#include <itkLBFGSOptimizer.h>

Inheritance diagram for itk::LBFGSOptimizer:

Collaboration diagram for itk::LBFGSOptimizer:

Public Types
using	ConstPointer = SmartPointer< const Self >

using	InternalOptimizerType = vnl_lbfgs

using	InternalParametersType = vnl_vector< double >

using	Pointer = SmartPointer< Self >

using	Self = LBFGSOptimizer

using	Superclass = SingleValuedNonLinearVnlOptimizer

Public Types inherited from itk::SingleValuedNonLinearVnlOptimizer
using	CommandType = ReceptorMemberCommand< Self >

using	ConstPointer = SmartPointer< const Self >

using	Pointer = SmartPointer< Self >

using	Self = SingleValuedNonLinearVnlOptimizer

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 double	GetDefaultStepLength ()

virtual double	GetGradientConvergenceTolerance ()

virtual double	GetLineSearchAccuracy ()

virtual unsigned int	GetMaximumNumberOfFunctionEvaluations ()

virtual const char *	GetNameOfClass () const

vnl_lbfgs *	GetOptimizer ()

const std::string	GetStopConditionDescription () const override

virtual bool	GetTrace ()

MeasureType	GetValue () const

void	SetCostFunction (SingleValuedCostFunction *costFunction) override

virtual void	SetDefaultStepLength (double f)

virtual void	SetGradientConvergenceTolerance (double f)

virtual void	SetLineSearchAccuracy (double f)

virtual void	SetMaximumNumberOfFunctionEvaluations (unsigned int n)

virtual void	SetTrace (bool flag)

void	StartOptimization () override

virtual void	TraceOff ()

virtual void	TraceOn ()

Public Member Functions inherited from itk::SingleValuedNonLinearVnlOptimizer
virtual const bool &	GetMaximize () const

virtual void	SetMaximize (bool _arg)

virtual void	MaximizeOn ()

virtual void	MaximizeOff ()

bool	GetMinimize () const

void	SetMinimize (bool v)

void	MinimizeOn ()

void	MinimizeOff ()

virtual const MeasureType &	GetCachedValue () const

virtual const DerivativeType &	GetCachedDerivative () const

virtual const ParametersType &	GetCachedCurrentPosition () 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 &	GetInitialPosition () const

virtual void	SetInitialPosition (const ParametersType &param)

void	SetScales (const ScalesType &scales)

virtual const ScalesType &	GetScales () const

virtual const ScalesType &	GetInverseScales () const

virtual const ParametersType &	GetCurrentPosition () const

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

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

unsigned long	AddObserver (const EventObject &event, std::function< void(const EventObject &)> function) 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 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 Types
using	CostFunctionAdaptorType = Superclass::CostFunctionAdaptorType

Protected Types inherited from itk::SingleValuedNonLinearVnlOptimizer
using	CostFunctionAdaptorType = SingleValuedVnlCostFunctionAdaptor

Protected Member Functions
	LBFGSOptimizer ()

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

	~LBFGSOptimizer () override

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

	~SingleValuedNonLinearVnlOptimizer () override

void	SetCostFunctionAdaptor (CostFunctionAdaptorType *adaptor)

const CostFunctionAdaptorType *	GetCostFunctionAdaptor () const

CostFunctionAdaptorType *	GetCostFunctionAdaptor ()

CostFunctionAdaptorType *	GetNonConstCostFunctionAdaptor () const

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

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

	~SingleValuedNonLinearOptimizer () override=default

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

	~NonLinearOptimizer () override

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

	~Optimizer () override=default

virtual void	SetCurrentPosition (const ParametersType &param)

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

	~Object () override

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

virtual void	SetTimeStamp (const TimeStamp &timeStamp)

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
double	m_DefaultStepLength

double	m_GradientConvergenceTolerance

double	m_LineSearchAccuracy

unsigned int	m_MaximumNumberOfFunctionEvaluations

bool	m_OptimizerInitialized

std::ostringstream	m_StopConditionDescription

bool	m_Trace

InternalOptimizerType *	m_VnlOptimizer

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

Protected Attributes inherited from itk::Optimizer
bool	m_ScalesInitialized { false }

ParametersType	m_CurrentPosition

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

Detailed Description

Wrap of the vnl_lbfgs algorithm for use in ITKv4 registration framework. The vnl_lbfgs is a wrapper for the NETLIB fortran code by Nocedal [1].

LBFGS is a quasi-Newton method. Quasi-Newton methods use an approximate estimate of the inverse Hessian $(\nabla^2 f(x) )^{-1}$ to scale the gradient step:

$x_{n+1} = x_n - s (\nabla^2 f(x_n) )^{-1} \nabla f(x)$

with $ s $ the step size.

The inverse Hessian is approximated from the gradients of previous iteration and thus only the gradient of the objective function is required.

