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