Base class for Newton's method. Defines the main algorithm, potentially using damping. More...

#include <newton_base.hh>

Detailed Description

Base class for Newton's method. Defines the main algorithm, potentially using damping.

This algorithm is defined in terms of abstract quantities. This is for the sake of reusability. It is design via virtual methods should provide flexibility to implement variants of this algorithm. As often with virtual functions: the base class specifies, when they are called, the derived class specifies what they do

Definition at line 88 of file newton_base.hh.

Inheritance diagram for Kaskade::NewtonsMethod:

Classes
class	CycleDetection

Public Types
typedef NewtonParameters	Parameters

Public Member Functions
virtual	~NewtonsMethod ()

	NewtonsMethod (AbstractNewtonDirection &l, AbstractChart &chart_, AbstractNorm &n, Parameters &p_)
	Create Newton's Method, providing a solver, a norm and algorithmic parameters. More...

void	solve (AbstractFunctional *f, AbstractFunctionSpaceElement &x)
	Solve the system f=0 with starting value x. On (successful) exit, the solution is x, otherwise it is left unmodified. More...

void	oneStep (AbstractFunctional f, AbstractLinearization l, AbstractFunctionSpaceElement &x)
	Perform one Newton step (which may be several trial steps, if damping is applied) More...

void	resolve (AbstractFunctionSpaceElement &x, AbstractLinearization const &l)

virtual Parameters &	getParameters ()

void	setDesiredAccuracy (double da)
	set the desired accuracy More...

virtual void	setDesiredRelativeAccuracy (double ra)
	set the desired accuracy More...

void	resetParameters ()
	Reset all algorithmic parameters to their default values. More...

int	stepsPerformed ()

bool	changedGrid ()

virtual void	getSearchDirection (AbstractFunctionSpaceElement &direction)

virtual void	computeTrialIterate (AbstractFunctionSpaceElement &trialIterate, AbstractFunctionSpaceElement const &direction, AbstractLinearization const &lin)

AbstractLinearization const &	getLastLinearization ()

AbstractLinearization const &	getLastSimplifiedLinearization ()

void	performTiming (bool doit)

void	reportOnIteration (int level)

Protected Member Functions
virtual void	initialize ()
	Called before Iteration. More...

virtual void	finalize (int)
	Called after Iteration. More...

virtual void	logQuantities ()
	Performs logging of quantities. More...

virtual void	initNewtonStep ()

virtual Convergence	convergenceTest (AbstractFunctionSpaceElement const &correction, AbstractFunctionSpaceElement const &iterate)=0
	Return true, if convergence is detected, false otherwise. More...

virtual void	predictNextDampingFactor (AbstractFunctionSpaceElement &correction)
	Should compute a damping factor. More...

virtual double &	dampingFactor ()
	Return a damping factor. More...

virtual double	maxSteps ()
	return the maximal number of steps More...

virtual void	updateIterate (AbstractFunctionSpaceElement &iterate, AbstractFunctionSpaceElement &trialIterate, AbstractLinearization const &lin)
	update an accepted iterate, default: iterate=trialIterate More...

virtual RegularityTest	regularityTest (double scalingFactor)

virtual AcceptanceTest	evaluateTrialIterate (AbstractFunctionSpaceElement const &trialIterate, AbstractFunctionSpaceElement const &correction, AbstractLinearization const &lin)=0

virtual void	terminationMessage (int flag)

int	algorithmWrapper ()
	Run algorithm, completely with initialization and finalization. More...

int	oneStepWrapper ()
	Run one step of algorithm. More...

Protected Attributes
AbstractFunctional *	functional

AbstractNewtonDirection &	linearSolver

AbstractChart &	chart

AbstractNorm &	norm

Parameters &	p

std::unique_ptr< AbstractFunctionSpaceElement >	iterate

std::unique_ptr< AbstractFunctionSpaceElement >	trialIterate

std::unique_ptr< AbstractFunctionSpaceElement >	correction

std::unique_ptr< AbstractLinearization >	newtonLinearization

std::unique_ptr< AbstractLinearization >	simplifiedLinearization

AbstractLinearization *	newtonPtr

int	step

int	report

Member Typedef Documentation

◆ Parameters

typedef NewtonParameters Kaskade::NewtonsMethod::Parameters

Definition at line 91 of file newton_base.hh.

