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### schur.h    116 lines (103 with data), 3.8 kB

  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 /*! * \file * \brief Definitions of Schur decomposition functions * \author Adam Piatyszek * * ------------------------------------------------------------------------- * * 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 SCHUR_H #define SCHUR_H #include namespace itpp { /*! * \ingroup matrixdecomp * \brief Schur decomposition of a real matrix * * This function computes the Schur form of a square real matrix * \f$\mathbf{A} \f$. The Schur decomposition satisfies the * following equation: * \f[ \mathbf{U} \mathbf{T} \mathbf{U}^{T} = \mathbf{A} \f] * where: \f$\mathbf{U} \f$ is a unitary, \f$\mathbf{T} \f$ is upper * quasi-triangular, and \f$\mathbf{U}^{T} \f$ is the transposed * \f$\mathbf{U} \f$ matrix. * * The upper quasi-triangular matrix may have \f$2 \times 2 \f$ blocks on * its diagonal. * * Uses the LAPACK routine DGEES. */ bool schur(const mat &A, mat &U, mat &T); /*! * \ingroup matrixdecomp * \brief Schur decomposition of a real matrix * * This function computes the Schur form of a square real matrix * \f$\mathbf{A} \f$. The Schur decomposition satisfies the * following equation: * \f[ \mathbf{U} \mathbf{T} \mathbf{U}^{T} = \mathbf{A} \f] * where: \f$\mathbf{U} \f$ is a unitary, \f$\mathbf{T} \f$ is upper * quasi-triangular, and \f$\mathbf{U}^{T} \f$ is the transposed * \f$\mathbf{U} \f$ matrix. * * The upper quasi-triangular matrix may have \f$2 \times 2 \f$ blocks on * its diagonal. * * \return Real Schur matrix \f$\mathbf{T} \f$ * * uses the LAPACK routine DGEES. */ mat schur(const mat &A); /*! * \ingroup matrixdecomp * \brief Schur decomposition of a complex matrix * * This function computes the Schur form of a square complex matrix * \f$\mathbf{A} \f$. The Schur decomposition satisfies * the following equation: * \f[ \mathbf{U} \mathbf{T} \mathbf{U}^{H} = \mathbf{A} \f] * where: \f$\mathbf{U} \f$ is a unitary, \f$\mathbf{T} \f$ is upper * triangular, and \f$\mathbf{U}^{H} \f$ is the Hermitian * transposition of the \f$\mathbf{U} \f$ matrix. * * Uses the LAPACK routine ZGEES. */ bool schur(const cmat &A, cmat &U, cmat &T); /*! * \ingroup matrixdecomp * \brief Schur decomposition of a complex matrix * * This function computes the Schur form of a square complex matrix * \f$\mathbf{A} \f$. The Schur decomposition satisfies * the following equation: * \f[ \mathbf{U} \mathbf{T} \mathbf{U}^{H} = \mathbf{A} \f] * where: \f$\mathbf{U} \f$ is a unitary, \f$\mathbf{T} \f$ is upper * triangular, and \f$\mathbf{U}^{H} \f$ is the Hermitian * transposition of the \f$\mathbf{U} \f$ matrix. * * \return Complex Schur matrix \f$\mathbf{T} \f$ * * Uses the LAPACK routine ZGEES. */ cmat schur(const cmat &A); } // namespace itpp #endif // #ifndef SCHUR_H