The core nonlinear function of the PCD model. More...

Detailed Description

The core nonlinear function of the PCD model.

Author: Daniel Wirtz

Date: 16.03.2010

New in 0.6:: (Daniel Wirtz, 2012-07-16) Added direct jacobian evaluation function.

Change in 0.5:: (Daniel Wirtz, 2011-11-02) Augmenting the mu parameters by the base system's models.pcd.BasePCDSystem.ReacCoeff vector. This removes the reaction coefficients from the system as true parameters but allows to quickly revert the process if needed.

Change in 0.5:: (Daniel Wirtz, 2011-10-17) Removed the ISimConstants class and unified the structure of the 1D-3D pcd models.

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 CoreFun2D.m.

Public Member Functions
	CoreFun2D (dynsys)

function copy =	clone ()
	System already copied in constructor (see below) More...

function	newSysDimension ()
	Create diffusion matrix. More...

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

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

function J =	getStateJacobian (colvec< double > x,double t)

Public Member Functions inherited from models.pcd.BaseCoreFun
	BaseCoreFun (dynsys)

function copy =	clone (copy)
	Call superclass method. More...

function	evaluateCoreFun ()

function	plotActivationFun (colvec< double > mu, pm)

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

function fx =	evaluateComponentSet (integer nr,colvec< double > x,double t)
	Computes the full or reduced component functions of the given point set. More...

function fx =	evaluateComponentSetMulti (integer nr,matrix< double > x,rowvec< double > t,matrix< double > mu)
	Computes the full component functions of the given point set. More...

function dfx =	evaluateComponentSetGradientsAt (integer nr,colvec< double > x,double t)
	Computes the full/reduced gradients of all component functions of the given point set. More...

function J =	evaluateJacobianSet (integer nr,colvec< double > x,double t)
	Returns the jacobian entries of the point set that have been specified using setPointSet's argument jpd. More...

function J =	evaluateJacobianSetMulti (integer nr,matrix< double > x,rowvec< double > t,colvec< double > mu)
	Returns the jacobian entries at multiple locations/times/parameters of the point set that have been specified using setPointSet's argument jpd. More...

function	setPointSet (nr, pts, jpd)
	Parameters: pts: A row vector with the desired points jpd: ("Jacobian Partial Derivatives") A cell array of size equal to the number of points. Each cell contains the indices for which the partial derivatives of the corresponding component function will be computed when calling evaluateJacobianSet. More...

function target =	project (V, W, target)

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

function res =	test_ComponentEvalMatch (xsize)
	Tests if the local implementation of evaluateComponents matches the full evaluation. 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...

Protected Member Functions
function fxj =	evaluateComponents (pts, ends, unused1, unused2, X,double t)

function fxj =	evaluateComponentsMulti (rowvec< integer > pts,rowvec< integer > ends, unused1, unused2,matrix< double > X,double t,matrix< double > mu)
	The vector embedding results from the fixed ordering of the full 4*m-vector into the components x_a, y_a, x_i, y_i. More...

function dfx =	evaluateComponentPartialDerivatives (rowvec< integer > pts,rowvec< integer > ends, unused1,rowvec< integer > deriv, unused2,colvec< double > X, unused3,colvec< double > mu, unused4)
	See dscomponents.ACompEvalCoreFun for more details. More...

Protected Member Functions inherited from models.pcd.BaseCoreFun
function f =	activationFun (double t,colvec< double > mu)

Protected Member Functions inherited from dscomponents.ACompEvalCoreFun
function matrix < double > dfx =	evaluateComponentGradientsAt (rowvec< integer > pts,rowvec< integer > ends,rowvec< integer > idx,rowvec< integer > self,colvec< double > x,double t)
	Default implementation of gradient computation via finite differences. More...

function dfx =	evaluateComponentPartialDerivatives (rowvec< integer > pts,rowvec< integer > ends,rowvec< integer > idx,rowvec< integer > deriv,rowvec< integer > self,colvec< double > x,double t, dfxsel)
	Computes specified partial derivatives of \(f\) of the components given by pts and the selected partial derivatives by dfxsel. More...

function dfx =	evaluateComponentPartialDerivativesMulti (pts, ends, idx, deriv, self,colvec< double > x,double t,colvec< double > mu, dfxsel)
	Multi-argument evaluation method for partial derivatives. Not used so far in KerMor, this is "legacy code" to keep around if needed at any stage as default finite difference-implementation. More...

function fx =	evaluateComponentsMulti (pts, ends, idx, self,colvec< double > x,double t,colvec< double > mu)

virtual function fx =	evaluateComponents (rowvec< integer > pts,rowvec< integer > ends,rowvec< integer > idx,rowvec< integer > self,matrix< double > x,rowvec< double > t,colvec< double > mu)
	This is the template method that actually evaluates the components at given points and values. 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 obj =	loadobj (obj)

Static Protected Member Functions inherited from models.pcd.BaseCoreFun
static function obj =	loadobj (obj, from)

Static Protected Member Functions inherited from dscomponents.ACompEvalCoreFun
static function obj =	loadobj (obj, from)

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)

Additional Inherited Members
Public Attributes inherited from models.pcd.BaseCoreFun
integer	ActivationFunType
	Type of the activation function. More...

