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Reference documentation for deal.II version 9.3.3
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Reference documentation for deal.II version 9.3.3
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#include <deal.II/lac/eigen.h>
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 > ¤t_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 > ¤t_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 ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
| static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
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.
| using EigenInverse< VectorType >::size_type = types::global_dof_index |
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inherited |
| EigenInverse< VectorType >::EigenInverse | ( | SolverControl & | cn, |
| VectorMemory< VectorType > & | mem, | ||
| const AdditionalData & | data = AdditionalData() |
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| ) |
| 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.
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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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protected |
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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.
1.9.4