Abstract base-class for iterative solvers. More...

#include <iterative.hpp>

Inheritance diagram for FEAT::Solver::IterativeSolver< Vector_ >:

Public Types
typedef SolverBase< VectorType >	BaseClass
	The base class. More...

typedef VectorType::DataType	DataType
	Floating point type. More...

typedef Vector_	VectorType
	The vector type this solver can be applied to. More...

Public Member Functions
virtual Status	apply (Vector_ &vec_cor, const Vector_ &vec_def)=0
	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)=0
	Solver correction method. More...

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

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

virtual void	done_symbolic ()
	Symbolic finalization 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 ()
	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 =0
	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_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_rel (DataType tol_rel)
	Sets the relative tolerance for the solver. More...

Protected Member Functions
	IterativeSolver (const String &plot_name)
	Protected constructor. More...

	IterativeSolver (const String &plot_name, const String &section_name, const PropertyMap *section)
	Constructor using a PropertyMap. More...

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

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

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

virtual Status	_set_initial_defect (const VectorType &vec_def, const VectorType &vec_sol)
	Internal function: sets the initial defect vector. 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...

Detailed Description

template<typename Vector_>
class FEAT::Solver::IterativeSolver< Vector_ >

Abstract base-class for iterative solvers.

This class template acts as an abstract base class for iterative solvers and it implements various auxiliary features for convergence control, output formatting and a posteriori convergence analysis.

Template Parameters

Vector_ The class of the vector that is passed to the solver in the solve() method.

Details about the convergence control mechanisms offered by this class:
This class offers a wide variety of convergence control mechanisms and stopping criterions, which are summarized in this section.

In the following, let \(k\geq 0\) denote the current iteration and let \(r_0 := b - Ax_0\) denote the initial defect/residual vector and let \(r_k := b - Ax_k\) denote the defect/residual vector of the current iteration.

1. Divergence Criterion: The first stopping criterion checks whether the residual vector norm has risen above a relative or absolute divergence tolerance and, if so, the solver stops and returns the status code Status::diverged.
The divergence criterion is defined as follows:

\[ (\vert \vert r_k\vert\vert \geq \text{div\_abs}) \lor (\vert \vert r_k\vert\vert \geq \text{div\_rel}\cdot\vert \vert r_0\vert\vert) \]

By default, the divergence tolerances are chosen as

div_abs = 1/eps^2
dil_rel = 1/eps

where eps is the machine precision constant for the solvers underlying data type, which evaluates to approximately div_abs = 1E+32 and div_rel = 1E+16 for double precision.

2. Maximum Iteration Number Criterion: The second stopping criterion checks whether the solver has reached the maximum number of allowed iterations, i.e. whether k >= max_iter, and, if so, the solver returns the status code Status::max_iter.

3. Convergence Criterion: The third stopping criterion checks whether the residual vector has fallen below a relative and/or absolute convergence tolerance and, if so, the solver returns the status code Status::converged. The convergence criterion consists of a relative tolerance and two absolute tolerances and is defined as follows:

\[ (\vert \vert r_k\vert\vert \leq \text{tol\_abs}) \land ((\vert \vert r_k\vert\vert \leq \text{tol\_rel}\cdot\vert \vert r_0\vert\vert) \lor (\vert \vert r_k\vert\vert \leq \text{tol\_abs\_low})) \]

By default, the convergence tolerances are chosen as

tol_rel = sqrt(eps)
tol_abs = 1/eps^2
tol_abs_low = 0

where eps is the machine precision constant for the solvers underlying data type, which evaluates to approximately tol_abs = 1E-8 and tol_rel = 1E+32 for double precision, which effectively "disables" both absolute tolerances therefore resulting in a convergence criterion that only depends on the relative tolerance.

The tol_abs_low parameter can be used to "disarm" an overly strict relative tolerance tol_rel in the case where the initial defect is already quite small and therefore fulfilling the relative tolerance may become impossible due to finite precision arithmetic combined with a large condition number. A typical use case would be to set tol_abs to 1E-8 and tol_rel to 1E-5 (thus asking that the solver should gain 5 digits) and tol_abs_low to 1E-12, which will "disable" the tol_rel criterion if (and only if) the initial defect norm is less than 1E-7. If the initial defect norm is larger than 1E-7, then the tol_abs_low parameter will become irrelevant and the tol_abs and tol_rel criterions have to be fulfilled for convergence.

