#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())

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< Vector< double > >
using	vector_type = Vector< double >

Private Member Functions inherited from SolverBase< Vector< double > >
	SolverBase (SolverControl &solver_control, VectorMemory< Vector< double > > &vector_memory)

	SolverBase (SolverControl &solver_control)

boost::signals2::connection	connect (const std::function< SolverControl::State(const unsigned int iteration, const double check_value, const Vector< double > &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< Vector< double > >
GrowingVectorMemory< Vector< double > >	static_vector_memory

VectorMemory< Vector< double > > &	memory

boost::signals2::signal< SolverControl::State(const unsigned int iteration, const double check_value, const Vector< double > &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 198 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 210 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 103 of file eigen.h.

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

include/deal.II/lac/eigen.h

Classes

Public Types

Public Member Functions

Protected Attributes

Additional Inherited Members