Quadratic penalty iteration. More...

#include <qpenalty.hpp>

Inheritance diagram for FEAT::Solver::QPenalty< Functional_ >:

Public Types
typedef IterativeSolver< VectorType >	BaseClass
	Our base class. More...

typedef VectorType::DataType	DataType
	Underlying floating point type. More...

typedef Functional_	FunctionalType
	The functional type. More...

typedef Functional_::VectorTypeR	VectorType
	The input vector type. More...

Public Member Functions
	QPenalty (const QPenalty &)=delete
	Explicitly delete the copy constructor.

	QPenalty (const String &section_name, const PropertyMap *section, FunctionalType &functional, std::shared_ptr< IterativeSolver< VectorType > > inner_solver)
	Constructor using a PropertyMap. More...

	QPenalty (FunctionalType &functional, std::shared_ptr< IterativeSolver< VectorType > > inner_solver, DataType initial_penalty_param=DataType(1))
	Constructor. More...

virtual	~QPenalty ()
	Virtual destructor. More...

virtual Status	apply (Vector_ &vec_cor, const Vector_ &vec_def)=0
	Solver application method. More...

virtual Status	apply (VectorType &vec_cor, const VectorType &vec_def) override
	Solver application method. More...

DataType	calc_convergence_rate () const
	Computes the overall convergence rate: (defect_final / defect_initial) ^ (1 / number of iterations) More...

DataType	calc_defect_reduction () const
	Computes the overall defect reduction factor: (defect_final / defect_inital) More...

virtual Status	correct (VectorType &vec_sol, const VectorType &vec_rhs) override
	Solver correction method. More...

virtual void	done ()
	Finalization method. More...

virtual void	done_numeric ()
	Numeric finalization method. More...

virtual void	done_symbolic () override
	Symbolic initialization method. More...

virtual void	force_defect_norm_calc (bool force)
	Forces the calculation of defect norms in every iteration. More...

DataType	get_def_final () const
	Returns the final defect. More...

DataType	get_def_initial () const
	Returns the initial defect. More...

DataType	get_div_abs () const
	Returns the absolute divergence. More...

DataType	get_div_rel () const
	Returns the relative divergence. More...

Index	get_max_iter () const
	Returns the maximum number of iterations. More...

Index	get_min_iter () const
	Returns the minimal number of iterations. More...

Index	get_min_stag_iter () const
	Returns the minimum stagnation iteration count. More...

Index	get_num_iter () const
	Returns number of performed iterations. More...

String	get_plot_name () const
	Returns the plot name of the solver. More...

DataType	get_stag_rate () const
	Returns the stagnation rate. More...

Status	get_status () const
	Returns the status. More...

virtual String	get_summary () const
	Returns a summary string. More...

DataType	get_tol_abs () const
	Returns the absolute tolerance. More...

DataType	get_tol_abs_low () const
	Returns the lower absolute tolerance. More...

DataType	get_tol_rel () const
	Returns the relative tolerance. More...

virtual void	init ()
	Initialization method. More...

virtual void	init_numeric ()
	Numeric initialization method. More...

virtual void	init_symbolic () override
	Symbolic initialization method. More...

bool	is_converged () const
	checks for convergence More...

bool	is_converged (const DataType def_cur) const
	checks for convergence More...

bool	is_diverged () const
	checks for divergence More...

bool	is_diverged (const DataType def_cur) const
	checks for divergence More...

virtual String	name () const override
	Returns a descriptive string. More...

virtual void	plot_summary () const
	Plot a summary of the last solver run. More...

void	set_div_abs (DataType div_abs)
	Sets the absolute divergence for the solver. More...

void	set_div_rel (DataType div_rel)
	Sets the relative divergence for the solver. More...

void	set_initial_penalty_param (DataType initial_penalty_param)
	Sets the initial penalty parameter. More...

void	set_max_iter (Index max_iter)
	Sets the maximum iteration count for the solver. More...

void	set_min_iter (Index min_iter)
	Sets the minimum iteration count for the solver. More...

void	set_min_stag_iter (Index min_iter)
	Sets the minimum stagnate iteration count for the solver. More...

void	set_plot_interval (const Index plot_interval)
	Sets the interval between two plot outputs, if any. More...

void	set_plot_mode (const PlotMode plot_mode)
	Sets the plot mode of the solver. More...

void	set_plot_name (const String &plot_name)
	Sets the plot name of the solver. More...

void	set_stag_rate (DataType rate)
	Sets the stagnation rate for the solver. More...

void	set_tol_abs (DataType tol_abs)
	Sets the absolute tolerance for the solver. More...

void	set_tol_abs_low (DataType tol_abs_low)
	Sets the lower absolute tolerance for the solver. More...

void	set_tol_penalty (DataType tol_penalty)
	Sets the initial penalty parameter. More...

void	set_tol_rel (DataType tol_rel)
	Sets the relative tolerance for the solver. More...

Protected Member Functions
virtual Status	_analyze_defect (Index num_iter, DataType def_cur, DataType def_prev, bool check_stag)
	Internal function: analyze the current defect. More...

virtual Status	_apply_intern (VectorType &vec_sol, const VectorType &vec_rhs)
	Internal function, applies the solver. More...

virtual DataType	_calc_def_norm (const VectorType &vec_def, const VectorType &vec_sol)
	Computes the defect norm. More...

bool	_plot_iter (Status st=Status::progress) const
	Plot the current iteration? More...

virtual void	_plot_iter_line (Index num_iter, DataType def_cur, DataType def_prev)
	Plots an iteration line. More...

bool	_plot_summary () const
	Plot summary? More...

void	_print_line (const String &line) const
	Prints a line. More...

bool	_progress () const
	Progress iteration? More...

void	_set_comm (const Dist::Comm *comm)
	Sets the communicator for the solver directly. More...

void	_set_comm_by_matrix (const Matrix_ &matrix)
	Sets the communicator for the solver from a matrix. More...

void	_set_comm_by_vector (const Functional_::VectorTypeR &vector)
	Sets the communicator for the solver from a vector. More...

