CGAL::Eigen_solver_traits< EigenSolverT > Class Template Reference

#include <CGAL/Eigen_solver_traits.h>

Definition

template<class EigenSolverT = Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType>>
class CGAL::Eigen_solver_traits< EigenSolverT >

The class Eigen_solver_traits provides an interface to the sparse solvers of Eigen.

Eigen version 3.1 (or later) must be available on the system.

Is Model Of:

SparseLinearAlgebraWithFactorTraits_d and NormalEquationSparseLinearAlgebraTraits_d

Template Parameters

EigenSolverT

A sparse solver of Eigen. The default solver is the iterative bi-conjugate gradient stabilized solver Eigen::BiCGSTAB for double.

See also

CGAL::Eigen_sparse_matrix<T>

CGAL::Eigen_sparse_symmetric_matrix<T>

CGAL::Eigen_vector<T>

http://eigen.tuxfamily.org/index.php?title=Main_Page

Instantiation Example

The instantiation of this class assumes an Eigen sparse solver is provided. Here are few examples:

typedef CGAL::Eigen_sparse_matrix<double>::EigenType EigenMatrix;

//iterative general solver
typedef CGAL::Eigen_solver_traits< Eigen::BiCGSTAB<EigenMatrix> > Iterative_general_solver;

//iterative symmetric solver
typedef CGAL::Eigen_solver_traits< Eigen::ConjugateGradient<EigenMatrix> > Iterative_symmetric_solver;

//direct symmetric solver
typedef CGAL::Eigen_solver_traits< Eigen::SimplicialCholesky<EigenMatrix> > Direct_symmetric_solver;

Examples:

Solver_interface/sparse_solvers.cpp.

Public Member Functions
	Eigen_solver_traits ()
	Constructor.
bool	linear_solver (const Matrix &A, const Vector &B, Vector &X, NT &D)
	Solve the sparse linear system \( A \times X = B \). More...
bool	factor (const Matrix &A, NT &D)
	Factorize the sparse matrix \( A \). More...
bool	linear_solver (const Vector &B, Vector &X)
	Solve the sparse linear system \( A \times X = B\), with \( A \) being the matrix provided in factor(). More...
bool	linear_solver (const Matrix &B, Vector &X)
	Solve the sparse linear system \( A \times X = B\), with \( A \) being the matrix provided in factor(). More...
bool	normal_equation_factor (const Matrix &A)
	Factorize the sparse matrix \( A^t \times A\), where \( A^t \) is the transpose matrix of \( A \). More...
bool	normal_equation_solver (const Vector &B, Vector &X)
	Solve the sparse linear system \( A^t \times A \times X = A^t \times B \), with \( A \) being the matrix provided in normal_equation_factor(), and \( A^t \) its transpose matrix. More...
bool	normal_equation_solver (const Matrix &A, const Vector &B, Vector &X)
	Equivalent to a call to normal_equation_factor(A) followed by a call to normal_equation_solver(B, X) . More...

Protected Attributes
const Matrix::EigenType *	m_mat
std::shared_ptr< EigenSolverT >	m_solver_sptr

Types
typedef EigenSolverT	Solver
typedef Scalar	NT
typedef CGAL::Eigen_vector< NT >	Vector
typedef Eigen::DenseIndex	Index
typedef unspecified_type	Matrix
	If T is Eigen::ConjugateGradient<M> or Eigen::SimplicialCholesky<M>, Matrix is CGAL::Eigen_sparse_symmetric_matrix<T>, and CGAL::Eigen_sparse_matrix<T> otherwise. More...

Operations
EigenSolverT &	solver ()
	Returns a reference to the internal Eigen solver. More...

Member Typedef Documentation

Matrix

template<class EigenSolverT = Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType>>

typedef unspecified_type CGAL::Eigen_solver_traits< EigenSolverT >::Matrix

If T is Eigen::ConjugateGradient<M> or Eigen::SimplicialCholesky<M>, Matrix is CGAL::Eigen_sparse_symmetric_matrix<T>, and CGAL::Eigen_sparse_matrix<T> otherwise.

Member Function Documentation

factor()

template<class EigenSolverT = Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType>>

bool CGAL::Eigen_solver_traits< EigenSolverT >::factor	(	const Matrix &	A,
		NT &	D
	)

Factorize the sparse matrix \( A \).

This factorization is used in linear_solver() to solve the system for different right-hand side vectors. See linear_solver() for the description of \( D \).

Returns

true if the factorization is successful and false otherwise.

linear_solver() [1/3]

template<class EigenSolverT = Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType>>

bool CGAL::Eigen_solver_traits< EigenSolverT >::linear_solver	(	const Matrix &	A,
		const Vector &	B,
		Vector &	X,
		NT &	D
	)

Solve the sparse linear system \( A \times X = B \).

Return true on success. The solution is then \( (1/D) \times X \).

Precondition

A.row_dimension() == B.dimension().

A.column_dimension() == X.dimension().

linear_solver() [2/3]

template<class EigenSolverT = Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType>>

bool CGAL::Eigen_solver_traits< EigenSolverT >::linear_solver	(	const Vector &	B,
		Vector &	X
	)

Solve the sparse linear system \( A \times X = B\), with \( A \) being the matrix provided in factor().

Returns

true if the solver is successful and false otherwise.

linear_solver() [3/3]

template<class EigenSolverT = Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType>>

bool CGAL::Eigen_solver_traits< EigenSolverT >::linear_solver	(	const Matrix &	B,
		Vector &	X
	)

Solve the sparse linear system \( A \times X = B\), with \( A \) being the matrix provided in factor().

Returns

true if the solver is successful and false otherwise.

normal_equation_factor()

template<class EigenSolverT = Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType>>

bool CGAL::Eigen_solver_traits< EigenSolverT >::normal_equation_factor

(

const Matrix &

A

)

Factorize the sparse matrix \( A^t \times A\), where \( A^t \) is the transpose matrix of \( A \).

This factorization is used in normal_equation_solver() to solve the system for different right-hand side vectors.

Returns

true if the factorization is successful and false otherwise.

normal_equation_solver() [1/2]

template<class EigenSolverT = Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType>>

bool CGAL::Eigen_solver_traits< EigenSolverT >::normal_equation_solver	(	const Vector &	B,
		Vector &	X
	)

Solve the sparse linear system \( A^t \times A \times X = A^t \times B \), with \( A \) being the matrix provided in normal_equation_factor(), and \( A^t \) its transpose matrix.

Returns

true if the solver is successful and false otherwise.

normal_equation_solver() [2/2]

template<class EigenSolverT = Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType>>

bool CGAL::Eigen_solver_traits< EigenSolverT >::normal_equation_solver	(	const Matrix &	A,
		const Vector &	B,
		Vector &	X
	)

Equivalent to a call to normal_equation_factor(A) followed by a call to normal_equation_solver(B, X) .

solver()

template<class EigenSolverT = Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType>>

EigenSolverT& CGAL::Eigen_solver_traits< EigenSolverT >::solver

(

)

Returns a reference to the internal Eigen solver.

This function can be used for example to set specific parameters of the solver.