Relative energy error termination criterion according to Strakos, Tichy: Error estimation in preconditioned conjugate gradients. Requires that IterateType::CG starts at \( x = 0 \). More general starting values might be used, but must be chosen such that the estimate for the energy norm of the solution stays positive (see the above mentioned paper for details). More...

#include <cgTerminationCriteria.hh>

Detailed Description

template<class R>
class Kaskade::StrakosTichyEnergyErrorTerminationCriterion< R >

Relative energy error termination criterion according to Strakos, Tichy: Error estimation in preconditioned conjugate gradients. Requires that IterateType::CG starts at \( x = 0 \). More general starting values might be used, but must be chosen such that the estimate for the energy norm of the solution stays positive (see the above mentioned paper for details).

Definition at line 80 of file cgTerminationCriteria.hh.

Inheritance diagram for Kaskade::StrakosTichyEnergyErrorTerminationCriterion< R >:

Public Types
typedef R	Real

Public Member Functions
	StrakosTichyEnergyErrorTerminationCriterion (Real tol_, int maxit_, double eps_=1e-12)
	constructor More...

	StrakosTichyEnergyErrorTerminationCriterion (Real tol_, Real minTol_, int maxit_, double eps_=1e-12)
	constructor More...

virtual void	clear ()
	re-initializes the termination criterion for a new IterateType::CG run More...

virtual void	setTolerance (Real tol_)
	set requested relative tolerance More...

virtual void	setLookAhead (int d_)
	set requested lookahead value More...

virtual void	addStepQuantities (Real stepLength, Real, Real, Real rPINVr)
	addStepQuantities supplies algorithmic quantities to the termination criterion More...

virtual int	getMaxIterationSteps ()
	get the maximum number of allowed iteration steps More...

virtual	operator bool ()
	termination decision More...

Real	relativeError ()
	returns the estimated absolute energy error More...

bool	minimalDecreaseAchieved ()

virtual PCGTerminationCriterion< R > &	tolerance (Real tol)=0
	set requested tolerance More...

virtual void	step (Real gamma2)=0
	supplies energy of step to the termination criterion More...

virtual void	residual (Real sigma)=0
	supplies the preconditioned residual to the termination criterion More...

virtual	operator bool () const =0
	termination decision More...

Member Typedef Documentation

◆ Real

template<class R >

typedef R Kaskade::StrakosTichyEnergyErrorTerminationCriterion< R >::Real

Definition at line 82 of file cgTerminationCriteria.hh.

Constructor & Destructor Documentation

◆ StrakosTichyEnergyErrorTerminationCriterion() [1/2]

template<class R >

Kaskade::StrakosTichyEnergyErrorTerminationCriterion< R >::StrakosTichyEnergyErrorTerminationCriterion	(	Real	tol_,
		int	maxit_,
		double	eps_ = `1e-12`
	)

inline

constructor

The pcg iteration is terminated as soon as either the estimated error satisfies \( [\epsilon] \le \mathrm{tol} \) or the number of iterations exceeds the limit maxit. Note that the estimate of the relative error requires a look ahead parameter L. Thus, if \(\mathrm{maxit}\ge\mathrm{L}\), then the error is first estimated in the (L+1)-th iteration.

Parameters

tol	the relative error tolerance for termination
maxit	the maximum number of iterations
eps	maximal attainable accuracy

Definition at line 95 of file cgTerminationCriteria.hh.

◆ StrakosTichyEnergyErrorTerminationCriterion() [2/2]

template<class R >

Kaskade::StrakosTichyEnergyErrorTerminationCriterion< R >::StrakosTichyEnergyErrorTerminationCriterion	(	Real	tol_,
		Real	minTol_,
		int	maxit_,
		double	eps_ = `1e-12`
	)

inline

constructor

The pcg iteration is terminated as soon as either the estimated error satisfies \( [\epsilon] \le \mathrm{tol} \) or the number of iterations exceeds the limit maxit. Note that the estimate of the relative error requires a look ahead parameter L. Thus, if \(\mathrm{maxit}\ge\mathrm{L}\), then the error is first estimated in the (L+1)-th iteration.

Parameters

tol	the relative error tolerance for termination
minTol	relative error tolerance to admit truncation in the hybrid cg implementation
maxit	the maximum number of iterations
eps	maximal attainable accuracy

Definition at line 111 of file cgTerminationCriteria.hh.

Member Function Documentation

◆ addStepQuantities()

template<class R >

virtual void Kaskade::StrakosTichyEnergyErrorTerminationCriterion< R >::addStepQuantities	(	Real	stepLength,
		Real	,
		Real	,
		Real	rPINVr
	)

inlinevirtual

addStepQuantities supplies algorithmic quantities to the termination criterion

Parameters

stepLength	scaling for the conjugate search direction \(q\)
qAq	squared energy norm of the conjugate search direction \(q\) (here: unused)
qPq	squared \(P\)-norm, i. e. the norm induced by the preconditioner, of the conjugate search direction \(q\) (here: unused)
rPINVr	squared \(P^{-1}\)-norm of the residual

Implements Kaskade::PCGTerminationCriterion< R >.

Definition at line 147 of file cgTerminationCriteria.hh.

