[35] | 1 | /*! |
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| 2 | * \file |
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| 3 | * \brief Definitions of eigenvalue decomposition functions |
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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 EIGEN_H |
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| 31 | #define EIGEN_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 | \ingroup matrixdecomp |
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| 40 | \brief Calculates the eigenvalues and eigenvectors of a symmetric real matrix |
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| 41 | |
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| 42 | The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors |
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| 43 | \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the real and symmetric \f$n \times n\f$ |
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| 44 | matrix \f$\mathbf{A}\f$ satisfies |
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| 45 | \f[ |
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| 46 | \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. |
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| 47 | \f] |
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| 48 | The eigenvectors are the columns of the matrix V. |
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| 49 | True is returned if the calculation was successful. Otherwise false. |
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| 50 | |
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| 51 | Uses the LAPACK routine DSYEV. |
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| 52 | */ |
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| 53 | bool eig_sym(const mat &A, vec &d, mat &V); |
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| 54 | |
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| 55 | /*! |
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| 56 | \ingroup matrixdecomp |
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| 57 | \brief Calculates the eigenvalues of a symmetric real matrix |
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| 58 | |
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| 59 | The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors |
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| 60 | \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the real and symmetric \f$n \times n\f$ |
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| 61 | matrix \f$\mathbf{A}\f$ satisfies |
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| 62 | \f[ |
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| 63 | \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. |
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| 64 | \f] |
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| 65 | True is returned if the calculation was successful. Otherwise false. |
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| 66 | |
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| 67 | Uses the LAPACK routine DSYEV. |
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| 68 | */ |
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| 69 | bool eig_sym(const mat &A, vec &d); |
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| 70 | |
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| 71 | /*! |
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| 72 | \ingroup matrixdecomp |
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| 73 | \brief Calculates the eigenvalues of a symmetric real matrix |
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| 74 | |
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| 75 | The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors |
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| 76 | \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the real and symmetric \f$n \times n\f$ |
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| 77 | matrix \f$\mathbf{A}\f$ satisfies |
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| 78 | \f[ |
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| 79 | \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. |
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| 80 | \f] |
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| 81 | |
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| 82 | Uses the LAPACK routine DSYEV. |
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| 83 | */ |
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| 84 | vec eig_sym(const mat &A); |
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| 85 | |
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| 86 | /*! |
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| 87 | \ingroup matrixdecomp |
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| 88 | \brief Calculates the eigenvalues and eigenvectors of a hermitian complex matrix |
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| 89 | |
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| 90 | The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors |
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| 91 | \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the complex and hermitian \f$n \times n\f$ |
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| 92 | matrix \f$\mathbf{A}\f$ satisfies |
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| 93 | \f[ |
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| 94 | \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. |
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| 95 | \f] |
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| 96 | The eigenvectors are the columns of the matrix V. |
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| 97 | True is returned if the calculation was successful. Otherwise false. |
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| 98 | |
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| 99 | Uses the LAPACK routine ZHEEV. |
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| 100 | */ |
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| 101 | bool eig_sym(const cmat &A, vec &d, cmat &V); |
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| 102 | |
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| 103 | /*! |
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| 104 | \ingroup matrixdecomp |
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| 105 | \brief Calculates the eigenvalues of a hermitian complex matrix |
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| 106 | |
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| 107 | The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors |
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| 108 | \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the complex and hermitian \f$n \times n\f$ |
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| 109 | matrix \f$\mathbf{A}\f$ satisfies |
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| 110 | \f[ |
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| 111 | \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. |
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| 112 | \f] |
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| 113 | True is returned if the calculation was successful. Otherwise false. |
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| 114 | |
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| 115 | Uses the LAPACK routine ZHEEV. |
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| 116 | */ |
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| 117 | bool eig_sym(const cmat &A, vec &d); |
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| 118 | |
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| 119 | /*! |
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| 120 | \ingroup matrixdecomp |
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| 121 | \brief Calculates the eigenvalues of a hermitian complex matrix |
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| 122 | |
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| 123 | The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors |
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| 124 | \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the complex and hermitian \f$n \times n\f$ |
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| 125 | matrix \f$\mathbf{A}\f$ satisfies |
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| 126 | \f[ |
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| 127 | \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. |
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| 128 | \f] |
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| 129 | |
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| 130 | Uses the LAPACK routine ZHEEV. |
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| 131 | */ |
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| 132 | vec eig_sym(const cmat &A); |
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| 133 | |
