IterationCompLemmaEstimator: A-posteriori error estimator for kernel-based systems using local lipschitz constants. More...

Detailed Description

IterationCompLemmaEstimator: A-posteriori error estimator for kernel-based systems using local lipschitz constants.

Implementation as in [WH10], but with updated ExtraODEDims and numerical computation.

Model requirements: ReducedModel.System.f is an instance of AKernelCoreFun FullModel.Approx is an instance of CompwiseKernelCoreFun

Author: Daniel Wirtz

Date: 2010-08-10

Change in 0.5:

(Daniel Wirtz, 2011-07-07)

New properties smallz_flag to correctly transform the input space dimension on beta-computation depending on whether rotation invariant kernels are used or not.
Also made the estimator work with kernels.ParamTimeKernelExpansions

Change in 0.5:: (Daniel Wirtz, 2011-07-04) Changed this class name to "IterationCompLemmaEstimator".

Change in 0.4:

(Daniel Wirtz, 2011-05-29)

Changed this classes name to "LocalKernelEstimator".
Restructured the error estimators to better adopt to the current formulation. Now the KernelEstimators have a function getBeta instead of implementing the evalODEPart by themselves.

Change in 0.4:: (Daniel Wirtz, 2011-05-25) Changed the computations to the comparison lemma type. This reduced the needed extra ODE dimensions to one and speeds up the evaluation process.

Change in 0.4:: (Daniel Wirtz, 2011-05-23) Adopted to the new error.BaseEstimator interface with separate output error computation.

Change in 0.3:: (Daniel Wirtz, 2011-05-02) Changed the implementation of the evalODEPart so that only two extra ODE dimensions are needed. This avoids NaN entries when exponential values grow too big.

Change in 0.3:: (Syed Ammar, 2011-04-23) Implemented Setters for the properties LocalLipschitzFcn and UseTimeDiscreteC

New in 0.1:: (Daniel Wirtz, 2010-08-10) 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 18 of file IterationCompLemmaEstimator.m.

Public Member Functions
function copy =	clone ()
	Creates a deep copy of this estimator instance. More...

function	offlineComputations (models.BaseFullModel fm)
	Overrides the method from BaseEstimator and performs additional computations. More...

function prepared =	prepareForReducedModel (models.ReducedModel rm)
	Prepares this estimator for use with a given reduced model. Basically uses the projection matrices and some other reduced quantities for local storage. More...

function b =	getBeta (colvec xfull, t)
	Compute the local lipschitz constant estimations. More...

function	clear ()

function ct =	prepareConstants (colvec< double > mu,integer inputidx)
	Return values: ct: The time needed for preprocessing. More...

function ct =	postProcess (colvec< double > x,double t,integer inputidx)
	Return values: ct: The time needed for postprocessing. More...

Public Member Functions inherited from error.BaseCompLemmaEstimator
	BaseCompLemmaEstimator ()

function	offlineComputations (models.BaseFullModel model)
	Overrides the method from BaseEstimator and performs additional computations. More...

function prepared =	prepareForReducedModel (models.ReducedModel rm)
	Prepares this estimator for use with a given reduced model. Basically uses the projection matrices and some other reduced quantities for local storage. More...

function e =	evalODEPart (colvec x,double t,double ut)
	Evaluates the auxiliary ode part for the comparison-lemma based error estimators. More...

function ct =	prepareConstants (colvec< double > mu,integer inputidx)

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

function	clear ()

function a =	getAlpha (colvec< double > x,double t,colvec< double > ut)
	Convenience access method for semi-implicit euler method. More...

function ct =	postProcess (colvec< double > x,double t,integer inputidx)
	Return values: ct: The time needed for postprocessing. More...

virtual function b =	getBeta (colvec x,double t)
	Computes the \(\beta(t)\) term from the error estimation ODE for given time and place. More...

Public Member Functions inherited from error.BaseEstimator
function	offlineComputations (models.BaseFullModel model)
	Performs a validity check for the given model and sets up the estimator for use with the specified model. More...

function double ct =	postProcess (unused1,rowvec t, unused2)
	Post-processes the error estimator ODE part after reduced simulation computation. More...

function	clear ()
	Clears the last error set by the estimator. More...

function copy =	clone (copy)
	Creates a copy of this error estimator. Call only allowed from subclasses. More...

function e0 =	getE0 (colvec< double > mu)
	Calls the inner initial error computation strategy. More...

function ct =	prepareConstants (colvec< double > mu, unused1)

function prepared =	prepareForReducedModel (models.ReducedModel rmodel)
	Default implementation which simply clones this (subclass!)instance and returns the copy to use in reduced models. 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 ()

Static Public Member Functions
static function errmsg =	validModelForEstimator (models.BaseFullModel model)
	Validations. More...

static function res =	test_IterationCompLemmaEstimator ()

Static Public Member Functions inherited from error.BaseCompLemmaEstimator
static function errmsg =	validModelForEstimator (models.BaseFullModel model)
	Validations. More...

