Reference documentation for deal.II version Git d902c8c1aa 2019-12-15 00:36:45 -0500
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Classes | Public Types | Public Member Functions | Protected Attributes | List of all members
EigenPower< VectorType > Class Template Reference

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

Inheritance diagram for EigenPower< VectorType >:
[legend]

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 ()
 
Subscriptoroperator= (const Subscriptor &)
 
Subscriptoroperator= (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 ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
 
static ::ExceptionBaseExcNoSubscriber (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), StateCombineriteration_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.


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