Chebyshev Polynomial implementation. More...

#include <chebyshev.hpp>

Inheritance diagram for FEAT::Solver::Chebyshev< Matrix_, Filter_ >:

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

typedef MatrixType::DataType	DataType
	The floating point precision. More...

typedef Filter_	FilterType
	The filter type. More...

typedef Matrix_	MatrixType
	The matrix type. More...

typedef MatrixType::VectorTypeL	VectorType
	The type of vector this solver can be applied to. More...

Public Member Functions
	Chebyshev (const MatrixType &matrix, const FilterType &filter, const DataType fraction_min_ev=DataType(0.5), const DataType fraction_max_ev=DataType(0.8))
	Constructor. More...

	Chebyshev (const String &section_name, const PropertyMap *section, const MatrixType &matrix, const FilterType &filter)
	Constructor using a PropertyMap. More...

virtual	~Chebyshev ()
	Empty 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

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

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 () override
	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 () override
	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_fraction_max_ev (DataType fraction_max_ev)
	Sets the maximum eigenvalue fraction. More...

void	set_fraction_min_ev (DataType fraction_min_ev)
	Sets the minimum eigenvalue fraction. 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
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)

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 Matrix_::VectorTypeR &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...

DataType	_fraction_max_ev
	maximum eigenvalue fraction More...

DataType	_fraction_min_ev
	minimum eigenvalue fraction More...

Index	_iter_digits
	iteration count digits for plotting More...

DataType	_max_ev
	the maximum eigenvalue of the matrix More...

Index	_max_iter
	maximum number of iterations More...

DataType	_min_ev
	the minium eigenvalue of the matrix 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...

const FilterType &	_system_filter
	the filter for the solver More...

const MatrixType &	_system_matrix
	the matrix for 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...

VectorType	_vec_cor
	correction vector More...

VectorType	_vec_def
	defect vector More...

Detailed Description

template<typename Matrix_, typename Filter_>
class FEAT::Solver::Chebyshev< Matrix_, Filter_ >

Chebyshev Polynomial implementation.

This class represents the Chebyshev-Polynomial "Solver"

[NLA:NLA1808]

Definition at line 25 of file chebyshev.hpp.

Member Typedef Documentation

◆ BaseClass

template<typename Matrix_ , typename Filter_ >

typedef IterativeSolver<VectorType> FEAT::Solver::Chebyshev< Matrix_, Filter_ >::BaseClass

Our base class.

Definition at line 38 of file chebyshev.hpp.

◆ DataType

template<typename Matrix_ , typename Filter_ >

typedef MatrixType::DataType FEAT::Solver::Chebyshev< Matrix_, Filter_ >::DataType

The floating point precision.

Definition at line 36 of file chebyshev.hpp.

◆ FilterType

template<typename Matrix_ , typename Filter_ >

typedef Filter_ FEAT::Solver::Chebyshev< Matrix_, Filter_ >::FilterType

The filter type.

Definition at line 32 of file chebyshev.hpp.

◆ MatrixType

template<typename Matrix_ , typename Filter_ >

typedef Matrix_ FEAT::Solver::Chebyshev< Matrix_, Filter_ >::MatrixType

The matrix type.

Definition at line 30 of file chebyshev.hpp.

◆ VectorType

template<typename Matrix_ , typename Filter_ >

typedef MatrixType::VectorTypeL FEAT::Solver::Chebyshev< Matrix_, Filter_ >::VectorType

The type of vector this solver can be applied to.

Definition at line 34 of file chebyshev.hpp.

Constructor & Destructor Documentation

◆ Chebyshev() [1/2]

template<typename Matrix_ , typename Filter_ >

FEAT::Solver::Chebyshev< Matrix_, Filter_ >::Chebyshev	(	const MatrixType &	matrix,
		const FilterType &	filter,
		const DataType	fraction_min_ev = `DataType(0.5)`,
		const DataType	fraction_max_ev = `DataType(0.8)`
	)

inlineexplicit

Constructor.

Parameters

[in]	matrix	The source matrix.
[in]	filter	The system filter.

Definition at line 69 of file chebyshev.hpp.

