ABase: Base class for any approximation generation algorithms for kernel expansions,. More...

Detailed Description

ABase: Base class for any approximation generation algorithms for kernel expansions,.

Author: Daniel Wirtz

Date: 2011-07-07

Change in 0.5:

(Daniel Wirtz, 2011-11-02)

New interface for approximation computation: Passing an data.ApproxTrainData instance now instead of xi,ti,mui parameters.
New default value false for the UsefScaling property; recent experiments suggested true might not be a wise default value but an extra source of errors.

Change in 0.5:: (Daniel Wirtz, 2011-10-14) Improved the parallel computation of kernel expansion coefficients.

Change in 0.5:: (Daniel Wirtz, 2011-09-12) Added initial values that can be passed to the CoeffComp algorithms. Now computing coefficients at once if MultiTargetComputation of the CoeffComp property is true.

New in 0.5:: (Daniel Wirtz, 2011-07-07) Added this class.

This class is part of the framework

KerMor - Model Order Reduction using Kernels

Homepage http://www.morepas.org/software/index.html
Documentation http://www.morepas.org/software/kermor/index.html
License KerMor license conditions

Definition at line 19 of file ABase.m.

Public Member Functions
	ABase ()

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

function kernels.KernelExpansion kexp =	computeApproximation (data.ApproxTrainData atd, avd)

function [ str , rangetab ] =	getApproximationSummary ()
	Setup. More...

function	plotSummary (pm, context)

function nc =	getTotalNumConfigurations ()

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
kernels.config.ExpansionConfig	ExpConfig = "[]"
	The different kernel expansion configurations to try. More...

	UsefScaling = false
	Flag that determines whether the approximation center f values should be scaled to [-1,1] before the approximation is computed. More...

function_handle	ErrorFun = @Norm.L2
	The error function to apply on each data vector. More...

double	LastCompTime = "[]"
	The computation time for the last run in seconds. More...

matrix< double >	MaxErrors = "[]"
	For each configuration, contains a row with the maximum errors on the training data. The number of columns depends on the type of algorithm implemented by the subclasses. More...

matrix< double >	MaxRelErrors = "[]"
	For each configuration, contains a row with the maximum relative errors on the training data. The number of columns depends on the type of algorithm implemented by the subclasses. More...

matrix< double >	ValidationErrors = "[]"
	For each configuration, contains a row with the maximum errors on the validation data. The number of columns depends on the type of algorithm implemented by the subclasses. More...

matrix< double >	ValidationRelErrors = "[]"
	For each configuration, contains a row with the maximum relative errors on the validation data. The number of columns depends on the type of algorithm implemented by the subclasses. More...

matrix< integer >	StopFlags = "[]"
	For each effective configuration, the stop flags are stored here. More...

integer	BestExpConfig
	Index of the best expansion config determined by the algorithm. 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 [ double val , integer idx , rowvec errs ] =	getError (kernels.KernelExpansion kexp,data.ApproxTrainData atd)
	Computes the error according to the chosen error function (see ErrorFun property) with respect to the current kernel expansion and the \(f(x_i)\) values in the training data. More...

virtual function	templateComputeApproximation (kernels.KernelExpansion kexp,data.ApproxTrainData atd, avd)
	Performs the actual approximation after scaling. More...

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, initfrom)

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)

Protected Attributes
	ScalingG
	If UsefScaling is set to true, this matrix contains the scaling matrix which has to be used in sub-algorithms in order to compute the correct approximation error on training data. More...

Constructor & Destructor Documentation

approx.algorithms.ABase.ABase ( )

Definition at line 232 of file ABase.m.

References KerMorObject.KerMorObject(), and DPCMObject.registerProps().

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Member Function Documentation

function copy = approx.algorithms.ABase.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.

Implements ICloneable.

Definition at line 239 of file ABase.m.

References BestExpConfig, kernels.config.ExpansionConfig.clone(), ErrorFun, ExpConfig, LastCompTime, MaxErrors, MaxRelErrors, ScalingG, StopFlags, UsefScaling, ValidationErrors, and ValidationRelErrors.

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function kernels.KernelExpansionkexp = approx.algorithms.ABase.computeApproximation	(	data.ApproxTrainData	atd,
			avd
	)

Definition at line 256 of file ABase.m.