If you want the solver to fulfill only a relative tolerance, then set tol_rel to the corresponding tolerance and leave tol_abs_low set to 0 and tol_abs to set a large value (1/eps^2 by default).
If you want the solver to fulfill only an absolute tolerance, then set both tol_abs and tol_abs_low to the corresponding tolerance and set tol_rel to any value you like, e.g. 0.
If you want the solver to fulfill either a relative or an absolute tolerance, then set tol_rel and tol_abs_low to the corresponding tolerances and leave tol_abs to set a large value (1/eps^2 by default).
If you want the solver to fulfill both a relative and an absolute tolerance, then set tol_rel and tol_abs to the corresponding tolerances and leave tol_abs_low set to 0.

5. Stagnation Criterion: The fifth stopping criterion checks whether the residual vector norms do not decrease by a minimum factor over the last few iterations, thus indicating that the solver seems to be stagnating and that further iterations will probably not improve the solution any further and, if so, the solver stops and returns the status code Status::stagnated.
The stagnation criterion is fulfilled if min_stag_iter is set to a value > 0 and if

\[ \vert \vert r_k\vert\vert \geq \text{stag\_rate}\cdot\vert \vert r_{k-1}\vert\vert \]

for at least min_stag_iter consecutive iterations.

By default, the stagnation criterion is disabled and its parameters are chosen as

stag_rate = 0.95
min_stag_iter = 0

It is important to keep in mind that the stagnation criterion can usually only be helpful for simple fix-point type iterative solvers, which have more or less monotonous convergence behavior. Other types of solvers, especially Krylov subspace solvers, often show a somewhat "ballistic" convergence curve, where the defect norms seem to indicate divergence for the first few dozen/hundred iterations before the defect norms start falling down very quickly – in this case, the stagnation criterion will trigger a false positive during the initial climb of the defect norms. Also, some solvers can run into a stagnation scenario where the defect norms oscillate, which will not be detected by the stagnation criterion because the defect norm drops every other iteration before rising back up again in the next iteration.

Author: Peter Zajac

Definition at line 196 of file iterative.hpp.

Member Typedef Documentation

◆ BaseClass

template<typename Vector_ >

typedef SolverBase<VectorType> FEAT::Solver::IterativeSolver< Vector_ >::BaseClass

The base class.

Definition at line 205 of file iterative.hpp.

◆ DataType

template<typename Vector_ >

typedef VectorType::DataType FEAT::Solver::IterativeSolver< Vector_ >::DataType

Floating point type.

Definition at line 203 of file iterative.hpp.

◆ VectorType

template<typename Vector_ >

typedef Vector_ FEAT::Solver::IterativeSolver< Vector_ >::VectorType

The vector type this solver can be applied to.

Definition at line 201 of file iterative.hpp.

Constructor & Destructor Documentation

◆ IterativeSolver() [1/2]

template<typename Vector_ >

FEAT::Solver::IterativeSolver< Vector_ >::IterativeSolver ( const String & plot_name )

inlineexplicitprotected

Protected constructor.

This constructor initializes the following values:

relative tolerance: sqrt(eps) (~1E-8 for double)
absolute tolerance: 1/eps^2 (~1E+32 for double)
lower absolute tolerance: 0
relative divergence: 1/eps (~1E+16 for double)
absolute divergence: 1/eps^2 (~1E+32 for double)
stagnation rate: 0.95
minimum iterations: 0
maximum iterations: 100
minimum stagnation iterations: 0
convergence plot: false

Parameters

[in] plot_name Specifies the name of the iterative solver. This is used as a prefix for the convergence plot.

Definition at line 270 of file iterative.hpp.

◆ IterativeSolver() [2/2]

template<typename Vector_ >

FEAT::Solver::IterativeSolver< Vector_ >::IterativeSolver	(	const String &	plot_name,
		const String &	section_name,
		const PropertyMap *	section
	)

inlineexplicitprotected

Constructor using a PropertyMap.

See also: Solver configuration via PropertyMaps

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]	plot_name	The name of the solver.

Definition at line 311 of file iterative.hpp.

References FEAT::PropertyMap::get_entry().

Member Function Documentation

◆ _analyze_defect()

template<typename Vector_ >

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

inlineprotectedvirtual

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.

References FEAT::Solver::IterativeSolver< Vector_ >::_min_iter, FEAT::Solver::aborted, FEAT::Solver::diverged, FEAT::Solver::IterativeSolver< Vector_ >::is_converged(), FEAT::Solver::IterativeSolver< Vector_ >::is_diverged(), FEAT::Math::isfinite(), FEAT::Solver::max_iter, FEAT::Solver::progress, FEAT::Solver::stagnated, and FEAT::Solver::success.

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::_set_new_defect(), and FEAT::Solver::IterativeSolver< Vector_ >::_update_defect().

◆ _calc_def_norm()

template<typename Vector_ >

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

inlineprotectedvirtual

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.

