qrdecomposition.java

一个关于java 的常用工具包

package org.jutil.math.matrix;
/**
 * This class represents a QR factorization of a matrix.
 *
 * The methods Qtimes and QtranposeTimes are provide because the matrix
 * Q itself isn't interesting most of the times, and isn't required 
 * explicitly to calculate Q * x and transpose(Q) * x.
 *
 * @path    $Source: /cvsroot/org-jutil/jutil.org/src/org/jutil/math/matrix/QRDecomposition.java,v $
 * @version $Revision: 1.4 $
 * @date    $Date: 2002/07/02 14:27:31 $
 * @state   $State: Exp $
 * @author  Marko van Dooren
 * @release $Name:  $
 */
public interface QRDecomposition {

	/* The revision of this class */
	public final static String CVS_REVISION ="$Revision: 1.4 $";

 /*@
	 @ public invariant Q().getNbColumns() == R().getNbRows();
	 @*/

	/**
	 * Return the Q matrix of this QR factorization.
	 */
 /*@
   @ public behavior
	 @
	 @ post \result != null;
	 @ post \result.getNbRows() == R().getNbRows();
	 @ post \result.getNbColumns() == R().getNbRows();
	 @ // TODO: post \result.isOrthoNormal();
	 @*/
	public Matrix Q();
	
	/**
	 * Return the R matrix of this QR factorization.
	 */
 /*@
   @ public behavior
	 @
	 @ post \result != null;
	 @ post \result.isUpperTriangular();
	 @*/
	public Matrix R();

	/**
	 * Return the reduced Q matrix.
	 */
 /*@
   @ public behavior
	 @
	 @ post \result.equals(Q().subMatrix(1,1,Q().getNbRows(), R().getNbColumns()));
	 @*/
	public Matrix Qreduced();

	/**
	 * Return the reduced R matrix.
	 */
 /*@
   @ public behavior
	 @
	 @ post \result.equals(R().subMatrix(1,1,R().getNbColumns(), R().getNbColumns()));
	 @*/
	public Matrix Rreduced();
	
	/**
	 * Return Q().times(column)
	 *
	 * @param column
	 *        The vector with which Q() must be multiplied
	 */
 /*@
   @ public behavior
	 @
	 @ pre column != null;
	 @ pre column.size() == Q().getNbColumns();
	 @
	 @ post \result.equals(Q().times(column));
	 @*/
	public Column Qtimes(Column column);

	/**
	 * Return Qreduced().times(column)
	 *
	 * @param column
	 *        The vector with which Qreduced must be multiplied
	 */
 /*@
   @ public behavior
	 @
	 @ pre column != null;
	 @ pre column.size() == Qreduced().getNbColumns();
	 @
	 @ post \result.equals(Qreduced().times(column));
	 @*/
	public Column QreducedTimes(Column column);

	
	/**
	 * Return Q().returnTranspose().times(column)
	 *
	 * @param column
	 *        The vector with which Q must be multiplied
	 */
 /*@
   @ public behavior
	 @
	 @ pre column != null;
	 @ pre column.size() == Q().getNbRows();
	 @
	 @ post \result.equals(Q().returnTranspose().times(column));
	 @*/
	public Column QtransposeTimes(Column column);

	/**
	 * Return Qreduced().returnTranspose().times(column)
	 *
	 * @param column
	 *        The vector with which Q must be multiplied
	 */
 /*@
   @ public behavior
	 @
	 @ pre column != null;
	 @ pre column.size() == Qreduced().getNbRows();
	 @
	 @ post \result.equals(Qreduced().returnTranspose().times(column));
	 @*/
	public Column QreducedTransposeTimes(Column column);
}

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