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/*!
* \file
* \brief Definitions of LU factorisation functions
* \author Tony Ottosson
*
* -------------------------------------------------------------------------
*
* 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 LU_H
#define LU_H
#include <itpp/base/mat.h>
namespace itpp
{
/*! \addtogroup matrixdecomp
*/
//!@{
/*!
\brief LU factorisation of real matrix
The LU factorization of the real matrix \f$\mathbf{X}\f$ of size \f$n \times n\f$ is given
by
\f[
\mathbf{X} = \mathbf{P}^T \mathbf{L} \mathbf{U} ,
\f]
where \f$\mathbf{L}\f$ and \f$\mathbf{U}\f$ are lower and upper triangular matrices
and \f$\mathbf{P}\f$ is a permutation matrix.
The interchange permutation vector \a p is such that \a k and \a p(k) should be
changed for all \a k. Given this vector a permutation matrix can be constructed using the
function
\code
bmat permutation_matrix(const ivec &p)
\endcode
If \a X is an \a n by \a n matrix \a lu(X,L,U,p) computes the LU decomposition.
\a L is a lower triangular, \a U an upper triangular matrix.
\a p is the interchange permutation vector such that \a k and \a p(k) should be
changed for all \a k.
Returns true is calculation succeeds. False otherwise.
*/
bool lu(const mat &X, mat &L, mat &U, ivec &p);
/*!
\brief LU factorisation of real matrix
The LU factorization of the complex matrix \f$\mathbf{X}\f$ of size \f$n \times n\f$ is given
by
\f[
\mathbf{X} = \mathbf{P}^T \mathbf{L} \mathbf{U} ,
\f]
where \f$\mathbf{L}\f$ and \f$\mathbf{U}\f$ are lower and upper triangular matrices
and \f$\mathbf{P}\f$ is a permutation matrix.
The interchange permutation vector \a p is such that \a k and \a p(k) should be
changed for all \a k. Given this vector a permutation matrix can be constructed using the
function
\code
bmat permutation_matrix(const ivec &p)
\endcode
If \a X is an \a n by \a n matrix \a lu(X,L,U,p) computes the LU decomposition.
\a L is a lower triangular, \a U an upper triangular matrix.
\a p is the interchange permutation vector such that elements \a k and row \a p(k) should be
interchanged.
Returns true is calculation succeeds. False otherwise.
*/
bool lu(const cmat &X, cmat &L, cmat &U, ivec &p);
//! Makes swapping of vector b according to the interchange permutation vector p.
void interchange_permutations(vec &b, const ivec &p);
//! Make permutation matrix P from the interchange permutation vector p.
bmat permutation_matrix(const ivec &p);
//!@}
} // namespace itpp
#endif // #ifndef LU_H

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