BELLFUNCTION Summary of this class goes here Detailed explanation goes here. More...

Detailed Description

BELLFUNCTION Summary of this class goes here Detailed explanation goes here.

Todo:: export different estimator strategies into external classes => simulation speedup, separation of concerns..

Todo:: investigate why the newton iteration sometimes exceeds max iteration limit (example: intermittently test_LinearModelParams is such a case)

Documentation Update:: Properties and class description

Change in 0.4:: (Daniel Wirtz, 2011-06-07) Moved the ModifiedNewton methods from error.lipfun.ImprovedLocalSecantLipschitz to this class as they are more appropriate here.

Change in 0.4:: (Daniel Wirtz, 2011-05-27) Changed \(x_0\) to \(r_0\) and \(x_R\) to \(r_m\) as adopted in the WH10 Paper.

Change in 0.4:: (Daniel Wirtz, 2011-05-20) Removed the getLipschitzFunction method as it causes LARGE overhead when being called very often. Instead, the estimator always uses the improved estimation procedure.

Change in 0.4:

(Daniel Wirtz, 2011-05-19)

Removed the PenaltyFactor property as no longer needed.
Modified the newton iteration penalization such that the 2nd degree polynomials extend the objective function both in value and derivative. This ensures propert continuation of the objective function into the penalized area with respect to the current kernel configuration (i.e. kernels.GaussKernel: small Gamma property causes high derivatives and thus large estimations.

New in 0.3:: (Daniel Wirtz, 2011-04-06) Added a new property kernels.BellFunction.MaxNewtonIterations that avoids computations to hang if the newton iteration does not come to a hold. An error will be thrown as finding the correct minima is necessary.

Definition at line 18 of file BellFunction.m.

Public Member Functions
	BellFunction ()

function c =	getGlobalLipschitz ()
	Computes the absolute value of the first derivative at x0 Implements the template method from BaseKernel. More...

function copy =	clone (copy)
	The interface method with returns a copy of the current class instance. More...

function rtmp =	ModifiedNewton (rstart, s)

virtual function dr =	evaluateD1 ()
	Method for first derivative evaluation. More...

virtual function ddr =	evaluateD2 ()
	Method for second derivative evaluation. More...

Public Member Functions inherited from kernels.ARBFKernel
	ARBFKernel ()

function K =	evaluate (matrix< double > x,matrix< double > y)
	Evaluates the rotation and translation invariant kernel. More...

function bool =	eq (B)

function r =	getSqDiffNorm (matrix< double > x,matrix< double > y)
	Returns the weighted squared norm \(r\) of the difference \(\noG{x-y}^2/\gamma^2\). More...

virtual function phir =	evaluateScalar (matrix< double > r)
	Allows the evaluation of the function \(\phi(r)\) for scalar \(r\) directly. More...

Public Member Functions inherited from kernels.BaseKernel
	BaseKernel ()

function fcn =	getLipschitzFunction ()
	Method that allows error estimators to obtain a lipschitz constant estimation function from this kernel. More...

function bool =	eq (B)
	Checks if a kernel equals another kernel. More...

virtual function Nabla =	getNabla (x, y)
	Computes the partial derivatives with respect to each component of the first argument. More...

Public Member Functions inherited from KerMorObject
	KerMorObject ()
	Constructs a new KerMor object. More...

function	display ()
	disp(object2str(this)); More...

function bool =	eq (B)
	Checks equality of two KerMor objects. More...

function bool =	ne (B)
	Checks if two KerMorObjects are different. More...

function cn =	getClassName ()
	Returns the simple class name of this object without packages. More...

Public Member Functions inherited from DPCMObject
	DPCMObject ()
	Creates a new DPCM object. More...

	DPCMObject ()

Public Attributes
	r0
	Point of maximum first derivative on scalar evaluation. More...

	NewtonTolerance = 1e-7
	Error tolerance for modified newton iteration. More...

