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/*!
* \file
* \brief Definitions of Cholesky 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 CHOLESKY_H
#define CHOLESKY_H
#include <itpp/base/mat.h>
namespace itpp
{
/*! \addtogroup matrixdecomp
*/
//!@{
/*!
\brief Cholesky factorisation of real symmetric and positive definite matrix
The Cholesky factorisation of a real symmetric positive-definite matrix \f$\mathbf{X}\f$
of size \f$n \times n\f$ is given by
\f[
\mathbf{X} = \mathbf{F}^T \mathbf{F}
\f]
where \f$\mathbf{F}\f$ is an upper triangular \f$n \times n\f$ matrix.
Returns true if calculation succeeded. False otherwise.
*/
bool chol(const mat &X, mat &F);
/*!
\brief Cholesky factorisation of real symmetric and positive definite matrix
The Cholesky factorisation of a real symmetric positive-definite matrix \f$\mathbf{X}\f$
of size \f$n \times n\f$ is given by
\f[
\mathbf{X} = \mathbf{F}^T \mathbf{F}
\f]
where \f$\mathbf{F}\f$ is an upper triangular \f$n \times n\f$ matrix.
*/
mat chol(const mat &X);
/*!
\brief Cholesky factorisation of complex hermitian and positive-definite matrix
The Cholesky factorisation of a hermitian positive-definite matrix \f$\mathbf{X}\f$
of size \f$n \times n\f$ is given by
\f[
\mathbf{X} = \mathbf{F}^H \mathbf{F}
\f]
where \f$\mathbf{F}\f$ is an upper triangular \f$n \times n\f$ matrix.
Returns true if calculation succeeded. False otherwise.
If \c X is positive definite, true is returned and \c F=chol(X)
produces an upper triangular \c F. If also \c X is symmetric then \c F'*F = X.
If \c X is not positive definite, false is returned.
*/
bool chol(const cmat &X, cmat &F);
/*!
\brief Cholesky factorisation of complex hermitian and positive-definite matrix
The Cholesky factorisation of a hermitian positive-definite matrix \f$\mathbf{X}\f$
of size \f$n \times n\f$ is given by
\f[
\mathbf{X} = \mathbf{F}^H \mathbf{F}
\f]
where \f$\mathbf{F}\f$ is an upper triangular \f$n \times n\f$ matrix.
*/
cmat chol(const cmat &X);
//!@}
} // namespace itpp
#endif // #ifndef CHOLESKY_H

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