Implements Powell optimization using Brent line search. More...

#include <itkPowellOptimizer.h>

Inheritance diagram for itk::PowellOptimizer:

Collaboration diagram for itk::PowellOptimizer:

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 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
Static Public Member Functions
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, ParametersType &tempCoord) const
double	GetLineValue (double x) const
virtual unsigned int	GetSpaceDimension ()
virtual bool	GetStop ()
virtual void	LineBracket (double ax, double bx, double cx, double fa, double fb, double fc, ParametersType &tempCoord)
virtual void	LineBracket (double ax, double bx, double cx, double fa, double fb, double fc)
	PowellOptimizer (const PowellOptimizer &)
	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 ()
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

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.

Member Typedef Documentation

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

Reimplemented from itk::SingleValuedNonLinearOptimizer.

Reimplemented in itk::FRPROptimizer.

Definition at line 69 of file itkPowellOptimizer.h.

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

Reimplemented from itk::SingleValuedNonLinearOptimizer.

Reimplemented in itk::FRPROptimizer.

Definition at line 82 of file itkPowellOptimizer.h.

typedef SingleValuedCostFunction itk::PowellOptimizer::CostFunctionType

Type of the Cost Function

Reimplemented from itk::SingleValuedNonLinearOptimizer.

Reimplemented in itk::FRPROptimizer.

Definition at line 78 of file itkPowellOptimizer.h.

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

Parameters type. It defines a position in the optimization search space.

Reimplemented from itk::SingleValuedNonLinearOptimizer.

Reimplemented in itk::FRPROptimizer.

Definition at line 72 of file itkPowellOptimizer.h.

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

Reimplemented from itk::SingleValuedNonLinearOptimizer.

Reimplemented in itk::FRPROptimizer.

Definition at line 68 of file itkPowellOptimizer.h.

typedef PowellOptimizer itk::PowellOptimizer::Self

Standard "Self" typedef.

Reimplemented from itk::SingleValuedNonLinearOptimizer.

Reimplemented in itk::FRPROptimizer.

Definition at line 66 of file itkPowellOptimizer.h.

typedef SingleValuedNonLinearOptimizer itk::PowellOptimizer::Superclass

Reimplemented from itk::SingleValuedNonLinearOptimizer.

Reimplemented in itk::FRPROptimizer.

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 ( ) [protected, virtual]

Member Function Documentation

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

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
	)		`[protected, virtual]`

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::SingleValuedNonLinearOptimizer.

Reimplemented in itk::FRPROptimizer.

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,
		ParametersType &	tempCoord
	)		const `[protected]`

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

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 ( ) [protected, virtual]

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 ( ) [protected, virtual]

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
	)		`[protected, virtual]`

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
	)		`[protected, virtual]`

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.

Reimplemented from itk::SingleValuedNonLinearOptimizer.

Reimplemented in itk::FRPROptimizer.

void itk::PowellOptimizer::PrintSelf	(	std::ostream &	os,
		Indent	indent
	)		const `[protected, virtual]`

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::SingleValuedNonLinearOptimizer.

Reimplemented in itk::FRPROptimizer.

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

virtual void itk::PowellOptimizer::SetCurrentCost ( double _arg ) [protected, virtual]

virtual void itk::PowellOptimizer::SetCurrentIteration ( unsigned int _arg ) [protected, virtual]

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 ) [inline, protected]

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 ) [protected, virtual]

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.

Reimplemented in itk::FRPROptimizer.

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 234 of file itkPowellOptimizer.h.

MeasureType itk::PowellOptimizer::m_CurrentCost [private]

Internal storage for the value type / used as a cache

Definition at line 250 of file itkPowellOptimizer.h.

unsigned int itk::PowellOptimizer::m_CurrentIteration [private]

Current iteration

Definition at line 227 of file itkPowellOptimizer.h.

unsigned int itk::PowellOptimizer::m_CurrentLineIteration [private]

Definition at line 228 of file itkPowellOptimizer.h.

vnl_vector< double > itk::PowellOptimizer::m_LineDirection [private]

Definition at line 245 of file itkPowellOptimizer.h.

ParametersType itk::PowellOptimizer::m_LineOrigin [private]

Definition at line 244 of file itkPowellOptimizer.h.

bool itk::PowellOptimizer::m_Maximize [private]

Set if the Metric should be maximized: Default = False

Definition at line 238 of file itkPowellOptimizer.h.

unsigned int itk::PowellOptimizer::m_MaximumIteration [private]

Maximum iteration limit.

Definition at line 231 of file itkPowellOptimizer.h.

unsigned int itk::PowellOptimizer::m_MaximumLineIteration [private]

Definition at line 232 of file itkPowellOptimizer.h.

double itk::PowellOptimizer::m_MetricWorstPossibleValue [private]

Definition at line 235 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 241 of file itkPowellOptimizer.h.

double itk::PowellOptimizer::m_StepTolerance [private]

Definition at line 242 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 256 of file itkPowellOptimizer.h.

std::ostringstream itk::PowellOptimizer::m_StopConditionDescription [private]

Definition at line 258 of file itkPowellOptimizer.h.

double itk::PowellOptimizer::m_ValueTolerance [private]

Definition at line 247 of file itkPowellOptimizer.h.

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

itkPowellOptimizer.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation