Simple affine-linear core function "f" for a dynamical system. More...

Detailed Description

Simple affine-linear core function "f" for a dynamical system.

Simply wraps an affine-linear function into the ACoreFun interface to enable use of simple affine-linear functions as core function. At projection, each summand matrix is base changed into the basis given by V.

Author: Daniel Wirtz

Date: 15.03.2010

Change in 0.6:: (Daniel Wirtz, 2012-02-02) Removed the former offset term \(b\) as it can be modeled via the input source \(B(t,\mu)u(t)\) with constant \(u \equiv 1\).

New in 0.6:: (Daniel Wirtz, 2011) Added an optional offset term \(b\) to the AffLinCoreFun to enable affine-linear affine-parametric core functions.

Change in 0.5:: (Daniel Wirtz, 2011-07-07) Updated this class to use the new general.AffParamMatrix class inside.

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 AffLinCoreFun.m.

Public Member Functions
	AffLinCoreFun (sys)
	Creates a new instance of the AffLinCoreFun. More...

function fx =	evaluate (colvec< double > x,double t)
	Evaluates affine-linear core function by matrix-vector multiplication. More...

function fx =	evaluateMulti (colvec< double > x,double t,colvec< double > mu)

function	prepareSimulation (colvec< double > mu)

function fx =	evaluateCoreFun ()
	This method will never be called as evaluate is overridden directly for performance. this is possible as AffLinCoreFuns have both CustomProjection and MultiArgumentEvaluations. More...

function J =	getStateJacobian (unused1,double t)
	Overrides the default jacobian finite difference implementation. Jacobian of linear operator is the operator itself, i.e. in this case the linear combination of the matrices. More...

function c =	getGlobalLipschitz (double t,colvec< double > mu)
	Implementation of the interface method from IGlobalLipschitz. More...

function proj =	project (V, W)

function	addMatrix (string coeff_fcn,matrix< double > mat)
	Adds a new matrix to the affine-linear core function. More...

function prod =	mtimes (other)
	Implements the default multiplication method. More...

function diff =	minus (other)
	Implements the default subtraction method. More...

function sum =	plus (other)
	Implements the default addition method. More...

function transp =	ctranspose ()
	Implements the default transposition method. More...

function copy =	clone ()

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...

Public Member Functions inherited from general.AffParamMatrix
function M =	compose (t, mu)
	Composes the affine-linear combination of matrices for given time \(t\) and parameter \(\mu\). More...

function c =	evalCoeffFun (double t,colvec< double > mu)

function copy =	clone (copy)
	Creates a copy of this affine parametric matrix. More...

function	addMatrix (coeff_fun, mat)
	Adds a matrix with corresponding coefficient function to the affine parametric matrix. More...

function pr =	mtimes (B)
	Implements the default multiplication method. More...

function diff =	minus (B)
	Implements the default substraction method. More...

function transp =	ctranspose ()
	Implements the transposition for affine parametric matrices. More...

function dotprod =	times (B)

function M =	getMatrix (idx)
	Returns the \(i\)-th matrix of the AffParamMatrix. More...

function general.AffParamMatrix target =	project (matrix< double > V,matrix< double > W,general.AffParamMatrix target)
	Projects the affine parametric matrix using \(V\) and \(W\). More...

function [ n , m ] =	size (dim)
	Implementation of ABlockedData.size. More...

function	clear ()

Public Attributes
char	CoeffClass = ""
	Export setting. Java class name for JKerMor model export. 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...

Public Attributes inherited from general.AffParamMatrix
integer	N = 0
	The number of affine matrices / size of the linear combination. More...

	Matrices = "[]"
	The matrices for the affine function. More...

string	funStr = {""}
	The function strings defining \(\theta_i(t,\mu)\) for the affine-linear combination of the matrices. 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)

Protected Attributes inherited from general.AffParamMatrix
handle	cfun = "[]"
	coefficient function handle as specified by funStr More...

rowvec< integer >	dims
	dimension of the matrices More...

Constructor & Destructor Documentation

dscomponents.AffLinCoreFun.AffLinCoreFun ( sys )

Creates a new instance of the AffLinCoreFun.

Definition at line 83 of file AffLinCoreFun.m.

References dscomponents.ACoreFun.CustomProjection, and dscomponents.ACoreFun.TimeDependent.

Member Function Documentation

function dscomponents.AffLinCoreFun.addMatrix	(	string	coeff_fcn,
		matrix< double >	mat
	)

Adds a new matrix to the affine-linear core function.