Status	_set_initial_defect (const DataType def_init_)
	Internal function: sets the initial defect. More...

virtual Status	_set_initial_defect (const VectorType &vec_def, const VectorType &vec_sol)
	Makes the BaseClass' routine available, which cannot be used but shuts up the overloaded virtual warning. More...

virtual Status	_set_new_defect (const VectorType &vec_def, const VectorType &vec_sol)
	Internal function: sets the new (next) defect vector. More...

virtual Status	_update_defect (const DataType def_cur_norm)
	Internal function: sets the new (next) defect norm. More...

Protected Attributes
const Dist::Comm *	_comm
	Communicator of the solver. More...

DataType	_def_cur
	current defect More...

DataType	_def_init
	initial defect More...

DataType	_def_prev
	previous iteration defect More...

DataType	_div_abs
	absolute divergence parameter More...

DataType	_div_rel
	relative divergence parameter More...

bool	_force_def_norm_calc
	whether skipping of defect computation is allowed or not More...

Index	_iter_digits
	iteration count digits for plotting More...

Index	_max_iter
	maximum number of iterations More...

Index	_min_iter
	minimum number of iterations More...

Index	_min_stag_iter
	minimum number of stagnation iterations More...

Index	_num_iter
	number of performed iterations More...

Index	_num_stag_iter
	number of consecutive stagnated iterations More...

Index	_plot_interval
	plot output interval More...

PlotMode	_plot_mode
	whether to plot something More...

String	_plot_name
	name of the solver in plots More...

DataType	_stag_rate
	stagnation rate More...

Status	_status
	current status of the solver More...

DataType	_tol_abs
	absolute tolerance parameter More...

DataType	_tol_abs_low
	absolute low tolerance parameter More...

DataType	_tol_rel
	relative tolerance parameter More...

Private Attributes
FunctionalType &	_functional
	The functional that takes the penalty parameters and is assembled in the inner solver. More...

DataType	_initial_penalty_param
	We start with this initial penalty parameter. More...

std::shared_ptr< IterativeSolver< VectorType > >	_inner_solver
	The inner solver for the penalized, unconstrained optimization problem. More...

DataType	_tol_penalty
	Maximum value the penalty parameter is allowed to take. More...

Detailed Description

template<typename Functional_>
class FEAT::Solver::QPenalty< Functional_ >

Quadratic penalty iteration.

Template Parameters

Functional_ The functional (or functional) for the constrained optimization problem.

This class implements an outer solver for a quadratic penalty iteration. Assume we have an optimization problem of the form

\[ x^* = \mathrm{argmin}_{x \in D} f(x) ~ \mathrm{subject~to~} \forall i \in E: c_i(x) = 0 \]

\( c_i \) are equality constraints turning the minimization of \( f \) into a constrained optimization problem. To solve this constrained problem, one can solve a series of unconstrained problems with the quadratic penalty iteration by defining the quadratic penalty function

\[ Q(x,\mu) := f(x) + \frac{\mu}{2} \sum_{i \in E} c_i^2(x) \]

and solving it for a series \( (\mu_k)_k \in \mathbb{N}, \mu_k \stackrel{k \to \infty}{\longrightarrow} \infty \). Because the penalty terms are smooth, tools from unconstrained optimization can be applied (see [NW06] Chapter 17.1). The greatest advantage of this is that this needs no constraint qualifications and is still applicable if \( \mathrm{dim}( \mathrm{ker} (\nabla c_{i_1}, \dots, \nabla c_{i_M}) ) > 0 \), which is required by all more sophisticated methods like augmented Lagragian etc.

All of this means that the Functional_ \( Q \) must be assembled anew in every iteration and the inner solver needs to take care of this.

One critical part is the choice of \(\mu_k\). It needs to start small (i.e. \(\mu_1 = 1\)) because the initial state might violate the constraints quite strongly. The rate of increase has to be fast enough that the number of penalty iterations remains small (i.e. \( \leq 10 \)), but the systematic ill-conditioning of the penalty function means that we cannot be too quick about this. If the increase is too quick, the previous iterate will be too far away of a minimizer of the new problem and the inner solver will fail to converge. So take care.

Author: Jordi Paul

Definition at line 47 of file qpenalty.hpp.

Member Typedef Documentation

◆ BaseClass

template<typename Functional_ >

typedef IterativeSolver<VectorType> FEAT::Solver::QPenalty< Functional_ >::BaseClass

Our base class.

Definition at line 57 of file qpenalty.hpp.

◆ DataType

template<typename Functional_ >

typedef VectorType::DataType FEAT::Solver::QPenalty< Functional_ >::DataType

Underlying floating point type.

Definition at line 55 of file qpenalty.hpp.

◆ FunctionalType

template<typename Functional_ >

typedef Functional_ FEAT::Solver::QPenalty< Functional_ >::FunctionalType

The functional type.

Definition at line 51 of file qpenalty.hpp.

◆ VectorType

template<typename Functional_ >

typedef Functional_::VectorTypeR FEAT::Solver::QPenalty< Functional_ >::VectorType

The input vector type.

Definition at line 53 of file qpenalty.hpp.

Constructor & Destructor Documentation

◆ QPenalty() [1/2]

template<typename Functional_ >

FEAT::Solver::QPenalty< Functional_ >::QPenalty	(	FunctionalType &	functional,
		std::shared_ptr< IterativeSolver< VectorType > >	inner_solver,
		DataType	initial_penalty_param = `DataType(1)`
	)

inlineexplicit

Constructor.

Parameters

[in]	functional	The functional for the inner constrained optimization problem.
[in]	inner_solver	The solver for the inner penalized unconstrained optimization problem.
[in]	initial_penalty_param	The starting penalty parameter, defaults to 1.

Definition at line 82 of file qpenalty.hpp.

References FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_set_comm_by_matrix().

◆ QPenalty() [2/2]

template<typename Functional_ >

FEAT::Solver::QPenalty< Functional_ >::QPenalty	(	const String &	section_name,
		const PropertyMap *	section,
		FunctionalType &	functional,
		std::shared_ptr< IterativeSolver< VectorType > >	inner_solver
	)

inlineexplicit

Constructor using a PropertyMap.

Template Parameters

Functional_ The type of the quadratic penalty function \( Q \).

Parameters

[in]	section_name	The name of the config section, which it does not know by itself.
[in]	section	A pointer to the PropertyMap section configuring this solver.
[in]	functional	The quadratic penalty function \( Q \).
[in]	inner_solver	The inner solver for solving the penalized unconstrained optimization problem.

Definition at line 112 of file qpenalty.hpp.

References FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_set_comm_by_matrix(), FEAT::PropertyMap::query(), FEAT::Solver::QPenalty< Functional_ >::set_initial_penalty_param(), and FEAT::Solver::QPenalty< Functional_ >::set_tol_penalty().

◆ ~QPenalty()

template<typename Functional_ >

virtual FEAT::Solver::QPenalty< Functional_ >::~QPenalty ( )

inlinevirtual

Virtual destructor.

Definition at line 142 of file qpenalty.hpp.

References FEAT::Solver::QPenalty< Functional_ >::_inner_solver.

Member Function Documentation

◆ _analyze_defect()

virtual Status FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_analyze_defect	(	Index	num_iter,
		DataType	def_cur,
		DataType	def_prev,
		bool	check_stag
	)

inlineprotectedvirtualinherited

Internal function: analyze the current defect.

Note: This function is called by _set_new_defect() and _update_defect().

Parameters

[in]	num_iter	Current number of iterations; usually = this->_num_iter.
[in]	def_cur	Current defect norm; usually = this->_def_cur.
[in]	def_prev	Previous defect norm; usually = this->_def_prev.
[in]	check_stag	Specifies whether to check (and update) the stagnation criterion. This is typically set to `false` if one wants to check anything else than the 'true' next defect norm.

Returns: The updated status code.

Definition at line 866 of file iterative.hpp.

◆ _apply_intern()

template<typename Functional_ >

virtual Status FEAT::Solver::QPenalty< Functional_ >::_apply_intern	(	VectorType &	vec_sol,
		const VectorType &	vec_rhs
	)

inlineprotectedvirtual

Internal function, applies the solver.

Parameters

[in,out]	vec_sol	The initial guess, gets overwritten by the solution
[in]	vec_rhs	The right-hand side.

Returns: A solver status code.

Definition at line 226 of file qpenalty.hpp.

Referenced by FEAT::Solver::QPenalty< Functional_ >::apply(), and FEAT::Solver::QPenalty< Functional_ >::correct().

◆ _calc_def_norm()

virtual DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_calc_def_norm	(	const VectorType &	vec_def,
		const VectorType &	vec_sol
	)

inlineprotectedvirtualinherited

Computes the defect norm.

Parameters

[in]	vec_def	The current defect vector.
[in]	vec_sol	The current solution vector approximation.

Definition at line 706 of file iterative.hpp.

◆ _plot_iter()

bool FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_plot_iter ( Status st = Status::progress ) const

inlineprotectedinherited

Plot the current iteration?

Parameters

[in] st The status of the current iteration.

Returns: true if the plot mode is set to iter or all and the plot interval matches or the solver does not continue to the next iteration

Definition at line 720 of file iterative.hpp.

◆ _plot_iter_line()

virtual void FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_plot_iter_line	(	Index	num_iter,
		DataType	def_cur,
		DataType	def_prev
	)

inlineprotectedvirtualinherited

Plots an iteration line.

Parameters

[in]	num_iter	Current number of iterations; usually = this->_num_iter.
[in]	def_cur	Current defect norm; usually = this->_def_cur.
[in]	def_prev	Previous defect norm; usually = this->_def_prev.

Definition at line 773 of file iterative.hpp.

◆ _plot_summary()

bool FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_plot_summary ( ) const

inlineprotectedinherited

Plot summary?

Returns: true if the plot mode is set to summary or all.

Definition at line 731 of file iterative.hpp.

◆ _print_line()

void FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_print_line ( const String & line ) const

inlineprotectedinherited

Prints a line.

Parameters

[in] line The line to be printed.

Definition at line 752 of file iterative.hpp.

◆ _progress()

bool FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_progress ( ) const

inlineprotectedinherited

Progress iteration?

Returns: true if the solver should process, otherwise false.

Definition at line 741 of file iterative.hpp.

◆ _set_comm()

void FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_set_comm ( const Dist::Comm * comm )

inlineprotectedinherited

Sets the communicator for the solver directly.

Parameters

[in] comm A pointer to the communicator that is to be used by the solver.

Definition at line 667 of file iterative.hpp.