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::_set_initial_defect(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_initial_defect(), FEAT::Solver::IterativeSolver< Vector_ >::_set_new_defect(), and FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_new_defect().

◆ _plot_iter()

template<typename Vector_ >

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

inlineprotected

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.

References FEAT::Solver::IterativeSolver< Vector_ >::_num_iter, FEAT::Solver::IterativeSolver< Vector_ >::_plot_interval, FEAT::Solver::IterativeSolver< Vector_ >::_plot_mode, FEAT::Solver::all, FEAT::Solver::iter, and FEAT::Solver::progress.

Referenced by FEAT::Solver::RBiCGStab< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::BiCGStab< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::IterativeSolver< Vector_ >::_set_initial_defect(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_initial_defect(), FEAT::Solver::IterativeSolver< Vector_ >::_set_new_defect(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_new_defect(), and FEAT::Solver::IterativeSolver< Vector_ >::_update_defect().

◆ _plot_iter_line()

template<typename Vector_ >

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

inlineprotectedvirtual

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.

References FEAT::Solver::IterativeSolver< Vector_ >::_print_line(), FEAT::String::pad_front(), FEAT::stringify(), FEAT::stringify_fp_fix(), and FEAT::stringify_fp_sci().

Referenced by FEAT::Solver::RBiCGStab< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::BiCGStab< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::IterativeSolver< Vector_ >::_set_initial_defect(), FEAT::Solver::IterativeSolver< Vector_ >::_set_new_defect(), and FEAT::Solver::IterativeSolver< Vector_ >::_update_defect().

◆ _plot_summary()

template<typename Vector_ >

bool FEAT::Solver::IterativeSolver< Vector_ >::_plot_summary ( ) const

inlineprotected

Plot summary?

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

Definition at line 731 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_plot_mode, FEAT::Solver::all, and FEAT::Solver::summary.

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::_set_initial_defect(), FEAT::Solver::IterativeSolver< Vector_ >::_set_new_defect(), and FEAT::Solver::IterativeSolver< Vector_ >::plot_summary().

◆ _print_line()

template<typename Vector_ >

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

inlineprotected

Prints a line.

Parameters

[in] line The line to be printed.

Definition at line 752 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_comm, and FEAT::Dist::Comm::print().

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::_plot_iter_line(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_initial_defect(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_new_defect(), and FEAT::Solver::IterativeSolver< Vector_ >::plot_summary().

◆ _progress()

template<typename Vector_ >

bool FEAT::Solver::IterativeSolver< Vector_ >::_progress ( ) const

inlineprotected

Progress iteration?

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

Definition at line 741 of file iterative.hpp.

References FEAT::Solver::progress.

◆ _set_comm()

template<typename Vector_ >

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

inlineprotected

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()

template<typename Vector_ >

template<typename Matrix_ >

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

inlineprotected

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()

template<typename Vector_ >

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

inlineprotected

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()

template<typename Vector_ >

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

inlineprotectedvirtual

Internal function: sets the initial defect vector.

Parameters

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

Returns: The updated Status code.

Reimplemented in FEAT::Solver::QPenalty< Functional_ >.

Definition at line 802 of file iterative.hpp.

Referenced by FEAT::Solver::PCG< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::PCR< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::PipePCG< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::RBiCGStab< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::BiCGStab< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::BiCGStabL< Matrix_, Filter_ >::_apply_intern(), and FEAT::Solver::GroppPCG< Matrix_, Filter_ >::_apply_intern().

◆ _set_new_defect()

template<typename Vector_ >

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

inlineprotectedvirtual

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.

Referenced by FEAT::Solver::PCG< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::PCR< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::BiCGStab< Matrix_, Filter_ >::_apply_intern(), and FEAT::Solver::BiCGStabL< Matrix_, Filter_ >::_apply_intern().

◆ _update_defect()

template<typename Vector_ >

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

inlineprotectedvirtual

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.

References FEAT::Solver::IterativeSolver< Vector_ >::_analyze_defect(), FEAT::Solver::IterativeSolver< Vector_ >::_def_cur, FEAT::Solver::IterativeSolver< Vector_ >::_num_iter, FEAT::Solver::IterativeSolver< Vector_ >::_plot_iter(), FEAT::Solver::IterativeSolver< Vector_ >::_plot_iter_line(), FEAT::Solver::IterativeSolver< Vector_ >::get_num_iter(), and FEAT::Solver::SolverBase< Vector_ >::name().

Referenced by FEAT::Solver::PipePCG< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::RBiCGStab< Matrix_, Filter_ >::_apply_intern(), and FEAT::Solver::GroppPCG< Matrix_, Filter_ >::_apply_intern().

◆ apply()

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().