See Also: general.AffParramMatrix

Parameters

coeff_fcn	A string describing the \(i\)-th coefficient function's evaluation as if entered into a function handle interior or a function. By convention, the passed arguments are named `t` and `mu`.
mat	The corresponding matrix \(A_i\)

Definition at line 196 of file AffLinCoreFun.m.

References all(), KerMor.App(), general.AffParamMatrix.cfun, dscomponents.ACoreFun.fDim, dscomponents.ACoreFun.JSparsityPattern, dscomponents.ACoreFun.mu, general.AffParamMatrix.size(), dscomponents.ACoreFun.TimeDependent, and dscomponents.ACoreFun.xDim.

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function copy = dscomponents.AffLinCoreFun.clone ( )

Definition at line 305 of file AffLinCoreFun.m.

References CoeffClass, and dscomponents.ACoreFun.System.

Referenced by project().

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function transp = dscomponents.AffLinCoreFun.ctranspose ( )

Implements the default transposition method.

Definition at line 276 of file AffLinCoreFun.m.

function fx = dscomponents.AffLinCoreFun.evaluate	(	colvec< double >	x,
		double	t
	)

Evaluates affine-linear core function by matrix-vector multiplication.

Parameters

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

Definition at line 97 of file AffLinCoreFun.m.

References general.AffParamMatrix.compose(), dscomponents.ACoreFun.mu, and dscomponents.ACoreFun.TimeDependent.

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function fx = dscomponents.AffLinCoreFun.evaluateCoreFun ( )

This method will never be called as evaluate is overridden directly for performance. this is possible as AffLinCoreFuns have both CustomProjection and MultiArgumentEvaluations.

Definition at line 137 of file AffLinCoreFun.m.

function fx = dscomponents.AffLinCoreFun.evaluateMulti	(	colvec< double >	x,
		double	t,
		colvec< double >	mu
	)

Definition at line 115 of file AffLinCoreFun.m.

References general.AffParamMatrix.compose(), k, dscomponents.ACoreFun.mu, general.AffParamMatrix.size(), t, and dscomponents.ACoreFun.TimeDependent.

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function c = dscomponents.AffLinCoreFun.getGlobalLipschitz	(	double	t,
		colvec< double >	mu
	)

virtual

Implementation of the interface method from IGlobalLipschitz.

Parameters

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

Implements dscomponents.IGlobalLipschitz.

Definition at line 169 of file AffLinCoreFun.m.

References general.AffParamMatrix.cfun.

function J = dscomponents.AffLinCoreFun.getStateJacobian	(		unused1,
		double	t
	)

Overrides the default jacobian finite difference implementation. Jacobian of linear operator is the operator itself, i.e. in this case the linear combination of the matrices.

Parameters

unused1	Marked as "~" in original m-file.
t	The current time(s) \(t \in [0, T]\)

Definition at line 150 of file AffLinCoreFun.m.

References general.AffParamMatrix.compose(), dscomponents.ACoreFun.mu, and dscomponents.ACoreFun.TimeDependent.

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function diff = dscomponents.AffLinCoreFun.minus ( other )

Implements the default subtraction method.

Definition at line 252 of file AffLinCoreFun.m.

function prod = dscomponents.AffLinCoreFun.mtimes ( other )

Implements the default multiplication method.

Definition at line 240 of file AffLinCoreFun.m.

function sum = dscomponents.AffLinCoreFun.plus ( other )

Implements the default addition method.

Definition at line 264 of file AffLinCoreFun.m.

function dscomponents.AffLinCoreFun.prepareSimulation ( colvec< double > mu )

Definition at line 128 of file AffLinCoreFun.m.

References general.AffParamMatrix.compose().

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function proj = dscomponents.AffLinCoreFun.project	(	V,
		W
	)

Definition at line 188 of file AffLinCoreFun.m.

References clone().

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Member Data Documentation

dscomponents.AffLinCoreFun.CoeffClass = ""

Export setting. Java class name for JKerMor model export.

Set this value to the class inside your JKerMor source that implements the IAffineCoefficients interface for this core function.

In order for this to work the coefficient functions must equal the AffParamMatrix' coefficient functions both mathematically and in the order of entry.

Property class data:: Set only if the model is intended for JKerMor export.

Default: '

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

Definition at line 52 of file AffLinCoreFun.m.

Referenced by clone().

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

core/+dscomponents/AffLinCoreFun.m

Detailed Description

Public Member Functions

Public Attributes

Additional Inherited Members

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation