#include <itkPowellOptimizer.h>

Inheritance diagram for itk::PowellOptimizer:

Collaboration diagram for itk::PowellOptimizer:

Detailed Description

Implements Powell optimization using Brent line search.

The code in this class was adapted from the Wikipedia and the netlib.org zeroin function.

http://www.netlib.org/go/zeroin.f http://en.wikipedia.org/wiki/Brent_method http://en.wikipedia.org/wiki/Golden_section_search

This optimizer needs a cost function. Partial derivatives of that function are not required.

For an N-dimensional parameter space, each iteration minimizes(maximizes) the function in N (initially orthogonal) directions. Typically only 2-5 iterations are required. If gradients are available, consider a conjugate gradient line search strategy.

The SetStepLength determines the initial distance to step in a line direction when bounding the minimum (using bracketing triple spaced using a golden search strategy).

The StepTolerance terminates optimization when the parameter values are known to be within this (scaled) distance of the local extreme.

The ValueTolerance terminates optimization when the cost function values at the current parameters and at the local extreme are likely (within a second order approximation) to be within this is tolerance.

Definition at line 62 of file itkPowellOptimizer.h.

Public Types
using	ConstPointer = SmartPointer< const Self >

using	CostFunctionPointer = CostFunctionType::Pointer

using	CostFunctionType = SingleValuedCostFunction

using	ParametersType = SingleValuedNonLinearOptimizer::ParametersType

using	Pointer = SmartPointer< Self >

using	Self = PowellOptimizer

using	Superclass = SingleValuedNonLinearOptimizer

Public Types inherited from itk::SingleValuedNonLinearOptimizer
using	ConstPointer = SmartPointer< const Self >

using	CostFunctionPointer = CostFunctionType::Pointer

using	CostFunctionType = SingleValuedCostFunction

using	DerivativeType = CostFunctionType::DerivativeType

using	MeasureType = CostFunctionType::MeasureType

using	ParametersType = Superclass::ParametersType

using	Pointer = SmartPointer< Self >

using	Self = SingleValuedNonLinearOptimizer

using	Superclass = NonLinearOptimizer

Public Types inherited from itk::NonLinearOptimizer
using	ConstPointer = SmartPointer< const Self >

using	ParametersType = Superclass::ParametersType

using	Pointer = SmartPointer< Self >

using	ScalesType = Superclass::ScalesType

using	Self = NonLinearOptimizer

using	Superclass = Optimizer

Public Types inherited from itk::Optimizer
using	ConstPointer = SmartPointer< const Self >

using	ParametersType = OptimizerParameters< double >

using	Pointer = SmartPointer< Self >

using	ScalesType = Array< double >

using	Self = Optimizer

using	Superclass = Object

Public Types inherited from itk::Object
using	ConstPointer = SmartPointer< const Self >

using	Pointer = SmartPointer< Self >

using	Self = Object

using	Superclass = LightObject

Public Types inherited from itk::LightObject
using	ConstPointer = SmartPointer< const Self >

using	Pointer = SmartPointer< Self >

using	Self = LightObject

Public Member Functions
virtual ::itk::LightObject::Pointer	CreateAnother () const

virtual const bool &	GetCatchGetValueException () const

virtual const unsigned int &	GetCurrentIteration () const

virtual const unsigned int &	GetCurrentLineIteration () const

virtual const double &	GetMetricWorstPossibleValue () const

virtual const char *	GetNameOfClass () const

const std::string	GetStopConditionDescription () const override

virtual void	SetCatchGetValueException (bool _arg)

virtual void	SetMetricWorstPossibleValue (double _arg)

void	StartOptimization () override

void	StopOptimization ()


virtual void	SetMaximize (bool _arg)

virtual void	MaximizeOn ()

virtual void	MaximizeOff ()

virtual const bool &	GetMaximize () const


virtual void	SetMaximumIteration (unsigned int _arg)

virtual const unsigned int &	GetMaximumIteration () const


virtual void	SetMaximumLineIteration (unsigned int _arg)

virtual unsigned int	GetMaximumLineIteration () const


virtual void	SetStepLength (double _arg)

virtual const double &	GetStepLength () const


virtual void	SetStepTolerance (double _arg)

virtual const double &	GetStepTolerance () const


virtual void	SetValueTolerance (double _arg)

virtual const double &	GetValueTolerance () const


virtual const MeasureType &	GetCurrentCost () const

MeasureType	GetValue () const

Public Member Functions inherited from itk::SingleValuedNonLinearOptimizer
virtual ::itk::LightObject::Pointer	CreateAnother () const

virtual const CostFunctionType *	GetCostFunction () const

virtual CostFunctionType *	GetModifiableCostFunction ()