◆ calc_convergence_rate()

template<typename Vector_ >

DataType FEAT::Solver::IterativeSolver< Vector_ >::calc_convergence_rate ( ) const

inline

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

Definition at line 582 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_def_cur, FEAT::Solver::IterativeSolver< Vector_ >::_def_init, FEAT::Solver::IterativeSolver< Vector_ >::_num_iter, and FEAT::Math::pow().

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::get_summary().

◆ calc_defect_reduction()

template<typename Vector_ >

DataType FEAT::Solver::IterativeSolver< Vector_ >::calc_defect_reduction ( ) const

inline

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

Definition at line 597 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_def_init, and FEAT::Math::abs().

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::get_summary().

◆ correct()

template<typename Vector_ >

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

pure virtual

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.

Implemented in FEAT::Solver::FixedStepLinesearch< Functional_, Filter_ >, FEAT::Solver::MQCLinesearch< Functional_, Filter_ >, FEAT::Solver::NewtonRaphsonLinesearch< Functional_, Filter_ >, FEAT::Solver::SecantLinesearch< Functional_, Filter_ >, and FEAT::Solver::QPenalty< Functional_ >.

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

◆ 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 Vector_ >

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

inlinevirtualinherited

Symbolic finalization method.

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

Definition at line 255 of file base.hpp.

◆ force_defect_norm_calc()

template<typename Vector_ >

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

inlinevirtual

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

Reimplemented in FEAT::Solver::BiCGStab< Matrix_, Filter_ >, FEAT::Solver::BiCGStabL< Matrix_, Filter_ >, FEAT::Solver::FGMRES< Matrix_, Filter_ >, FEAT::Solver::GMRES< Matrix_, Filter_ >, and FEAT::Solver::RBiCGStab< Matrix_, Filter_ >.

Definition at line 490 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_force_def_norm_calc.

◆ get_def_final()

template<typename Vector_ >

DataType FEAT::Solver::IterativeSolver< Vector_ >::get_def_final ( ) const

inline

Returns the final defect.

Definition at line 570 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_def_cur.

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::get_summary().

◆ get_def_initial()

template<typename Vector_ >

DataType FEAT::Solver::IterativeSolver< Vector_ >::get_def_initial ( ) const

inline

Returns the initial defect.

Definition at line 564 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_def_init.

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::get_summary().

◆ get_div_abs()

template<typename Vector_ >

DataType FEAT::Solver::IterativeSolver< Vector_ >::get_div_abs ( ) const

inline

Returns the absolute divergence.

Definition at line 419 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_div_abs.

◆ get_div_rel()

template<typename Vector_ >

DataType FEAT::Solver::IterativeSolver< Vector_ >::get_div_rel ( ) const

inline

Returns the relative divergence.

Definition at line 413 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_div_rel.

◆ get_max_iter()

template<typename Vector_ >

Index FEAT::Solver::IterativeSolver< Vector_ >::get_max_iter ( ) const

inline

Returns the maximum number of iterations.

Definition at line 474 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_max_iter.

◆ get_min_iter()

template<typename Vector_ >

Index FEAT::Solver::IterativeSolver< Vector_ >::get_min_iter ( ) const

inline

Returns the minimal number of iterations.

Definition at line 468 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_min_iter.

◆ get_min_stag_iter()

template<typename Vector_ >

Index FEAT::Solver::IterativeSolver< Vector_ >::get_min_stag_iter ( ) const

inline

Returns the minimum stagnation iteration count.

Definition at line 443 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_min_stag_iter.

◆ get_num_iter()

template<typename Vector_ >

Index FEAT::Solver::IterativeSolver< Vector_ >::get_num_iter ( ) const

inline

Returns number of performed iterations.

Definition at line 462 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_num_iter.

◆ get_plot_name()

template<typename Vector_ >

String FEAT::Solver::IterativeSolver< Vector_ >::get_plot_name ( ) const

inline

Returns the plot name of the solver.

Definition at line 523 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_plot_name.

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::get_summary(), and FEAT::Solver::NLOptLS< Functional_, Filter_ >::get_summary().

◆ get_stag_rate()

template<typename Vector_ >

DataType FEAT::Solver::IterativeSolver< Vector_ >::get_stag_rate ( ) const

inline

Returns the stagnation rate.

Definition at line 431 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_stag_rate.

◆ get_status()

template<typename Vector_ >

Status FEAT::Solver::IterativeSolver< Vector_ >::get_status ( ) const

inline

Returns the status.

Definition at line 576 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_status.

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::get_summary(), and FEAT::Solver::NLOptLS< Functional_, Filter_ >::get_summary().

◆ get_summary()

template<typename Vector_ >

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

inlinevirtual

Returns a summary string.

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

Definition at line 610 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::calc_convergence_rate(), FEAT::Solver::IterativeSolver< Vector_ >::calc_defect_reduction(), FEAT::Solver::IterativeSolver< Vector_ >::get_def_final(), FEAT::Solver::IterativeSolver< Vector_ >::get_def_initial(), FEAT::Solver::IterativeSolver< Vector_ >::get_num_iter(), FEAT::Solver::IterativeSolver< Vector_ >::get_plot_name(), FEAT::Solver::IterativeSolver< Vector_ >::get_status(), FEAT::stringify(), FEAT::stringify_fp_fix(), and FEAT::stringify_fp_sci().

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::plot_summary().

◆ get_tol_abs()

template<typename Vector_ >

DataType FEAT::Solver::IterativeSolver< Vector_ >::get_tol_abs ( ) const

inline

Returns the absolute tolerance.

Definition at line 389 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_tol_abs.

◆ get_tol_abs_low()

template<typename Vector_ >

DataType FEAT::Solver::IterativeSolver< Vector_ >::get_tol_abs_low ( ) const

inline

Returns the lower absolute tolerance.

Definition at line 395 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_tol_abs_low.

◆ get_tol_rel()

template<typename Vector_ >

DataType FEAT::Solver::IterativeSolver< Vector_ >::get_tol_rel ( ) const

inline

Returns the relative tolerance.

Definition at line 383 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_tol_rel.

◆ 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 Vector_ >

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

inlinevirtualinherited

Symbolic initialization method.

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

Definition at line 227 of file base.hpp.

◆ is_converged() [1/2]

template<typename Vector_ >

bool FEAT::Solver::IterativeSolver< Vector_ >::is_converged ( ) const

inline

checks for convergence

Returns: true, if converged, else false

Definition at line 533 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_def_cur, and FEAT::Solver::IterativeSolver< Vector_ >::is_converged().

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::_analyze_defect(), FEAT::Solver::RBiCGStab< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::BiCGStab< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_new_defect(), and FEAT::Solver::IterativeSolver< Vector_ >::is_converged().

◆ is_converged() [2/2]

template<typename Vector_ >

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

inline

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.

References FEAT::Solver::IterativeSolver< Vector_ >::_def_init, FEAT::Solver::IterativeSolver< Vector_ >::_tol_abs, FEAT::Solver::IterativeSolver< Vector_ >::_tol_abs_low, and FEAT::Solver::IterativeSolver< Vector_ >::_tol_rel.

◆ is_diverged() [1/2]

template<typename Vector_ >

bool FEAT::Solver::IterativeSolver< Vector_ >::is_diverged ( ) const

inline

checks for divergence

Definition at line 552 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_def_cur, and FEAT::Solver::IterativeSolver< Vector_ >::is_diverged().

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::_analyze_defect(), FEAT::Solver::RBiCGStab< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::BiCGStab< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_new_defect(), and FEAT::Solver::IterativeSolver< Vector_ >::is_diverged().

◆ is_diverged() [2/2]

template<typename Vector_ >

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

inline

checks for divergence

Definition at line 558 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_def_init, FEAT::Solver::IterativeSolver< Vector_ >::_div_abs, and FEAT::Solver::IterativeSolver< Vector_ >::_div_rel.

◆ name()

template<typename Vector_ >

virtual String FEAT::Solver::SolverBase< Vector_ >::name ( ) const

pure virtualinherited

Returns a descriptive string.

Returns: A string describing the solver.

Referenced by FEAT::Solver::PreconditionedIterativeSolver< Vector_ >::_apply_precond(), FEAT::Solver::Linesearch< Functional_, Filter_ >::_check_convergence(), FEAT::Solver::IterativeSolver< Vector_ >::_set_initial_defect(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_initial_defect(), FEAT::Solver::IterativeSolver< Vector_ >::_set_new_defect(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_new_defect(), and FEAT::Solver::IterativeSolver< Vector_ >::_update_defect().

◆ plot_summary()

template<typename Vector_ >

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

inlinevirtual

Plot a summary of the last solver run.

Definition at line 627 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_plot_summary(), FEAT::Solver::IterativeSolver< Vector_ >::_print_line(), and FEAT::Solver::IterativeSolver< Vector_ >::get_summary().

◆ set_div_abs()

template<typename Vector_ >

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

inline

Sets the absolute divergence for the solver.

Definition at line 407 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_div_abs.

◆ set_div_rel()

template<typename Vector_ >

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

inline

Sets the relative divergence for the solver.

Definition at line 401 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_div_rel.

