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A fast and easy to use dense matrix linear algebra library written in Java.
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/*
 * Copyright (c) 2009-2014, Peter Abeles. All Rights Reserved.
 *
 * This file is part of Efficient Java Matrix Library (EJML).
 *
 * 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 org.ejml.interfaces.decomposition;

import org.ejml.data.Matrix64F;


/**
 * 
 * QR decompositions decompose a rectangular matrix 'A' such that 'A=QR'.  Where
 * A ∈ ℜ ^{n × m} , n ≥ m, Q ∈ ℜ ^{n × n} is an orthogonal matrix,
 * and R ∈ ℜ ^{n × m} is an upper triangular matrix.  Some implementations
 * of QR decomposition require that A has full rank.
 * 
 * 
 * Some features of QR decompositions:
 * 

 *  Can decompose rectangular matrices. 
 *  Numerically stable solutions to least-squares problem, but not as stable as SVD 
 *  Can incrementally add and remove columns from the decomposed matrix.  See {@link org.ejml.alg.dense.linsol.qr.AdjLinearSolverQr} 
 * 
 * 
 * 
 * Orthogonal matrices have the following properties:
 * 

 * QQ^T=I
 * Q^T=Q^-1
 * 
 * 

 * @see org.ejml.alg.dense.decomposition.qr.QRDecompositionHouseholder_D64
 * @see org.ejml.alg.dense.decomposition.qr.QRDecompositionHouseholderColumn_D64
 *
 * @author Peter Abeles
 */
public interface QRDecomposition 
        extends DecompositionInterface {
    /**
     * 
     * Returns the Q matrix from the decomposition.  Should only
     * be called after {@link #decompose(org.ejml.data.Matrix64F)} has
     * been called.
     * 
     *
     * 
     * If parameter Q is not null, then that matrix is used to store the Q matrix.  Otherwise
     * a new matrix is created.
     * 
     *
     * @param Q If not null then the Q matrix is written to it.  Modified.
     * @param compact If true an m by n matrix is created, otherwise n by n.
     * @return The Q matrix.
     */
    public T getQ( T Q, boolean compact);

    /**
     * 
     * Returns the R matrix from the decomposition.  Should only be
     * called after {@link #decompose(org.ejml.data.Matrix64F)} has been.
     * 
     * 
     * If setZeros is true then an n × m matrix is required and all the elements are set.
     * If setZeros is false then the matrix must be at least m × m and only the upper triangular
     * elements are set.
     * 
     *
     * 
     * If parameter R is not null, then that matrix is used to store the R matrix.  Otherwise
     * a new matrix is created.
     * 
     *
     * @param R If not null then the R matrix is written to it. Modified.
     * @param compact If true only the upper triangular elements are set
     * @return The R matrix.
     */
    public T getR( T R, boolean compact);
}