◆ _set_comm_by_matrix()

void FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_set_comm_by_matrix ( const Matrix_ & matrix )

inlineprotectedinherited

Sets the communicator for the solver from a matrix.

Parameters

[in] matrix A reference to a matrix. If 'Matrix_' is a 'Global::Matrix', then the communicator of the matrix gate is taken.

Definition at line 680 of file iterative.hpp.

◆ _set_comm_by_vector()

void FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_set_comm_by_vector ( const Functional_::VectorTypeR & vector )

inlineprotectedinherited

Sets the communicator for the solver from a vector.

Parameters

[in] vector A reference to a vector. If 'Vector_' is a 'Global::Vector', then the communicator of the vector gate is taken.

Definition at line 692 of file iterative.hpp.

◆ _set_initial_defect() [1/2]

template<typename Functional_ >

Status FEAT::Solver::QPenalty< Functional_ >::_set_initial_defect ( const DataType def_init_ )

inlineprotected

Internal function: sets the initial defect.

Parameters

[in] def_init_ The initial constraint violation.

Returns: A Status code.

Definition at line 331 of file qpenalty.hpp.

Referenced by FEAT::Solver::QPenalty< Functional_ >::_apply_intern().

◆ _set_initial_defect() [2/2]

template<typename Functional_ >

virtual Status FEAT::Solver::IterativeSolver< Vector_ >::_set_initial_defect	(	const VectorType &	vec_def,
		const VectorType &	vec_sol
	)

inlineprotectedvirtual

Makes the BaseClass' routine available, which cannot be used but shuts up the overloaded virtual warning.

Reimplemented from FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >.

Definition at line 802 of file iterative.hpp.

◆ _set_new_defect()

virtual Status FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_set_new_defect	(	const VectorType &	vec_def,
		const VectorType &	vec_sol
	)

inlineprotectedvirtualinherited

Internal function: sets the new (next) defect vector.

This function computes the defect vector's norm, increments the iteration count, plots an output line to std::cout and checks whether any of the stopping criterions is fulfilled.

Parameters

[in]	vec_def	The new defect vector.
[in]	vec_sol	The current solution vector approximation.

Returns: The updated Status code.

Definition at line 924 of file iterative.hpp.

◆ _update_defect()

virtual Status FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_update_defect ( const DataType def_cur_norm )

inlineprotectedvirtualinherited

Internal function: sets the new (next) defect norm.

This function takes a pre-calculated defect vector norm, increments the iteration count, plots an output line to std::cout and checks whether any of the stopping criterions is fulfilled.

Parameters

[in] def_cur_norm The new defect norm.

Returns: The updated Status code.

Note: This function is preferred over _set_new_defect when using asynchronous mpi operations.

Definition at line 970 of file iterative.hpp.

◆ apply() [1/2]

template<typename Vector_ >

virtual Status FEAT::Solver::SolverBase< Vector_ >::apply	(	Vector_ &	vec_cor,
		const Vector_ &	vec_def
	)

pure virtualinherited

Solver application method.

This method applies the solver represented by this object onto a given defect vector and returns the corresponding correction vector.

Note: Solvers which derive from the IterativeSolver base class also provide a correct() method which corrects an initial solution instead of starting with the null vector.

Parameters

[out]	vec_cor	The vector that shall receive the solution of the linear system. It is assumed to be allocated, but its numerical contents may be undefined upon calling this method.
[in]	vec_def	The vector that represents the right-hand-side of the linear system to be solved.

Attention: vec_cor and vec_def must not refer to the same vector object!

Returns: A Status code that represents the status of the solution step.

Implemented in FEAT::Solver::SchwarzPrecond< Global::Vector< LocalVector_, Mirror_ >, Global::Filter< LocalFilter_, Mirror_ > >, FEAT::Solver::CuSolverLU, FEAT::Solver::CuSolverQR, FEAT::Solver::ScalePrecond< Vector_, Filter_ >, FEAT::Solver::DiagonalPrecond< Vector_, Filter_ >, FEAT::Solver::MultiGrid< SystemMatrix_, SystemFilter_, TransferOperator_ >, FEAT::Solver::NLOptPrecond< VectorType_, FilterType_ >, FEAT::Solver::AmaVanka< Matrix_, Filter_ >, FEAT::Solver::ConvertPrecond< VectorOuter_, VectorInner_ >, FEAT::Solver::ConvertPrecond< Global::Vector< LocalVectorOuter_, MirrorOuter_ >, Global::Vector< LocalVectorInner_, MirrorInner_ > >, and FEAT::Solver::BFBT< MatrixA_, MatrixB_, MatrixD_, FilterV_, FilterP_ >.

Referenced by FEAT::Solver::solve().

◆ apply() [2/2]

template<typename Functional_ >

virtual Status FEAT::Solver::QPenalty< Functional_ >::apply	(	VectorType &	vec_cor,
		const VectorType &	vec_def
	)

inlineoverridevirtual

Solver application method.

This method applies the solver represented by this object onto a given defect vector and returns the corresponding correction vector.

Note: Solvers which derive from the IterativeSolver base class also provide a correct() method which corrects an initial solution instead of starting with the null vector.

Parameters

[out]	vec_cor	The vector that shall receive the solution of the linear system. It is assumed to be allocated, but its numerical contents may be undefined upon calling this method.
[in]	vec_def	The vector that represents the right-hand-side of the linear system to be solved.

Attention: vec_cor and vec_def must not refer to the same vector object!

Returns: A Status code that represents the status of the solution step.

Definition at line 188 of file qpenalty.hpp.