MeasureType	GetValue (const ParametersType &parameters) const

virtual void	SetCostFunction (CostFunctionType *costFunction)

Public Member Functions inherited from itk::Optimizer
virtual const ParametersType &	GetCurrentPosition () const

virtual const ParametersType &	GetInitialPosition () const

virtual void	SetInitialPosition (const ParametersType &param)

void	SetScales (const ScalesType &scales)

virtual const ScalesType &	GetScales () const

virtual const ScalesType &	GetInverseScales () const

Public Member Functions inherited from itk::Object
unsigned long	AddObserver (const EventObject &event, Command *)

unsigned long	AddObserver (const EventObject &event, Command *) const

virtual void	DebugOff () const

virtual void	DebugOn () const

Command *	GetCommand (unsigned long tag)

bool	GetDebug () const

MetaDataDictionary &	GetMetaDataDictionary ()

const MetaDataDictionary &	GetMetaDataDictionary () const

virtual ModifiedTimeType	GetMTime () const

virtual const TimeStamp &	GetTimeStamp () const

bool	HasObserver (const EventObject &event) const

void	InvokeEvent (const EventObject &)

void	InvokeEvent (const EventObject &) const

virtual void	Modified () const

void	Register () const override

void	RemoveAllObservers ()

void	RemoveObserver (unsigned long tag)

void	SetDebug (bool debugFlag) const

void	SetReferenceCount (int) override

void	UnRegister () const noexceptoverride

void	SetMetaDataDictionary (const MetaDataDictionary &rhs)

void	SetMetaDataDictionary (MetaDataDictionary &&rrhs)

virtual void	SetObjectName (std::string _arg)

virtual const std::string &	GetObjectName () const

Public Member Functions inherited from itk::LightObject
virtual void	Delete ()

virtual int	GetReferenceCount () const

	itkCloneMacro (Self)

void	Print (std::ostream &os, Indent indent=0) const

Static Public Member Functions
static Pointer	New ()

Static Public Member Functions inherited from itk::SingleValuedNonLinearOptimizer
static Pointer	New ()

Static Public Member Functions inherited from itk::NonLinearOptimizer
static Pointer	New ()

Static Public Member Functions inherited from itk::Optimizer
static Pointer	New ()

Static Public Member Functions inherited from itk::Object
static bool	GetGlobalWarningDisplay ()

static void	GlobalWarningDisplayOff ()

static void	GlobalWarningDisplayOn ()

static Pointer	New ()

static void	SetGlobalWarningDisplay (bool flag)

Static Public Member Functions inherited from itk::LightObject
static void	BreakOnError ()

static Pointer	New ()

Protected Member Functions
virtual void	BracketedLineOptimize (double ax, double bx, double cx, double fa, double fb, double fc, double extX, double extVal)

virtual void	BracketedLineOptimize (double ax, double bx, double cx, double fa, double fb, double fc, double extX, double extVal, ParametersType &tempCoord)

double	GetLineValue (double x) const

double	GetLineValue (double x, ParametersType &tempCoord) const

virtual unsigned int	GetSpaceDimension ()

virtual bool	GetStop ()

virtual void	LineBracket (double ax, double bx, double cx, double fa, double fb, double fc)

virtual void	LineBracket (double ax, double bx, double cx, double fa, double fb, double fc, ParametersType &tempCoord)

	PowellOptimizer ()

	PowellOptimizer (const PowellOptimizer &)

void	PrintSelf (std::ostream &os, Indent indent) const override

virtual void	SetCurrentCost (double _arg)

virtual void	SetCurrentIteration (unsigned int _arg)

void	SetCurrentLinePoint (double x, double fx)

void	SetLine (const ParametersType &origin, const vnl_vector< double > &direction)

void	SetSpaceDimension (unsigned int dim)

virtual void	SetStop (bool _arg)

void	Shift (double a, double b, double *c, double d) const

void	Swap (double a, double b) const

	~PowellOptimizer () override

Protected Member Functions inherited from itk::SingleValuedNonLinearOptimizer
void	PrintSelf (std::ostream &os, Indent indent) const override

	SingleValuedNonLinearOptimizer ()

	~SingleValuedNonLinearOptimizer () override=default

Protected Member Functions inherited from itk::NonLinearOptimizer
	NonLinearOptimizer ()=default

	~NonLinearOptimizer () override

Protected Member Functions inherited from itk::Optimizer
	Optimizer ()

virtual void	SetCurrentPosition (const ParametersType &param)

