/*
 * 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 now defunct
 * <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 $Revision$ $Date$
 * @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 &times; X = B solution in least square
	 * sense.
	 * 
	 * @return a solver
	 */
	DecompositionSolver getSolver();

}
