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/*!
* \file
* \brief Definitions of determinant calculations
* \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 DET_H
#define DET_H
#include <itpp/base/mat.h>
namespace itpp {
/*!
\brief Determinant of real square matrix.
\ingroup determinant
Calculate determinant of the real matrix \f$\mathbf{X}\f$
Uses LU-factorisation.
\f[
\det(\mathbf{X}) = \det(\mathbf{P}^T \mathbf{L}) \det(\mathbf{U}) = \det(\mathbf{P}^T) \prod(\mathrm{diag}(\mathbf{U}))
\f]
and the determinant of the permuation matrix is \f$ \pm 1\f$ depending on the number of row permutations
*/
double det(const mat &X);
/*!
\brief Determinant of complex square matrix.
\ingroup determinant
Calculate determinant of the complex matrix \f$\mathbf{X}\f$
Uses LU-factorisation.
\f[
\det(\mathbf{X}) = \det(\mathbf{P}^T \mathbf{L}) \det(\mathbf{U}) = \det(\mathbf{P}^T) \prod(\mathrm{diag}(\mathbf{U}))
\f]
and the determinant of the permuation matrix is \f$ \pm 1\f$ depending on the number of row permutations
*/
std::complex<double> det(const cmat &X);
} // namespace itpp
#endif // #ifndef DET_H
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