References FEAT::Solver::QPenalty< Functional_ >::_apply_intern(), FEAT::Solver::QPenalty< Functional_ >::_functional, FEAT::Solver::QPenalty< Functional_ >::_initial_penalty_param, FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_status, and FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::plot_summary().

◆ calc_convergence_rate()

DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::calc_convergence_rate ( ) const

inlineinherited

Computes the overall convergence rate: (defect_final / defect_initial) ^ (1 / number of iterations)

Definition at line 582 of file iterative.hpp.

◆ calc_defect_reduction()

DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::calc_defect_reduction ( ) const

inlineinherited

Computes the overall defect reduction factor: (defect_final / defect_inital)

Definition at line 597 of file iterative.hpp.

◆ correct()

template<typename Functional_ >

virtual Status FEAT::Solver::QPenalty< Functional_ >::correct	(	VectorType &	vec_sol,
		const VectorType &	vec_rhs
	)

inlineoverridevirtual

Solver correction method.

This method applies the solver represented by this object onto a given right-hand-side vector and updates the corresponding solution vector.

In contrast to the apply() method of the SolverBase base class, this method uses the vector vec_sol as the initial solution vector for the iterative solution process instead of ignoring its contents upon entry and starting with the null vector.

Parameters

[in,out]	vec_sol	The vector that contains the initial solution upon entry and receives the solution of the linear system upon exit.
[in]	vec_rhs	The vector that represents the right-hand-side of the linear system to be solved.

Attention: vec_sol and vec_rhs must not refer to the same vector object!

Returns: A Status code that represents the status of the solution step.

Implements FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >.

Definition at line 202 of file qpenalty.hpp.

References FEAT::Solver::QPenalty< Functional_ >::_apply_intern(), FEAT::Solver::QPenalty< Functional_ >::_functional, FEAT::Solver::QPenalty< Functional_ >::_initial_penalty_param, FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_status, and FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::plot_summary().

◆ done()

template<typename Vector_ >

virtual void FEAT::Solver::SolverBase< Vector_ >::done ( )

inlinevirtualinherited

Finalization method.

This function performs both the symbolic and numeric finalization, i.e. it simply performs

this->done_numeric();
this->done_symbolic();

Definition at line 283 of file base.hpp.

References FEAT::Solver::SolverBase< Vector_ >::done_numeric(), and FEAT::Solver::SolverBase< Vector_ >::done_symbolic().

◆ done_numeric()

template<typename Vector_ >

virtual void FEAT::Solver::SolverBase< Vector_ >::done_numeric ( )

inlinevirtualinherited

Numeric finalization method.

This method is called to release any data allocated in the numeric initialization step.

Reimplemented in FEAT::Solver::BFBT< MatrixA_, MatrixB_, MatrixD_, FilterV_, FilterP_ >, FEAT::Solver::BFBT< Global::Matrix< MatrixA_, MirrorV_, MirrorV_ >, Global::Matrix< MatrixB_, MirrorV_, MirrorP_ >, Global::Matrix< MatrixD_, MirrorP_, MirrorV_ >, Global::Filter< FilterV_, MirrorV_ >, Global::Filter< FilterP_, MirrorP_ > >, FEAT::Solver::ConvertPrecond< VectorOuter_, VectorInner_ >, FEAT::Solver::ConvertPrecond< Global::Vector< LocalVectorOuter_, MirrorOuter_ >, Global::Vector< LocalVectorInner_, MirrorInner_ > >, FEAT::Solver::CUDSS, FEAT::Solver::DirectStokesSolver< LAFEM::SaddlePointMatrix< MatrixA_, MatrixB_, MatrixD_ >, LAFEM::TupleFilter< FilterV_, FilterP_ > >, FEAT::Solver::DirectStokesSolver< Global::Matrix< LocalMatrix_, Mirror_, Mirror_ >, Global::Filter< LocalFilter_, Mirror_ > >, FEAT::Solver::ParaSailsPrecond< Matrix_, Filter_ >, FEAT::Solver::EuclidPrecond< Matrix_, Filter_ >, FEAT::Solver::BoomerAMG< Matrix_, Filter_ >, FEAT::Solver::PreconditionedIterativeSolver< Vector_ >, FEAT::Solver::PreconditionedIterativeSolver< Matrix_::VectorTypeR >, FEAT::Solver::PreconditionedIterativeSolver< Functional_::VectorTypeR >, FEAT::Solver::MKLDSS, FEAT::Solver::MultiGrid< SystemMatrix_, SystemFilter_, TransferOperator_ >, FEAT::Solver::PCGNR< Matrix_, Filter_ >, FEAT::Solver::SchwarzPrecond< Global::Vector< LocalVector_, Mirror_ >, Global::Filter< LocalFilter_, Mirror_ > >, FEAT::Solver::Umfpack, FEAT::Solver::UmfpackMean, FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >, FEAT::Solver::GenericUmfpack< Matrix_ >, FEAT::Solver::UzawaPrecond< MatrixA_, MatrixB_, MatrixD_, FilterV_, FilterP_ >, and FEAT::Solver::UzawaPrecond< Global::Matrix< MatrixA_, MirrorV_, MirrorV_ >, Global::Matrix< MatrixB_, MirrorV_, MirrorP_ >, Global::Matrix< MatrixD_, MirrorP_, MirrorV_ >, Global::Filter< FilterV_, MirrorV_ >, Global::Filter< FilterP_, MirrorP_ > >.

Definition at line 246 of file base.hpp.

◆ done_symbolic()

template<typename Functional_ >

virtual void FEAT::Solver::QPenalty< Functional_ >::done_symbolic ( )

inlineoverridevirtual

Symbolic initialization method.

This method is called to perform symbolic initialization of the solver.

