mirror of https://github.com/CGAL/cgal
127 lines
3.4 KiB
C++
127 lines
3.4 KiB
C++
// ======================================================================
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//
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// Copyright (c) 1999 The CGAL Consortium
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//
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// This software and related documentation is part of an INTERNAL release
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// of the Computational Geometry Algorithms Library (CGAL). It is not
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// intended for general use.
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//
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// ----------------------------------------------------------------------
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//
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// release : 1.1
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// release_date : %-e Dec 1999
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//
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// file : include/CGAL/Linear_algebraCd.h
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// package : Kernel_d
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// revision : $Revision$
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// revision_date : $Date$
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// author(s) : Herve.Bronnimann@sophia.inria.fr
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// coordinator : Michael.Seel@mpi-sb.mpg.de
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//
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// ======================================================================
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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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#undef _DEBUG
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#define _DEBUG 13
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#include <CGAL/Kernel_d/debug.h>
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//#define CGAL_LA_SELFTEST
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CGAL_BEGIN_NAMESPACE
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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 CGALLA::Vector_<FT,AL> Vector;
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typedef CGALLA::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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CGAL_END_NAMESPACE
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#include <CGAL/Kernel_d/Linear_algebraCd.C>
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#endif // CGAL_LINEAR_ALGEBRACD_H
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