◆ set_max_iter()

template<typename Vector_ >

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

inline

Sets the maximum iteration count for the solver.

Definition at line 455 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_iter_digits, FEAT::Solver::IterativeSolver< Vector_ >::_max_iter, FEAT::Math::ilog10(), and FEAT::Solver::max_iter.

Referenced by FEAT::Solver::ALGLIBMinLBFGS< Functional_, Filter_ >::set_max_iter(), and FEAT::Solver::ALGLIBMinCG< Functional_, Filter_ >::set_max_iter().

◆ set_min_iter()

template<typename Vector_ >

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

inline

Sets the minimum iteration count for the solver.

Definition at line 449 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_min_iter.

◆ set_min_stag_iter()

template<typename Vector_ >

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

inline

Sets the minimum stagnate iteration count for the solver.

Definition at line 437 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_min_stag_iter.

◆ set_plot_interval()

template<typename Vector_ >

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

inline

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.

References FEAT::Solver::IterativeSolver< Vector_ >::_plot_interval.

◆ set_plot_mode()

template<typename Vector_ >

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

inline

Sets the plot mode of the solver.

Parameters

[in] plot_mode The desired plot mode

Definition at line 501 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_plot_mode.

◆ set_plot_name()

template<typename Vector_ >

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

inline

Sets the plot name of the solver.

Definition at line 517 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_plot_name.

Referenced by FEAT::Solver::BiCGStabL< Matrix_, Filter_ >::BiCGStabL(), and FEAT::Solver::Descent< Matrix_, Filter_ >::Descent().

◆ set_stag_rate()

template<typename Vector_ >

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

inline

Sets the stagnation rate for the solver.

Definition at line 425 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_stag_rate.

◆ set_tol_abs()

template<typename Vector_ >

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

inline

Sets the absolute tolerance for the solver.

Definition at line 371 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_tol_abs.

Referenced by FEAT::Solver::ALGLIBMinLBFGS< Functional_, Filter_ >::set_tol_abs(), and FEAT::Solver::ALGLIBMinCG< Functional_, Filter_ >::set_tol_abs().

◆ set_tol_abs_low()

template<typename Vector_ >

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

inline

Sets the lower absolute tolerance for the solver.

Definition at line 377 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_tol_abs_low.

◆ set_tol_rel()

template<typename Vector_ >

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

inline

Sets the relative tolerance for the solver.

Definition at line 365 of file iterative.hpp.

References FEAT::Solver::IterativeSolver< Vector_ >::_tol_rel.

Member Data Documentation

◆ _comm

template<typename Vector_ >

const Dist::Comm* FEAT::Solver::IterativeSolver< Vector_ >::_comm

protected

Communicator of the solver.

Definition at line 209 of file iterative.hpp.

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::_print_line().

◆ _def_cur

template<typename Vector_ >

DataType FEAT::Solver::IterativeSolver< Vector_ >::_def_cur

protected

current defect

Definition at line 239 of file iterative.hpp.

Referenced by FEAT::Solver::RBiCGStab< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::BiCGStab< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_initial_defect(), FEAT::Solver::IterativeSolver< Vector_ >::_set_new_defect(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_new_defect(), FEAT::Solver::IterativeSolver< Vector_ >::_update_defect(), FEAT::Solver::IterativeSolver< Vector_ >::calc_convergence_rate(), FEAT::Solver::IterativeSolver< Vector_ >::get_def_final(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::get_summary(), FEAT::Solver::IterativeSolver< Vector_ >::is_converged(), and FEAT::Solver::IterativeSolver< Vector_ >::is_diverged().

◆ _def_init

template<typename Vector_ >

DataType FEAT::Solver::IterativeSolver< Vector_ >::_def_init

protected

initial defect

Definition at line 237 of file iterative.hpp.

Referenced by FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_initial_defect(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_new_defect(), FEAT::Solver::IterativeSolver< Vector_ >::calc_convergence_rate(), FEAT::Solver::IterativeSolver< Vector_ >::calc_defect_reduction(), FEAT::Solver::IterativeSolver< Vector_ >::get_def_initial(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::get_summary(), FEAT::Solver::IterativeSolver< Vector_ >::is_converged(), and FEAT::Solver::IterativeSolver< Vector_ >::is_diverged().

◆ _def_prev

template<typename Vector_ >

DataType FEAT::Solver::IterativeSolver< Vector_ >::_def_prev

protected

previous iteration defect

Definition at line 241 of file iterative.hpp.

Referenced by FEAT::Solver::RBiCGStab< Matrix_, Filter_ >::_apply_intern(), and FEAT::Solver::BiCGStab< Matrix_, Filter_ >::_apply_intern().

