| [35] | 1 | /*! |
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| 2 | * \file |
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| 3 | * \brief Definitions of QR factorisation functions |
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| 4 | * \author Tony Ottosson |
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| 5 | * |
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| 6 | * ------------------------------------------------------------------------- |
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| 7 | * |
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| 8 | * IT++ - C++ library of mathematical, signal processing, speech processing, |
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| 9 | * and communications classes and functions |
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| 10 | * |
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| 11 | * Copyright (C) 1995-2007 (see AUTHORS file for a list of contributors) |
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| 12 | * |
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| 13 | * This program is free software; you can redistribute it and/or modify |
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| 14 | * it under the terms of the GNU General Public License as published by |
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| 15 | * the Free Software Foundation; either version 2 of the License, or |
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| 16 | * (at your option) any later version. |
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| 17 | * |
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| 18 | * This program is distributed in the hope that it will be useful, |
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| 19 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
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| 20 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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| 21 | * GNU General Public License for more details. |
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| 22 | * |
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| 23 | * You should have received a copy of the GNU General Public License |
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| 24 | * along with this program; if not, write to the Free Software |
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| 25 | * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA |
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| 26 | * |
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| 27 | * ------------------------------------------------------------------------- |
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| 28 | */ |
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| 29 | |
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| 30 | #ifndef QR_H |
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| 31 | #define QR_H |
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| 32 | |
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| 33 | #include <itpp/base/mat.h> |
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| 34 | |
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| 35 | |
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| 36 | namespace itpp { |
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| 37 | |
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| 38 | |
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| 39 | /*! \addtogroup matrixdecomp |
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| 40 | */ |
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| 41 | //!@{ |
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| 42 | /*! |
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| 43 | \brief QR factorisation of real matrix |
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| 44 | |
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| 45 | The QR factorization of the real matrix \f$\mathbf{A}\f$ of size \f$m \times n\f$ is given |
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| 46 | by |
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| 47 | \f[ |
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| 48 | \mathbf{A} = \mathbf{Q} \mathbf{R} , |
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| 49 | \f] |
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| 50 | where \f$\mathbf{Q}\f$ is an \f$m \times m\f$ orthogonal matrix and \f$\mathbf{R}\f$ is an \f$m \times n\f$ upper triangular matrix. |
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| 51 | |
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| 52 | Returns true is calculation succeeds. False otherwise. |
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| 53 | Uses the LAPACK routine DGEQRF and DORGQR. |
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| 54 | */ |
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| 55 | bool qr(const mat &A, mat &Q, mat &R); |
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| 56 | |
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| 57 | /*! |
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| 58 | \brief QR factorisation of real matrix with pivoting |
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| 59 | |
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| 60 | The QR factorization of the real matrix \f$\mathbf{A}\f$ of size \f$m \times n\f$ is given |
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| 61 | by |
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| 62 | \f[ |
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| 63 | \mathbf{A} \mathbf{P} = \mathbf{Q} \mathbf{R} , |
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| 64 | \f] |
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| 65 | where \f$\mathbf{Q}\f$ is an \f$m \times m\f$ orthogonal matrix, \f$\mathbf{R}\f$ is an \f$m \times n\f$ upper triangular matrix |
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| 66 | and \f$\mathbf{P}\f$ is an \f$n \times n\f$ permutation matrix. |
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| 67 | |
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| 68 | Returns true is calculation succeeds. False otherwise. |
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| 69 | Uses the LAPACK routines DGEQP3 and DORGQR. |
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| 70 | */ |
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| 71 | bool qr(const mat &A, mat &Q, mat &R, bmat &P); |
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| 72 | |
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| 73 | /*! |
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| 74 | \brief QR factorisation of a complex matrix |
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| 75 | |
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| 76 | The QR factorization of the complex matrix \f$\mathbf{A}\f$ of size \f$m \times n\f$ is given |
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| 77 | by |
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| 78 | \f[ |
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| 79 | \mathbf{A} = \mathbf{Q} \mathbf{R} , |
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| 80 | \f] |
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| 81 | where \f$\mathbf{Q}\f$ is an \f$m \times m\f$ unitary matrix and \f$\mathbf{R}\f$ is an \f$m \times n\f$ upper triangular matrix. |
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| 82 | |
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| 83 | Returns true is calculation succeeds. False otherwise. |
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| 84 | Uses the LAPACK routines ZGEQRF and ZUNGQR. |
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| 85 | */ |
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| 86 | bool qr(const cmat &A, cmat &Q, cmat &R); |
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| 87 | |
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| 88 | /*! |
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| 89 | \brief QR factorisation of a complex matrix with pivoting |
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| 90 | |
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| 91 | The QR factorization of the complex matrix \f$\mathbf{A}\f$ of size \f$m \times n\f$ is given |
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| 92 | by |
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| 93 | \f[ |
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| 94 | \mathbf{A} \mathbf{P} = \mathbf{Q} \mathbf{R} , |
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| 95 | \f] |
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| 96 | where \f$\mathbf{Q}\f$ is an \f$m \times m\f$ unitary matrix, \f$\mathbf{R}\f$ is an \f$m \times n\f$ upper triangular matrix |
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| 97 | and \f$\mathbf{P}\f$ is an \f$n \times n\f$ permutation matrix. |
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| 98 | |
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| 99 | Returns true is calculation succeeds. False otherwise. |
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| 100 | Uses the LAPACK routines ZGEQP3 and ZUNGQR. |
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| 101 | */ |
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| 102 | bool qr(const cmat &A, cmat &Q, cmat &R, bmat &P); |
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| 103 | |
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| 104 | //!@} |
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| 105 | |
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| 106 | |
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| 107 | } // namespace itpp |
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| 108 | |
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| 109 | #endif // #ifndef QR_H |
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