DEIMEstimator: A-posteriori error estimation for DEIM reduced models. More...

Detailed Description

DEIMEstimator: A-posteriori error estimation for DEIM reduced models.

Author: Daniel Wirtz

Date: 2012-05-10

Change in 0.6:

(Daniel Wirtz, 2012-06-11)

Added support for different norm-inducing matrices \(\vG\).
New property UseTrueDEIMErr to enable use of the actual DEIM approximation error within the alpha term computation (Experimental use)

New in 0.6:

(Daniel Wirtz, 2012-06-08)

Introduced the property JacMatDEIMMaxOrder to control the jacobian DEIM approximation quality
Made the JacMDEIM property private
Introduced flags for more expensive (comparison-purpose) estimators
Removed the ErrorOrder setting as the DEIMEstimator directly depends on the Order setting of the reduced model's DEIM approximation. Setting the DEIM order "remotely" from the error estimator introduced more trouble than necessary
Not re-using the previously computed JacMDEIM approximation upon new runs of offlineGenerations (mess)
Giving out a warning if no sufficient reduction by the similarity transformation is achieved and disabling it for less than 20% reduction.
Using an event listener for the DEIM OrderUpdated event to re-compute local error estimation matrices

Change in 0.6:: (Daniel Wirtz, 2012-05-26) Updated the computation to the new structure of systems (A + f components) and replaced the previous (errorneous) one

New in 0.6:: (Daniel Wirtz, 2012-05-10) 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 DEIMEstimator.m.

Public Member Functions
	DEIMEstimator ()

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

function a =	getAlpha (colvec< double > x,double t,colvec< double > ut)
	More expensive variant, using the true DEIM approximation error instead of the estimated ones using M,M' technique. More...

function b =	getBeta (colvec< double > x,double t)
	Old log lip const kernel learning code x = x .* (this.scale(:,2) - this.scale(:,1)) + this.scale(:,1); x = (x - this.scale(:,1)) ./ (this.scale(:,2) - this.scale(:,1)); b = this.kexp.evaluate(x, t, mu)*olderr + sqrt(abs(a));. More...

function eint =	evalODEPart (colvec< double > x,double t,colvec< double > ut)
	Compose the ode function. More...

function time =	postProcess (matrix< double > x,double t,integer inputidx)
	Postprocessing for the error estimate. More...

function copy =	clone ()

function	plotSummary (pm, context)

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...

virtual function eint =	evalODEPart (colvec x,double t,double ut)
	Template method for evaluation of the auxiliary ode part of the error estimator. 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)
	Abstract static method that forces subclasses to specify whether an estimator can be used for a given model or not. 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
integer	JacSimTransMaxSize = 50
	The maximum size of the similarity transformation. More...

integer	JacMatDEIMMaxOrder = 50
	Maximum order for the DEIM approximation of the state space jacobian. More...

data.selection.ASelector	TrainDataSelector
	The selector that chooses the full model's trajectory points that are used for the MatrixDEIM approximation of the jacobian and the partial similarity transformation. More...

	UseFullJacobian = false
	"Expensive version": Using the full system's jacobian for logarithmic norm computation. Included for easy error estimator comparison. More...

	UseTrueLogLipConst = false
	"Even More Expensive version": Precompute the full solution and use the true logarithmic lipschitz constant of \(f\) in computations. Included for easy error estimator comparison. More...

	UseJacobianLogLipConst = false
	"Even More Expensive version 2": Precompute the full solution and use the true logarithmic lipschitz constant of the jacobian of \(f\) in computations. Included for easy error estimator comparison. More...

	UseJacobianNorm = false
	Expensive conservative guess. More...

	UseTrueDEIMErr = false
	"Expensive" version that uses the true approximation error between the DEIM approximation and the full system function instead of the \(M'\) variant. More...

matrix< double >	QFull = "[]"
	The complete similarity transformation \(\vQ\) matrix of size \(d \times JacSimTransMaxSize\). More...

rowvec< double >	QSingVals = "[]"
	The singular values computed by the SimTransPOD in the offline stage. More...

general.MatrixDEIM	JacMDEIM
	The MatrixDEIM instance used to approximate the state space jacobian matrices. More...

