## [4ede1e]: itpp / base / algebra / lu.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 /*! * \file * \brief Definitions of LU factorisation functions * \author Tony Ottosson * * ------------------------------------------------------------------------- * * Copyright (C) 1995-2010 (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 LU_H #define LU_H #include namespace itpp { /*! \addtogroup matrixdecomp */ //!@{ /*! \brief LU factorisation of real matrix The LU factorization of the real matrix \f$\mathbf{X}\f$ of size \f$n \times n\f$ is given by \f[ \mathbf{X} = \mathbf{P}^T \mathbf{L} \mathbf{U} , \f] where \f$\mathbf{L}\f$ and \f$\mathbf{U}\f$ are lower and upper triangular matrices and \f$\mathbf{P}\f$ is a permutation matrix. The interchange permutation vector \a p is such that \a k and \a p(k) should be changed for all \a k. Given this vector a permutation matrix can be constructed using the function \code bmat permutation_matrix(const ivec &p) \endcode If \a X is an \a n by \a n matrix \a lu(X,L,U,p) computes the LU decomposition. \a L is a lower triangular, \a U an upper triangular matrix. \a p is the interchange permutation vector such that \a k and \a p(k) should be changed for all \a k. Returns true is calculation succeeds. False otherwise. */ bool lu(const mat &X, mat &L, mat &U, ivec &p); /*! \brief LU factorisation of real matrix The LU factorization of the complex matrix \f$\mathbf{X}\f$ of size \f$n \times n\f$ is given by \f[ \mathbf{X} = \mathbf{P}^T \mathbf{L} \mathbf{U} , \f] where \f$\mathbf{L}\f$ and \f$\mathbf{U}\f$ are lower and upper triangular matrices and \f$\mathbf{P}\f$ is a permutation matrix. The interchange permutation vector \a p is such that \a k and \a p(k) should be changed for all \a k. Given this vector a permutation matrix can be constructed using the function \code bmat permutation_matrix(const ivec &p) \endcode If \a X is an \a n by \a n matrix \a lu(X,L,U,p) computes the LU decomposition. \a L is a lower triangular, \a U an upper triangular matrix. \a p is the interchange permutation vector such that elements \a k and row \a p(k) should be interchanged. Returns true is calculation succeeds. False otherwise. */ bool lu(const cmat &X, cmat &L, cmat &U, ivec &p); //! Makes swapping of vector b according to the interchange permutation vector p. void interchange_permutations(vec &b, const ivec &p); //! Make permutation matrix P from the interchange permutation vector p. bmat permutation_matrix(const ivec &p); //!@} } // namespace itpp #endif // #ifndef LU_H