Trajectory-piecewise function approximation. More...

Detailed Description

Trajectory-piecewise function approximation.

Implements the trajectory-piecewise approximation algorithm proposed in [RW01/Re03], Rewienski, M.: A trajectory piecewise-linear approach to model order reduction of nonlinear dynamical systems. Ph.D. thesis, Citeseer (2003)

The implementation is only completely like the proposed one if the data.selection.EpsSelector is used in conjunction with this class.

Author: Daniel Wirtz

Date: 2011-04-01

Change in 0.5:: (Daniel Wirtz, 2011-07-07) Changed this class to adopt to the new BaseApprox interface.

Change in 0.4:

(Daniel Wirtz, 2011-05-10)

The \(A_i\) matrices are now sparse if applicable (numel ~= 0 / numel < .5)
Removed the WeightFun property and reintroduced the Beta property, correctly forwarding the setting to the internally used gauss kernel.

New in 0.4:: (Daniel Wirtz, 2011-05-06) Finished the TPWL implementation. Multiargument-evaluations now work and the WeightFun was set to the TPWL source papers default \(e^{-\beta \frac{d_i}{m}}\).

Change in 0.3:: (Syed Ammar, 2011-04-21) Implemented Setters for the properties

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 TPWLApprox.m.

Public Member Functions
	TPWLApprox (sys)

function copy =	clone ()

function projected =	project (V, W)
	Implements AProjectable.project() More...

function matrix < double > y =	evaluate (colvec< double > x,double t,colvec< double > mu)
	Directly overrides the evaluate method of the ACoreFun as custom projection and multi-argument evaluations are natively possible. More...

function	approximateSystemFunction (models.BaseFullModel model)

function matrix < double > y =	evaluateCoreFun ()
	Noting to do here, evaluate is implemented directly. This method will never be called. More...

Public Member Functions inherited from approx.BaseApprox
	BaseApprox (sys)

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

virtual function	approximateSystemFunction (model)
	Computes the approximation according to the concrete approximation strategy. More...

Public Member Functions inherited from dscomponents.ACoreFun
	ACoreFun (sys)

function	setSystem (sys)

function target =	project (V, W, target)
	Sets the protected \(\vV,\vW\) matrices that can be utilized on core function evaluations after projection. More...

function fx =	evaluate (x, t)
	Evaluates the f-approximation. Depending on a possible projection and the CustomProjection-property the function either calls the inner evaluation directly which assumes \(f = f^r(z)\) or projects the reduced state variable z into the original space and evaluates the function there, so via \(f = V'f(Vz)\). More...

function fx =	evaluateMulti (colvec< double > x,double t,colvec< double > mu)
	Evaluates this function on multiple locations and maybe multiple times and parameters. More...

function	prepareSimulation (colvec< double > mu)
	A method that allows parameter-dependent computations to be performed before a simulation using this parameter starts. More...

function J =	getStateJacobian (x, t)
	Default implementation of jacobian matrix evaluation via finite differences. More...

function J =	getStateJacobianImpl (colvec< double > x,double t)
	Default implementation of state jacobians. uses finite differences. More...

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

function [ matrix< double > J , dx ] =	getStateJacobianFD (x, t,rowvec< integer > partidx)
	Implementation of jacobian matrix evaluation via finite differences. More...

virtual function fx =	evaluateCoreFun (colvec< double > x,double t)
	Actual method used to evaluate the dynamical sytems' core function. More...

function res =	test_MultiArgEval (mudim)
	Convenience function that tests if a custom MultiArgumentEvaluation works as if called with single arguments. More...

function logical res =	test_Jacobian (matrix< double > xa,rowvec< double > ta,matrix< double > mua)
	Tests the custom provided jacobian matrix against the default finite difference computed one. 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 Member Functions inherited from general.AProjectable
function handle target =	project (matrix< double > V,matrix< double > W,handle target)
	Returns a NEW INSTANCE of the projected object that does not rely on data of the old one via references (everything must be copied to ensure separability of reduced(=projected) versions and full versions, unless. More...

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

Static Public Member Functions
static function res =	test_TWPLApprox ()

Static Public Member Functions inherited from approx.BaseApprox
static function res =	test_ApproxProjections ()

Public Attributes
	MinWeightValue = 1e-10
	The minimum value a weight needs to have after normalization in order to affect the evaluation. Set this value to a certain threshold in order to restrict globally supported weight functions (i.e. the Gaussian) to a local support. More...

	Beta

	xi
	The centers. More...

	Ai
	The gradient matrix. More...

	bi

	GaussWeight

	fBeta = 25

Public Attributes inherited from approx.BaseApprox
data.selection.ASelector	TrainDataSelector
	The algorithm that selects the approximation training data. More...

Public Attributes inherited from dscomponents.ACoreFun
logical	TimeDependent = true
	Flag that indicates if the ACoreFun is (truly) time-dependent. More...