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| 134 | /*! |
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| 135 | \ingroup matrixdecomp |
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| 136 | \brief Caclulates the eigenvalues and eigenvectors of a real non-symmetric matrix |
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| 137 | |
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| 138 | The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors |
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| 139 | \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the real \f$n \times n\f$ |
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| 140 | matrix \f$\mathbf{A}\f$ satisfies |
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| 141 | \f[ |
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| 142 | \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. |
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| 143 | \f] |
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| 144 | The eigenvectors are the columns of the matrix V. |
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| 145 | True is returned if the calculation was successful. Otherwise false. |
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| 146 | |
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| 147 | Uses the LAPACK routine DGEEV. |
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| 148 | */ |
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| 149 | bool eig(const mat &A, cvec &d, cmat &V); |
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| 150 | |
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| 151 | /*! |
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| 152 | \ingroup matrixdecomp |
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| 153 | \brief Caclulates the eigenvalues of a real non-symmetric matrix |
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| 154 | |
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| 155 | The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors |
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| 156 | \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the real \f$n \times n\f$ |
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| 157 | matrix \f$\mathbf{A}\f$ satisfies |
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| 158 | \f[ |
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| 159 | \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. |
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| 160 | \f] |
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| 161 | True is returned if the calculation was successful. Otherwise false. |
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| 162 | |
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| 163 | Uses the LAPACK routine DGEEV. |
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| 164 | */ |
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| 165 | bool eig(const mat &A, cvec &d); |
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| 166 | |
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| 167 | /*! |
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| 168 | \ingroup matrixdecomp |
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| 169 | \brief Caclulates the eigenvalues of a real non-symmetric matrix |
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| 170 | |
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| 171 | The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors |
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| 172 | \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the real \f$n \times n\f$ |
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| 173 | matrix \f$\mathbf{A}\f$ satisfies |
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| 174 | \f[ |
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| 175 | \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. |
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| 176 | \f] |
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| 177 | |
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| 178 | Uses the LAPACK routine DGEEV. |
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| 179 | */ |
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| 180 | cvec eig(const mat &A); |
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| 181 | |
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| 182 | /*! |
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| 183 | \ingroup matrixdecomp |
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| 184 | \brief Calculates the eigenvalues and eigenvectors of a complex non-hermitian matrix |
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| 185 | |
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| 186 | The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors |
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| 187 | \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the complex \f$n \times n\f$ |
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| 188 | matrix \f$\mathbf{A}\f$ satisfies |
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| 189 | \f[ |
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| 190 | \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. |
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| 191 | \f] |
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| 192 | The eigenvectors are the columns of the matrix V. |
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| 193 | True is returned if the calculation was successful. Otherwise false. |
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| 194 | |
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| 195 | Uses the LAPACK routine ZGEEV. |
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| 196 | */ |
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| 197 | bool eig(const cmat &A, cvec &d, cmat &V); |
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| 198 | |
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| 199 | /*! |
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| 200 | \ingroup matrixdecomp |
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| 201 | \brief Calculates the eigenvalues of a complex non-hermitian matrix |
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| 202 | |
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| 203 | The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors |
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| 204 | \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the complex \f$n \times n\f$ |
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| 205 | matrix \f$\mathbf{A}\f$ satisfies |
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| 206 | \f[ |
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| 207 | \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. |
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| 208 | \f] |
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| 209 | True is returned if the calculation was successful. Otherwise false. |
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| 210 | |
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| 211 | Uses the LAPACK routine ZGEEV. |
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| 212 | */ |
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| 213 | bool eig(const cmat &A, cvec &d); |
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| 214 | |
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| 215 | /*! |
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| 216 | \ingroup matrixdecomp |
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| 217 | \brief Calculates the eigenvalues of a complex non-hermitian matrix |
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| 218 | |
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| 219 | The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors |
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| 220 | \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the complex \f$n \times n\f$ |
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| 221 | matrix \f$\mathbf{A}\f$ satisfies |
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| 222 | \f[ |
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| 223 | \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. |
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| 224 | \f] |
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| 225 | |
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| 226 | Uses the LAPACK routine ZGEEV. |
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| 227 | */ |
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| 228 | cvec eig(const cmat &A); |
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| 229 | |
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| 230 | } // namespace itpp |
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| 231 | |
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| 232 | #endif // #ifndef EIGEN_H |
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