[4ede1e]: itpp / base / algebra / det.h  Maximize  Restore  History

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/*!
* \file
* \brief Definitions of determinant calculations
* \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 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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