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

◆ Chebyshev() [2/2]

template<typename Matrix_ , typename Filter_ >

FEAT::Solver::Chebyshev< Matrix_, Filter_ >::Chebyshev	(	const String &	section_name,
		const PropertyMap *	section,
		const MatrixType &	matrix,
		const FilterType &	filter
	)

inlineexplicit

Constructor using a PropertyMap.

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]	matrix	The system matrix.
[in]	filter	The system filter.

Returns: A shared pointer to a new Chebyshev object.

Definition at line 101 of file chebyshev.hpp.

References FEAT::Solver::IterativeSolver< Matrix_::VectorTypeR >::_set_comm_by_matrix(), and FEAT::PropertyMap::query().

◆ ~Chebyshev()

template<typename Matrix_ , typename Filter_ >

virtual FEAT::Solver::Chebyshev< Matrix_, Filter_ >::~Chebyshev ( )

inlinevirtual

Empty virtual destructor.

Definition at line 125 of file chebyshev.hpp.

Member Function Documentation

◆ _analyze_defect()

virtual Status FEAT::Solver::IterativeSolver< Matrix_::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 Matrix_ , typename Filter_ >

virtual Status FEAT::Solver::Chebyshev< Matrix_, Filter_ >::_apply_intern	(	VectorType &	vec_sol,
		const VectorType &	vec_rhs
	)

inlineprotectedvirtual

Definition at line 232 of file chebyshev.hpp.

◆ _calc_def_norm()

virtual DataType FEAT::Solver::IterativeSolver< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::VectorTypeR >::_set_comm_by_vector ( const Matrix_::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()

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

inlineprotectedvirtualinherited

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.

Definition at line 802 of file iterative.hpp.

◆ _set_new_defect()

virtual Status FEAT::Solver::IterativeSolver< Matrix_::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< Matrix_::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 Matrix_ , typename Filter_ >

virtual Status FEAT::Solver::Chebyshev< Matrix_, Filter_ >::apply	(	VectorType &	vec_cor,
		const VectorType &	vec_def
	)

inlineoverridevirtual

Definition at line 205 of file chebyshev.hpp.

◆ calc_convergence_rate()

DataType FEAT::Solver::IterativeSolver< Matrix_::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< Matrix_::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() [1/2]

template<typename Matrix_ , typename Filter_ >

virtual Status FEAT::Solver::Chebyshev< Matrix_, Filter_ >::correct	(	VectorType &	vec_sol,
		const VectorType &	vec_rhs
	)

inlineoverridevirtual

Definition at line 219 of file chebyshev.hpp.

◆ correct() [2/2]

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

pure virtualinherited

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.

◆ 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 Matrix_ , typename Filter_ >

virtual void FEAT::Solver::Chebyshev< Matrix_, Filter_ >::done_symbolic ( )

inlineoverridevirtual

Symbolic finalization method.

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

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

Definition at line 168 of file chebyshev.hpp.

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

◆ force_defect_norm_calc()

virtual void FEAT::Solver::IterativeSolver< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::VectorTypeR >::get_stag_rate ( ) const

inlineinherited

Returns the stagnation rate.

Definition at line 431 of file iterative.hpp.

◆ get_status()

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

inlineinherited

Returns the status.

Definition at line 576 of file iterative.hpp.

◆ get_summary()

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

inlinevirtualinherited

Returns a summary string.

Definition at line 610 of file iterative.hpp.

◆ get_tol_abs()

DataType FEAT::Solver::IterativeSolver< Matrix_::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< Matrix_::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< Matrix_::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 Matrix_ , typename Filter_ >

virtual void FEAT::Solver::Chebyshev< Matrix_, Filter_ >::init_numeric ( )

inlineoverridevirtual

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.

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

Definition at line 176 of file chebyshev.hpp.

References FEAT::Solver::Chebyshev< Matrix_, Filter_ >::_fraction_max_ev, FEAT::Solver::Chebyshev< Matrix_, Filter_ >::_fraction_min_ev, FEAT::Solver::Chebyshev< Matrix_, Filter_ >::_max_ev, FEAT::Solver::Chebyshev< Matrix_, Filter_ >::_min_ev, FEAT::Math::abs(), and FEAT::Solver::SolverBase< Vector_ >::init_numeric().

