.getNbRows();
		Column[] vs = new Column[columns];
	  for (int k=1; k<=columns; k++) {
			Column x = R.getColumn(k).subColumn(k, rows);
			Column v = new Column(rows - k + 1);
			double x1 = x.elementAt(1);
			double signX1 = org.jutil.math.Math.sign(x1);
			v.setElementAt(1,x.norm(2)*signX1);
			v.add(x);
			v.normalize();
			vs[k-1]=v;
			Matrix A = R.subMatrix(k,k,rows,columns);
			// subtracting from A saves us a clone()
			// mutating temp saves us another one ( <-> .times(2))
			Matrix temp = v.times(v.returnTranspose().times(A));
			temp.multiply(2);
			A.subtract(temp);
			R.setSubMatrix(k,k,A);
		}
		// explicitly make R an upper triangular matrix.
		for(int col=1; col<=columns; col++) {
			for(int row=col+1; row<=rows; row++) {
				R.setElementAt(row,col,0);
      }
    }
		return new HouseholderQRDecomposition(R,vs);
	}

}

/*<copyright>Copyright (C) 1997-2002. This software is copyrighted by 
the people and entities mentioned after the "@author" tags above, on 
behalf of the JUTIL.ORG Project. The copyright is dated by the dates 
after the "@date" tags above. All rights reserved.
This software is published under the terms of the JUTIL.ORG Software
License version 1.1 or later, a copy of which has been included with
this distribution in the LICENSE file, which can also be found at
http://www.jutil.org/LICENSE. This software is distributed WITHOUT 
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 
or FITNESS FOR A PARTICULAR PURPOSE. See the JUTIL.ORG Software 
License for more details.
For more information, please see http://jutil.org/</copyright>*/