EigenPower< VectorType > Class Template Reference

#include <deal.II/lac/eigen.h>

Inheritance diagram for EigenPower< VectorType >:

Classes
struct	AdditionalData

Public Types
using	size_type = types::global_dof_index

Public Member Functions
	EigenPower (SolverControl &cn, VectorMemory< VectorType > &mem, const AdditionalData &data=AdditionalData())
virtual	~EigenPower ()
template<typename MatrixType >
void	solve (double &value, const MatrixType &A, VectorType &x)

Protected Attributes
AdditionalData	additional_data

Additional Inherited Members
Private Types inherited from SolverBase< VectorType >
using	vector_type = VectorType
Private Member Functions inherited from SolverBase< VectorType >
	SolverBase (SolverControl &solver_control, VectorMemory< VectorType > &vector_memory)
	SolverBase (SolverControl &solver_control)
boost::signals2::connection	connect (const std::function< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType &current_iterate)> &slot)
Private Member Functions inherited from Subscriptor
	Subscriptor ()
	Subscriptor (const Subscriptor &)
	Subscriptor (Subscriptor &&) noexcept
virtual	~Subscriptor ()
Subscriptor &	operator= (const Subscriptor &)
Subscriptor &	operator= (Subscriptor &&) noexcept
void	subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
void	unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
unsigned int	n_subscriptions () const
template<typename StreamType >
void	list_subscribers (StreamType &stream) const
void	list_subscribers () const
template<class Archive >
void	serialize (Archive &ar, const unsigned int version)
Static Private Member Functions inherited from Subscriptor
static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)
static ::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)
Private Attributes inherited from SolverBase< VectorType >
GrowingVectorMemory< VectorType >	static_vector_memory
VectorMemory< VectorType > &	memory
boost::signals2::signal< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType &current_iterate), StateCombiner >	iteration_status

Detailed Description

template<typename VectorType = Vector<double>>
class EigenPower< VectorType >

Power method (von Mises) for eigenvalue computations.

This method determines the largest eigenvalue of a matrix by applying increasing powers of this matrix to a vector. If there is an eigenvalue \(l\) with dominant absolute value, the iteration vectors will become aligned to its eigenspace and \(Ax = lx\).

A shift parameter allows to shift the spectrum, so it is possible to compute the smallest eigenvalue, too.

Convergence of this method is known to be slow.

Author

Guido Kanschat, 2000

Definition at line 55 of file eigen.h.

Member Typedef Documentation

size_type

template<typename VectorType = Vector<double>>

using EigenPower< VectorType >::size_type = types::global_dof_index

Declare type of container size.

Definition at line 61 of file eigen.h.

Constructor & Destructor Documentation

EigenPower()

template<class VectorType >

EigenPower< VectorType >::EigenPower	(	SolverControl &	cn,
		VectorMemory< VectorType > &	mem,
		const AdditionalData &	data = AdditionalData()
	)

Constructor.

Definition at line 208 of file eigen.h.

~EigenPower()

template<class VectorType >

EigenPower< VectorType >::~EigenPower ( )

virtual

Virtual destructor.

Definition at line 218 of file eigen.h.

Member Function Documentation

solve()

template<class VectorType >

template<typename MatrixType >

void EigenPower< VectorType >::solve	(	double &	value,
		const MatrixType &	A,
		VectorType &	x
	)

Power method. x is the (not necessarily normalized, but nonzero) start vector for the power method. After the iteration, value is the approximated eigenvalue and x is the corresponding eigenvector, normalized with respect to the l2-norm.

Definition at line 226 of file eigen.h.

Member Data Documentation

additional_data

template<typename VectorType = Vector<double>>

AdditionalData EigenPower< VectorType >::additional_data

protected

Shift parameter.

Definition at line 107 of file eigen.h.

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The documentation for this class was generated from the following file:

• deal.II/lac/eigen.h