itk::PowellOptimizer Class Reference

#include <itkPowellOptimizer.h>

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.

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

Inheritance diagram for itk::PowellOptimizer:

Collaboration diagram for itk::PowellOptimizer:

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 const bool &	GetCatchGetValueException () const
virtual const unsigned int &	GetCurrentIteration () const
virtual const unsigned int &	GetCurrentLineIteration () const
virtual const double &	GetMetricWorstPossibleValue () const
const char *	GetNameOfClass () const override
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 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 CostFunctionType *	GetModifiableCostFunction ()
const char *	GetNameOfClass () const override
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 *cmd) const
unsigned long	AddObserver (const EventObject &event, std::function< void(const EventObject &)> function) const
LightObject::Pointer	CreateAnother () const override
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) const
void	SetDebug (bool debugFlag) const
void	SetReferenceCount (int) override
void	UnRegister () const noexcept override
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
Pointer	Clone () const
virtual void	Delete ()
virtual int	GetReferenceCount () const
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 val)
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 functionValueOfb, double fc, double *extX, double *extVal)
virtual void	BracketedLineOptimize (double ax, double bx, double cx, double fa, double functionValueOfb, 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 *x1, double *x2, double *x3, double *f1, double *f2, double *f3)
virtual void	LineBracket (double *x1, double *x2, double *x3, double *f1, double *f2, double *f3, 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 &timeStamp)
	~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

ConstPointer

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

Definition at line 69 of file itkPowellOptimizer.h.

CostFunctionPointer

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

Definition at line 81 of file itkPowellOptimizer.h.

CostFunctionType

using itk::PowellOptimizer::CostFunctionType = SingleValuedCostFunction

Type of the Cost Function

Definition at line 80 of file itkPowellOptimizer.h.

ParametersType

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

Definition at line 71 of file itkPowellOptimizer.h.

Pointer

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

Definition at line 68 of file itkPowellOptimizer.h.

Self

using itk::PowellOptimizer::Self = PowellOptimizer

Standard "Self" type alias.

Definition at line 66 of file itkPowellOptimizer.h.

Superclass

using itk::PowellOptimizer::Superclass = SingleValuedNonLinearOptimizer

Definition at line 67 of file itkPowellOptimizer.h.

Constructor & Destructor Documentation

PowellOptimizer() [1/2]

itk::PowellOptimizer::PowellOptimizer ( )

protected

PowellOptimizer() [2/2]

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

protected

~PowellOptimizer()

itk::PowellOptimizer::~PowellOptimizer ( )

overrideprotected

Member Function Documentation

BracketedLineOptimize() [1/2]

virtual void itk::PowellOptimizer::BracketedLineOptimize ( double  ax, double  bx, double  cx, double  fa, double  functionValueOfb, 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 optimizers from NRC.

BracketedLineOptimize() [2/2]

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

protectedvirtual

GetCatchGetValueException()

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

virtual

GetCurrentCost()

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

virtual

Return Current Value

GetCurrentIteration()

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

virtual

Return Current Iteration

GetCurrentLineIteration()

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

virtual

Get the current line search iteration

GetLineValue() [1/2]

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

GetLineValue() [2/2]

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

protected

GetMaximize()

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

virtual

Set if the Optimizer should Maximize the metric

GetMaximumIteration()

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

virtual

Set/Get maximum iteration limit.

GetMaximumLineIteration()

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

virtual

Set/Get the maximum number of line search iterations

GetMetricWorstPossibleValue()

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

virtual

GetNameOfClass()

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

overridevirtual

See also

LightObject::GetNameOfClass()

Reimplemented from itk::NonLinearOptimizer.

GetSpaceDimension()

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

protectedvirtual

GetStepLength()

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

GetStepTolerance()

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

GetStop()

virtual bool itk::PowellOptimizer::GetStop ( )

protectedvirtual

GetStopConditionDescription()

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

overridevirtual

Get the reason for termination

Reimplemented from itk::Optimizer.

GetValue()

MeasureType itk::PowellOptimizer::GetValue ( ) const

inline

Return Current Value

Definition at line 121 of file itkPowellOptimizer.h.

GetValueTolerance()

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

LineBracket() [1/2]

virtual void itk::PowellOptimizer::LineBracket ( double *  x1, double *  x2, double *  x3, double *  f1, double *  f2, double *  f3  )

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.

LineBracket() [2/2]

virtual void itk::PowellOptimizer::LineBracket ( double *  x1, double *  x2, double *  x3, double *  f1, double *  f2, double *  f3, ParametersType &  tempCoord  )

protectedvirtual

MaximizeOn()

virtual void itk::PowellOptimizer::MaximizeOn ( )

virtual

Set if the Optimizer should Maximize the metric

New()

static Pointer itk::PowellOptimizer::New ( )

static

Method for creation through the object factory.

PrintSelf()

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.

SetCatchGetValueException()

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

virtual

SetCurrentCost()

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

protectedvirtual

SetCurrentIteration()

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

protectedvirtual

SetCurrentLinePoint()

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.

SetLine()

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.

SetMaximize()

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

virtual

Set if the Optimizer should Maximize the metric

SetMaximumIteration()

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

virtual

Set/Get maximum iteration limit.

SetMaximumLineIteration()

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

virtual

Set/Get the maximum number of line search iterations

SetMetricWorstPossibleValue()

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

virtual

SetSpaceDimension()

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

inlineprotected

Definition at line 236 of file itkPowellOptimizer.h.

SetStepLength()

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

SetStepTolerance()

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

SetStop()

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

protectedvirtual

SetValueTolerance()

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

Shift()

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

StartOptimization()

void itk::PowellOptimizer::StartOptimization ( )

overridevirtual

Start optimization.

Reimplemented from itk::Optimizer.

StopOptimization()

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 141 of file itkPowellOptimizer.h.

Swap()

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

m_CatchGetValueException

bool itk::PowellOptimizer::m_CatchGetValueException {}

private

Definition at line 261 of file itkPowellOptimizer.h.

m_CurrentCost

MeasureType itk::PowellOptimizer::m_CurrentCost {}

private

Internal storage for the value type / used as a cache

Definition at line 277 of file itkPowellOptimizer.h.

m_CurrentIteration

unsigned int itk::PowellOptimizer::m_CurrentIteration {}

private

Current iteration

Definition at line 254 of file itkPowellOptimizer.h.

m_CurrentLineIteration

unsigned int itk::PowellOptimizer::m_CurrentLineIteration {}

private

Definition at line 255 of file itkPowellOptimizer.h.

m_LineDirection

vnl_vector<double> itk::PowellOptimizer::m_LineDirection {}

private

Definition at line 272 of file itkPowellOptimizer.h.

m_LineOrigin

ParametersType itk::PowellOptimizer::m_LineOrigin {}

private

Definition at line 271 of file itkPowellOptimizer.h.

m_Maximize

bool itk::PowellOptimizer::m_Maximize {}

private

Set if the Metric should be maximized: Default = False

Definition at line 265 of file itkPowellOptimizer.h.

m_MaximumIteration

unsigned int itk::PowellOptimizer::m_MaximumIteration {}

private

Maximum iteration limit.

Definition at line 258 of file itkPowellOptimizer.h.

m_MaximumLineIteration

unsigned int itk::PowellOptimizer::m_MaximumLineIteration {}

private

Definition at line 259 of file itkPowellOptimizer.h.

m_MetricWorstPossibleValue

double itk::PowellOptimizer::m_MetricWorstPossibleValue {}

private

Definition at line 262 of file itkPowellOptimizer.h.

m_SpaceDimension

unsigned int itk::PowellOptimizer::m_SpaceDimension {}

private

Definition at line 251 of file itkPowellOptimizer.h.

m_StepLength

double itk::PowellOptimizer::m_StepLength {}

private

The minimal size of search

Definition at line 268 of file itkPowellOptimizer.h.

m_StepTolerance

double itk::PowellOptimizer::m_StepTolerance {}

private

Definition at line 269 of file itkPowellOptimizer.h.

m_Stop

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 283 of file itkPowellOptimizer.h.

m_StopConditionDescription

std::ostringstream itk::PowellOptimizer::m_StopConditionDescription {}

private

Definition at line 285 of file itkPowellOptimizer.h.

m_ValueTolerance

double itk::PowellOptimizer::m_ValueTolerance {}

private

Definition at line 274 of file itkPowellOptimizer.h.

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

• itkPowellOptimizer.h