Public Attributes inherited from dscomponents.ACompEvalCoreFun
	PointSets

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...

Static Public Attributes inherited from models.pcd.BaseCoreFun
static const ::double	ActivationTransitionTime = 10
	The time in seconds needed before the activation function reaches its maximum value and decays back to zero. [s]. More...

static const ::double	MaxActivationTime = 400
	The maximum time in seconds that spans the support of the piecewise activation function. It is composed of gaussian-shaped increase/decrease ends and a constant one in between. For the default settings, we would have a maximum duration of 500s-2*30s=440s for the activation rate of level one. [s]. More...

Protected Attributes inherited from dscomponents.ACompEvalCoreFun
matrix< double >	S = {""}
	The x-component selection matrices (precomputed on setting PointSet/AltPointSet). �S� is passed to the function evaluating the components of �� or its derivatives. More...

Constructor & Destructor Documentation

models.pcd.CoreFun2D.CoreFun2D ( dynsys )

Definition at line 58 of file CoreFun2D.m.

Member Function Documentation

function copy = models.pcd.CoreFun2D.clone ( )

System already copied in constructor (see below)

Generated fields of copy:

Definition at line 63 of file CoreFun2D.m.

References dscomponents.ACoreFun.System.

function fx = models.pcd.CoreFun2D.evaluate	(	colvec< double >	x,
		double	t
	)

Definition at line 131 of file CoreFun2D.m.

References models.pcd.BaseCoreFun.activationFun(), dscomponents.ACoreFun.mu, dscomponents.ACoreFun.System, general.AProjectable.V, and general.AProjectable.W.

Here is the call graph for this function:

function dfx = models.pcd.CoreFun2D.evaluateComponentPartialDerivatives	(	rowvec< integer >	pts,
		rowvec< integer >	ends,
			unused1,
		rowvec< integer >	deriv,
			unused2,
		colvec< double >	X,
			unused3,
		colvec< double >	mu,
			unused4
	)

protected

See dscomponents.ACompEvalCoreFun for more details.

Parameters

pts	The components of \(f\) for which derivatives are required
ends	At the \(i\)-th entry it contains the last position in the \(\vx\) vector that indicates an input value relevant for the \(i\)-th point evaluation, i.e. \(f_i(\vx) = f_i(\vx(ends(i-1){:}ends(i)));\)
unused1	Marked as "~" in original m-file.
deriv	The indices within \(\vx\) that derivatives are required for.
unused2	Marked as "~" in original m-file.
X	The state space location \(\vx\)
unused3	Marked as "~" in original m-file.
mu	The corresponding parameter \(\mu\) for the state \(\vx\)
unused4	Marked as "~" in original m-file.

Return values

dfx	A column vector with `numel(deriv)` rows containing the derivatives at all specified pts i with respect to the coordinates given by `idx(ends(i-1):ends(i))`

Definition at line 465 of file CoreFun2D.m.

References dscomponents.ACoreFun.mu, dscomponents.ACoreFun.System, and X.

function fxj = models.pcd.CoreFun2D.evaluateComponents	(		pts,
			ends,
			unused1,
			unused2,
			X,
		double	t
	)

protected

Definition at line 339 of file CoreFun2D.m.

References evaluateComponentsMulti(), and dscomponents.ACoreFun.mu.

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function fxj = models.pcd.CoreFun2D.evaluateComponentsMulti	(	rowvec< integer >	pts,
		rowvec< integer >	ends,
			unused1,
			unused2,
		matrix< double >	X,
		double	t,
		matrix< double >	mu
	)

protected

The vector embedding results from the fixed ordering of the full 4*m-vector into the components x_a, y_a, x_i, y_i.

Parameters

pts	The components of \(\vf\) for which derivatives are required
ends	At the \(i\)-th entry it contains the last position in the \(\vx\) vector that indicates an input value relevant for the \(i\)-th point evaluation, i.e. \(f_i(\vx) = f_i(\vx(ends(i-1){:}ends(i)));\)
unused1	Marked as "~" in original m-file.
unused2	Marked as "~" in original m-file.
X	A matrix \(\vX\) with the state space locations \(\vx_i\) in its columns
t	The current time(s) \(t \in [0, T]\)
mu	The corresponding parameters \(\mu_i\) for each state \(\vx_i\), as column matrix