Constructor & Destructor Documentation

◆ ~NewtonsMethod()

virtual Kaskade::NewtonsMethod::~NewtonsMethod ( )

inlinevirtual

Definition at line 93 of file newton_base.hh.

◆ NewtonsMethod()

Kaskade::NewtonsMethod::NewtonsMethod	(	AbstractNewtonDirection &	l,
		AbstractChart &	chart_,
		AbstractNorm &	n,
		Parameters &	p_
	)

inline

Create Newton's Method, providing a solver, a norm and algorithmic parameters.

Definition at line 96 of file newton_base.hh.

Member Function Documentation

◆ algorithmWrapper()

int Kaskade::Algorithm::algorithmWrapper ( )

protectedinherited

Run algorithm, completely with initialization and finalization.

◆ changedGrid()

bool Kaskade::NewtonsMethod::changedGrid ( )

inline

Definition at line 125 of file newton_base.hh.

◆ computeTrialIterate()

virtual void Kaskade::NewtonsMethod::computeTrialIterate	(	AbstractFunctionSpaceElement &	trialIterate,
		AbstractFunctionSpaceElement const &	direction,
		AbstractLinearization const &	lin
	)

inlinevirtual

Reimplemented in Kaskade::DampedCovariantNewtonMethod.

Definition at line 134 of file newton_base.hh.

◆ convergenceTest()

virtual Convergence Kaskade::NewtonsMethod::convergenceTest	(	AbstractFunctionSpaceElement const &	correction,
		AbstractFunctionSpaceElement const &	iterate
	)

protectedpure virtual

Return true, if convergence is detected, false otherwise.

Implemented in Kaskade::DampedCovariantNewtonMethod, and Kaskade::StateConstraintsNewtonMethod.

◆ dampingFactor()

virtual double & Kaskade::NewtonsMethod::dampingFactor ( )

inlineprotectedvirtual

Return a damping factor.

Reimplemented in Kaskade::DampedCovariantNewtonMethod.

Definition at line 161 of file newton_base.hh.

◆ evaluateTrialIterate()

virtual AcceptanceTest Kaskade::NewtonsMethod::evaluateTrialIterate	(	AbstractFunctionSpaceElement const &	trialIterate,
		AbstractFunctionSpaceElement const &	correction,
		AbstractLinearization const &	lin
	)

protectedpure virtual

function to evaluate the quality of the trial iterate. returns true if trial iterate is acceptable as new iterate i.e. if some damping factor is of appropriate size

Implemented in Kaskade::DampedCovariantNewtonMethod, and Kaskade::StateConstraintsNewtonMethod.

◆ finalize()

virtual void Kaskade::NewtonsMethod::finalize ( int )

protectedvirtual

Called after Iteration.

Reimplemented from Kaskade::Algorithm.

◆ getLastLinearization()

AbstractLinearization const & Kaskade::NewtonsMethod::getLastLinearization ( )

inline

Definition at line 139 of file newton_base.hh.

◆ getLastSimplifiedLinearization()

AbstractLinearization const & Kaskade::NewtonsMethod::getLastSimplifiedLinearization ( )

inline

Definition at line 141 of file newton_base.hh.

◆ getParameters()

virtual Parameters & Kaskade::NewtonsMethod::getParameters ( )

inlinevirtual

Reimplemented in Kaskade::DampedCovariantNewtonMethod.

Definition at line 115 of file newton_base.hh.

◆ getSearchDirection()

virtual void Kaskade::NewtonsMethod::getSearchDirection ( AbstractFunctionSpaceElement & direction )

inlinevirtual

Definition at line 127 of file newton_base.hh.

◆ initialize()

virtual void Kaskade::NewtonsMethod::initialize ( )

protectedvirtual

Called before Iteration.

Reimplemented from Kaskade::Algorithm.

Reimplemented in Kaskade::DampedCovariantNewtonMethod, and Kaskade::StateConstraintsNewtonMethod.

◆ initNewtonStep()

virtual void Kaskade::NewtonsMethod::initNewtonStep ( )

inlineprotectedvirtual

Reimplemented in Kaskade::DampedCovariantNewtonMethod, and Kaskade::StateConstraintsNewtonMethod.