Reimplemented from FEAT::Solver::SolverBase< Vector_ >.

Definition at line 161 of file qpenalty.hpp.

References FEAT::Solver::QPenalty< Functional_ >::_inner_solver, and FEAT::Solver::SolverBase< Vector_ >::done_symbolic().

◆ force_defect_norm_calc()

virtual void FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::force_defect_norm_calc ( bool force )

inlinevirtualinherited

Forces the calculation of defect norms in every iteration.

Note: Please note that allowing the skipping of defect norm calculations is merely a hint and a derived class may override this function therefore always forcing the calculation of defect norms. One possible reason is that the derived solver class may require defect norms as part of its solver algorithm and therefore skipping the computation of the defect norms may break the solver; two examples are the BiCGStab and GMRES solvers.

Parameters

[in] force Specifies whether defect norm computation is to be enforced in every iteration

Definition at line 490 of file iterative.hpp.

◆ get_def_final()

DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::get_def_final ( ) const

inlineinherited

Returns the final defect.

Definition at line 570 of file iterative.hpp.

◆ get_def_initial()

DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::get_def_initial ( ) const

inlineinherited

Returns the initial defect.

Definition at line 564 of file iterative.hpp.

◆ get_div_abs()

DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::get_div_abs ( ) const

inlineinherited

Returns the absolute divergence.

Definition at line 419 of file iterative.hpp.

◆ get_div_rel()

DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::get_div_rel ( ) const

inlineinherited

Returns the relative divergence.

Definition at line 413 of file iterative.hpp.

◆ get_max_iter()

Index FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::get_max_iter ( ) const

inlineinherited

Returns the maximum number of iterations.

Definition at line 474 of file iterative.hpp.

◆ get_min_iter()

Index FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::get_min_iter ( ) const

inlineinherited

Returns the minimal number of iterations.

Definition at line 468 of file iterative.hpp.

◆ get_min_stag_iter()

Index FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::get_min_stag_iter ( ) const

inlineinherited

Returns the minimum stagnation iteration count.

Definition at line 443 of file iterative.hpp.

◆ get_num_iter()

Index FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::get_num_iter ( ) const

inlineinherited

Returns number of performed iterations.

Definition at line 462 of file iterative.hpp.

◆ get_plot_name()

String FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::get_plot_name ( ) const

inlineinherited

Returns the plot name of the solver.

Definition at line 523 of file iterative.hpp.

◆ get_stag_rate()

DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::get_stag_rate ( ) const

inlineinherited

Returns the stagnation rate.

Definition at line 431 of file iterative.hpp.

◆ get_status()

Status FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::get_status ( ) const

inlineinherited

Returns the status.

Definition at line 576 of file iterative.hpp.

◆ get_summary()

virtual String FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::get_summary ( ) const

inlinevirtualinherited

Returns a summary string.

Reimplemented in FEAT::Solver::Linesearch< Functional_, Filter_ >.

Definition at line 610 of file iterative.hpp.

◆ get_tol_abs()

DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::get_tol_abs ( ) const

inlineinherited

Returns the absolute tolerance.

Definition at line 389 of file iterative.hpp.

◆ get_tol_abs_low()

DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::get_tol_abs_low ( ) const

inlineinherited

Returns the lower absolute tolerance.

Definition at line 395 of file iterative.hpp.

◆ get_tol_rel()

DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::get_tol_rel ( ) const

inlineinherited

Returns the relative tolerance.

Definition at line 383 of file iterative.hpp.

◆ init()

template<typename Vector_ >

virtual void FEAT::Solver::SolverBase< Vector_ >::init ( )

inlinevirtualinherited

Initialization method.

This function performs both the symbolic and numeric initialization, i.e. it simply performs

this->init_symbolic();
this->init_numeric();

Definition at line 268 of file base.hpp.

References FEAT::Solver::SolverBase< Vector_ >::init_numeric(), and FEAT::Solver::SolverBase< Vector_ >::init_symbolic().

◆ init_numeric()

template<typename Vector_ >

virtual void FEAT::Solver::SolverBase< Vector_ >::init_numeric ( )

inlinevirtualinherited

Numeric initialization method.

This method is called to perform numeric initialization of the solver.
Before this function can be called, the symbolic initialization must be performed.

Definition at line 237 of file base.hpp.

◆ init_symbolic()

template<typename Functional_ >

virtual void FEAT::Solver::QPenalty< Functional_ >::init_symbolic ( )

inlineoverridevirtual

Symbolic initialization method.

This method is called to perform symbolic initialization of the solver.

Reimplemented from FEAT::Solver::SolverBase< Vector_ >.

Definition at line 154 of file qpenalty.hpp.

References FEAT::Solver::QPenalty< Functional_ >::_inner_solver, and FEAT::Solver::SolverBase< Vector_ >::init_symbolic().

◆ is_converged() [1/2]

bool FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::is_converged ( ) const

inlineinherited

checks for convergence

Returns: true, if converged, else false

Definition at line 533 of file iterative.hpp.

◆ is_converged() [2/2]

bool FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::is_converged ( const DataType def_cur ) const

inlineinherited

checks for convergence

Parameters

[in] def_cur The defect norm that is to be analyzed

Returns: true, if converged, else false

Definition at line 546 of file iterative.hpp.

◆ is_diverged() [1/2]

bool FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::is_diverged ( ) const

inlineinherited

checks for divergence

Definition at line 552 of file iterative.hpp.

◆ is_diverged() [2/2]

bool FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::is_diverged ( const DataType def_cur ) const

inlineinherited

checks for divergence

Definition at line 558 of file iterative.hpp.