	MaxNewtonIterations = 5000
	Hard break for iteration count of modified newton algorithm. More...

	rm
	The maximum ("right") value for any \(r_s\). More...

Public Attributes inherited from kernels.ARBFKernel
double	Gamma = 1
	Univariate scaling. More...

Public Attributes inherited from kernels.BaseKernel
matrix< double >	G = 1
	The matrix \(\vG\) that induces the state space scalar product \(\spG{x}{y}\) and norm \(\noG{x-y}\) to use. More...

matrix< double >	P = "[]"
	Projection/selection matrix \(\vP\) for argument components. More...

logical	IsRBF = false
	Flag that determines if the current kernel is a radial basis function, i.e. its evaluation is of the form \(\K(x,y) = \phi(\noG{x-y})\) for some scalar function \(\phi\). More...

logical	IsScProd = false
	Flag that determines if the current kernel bases on scalar product evaluations, i.e. are of the form \(\K(x,y) = \phi(\spG{x}{y})\) for some scalar function \(\phi\). More...

Public Attributes inherited from DPCMObject
	WorkspaceVariableName = ""
	The workspace variable name of this class. Optional. More...

	ID = "[]"
	An ID that allows to uniquely identify this DPCMObject (at least within the current MatLab session/context). More...

	PropertiesChanged = "[]"
	The Dictionary containing all the property settings as key/value pairs. More...

Public Attributes inherited from handle
	addlistener
	Creates a listener for the specified event and assigns a callback function to execute when the event occurs. More...

	notify
	Broadcast a notice that a specific event is occurring on a specified handle object or array of handle objects. More...

	delete
	Handle object destructor method that is called when the object's lifecycle ends. More...

	disp
	Handle object disp method which is called by the display method. See the MATLAB disp function. More...

	display
	Handle object display method called when MATLAB software interprets an expression returning a handle object that is not terminated by a semicolon. See the MATLAB display function. More...

	findobj
	Finds objects matching the specified conditions from the input array of handle objects. More...

	findprop
	Returns a meta.property objects associated with the specified property name. More...

	fields
	Returns a cell array of string containing the names of public properties. More...

	fieldnames
	Returns a cell array of string containing the names of public properties. See the MATLAB fieldnames function. More...

	isvalid
	Returns a logical array in which elements are true if the corresponding elements in the input array are valid handles. This method is Sealed so you cannot override it in a handle subclass. More...

	eq
	Relational functions example. See details for more information. More...

	transpose
	Transposes the elements of the handle object array. More...

	permute
	Rearranges the dimensions of the handle object array. See the MATLAB permute function. More...

	reshape
	hanges the dimensions of the handle object array to the specified dimensions. See the MATLAB reshape function. More...

	sort
	ort the handle objects in any array in ascending or descending order. More...

Protected Member Functions
function [ g , dg , pi , pl , pr ] =	optFun (r, s, n, dn)

Protected Member Functions inherited from KerMorObject
function	checkType (obj, type)
	Object typechecker. More...

Protected Member Functions inherited from DPCMObject
function	registerProps (varargin)
	Call this method at any class that defines DPCM observed properties. More...

function	registerProps (varargin)

Static Protected Member Functions
static function this =	loadobj (this, from)
	As the constant properties are transient, they have to be re-computed upon loading. More...

Static Protected Member Functions inherited from DPCMObject
static function obj =	loadobj (obj, from)
	Re-register any registered change listeners! More...

static function obj =	loadobj (obj, from)

Additional Inherited Members
Protected Attributes inherited from kernels.BaseKernel
	fG = 1

	fP = "[]"

Constructor & Destructor Documentation

kernels.BellFunction.BellFunction ( )

Definition at line 139 of file BellFunction.m.

References DPCMObject.registerProps().

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Member Function Documentation

function copy = kernels.BellFunction.clone ( target )

virtual

The interface method with returns a copy of the current class instance.

