126 lines
3.6 KiB
C
126 lines
3.6 KiB
C
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// Copyright (c) 1999
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// Utrecht University (The Netherlands),
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// ETH Zurich (Switzerland),
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// INRIA Sophia-Antipolis (France),
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// Max-Planck-Institute Saarbruecken (Germany),
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// and Tel-Aviv University (Israel). All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public License as
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// published by the Free Software Foundation; either version 3 of the License,
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// or (at your option) any later version.
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//
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// Licensees holding a valid commercial license may use this file in
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// accordance with the commercial license agreement provided with the software.
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//
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// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
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// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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//
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// $URL$
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// $Id$
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// SPDX-License-Identifier: LGPL-3.0+
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//
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//
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// Author(s) : Herve.Bronnimann@sophia.inria.fr
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#ifndef CGAL_LINEAR_ALGEBRACD_H
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#define CGAL_LINEAR_ALGEBRACD_H
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#include <CGAL/Kernel_d/Vector__.h>
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#include <CGAL/Kernel_d/Matrix__.h>
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#include <memory>
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#include <vector>
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#include <CGAL/Kernel_d/debug.h>
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//#define CGAL_LA_SELFTEST
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namespace CGAL {
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template < class _FT, class _AL = CGAL_ALLOCATOR(_FT) >
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class Linear_algebraCd
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{
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public:
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typedef _FT FT;
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typedef _FT RT;
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typedef _AL AL;
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typedef Linear_algebraCd<FT,AL> Self;
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typedef Linear_Algebra::Vector_<FT,AL> Vector;
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typedef Linear_Algebra::Matrix_<FT,AL> Matrix;
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typedef const FT* const_iterator;
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typedef FT* iterator;
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Linear_algebraCd() {}
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protected:
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// Major routines for Linear_algebra_d
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static
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void Gaussian_elimination(const Matrix &M,
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Matrix &L, Matrix &U,
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std::vector<int> &row_permutation,
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std::vector<int> &column_permutation,
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FT &det, int &rank, Vector &c);
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static
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bool Triangular_system_solver(const Matrix &U, const Matrix &L,
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const Vector &b, int rank, Vector &x, FT &det);
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static
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void Triangular_left_inverse(const Matrix &U, Matrix &Uinv);
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public:
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static
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std::pair<int,int> transpose(std::pair<int,int> dim)
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{ std::swap(dim.first,dim.second); return dim; }
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static
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Matrix transpose(const Matrix &M);
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static
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bool inverse(const Matrix &M, Matrix &I, FT &D, Vector &c);
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static
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Matrix inverse(const Matrix &M, RT &D);
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static
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FT determinant(const Matrix &M, Matrix &L, Matrix &U,
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std::vector<int> &q, Vector &c);
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static
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FT determinant(const Matrix &M);
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static
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Sign sign_of_determinant(const Matrix &M);
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static
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bool verify_determinant(const Matrix &M, const RT &D,
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const Matrix &L, const Matrix &U,
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const std::vector<int> &q, const Vector &c);
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static
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bool linear_solver(const Matrix &M, const Vector &b,
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Vector &x, RT &D, Matrix &spanning_vectors, Vector &c);
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static
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bool linear_solver(const Matrix &M, const Vector &b,
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Vector &x, RT &D, Vector &c);
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static
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bool linear_solver(const Matrix &M, const Vector &b,
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Vector &x, RT &D);
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static
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bool is_solvable(const Matrix &M, const Vector &b);
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static
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bool homogeneous_linear_solver(const Matrix &M, Vector &x);
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static
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int homogeneous_linear_solver(const Matrix &M,
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Matrix &spanning_vectors);
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static
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int rank(const Matrix &M);
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static
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int independent_columns(const Matrix& M, std::vector<int>& columns);
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};
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} //namespace CGAL
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#include <CGAL/Kernel_d/Linear_algebraCd_impl.h>
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//#include <CGAL/Kernel_d/Interval_linear_algebra.h>
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#endif // CGAL_LINEAR_ALGEBRACD_H
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