itk::FRPROptimizer Class Reference
[Numerics]

#include <itkFRPROptimizer.h>

Inheritance diagram for itk::FRPROptimizer:

[legend]Collaboration diagram for itk::FRPROptimizer:

[legend]List of all members.

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Detailed Description

Implements Fletch-Reeves & Polak-Ribiere optimization using dBrent line search - adapted from Numerical Recipes in C (first edition).

This optimizer needs a cost function. This optimizer needs to be able to compute partial derivatives of the cost function with respect to each parameter.

The SetStepLength determines the initial distance to step in a line direction when bounding the minimum (using bracketing triple spaced using a derivative-based 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.

Optimizers

Definition at line 50 of file itkFRPROptimizer.h.

Public Types
typedef SmartPointer< const Self >	ConstPointer
typedef CostFunctionType::Pointer	CostFunctionPointer
typedef SingleValuedCostFunction	CostFunctionType
typedef CostFunctionType::DerivativeType	DerivativeType
typedef CostFunctionType::MeasureType	MeasureType
typedef SingleValuedNonLinearOptimizer::ParametersType	ParametersType
typedef SmartPointer< Self >	Pointer
typedef Superclass::ScalesType	ScalesType
typedef FRPROptimizer	Self
typedef PowellOptimizer	Superclass
Public Member Functions
virtual LightObject::Pointer	CreateAnother () const
virtual void	DebugOff () const
virtual void	DebugOn () const
virtual void	Delete ()
Command *	GetCommand (unsigned long tag)
virtual const CostFunctionType *	GetCostFunction ()
Return Current Value *virtual const MeasureType &	GetCurrentCost ()
virtual const unsigned int &	GetCurrentIteration ()
virtual const unsigned int &	GetCurrentLineIteration ()
virtual const ParametersType &	GetCurrentPosition ()
bool	GetDebug () const
virtual const ParametersType &	GetInitialPosition ()
virtual const bool &	GetMaximize ()
virtual const unsigned int &	GetMaximumIteration ()
virtual unsigned int	GetMaximumLineIteration () const
const MetaDataDictionary &	GetMetaDataDictionary (void) const
MetaDataDictionary &	GetMetaDataDictionary (void)
virtual unsigned long	GetMTime () const
virtual const char *	GetNameOfClass () const
virtual int	GetReferenceCount () const
virtual const ScalesType &	GetScales ()
virtual const double &	GetStepLength ()
virtual const double &	GetStepTolerance ()
MeasureType	GetValue (const ParametersType &parameters) const
MeasureType	GetValue () const
virtual const double &	GetValueTolerance ()
bool	HasObserver (const EventObject &event) const
void	InvokeEvent (const EventObject &) const
void	InvokeEvent (const EventObject &)
virtual void	Modified () const
void	Print (std::ostream &os, Indent indent=0) const
virtual void	Register () const
void	RemoveAllObservers ()
void	RemoveObserver (unsigned long tag)
virtual void	SetCostFunction (CostFunctionType *costFunction)
void	SetDebug (bool debugFlag) const
virtual void	SetInitialPosition (const ParametersType &param)
Set if the Optimizer should Maximize the metric *virtual void	SetMaximize (bool _arg)
Set Get maximum iteration limit *virtual void	SetMaximumIteration (unsigned int _arg)
Set Get the maximum number of line search iterations *virtual void	SetMaximumLineIteration (unsigned int _arg)
void	SetMetaDataDictionary (const MetaDataDictionary &rhs)
virtual void	SetReferenceCount (int)
void	SetScales (const ScalesType &scales)
Set Get StepTolerance Once the local extreme is known to be within this *distance of the current parameter optimization terminates *virtual void	SetStepTolerance (double _arg)
void	SetToFletchReeves ()
void	SetToPolakRibiere ()
Set Get ValueTolerance Once this current cost function value is known *to be within this tolerance of the cost function value at the local optimization terminates *virtual void	SetValueTolerance (double _arg)
void	StartOptimization ()
void	StopOptimization ()
Set Get StepLength for	the (scaled) spacing of the sampling of *parameter space while bracketing the extremum */virtual void SetStepLength(double _arg)
virtual void	UnRegister () const
Static Public Member Functions
static void	BreakOnError ()
static bool	GetGlobalWarningDisplay ()
static void	GlobalWarningDisplayOff ()
static void	GlobalWarningDisplayOn ()
static Pointer	New ()
This is a global flag that controls whether any warning *or error messages are displayed *static void	SetGlobalWarningDisplay (bool flag)
Public Attributes
Allow people to add remove invoke observers(callbacks) to any ITK *object.This is an implementation of the subject/observer design *pattern.An observer is added by specifying an event to respond to *and an itk unsigned lon	AddObserver )(const EventObject &event, Command *) const
This is a global flag that controls whether any	debug
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
Set Get StepTolerance Once the local extreme is known to be within this *distance of the current parameter	values
Protected Member Functions
virtual void	BracketedLineOptimize (double ax, double bx, double cx, double fa, double fb, double fc, double *extX, double *extVal)
	FRPROptimizer ()
double	GetLineValue (double x) const
virtual unsigned int	GetSpaceDimension ()
virtual bool	GetStop ()
virtual void	GetValueAndDerivative (ParametersType p, double *val, ParametersType *xi)
virtual void	LineBracket (double *ax, double *bx, double *cx, double *fa, double *fb, double *fc)
virtual void	LineOptimize (ParametersType *p, ParametersType xi, double *val)
bool	PrintObservers (std::ostream &os, Indent indent) const
void	PrintSelf (std::ostream &os, Indent indent) const
virtual void	PrintTrailer (std::ostream &os, Indent indent) const
virtual void	SetCurrentCost (double _arg)
virtual void	SetCurrentIteration (unsigned int _arg)
void	SetCurrentLinePoint (double x, double fx)
virtual void	SetCurrentPosition (const ParametersType &param)
void	SetLine (const ParametersType &origin, const vnl_vector< double > &direction)
virtual void	SetSpaceDimension (unsigned int _arg)
virtual void	SetStop (bool _arg)
void	Shift (double *a, double *b, double *c, double d) const
void	Swap (double *a, double *b) const
virtual	~FRPROptimizer ()
Protected Attributes
CostFunctionPointer	m_CostFunction
int	m_ReferenceCount
SimpleFastMutexLock	m_ReferenceCountLock
bool	m_ScalesInitialized
Methods invoked by virtual 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.*/virtual void PrintSelf(std voi	PrintHeader )(std::ostream &os, Indent indent) const

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Member Typedef Documentation

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

Reimplemented from itk::PowellOptimizer. Definition at line 58 of file itkFRPROptimizer.h.

typedef CostFunctionType::Pointer itk::FRPROptimizer::CostFunctionPointer

Reimplemented from itk::PowellOptimizer. Definition at line 71 of file itkFRPROptimizer.h.

typedef SingleValuedCostFunction itk::FRPROptimizer::CostFunctionType

Type of the Cost Function Reimplemented from itk::PowellOptimizer. Definition at line 67 of file itkFRPROptimizer.h.

typedef CostFunctionType::DerivativeType itk::SingleValuedNonLinearOptimizer::DerivativeType [inherited]

Derivative type. It defines a type used to return the cost function derivative. Definition at line 64 of file itkSingleValuedNonLinearOptimizer.h.

typedef CostFunctionType::MeasureType itk::SingleValuedNonLinearOptimizer::MeasureType [inherited]

Measure type. It defines a type used to return the cost function value. Reimplemented in itk::LBFGSBOptimizer. Definition at line 60 of file itkSingleValuedNonLinearOptimizer.h.

typedef SingleValuedNonLinearOptimizer::ParametersType itk::FRPROptimizer::ParametersType

Parameters type. It defines a position in the optimization search space. Reimplemented from itk::PowellOptimizer. Definition at line 61 of file itkFRPROptimizer.h.

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

Reimplemented from itk::PowellOptimizer. Definition at line 57 of file itkFRPROptimizer.h.

typedef Superclass::ScalesType itk::NonLinearOptimizer::ScalesType [inherited]

Scale type. This array defines scale to be applied to parameters before being evaluated in the cost function. This allows to map to a more convenient space. In particular this is used to normalize parameter spaces in which some parameters have a different dynamic range. Reimplemented from itk::Optimizer. Definition at line 52 of file itkNonLinearOptimizer.h.

typedef FRPROptimizer itk::FRPROptimizer::Self

Standard "Self" typedef. Reimplemented from itk::PowellOptimizer. Definition at line 55 of file itkFRPROptimizer.h.

typedef PowellOptimizer itk::FRPROptimizer::Superclass

Reimplemented from itk::PowellOptimizer. Definition at line 56 of file itkFRPROptimizer.h.