Definition at line 152 of file newton_base.hh.

◆ logQuantities()

virtual void Kaskade::NewtonsMethod::logQuantities ( )

inlineprotectedvirtual

Performs logging of quantities.

Definition at line 150 of file newton_base.hh.

◆ maxSteps()

virtual double Kaskade::NewtonsMethod::maxSteps ( )

inlineprotectedvirtual

return the maximal number of steps

Definition at line 163 of file newton_base.hh.

◆ oneStep()

void Kaskade::NewtonsMethod::oneStep	(	AbstractFunctional *	f,
		AbstractLinearization *	l,
		AbstractFunctionSpaceElement &	x
	)

Perform one Newton step (which may be several trial steps, if damping is applied)

◆ oneStepWrapper()

int Kaskade::Algorithm::oneStepWrapper ( )

protectedinherited

Run one step of algorithm.

◆ performTiming()

void Kaskade::Algorithm::performTiming ( bool doit )

inlineinherited

Definition at line 181 of file algorithm_base.hh.

◆ predictNextDampingFactor()

virtual void Kaskade::NewtonsMethod::predictNextDampingFactor ( AbstractFunctionSpaceElement & correction )

inlineprotectedvirtual

Should compute a damping factor.

Reimplemented in Kaskade::DampedCovariantNewtonMethod, and Kaskade::StateConstraintsNewtonMethod.

Definition at line 158 of file newton_base.hh.

◆ regularityTest()

virtual RegularityTest Kaskade::NewtonsMethod::regularityTest ( double scalingFactor )

inlineprotectedvirtual

trial iterate = iterate + scalingFactor * correction if this was successful, return RegularityTest::Passed, otherwise (e.g. if scalingFactor is too small) RegularityTest::Failed false will lead to an unsuccessful exit of algorithm

Reimplemented in Kaskade::DampedCovariantNewtonMethod, and Kaskade::StateConstraintsNewtonMethod.

Definition at line 175 of file newton_base.hh.

◆ reportOnIteration()

void Kaskade::Algorithm::reportOnIteration ( int level )

inlineinherited

Definition at line 182 of file algorithm_base.hh.

◆ resetParameters()

void Kaskade::NewtonsMethod::resetParameters ( )

inline

Reset all algorithmic parameters to their default values.

Definition at line 121 of file newton_base.hh.

◆ resolve()

void Kaskade::NewtonsMethod::resolve	(	AbstractFunctionSpaceElement &	x,
		AbstractLinearization const &	l
	)

inline

Definition at line 105 of file newton_base.hh.

◆ setDesiredAccuracy()

void Kaskade::NewtonsMethod::setDesiredAccuracy ( double da )

inline

set the desired accuracy

Definition at line 117 of file newton_base.hh.

◆ setDesiredRelativeAccuracy()

virtual void Kaskade::NewtonsMethod::setDesiredRelativeAccuracy ( double ra )

inlinevirtual

set the desired accuracy

Reimplemented in Kaskade::DampedCovariantNewtonMethod, and Kaskade::StateConstraintsNewtonMethod.

Definition at line 119 of file newton_base.hh.

◆ solve()

void Kaskade::NewtonsMethod::solve	(	AbstractFunctional *	f,
		AbstractFunctionSpaceElement &	x
	)

Solve the system f=0 with starting value x. On (successful) exit, the solution is x, otherwise it is left unmodified.

◆ stepsPerformed()

int Kaskade::NewtonsMethod::stepsPerformed ( )

inline

Definition at line 123 of file newton_base.hh.

Referenced by Kaskade::InteriorPointSqrtModel::finalizeCorrector(), and Kaskade::InteriorPointSlopeEstimate::finalizeCorrector().

◆ terminationMessage()

virtual void Kaskade::NewtonsMethod::terminationMessage ( int flag )

protectedvirtual

Reimplemented from Kaskade::Algorithm.

◆ updateIterate()

virtual void Kaskade::NewtonsMethod::updateIterate	(	AbstractFunctionSpaceElement &	iterate,
		AbstractFunctionSpaceElement &	trialIterate,
		AbstractLinearization const &	lin
	)

protectedvirtual

update an accepted iterate, default: iterate=trialIterate

Reimplemented in Kaskade::DampedCovariantNewtonMethod, and Kaskade::StateConstraintsNewtonMethod.