◆ init_symbolic()

template<typename Matrix_ , typename Filter_ >

virtual void FEAT::Solver::Chebyshev< Matrix_, Filter_ >::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 160 of file chebyshev.hpp.

References FEAT::Solver::Chebyshev< Matrix_, Filter_ >::_vec_cor, FEAT::Solver::Chebyshev< Matrix_, Filter_ >::_vec_def, and FEAT::Solver::SolverBase< Vector_ >::init_symbolic().

◆ is_converged() [1/2]

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

inlineinherited

checks for divergence

Definition at line 552 of file iterative.hpp.

◆ is_diverged() [2/2]

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

inlineinherited

checks for divergence

Definition at line 558 of file iterative.hpp.

◆ name()

template<typename Matrix_ , typename Filter_ >

virtual String FEAT::Solver::Chebyshev< Matrix_, Filter_ >::name ( ) const

inlineoverridevirtual

Returns a descriptive string.

Returns: A string describing the solver.

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

Definition at line 130 of file chebyshev.hpp.

◆ plot_summary()

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

inlineinherited

Sets the relative divergence for the solver.

Definition at line 401 of file iterative.hpp.

◆ set_fraction_max_ev()

template<typename Matrix_ , typename Filter_ >

void FEAT::Solver::Chebyshev< Matrix_, Filter_ >::set_fraction_max_ev ( DataType fraction_max_ev )

inline

Sets the maximum eigenvalue fraction.

Parameters

[in] fraction_max_ev The new maximum eigenvalue fraction.

Definition at line 154 of file chebyshev.hpp.

References FEAT::Solver::Chebyshev< Matrix_, Filter_ >::_fraction_max_ev.

◆ set_fraction_min_ev()

template<typename Matrix_ , typename Filter_ >

void FEAT::Solver::Chebyshev< Matrix_, Filter_ >::set_fraction_min_ev ( DataType fraction_min_ev )

inline

Sets the minimum eigenvalue fraction.

Parameters

[in] fraction_min_ev The new minimum eigenvalue fraction.

Definition at line 142 of file chebyshev.hpp.

References FEAT::Solver::Chebyshev< Matrix_, Filter_ >::_fraction_min_ev.

◆ set_max_iter()

void FEAT::Solver::IterativeSolver< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::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< Matrix_::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_rel()

void FEAT::Solver::IterativeSolver< Matrix_::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< Matrix_::VectorTypeR >::_comm

protectedinherited

Communicator of the solver.

Definition at line 209 of file iterative.hpp.

◆ _def_cur

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

protectedinherited

current defect

Definition at line 239 of file iterative.hpp.

◆ _def_init

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

protectedinherited

initial defect

Definition at line 237 of file iterative.hpp.

◆ _def_prev

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

protectedinherited

previous iteration defect

Definition at line 241 of file iterative.hpp.

◆ _div_abs

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

protectedinherited

absolute divergence parameter

Definition at line 223 of file iterative.hpp.

◆ _div_rel

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

protectedinherited

relative divergence parameter

Definition at line 221 of file iterative.hpp.

◆ _force_def_norm_calc

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

protectedinherited

whether skipping of defect computation is allowed or not

Definition at line 249 of file iterative.hpp.

◆ _fraction_max_ev

template<typename Matrix_ , typename Filter_ >

DataType FEAT::Solver::Chebyshev< Matrix_, Filter_ >::_fraction_max_ev

protected

maximum eigenvalue fraction

Definition at line 56 of file chebyshev.hpp.

Referenced by FEAT::Solver::Chebyshev< Matrix_, Filter_ >::init_numeric(), and FEAT::Solver::Chebyshev< Matrix_, Filter_ >::set_fraction_max_ev().

◆ _fraction_min_ev

template<typename Matrix_ , typename Filter_ >

DataType FEAT::Solver::Chebyshev< Matrix_, Filter_ >::_fraction_min_ev

protected

minimum eigenvalue fraction

Definition at line 54 of file chebyshev.hpp.

Referenced by FEAT::Solver::Chebyshev< Matrix_, Filter_ >::init_numeric(), and FEAT::Solver::Chebyshev< Matrix_, Filter_ >::set_fraction_min_ev().

◆ _iter_digits

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

protectedinherited

iteration count digits for plotting

Definition at line 243 of file iterative.hpp.