◆ name()

template<typename Functional_ >

virtual String FEAT::Solver::QPenalty< Functional_ >::name ( ) const

inlineoverridevirtual

Returns a descriptive string.

Returns: A string describing the solver.

Implements FEAT::Solver::SolverBase< Vector_ >.

Definition at line 148 of file qpenalty.hpp.

Referenced by FEAT::Solver::QPenalty< Functional_ >::_apply_intern(), and FEAT::Solver::QPenalty< Functional_ >::_set_initial_defect().

◆ plot_summary()

virtual void FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::plot_summary ( ) const

inlinevirtualinherited

Plot a summary of the last solver run.

Definition at line 627 of file iterative.hpp.

◆ set_div_abs()

void FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::set_div_abs ( DataType div_abs )

inlineinherited

Sets the absolute divergence for the solver.

Definition at line 407 of file iterative.hpp.

◆ set_div_rel()

void FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::set_div_rel ( DataType div_rel )

inlineinherited

Sets the relative divergence for the solver.

Definition at line 401 of file iterative.hpp.

◆ set_initial_penalty_param()

template<typename Functional_ >

void FEAT::Solver::QPenalty< Functional_ >::set_initial_penalty_param ( DataType initial_penalty_param )

inline

Sets the initial penalty parameter.

Definition at line 170 of file qpenalty.hpp.

References FEAT::Solver::QPenalty< Functional_ >::_initial_penalty_param, and XASSERT.

Referenced by FEAT::Solver::QPenalty< Functional_ >::QPenalty().

◆ set_max_iter()

void FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::set_max_iter ( Index max_iter )

inlineinherited

Sets the maximum iteration count for the solver.

Definition at line 455 of file iterative.hpp.

◆ set_min_iter()

void FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::set_min_iter ( Index min_iter )

inlineinherited

Sets the minimum iteration count for the solver.

Definition at line 449 of file iterative.hpp.

◆ set_min_stag_iter()

void FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::set_min_stag_iter ( Index min_iter )

inlineinherited

Sets the minimum stagnate iteration count for the solver.

Definition at line 437 of file iterative.hpp.

◆ set_plot_interval()

void FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::set_plot_interval ( const Index plot_interval )

inlineinherited

Sets the interval between two plot outputs, if any.

Parameters

[in] plot_interval The desired interval of iteration plots

Definition at line 511 of file iterative.hpp.

◆ set_plot_mode()

void FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::set_plot_mode ( const PlotMode plot_mode )

inlineinherited

Sets the plot mode of the solver.

Parameters

[in] plot_mode The desired plot mode

Definition at line 501 of file iterative.hpp.

◆ set_plot_name()

void FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::set_plot_name ( const String & plot_name )

inlineinherited

Sets the plot name of the solver.

Definition at line 517 of file iterative.hpp.

◆ set_stag_rate()

void FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::set_stag_rate ( DataType rate )

inlineinherited

Sets the stagnation rate for the solver.

Definition at line 425 of file iterative.hpp.

◆ set_tol_abs()

void FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::set_tol_abs ( DataType tol_abs )

inlineinherited

Sets the absolute tolerance for the solver.

Definition at line 371 of file iterative.hpp.

◆ set_tol_abs_low()

void FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::set_tol_abs_low ( DataType tol_abs_low )

inlineinherited

Sets the lower absolute tolerance for the solver.

Definition at line 377 of file iterative.hpp.

◆ set_tol_penalty()

template<typename Functional_ >

void FEAT::Solver::QPenalty< Functional_ >::set_tol_penalty ( DataType tol_penalty )

inline

Sets the initial penalty parameter.

Definition at line 180 of file qpenalty.hpp.

References FEAT::Solver::QPenalty< Functional_ >::_tol_penalty, and XASSERT.

Referenced by FEAT::Solver::QPenalty< Functional_ >::QPenalty().

◆ set_tol_rel()

void FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::set_tol_rel ( DataType tol_rel )

inlineinherited

Sets the relative tolerance for the solver.

Definition at line 365 of file iterative.hpp.

Member Data Documentation

◆ _comm

const Dist::Comm* FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_comm

protectedinherited

Communicator of the solver.

Definition at line 209 of file iterative.hpp.

◆ _def_cur

DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_def_cur

protectedinherited

current defect

Definition at line 239 of file iterative.hpp.

◆ _def_init

DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_def_init

protectedinherited

initial defect

Definition at line 237 of file iterative.hpp.

◆ _def_prev

DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_def_prev

protectedinherited

previous iteration defect

Definition at line 241 of file iterative.hpp.

◆ _div_abs

DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_div_abs

protectedinherited

absolute divergence parameter

Definition at line 223 of file iterative.hpp.

◆ _div_rel

DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_div_rel

protectedinherited

relative divergence parameter

Definition at line 221 of file iterative.hpp.

◆ _force_def_norm_calc

bool FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_force_def_norm_calc

protectedinherited

whether skipping of defect computation is allowed or not

Definition at line 249 of file iterative.hpp.

◆ _functional

template<typename Functional_ >

FunctionalType& FEAT::Solver::QPenalty< Functional_ >::_functional

private

The functional that takes the penalty parameters and is assembled in the inner solver.

Definition at line 61 of file qpenalty.hpp.

Referenced by FEAT::Solver::QPenalty< Functional_ >::_apply_intern(), FEAT::Solver::QPenalty< Functional_ >::apply(), and FEAT::Solver::QPenalty< Functional_ >::correct().

◆ _initial_penalty_param

template<typename Functional_ >

DataType FEAT::Solver::QPenalty< Functional_ >::_initial_penalty_param

private

We start with this initial penalty parameter.