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Constructor & Destructor Documentation

itk::FRPROptimizer::FRPROptimizer (   )  [protected]

virtual itk::FRPROptimizer::~FRPROptimizer (   )  [protected, virtual]

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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, inherited]

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.

static void itk::LightObject::BreakOnError (   )  [static, inherited]

This method is called when itkExceptionMacro executes. It allows the debugger to break on error.

virtual LightObject::Pointer itk::Object::CreateAnother (   )  const [virtual, inherited]

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::LightObject.

virtual void itk::Object::DebugOff (   )  const [virtual, inherited]

Turn debugging output off.

virtual void itk::Object::DebugOn (   )  const [virtual, inherited]

Turn debugging output on.

virtual void itk::LightObject::Delete (   )  [virtual, inherited]

Delete an itk object. This method should always be used to delete an object when the new operator was used to create it. Using the C delete method will not work with reference counting.

Command* itk::Object::GetCommand (  unsigned long  tag  )  [inherited]

Get the command associated with the given tag. NOTE: This returns a pointer to a Command, but it is safe to asign this to a Command::Pointer. Since Command inherits from LightObject, at this point in the code, only a pointer or a reference to the Command can be used.

virtual const CostFunctionType* itk::SingleValuedNonLinearOptimizer::GetCostFunction (   )  [virtual, inherited]

Get the cost function.

Return Current Value* virtual const MeasureType& itk::PowellOptimizer::GetCurrentCost (   )  [virtual, inherited]

virtual const unsigned int& itk::PowellOptimizer::GetCurrentIteration (   )  [virtual, inherited]

Return Current Iteration

virtual const unsigned int& itk::PowellOptimizer::GetCurrentLineIteration (   )  [virtual, inherited]

Get the current line search iteration

virtual const ParametersType& itk::Optimizer::GetCurrentPosition (   )  [virtual, inherited]

Get current position of the optimization.

bool itk::Object::GetDebug (   )  const [inherited]

Get the value of the debug flag.

static bool itk::Object::GetGlobalWarningDisplay (   )  [static, inherited]

virtual const ParametersType& itk::Optimizer::GetInitialPosition (   )  [virtual, inherited]

Get the position to initialize the optimization.

double itk::PowellOptimizer::GetLineValue (  double  x  )  const [protected, inherited]

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, inherited]

virtual const unsigned int& itk::PowellOptimizer::GetMaximumIteration (   )  [virtual, inherited]

virtual unsigned int itk::PowellOptimizer::GetMaximumLineIteration (   )  const [virtual, inherited]

const MetaDataDictionary& itk::Object::GetMetaDataDictionary (  void   )  const [inherited]

Returns: A constant reference to this objects MetaDataDictionary.

MetaDataDictionary& itk::Object::GetMetaDataDictionary (  void   )  [inherited]

Returns: A reference to this objects MetaDataDictionary. Warning: This reference may be changed.

virtual unsigned long itk::Object::GetMTime (   )  const [virtual, inherited]

Return this objects modified time. Reimplemented in itk::ImageRegistrationMethod< TFixedImage, TMovingImage >, itk::DeformationFieldSource< TOutputImage >, itk::InverseDeformationFieldImageFilter< TInputImage, TOutputImage >, itk::ResampleImageFilter< TInputImage, TOutputImage, TInterpolatorPrecisionType >, itk::VectorResampleImageFilter< TInputImage, TOutputImage, TInterpolatorPrecisionType >, itk::BoundingBox< TPointIdentifier, VPointDimension, TCoordRep, TPointsContainer >, itk::SceneSpatialObject< SpaceDimension >, and itk::SceneSpatialObject< NDimensions >.

virtual const char* itk::FRPROptimizer::GetNameOfClass (   )  const [virtual]

Run-time type information (and related methods). Reimplemented from itk::PowellOptimizer.

virtual int itk::LightObject::GetReferenceCount (   )  const [inline, virtual, inherited]

Gets the reference count on this object. Definition at line 98 of file itkLightObject.h.

virtual const ScalesType& itk::Optimizer::GetScales (   )  [virtual, inherited]

Get current parameters scaling.

virtual unsigned int itk::PowellOptimizer::GetSpaceDimension (   )  [protected, virtual, inherited]

virtual const double& itk::PowellOptimizer::GetStepLength (   )  [virtual, inherited]

virtual const double& itk::PowellOptimizer::GetStepTolerance (   )  [virtual, inherited]

virtual bool itk::PowellOptimizer::GetStop (   )  [protected, virtual, inherited]

MeasureType itk::SingleValuedNonLinearOptimizer::GetValue (  const ParametersType &  parameters  )  const [inherited]

Get the cost function value at the given parameters. Reimplemented in itk::SPSAOptimizer.

