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// Copyright (c) 2014
// INRIA Saclay-Ile de France (France)
//
// 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; either version 3 of the License,
// or (at your option) any later version.
//
// 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.
//
// $URL$
// $Id$
//
// Author(s) : Marc Glisse
#ifndef CGAL_LA_EIGEN_H
#define CGAL_LA_EIGEN_H
#include <CGAL/config.h>
#ifndef CGAL_EIGEN3_ENABLED
#error Requires Eigen
#endif
#include <boost/type_traits/is_arithmetic.hpp>
#include <boost/utility/enable_if.hpp>
#include <CGAL/Dimension.h>
#include <Eigen/Dense>
#include <CGAL/NewKernel_d/LA_eigen/constructors.h>
#include <CGAL/iterator_from_indices.h>
namespace CGAL {
//FIXME: where could we use Matrix_base instead of Matrix?
// Dim_ real dimension
// Max_dim_ upper bound on the dimension
template<class NT_,class Dim_,class Max_dim_=Dim_> struct LA_eigen {
typedef NT_ NT;
typedef Dim_ Dimension;
typedef Max_dim_ Max_dimension;
enum { dimension = Eigen_dimension<Dimension>::value };
enum { max_dimension = Eigen_dimension<Max_dimension>::value };
template< class D2, class D3=D2 >
struct Rebind_dimension {
typedef LA_eigen< NT, D2, D3 > Other;
};
template<class,class=void> struct Property : boost::false_type {};
template<class D> struct Property<Has_vector_plus_minus_tag,D> : boost::true_type {};
template<class D> struct Property<Has_vector_scalar_ops_tag,D> : boost::true_type {};
template<class D> struct Property<Has_dot_product_tag,D> : boost::true_type {};
typedef Eigen::Matrix<NT,Eigen_dimension<Dim_>::value,1,Eigen::ColMajor|Eigen::AutoAlign,Eigen_dimension<Max_dim_>::value,1> Vector;
typedef Eigen::Matrix<NT,Eigen::Dynamic,1> Dynamic_vector;
typedef Construct_eigen<Vector> Construct_vector;
#if (EIGEN_WORLD_VERSION>=3)
typedef NT const* Vector_const_iterator;
#else
typedef Iterator_from_indices<const type,const NT
#ifndef CGAL_CXX11
,NT
#endif
> Vector_const_iterator;
#endif
template<class Vec_>static Vector_const_iterator vector_begin(Vec_ const&a){
#if (EIGEN_WORLD_VERSION>=3)
return &a[0];
#else
return Vector_const_iterator(a,0);
#endif
}
template<class Vec_>static Vector_const_iterator vector_end(Vec_ const&a){
#if (EIGEN_WORLD_VERSION>=3)
// FIXME: Isn't that dangerous if a is an expression and not a concrete vector?
return &a[0]+a.size();
#else
return Vector_const_iterator(a,a.size());
#endif
}
typedef Eigen::Matrix<NT,dimension,dimension,Eigen::ColMajor|Eigen::AutoAlign,max_dimension,max_dimension> Square_matrix;
typedef Eigen::Matrix<NT,dimension,Eigen::Dynamic,Eigen::ColMajor|Eigen::AutoAlign,max_dimension,Eigen::Dynamic> Dynamic_matrix;
//TODO: don't pass on the values of Max_* for an expensive NT
// typedef ... Constructor
// typedef ... Accessor
#if 0
private:
template <class T> class Canonicalize_vector {
typedef typename Dimension_eigen<T::SizeAtCompileTime>::type S1;
typedef typename Dimension_eigen<T::MaxSizeAtCompileTime>::type S2;
public:
typedef typename Vector<S1,S2>::type type;
};
public:
#endif
template<class Vec_>static int size_of_vector(Vec_ const&v){
return (int)v.size();
}
template<class Vec_>static NT dot_product(Vec_ const&a,Vec_ const&b){
return a.dot(b);
}
template<class Vec_> static int rows(Vec_ const&v) {
return (int)v.rows();
}
template<class Vec_> static int columns(Vec_ const&v) {
return (int)v.cols();
}
template<class Mat_> static NT determinant(Mat_ const&m,bool=false){
return m.determinant();
}
template<class Mat_> static typename
Same_uncertainty_nt<CGAL::Sign, NT>::type
sign_of_determinant(Mat_ const&m,bool=false)
{
return CGAL::sign(m.determinant());
}
template<class Mat_> static int rank(Mat_ const&m){
// return m.rank();
// This one uses sqrt so cannot be used with Gmpq
// TODO: use different algo for different NT?
// Eigen::ColPivHouseholderQR<Mat_> decomp(m);
Eigen::FullPivLU<Mat_> decomp(m);
// decomp.setThreshold(0);
return static_cast<int>(decomp.rank());
}
// m*a==b
template<class DV, class DM, class V>
static void solve(DV&a, DM const&m, V const& b){
//a = m.colPivHouseholderQr().solve(b);
a = m.fullPivLu().solve(b);
}
template<class DV, class DM, class V>
static bool solve_and_check(DV&a, DM const&m, V const& b){
//a = m.colPivHouseholderQr().solve(b);
a = m.fullPivLu().solve(b);
return b.isApprox(m*a);
}
static Dynamic_matrix basis(Dynamic_matrix const&m){
return m.fullPivLu().image(m);
}
template<class Vec1,class Vec2> static Vector homogeneous_add(Vec1 const&a,Vec2 const&b){
//TODO: use compile-time size when available
int d=a.size();
Vector v(d);
v << b[d-1]*a.topRows(d-1)+a[d-1]*b.topRows(d-1), a[d-1]*b[d-1];
return v;
}
template<class Vec1,class Vec2> static Vector homogeneous_sub(Vec1 const&a,Vec2 const&b){
int d=a.size();
Vector v(d);
v << b[d-1]*a.topRows(d-1)-a[d-1]*b.topRows(d-1), a[d-1]*b[d-1];
return v;
}
template<class Vec1,class Vec2> static std::pair<NT,NT> homogeneous_dot_product(Vec1 const&a,Vec2 const&b){
int d=a.size();
return make_pair(a.topRows(d-1).dot(b.topRows(d-1)), a[d-1]*b[d-1]);
}
};
}
#endif
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