/*! * \file * \brief Definitions of QR factorisation functions * \author Tony Ottosson * * ------------------------------------------------------------------------- * * IT++ - C++ library of mathematical, signal processing, speech processing, *        and communications classes and functions * * Copyright (C) 1995-2008  (see AUTHORS file for a list of contributors) * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * This program 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 General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA * * ------------------------------------------------------------------------- */#ifndef QR_H#define QR_H#include <itpp/base/mat.h>namespace itpp {  /*! \addtogroup matrixdecomp   */  //!@{  /*!    \brief QR factorisation of real matrix    The QR factorization of the real matrix \f$\mathbf{A}\f$ of size \f$m \times n\f$ is given    by    \f[    \mathbf{A} = \mathbf{Q} \mathbf{R} ,    \f]    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.    Returns true is calculation succeeds. False otherwise.    Uses the LAPACK routine DGEQRF and DORGQR.  */  bool qr(const mat &A, mat &Q, mat &R);  /*!    \brief QR factorisation of real matrix with pivoting    The QR factorization of the real matrix \f$\mathbf{A}\f$ of size \f$m \times n\f$ is given    by    \f[    \mathbf{A} \mathbf{P} = \mathbf{Q} \mathbf{R} ,    \f]    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    and \f$\mathbf{P}\f$ is an \f$n \times n\f$ permutation matrix.    Returns true is calculation succeeds. False otherwise.    Uses the LAPACK routines DGEQP3 and DORGQR.  */  bool qr(const mat &A, mat &Q, mat &R, bmat &P);  /*!    \brief QR factorisation of a complex matrix    The QR factorization of the complex matrix \f$\mathbf{A}\f$ of size \f$m \times n\f$ is given    by    \f[    \mathbf{A} = \mathbf{Q} \mathbf{R} ,    \f]    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.    Returns true is calculation succeeds. False otherwise.    Uses the LAPACK routines ZGEQRF and ZUNGQR.  */  bool qr(const cmat &A, cmat &Q, cmat &R);  /*!    \brief QR factorisation of a complex matrix with pivoting    The QR factorization of the complex matrix \f$\mathbf{A}\f$ of size \f$m \times n\f$ is given    by    \f[    \mathbf{A} \mathbf{P} = \mathbf{Q} \mathbf{R} ,    \f]    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    and \f$\mathbf{P}\f$ is an \f$n \times n\f$ permutation matrix.    Returns true is calculation succeeds. False otherwise.    Uses the LAPACK routines ZGEQP3 and ZUNGQR.  */  bool qr(const cmat &A, cmat &Q, cmat &R, bmat &P);  //!@}} // namespace itpp#endif // #ifndef QR_H