	M3 = "[]"

	M4 = "[]"

	M5 = "[]"

	M6 = "[]"

	M7 = "[]"

	M8 = "[]"

	M9 = "[]"

	M10 = "[]"

	M11 = "[]"

	M12 = "[]"

	Ah
	the \(\hat{A}\) component More...

	Bh
	the \(\hat{B}\) component More...

	Aln
	The precomputed logarithmic norms of the system's A components. More...

	scale
	Stores zi min- and max scaling. More...

	LastAlpha

	LastBeta

	kexp
	The local logarithmic norm estimation. More...

integer	JacSimTransSize
	The size of the partial similarity transform to apply to the matrix DEIM approximated jacobians. More...

integer	JacMatDEIMOrder
	The actual order of the DEIM approximation for the system's jacobian. More...

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...

Static Protected Member Functions
static function obj =	loadobj (obj)

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 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)

Constructor & Destructor Documentation

error.DEIMEstimator.DEIMEstimator ( )

Definition at line 349 of file DEIMEstimator.m.

References error.BaseEstimator.ExtraODEDims, and TrainDataSelector.

Member Function Documentation

function copy = error.DEIMEstimator.clone ( )

Definition at line 702 of file DEIMEstimator.m.

References handle.addlistener, Ah, Aln, Bh, ICloneable.clone(), general.MatrixDEIM.clone(), JacMatDEIMMaxOrder, JacMDEIM, JacSimTransMaxSize, kexp, M10, M11, M12, M3, M4, M5, M6, M7, M8, M9, QFull, QSingVals, scale, TrainDataSelector, UseFullJacobian, UseTrueDEIMErr, and UseTrueLogLipConst.

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function eint = error.DEIMEstimator.evalODEPart	(	colvec< double >	x,
		double	t,
		colvec< double >	ut
	)

Compose the ode function.

Parameters

x	The state variable vector \(\vx(t)\)
t	The current time(s) \(t \in [0, T]\)
ut	The value \(\vu(t)\) of the current input function \(\vu\) at time \(t\), [] else.

Definition at line 656 of file DEIMEstimator.m.

References getAlpha(), and getBeta().

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function a = error.DEIMEstimator.getAlpha	(	colvec< double >	x,
		double	t,
		colvec< double >	ut
	)

More expensive variant, using the true DEIM approximation error instead of the estimated ones using M,M' technique.

Parameters

x	The state variable vector \(\vx(t)\)
t	The current time(s) \(t \in [0, T]\)
ut	The value \(\vu(t)\) of the current input function \(\vu\) at time \(t\), [] else.

Definition at line 507 of file DEIMEstimator.m.

References models.BaseFirstOrderSystem.A, dscomponents.LinearCoreFun.evaluate(), models.BaseFirstOrderSystem.f, models.ReducedModel.FullModel, LastAlpha, Norm.LG(), M11, M12, M4, M5, M6, M7, M8, M9, error.BaseEstimator.mu, error.BaseEstimator.ReducedModel, models.BaseModel.System, and UseTrueDEIMErr.

Referenced by evalODEPart(), and postProcess().

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function b = error.DEIMEstimator.getBeta	(	colvec< double >	x,
		double	t
	)

Old log lip const kernel learning code x = x .* (this.scale(:,2) - this.scale(:,1)) + this.scale(:,1); x = (x - this.scale(:,1)) ./ (this.scale(:,2) - this.scale(:,1)); b = this.kexp.evaluate(x, t, mu)*olderr + sqrt(abs(a));.

Parameters

x	The state variable vector \(\vx(t)\)
t	The current time(s) \(t \in [0, T]\)

Definition at line 580 of file DEIMEstimator.m.

References Aln, general.MatrixDEIM.evaluate(), models.BaseFirstOrderSystem.f, models.ReducedModel.FullModel, dscomponents.ACoreFun.getStateJacobian(), JacMDEIM, LastBeta, Utils.logNorm(), error.BaseEstimator.mu, error.BaseEstimator.ReducedModel, models.BaseModel.System, UseFullJacobian, UseJacobianLogLipConst, UseJacobianNorm, and UseTrueLogLipConst.

Referenced by evalODEPart(), and postProcess().

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static function obj = error.DEIMEstimator.loadobj ( obj )

staticprotected

Definition at line 1044 of file DEIMEstimator.m.