Parameters

target If clone was called for a subclass of this class, target must contain the new instance of the subclass that is to be the cloned result.

Reimplemented from kernels.ARBFKernel.

Definition at line 156 of file BellFunction.m.

References MaxNewtonIterations, NewtonTolerance, r0, and rm.

function dr = kernels.BellFunction.evaluateD1 ( )

pure virtual

Method for first derivative evaluation.

Referenced by getGlobalLipschitz(), optFun(), and demos.BellFunctions.SecantGradientPlots().

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function ddr = kernels.BellFunction.evaluateD2 ( )

pure virtual

Method for second derivative evaluation.

Referenced by ModifiedNewton(), and optFun().

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function c = kernels.BellFunction.getGlobalLipschitz ( )

virtual

Computes the absolute value of the first derivative at x0 Implements the template method from BaseKernel.

Implements kernels.BaseKernel.

Definition at line 145 of file BellFunction.m.

References evaluateD1(), and r0.

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function this = kernels.BellFunction.loadobj	(	this,
		from
	)

staticprotected

As the constant properties are transient, they have to be re-computed upon loading.

Any subclasser MUST call this superclasses loadobj function explicitly!

Required fields of from:

Required fields of this:

Generated fields of this:

Definition at line 371 of file BellFunction.m.

References KerMorObject.KerMorObject(), MaxNewtonIterations, and NewtonTolerance.

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function rtmp = kernels.BellFunction.ModifiedNewton	(	rstart,
		s
	)

Definition at line 170 of file BellFunction.m.

References evaluateD2(), kernels.ARBFKernel.evaluateScalar(), MaxNewtonIterations, NewtonTolerance, and optFun().

Referenced by demos.BellFunctions.SecantGradientPlots().

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function [g , dg , pi , pl , pr ] = kernels.BellFunction.optFun	(	r,
		s,
		n,
		dn
	)

protected

Definition at line 310 of file BellFunction.m.

References evaluateD1(), evaluateD2(), kernels.ARBFKernel.evaluateScalar(), r0, and rm.

Referenced by ModifiedNewton().

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Member Data Documentation

kernels.BellFunction.MaxNewtonIterations = 5000

Hard break for iteration count of modified newton algorithm.

Property class alglimit:: Emergency break if iteration does not converge.

Default: 5000

Note: This property has the MATLAB attribute SetObservable set to true.; Matlab documentation of property attributes.

Definition at line 92 of file BellFunction.m.

Referenced by clone(), loadobj(), and ModifiedNewton().

kernels.BellFunction.NewtonTolerance = 1e-7

Error tolerance for modified newton iteration.

Property class optional:: The default precision is sufficient for all cases encountered so far.

Default: 1e-7

Note: This property has the MATLAB attribute SetObservable set to true.; Matlab documentation of property attributes.

Definition at line 77 of file BellFunction.m.

Referenced by clone(), loadobj(), and ModifiedNewton().

kernels.BellFunction.r0

Point of maximum first derivative on scalar evaluation.

Property class critical:: This value is essential for any bell function.

Note: This property has the MATLAB attribute Dependent set to true.; This property has the MATLAB attribute SetObservable set to true.; Matlab documentation of property attributes.

Definition at line 61 of file BellFunction.m.

Referenced by clone(), getGlobalLipschitz(), optFun(), and demos.BellFunctions.SecantGradientPlots().

kernels.BellFunction.rm

The maximum ("right") value for any \(r_s\).

Note: This property has non-standard access specifiers: SetAccess = Private, GetAccess = Public; Matlab documentation of property attributes.

Definition at line 109 of file BellFunction.m.

Referenced by clone(), optFun(), and demos.BellFunctions.SecantGradientPlots().

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

core/+kernels/BellFunction.m

Detailed Description

Public Member Functions

Public Attributes

Protected Member Functions

Static Protected Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation