QRDecomposition.java :  » Algebra » efficient-java-matrix-library » org » ejml » alg » dense » decomposition » Java Open Source

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 efficient java matrix library » org » ejml » alg » dense » decomposition » QRDecomposition.java ``````/* * Copyright (c) 2009-2011, Peter Abeles. All Rights Reserved. * * This file is part of Efficient Java Matrix Library (EJML). * * EJML is free software: you can redistribute it and/or modify * it under the terms of the GNU Lesser General Public License as * published by the Free Software Foundation, either version 3 * of the License, or (at your option) any later version. * * EJML is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU Lesser General Public License for more details. * * You should have received a copy of the GNU Lesser General Public * License along with EJML. If not, see . */ package org.ejml.alg.dense.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
• *
• *
*

*

* Orthogonal matrices have the following properties: *

*
• QQT=I
• *
• QT=Q-1
• *
*

* @see org.ejml.alg.dense.decomposition.qr.QRDecompositionHouseholder * @see org.ejml.alg.dense.decomposition.qr.QRDecompositionHouseholderColumn * * @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); } ``````