MeasureType itk::PowellOptimizer::GetValue (   )  const [inline, inherited]

Definition at line 113 of file itkPowellOptimizer.h.

virtual void itk::FRPROptimizer::GetValueAndDerivative (  ParametersType  p, double *  val, ParametersType *  xi )  [protected, virtual]

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 double& itk::PowellOptimizer::GetValueTolerance (   )  [virtual, inherited]

static void itk::Object::GlobalWarningDisplayOff (   )  [inline, static, inherited]

Definition at line 100 of file itkObject.h. References itk::Object::SetGlobalWarningDisplay().

static void itk::Object::GlobalWarningDisplayOn (   )  [inline, static, inherited]

Definition at line 98 of file itkObject.h. References itk::Object::SetGlobalWarningDisplay().

bool itk::Object::HasObserver (  const EventObject &  event  )  const [inherited]

Return true if an observer is registered for this event.

void itk::Object::InvokeEvent (  const EventObject &   )  const [inherited]

Call Execute on all the Commands observing this event id. The actions triggered by this call doesn't modify this object.

void itk::Object::InvokeEvent (  const EventObject &   )  [inherited]

Call Execute on all the Commands observing this event id.

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

The LineBracket routine from NRC. 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::FRPROptimizer::LineOptimize (  ParametersType *  p, ParametersType  xi, double *  val )  [protected, virtual]

virtual void itk::Object::Modified (   )  const [virtual, inherited]

Update the modification time for this object. Many filters rely on the modification time to determine if they need to recompute their data. Referenced by itk::MatrixOffsetTransformBase< TScalarType, 3, 3 >::SetCenter(), itk::HistogramAlgorithmBase< TInputHistogram >::SetInputHistogram(), itk::MatrixOffsetTransformBase< TScalarType, 3, 3 >::SetMatrix(), itk::MatrixOffsetTransformBase< TScalarType, 3, 3 >::SetOffset(), itk::ThresholdLabelerImageFilter< TInputImage, TOutputImage >::SetRealThresholds(), itk::CollidingFrontsImageFilter< TInputImage, TOutputImage >::SetSeedPoints1(), itk::CollidingFrontsImageFilter< TInputImage, TOutputImage >::SetSeedPoints2(), itk::NonUniformBSpline< TDimension >::SetSplineOrder(), itk::ThresholdLabelerImageFilter< TInputImage, TOutputImage >::SetThresholds(), itk::Statistics::GoodnessOfFitFunctionBase< typename ComponentType::HistogramType >::SetTotalObservedScale(), and itk::MatrixOffsetTransformBase< TScalarType, 3, 3 >::SetTranslation().

static Pointer itk::FRPROptimizer::New (   )  [static]

Method for creation through the object factory. Reimplemented from itk::PowellOptimizer.

void itk::LightObject::Print (  std::ostream &  os, Indent  indent = 0 )  const [inherited]

Cause the object to print itself out.

bool itk::Object::PrintObservers (  std::ostream &  os, Indent  indent )  const [protected, inherited]

void itk::FRPROptimizer::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::PowellOptimizer.

virtual void itk::LightObject::PrintTrailer (  std::ostream &  os, Indent  indent )  const [protected, virtual, inherited]

virtual void itk::Object::Register (   )  const [virtual, inherited]

Increase the reference count (mark as used by another object). Reimplemented from itk::LightObject.

void itk::Object::RemoveAllObservers (   )  [inherited]

Remove all observers .

void itk::Object::RemoveObserver (  unsigned long  tag  )  [inherited]

Remove the observer with this tag value.

virtual void itk::SingleValuedNonLinearOptimizer::SetCostFunction (  CostFunctionType *  costFunction  )  [virtual, inherited]

Set the cost function.

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

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

void itk::PowellOptimizer::SetCurrentLinePoint (  double  x, double  fx )  [protected, inherited]

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

virtual void itk::Optimizer::SetCurrentPosition (  const ParametersType &  param  )  [protected, virtual, inherited]

Set the current position.

void itk::Object::SetDebug (  bool  debugFlag  )  const [inherited]

Set the value of the debug flag. A non-zero value turns debugging on.