Static Public Member Functions inherited from error.BaseEstimator
static function est =	getEstimator (models.BaseFullModel model)
	Factory method that creates a suitable error estimator for the given model. More...

static function errmsg =	validModelForEstimator (models.ReducedModel rmodel)
	Abstract static method that forces subclasses to specify whether an estimator can be used for a given model or not. More...

Public Attributes
error.lipfun.Base	LocalLipschitzFcn
	The internal kernel Lipschitz function to use. More...

	Iterations
	Determines how many postprocessing iterations for the estimator are performed. More...

logical	UseTimeDiscreteC = true
	For the local Lipschitz constant estimation the parameter C can be chosen to equal the error from the last time step. This has to be investigated more thoroughly as integration errors from the solver may lead to a loss of rigorousity. More...

	d_iValues
	The \(d_i(t)\) values for each integration time-step \(t\). More...

Public Attributes inherited from error.BaseCompLemmaEstimator
	EstimationData = "[]"
	\(3\times n\) matrix containing the \(t,\alpha(t),\beta(t)\) values at each time step. More...

	aComp

Public Attributes inherited from error.BaseEstimator
	Enabled
	Flag that indicates whether error estimation is used or not. More...

	StateError = "[]"
	The reduction state-space error from the last simulation. More...

	ExtraODEDims = 0
	The dimensions added to the ODE function by the estimator. More...

	OutputError = "[]"
	The output error from the last simulation. More...

models.ReducedModel	ReducedModel = "[]"
	The reduced model associated with the error estimator. More...

	mu

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...

Additional Inherited Members
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 inherited from DPCMObject
static function obj =	loadobj (obj, from)
	Re-register any registered change listeners! More...

static function obj =	loadobj (obj, from)

Protected Attributes inherited from error.BaseCompLemmaEstimator
	StepNr
	The current step. More...

Member Function Documentation

function error.IterationCompLemmaEstimator.clear ( )

Definition at line 332 of file IterationCompLemmaEstimator.m.

References d_iValues.

Referenced by prepareForReducedModel().

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function copy = error.IterationCompLemmaEstimator.clone ( )

Creates a deep copy of this estimator instance.

Generated fields of copy:

Definition at line 179 of file IterationCompLemmaEstimator.m.

References handle.addlistener, ICloneable.clone(), d_iValues, Iterations, LocalLipschitzFcn, and UseTimeDiscreteC.

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function b = error.IterationCompLemmaEstimator.getBeta	(	colvec	xfull,
			t
	)

Compute the local lipschitz constant estimations.

Parameters

xfull	The current state variable vector
t	The current time \(t\)
mu	The current parameter \(\mu\)

Definition at line 287 of file IterationCompLemmaEstimator.m.

References d_iValues, error.lipfun.Base.evaluate(), models.BaseFirstOrderSystem.f, Iterations, LocalLipschitzFcn, error.BaseEstimator.mu, error.BaseEstimator.ReducedModel, error.BaseCompLemmaEstimator.StepNr, models.BaseModel.System, t, UseTimeDiscreteC, and models.ReducedModel.V.

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function error.IterationCompLemmaEstimator.offlineComputations ( models.BaseFullModel fm )

Overrides the method from BaseEstimator and performs additional computations.

Parameters

fm	The full model.

Required fields of fm:

Definition at line 210 of file IterationCompLemmaEstimator.m.

References models.BaseFullModel.Approx, models.BaseFirstOrderSystem.f, Utils.getBoundingBox(), LocalLipschitzFcn, models.BaseModel.System, and X.

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function ct = error.IterationCompLemmaEstimator.postProcess	(	colvec< double >	x,
		double	t,
		integer	inputidx
	)

Return values: ct: The time needed for postprocessing.

Parameters

x	The state variable vector \(\vx(t)\)
t	The current time(s) \(t \in [0, T]\)
inputidx	The index \(i\) of the currently used input function \(u_i(t)\). Set to \([]\) if not used.

Definition at line 372 of file IterationCompLemmaEstimator.m.

