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/*!
* \file
* \brief Definitions of QR factorisation functions
* \author Tony Ottosson, Simon Wood, Adam Piatyszek and Vasek Smidl
*
* -------------------------------------------------------------------------
*
* Copyright (C) 1995-2010 (see AUTHORS file for a list of contributors)
*
* This file is part of IT++ - a C++ library of mathematical, signal
* processing, speech processing, and communications classes and functions.
*
* IT++ 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 3 of the License, or (at your option) any
* later version.
*
* IT++ 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 IT++. If not, see <http://www.gnu.org/licenses/>.
*
* -------------------------------------------------------------------------
*/
#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 suppressed evaluation of Q
*
* For certain type of applications only the \f$\mathbf{R}\f$ matrix of full
* QR factorization of the real matrix \f$\mathbf{A}=\mathbf{Q}\mathbf{R}\f$
* is needed. These situations arise typically in designs of square-root
* algorithms where it is required that
* \f$\mathbf{A}^{T}\mathbf{A}=\mathbf{R}^{T}\mathbf{R}\f$. In such cases,
* evaluation of \f$\mathbf{Q}\f$ can be skipped.
*
* Modification of qr(A,Q,R).
*
* \author Vasek Smidl
*/
bool qr(const mat &A, 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 complex matrix with suppressed evaluation of Q
*
* For certain type of applications only the \f$\mathbf{R}\f$ matrix of full
* QR factorization of the complex matrix
* \f$\mathbf{A}=\mathbf{Q}\mathbf{R}\f$ is needed. These situations arise
* typically in designs of square-root algorithms where it is required that
* \f$\mathbf{A}^{H}\mathbf{A}=\mathbf{R}^{H}\mathbf{R}\f$. In such cases,
* evaluation of \f$\mathbf{Q}\f$ can be skipped.
*
* Modification of qr(A,Q,R).
*
* \author Vasek Smidl
*/
bool qr(const cmat &A, 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