	~Optimizer () override=default

Protected Member Functions inherited from itk::Object
	Object ()

bool	PrintObservers (std::ostream &os, Indent indent) const

virtual void	SetTimeStamp (const TimeStamp &time)

	~Object () override

Protected Member Functions inherited from itk::LightObject
virtual LightObject::Pointer	InternalClone () const

	LightObject ()

virtual void	PrintHeader (std::ostream &os, Indent indent) const

virtual void	PrintTrailer (std::ostream &os, Indent indent) const

virtual	~LightObject ()

Private Attributes
bool	m_CatchGetValueException

MeasureType	m_CurrentCost

unsigned int	m_CurrentIteration

unsigned int	m_CurrentLineIteration

vnl_vector< double >	m_LineDirection

ParametersType	m_LineOrigin

bool	m_Maximize

unsigned int	m_MaximumIteration

unsigned int	m_MaximumLineIteration

double	m_MetricWorstPossibleValue

unsigned int	m_SpaceDimension

double	m_StepLength

double	m_StepTolerance

bool	m_Stop

std::ostringstream	m_StopConditionDescription

double	m_ValueTolerance

Additional Inherited Members
Protected Attributes inherited from itk::SingleValuedNonLinearOptimizer
CostFunctionPointer	m_CostFunction

Protected Attributes inherited from itk::Optimizer
ParametersType	m_CurrentPosition

bool	m_ScalesInitialized { false }

Protected Attributes inherited from itk::LightObject
std::atomic< int >	m_ReferenceCount

Member Typedef Documentation

using itk::PowellOptimizer::ConstPointer = SmartPointer< const Self >

Definition at line 70 of file itkPowellOptimizer.h.

using itk::PowellOptimizer::CostFunctionPointer = CostFunctionType::Pointer

Definition at line 82 of file itkPowellOptimizer.h.

using itk::PowellOptimizer::CostFunctionType = SingleValuedCostFunction

Type of the Cost Function

Definition at line 81 of file itkPowellOptimizer.h.

using itk::PowellOptimizer::ParametersType = SingleValuedNonLinearOptimizer::ParametersType

Definition at line 72 of file itkPowellOptimizer.h.

using itk::PowellOptimizer::Pointer = SmartPointer< Self >

Definition at line 69 of file itkPowellOptimizer.h.

using itk::PowellOptimizer::Self = PowellOptimizer

Standard "Self" type alias.

Definition at line 67 of file itkPowellOptimizer.h.

using itk::PowellOptimizer::Superclass = SingleValuedNonLinearOptimizer

Definition at line 68 of file itkPowellOptimizer.h.

Constructor & Destructor Documentation

itk::PowellOptimizer::PowellOptimizer ( )

protected

itk::PowellOptimizer::PowellOptimizer ( const PowellOptimizer & )

protected

itk::PowellOptimizer::~PowellOptimizer ( )

overrideprotected

Member Function Documentation

virtual void itk::PowellOptimizer::BracketedLineOptimize	(	double	ax,
		double	bx,
		double	cx,
		double	fa,
		double	fb,
		double	fc,
		double *	extX,
		double *	extVal
	)

protectedvirtual

Given a bracketing triple of points and their function values, returns a bounded extreme. These values are in parameter space, along the current line and wrt the current origin set via SetLine. Optimization terminates based on MaximumIteration, StepTolerance, or ValueTolerance. Implemented as Brent line optimers from NRC.

virtual void itk::PowellOptimizer::BracketedLineOptimize	(	double	ax,
		double	bx,
		double	cx,
		double	fa,
		double	fb,
		double	fc,
		double *	extX,
		double *	extVal,
		ParametersType &	tempCoord
	)

protectedvirtual

virtual::itk::LightObject::Pointer itk::PowellOptimizer::CreateAnother ( ) const

virtual

Create an object from an instance, potentially deferring to a factory. This method allows you to create an instance of an object that is exactly the same type as the referring object. This is useful in cases where an object has been cast back to a base class.