References error.BaseEstimator.getE0(), Iterations, error.BaseEstimator.mu, models.BaseModel.ODESolver, error.BaseEstimator.ReducedModel, and error.BaseEstimator.StateError.

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function ct = error.IterationCompLemmaEstimator.prepareConstants	(	colvec< double >	mu,
		integer	inputidx
	)

Return values: ct: The time needed for preprocessing.

Parameters

mu	The currently used parameter \(\vmu\). Set to \([]\) if not used.
inputidx	The index \(i\) of the currently used input function \(u_i(t)\). Set to \([]\) if not used.

Definition at line 338 of file IterationCompLemmaEstimator.m.

References handle.addlistener, Iterations, LocalLipschitzFcn, models.BaseModel.ODESolver, error.BaseEstimator.ReducedModel, and UseTimeDiscreteC.

function prepared = error.IterationCompLemmaEstimator.prepareForReducedModel ( models.ReducedModel rm )

Prepares this estimator for use with a given reduced model. Basically uses the projection matrices and some other reduced quantities for local storage.

Parameters

rm	The reduced model

Return values

prepared A clone of this estimator, with accordingly projected components

Required fields of rm:

Generated fields of prepared:

Definition at line 248 of file IterationCompLemmaEstimator.m.

References handle.addlistener, models.BaseFullModel.Approx, clear(), models.BaseFirstOrderSystem.f, models.ReducedModel.FullModel, models.BaseModel.G, models.BaseModel.ODESolver, dscomponents.ACoreFun.project(), models.BaseModel.System, t, models.ReducedModel.V, and models.ReducedModel.W.

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static function res = error.IterationCompLemmaEstimator.test_IterationCompLemmaEstimator ( )

static

Definition at line 547 of file IterationCompLemmaEstimator.m.

function errmsg = error.IterationCompLemmaEstimator.validModelForEstimator ( models.BaseFullModel model )

static

Validations.

Parameters

model A KerMor full model

Required fields of model:

Definition at line 526 of file IterationCompLemmaEstimator.m.

References models.BaseFullModel.Approx, models.BaseFirstOrderSystem.f, and models.BaseModel.System.

Member Data Documentation

error.IterationCompLemmaEstimator.d_iValues

The \(d_i(t)\) values for each integration time-step \(t\).

Note: This property has the MATLAB attribute Transient set to true.; This property has non-standard access specifiers: SetAccess = Private, GetAccess = Public; Matlab documentation of property attributes.

Definition at line 127 of file IterationCompLemmaEstimator.m.

Referenced by clear(), clone(), and getBeta().

error.IterationCompLemmaEstimator.Iterations

Determines how many postprocessing iterations for the estimator are performed.

Has computationally no effect if UseTimeDiscreteC is switched on.

Default: 0

Note: This property has custom functionality when its value is changed.

Definition at line 97 of file IterationCompLemmaEstimator.m.

Referenced by clone(), getBeta(), postProcess(), and prepareConstants().

error.IterationCompLemmaEstimator.LocalLipschitzFcn

The internal kernel Lipschitz function to use.

Depending on the underlying kernel, a specific lipschitz constant estimation can be used. Each kernel has the method "getLipschitzFcn" which is by default implemented in BaseKernel. The resulting function handle is used by default; however, to enhance customizability, one can manually define a lipschitz estimation function here. (For an example: see the BellFunction kernel interface for different possibilities)

Function handle signature: di: The distances from the reduced system to the centers C: The locality constant that determines how far away the true system can maximally be (can be \(\infty\)) t: The current time \(t\) mu: The current parameter \(\mu\)

See Also: kernels.BaseKernel kernels.BellFunction error.lipfun.Base

Note: This property has custom functionality when its value is changed.

Definition at line 70 of file IterationCompLemmaEstimator.m.

Referenced by clone(), getBeta(), offlineComputations(), and prepareConstants().

error.IterationCompLemmaEstimator.UseTimeDiscreteC = true

For the local Lipschitz constant estimation the parameter C can be chosen to equal the error from the last time step. This has to be investigated more thoroughly as integration errors from the solver may lead to a loss of rigorousity.

Default: true

Defaults to true. (As is best estimator atm)

Note: This property has custom functionality when its value is changed.

Definition at line 110 of file IterationCompLemmaEstimator.m.

Referenced by clone(), getBeta(), and prepareConstants().

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

core/+error/IterationCompLemmaEstimator.m

Detailed Description

Public Member Functions

Static Public Member Functions

Public Attributes

Additional Inherited Members

Member Function Documentation

Member Data Documentation