◆ _max_ev

template<typename Matrix_ , typename Filter_ >

DataType FEAT::Solver::Chebyshev< Matrix_, Filter_ >::_max_ev

protected

the maximum eigenvalue of the matrix

Definition at line 52 of file chebyshev.hpp.

Referenced by FEAT::Solver::Chebyshev< Matrix_, Filter_ >::init_numeric().

◆ _max_iter

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

protectedinherited

maximum number of iterations

Definition at line 229 of file iterative.hpp.

◆ _min_ev

template<typename Matrix_ , typename Filter_ >

DataType FEAT::Solver::Chebyshev< Matrix_, Filter_ >::_min_ev

protected

the minium eigenvalue of the matrix

Definition at line 50 of file chebyshev.hpp.

Referenced by FEAT::Solver::Chebyshev< Matrix_, Filter_ >::init_numeric().

◆ _min_iter

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

protectedinherited

minimum number of iterations

Definition at line 227 of file iterative.hpp.

◆ _min_stag_iter

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

protectedinherited

minimum number of stagnation iterations

Definition at line 233 of file iterative.hpp.

◆ _num_iter

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

protectedinherited

number of performed iterations

Definition at line 231 of file iterative.hpp.

◆ _num_stag_iter

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

protectedinherited

number of consecutive stagnated iterations

Definition at line 235 of file iterative.hpp.

◆ _plot_interval

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

protectedinherited

plot output interval

Definition at line 247 of file iterative.hpp.

◆ _plot_mode

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

protectedinherited

whether to plot something

Definition at line 245 of file iterative.hpp.

◆ _plot_name

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

protectedinherited

name of the solver in plots

Definition at line 211 of file iterative.hpp.

◆ _stag_rate

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

protectedinherited

stagnation rate

Definition at line 225 of file iterative.hpp.

◆ _status

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

protectedinherited

current status of the solver

Definition at line 213 of file iterative.hpp.

◆ _system_filter

template<typename Matrix_ , typename Filter_ >

const FilterType& FEAT::Solver::Chebyshev< Matrix_, Filter_ >::_system_filter

protected

the filter for the solver

Definition at line 44 of file chebyshev.hpp.

◆ _system_matrix

template<typename Matrix_ , typename Filter_ >

const MatrixType& FEAT::Solver::Chebyshev< Matrix_, Filter_ >::_system_matrix

protected

the matrix for the solver

Definition at line 42 of file chebyshev.hpp.

◆ _tol_abs

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

protectedinherited

absolute tolerance parameter

Definition at line 217 of file iterative.hpp.

◆ _tol_abs_low

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

protectedinherited

absolute low tolerance parameter

Definition at line 219 of file iterative.hpp.

◆ _tol_rel

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

protectedinherited

relative tolerance parameter

Definition at line 215 of file iterative.hpp.

◆ _vec_cor

template<typename Matrix_ , typename Filter_ >

VectorType FEAT::Solver::Chebyshev< Matrix_, Filter_ >::_vec_cor

protected

correction vector

Definition at line 48 of file chebyshev.hpp.

Referenced by FEAT::Solver::Chebyshev< Matrix_, Filter_ >::init_symbolic().

◆ _vec_def

template<typename Matrix_ , typename Filter_ >

VectorType FEAT::Solver::Chebyshev< Matrix_, Filter_ >::_vec_def

protected

defect vector

Definition at line 46 of file chebyshev.hpp.

Referenced by FEAT::Solver::Chebyshev< Matrix_, Filter_ >::init_symbolic().

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

kernel/solver/chebyshev.hpp

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ BaseClass

◆ DataType

◆ FilterType

◆ MatrixType

◆ VectorType

Constructor & Destructor Documentation

◆ Chebyshev() [1/2]

◆ Chebyshev() [2/2]

◆ ~Chebyshev()

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()

◆ _set_new_defect()

◆ _update_defect()

◆ apply() [1/2]

◆ apply() [2/2]

◆ calc_convergence_rate()

◆ calc_defect_reduction()

◆ correct() [1/2]

◆ correct() [2/2]

◆ 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_fraction_max_ev()

◆ set_fraction_min_ev()

◆ 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