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Reference documentation for deal.II version 9.6.0
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Reference documentation for deal.II version 9.6.0
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#include <deal.II/lac/solver_gmres.h>
Classes | |
| struct | AdditionalData |
Public Types | |
| using | vector_type = VectorType |
Public Member Functions | |
| SolverGMRES (SolverControl &cn, VectorMemory< VectorType > &mem, const AdditionalData &data=AdditionalData()) | |
| SolverGMRES (SolverControl &cn, const AdditionalData &data=AdditionalData()) | |
| SolverGMRES (const SolverGMRES< VectorType > &)=delete | |
| template<typename MatrixType , typename PreconditionerType > | |
| void | solve (const MatrixType &A, VectorType &x, const VectorType &b, const PreconditionerType &preconditioner) |
| 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< std::complex< double > > &)> &slot, const bool every_iteration=false) |
| boost::signals2::connection | connect_hessenberg_slot (const std::function< void(const FullMatrix< double > &)> &slot, const bool every_iteration=true) |
| boost::signals2::connection | connect_krylov_space_slot (const std::function< void(const internal::SolverGMRESImplementation::TmpVectors< VectorType > &)> &slot) |
| boost::signals2::connection | connect_re_orthogonalization_slot (const std::function< void(int)> &slot) |
| 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 & | ExcTooFewTmpVectors (int arg1) |
| static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
| static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
Protected Member Functions | |
| virtual double | criterion () |
Static Protected Member Functions | |
| static void | compute_eigs_and_cond (const FullMatrix< double > &H_orig, const unsigned int n, const boost::signals2::signal< void(const std::vector< std::complex< double > > &)> &eigenvalues_signal, const boost::signals2::signal< void(const FullMatrix< double > &)> &hessenberg_signal, const boost::signals2::signal< void(double)> &cond_signal) |
Protected Attributes | |
| AdditionalData | additional_data |
| boost::signals2::signal< void(double)> | condition_number_signal |
| boost::signals2::signal< void(double)> | all_condition_numbers_signal |
| boost::signals2::signal< void(const std::vector< std::complex< double > > &)> | eigenvalues_signal |
| boost::signals2::signal< void(const std::vector< std::complex< double > > &)> | all_eigenvalues_signal |
| boost::signals2::signal< void(const FullMatrix< double > &)> | hessenberg_signal |
| boost::signals2::signal< void(const FullMatrix< double > &)> | all_hessenberg_signal |
| boost::signals2::signal< void(const internal::SolverGMRESImplementation::TmpVectors< VectorType > &)> | krylov_space_signal |
| boost::signals2::signal< void(int)> | re_orthogonalize_signal |
| SolverControl & | solver_control |
| internal::SolverGMRESImplementation::ArnoldiProcess | arnoldi_process |
| 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 |
Private Types | |
| using | map_value_type = decltype(counter_map)::value_type |
| using | map_iterator = decltype(counter_map)::iterator |
Private Member Functions | |
| void | check_no_subscribers () const noexcept |
Private Attributes | |
| 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 |
Static Private Attributes | |
| static std::mutex | mutex |
Implementation of the Restarted Preconditioned Direct Generalized Minimal Residual Method. The stopping criterion is the norm of the residual.
The AdditionalData structure allows to control the size of the Arnoldi basis used for orthogonalization (default: 30 vectors). It is related to the number of temporary vectors used, which is the basis size plus two. Additionally, it allows you to choose between right or left preconditioning (default: left preconditioning). Furthermore, it includes a flag indicating whether or not the default residual is used as stopping criterion and an option for the orthogonalization algorithm, see LinearAlgebra::OrthogonalizationStrategy for available options.
AdditionalData allows you to choose between left and right preconditioning. As expected, this switches between solving for the systems P-1A and AP-1, respectively.
A second consequence is the type of residual used to measure convergence. With left preconditioning, this is the preconditioned residual, while with right preconditioning, it is the residual of the unpreconditioned system.
Optionally, this behavior can be overridden by using the flag AdditionalData::use_default_residual. A true value refers to the behavior described in the previous paragraph, while false reverts it. Be aware though that additional residuals have to be computed in this case, impeding the overall performance of the solver.
The maximal basis size is controlled by AdditionalData::max_basis_size. If the number of iteration steps exceeds this number, all basis vectors are discarded and the iteration starts anew from the approximation obtained so far. This algorithm strategy is typically called restarted GMRES method.
Note that the minimizing property of GMRES only pertains to the Krylov space spanned by the Arnoldi basis. Therefore, restarted GMRES is not minimizing anymore. The choice of the basis length is a trade-off between memory consumption and convergence speed, since a longer basis means minimization over a larger space.
For the requirements on matrices and vectors in order to work with this class, see the documentation of the Solver base class.
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.
This class can estimate eigenvalues and condition number during the solution process. This is done by creating the Hessenberg matrix during the inner iterations. The eigenvalues are estimated as the eigenvalues of the Hessenberg matrix and the condition number is estimated as the ratio of the largest and smallest singular value of the Hessenberg matrix. The estimates can be obtained by connecting a function as a slot using connect_condition_number_slot and connect_eigenvalues_slot. These slots will then be called from the solver with the estimates as argument.
Definition at line 352 of file solver_gmres.h.
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inherited |
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privateinherited |
The data type used in counter_map.
Definition at line 229 of file subscriptor.h.
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privateinherited |
The iterator type used in counter_map.
Definition at line 234 of file subscriptor.h.
| SolverGMRES< VectorType >::SolverGMRES | ( | SolverControl & | cn, |
| VectorMemory< VectorType > & | mem, | ||
| const AdditionalData & | data = AdditionalData() ) |
Constructor.
| SolverGMRES< VectorType >::SolverGMRES | ( | SolverControl & | cn, |
| const AdditionalData & | data = AdditionalData() ) |
Constructor. Use an object of type GrowingVectorMemory as a default to allocate memory.