◆ _div_abs

template<typename Vector_ >

DataType FEAT::Solver::IterativeSolver< Vector_ >::_div_abs

protected

absolute divergence parameter

Definition at line 223 of file iterative.hpp.

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::get_div_abs(), FEAT::Solver::IterativeSolver< Vector_ >::is_diverged(), and FEAT::Solver::IterativeSolver< Vector_ >::set_div_abs().

◆ _div_rel

template<typename Vector_ >

DataType FEAT::Solver::IterativeSolver< Vector_ >::_div_rel

protected

relative divergence parameter

Definition at line 221 of file iterative.hpp.

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::get_div_rel(), FEAT::Solver::IterativeSolver< Vector_ >::is_diverged(), and FEAT::Solver::IterativeSolver< Vector_ >::set_div_rel().

◆ _force_def_norm_calc

template<typename Vector_ >

bool FEAT::Solver::IterativeSolver< Vector_ >::_force_def_norm_calc

protected

whether skipping of defect computation is allowed or not

Definition at line 249 of file iterative.hpp.

Referenced by FEAT::Solver::BiCGStab< Matrix_, Filter_ >::BiCGStab(), FEAT::Solver::BiCGStabL< Matrix_, Filter_ >::BiCGStabL(), FEAT::Solver::FGMRES< Matrix_, Filter_ >::FGMRES(), FEAT::Solver::GMRES< Matrix_, Filter_ >::GMRES(), FEAT::Solver::RBiCGStab< Matrix_, Filter_ >::RBiCGStab(), FEAT::Solver::IterativeSolver< Vector_ >::_set_initial_defect(), FEAT::Solver::IterativeSolver< Vector_ >::_set_new_defect(), and FEAT::Solver::IterativeSolver< Vector_ >::force_defect_norm_calc().

◆ _iter_digits

template<typename Vector_ >

Index FEAT::Solver::IterativeSolver< Vector_ >::_iter_digits

protected

iteration count digits for plotting

Definition at line 243 of file iterative.hpp.

Referenced by FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_initial_defect(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_new_defect(), and FEAT::Solver::IterativeSolver< Vector_ >::set_max_iter().

◆ _max_iter

template<typename Vector_ >

Index FEAT::Solver::IterativeSolver< Vector_ >::_max_iter

protected

maximum number of iterations

Definition at line 229 of file iterative.hpp.

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::_set_initial_defect(), FEAT::Solver::IterativeSolver< Vector_ >::_set_new_defect(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_new_defect(), FEAT::Solver::IterativeSolver< Vector_ >::get_max_iter(), FEAT::Solver::ALGLIBMinLBFGS< Functional_, Filter_ >::init_symbolic(), FEAT::Solver::ALGLIBMinCG< Functional_, Filter_ >::init_symbolic(), FEAT::Solver::ALGLIBMinLBFGS< Functional_, Filter_ >::set_max_iter(), FEAT::Solver::ALGLIBMinCG< Functional_, Filter_ >::set_max_iter(), FEAT::Solver::IterativeSolver< Vector_ >::set_max_iter(), FEAT::Solver::ALGLIBMinLBFGS< Functional_, Filter_ >::set_tol_abs(), FEAT::Solver::ALGLIBMinCG< Functional_, Filter_ >::set_tol_abs(), FEAT::Solver::ALGLIBMinLBFGS< Functional_, Filter_ >::set_tol_fval(), and FEAT::Solver::ALGLIBMinCG< Functional_, Filter_ >::set_tol_fval().

◆ _min_iter

template<typename Vector_ >

Index FEAT::Solver::IterativeSolver< Vector_ >::_min_iter

protected

minimum number of iterations

Definition at line 227 of file iterative.hpp.

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::_analyze_defect(), FEAT::Solver::BiCGStab< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_new_defect(), FEAT::Solver::IterativeSolver< Vector_ >::get_min_iter(), and FEAT::Solver::IterativeSolver< Vector_ >::set_min_iter().

◆ _min_stag_iter

template<typename Vector_ >

Index FEAT::Solver::IterativeSolver< Vector_ >::_min_stag_iter

protected

minimum number of stagnation iterations

Definition at line 233 of file iterative.hpp.

Referenced by FEAT::Solver::NLCG< Functional_, Filter_ >::NLCG(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_new_defect(), FEAT::Solver::IterativeSolver< Vector_ >::get_min_stag_iter(), and FEAT::Solver::IterativeSolver< Vector_ >::set_min_stag_iter().

◆ _num_iter

template<typename Vector_ >

Index FEAT::Solver::IterativeSolver< Vector_ >::_num_iter

protected

number of performed iterations

Definition at line 231 of file iterative.hpp.