References ExpConfig, data.ApproxTrainData.fxi, data.FileMatrix.getColBoundingBox(), kernels.config.ExpansionConfig.getNumConfigurations(), LastCompTime, ScalingG, templateComputeApproximation(), data.ABlockedData.toMemoryMatrix(), and UsefScaling.

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function [ str , rangetab ] = approx.algorithms.ABase.getApproximationSummary ( )

Setup.

Definition at line 329 of file ABase.m.

References BestExpConfig, handle.disp, ExpConfig, IClassConfig.getValueRanges(), and object2str().

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function [ double val , integer idx , rowvec errs ] = approx.algorithms.ABase.getError	(	kernels.KernelExpansion	kexp,
		data.ApproxTrainData	atd
	)

protected

Computes the error according to the chosen error function (see ErrorFun property) with respect to the current kernel expansion and the \(f(x_i)\) values in the training data.

See Also: ErrorFun

Parameters

kexp	The kernel expansion
atd	The approximation training data

Return values

val	The maximum error \(\max \|\|f(x_i,t_i,\mu_i) - \hat{f}(x_i,t_i,\mu_i)\|\|_{\{2,\infty\}}\)
idx	The index of the maximum error inside the errs vector
errs	A row vector of the errors for each sample

Required fields of atd:

Required fields of kexp:

Definition at line 408 of file ABase.m.

References ErrorFun, kernels.KernelExpansion.evaluate(), data.ApproxTrainData.fxi, data.ApproxTrainData.mui, ScalingG, data.ApproxTrainData.ti, and data.ApproxTrainData.xi.

Referenced by approx.algorithms.Componentwise.templateComputeApproximation().

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function nc = approx.algorithms.ABase.getTotalNumConfigurations ( )

Definition at line 398 of file ABase.m.

References ExpConfig, IClassConfig.getNumConfigurations(), and kernels.config.ExpansionConfig.StateConfig.

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static function this = approx.algorithms.ABase.loadobj	(	this,
		initfrom
	)

staticprotected

Definition at line 451 of file ABase.m.

References ErrorFun, ExpConfig, KerMorObject.KerMorObject(), LastCompTime, MaxErrors, MaxRelErrors, StopFlags, UsefScaling, ValidationErrors, and ValidationRelErrors.

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function approx.algorithms.ABase.plotSummary	(	pm,
		context
	)

virtual

Implements IReductionSummaryPlotProvider.

Definition at line 356 of file ABase.m.

References BestExpConfig, ExpConfig, MaxErrors, MaxRelErrors, t, ValidationErrors, and ValidationRelErrors.

function approx.algorithms.ABase.templateComputeApproximation	(	kernels.KernelExpansion	kexp,
		data.ApproxTrainData	atd,
			avd
	)

protectedpure virtual

Performs the actual approximation after scaling.

Template method.

Parameters

kexp	A kernel expansion.
atd	The approximation training data.

Referenced by computeApproximation().

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Member Data Documentation

approx.algorithms.ABase.BestExpConfig

Index of the best expansion config determined by the algorithm.

Definition at line 201 of file ABase.m.

Referenced by clone(), approx.algorithms.Componentwise.collectFromExpConfigSplit(), getApproximationSummary(), plotSummary(), approx.algorithms.VKOGA.startAdaptiveExtension(), and approx.algorithms.Componentwise.templateComputeApproximation().

approx.algorithms.ABase.ErrorFun = @Norm.L2

The error function to apply on each data vector.

Must be a function_handle that takes one matrix argument. The result is computed along the first dimension, i.e. the return value has the same number of columns than the input matrix.

Property class important:: Depending on the approximation goal different error functions are suitable.

Default: Norm.L2

See Also: Norm

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

Definition at line 87 of file ABase.m.

Referenced by clone(), getError(), loadobj(), and approx.algorithms.VKOGA.startAdaptiveExtension().

approx.algorithms.ABase.ExpConfig = "[]"

The different kernel expansion configurations to try.

Property class critical:: Without this setting this algorithm makes little sense.

Default: []

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

Definition at line 55 of file ABase.m.

Referenced by clone(), approx.algorithms.Componentwise.collectFromExpConfigSplit(), computeApproximation(), getApproximationSummary(), getTotalNumConfigurations(), loadobj(), approx.algorithms.Componentwise.plotSummary(), plotSummary(), approx.algorithms.VKOGA.startAdaptiveExtension(), approx.algorithms.AAdaptiveBase.templateComputeApproximation(), and approx.algorithms.Componentwise.templateComputeApproximation().

approx.algorithms.ABase.LastCompTime = "[]"

The computation time for the last run in seconds.