Reimplemented from itk::NonLinearOptimizer.

virtual const bool& itk::PowellOptimizer::GetCatchGetValueException ( ) const

virtual

virtual const MeasureType& itk::PowellOptimizer::GetCurrentCost ( ) const

virtual

Return Current Value

virtual const unsigned int& itk::PowellOptimizer::GetCurrentIteration ( ) const

virtual

Return Current Iteration

virtual const unsigned int& itk::PowellOptimizer::GetCurrentLineIteration ( ) const

virtual

Get the current line search iteration

double itk::PowellOptimizer::GetLineValue ( double x ) const

protected

Get the value of the n-dimensional cost function at this scalar step distance along the current line direction from the current line origin. Line origin and distances are set via SetLine

double itk::PowellOptimizer::GetLineValue	(	double	x,
		ParametersType &	tempCoord
	)		const

protected

virtual const bool& itk::PowellOptimizer::GetMaximize ( ) const

virtual

Set if the Optimizer should Maximize the metric

virtual const unsigned int& itk::PowellOptimizer::GetMaximumIteration ( ) const

virtual

Set/Get maximum iteration limit.

virtual unsigned int itk::PowellOptimizer::GetMaximumLineIteration ( ) const

virtual

Set/Get the maximum number of line search iterations

virtual const double& itk::PowellOptimizer::GetMetricWorstPossibleValue ( ) const

virtual

virtual const char* itk::PowellOptimizer::GetNameOfClass ( ) const

virtual

Run-time type information (and related methods).

Reimplemented from itk::SingleValuedNonLinearOptimizer.

Reimplemented in itk::FRPROptimizer.

virtual unsigned int itk::PowellOptimizer::GetSpaceDimension ( )

protectedvirtual

virtual const double& itk::PowellOptimizer::GetStepLength ( ) const

virtual

Set/Get StepLength for the (scaled) spacing of the sampling of parameter space while bracketing the extremum

virtual const double& itk::PowellOptimizer::GetStepTolerance ( ) const

virtual

Set/Get StepTolerance. Once the local extreme is known to be within this distance of the current parameter values, optimization terminates

virtual bool itk::PowellOptimizer::GetStop ( )

protectedvirtual

const std::string itk::PowellOptimizer::GetStopConditionDescription ( ) const

overridevirtual

Get the reason for termination

Reimplemented from itk::Optimizer.

MeasureType itk::PowellOptimizer::GetValue ( ) const

inline

Return Current Value

Definition at line 121 of file itkPowellOptimizer.h.

virtual const double& itk::PowellOptimizer::GetValueTolerance ( ) const

virtual

Set/Get ValueTolerance. Once this current cost function value is known to be within this tolerance of the cost function value at the local extreme, optimization terminates

virtual void itk::PowellOptimizer::LineBracket	(	double *	ax,
		double *	bx,
		double *	cx,
		double *	fa,
		double *	fb,
		double *	fc
	)

protectedvirtual

The LineBracket routine from NRC. Later reimplemented from the description of the method available in the Wikipedia.

Uses current origin and line direction (from SetLine) to find a triple of points (ax, bx, cx) that bracket the extreme "near" the origin. Search first considers the point StepLength distance from ax.

IMPORTANT: The value of ax and the value of the function at ax (i.e., fa), must both be provided to this function.

virtual void itk::PowellOptimizer::LineBracket	(	double *	ax,
		double *	bx,
		double *	cx,
		double *	fa,
		double *	fb,
		double *	fc,
		ParametersType &	tempCoord
	)

protectedvirtual

virtual void itk::PowellOptimizer::MaximizeOff ( )

virtual

Set if the Optimizer should Maximize the metric

virtual void itk::PowellOptimizer::MaximizeOn ( )

virtual

Set if the Optimizer should Maximize the metric

static Pointer itk::PowellOptimizer::New ( )

static

Method for creation through the object factory.

void itk::PowellOptimizer::PrintSelf	(	std::ostream &	os,
		Indent	indent
	)		const

overrideprotectedvirtual

Methods invoked by Print() to print information about the object including superclasses. Typically not called by the user (use Print() instead) but used in the hierarchical print process to combine the output of several classes.

Reimplemented from itk::Optimizer.

virtual void itk::PowellOptimizer::SetCatchGetValueException ( bool _arg )

virtual

virtual void itk::PowellOptimizer::SetCurrentCost ( double _arg )

protectedvirtual

virtual void itk::PowellOptimizer::SetCurrentIteration ( unsigned int _arg )

protectedvirtual

void itk::PowellOptimizer::SetCurrentLinePoint	(	double	x,
		double	fx
	)

protected

Set the given scalar step distance (x) and function value (fx) as the "best-so-far" optimizer values.

void itk::PowellOptimizer::SetLine	(	const ParametersType &	origin,
		const vnl_vector< double > &	direction
	)

protected

Used to specify the line direction through the n-dimensional parameter space the is currently being bracketed and optimized.

virtual void itk::PowellOptimizer::SetMaximize ( bool _arg )

virtual

Set if the Optimizer should Maximize the metric

virtual void itk::PowellOptimizer::SetMaximumIteration ( unsigned int _arg )

virtual

Set/Get maximum iteration limit.

virtual void itk::PowellOptimizer::SetMaximumLineIteration ( unsigned int _arg )

virtual

Set/Get the maximum number of line search iterations

virtual void itk::PowellOptimizer::SetMetricWorstPossibleValue ( double _arg )

virtual

void itk::PowellOptimizer::SetSpaceDimension ( unsigned int dim )

inlineprotected

Definition at line 210 of file itkPowellOptimizer.h.

virtual void itk::PowellOptimizer::SetStepLength ( double _arg )

virtual

Set/Get StepLength for the (scaled) spacing of the sampling of parameter space while bracketing the extremum

virtual void itk::PowellOptimizer::SetStepTolerance ( double _arg )

virtual

Set/Get StepTolerance. Once the local extreme is known to be within this distance of the current parameter values, optimization terminates

virtual void itk::PowellOptimizer::SetStop ( bool _arg )

protectedvirtual

virtual void itk::PowellOptimizer::SetValueTolerance ( double _arg )

virtual

Set/Get ValueTolerance. Once this current cost function value is known to be within this tolerance of the cost function value at the local extreme, optimization terminates

void itk::PowellOptimizer::Shift	(	double *	a,
		double *	b,
		double *	c,
		double	d
	)		const

protected

Used in bracketing the extreme along the current line. Adapted from NRC

void itk::PowellOptimizer::StartOptimization ( )

overridevirtual

Start optimization.

Reimplemented from itk::Optimizer.

void itk::PowellOptimizer::StopOptimization ( )

inline

When users call StartOptimization, this value will be set false. By calling StopOptimization, this flag will be set true, and optimization will stop at the next iteration.

Definition at line 136 of file itkPowellOptimizer.h.

void itk::PowellOptimizer::Swap	(	double *	a,
		double *	b
	)		const

protected

Used in bracketing the extreme along the current line. Adapted from NRC

Member Data Documentation

bool itk::PowellOptimizer::m_CatchGetValueException

private

Definition at line 235 of file itkPowellOptimizer.h.

MeasureType itk::PowellOptimizer::m_CurrentCost

private

Internal storage for the value type / used as a cache

Definition at line 251 of file itkPowellOptimizer.h.

unsigned int itk::PowellOptimizer::m_CurrentIteration

private

Current iteration

Definition at line 228 of file itkPowellOptimizer.h.

unsigned int itk::PowellOptimizer::m_CurrentLineIteration

private

Definition at line 229 of file itkPowellOptimizer.h.

vnl_vector< double > itk::PowellOptimizer::m_LineDirection

private

Definition at line 246 of file itkPowellOptimizer.h.

ParametersType itk::PowellOptimizer::m_LineOrigin

private

Definition at line 245 of file itkPowellOptimizer.h.

bool itk::PowellOptimizer::m_Maximize

private

Set if the Metric should be maximized: Default = False

Definition at line 239 of file itkPowellOptimizer.h.

unsigned int itk::PowellOptimizer::m_MaximumIteration

private

Maximum iteration limit.

Definition at line 232 of file itkPowellOptimizer.h.

unsigned int itk::PowellOptimizer::m_MaximumLineIteration

private

Definition at line 233 of file itkPowellOptimizer.h.

double itk::PowellOptimizer::m_MetricWorstPossibleValue

private

Definition at line 236 of file itkPowellOptimizer.h.

unsigned int itk::PowellOptimizer::m_SpaceDimension

private

Definition at line 222 of file itkPowellOptimizer.h.

double itk::PowellOptimizer::m_StepLength

private

The minimal size of search

Definition at line 242 of file itkPowellOptimizer.h.

double itk::PowellOptimizer::m_StepTolerance

private

Definition at line 243 of file itkPowellOptimizer.h.

bool itk::PowellOptimizer::m_Stop

private

this is user-settable flag to stop optimization. when users call StartOptimization, this value will be set false. By calling StopOptimization, this flag will be set true, and optimization will stop at the next iteration.

Definition at line 257 of file itkPowellOptimizer.h.

std::ostringstream itk::PowellOptimizer::m_StopConditionDescription

private

Definition at line 259 of file itkPowellOptimizer.h.

double itk::PowellOptimizer::m_ValueTolerance

private

Definition at line 248 of file itkPowellOptimizer.h.

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

itkPowellOptimizer.h

Detailed Description

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Private Attributes

Additional Inherited Members

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation