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// Copyright (c) 1999 // Utrecht University (The Netherlands), // ETH Zurich (Switzerland), // INRIA Sophia-Antipolis (France), // Max-Planck-Institute Saarbruecken (Germany), // and Tel-Aviv University (Israel). All rights reserved. // // This file is part of CGAL (www.cgal.org) // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Kernel_d/include/CGAL/Linear_algebraCd.h $ // $Id: include/CGAL/Linear_algebraCd.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Herve.Bronnimann@sophia.inria.fr #ifndef CGAL_LINEAR_ALGEBRACD_H #define CGAL_LINEAR_ALGEBRACD_H #include #include #include #include #include //#define CGAL_LA_SELFTEST namespace CGAL { template < class _FT, class _AL = CGAL_ALLOCATOR(_FT) > class Linear_algebraCd { public: typedef _FT FT; typedef _FT RT; typedef _AL AL; typedef Linear_algebraCd Self; typedef Linear_Algebra::Vector_ Vector; typedef Linear_Algebra::Matrix_ Matrix; typedef const FT* const_iterator; typedef FT* iterator; Linear_algebraCd() {} protected: // Major routines for Linear_algebra_d static void Gaussian_elimination(const Matrix &M, Matrix &L, Matrix &U, std::vector &row_permutation, std::vector &column_permutation, FT &det, int &rank, Vector &c); static bool Triangular_system_solver(const Matrix &U, const Matrix &L, const Vector &b, int rank, Vector &x, FT &det); static void Triangular_left_inverse(const Matrix &U, Matrix &Uinv); public: static std::pair transpose(std::pair dim) { std::swap(dim.first,dim.second); return dim; } static Matrix transpose(const Matrix &M); static bool inverse(const Matrix &M, Matrix &I, FT &D, Vector &c); static Matrix inverse(const Matrix &M, RT &D); static FT determinant(const Matrix &M, Matrix &L, Matrix &U, std::vector &q, Vector &c); static FT determinant(const Matrix &M); static Sign sign_of_determinant(const Matrix &M); static bool verify_determinant(const Matrix &M, const RT &D, const Matrix &L, const Matrix &U, const std::vector &q, const Vector &c); static bool linear_solver(const Matrix &M, const Vector &b, Vector &x, RT &D, Matrix &spanning_vectors, Vector &c); static bool linear_solver(const Matrix &M, const Vector &b, Vector &x, RT &D, Vector &c); static bool linear_solver(const Matrix &M, const Vector &b, Vector &x, RT &D); static bool is_solvable(const Matrix &M, const Vector &b); static bool homogeneous_linear_solver(const Matrix &M, Vector &x); static int homogeneous_linear_solver(const Matrix &M, Matrix &spanning_vectors); static int rank(const Matrix &M); static int independent_columns(const Matrix& M, std::vector& columns); }; } //namespace CGAL #include //#include #endif // CGAL_LINEAR_ALGEBRACD_H