	CustomProjection = false
	Set this property if the projection process is customized by overriding the default project method. More...

sparse< logical >	JSparsityPattern = "[]"
	Sparsity pattern for the jacobian matrix. More...

integer	xDim = "[]"
	The current state space dimension of the function's argument \(x\). More...

integer	fDim = "[]"
	The current output dimension of the function. More...

models.BaseFirstOrderSystem	System
	The system associated with the current ACoreFun. More...

colvec< double >	mu = "[]"
	The current model parameter mu for evaluations. Will not be persisted as only valid for runtime during simulations. More...

	Vcache

	Wcache

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...

Public Attributes inherited from general.AProjectable
	V
	The \(V\) matrix of the biorthogonal pair \(V,W\). More...

	W
	The \(W\) matrix of the biorthogonal pair \(V,W\). 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 dscomponents.ACoreFun
static function obj =	loadobj (obj, from)

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)

Static Protected Member Functions inherited from general.AProjectable
static function obj =	loadobj (obj, from)

Constructor & Destructor Documentation

approx.TPWLApprox.TPWLApprox ( sys )

Definition at line 151 of file TPWLApprox.m.

References Beta, dscomponents.ACoreFun.CustomProjection, GaussWeight, DPCMObject.registerProps(), and approx.BaseApprox.TrainDataSelector.

Here is the call graph for this function:

Member Function Documentation

function approx.TPWLApprox.approximateSystemFunction ( models.BaseFullModel model )

Definition at line 247 of file TPWLApprox.m.

References Ai, data.ModelData.ApproxTrainData, bi, models.BaseFullModel.Data, models.BaseModel.DefaultInput, models.BaseFirstOrderSystem.f, dscomponents.ACoreFun.getStateJacobian(), dscomponents.ACoreFun.mu, models.BaseFirstOrderSystem.setConfig(), models.BaseModel.System, and xi.

Here is the call graph for this function:

function copy = approx.TPWLApprox.clone ( )

Definition at line 165 of file TPWLApprox.m.

References Ai, Beta, bi, MinWeightValue, dscomponents.ACoreFun.System, and xi.

Referenced by project().

Here is the caller graph for this function:

function matrix< double > y = approx.TPWLApprox.evaluate	(	colvec< double >	x,
		double	t,
		colvec< double >	mu
	)

Directly overrides the evaluate method of the ACoreFun as custom projection and multi-argument evaluations are natively possible.

Implements ACoreFun abstract template method

Parameters

x	The state variable vector \(\vx(t)\)
t	The current time(s) \(t \in [0, T]\)
mu	The currently used parameter \(\vmu\). Set to \([]\) if not used.

Definition at line 194 of file TPWLApprox.m.

References Ai, bi, GaussWeight, MinWeightValue, handle.reshape, t, and xi.

function matrix< double > y = approx.TPWLApprox.evaluateCoreFun ( )

Noting to do here, evaluate is implemented directly. This method will never be called.

Definition at line 269 of file TPWLApprox.m.

function projected = approx.TPWLApprox.project	(	V,
		W
	)

Implements AProjectable.project()

Generated fields of projected:

Definition at line 176 of file TPWLApprox.m.

References Ai, bi, clone(), t, general.AProjectable.V, and xi.

Here is the call graph for this function:

static function res = approx.TPWLApprox.test_TWPLApprox ( )

static

Definition at line 280 of file TPWLApprox.m.

References Norm.L2(), and dscomponents.ACoreFun.mu.

Here is the call graph for this function:

Member Data Documentation

approx.TPWLApprox.Ai

The gradient matrix.

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

Definition at line 98 of file TPWLApprox.m.

Referenced by approximateSystemFunction(), clone(), evaluate(), and project().

approx.TPWLApprox.Beta

Property class critical:

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 74 of file TPWLApprox.m.

Referenced by clone(), and TPWLApprox().

approx.TPWLApprox.bi

Definition at line 108 of file TPWLApprox.m.

Referenced by approximateSystemFunction(), clone(), evaluate(), and project().

approx.TPWLApprox.fBeta = 25

Definition at line 112 of file TPWLApprox.m.

approx.TPWLApprox.GaussWeight

Definition at line 110 of file TPWLApprox.m.

Referenced by evaluate(), and TPWLApprox().

approx.TPWLApprox.MinWeightValue = 1e-10

The minimum value a weight needs to have after normalization in order to affect the evaluation. Set this value to a certain threshold in order to restrict globally supported weight functions (i.e. the Gaussian) to a local support.

Property class experimental:: Might not be used in the end, so far only for speedup (locality)

Note: This property has the MATLAB attribute SetObservable set to true.; Matlab documentation of property attributes.
Default: 1e-10; This property has custom functionality when its value is changed.

Definition at line 55 of file TPWLApprox.m.

Referenced by clone(), and evaluate().

approx.TPWLApprox.xi

The centers.

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

Definition at line 88 of file TPWLApprox.m.

Referenced by approximateSystemFunction(), clone(), evaluate(), and project().

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

core/+approx/TPWLApprox.m

Detailed Description

Public Member Functions

Static Public Member Functions

Public Attributes

Additional Inherited Members

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation