## [5cfaaf]: itpp / base / algebra / eigen.h  Maximize  Restore  History

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  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 /*! * \file * \brief Definitions of eigenvalue decomposition functions * \author Tony Ottosson * * ------------------------------------------------------------------------- * * Copyright (C) 1995-2008 (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 . * * ------------------------------------------------------------------------- */ #ifndef EIGEN_H #define EIGEN_H #include namespace itpp { /*! \ingroup matrixdecomp \brief Calculates the eigenvalues and eigenvectors of a symmetric real matrix The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the real and symmetric \f$n \times n\f$ matrix \f$\mathbf{A}\f$ satisfies \f[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \f] The eigenvectors are the columns of the matrix V. True is returned if the calculation was successful. Otherwise false. Uses the LAPACK routine DSYEV. */ bool eig_sym(const mat &A, vec &d, mat &V); /*! \ingroup matrixdecomp \brief Calculates the eigenvalues of a symmetric real matrix The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the real and symmetric \f$n \times n\f$ matrix \f$\mathbf{A}\f$ satisfies \f[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \f] True is returned if the calculation was successful. Otherwise false. Uses the LAPACK routine DSYEV. */ bool eig_sym(const mat &A, vec &d); /*! \ingroup matrixdecomp \brief Calculates the eigenvalues of a symmetric real matrix The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the real and symmetric \f$n \times n\f$ matrix \f$\mathbf{A}\f$ satisfies \f[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \f] Uses the LAPACK routine DSYEV. */ vec eig_sym(const mat &A); /*! \ingroup matrixdecomp \brief Calculates the eigenvalues and eigenvectors of a hermitian complex matrix The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the complex and hermitian \f$n \times n\f$ matrix \f$\mathbf{A}\f$ satisfies \f[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \f] The eigenvectors are the columns of the matrix V. True is returned if the calculation was successful. Otherwise false. Uses the LAPACK routine ZHEEV. */ bool eig_sym(const cmat &A, vec &d, cmat &V); /*! \ingroup matrixdecomp \brief Calculates the eigenvalues of a hermitian complex matrix The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the complex and hermitian \f$n \times n\f$ matrix \f$\mathbf{A}\f$ satisfies \f[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \f] True is returned if the calculation was successful. Otherwise false. Uses the LAPACK routine ZHEEV. */ bool eig_sym(const cmat &A, vec &d); /*! \ingroup matrixdecomp \brief Calculates the eigenvalues of a hermitian complex matrix The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the complex and hermitian \f$n \times n\f$ matrix \f$\mathbf{A}\f$ satisfies \f[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \f] Uses the LAPACK routine ZHEEV. */ vec eig_sym(const cmat &A); /*! \ingroup matrixdecomp \brief Caclulates the eigenvalues and eigenvectors of a real non-symmetric matrix The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the real \f$n \times n\f$ matrix \f$\mathbf{A}\f$ satisfies \f[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \f] The eigenvectors are the columns of the matrix V. True is returned if the calculation was successful. Otherwise false. Uses the LAPACK routine DGEEV. */ bool eig(const mat &A, cvec &d, cmat &V); /*! \ingroup matrixdecomp \brief Caclulates the eigenvalues of a real non-symmetric matrix The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the real \f$n \times n\f$ matrix \f$\mathbf{A}\f$ satisfies \f[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \f] True is returned if the calculation was successful. Otherwise false. Uses the LAPACK routine DGEEV. */ bool eig(const mat &A, cvec &d); /*! \ingroup matrixdecomp \brief Caclulates the eigenvalues of a real non-symmetric matrix The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the real \f$n \times n\f$ matrix \f$\mathbf{A}\f$ satisfies \f[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \f] Uses the LAPACK routine DGEEV. */ cvec eig(const mat &A); /*! \ingroup matrixdecomp \brief Calculates the eigenvalues and eigenvectors of a complex non-hermitian matrix The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the complex \f$n \times n\f$ matrix \f$\mathbf{A}\f$ satisfies \f[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \f] The eigenvectors are the columns of the matrix V. True is returned if the calculation was successful. Otherwise false. Uses the LAPACK routine ZGEEV. */ bool eig(const cmat &A, cvec &d, cmat &V); /*! \ingroup matrixdecomp \brief Calculates the eigenvalues of a complex non-hermitian matrix The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the complex \f$n \times n\f$ matrix \f$\mathbf{A}\f$ satisfies \f[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \f] True is returned if the calculation was successful. Otherwise false. Uses the LAPACK routine ZGEEV. */ bool eig(const cmat &A, cvec &d); /*! \ingroup matrixdecomp \brief Calculates the eigenvalues of a complex non-hermitian matrix The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the complex \f$n \times n\f$ matrix \f$\mathbf{A}\f$ satisfies \f[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \f] Uses the LAPACK routine ZGEEV. */ cvec eig(const cmat &A); } // namespace itpp #endif // #ifndef EIGEN_H