QRDecomposition.java

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You 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 org.apache.commons.math.linear;


/**
 * An interface to classes that implement an algorithm to calculate the
 * QR-decomposition of a real matrix.
 * <p>This interface is based on the class with similar name from the
 * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library, with the
 * following changes:</p>
 * <ul>
 *   <li>a {@link #getQT() getQT} method has been added,</li>
 *   <li>the <code>solve</code> and <code>isFullRank</code> methods have been replaced
 *   by a {@link #getSolver() getSolver} method and the equivalent methods provided by
 *   the returned {@link DecompositionSolver}.</li>
 * </ul>
 *
 * @see <a href="http://mathworld.wolfram.com/QRDecomposition.html">MathWorld</a>
 * @see <a href="http://en.wikipedia.org/wiki/QR_decomposition">Wikipedia</a>
 * @version $Id: QRDecomposition.java 1131229 2011-06-03 20:49:25Z luc $
 * @since 1.2
 */
public interface QRDecomposition {

    /**
     * Returns the matrix R of the decomposition.
     * <p>R is an upper-triangular matrix</p>
     * @return the R matrix
     */
    RealMatrix getR();

    /**
     * Returns the matrix Q of the decomposition.
     * <p>Q is an orthogonal matrix</p>
     * @return the Q matrix
     */
    RealMatrix getQ();

    /**
     * Returns the transpose of the matrix Q of the decomposition.
     * <p>Q is an orthogonal matrix</p>
     * @return the Q matrix
     */
    RealMatrix getQT();

    /**
     * Returns the Householder reflector vectors.
     * <p>H is a lower trapezoidal matrix whose columns represent
     * each successive Householder reflector vector. This matrix is used
     * to compute Q.</p>
     * @return a matrix containing the Householder reflector vectors
     */
    RealMatrix getH();

    /**
     * Get a solver for finding the A × X = B solution in least square sense.
     * @return a solver
     */
    DecompositionSolver getSolver();

}