Member Data Documentation

◆ chart

AbstractChart& Kaskade::NewtonsMethod::chart

protected

Definition at line 232 of file newton_base.hh.

Referenced by computeTrialIterate().

◆ correction

std::unique_ptr<AbstractFunctionSpaceElement> Kaskade::NewtonsMethod::correction

protected

Definition at line 236 of file newton_base.hh.

Referenced by Kaskade::StateConstraintsNewtonMethod::predictNextDampingFactor().

◆ functional

AbstractFunctional* Kaskade::NewtonsMethod::functional

protected

Definition at line 230 of file newton_base.hh.

◆ iterate

std::unique_ptr<AbstractFunctionSpaceElement> Kaskade::NewtonsMethod::iterate

protected

Definition at line 236 of file newton_base.hh.

◆ linearSolver

AbstractNewtonDirection& Kaskade::NewtonsMethod::linearSolver

protected

Definition at line 231 of file newton_base.hh.

Referenced by getSearchDirection(), and resolve().

◆ newtonLinearization

std::unique_ptr<AbstractLinearization> Kaskade::NewtonsMethod::newtonLinearization

protected

Definition at line 238 of file newton_base.hh.

Referenced by getLastLinearization(), and getSearchDirection().

◆ newtonPtr

AbstractLinearization* Kaskade::NewtonsMethod::newtonPtr

protected

Definition at line 240 of file newton_base.hh.

◆ norm

AbstractNorm& Kaskade::NewtonsMethod::norm

protected

Definition at line 233 of file newton_base.hh.

Referenced by Kaskade::StateConstraintsNewtonMethod::predictNextDampingFactor().

◆ p

Parameters& Kaskade::NewtonsMethod::p

protected

Definition at line 234 of file newton_base.hh.

Referenced by getParameters(), logQuantities(), maxSteps(), resetParameters(), resolve(), and setDesiredAccuracy().

◆ report

int Kaskade::Algorithm::report

protectedinherited

Definition at line 193 of file algorithm_base.hh.

Referenced by Kaskade::Algorithm::reportOnIteration().

◆ simplifiedLinearization

std::unique_ptr<AbstractLinearization> Kaskade::NewtonsMethod::simplifiedLinearization

protected

Definition at line 239 of file newton_base.hh.

Referenced by getLastSimplifiedLinearization().

◆ step

int Kaskade::NewtonsMethod::step

protected

Definition at line 242 of file newton_base.hh.

Referenced by stepsPerformed().

◆ trialIterate

std::unique_ptr<AbstractFunctionSpaceElement> Kaskade::NewtonsMethod::trialIterate

protected

Definition at line 236 of file newton_base.hh.

Referenced by computeTrialIterate().

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

newton_base.hh

Detailed Description

Classes

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Member Typedef Documentation

◆ Parameters

Constructor & Destructor Documentation

◆ ~NewtonsMethod()

◆ NewtonsMethod()

Member Function Documentation

◆ algorithmWrapper()

◆ changedGrid()

◆ computeTrialIterate()

◆ convergenceTest()

◆ dampingFactor()

◆ evaluateTrialIterate()

◆ finalize()

◆ getLastLinearization()

◆ getLastSimplifiedLinearization()

◆ getParameters()

◆ getSearchDirection()

◆ initialize()

◆ initNewtonStep()

◆ logQuantities()

◆ maxSteps()

◆ oneStep()

◆ oneStepWrapper()

◆ performTiming()

◆ predictNextDampingFactor()

◆ regularityTest()

◆ reportOnIteration()

◆ resetParameters()

◆ resolve()

◆ setDesiredAccuracy()

◆ setDesiredRelativeAccuracy()

◆ solve()

◆ stepsPerformed()

◆ terminationMessage()

◆ updateIterate()

Member Data Documentation

◆ chart

◆ correction

◆ functional

◆ iterate

◆ linearSolver

◆ newtonLinearization

◆ newtonPtr

◆ norm

◆ p

◆ report

◆ simplifiedLinearization

◆ step

◆ trialIterate