Reference documentation for deal.II version 9.4.1
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SolverFlexibleCG< VectorType > Class Template Reference

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

Inheritance diagram for SolverFlexibleCG< VectorType >:
[legend]

## Public Types

using size_type = types::global_dof_index

using vector_type = VectorType

## Public Member Functions

template<typename MatrixType , typename PreconditionerType >
void solve (const MatrixType &A, VectorType &x, const VectorType &b, const PreconditionerType &preconditioner)

boost::signals2::connection connect_coefficients_slot (const std::function< void(typename VectorType::value_type, typename VectorType::value_type)> &slot)

boost::signals2::connection connect_condition_number_slot (const std::function< void(double)> &slot, const bool every_iteration=false)

boost::signals2::connection connect_eigenvalues_slot (const std::function< void(const std::vector< double > &)> &slot, const bool every_iteration=false)

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

## Protected Member Functions

virtual void print_vectors (const unsigned int step, const VectorType &x, const VectorType &r, const VectorType &d) const

## Static Protected Member Functions

static void compute_eigs_and_cond (const std::vector< typename VectorType::value_type > &diagonal, const std::vector< typename VectorType::value_type > &offdiagonal, const boost::signals2::signal< void(const std::vector< double > &)> &eigenvalues_signal, const boost::signals2::signal< void(double)> &cond_signal)

## Protected Attributes

boost::signals2::signal< void(typename VectorType::value_type, typename VectorType::value_type)> coefficients_signal

boost::signals2::signal< void(double)> condition_number_signal

boost::signals2::signal< void(double)> all_condition_numbers_signal

boost::signals2::signal< void(const std::vector< double > &)> eigenvalues_signal

boost::signals2::signal< void(const std::vector< double > &)> all_eigenvalues_signal

bool determine_beta_by_flexible_formula

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

## Subscriptor functionality

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

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)

using map_value_type = decltype(counter_map)::value_type

using map_iterator = decltype(counter_map)::iterator

std::atomic< unsigned intcounter

std::map< std::string, unsigned intcounter_map

std::vector< std::atomic< bool > * > validity_pointers

const std::type_info * object_info

static std::mutex mutex

static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)

void check_no_subscribers () const noexcept

## Detailed Description

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

This class implements a flexible variant of the conjugate gradient method, which is based on a different formula to compute $$\beta_k$$ in the process of constructing a new search direction that is A-orthogonal against the previous one. Rather than using the Fletcher–Reeves update formula with $$\beta_k = \frac{\mathbf{r}^T_{k+1} \mathbf{z}_{k+1}}{\mathbf{r}^T_{k} \mathbf{z}_{k}}$$ for computing the new search direction (here $$\mathbf{r}_{k+1}$$ is the residual in step $$k+1$$ and $$\mathbf{z}_{k+1} = P^{-1} \mathbf{r}_{k+1}$$) as in the classical conjugate gradient algorithm, this class selects the Polak-Ribiere formula $$\beta_k = \frac{\mathbf{r}^T_{k+1} \left(\mathbf{z}_{k+1} - \mathbf{z}_{k}\right)}{\mathbf{r}^T_{k} \mathbf{z}_{k}}$$. The additional term $$\mathbf{r}^T_{k+1} \mathbf{z}_{k}$$ is zero for linear symmetric-positive definite preconditioners due to the construction of the search directions, so the behavior of SolverFlexibleCG is equivalent for those kinds of situations and merely increases costs by requiring an additional stored vector and associated vector operations. While there are no theoretical guarantees for convergence as in the classical CG algorithm, the current class has been documented to be much more robust for variable preconditioners (e.g., involving some iterative inverse that is not fully converged) or a preconditioner with some slight non-symmetry (like weighted Schwarz methods), which results from the local optimality of the search direction with at least as good progress as the locally optimal steepest descent method.

Definition at line 354 of file solver_cg.h.

## ◆ size_type

template<typename VectorType = Vector<double>>
 using SolverFlexibleCG< VectorType >::size_type = types::global_dof_index

Declare type for container size.

Definition at line 360 of file solver_cg.h.

## ◆ vector_type

template<class VectorType = Vector<double>>
 using SolverBase< VectorType >::vector_type = VectorType
inherited

An alias for the underlying vector type

Definition at line 346 of file solver.h.

## ◆ SolverFlexibleCG() [1/2]

template<typename VectorType = Vector<double>>
 SolverFlexibleCG< VectorType >::SolverFlexibleCG ( SolverControl & cn, VectorMemory< VectorType > & mem, const AdditionalData & data = AdditionalData() )

Constructor.

## ◆ SolverFlexibleCG() [2/2]

template<typename VectorType = Vector<double>>
 SolverFlexibleCG< VectorType >::SolverFlexibleCG ( SolverControl & cn, const AdditionalData & data = AdditionalData() )

Constructor. Use an object of type GrowingVectorMemory as a default to allocate memory.

## ◆ solve()

template<typename VectorType = Vector<double>>
template<typename MatrixType , typename PreconditionerType >
 void SolverCG< VectorType >::solve ( const MatrixType & A, VectorType & x, const VectorType & b, const PreconditionerType & preconditioner )
inherited

Solve the linear system $$Ax=b$$ for x.

## ◆ connect_coefficients_slot()

template<typename VectorType = Vector<double>>
 boost::signals2::connection SolverCG< VectorType >::connect_coefficients_slot ( const std::function< void(typename VectorType::value_type, typename VectorType::value_type)> & slot )
inherited

Connect a slot to retrieve the CG coefficients. The slot will be called with alpha as the first argument and with beta as the second argument, where alpha and beta follow the notation in Y. Saad: "Iterative methods for Sparse Linear Systems", section 6.7. Called once per iteration

## ◆ connect_condition_number_slot()

template<typename VectorType = Vector<double>>
 boost::signals2::connection SolverCG< VectorType >::connect_condition_number_slot ( const std::function< void(double)> & slot, const bool every_iteration = false )
inherited

Connect a slot to retrieve the estimated condition number. Called on each iteration if every_iteration=true, otherwise called once when iterations are ended (i.e., either because convergence has been achieved, or because divergence has been detected).

## ◆ connect_eigenvalues_slot()

template<typename VectorType = Vector<double>>
 boost::signals2::connection SolverCG< VectorType >::connect_eigenvalues_slot ( const std::function< void(const std::vector< double > &)> & slot, const bool every_iteration = false )
inherited

Connect a slot to retrieve the estimated eigenvalues. Called on each iteration if every_iteration=true, otherwise called once when iterations are ended (i.e., either because convergence has been achieved, or because divergence has been detected).

## ◆ print_vectors()

template<typename VectorType = Vector<double>>
 virtual void SolverCG< VectorType >::print_vectors ( const unsigned int step, const VectorType & x, const VectorType & r, const VectorType & d ) const
protectedvirtualinherited

Interface for derived class. This function gets the current iteration vector, the residual and the update vector in each step. It can be used for graphical output of the convergence history.

## ◆ compute_eigs_and_cond()

template<typename VectorType = Vector<double>>
 static void SolverCG< VectorType >::compute_eigs_and_cond ( const std::vector< typename VectorType::value_type > & diagonal, const std::vector< typename VectorType::value_type > & offdiagonal, const boost::signals2::signal< void(const std::vector< double > &)> & eigenvalues_signal, const boost::signals2::signal< void(double)> & cond_signal )
staticprotectedinherited

Estimates the eigenvalues from diagonal and offdiagonal. Uses these estimate to compute the condition number. Calls the signals eigenvalues_signal and cond_signal with these estimates as arguments.

## ◆ connect()

template<class VectorType = Vector<double>>
 boost::signals2::connection SolverBase< VectorType >::connect ( const std::function< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType ¤t_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
 slot A 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

template<typename VectorType = Vector<double>>
protectedinherited

Definition at line 281 of file solver_cg.h.

## ◆ coefficients_signal

template<typename VectorType = Vector<double>>
 boost::signals2::signal SolverCG< VectorType >::coefficients_signal
protectedinherited

Signal used to retrieve the CG coefficients. Called on each iteration.

Definition at line 288 of file solver_cg.h.

## ◆ condition_number_signal

template<typename VectorType = Vector<double>>
 boost::signals2::signal SolverCG< VectorType >::condition_number_signal
protectedinherited

Signal used to retrieve the estimated condition number. Called once when all iterations are ended.

Definition at line 294 of file solver_cg.h.

## ◆ all_condition_numbers_signal

template<typename VectorType = Vector<double>>
 boost::signals2::signal SolverCG< VectorType >::all_condition_numbers_signal
protectedinherited

Signal used to retrieve the estimated condition numbers. Called on each iteration.

Definition at line 300 of file solver_cg.h.

## ◆ eigenvalues_signal

template<typename VectorType = Vector<double>>
 boost::signals2::signal &)> SolverCG< VectorType >::eigenvalues_signal
protectedinherited

Signal used to retrieve the estimated eigenvalues. Called once when all iterations are ended.

Definition at line 306 of file solver_cg.h.

## ◆ all_eigenvalues_signal

template<typename VectorType = Vector<double>>
 boost::signals2::signal &)> SolverCG< VectorType >::all_eigenvalues_signal
protectedinherited

Signal used to retrieve the estimated eigenvalues. Called on each iteration.

Definition at line 313 of file solver_cg.h.

## ◆ determine_beta_by_flexible_formula

template<typename VectorType = Vector<double>>
 bool SolverCG< VectorType >::determine_beta_by_flexible_formula
protectedinherited

Flag to indicate whether the classical Fletcher–Reeves update formula for the parameter $$\beta_k$$ (standard CG algorithm, minimal storage needs) or the flexible conjugate gradient method with Polak-Ribiere formula for $$\beta_k$$ should be used. This base class implementation of SolverCG will always use the former method, whereas the derived class SolverFlexibleCG will use the latter.

Definition at line 323 of file solver_cg.h.

## ◆ static_vector_memory

template<class VectorType = Vector<double>>
 GrowingVectorMemory SolverBase< VectorType >::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

template<class VectorType = Vector<double>>
 VectorMemory& SolverBase< VectorType >::memory
protectedinherited

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

Definition at line 419 of file solver.h.

## ◆ iteration_status

template<class VectorType = Vector<double>>
 boost::signals2::signal< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType & current_iterate), StateCombiner> SolverBase< VectorType >::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: