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

Inheritance diagram for EigenInverse< VectorType >:

Classes
struct	AdditionalData

Public Types
using	size_type = types::global_dof_index

Public Member Functions
	EigenInverse (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 EigenInverse< VectorType >

Inverse iteration (Wieland) for eigenvalue computations.

This class implements an adaptive version of the inverse iteration by Wieland.

There are two choices for the stopping criterion: by default, the norm of the residual \(A x - l x\) is computed. Since this might not converge to zero for non-symmetric matrices with non-trivial Jordan blocks, it can be replaced by checking the difference of successive eigenvalues. Use AdditionalData::use_residual for switching this option.

Usually, the initial guess entering this method is updated after each step, replacing it with the new approximation of the eigenvalue. Using a parameter AdditionalData::relaxation between 0 and 1, this update can be damped. With relaxation parameter 0, no update is performed. This damping allows for slower adaption of the shift value to make sure that the method converges to the eigenvalue closest to the initial guess. This can be aided by the parameter AdditionalData::start_adaption, which indicates the first iteration step in which the shift value should be adapted.

Author: Guido Kanschat, 2000, 2003

Definition at line 130 of file eigen.h.

Member Typedef Documentation

◆ size_type

template<typename VectorType = Vector<double>>

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

Declare type of container size.

Definition at line 136 of file eigen.h.

Constructor & Destructor Documentation

◆ EigenInverse()

template<class VectorType >

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

Constructor.

Definition at line 281 of file eigen.h.

Member Function Documentation

◆ solve()

template<class VectorType >

template<typename MatrixType >

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

Inverse method. value is the start guess for the eigenvalue and 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 293 of file eigen.h.

Member Data Documentation

◆ additional_data

template<typename VectorType = Vector<double>>

AdditionalData EigenInverse< VectorType >::additional_data

protected

Flags for execution.

Definition at line 190 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