## [5cfaaf]: itpp / base / algebra / cholesky.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 /*! * \file * \brief Definitions of Cholesky factorisation 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 CHOLESKY_H #define CHOLESKY_H #include namespace itpp { /*! \addtogroup matrixdecomp */ //!@{ /*! \brief Cholesky factorisation of real symmetric and positive definite matrix The Cholesky factorisation of a real symmetric positive-definite matrix \f$\mathbf{X}\f$ of size \f$n \times n\f$ is given by \f[ \mathbf{X} = \mathbf{F}^T \mathbf{F} \f] where \f$\mathbf{F}\f$ is an upper trangular \f$n \times n\f$ matrix. Returns true if calcuation succeeded. False otherwise. */ bool chol(const mat &X, mat &F); /*! \brief Cholesky factorisation of real symmetric and positive definite matrix The Cholesky factorisation of a real symmetric positive-definite matrix \f$\mathbf{X}\f$ of size \f$n \times n\f$ is given by \f[ \mathbf{X} = \mathbf{F}^T \mathbf{F} \f] where \f$\mathbf{F}\f$ is an upper trangular \f$n \times n\f$ matrix. */ mat chol(const mat &X); /*! \brief Cholesky factorisation of complex hermitian and positive-definite matrix The Cholesky factorisation of a hermitian positive-definite matrix \f$\mathbf{X}\f$ of size \f$n \times n\f$ is given by \f[ \mathbf{X} = \mathbf{F}^H \mathbf{F} \f] where \f$\mathbf{F}\f$ is an upper trangular \f$n \times n\f$ matrix. Returns true if calcuation succeeded. False otherwise. If \c X is positive definite, true is returned and \c F=chol(X) produces an upper triangular \c F. If also \c X is symmetric then \c F'*F = X. If \c X is not positive definite, false is returned. */ bool chol(const cmat &X, cmat &F); /*! \brief Cholesky factorisation of complex hermitian and positive-definite matrix The Cholesky factorisation of a hermitian positive-definite matrix \f$\mathbf{X}\f$ of size \f$n \times n\f$ is given by \f[ \mathbf{X} = \mathbf{F}^H \mathbf{F} \f] where \f$\mathbf{F}\f$ is an upper trangular \f$n \times n\f$ matrix. */ cmat chol(const cmat &X); //!@} } // namespace itpp #endif // #ifndef CHOLESKY_H