◆ clear()

template<class R >

virtual void Kaskade::StrakosTichyEnergyErrorTerminationCriterion< R >::clear ( )

inlinevirtual

re-initializes the termination criterion for a new IterateType::CG run

Implements Kaskade::PCGTerminationCriterion< R >.

Definition at line 118 of file cgTerminationCriteria.hh.

◆ getMaxIterationSteps()

template<class R >

virtual int Kaskade::StrakosTichyEnergyErrorTerminationCriterion< R >::getMaxIterationSteps ( )

inlinevirtual

get the maximum number of allowed iteration steps

Implements Kaskade::PCGTerminationCriterion< R >.

Definition at line 156 of file cgTerminationCriteria.hh.

◆ minimalDecreaseAchieved()

template<class R >

bool Kaskade::StrakosTichyEnergyErrorTerminationCriterion< R >::minimalDecreaseAchieved ( )

inlinevirtual

Reimplemented from Kaskade::PCGTerminationCriterion< R >.

Definition at line 178 of file cgTerminationCriteria.hh.

◆ operator bool() [1/2]

template<class R >

virtual Kaskade::StrakosTichyEnergyErrorTerminationCriterion< R >::operator bool ( )

inlinevirtual

termination decision

Returns: true if the iteration has reached the required accuracy

Implements Kaskade::PCGTerminationCriterion< R >.

Definition at line 164 of file cgTerminationCriteria.hh.

◆ operator bool() [2/2]

template<class R >

virtual Kaskade::PCGTerminationCriterion< R >::operator bool ( ) const

pure virtualinherited

termination decision

Returns: true if the iteration has reached the required accuracy

Implemented in Kaskade::PCGCountingTerminationCriterion< R >, and Kaskade::PCGEnergyErrorTerminationCriterion< R >.

◆ relativeError()

template<class R >

Real Kaskade::StrakosTichyEnergyErrorTerminationCriterion< R >::relativeError ( )

inline

returns the estimated absolute energy error

Definition at line 172 of file cgTerminationCriteria.hh.

Referenced by Kaskade::StrakosTichyEnergyErrorTerminationCriterion< R >::minimalDecreaseAchieved(), and Kaskade::StrakosTichyEnergyErrorTerminationCriterion< R >::operator bool().

◆ residual()

template<class R >

virtual void Kaskade::PCGTerminationCriterion< R >::residual ( Real sigma )

pure virtualinherited

supplies the preconditioned residual to the termination criterion

Parameters

sigma the preconditioned residual norm

Implemented in Kaskade::PCGEnergyErrorTerminationCriterion< R >, and Kaskade::PCGCountingTerminationCriterion< R >.

Referenced by Kaskade::Pcg< X, Xstar >::apply().

◆ setLookAhead()

template<class R >

virtual void Kaskade::StrakosTichyEnergyErrorTerminationCriterion< R >::setLookAhead ( int d_ )

inlinevirtual

set requested lookahead value

Parameters

lah	the requested lookahead (nonnegative)

The default value is 50.

Implements Kaskade::PCGTerminationCriterion< R >.

Definition at line 138 of file cgTerminationCriteria.hh.

◆ setTolerance()

template<class R >

virtual void Kaskade::StrakosTichyEnergyErrorTerminationCriterion< R >::setTolerance ( Real tol_ )

inlinevirtual

set requested relative tolerance

Parameters

tol	the requested tolerance (nonnegative)

Implements Kaskade::PCGTerminationCriterion< R >.

Definition at line 129 of file cgTerminationCriteria.hh.

◆ step()

template<class R >

virtual void Kaskade::PCGTerminationCriterion< R >::step ( Real gamma2 )

pure virtualinherited

supplies energy of step to the termination criterion

Parameters

gamma2 the energy \( \alpha^2 q^T A q \) of the step \( \alpha q \)

Implemented in Kaskade::PCGEnergyErrorTerminationCriterion< R >, and Kaskade::PCGCountingTerminationCriterion< R >.

Referenced by Kaskade::Pcg< X, Xstar >::apply().

◆ tolerance()

template<class R >

virtual PCGTerminationCriterion< R > & Kaskade::PCGTerminationCriterion< R >::tolerance ( Real tol )

pure virtualinherited

set requested tolerance

Parameters

tol	the requested tolerance (nonnegative)

Implemented in Kaskade::PCGEnergyErrorTerminationCriterion< R >, and Kaskade::PCGCountingTerminationCriterion< R >.

Referenced by Kaskade::Pcg< X, Xstar >::apply().

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

cgTerminationCriteria.hh

Detailed Description

Public Types

Public Member Functions

Member Typedef Documentation

◆ Real

Constructor & Destructor Documentation

◆ StrakosTichyEnergyErrorTerminationCriterion() [1/2]

◆ StrakosTichyEnergyErrorTerminationCriterion() [2/2]

Member Function Documentation

◆ addStepQuantities()

◆ clear()

◆ getMaxIterationSteps()

◆ minimalDecreaseAchieved()

◆ operator bool() [1/2]

◆ operator bool() [2/2]

◆ relativeError()

◆ residual()

◆ setLookAhead()

◆ setTolerance()

◆ step()

◆ tolerance()