Referenced by FEAT::Solver::NLCG< Functional_, Filter_ >::_apply_intern(), FEAT::Solver::PipePCG< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::RBiCGStab< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::BiCGStab< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::IterativeSolver< Vector_ >::_plot_iter(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_initial_defect(), FEAT::Solver::IterativeSolver< Vector_ >::_set_new_defect(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_new_defect(), FEAT::Solver::IterativeSolver< Vector_ >::_update_defect(), FEAT::Solver::IterativeSolver< Vector_ >::calc_convergence_rate(), and FEAT::Solver::IterativeSolver< Vector_ >::get_num_iter().

◆ _num_stag_iter

template<typename Vector_ >

Index FEAT::Solver::IterativeSolver< Vector_ >::_num_stag_iter

protected

number of consecutive stagnated iterations

Definition at line 235 of file iterative.hpp.

Referenced by FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_initial_defect(), and FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_new_defect().

◆ _plot_interval

template<typename Vector_ >

Index FEAT::Solver::IterativeSolver< Vector_ >::_plot_interval

protected

plot output interval

Definition at line 247 of file iterative.hpp.

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::_plot_iter(), and FEAT::Solver::IterativeSolver< Vector_ >::set_plot_interval().

◆ _plot_mode

template<typename Vector_ >

PlotMode FEAT::Solver::IterativeSolver< Vector_ >::_plot_mode

protected

whether to plot something

Definition at line 245 of file iterative.hpp.

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::_plot_iter(), FEAT::Solver::IterativeSolver< Vector_ >::_plot_summary(), and FEAT::Solver::IterativeSolver< Vector_ >::set_plot_mode().

◆ _plot_name

template<typename Vector_ >

String FEAT::Solver::IterativeSolver< Vector_ >::_plot_name

protected

name of the solver in plots

Definition at line 211 of file iterative.hpp.

Referenced by FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_initial_defect(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_new_defect(), FEAT::Solver::IterativeSolver< Vector_ >::get_plot_name(), and FEAT::Solver::IterativeSolver< Vector_ >::set_plot_name().

◆ _stag_rate

template<typename Vector_ >

DataType FEAT::Solver::IterativeSolver< Vector_ >::_stag_rate

protected

stagnation rate

Definition at line 225 of file iterative.hpp.

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::get_stag_rate(), and FEAT::Solver::IterativeSolver< Vector_ >::set_stag_rate().

◆ _status

template<typename Vector_ >

Status FEAT::Solver::IterativeSolver< Vector_ >::_status

protected

current status of the solver

Definition at line 213 of file iterative.hpp.

◆ _tol_abs

template<typename Vector_ >

DataType FEAT::Solver::IterativeSolver< Vector_ >::_tol_abs

protected

absolute tolerance parameter

Definition at line 217 of file iterative.hpp.

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::get_tol_abs(), FEAT::Solver::IterativeSolver< Vector_ >::is_converged(), and FEAT::Solver::IterativeSolver< Vector_ >::set_tol_abs().

◆ _tol_abs_low

template<typename Vector_ >

DataType FEAT::Solver::IterativeSolver< Vector_ >::_tol_abs_low

protected

absolute low tolerance parameter

Definition at line 219 of file iterative.hpp.

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::_set_initial_defect(), FEAT::Solver::IterativeSolver< Vector_ >::get_tol_abs_low(), FEAT::Solver::IterativeSolver< Vector_ >::is_converged(), and FEAT::Solver::IterativeSolver< Vector_ >::set_tol_abs_low().

◆ _tol_rel

template<typename Vector_ >

DataType FEAT::Solver::IterativeSolver< Vector_ >::_tol_rel

protected

relative tolerance parameter

Definition at line 215 of file iterative.hpp.

Referenced by FEAT::Solver::NLCG< Functional_, Filter_ >::_apply_intern(), FEAT::Solver::IterativeSolver< Vector_ >::get_tol_rel(), FEAT::Solver::IterativeSolver< Vector_ >::is_converged(), and FEAT::Solver::IterativeSolver< Vector_ >::set_tol_rel().

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

kernel/solver/iterative.hpp

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ BaseClass

◆ DataType

◆ VectorType

Constructor & Destructor Documentation

◆ IterativeSolver() [1/2]

◆ IterativeSolver() [2/2]

Member Function Documentation

◆ _analyze_defect()

◆ _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()

◆ _set_new_defect()

◆ _update_defect()

◆ apply()

◆ 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_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_rel()

Member Data Documentation

◆ _comm

◆ _def_cur

◆ _def_init

◆ _def_prev

◆ _div_abs

◆ _div_rel

◆ _force_def_norm_calc

◆ _iter_digits

◆ _max_iter