References handle.addlistener.

function error.DEIMEstimator.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 356 of file DEIMEstimator.m.

References models.BaseFirstOrderSystem.A, Aln, KerMor.App(), Utils.logNorm(), and models.BaseModel.System.

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function error.DEIMEstimator.plotSummary	(	pm,
		context
	)

virtual

Implements IReductionSummaryPlotProvider.

Definition at line 770 of file DEIMEstimator.m.

References QSingVals.

function time = error.DEIMEstimator.postProcess	(	matrix< double >	x,
		double	t,
		integer	inputidx
	)

Postprocessing for the error estimate.

t, mu, inputidx do nothing

Parameters

x	The whole just computed trajectory
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.
varargin	Any further arguments that are passed, but ignored here as not necessary.

Definition at line 670 of file DEIMEstimator.m.

References getAlpha(), getBeta(), LastAlpha, LastBeta, error.BaseEstimator.mu, error.BaseEstimator.ReducedModel, models.BaseModel.scaledTimes, and error.BaseEstimator.StateError.

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

Definition at line 469 of file DEIMEstimator.m.

References error.BaseEstimator.Enabled, general.DEIM.f, JacMDEIM, kexp, LastAlpha, LastBeta, M6, M7, M8, M9, dscomponents.ACoreFun.prepareSimulation(), error.BaseEstimator.ReducedModel, UseJacobianLogLipConst, and UseTrueLogLipConst.

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function prepared = error.DEIMEstimator.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

Required fields of rm:

Generated fields of prepared:

Definition at line 402 of file DEIMEstimator.m.

References handle.addlistener, models.BaseFirstOrderSystem.f, models.ReducedModel.FullModel, G, JacMDEIM, general.MatrixDEIM.project(), models.BaseModel.System, t, models.ReducedModel.V, and models.ReducedModel.W.

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

static

Abstract static method that forces subclasses to specify whether an estimator can be used for a given model or not.

Parameters

model A KerMor full model

Required fields of model:

Definition at line 1054 of file DEIMEstimator.m.

References models.BaseFirstOrderSystem.A, models.BaseFullModel.Approx, models.BaseFirstOrderSystem.B, and models.BaseModel.System.

Member Data Documentation

error.DEIMEstimator.Ah

the \(\hat{A}\) component

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

Definition at line 231 of file DEIMEstimator.m.

Referenced by clone().

error.DEIMEstimator.Aln

The precomputed logarithmic norms of the system's A components.

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

Definition at line 250 of file DEIMEstimator.m.

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

error.DEIMEstimator.Bh

the \(\hat{B}\) component

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

Definition at line 240 of file DEIMEstimator.m.

Referenced by clone().

error.DEIMEstimator.JacMatDEIMMaxOrder = 50

Maximum order for the DEIM approximation of the state space jacobian.

Default: 50

Definition at line 80 of file DEIMEstimator.m.

Referenced by clone().

error.DEIMEstimator.JacMatDEIMOrder

The actual order of the DEIM approximation for the system's jacobian.

Upper bounded by JacMatDEIMMaxOrder and defaults to the ceiled half of the maximum size (set during offlineComputations)

Default: ceil(JacMatDEIMMaxOrder/2)

See Also: JacMatDEIMMaxOrder

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

Definition at line 310 of file DEIMEstimator.m.

error.DEIMEstimator.JacMDEIM

The MatrixDEIM instance used to approximate the state space jacobian matrices.

The default MaxOrder setting is 50.

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

Definition at line 193 of file DEIMEstimator.m.

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

error.DEIMEstimator.JacSimTransMaxSize = 50

The maximum size of the similarity transformation.

Set to empty if not wanted. The BaseFullModel sets this value at offline generations phase

Default: 50

See Also: JacSimTransSize

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

Definition at line 65 of file DEIMEstimator.m.

Referenced by clone().

error.DEIMEstimator.JacSimTransSize

The size of the partial similarity transform to apply to the matrix DEIM approximated jacobians.

Upper bounded by JacSimTransMaxSize and defaults to the ceiled half of the maximum size (set during offlineComputations)

Default: ceil(JacSimTransMaxSize/2)

See Also: JacSimTransMaxSize

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

Definition at line 291 of file DEIMEstimator.m.

error.DEIMEstimator.kexp

The local logarithmic norm estimation.

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

Definition at line 278 of file DEIMEstimator.m.

Referenced by clone(), and prepareConstants().

error.DEIMEstimator.LastAlpha

Definition at line 272 of file DEIMEstimator.m.

Referenced by getAlpha(), postProcess(), and prepareConstants().

error.DEIMEstimator.LastBeta

Definition at line 275 of file DEIMEstimator.m.

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

error.DEIMEstimator.M10 = "[]"

Definition at line 225 of file DEIMEstimator.m.

Referenced by clone().

error.DEIMEstimator.M11 = "[]"

Definition at line 227 of file DEIMEstimator.m.

Referenced by clone(), and getAlpha().

error.DEIMEstimator.M12 = "[]"

Definition at line 229 of file DEIMEstimator.m.

Referenced by clone(), and getAlpha().

error.DEIMEstimator.M3 = "[]"

Definition at line 211 of file DEIMEstimator.m.

Referenced by clone().

error.DEIMEstimator.M4 = "[]"

Definition at line 213 of file DEIMEstimator.m.

Referenced by clone(), and getAlpha().

error.DEIMEstimator.M5 = "[]"

Definition at line 215 of file DEIMEstimator.m.

Referenced by clone(), and getAlpha().

error.DEIMEstimator.M6 = "[]"

Definition at line 217 of file DEIMEstimator.m.

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

error.DEIMEstimator.M7 = "[]"

Definition at line 219 of file DEIMEstimator.m.

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

error.DEIMEstimator.M8 = "[]"

Definition at line 221 of file DEIMEstimator.m.

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

error.DEIMEstimator.M9 = "[]"

Definition at line 223 of file DEIMEstimator.m.

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

error.DEIMEstimator.QFull = "[]"

The complete similarity transformation \(\vQ\) matrix of size \(d \times JacSimTransMaxSize\).

(Debug/testing use)

Default: []

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

Definition at line 161 of file DEIMEstimator.m.

Referenced by clone().

error.DEIMEstimator.QSingVals = "[]"

The singular values computed by the SimTransPOD in the offline stage.

(Debug/testing use)

Default: []

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

Definition at line 177 of file DEIMEstimator.m.

Referenced by clone(), and plotSummary().

error.DEIMEstimator.scale

Stores zi min- and max scaling.

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

Definition at line 261 of file DEIMEstimator.m.

Referenced by clone().

error.DEIMEstimator.TrainDataSelector

The selector that chooses the full model's trajectory points that are used for the MatrixDEIM approximation of the jacobian and the partial similarity transformation.

Default:: data.selection.DefaultSelector

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

Definition at line 91 of file DEIMEstimator.m.

Referenced by clone(), and DEIMEstimator().

error.DEIMEstimator.UseFullJacobian = false

"Expensive version": Using the full system's jacobian for logarithmic norm computation. Included for easy error estimator comparison.

Default: false

Definition at line 104 of file DEIMEstimator.m.

Referenced by clone(), and getBeta().

error.DEIMEstimator.UseJacobianLogLipConst = false

"Even More Expensive version 2": Precompute the full solution and use the true logarithmic lipschitz constant of the jacobian of \(f\) in computations. Included for easy error estimator comparison.

Default: false

Definition at line 127 of file DEIMEstimator.m.

Referenced by getBeta(), and prepareConstants().

error.DEIMEstimator.UseJacobianNorm = false

Expensive conservative guess.

Default: false

Definition at line 139 of file DEIMEstimator.m.

Referenced by getBeta().

error.DEIMEstimator.UseTrueDEIMErr = false

"Expensive" version that uses the true approximation error between the DEIM approximation and the full system function instead of the \(M'\) variant.

Default: false

Definition at line 148 of file DEIMEstimator.m.

Referenced by clone(), and getAlpha().

error.DEIMEstimator.UseTrueLogLipConst = false

"Even More Expensive version": Precompute the full solution and use the true logarithmic lipschitz constant of \(f\) in computations. Included for easy error estimator comparison.

Default: false

Definition at line 115 of file DEIMEstimator.m.

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

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

core/+error/DEIMEstimator.m

Detailed Description

Public Member Functions

Static Public Member Functions

Public Attributes

Static Protected Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation