Reference documentation for deal.II version 9.3.0

#include <deal.II/lac/solver_cg.h>
Classes  
struct  AdditionalData 
Public Types  
using  size_type = types::global_dof_index 
using  vector_type = VectorType 
Public Member Functions  
SolverCG (SolverControl &cn, VectorMemory< VectorType > &mem, const AdditionalData &data=AdditionalData())  
SolverCG (SolverControl &cn, const AdditionalData &data=AdditionalData())  
virtual  ~SolverCG () override=default 
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 ¤t_iterate)> &slot) 
template<class Archive >  
void  serialize (Archive &ar, const unsigned int version) 
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 
Static Public Member Functions  
static ::ExceptionBase &  ExcInUse (int arg1, std::string arg2, std::string arg3) 
static ::ExceptionBase &  ExcNoSubscriber (std::string arg1, std::string arg2) 
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  
AdditionalData  additional_data 
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 
GrowingVectorMemory< VectorType >  static_vector_memory 
VectorMemory< VectorType > &  memory 
boost::signals2::signal< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType ¤t_iterate), StateCombiner >  iteration_status 
This class implements the preconditioned Conjugate Gradients (CG) method that can be used to solve linear systems with a symmetric positive definite matrix. This class is used first in step3 and step4, but is used in many other tutorial programs as well. Like all other solver classes, it can work on any kind of vector and matrix as long as they satisfy certain requirements (for the requirements on matrices and vectors in order to work with this class, see the documentation of the Solver base class). The type of the solution vector must be passed as template argument, and defaults to Vector<double>.
The cgmethod performs an orthogonal projection of the original preconditioned linear system to another system of smaller dimension. Furthermore, the projected matrix T
is tridiagonal. Since the projection is orthogonal, the eigenvalues of T
approximate those of the original preconditioned matrix PA
. In fact, after n
steps, where n
is the dimension of the original system, the eigenvalues of both matrices are equal. But, even for small numbers of iteration steps, the condition number of T
is a good estimate for the one of PA
.
After m
steps the matrix T_m can be written in terms of the coefficients alpha
and beta
as the tridiagonal matrix with diagonal elements 1/alpha_0
, 1/alpha_1 + beta_0/alpha_0
, ..., 1/alpha_{m1
+beta_{m2}/alpha_{m2}} and offdiagonal elements sqrt(beta_0)/alpha_0
, ..., sqrt(beta_{m2
)/alpha_{m2}}. The eigenvalues of this matrix can be computed by postprocessing.
The coefficients, eigenvalues and condition number (computed as the ratio of the largest over smallest eigenvalue) can be obtained by connecting a function as a slot to the solver using one of the functions connect_coefficients_slot
, connect_eigenvalues_slot
and connect_condition_number_slot
. These slots will then be called from the solver with the estimates as argument.
The solve() function of this class uses the mechanism described in the Solver base class to determine convergence. This mechanism can also be used to observe the progress of the iteration.
Definition at line 95 of file solver_cg.h.
using SolverCG< VectorType >::size_type = types::global_dof_index 
Declare type for container size.
Definition at line 101 of file solver_cg.h.

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

) 
Constructor.
SolverCG< VectorType >::SolverCG  (  SolverControl &  cn, 
const AdditionalData &  data = AdditionalData() 

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

overridevirtualdefault 
Virtual destructor.
void SolverCG< VectorType >::solve  (  const MatrixType &  A, 
VectorType &  x,  
const VectorType &  b,  
const PreconditionerType &  preconditioner  
) 
Solve the linear system \(Ax=b\) for x.
boost::signals2::connection SolverCG< VectorType >::connect_coefficients_slot  (  const std::function< void(typename VectorType::value_type, typename VectorType::value_type)> &  slot  ) 
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
boost::signals2::connection SolverCG< VectorType >::connect_condition_number_slot  (  const std::function< void(double)> &  slot, 
const bool  every_iteration = false 

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

) 
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).

protectedvirtual 
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.

staticprotected 
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.

inlineinherited 
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.
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. 

inherited 
Subscribes a user of the object by storing the pointer validity
. The subscriber may be identified by text supplied as identifier
.
Definition at line 136 of file subscriptor.cc.

inherited 
Unsubscribes a user from the object.
identifier
and the validity
pointer must be the same as the one supplied to subscribe(). Definition at line 156 of file subscriptor.cc.

inlineinherited 
Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.
Definition at line 301 of file subscriptor.h.

inlineinherited 
List the subscribers to the input stream
.
Definition at line 318 of file subscriptor.h.

inherited 
List the subscribers to deallog
.
Definition at line 204 of file subscriptor.cc.

inlineinherited 
Read or write the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.
This function does not actually serialize any of the member variables of this class. The reason is that what this class stores is only who subscribes to this object, but who does so at the time of storing the contents of this object does not necessarily have anything to do with who subscribes to the object when it is restored. Consequently, we do not want to overwrite the subscribers at the time of restoring, and then there is no reason to write the subscribers out in the first place.
Definition at line 310 of file subscriptor.h.

protected 
Additional parameters.
Definition at line 199 of file solver_cg.h.

protected 
Signal used to retrieve the CG coefficients. Called on each iteration.
Definition at line 206 of file solver_cg.h.

protected 
Signal used to retrieve the estimated condition number. Called once when all iterations are ended.
Definition at line 212 of file solver_cg.h.

protected 
Signal used to retrieve the estimated condition numbers. Called on each iteration.
Definition at line 218 of file solver_cg.h.

protected 
Signal used to retrieve the estimated eigenvalues. Called once when all iterations are ended.
Definition at line 224 of file solver_cg.h.

protected 
Signal used to retrieve the estimated eigenvalues. Called on each iteration.
Definition at line 231 of file solver_cg.h.

mutableprotectedinherited 

protectedinherited 

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.