Default: []

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

Definition at line 111 of file ABase.m.

Referenced by clone(), approx.algorithms.Componentwise.collectFromExpConfigSplit(), computeApproximation(), and loadobj().

approx.algorithms.ABase.MaxErrors = "[]"

For each configuration, contains a row with the maximum errors on the training data. The number of columns depends on the type of algorithm implemented by the subclasses.

Default: []

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

Definition at line 124 of file ABase.m.

Referenced by clone(), approx.algorithms.Componentwise.collectFromExpConfigSplit(), approx.algorithms.VKOGA.loadobj(), loadobj(), approx.algorithms.Componentwise.plotSummary(), plotSummary(), approx.algorithms.VKOGA.startAdaptiveExtension(), approx.algorithms.AAdaptiveBase.templateComputeApproximation(), and approx.algorithms.Componentwise.templateComputeApproximation().

approx.algorithms.ABase.MaxRelErrors = "[]"

For each configuration, contains a row with the maximum relative errors on the training data. The number of columns depends on the type of algorithm implemented by the subclasses.

Default: []

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

Definition at line 139 of file ABase.m.

Referenced by approx.algorithms.VKOGA.clone(), clone(), approx.algorithms.Componentwise.collectFromExpConfigSplit(), loadobj(), approx.algorithms.Componentwise.plotSummary(), plotSummary(), approx.algorithms.VKOGA.startAdaptiveExtension(), approx.algorithms.AAdaptiveBase.templateComputeApproximation(), and approx.algorithms.Componentwise.templateComputeApproximation().

approx.algorithms.ABase.ScalingG

protected

If UsefScaling is set to true, this matrix contains the scaling matrix which has to be used in sub-algorithms in order to compute the correct approximation error on training data.

This is automatically done upon calls to ABase.getError.

See Also: UsefScaling

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

Definition at line 213 of file ABase.m.

Referenced by clone(), computeApproximation(), and getError().

approx.algorithms.ABase.StopFlags = "[]"

For each effective configuration, the stop flags are stored here.

Default: []

See Also: StopFlag

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

Definition at line 184 of file ABase.m.

Referenced by clone(), approx.algorithms.Componentwise.collectFromExpConfigSplit(), approx.algorithms.VKOGA.loadobj(), loadobj(), approx.algorithms.VKOGA.startAdaptiveExtension(), and approx.algorithms.Componentwise.templateComputeApproximation().

approx.algorithms.ABase.UsefScaling = false

Flag that determines whether the approximation center f values should be scaled to [-1,1] before the approximation is computed.

Property class optional:: This option makes sense when using univariate rotation-invariant kernels as different dimensions might have different scales

Default: false

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

Definition at line 70 of file ABase.m.

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

approx.algorithms.ABase.ValidationErrors = "[]"

For each configuration, contains a row with the maximum errors on the validation data. The number of columns depends on the type of algorithm implemented by the subclasses.

Default: []

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

Definition at line 154 of file ABase.m.

Referenced by clone(), approx.algorithms.Componentwise.collectFromExpConfigSplit(), loadobj(), approx.algorithms.Componentwise.plotSummary(), plotSummary(), approx.algorithms.VKOGA.startAdaptiveExtension(), approx.algorithms.AAdaptiveBase.templateComputeApproximation(), and approx.algorithms.Componentwise.templateComputeApproximation().

approx.algorithms.ABase.ValidationRelErrors = "[]"

For each configuration, contains a row with the maximum relative errors on the validation data. The number of columns depends on the type of algorithm implemented by the subclasses.

Default: []

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

Definition at line 169 of file ABase.m.

Referenced by clone(), approx.algorithms.Componentwise.collectFromExpConfigSplit(), loadobj(), approx.algorithms.Componentwise.plotSummary(), plotSummary(), approx.algorithms.VKOGA.startAdaptiveExtension(), approx.algorithms.AAdaptiveBase.templateComputeApproximation(), and approx.algorithms.Componentwise.templateComputeApproximation().

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

core/+approx/+algorithms/ABase.m

Detailed Description

Public Member Functions

Public Attributes

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation