itk::PowellOptimizer Class Reference

#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 61 of file itkPowellOptimizer.h.

Public Types
typedef SmartPointer< const Self >	ConstPointer
typedef CostFunctionType::Pointer	CostFunctionPointer
typedef SingleValuedCostFunction	CostFunctionType
typedef SingleValuedNonLinearOptimizer::ParametersType	ParametersType
typedef SmartPointer< Self >	Pointer
typedef PowellOptimizer	Self
typedef SingleValuedNonLinearOptimizer	Superclass
Public Types inherited from itk::SingleValuedNonLinearOptimizer
typedef SmartPointer< const Self >	ConstPointer
typedef CostFunctionType::Pointer	CostFunctionPointer
typedef SingleValuedCostFunction	CostFunctionType
typedef CostFunctionType::DerivativeType	DerivativeType
typedef CostFunctionType::MeasureType	MeasureType
typedef Superclass::ParametersType	ParametersType
typedef SmartPointer< Self >	Pointer
typedef SingleValuedNonLinearOptimizer	Self
typedef NonLinearOptimizer	Superclass
Public Types inherited from itk::NonLinearOptimizer
typedef SmartPointer< const Self >	ConstPointer
typedef Superclass::ParametersType	ParametersType
typedef SmartPointer< Self >	Pointer
typedef Superclass::ScalesType	ScalesType
typedef NonLinearOptimizer	Self
typedef Optimizer	Superclass
Public Types inherited from itk::Optimizer
typedef SmartPointer< const Self >	ConstPointer
typedef OptimizerParameters < double >	ParametersType
typedef SmartPointer< Self >	Pointer
typedef Array< double >	ScalesType
typedef Optimizer	Self
typedef Object	Superclass
Public Types inherited from itk::Object
typedef SmartPointer< const Self >	ConstPointer
typedef SmartPointer< Self >	Pointer
typedef Object	Self
typedef LightObject	Superclass
Public Types inherited from itk::LightObject
typedef SmartPointer< const Self >	ConstPointer
typedef SmartPointer< Self >	Pointer
typedef LightObject	Self

Public Member Functions
virtual ::itk::LightObject::Pointer	CreateAnother (void) const
virtual const bool &	GetCatchGetValueException ()
virtual const unsigned int &	GetCurrentIteration ()
virtual const unsigned int &	GetCurrentLineIteration ()
virtual const double &	GetMetricWorstPossibleValue ()
virtual const char *	GetNameOfClass () const
const std::string	GetStopConditionDescription () const
virtual void	SetCatchGetValueException (bool _arg)
virtual void	SetMetricWorstPossibleValue (double _arg)
void	StartOptimization ()
void	StopOptimization ()
virtual void	SetMaximize (bool _arg)
virtual void	MaximizeOn ()
virtual void	MaximizeOff ()
virtual const bool &	GetMaximize ()
virtual void	SetMaximumIteration (unsigned int _arg)
virtual const unsigned int &	GetMaximumIteration ()
virtual void	SetMaximumLineIteration (unsigned int _arg)
virtual unsigned int	GetMaximumLineIteration () const
virtual void	SetStepLength (double _arg)
virtual const double &	GetStepLength ()
virtual void	SetStepTolerance (double _arg)
virtual const double &	GetStepTolerance ()
virtual void	SetValueTolerance (double _arg)
virtual const double &	GetValueTolerance ()
virtual const MeasureType &	GetCurrentCost ()
MeasureType	GetValue () const
Public Member Functions inherited from itk::SingleValuedNonLinearOptimizer
virtual ::itk::LightObject::Pointer	CreateAnother (void) const
virtual const CostFunctionType *	GetCostFunction () const
virtual CostFunctionType *	GetModifiableCostFunction ()
MeasureType	GetValue (const ParametersType &parameters) const
virtual void	SetCostFunction (CostFunctionType *costFunction)

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
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
virtual	~PowellOptimizer ()
Protected Member Functions inherited from itk::SingleValuedNonLinearOptimizer
void	PrintSelf (std::ostream &os, Indent indent) const
	SingleValuedNonLinearOptimizer ()
virtual	~SingleValuedNonLinearOptimizer ()
Protected Member Functions inherited from itk::NonLinearOptimizer
	NonLinearOptimizer ()
virtual	~NonLinearOptimizer ()
Protected Member Functions inherited from itk::Optimizer
	Optimizer ()
virtual void	SetCurrentPosition (const ParametersType &param)
virtual	~Optimizer ()
Protected Member Functions inherited from itk::Object
	Object ()
bool	PrintObservers (std::ostream &os, Indent indent) const
virtual void	SetTimeStamp (const TimeStamp &time)
virtual	~Object ()
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 Types inherited from itk::LightObject
typedef int	InternalReferenceCountType
Protected Attributes inherited from itk::SingleValuedNonLinearOptimizer
CostFunctionPointer	m_CostFunction

Member Typedef Documentation

typedef SmartPointer< const Self > itk::PowellOptimizer::ConstPointer

Definition at line 69 of file itkPowellOptimizer.h.

typedef CostFunctionType::Pointer itk::PowellOptimizer::CostFunctionPointer

Definition at line 82 of file itkPowellOptimizer.h.

typedef SingleValuedCostFunction itk::PowellOptimizer::CostFunctionType

Type of the Cost Function

Definition at line 78 of file itkPowellOptimizer.h.

typedef SingleValuedNonLinearOptimizer::ParametersType itk::PowellOptimizer::ParametersType

Definition at line 72 of file itkPowellOptimizer.h.

typedef SmartPointer< Self > itk::PowellOptimizer::Pointer

Definition at line 68 of file itkPowellOptimizer.h.

typedef PowellOptimizer itk::PowellOptimizer::Self

Standard "Self" typedef.

Definition at line 66 of file itkPowellOptimizer.h.

typedef SingleValuedNonLinearOptimizer itk::PowellOptimizer::Superclass

Definition at line 67 of file itkPowellOptimizer.h.

Constructor & Destructor Documentation

itk::PowellOptimizer::PowellOptimizer ( )

protected

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

protected

virtual itk::PowellOptimizer::~PowellOptimizer ( )

protectedvirtual

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 ( void  ) 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 ( )

virtual

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

virtual

Return Current Value

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

virtual

Return Current Iteration

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

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 ( )

virtual

Set if the Optimizer should Maximize the metric

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

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 ( )

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 ( )

virtual

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

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

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

virtual

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 ( )

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

protectedvirtual

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 ( )

virtual

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