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ITK
4.13.0
Insight Segmentation and Registration Toolkit
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#include <itkLBFGSOptimizer.h>
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 to scale the gradient step:
with 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 is determined through line search with the approach by More and Thuente [4]. This line search approach finds a step size such that
The parameter 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
or a maximum number of function evaluations has been reached. The tolerance 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.
Definition at line 85 of file itkLBFGSOptimizer.h.
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 () |
virtual const std::string | GetStopConditionDescription () const override |
virtual bool | GetTrace () |
MeasureType | GetValue () const |
virtual void | SetCostFunction (SingleValuedCostFunction *costFunction) override |
virtual void | SetDefaultStepLength (double stp) |
virtual void | SetGradientConvergenceTolerance (double gtol) |
virtual void | SetLineSearchAccuracy (double tol) |
virtual void | SetMaximumNumberOfFunctionEvaluations (unsigned int n) |
virtual void | SetTrace (bool flag) |
virtual void | StartOptimization (void) override |
virtual void | TraceOff () |
virtual void | TraceOn () |
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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 |
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virtual ::itk::LightObject::Pointer | CreateAnother () const |
virtual const CostFunctionType * | GetCostFunction () const |
virtual CostFunctionType * | GetModifiableCostFunction () |
MeasureType | GetValue (const ParametersType ¶meters) const |
virtual void | SetCostFunction (CostFunctionType *costFunction) |
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virtual const ParametersType & | GetCurrentPosition () const |
virtual const ParametersType & | GetInitialPosition () const |
virtual void | SetInitialPosition (const ParametersType ¶m) |
void | SetScales (const ScalesType &scales) |
virtual const ScalesType & | GetScales () const |
virtual const ScalesType & | GetInverseScales () const |
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unsigned long | AddObserver (const EventObject &event, Command *) |
unsigned long | AddObserver (const EventObject &event, Command *) 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 |
virtual void | Register () const override |
void | RemoveAllObservers () |
void | RemoveObserver (unsigned long tag) |
void | SetDebug (bool debugFlag) const |
void | SetMetaDataDictionary (const MetaDataDictionary &rhs) |
virtual void | SetReferenceCount (int) override |
virtual void | UnRegister () const noexceptoverride |
virtual void | SetObjectName (std::string _arg) |
virtual const std::string & | GetObjectName () const |
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virtual void | Delete () |
virtual int | GetReferenceCount () const |
itkCloneMacro (Self) | |
void | Print (std::ostream &os, Indent indent=0) const |
Static Public Member Functions | |
static Pointer | New () |
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static Pointer | New () |
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static Pointer | New () |
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static Pointer | New () |
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static bool | GetGlobalWarningDisplay () |
static void | GlobalWarningDisplayOff () |
static void | GlobalWarningDisplayOn () |
static Pointer | New () |
static void | SetGlobalWarningDisplay (bool flag) |
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static void | BreakOnError () |
static Pointer | New () |
Protected Types | |
typedef Superclass::CostFunctionAdaptorType | CostFunctionAdaptorType |
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typedef SingleValuedVnlCostFunctionAdaptor | CostFunctionAdaptorType |
Protected Member Functions | |
LBFGSOptimizer () | |
virtual void | PrintSelf (std::ostream &os, Indent indent) const override |
virtual | ~LBFGSOptimizer () override |
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const CostFunctionAdaptorType * | GetCostFunctionAdaptor () const |
CostFunctionAdaptorType * | GetCostFunctionAdaptor () |
CostFunctionAdaptorType * | GetNonConstCostFunctionAdaptor () const |
void | SetCostFunctionAdaptor (CostFunctionAdaptorType *adaptor) |
SingleValuedNonLinearVnlOptimizer () | |
virtual | ~SingleValuedNonLinearVnlOptimizer () override |
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SingleValuedNonLinearOptimizer () | |
virtual | ~SingleValuedNonLinearOptimizer () override |
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NonLinearOptimizer () | |
virtual | ~NonLinearOptimizer () override |
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Optimizer () | |
virtual void | SetCurrentPosition (const ParametersType ¶m) |
virtual | ~Optimizer () override |
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Object () | |
bool | PrintObservers (std::ostream &os, Indent indent) const |
virtual void | SetTimeStamp (const TimeStamp &time) |
virtual | ~Object () override |
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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 | |
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CostFunctionPointer | m_CostFunction |
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ParametersType | m_CurrentPosition |
bool | m_ScalesInitialized |
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AtomicInt< int > | m_ReferenceCount |
typedef SmartPointer< const Self > itk::LBFGSOptimizer::ConstPointer |
Definition at line 93 of file itkLBFGSOptimizer.h.
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Definition at line 167 of file itkLBFGSOptimizer.h.
typedef vnl_lbfgs itk::LBFGSOptimizer::InternalOptimizerType |
Internal optimizer type.
Definition at line 105 of file itkLBFGSOptimizer.h.
typedef vnl_vector< double > itk::LBFGSOptimizer::InternalParametersType |
InternalParameters typedef.
Definition at line 99 of file itkLBFGSOptimizer.h.
typedef SmartPointer< Self > itk::LBFGSOptimizer::Pointer |
Definition at line 92 of file itkLBFGSOptimizer.h.
Standard "Self" typedef.
Definition at line 90 of file itkLBFGSOptimizer.h.
Definition at line 91 of file itkLBFGSOptimizer.h.
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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.
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Run-time type information (and related methods).
Reimplemented from itk::SingleValuedNonLinearVnlOptimizer.
vnl_lbfgs* itk::LBFGSOptimizer::GetOptimizer | ( | ) |
Method for getting access to the internal optimizer.
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Get the reason for termination
Reimplemented from itk::Optimizer.
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MeasureType itk::LBFGSOptimizer::GetValue | ( | ) | const |
Return Current Value
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Method for creation through the object factory.
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Print out internal state
Reimplemented from itk::SingleValuedNonLinearVnlOptimizer.
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Plug in a Cost Function into the optimizer
Implements itk::SingleValuedNonLinearVnlOptimizer.
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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.
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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.
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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 evalutions 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).
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Set/Get the maximum number of function evaluations allowed.
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Set/Get the optimizer trace flag. If set to true, the optimizer prints out information every iteration.
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Start optimization with an initial value.
Reimplemented from itk::Optimizer.
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Definition at line 180 of file itkLBFGSOptimizer.h.
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Definition at line 178 of file itkLBFGSOptimizer.h.
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Definition at line 179 of file itkLBFGSOptimizer.h.
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Definition at line 177 of file itkLBFGSOptimizer.h.
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Definition at line 170 of file itkLBFGSOptimizer.h.
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Definition at line 174 of file itkLBFGSOptimizer.h.
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Definition at line 176 of file itkLBFGSOptimizer.h.
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Definition at line 173 of file itkLBFGSOptimizer.h.