Definition at line 65 of file qpenalty.hpp.

Referenced by FEAT::Solver::QPenalty< Functional_ >::apply(), FEAT::Solver::QPenalty< Functional_ >::correct(), and FEAT::Solver::QPenalty< Functional_ >::set_initial_penalty_param().

◆ _inner_solver

template<typename Functional_ >

std::shared_ptr<IterativeSolver<VectorType> > FEAT::Solver::QPenalty< Functional_ >::_inner_solver

private

The inner solver for the penalized, unconstrained optimization problem.

Definition at line 63 of file qpenalty.hpp.

Referenced by FEAT::Solver::QPenalty< Functional_ >::~QPenalty(), FEAT::Solver::QPenalty< Functional_ >::_apply_intern(), FEAT::Solver::QPenalty< Functional_ >::done_symbolic(), and FEAT::Solver::QPenalty< Functional_ >::init_symbolic().

◆ _iter_digits

Index FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_iter_digits

protectedinherited

iteration count digits for plotting

Definition at line 243 of file iterative.hpp.

◆ _max_iter

Index FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_max_iter

protectedinherited

maximum number of iterations

Definition at line 229 of file iterative.hpp.

◆ _min_iter

Index FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_min_iter

protectedinherited

minimum number of iterations

Definition at line 227 of file iterative.hpp.

◆ _min_stag_iter

Index FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_min_stag_iter

protectedinherited

minimum number of stagnation iterations

Definition at line 233 of file iterative.hpp.

◆ _num_iter

Index FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_num_iter

protectedinherited

number of performed iterations

Definition at line 231 of file iterative.hpp.

◆ _num_stag_iter

Index FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_num_stag_iter

protectedinherited

number of consecutive stagnated iterations

Definition at line 235 of file iterative.hpp.

◆ _plot_interval

Index FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_plot_interval

protectedinherited

plot output interval

Definition at line 247 of file iterative.hpp.

◆ _plot_mode

PlotMode FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_plot_mode

protectedinherited

whether to plot something

Definition at line 245 of file iterative.hpp.

◆ _plot_name

String FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_plot_name

protectedinherited

name of the solver in plots

Definition at line 211 of file iterative.hpp.

◆ _stag_rate

DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_stag_rate

protectedinherited

stagnation rate

Definition at line 225 of file iterative.hpp.

◆ _status

Status FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_status

protectedinherited

current status of the solver

Definition at line 213 of file iterative.hpp.

◆ _tol_abs

DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_tol_abs

protectedinherited

absolute tolerance parameter

Definition at line 217 of file iterative.hpp.

◆ _tol_abs_low

DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_tol_abs_low

protectedinherited

absolute low tolerance parameter

Definition at line 219 of file iterative.hpp.

◆ _tol_penalty

template<typename Functional_ >

DataType FEAT::Solver::QPenalty< Functional_ >::_tol_penalty

private

Maximum value the penalty parameter is allowed to take.

Definition at line 67 of file qpenalty.hpp.

Referenced by FEAT::Solver::QPenalty< Functional_ >::_apply_intern(), and FEAT::Solver::QPenalty< Functional_ >::set_tol_penalty().

◆ _tol_rel

DataType FEAT::Solver::IterativeSolver< Functional_::VectorTypeR >::_tol_rel

protectedinherited

relative tolerance parameter

Definition at line 215 of file iterative.hpp.

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

kernel/solver/qpenalty.hpp

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Private Attributes

Detailed Description

Member Typedef Documentation

◆ BaseClass

◆ DataType

◆ FunctionalType

◆ VectorType

Constructor & Destructor Documentation

◆ QPenalty() [1/2]

◆ QPenalty() [2/2]

◆ ~QPenalty()

Member Function Documentation

◆ _analyze_defect()

◆ _apply_intern()

◆ _calc_def_norm()

◆ _plot_iter()

◆ _plot_iter_line()

◆ _plot_summary()

◆ _print_line()

◆ _progress()

◆ _set_comm()

◆ _set_comm_by_matrix()

◆ _set_comm_by_vector()

◆ _set_initial_defect() [1/2]

◆ _set_initial_defect() [2/2]

◆ _set_new_defect()

◆ _update_defect()

◆ apply() [1/2]

◆ apply() [2/2]

◆ calc_convergence_rate()

◆ calc_defect_reduction()

◆ correct()

◆ done()

◆ done_numeric()

◆ done_symbolic()

◆ force_defect_norm_calc()

◆ get_def_final()

◆ get_def_initial()

◆ get_div_abs()

◆ get_div_rel()

◆ get_max_iter()

◆ get_min_iter()

◆ get_min_stag_iter()

◆ get_num_iter()

◆ get_plot_name()

◆ get_stag_rate()

◆ get_status()

◆ get_summary()

◆ get_tol_abs()

◆ get_tol_abs_low()

◆ get_tol_rel()

◆ init()

◆ init_numeric()

◆ init_symbolic()

◆ is_converged() [1/2]

◆ is_converged() [2/2]

◆ is_diverged() [1/2]

◆ is_diverged() [2/2]

◆ name()

◆ plot_summary()

◆ set_div_abs()

◆ set_div_rel()

◆ set_initial_penalty_param()

◆ set_max_iter()

◆ set_min_iter()

◆ set_min_stag_iter()

◆ set_plot_interval()

◆ set_plot_mode()

◆ set_plot_name()

◆ set_stag_rate()

◆ set_tol_abs()

◆ set_tol_abs_low()

◆ set_tol_penalty()

◆ set_tol_rel()

Member Data Documentation

◆ _comm