The step size $ s $ is determined through line search with the approach by More and Thuente [4]. This line search approach finds a step size such that

$\lVert \nabla f(x + s (\nabla^2 f(x_n) )^{-1} \nabla f(x) ) \rVert \le \nu \lVert \nabla f(x) \rVert$

The parameter $\nu$ is set through SetLineSearchAccuracy() (default 0.9) The default step length, i.e. starting step length for the line search, is set through SetDefaultStepLength() (default 1.0).

The optimization stops when either the gradient satisfies the condition

$\lVert \nabla f(x) \rVert \le \epsilon \max(1, \lVert X \rVert)$

or a maximum number of function evaluations has been reached. The tolerance $\epsilon$ is set through SetGradientConvergenceTolerance() (default 1e-5) and the maximum number of function evaluations is set through SetMaximumNumberOfFunctionEvaluations() (default 2000).

Note: The scales set through SetScales should be set or left at one. Otherwise the Hessian approximation will be disturbed and the optimizer is unlikely to find a minima.

References:

[1] NETLIB lbfgs

[2] Jorge Nocedal. Updating Quasi-Newton Matrices with Limited Storage. Mathematics of Computation, Vol. 35, No. 151, pp. 773-782, 1980.

[3] Dong C. Liu and Jorge Nocedal. On the limited memory BFGS method for large scale optimization. Mathematical Programming B, Vol. 45, No. 3, pp. 503-528, 1989.

[4] More, J. J. and D. J. Thuente. Line Search Algorithms with Guaranteed Sufficient Decrease. ACM Transactions on Mathematical Software 20, no. 3 (1994): 286-307.

Examples: SphinxExamples/src/Core/Transform/GlobalRegistrationTwoImagesBSpline/Code.cxx.

Definition at line 85 of file itkLBFGSOptimizer.h.

Member Typedef Documentation

◆ ConstPointer

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

Definition at line 94 of file itkLBFGSOptimizer.h.

◆ CostFunctionAdaptorType

using itk::LBFGSOptimizer::CostFunctionAdaptorType = Superclass::CostFunctionAdaptorType

protected

Definition at line 179 of file itkLBFGSOptimizer.h.

◆ InternalOptimizerType

using itk::LBFGSOptimizer::InternalOptimizerType = vnl_lbfgs

Internal optimizer type.

Definition at line 106 of file itkLBFGSOptimizer.h.

◆ InternalParametersType

using itk::LBFGSOptimizer::InternalParametersType = vnl_vector<double>

InternalParameters type alias.

Definition at line 103 of file itkLBFGSOptimizer.h.

◆ Pointer

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

Definition at line 93 of file itkLBFGSOptimizer.h.

◆ Self

using itk::LBFGSOptimizer::Self = LBFGSOptimizer

Standard "Self" type alias.

Definition at line 91 of file itkLBFGSOptimizer.h.

◆ Superclass

using itk::LBFGSOptimizer::Superclass = SingleValuedNonLinearVnlOptimizer

Definition at line 92 of file itkLBFGSOptimizer.h.

Constructor & Destructor Documentation

◆ LBFGSOptimizer()

itk::LBFGSOptimizer::LBFGSOptimizer ( )

protected

◆ ~LBFGSOptimizer()

itk::LBFGSOptimizer::~LBFGSOptimizer ( )

overrideprotected

Member Function Documentation

◆ CreateAnother()

virtual::itk::LightObject::Pointer itk::LBFGSOptimizer::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::Object.

◆ GetDefaultStepLength()

virtual double itk::LBFGSOptimizer::GetDefaultStepLength ( )

virtual

◆ GetGradientConvergenceTolerance()

virtual double itk::LBFGSOptimizer::GetGradientConvergenceTolerance ( )

virtual

◆ GetLineSearchAccuracy()

virtual double itk::LBFGSOptimizer::GetLineSearchAccuracy ( )

virtual

◆ GetMaximumNumberOfFunctionEvaluations()

virtual unsigned int itk::LBFGSOptimizer::GetMaximumNumberOfFunctionEvaluations ( )

virtual

◆ GetNameOfClass()

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

virtual

Run-time type information (and related methods).

Reimplemented from itk::SingleValuedNonLinearVnlOptimizer.

◆ GetOptimizer()

vnl_lbfgs* itk::LBFGSOptimizer::GetOptimizer ( )

Method for getting access to the internal optimizer.

◆ GetStopConditionDescription()

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

overridevirtual

Get the reason for termination

Reimplemented from itk::Optimizer.

◆ GetTrace()

virtual bool itk::LBFGSOptimizer::GetTrace ( )

virtual

◆ GetValue()

MeasureType itk::LBFGSOptimizer::GetValue ( ) const

Return Current Value

◆ New()

static Pointer itk::LBFGSOptimizer::New ( )

static

Method for creation through the object factory.

◆ PrintSelf()

void itk::LBFGSOptimizer::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::Object.

◆ SetCostFunction()

void itk::LBFGSOptimizer::SetCostFunction ( SingleValuedCostFunction * costFunction )

overridevirtual

Plug in a Cost Function into the optimizer

Implements itk::SingleValuedNonLinearVnlOptimizer.

◆ SetDefaultStepLength()

virtual void itk::LBFGSOptimizer::SetDefaultStepLength ( double f )

virtual

Set/Get the default step size. This is a positive real number with a default value of 1.0 which determines the stpe size in the line search.

◆ SetGradientConvergenceTolerance()

virtual void itk::LBFGSOptimizer::SetGradientConvergenceTolerance ( double f )

virtual

Set/Get the gradient convergence tolerance. This is a positive real number that determines the accuracy with which the solution is to be found. The optimization terminates when: ||G|| < gtol max(1,||X||) where ||.|| denotes the Euclidean norm.

◆ SetLineSearchAccuracy()

virtual void itk::LBFGSOptimizer::SetLineSearchAccuracy ( double f )

virtual

Set/Get the line search accuracy. This is a positive real number with a default value of 0.9, which controls the accuracy of the line search. If the function and gradient evaluations are inexpensive with respect to the cost of the iterations it may be advantageous to set the value to a small value (say 0.1).

◆ SetMaximumNumberOfFunctionEvaluations()

virtual void itk::LBFGSOptimizer::SetMaximumNumberOfFunctionEvaluations ( unsigned int n )

virtual

Set/Get the maximum number of function evaluations allowed.

◆ SetTrace()

virtual void itk::LBFGSOptimizer::SetTrace ( bool flag )

virtual

Set/Get the optimizer trace flag. If set to true, the optimizer prints out information every iteration.

◆ StartOptimization()

void itk::LBFGSOptimizer::StartOptimization ( )

overridevirtual

Start optimization with an initial value.

Reimplemented from itk::Optimizer.

◆ TraceOff()

virtual void itk::LBFGSOptimizer::TraceOff ( )

virtual

◆ TraceOn()

virtual void itk::LBFGSOptimizer::TraceOn ( )

virtual

Member Data Documentation

◆ m_DefaultStepLength

double itk::LBFGSOptimizer::m_DefaultStepLength

private

Definition at line 190 of file itkLBFGSOptimizer.h.

◆ m_GradientConvergenceTolerance

double itk::LBFGSOptimizer::m_GradientConvergenceTolerance

private

Definition at line 188 of file itkLBFGSOptimizer.h.

◆ m_LineSearchAccuracy

double itk::LBFGSOptimizer::m_LineSearchAccuracy

private

Definition at line 189 of file itkLBFGSOptimizer.h.

◆ m_MaximumNumberOfFunctionEvaluations

unsigned int itk::LBFGSOptimizer::m_MaximumNumberOfFunctionEvaluations

private

Definition at line 187 of file itkLBFGSOptimizer.h.

◆ m_OptimizerInitialized

bool itk::LBFGSOptimizer::m_OptimizerInitialized

private

Definition at line 182 of file itkLBFGSOptimizer.h.

◆ m_StopConditionDescription

std::ostringstream itk::LBFGSOptimizer::m_StopConditionDescription

mutableprivate

Definition at line 184 of file itkLBFGSOptimizer.h.

◆ m_Trace

bool itk::LBFGSOptimizer::m_Trace

private

Definition at line 186 of file itkLBFGSOptimizer.h.

◆ m_VnlOptimizer

InternalOptimizerType* itk::LBFGSOptimizer::m_VnlOptimizer

private

Definition at line 183 of file itkLBFGSOptimizer.h.

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

itkLBFGSOptimizer.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Types

Protected Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ ConstPointer

◆ CostFunctionAdaptorType

◆ InternalOptimizerType

◆ InternalParametersType

◆ Pointer

◆ Self

◆ Superclass

Constructor & Destructor Documentation

◆ LBFGSOptimizer()

◆ ~LBFGSOptimizer()

Member Function Documentation

◆ CreateAnother()

◆ GetDefaultStepLength()

◆ GetGradientConvergenceTolerance()

◆ GetLineSearchAccuracy()

◆ GetMaximumNumberOfFunctionEvaluations()

◆ GetNameOfClass()

◆ GetOptimizer()

◆ GetStopConditionDescription()

◆ GetTrace()

◆ GetValue()

◆ New()

◆ PrintSelf()

◆ SetCostFunction()

◆ SetDefaultStepLength()

◆ SetGradientConvergenceTolerance()

◆ SetLineSearchAccuracy()

◆ SetMaximumNumberOfFunctionEvaluations()

◆ SetTrace()

◆ StartOptimization()

◆ TraceOff()

◆ TraceOn()

Member Data Documentation

◆ m_DefaultStepLength

◆ m_GradientConvergenceTolerance

◆ m_LineSearchAccuracy

◆ m_MaximumNumberOfFunctionEvaluations

◆ m_OptimizerInitialized

◆ m_StopConditionDescription

◆ m_Trace

◆ m_VnlOptimizer