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delete |
The copy constructor is deleted.
| void SolverGMRES< VectorType >::solve | ( | const MatrixType & | A, |
| VectorType & | x, | ||
| const VectorType & | b, | ||
| const PreconditionerType & | preconditioner ) |
Solve the linear system \(Ax=b\) for x.
| boost::signals2::connection SolverGMRES< 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 outer 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 SolverGMRES< VectorType >::connect_eigenvalues_slot | ( | const std::function< void(const std::vector< std::complex< double > > &)> & | slot, |
| const bool | every_iteration = false ) |
Connect a slot to retrieve the estimated eigenvalues. Called on each outer 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 SolverGMRES< VectorType >::connect_hessenberg_slot | ( | const std::function< void(const FullMatrix< double > &)> & | slot, |
| const bool | every_iteration = true ) |
Connect a slot to retrieve the Hessenberg matrix obtained by the projection of the initial matrix on the Krylov basis. Called on each outer 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 SolverGMRES< VectorType >::connect_krylov_space_slot | ( | const std::function< void(const internal::SolverGMRESImplementation::TmpVectors< VectorType > &)> & | slot | ) |
Connect a slot to retrieve the basis vectors of the Krylov space generated by the Arnoldi algorithm. Called at once when iterations are completed (i.e., either because convergence has been achieved, or because divergence has been detected).
| boost::signals2::connection SolverGMRES< VectorType >::connect_re_orthogonalization_slot | ( | const std::function< void(int)> & | slot | ) |
Connect a slot to retrieve a notification when the vectors are re-orthogonalized.
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protectedvirtual |
Implementation of the computation of the norm of the residual.
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staticprotected |
Estimates the eigenvalues from the Hessenberg matrix, H_orig, generated during the inner iterations for n vectors in total. Uses these estimates to compute the condition number. Calls the signals eigenvalues_signal and cond_signal with these estimates as arguments.
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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.
| 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. |
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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 135 of file subscriptor.cc.
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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 155 of file subscriptor.cc.
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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 300 of file subscriptor.h.
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inlineinherited |
List the subscribers to the input stream.
Definition at line 317 of file subscriptor.h.
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inherited |
List the subscribers to deallog.
Definition at line 203 of file subscriptor.cc.
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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 309 of file subscriptor.h.
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privatenoexceptinherited |
Check that there are no objects subscribing to this object. If this check passes then it is safe to destroy the current object. It this check fails then this function will either abort or print an error message to deallog (by using the AssertNothrow mechanism), but will not throw an exception.
Definition at line 52 of file subscriptor.cc.
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protected |
Includes the maximum number of tmp vectors.
Definition at line 532 of file solver_gmres.h.
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protected |
Signal used to retrieve the estimated condition number. Called once when all iterations are ended.
Definition at line 538 of file solver_gmres.h.
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protected |
Signal used to retrieve the estimated condition numbers. Called on each outer iteration.
Definition at line 544 of file solver_gmres.h.
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protected |
Signal used to retrieve the estimated eigenvalues. Called once when all iterations are ended.
Definition at line 551 of file solver_gmres.h.
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protected |
Signal used to retrieve the estimated eigenvalues. Called on each outer iteration.
Definition at line 558 of file solver_gmres.h.
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protected |
Signal used to retrieve the Hessenberg matrix. Called once when all iterations are ended.
Definition at line 564 of file solver_gmres.h.
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protected |
Signal used to retrieve the Hessenberg matrix. Called on each outer iteration.
Definition at line 571 of file solver_gmres.h.
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protected |
Signal used to retrieve the Krylov space basis vectors. Called once when all iterations are ended.
Definition at line 579 of file solver_gmres.h.
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protected |
Signal used to retrieve a notification when the vectors are re-orthogonalized.
Definition at line 585 of file solver_gmres.h.
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protected |
A reference to the underlying SolverControl object. In the regular case, this is not needed, as the signal from the base class is used, but the batched variant cannot use those mechanisms due to the high costs.
Definition at line 592 of file solver_gmres.h.
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protected |
Class that performs the actual orthogonalization process and solves the projected linear system.
Definition at line 620 of file solver_gmres.h.
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mutableprotectedinherited |
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protectedinherited |
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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.
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mutableprivateinherited |
Store the number of objects which subscribed to this object. Initially, this number is zero, and upon destruction it shall be zero again (i.e. all objects which subscribed should have unsubscribed again).
The creator (and owner) of an object is counted in the map below if HE manages to supply identification.
We use the mutable keyword in order to allow subscription to constant objects also.
This counter may be read from and written to concurrently in multithreaded code: hence we use the std::atomic class template.
Definition at line 218 of file subscriptor.h.
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mutableprivateinherited |
In this map, we count subscriptions for each different identification string supplied to subscribe().
Definition at line 224 of file subscriptor.h.
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mutableprivateinherited |
In this vector, we store pointers to the validity bool in the SmartPointer objects that subscribe to this class.
Definition at line 240 of file subscriptor.h.
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mutableprivateinherited |
Pointer to the typeinfo object of this object, from which we can later deduce the class name. Since this information on the derived class is neither available in the destructor, nor in the constructor, we obtain it in between and store it here.
Definition at line 248 of file subscriptor.h.
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staticprivateinherited |
A mutex used to ensure data consistency when accessing the mutable members of this class. This lock is used in the subscribe() and unsubscribe() functions, as well as in list_subscribers().
Definition at line 271 of file subscriptor.h.
1.11.0