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// Copyright (c) 1999 Utrecht University (The Netherlands),
// ETH Zurich (Switzerland), Freie Universitaet Berlin (Germany),
// INRIA Sophia-Antipolis (France), Martin-Luther-University Halle-Wittenberg
// (Germany), Max-Planck-Institute Saarbruecken (Germany), RISC Linz (Austria),
// and Tel-Aviv University (Israel). All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; version 2.1 of the License.
// See the file LICENSE.LGPL distributed with CGAL.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL: svn+ssh://scm.gforge.inria.fr/svn/cgal/branches/CGAL-3.5-branch/Kernel_d/include/CGAL/Linear_algebraCd.h $
// $Id: Linear_algebraCd.h 41674 2008-01-18 10:20:44Z spion $
//
//
// Author(s) : Herve.Bronnimann@sophia.inria.fr
#ifndef CGAL_LINEAR_ALGEBRACD_H
#define CGAL_LINEAR_ALGEBRACD_H
#include <CGAL/Kernel_d/Vector__.h>
#include <CGAL/Kernel_d/Matrix__.h>
#include <memory>
#include <vector>
#include <CGAL/Kernel_d/debug.h>
//#define CGAL_LA_SELFTEST
CGAL_BEGIN_NAMESPACE
template < class _FT, class _AL = CGAL_ALLOCATOR(_FT) >
class Linear_algebraCd
{
public:
typedef _FT FT;
typedef _FT RT;
typedef _AL AL;
typedef Linear_algebraCd<FT,AL> Self;
typedef Linear_Algebra::Vector_<FT,AL> Vector;
typedef Linear_Algebra::Matrix_<FT,AL> 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<int> &row_permutation,
std::vector<int> &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<int,int> transpose(std::pair<int,int> 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<int> &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<int> &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<int>& columns);
};
CGAL_END_NAMESPACE
#include <CGAL/Kernel_d/Linear_algebraCd_impl.h>
#endif // CGAL_LINEAR_ALGEBRACD_H
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