[35] | 1 | /*! |
---|
| 2 | * \file |
---|
| 3 | * \brief Definitions of determinant calculations |
---|
| 4 | * \author Tony Ottosson |
---|
| 5 | * |
---|
| 6 | * ------------------------------------------------------------------------- |
---|
| 7 | * |
---|
| 8 | * IT++ - C++ library of mathematical, signal processing, speech processing, |
---|
| 9 | * and communications classes and functions |
---|
| 10 | * |
---|
| 11 | * Copyright (C) 1995-2007 (see AUTHORS file for a list of contributors) |
---|
| 12 | * |
---|
| 13 | * This program is free software; you can redistribute it and/or modify |
---|
| 14 | * it under the terms of the GNU General Public License as published by |
---|
| 15 | * the Free Software Foundation; either version 2 of the License, or |
---|
| 16 | * (at your option) any later version. |
---|
| 17 | * |
---|
| 18 | * This program is distributed in the hope that it will be useful, |
---|
| 19 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
---|
| 20 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
---|
| 21 | * GNU General Public License for more details. |
---|
| 22 | * |
---|
| 23 | * You should have received a copy of the GNU General Public License |
---|
| 24 | * along with this program; if not, write to the Free Software |
---|
| 25 | * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA |
---|
| 26 | * |
---|
| 27 | * ------------------------------------------------------------------------- |
---|
| 28 | */ |
---|
| 29 | |
---|
| 30 | #ifndef DET_H |
---|
| 31 | #define DET_H |
---|
| 32 | |
---|
| 33 | #include <itpp/base/mat.h> |
---|
| 34 | |
---|
| 35 | |
---|
| 36 | namespace itpp { |
---|
| 37 | |
---|
| 38 | /*! |
---|
| 39 | \brief Determinant of real square matrix. |
---|
| 40 | \ingroup determinant |
---|
| 41 | |
---|
| 42 | Calculate determinant of the real matrix \f$\mathbf{X}\f$ |
---|
| 43 | |
---|
| 44 | Uses LU-factorisation. |
---|
| 45 | \f[ |
---|
| 46 | \det(\mathbf{X}) = \det(\mathbf{P}^T \mathbf{L}) \det(\mathbf{U}) = \det(\mathbf{P}^T) \prod(\mathrm{diag}(\mathbf{U})) |
---|
| 47 | \f] |
---|
| 48 | and the determinant of the permuation matrix is \f$ \pm 1\f$ dependening on the number of row permuations |
---|
| 49 | */ |
---|
| 50 | double det(const mat &X); |
---|
| 51 | |
---|
| 52 | |
---|
| 53 | /*! |
---|
| 54 | \brief Determinant of complex square matrix. |
---|
| 55 | \ingroup determinant |
---|
| 56 | |
---|
| 57 | Calculate determinant of the complex matrix \f$\mathbf{X}\f$ |
---|
| 58 | |
---|
| 59 | Uses LU-factorisation. |
---|
| 60 | \f[ |
---|
| 61 | \det(\mathbf{X}) = \det(\mathbf{P}^T \mathbf{L}) \det(\mathbf{U}) = \det(\mathbf{P}^T) \prod(\mathrm{diag}(\mathbf{U})) |
---|
| 62 | \f] |
---|
| 63 | and the determinant of the permuation matrix is \f$ \pm 1\f$ dependening on the number of row permuations |
---|
| 64 | */ |
---|
| 65 | std::complex<double> det(const cmat &X); |
---|
| 66 | |
---|
| 67 | |
---|
| 68 | } // namespace itpp |
---|
| 69 | |
---|
| 70 | #endif // #ifndef DET_H |
---|