Reference documentation for deal.II version GIT dad323def1 2022-06-25 19:00:02+00:00
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Classes | Public Types | Public Member Functions | Protected Attributes | Private Types | Private Member Functions | Private Attributes | List of all members
EigenInverse< VectorType > Class Template Reference

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

Inheritance diagram for EigenInverse< VectorType >:
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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
 

Private Types

using vector_type = Vector< double >
 

Private Member Functions

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

Private Attributes

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
 

Subscriptor functionality

Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.

using map_value_type = decltype(counter_map)::value_type
 
using map_iterator = decltype(counter_map)::iterator
 
std::atomic< unsigned int > counter
 
std::map< std::string, unsigned int > counter_map
 
std::vector< std::atomic< bool > * > validity_pointers
 
const std::type_info * object_info
 
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)
 
void check_no_subscribers () const noexcept
 
static std::mutex mutex
 
static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
 
static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)
 

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.

Definition at line 126 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 132 of file eigen.h.

◆ vector_type

using SolverBase< Vector< double > >::vector_type = Vector< double >
inherited

An alias for the underlying vector type

Definition at line 346 of file solver.h.

Constructor & Destructor Documentation

◆ EigenInverse()

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

Constructor.

Definition at line 277 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 289 of file eigen.h.

◆ connect()

boost::signals2::connection SolverBase< Vector< double > >::connect ( const std::function< SolverControl::State(const unsigned int iteration, const double check_value, const Vector< double > &current_iterate)> &  slot)
inherited

Connect a function object that will be called periodically within iterative solvers. This function is used to attach monitors to iterative solvers, either to determine when convergence has happened, or simply to observe the progress of an iteration. See the documentation of this class for more information.

Parameters
slotA function object specified here will, with each call, receive the number of the current iteration, the value that is used to check for convergence (typically the residual of the current iterate with respect to the linear system to be solved) and the currently best available guess for the current iterate. Note that some solvers do not update the approximate solution in every iteration but only after convergence or failure has been determined (GMRES is an example); in such cases, the vector passed as the last argument to the signal is simply the best approximate at the time the signal is called, but not the vector that will be returned if the signal's return value indicates that the iteration should be terminated. The function object must return a SolverControl::State value that indicates whether the iteration should continue, has failed, or has succeeded. The results of all connected functions will then be combined to determine what should happen with the iteration.
Returns
A connection object that represents the connection from the signal to the function object. It can be used to disconnect the function object again from the signal. See the documentation of the BOOST Signals2 library for more information on connection management.

Member Data Documentation

◆ additional_data

template<typename VectorType = Vector<double>>
AdditionalData EigenInverse< VectorType >::additional_data
protected

Flags for execution.

Definition at line 186 of file eigen.h.

◆ static_vector_memory

GrowingVectorMemory<Vector< double > > SolverBase< Vector< double > >::static_vector_memory
mutableprotectedinherited

A static vector memory object to be used whenever no such object has been given to the constructor.

Definition at line 414 of file solver.h.

◆ memory

VectorMemory<Vector< double > >& SolverBase< Vector< double > >::memory
protectedinherited

A reference to an object that provides memory for auxiliary vectors.

Definition at line 419 of file solver.h.

◆ iteration_status

boost::signals2::signal< SolverControl::State(const unsigned int iteration, const double check_value, const Vector< double > & current_iterate), StateCombiner> SolverBase< Vector< double > >::iteration_status
protectedinherited

A signal that iterative solvers can execute at the end of every iteration (or in an otherwise periodic fashion) to find out whether we should continue iterating or not. The signal may call one or more slots that each will make this determination by themselves, and the result over all slots (function calls) will be determined by the StateCombiner object.

The arguments passed to the signal are (i) the number of the current iteration; (ii) the value that is used to determine convergence (oftentimes the residual, but in other cases other quantities may be used as long as they converge to zero as the iterate approaches the solution of the linear system); and (iii) a vector that corresponds to the current best guess for the solution at the point where the signal is called. Note that some solvers do not update the approximate solution in every iteration but only after convergence or failure has been determined (GMRES is an example); in such cases, the vector passed as the last argument to the signal is simply the best approximate at the time the signal is called, but not the vector that will be returned if the signal's return value indicates that the iteration should be terminated.

Definition at line 470 of file solver.h.


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