This is a global flag that controls whether any warning* or error messages are displayed* static void itk::Object::SetGlobalWarningDisplay (  bool  flag  )  [static, inherited]

Referenced by itk::Object::GlobalWarningDisplayOff(), and itk::Object::GlobalWarningDisplayOn().

virtual void itk::Optimizer::SetInitialPosition (  const ParametersType &  param  )  [virtual, inherited]

Set the position to initialize the optimization.

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

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

Set if the Optimizer should Maximize the metric* virtual void itk::PowellOptimizer::SetMaximize (  bool  _arg  )  [virtual, inherited]

Set Get maximum iteration limit* virtual void itk::PowellOptimizer::SetMaximumIteration (  unsigned int  _arg  )  [virtual, inherited]

Set Get the maximum number of line search iterations* virtual void itk::PowellOptimizer::SetMaximumLineIteration (  unsigned int  _arg  )  [virtual, inherited]

void itk::Object::SetMetaDataDictionary (  const MetaDataDictionary &  rhs  )  [inherited]

Returns: Set the MetaDataDictionary

virtual void itk::Object::SetReferenceCount (  int   )  [virtual, inherited]

Sets the reference count (use with care) Reimplemented from itk::LightObject.

void itk::Optimizer::SetScales (  const ScalesType &  scales  )  [inherited]

Set current parameters scaling. Reimplemented in itk::LBFGSBOptimizer.

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

Set Get StepTolerance Once the local extreme is known to be within this* distance of the current parameter optimization terminates* virtual void itk::PowellOptimizer::SetStepTolerance (  double  _arg  )  [virtual, inherited]

virtual void itk::PowellOptimizer::SetStop (  bool  _arg  )  [protected, virtual, inherited]

void itk::FRPROptimizer::SetToFletchReeves (   )

Set it to the Fletch-Reeves optimizer

void itk::FRPROptimizer::SetToPolakRibiere (   )

Set it to the Fletch-Reeves optimizer

Set Get ValueTolerance Once this current cost function value is known* to be within this tolerance of the cost function value at the local optimization terminates* virtual void itk::PowellOptimizer::SetValueTolerance (  double  _arg  )  [virtual, inherited]

void itk::PowellOptimizer::Shift (  double *  a, double *  b, double *  c, double  d )  const [protected, inherited]

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

void itk::FRPROptimizer::StartOptimization (   )  [virtual]

Start optimization. Reimplemented from itk::PowellOptimizer.

void itk::PowellOptimizer::StopOptimization (  void   )  [inline, inherited]

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 128 of file itkPowellOptimizer.h.

void itk::PowellOptimizer::Swap (  double *  a, double *  b )  const [protected, inherited]

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

Set Get StepLength for itk::PowellOptimizer::the (  scaled   )  [inherited]

virtual void itk::Object::UnRegister (   )  const [virtual, inherited]

Decrease the reference count (release by another object). Reimplemented from itk::LightObject.

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Member Data Documentation

Allow people to add remove invoke observers (callbacks) to any ITK * object. This is an implementation of the subject/observer design * pattern. An observer is added by specifying an event to respond to * and an itk unsigned lon itk::Object::AddObserver)(const EventObject &event, Command *) const [inherited]

This is a global flag that controls whether any itk::Object::debug [inherited]

Definition at line 94 of file itkObject.h.

Set Get ValueTolerance Once this current cost function value is known* to be within this tolerance of the cost function value at the local* itk::PowellOptimizer::extreme [inherited]

Definition at line 101 of file itkPowellOptimizer.h.

CostFunctionPointer itk::SingleValuedNonLinearOptimizer::m_CostFunction [protected, inherited]

Definition at line 80 of file itkSingleValuedNonLinearOptimizer.h.

int itk::LightObject::m_ReferenceCount [mutable, protected, inherited]

Number of uses of this object by other objects. Definition at line 119 of file itkLightObject.h.

SimpleFastMutexLock itk::LightObject::m_ReferenceCountLock [mutable, protected, inherited]

Mutex lock to protect modification to the reference count Definition at line 122 of file itkLightObject.h.

bool itk::Optimizer::m_ScalesInitialized [protected, inherited]

Definition at line 90 of file itkOptimizer.h.

Methods invoked by virtual 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. */ virtual void PrintSelf(std voi itk::LightObject::PrintHeader)(std::ostream &os, Indent indent) const [protected, inherited]

Set Get StepTolerance Once the local extreme is known to be within this* distance of the current parameter itk::PowellOptimizer::values [inherited]

Definition at line 95 of file itkPowellOptimizer.h.

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

• itkFRPROptimizer.h

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