DEIM: Wrapper for KerMor dynamical systems of the general.DEIM class. More...

Detailed Description

DEIM: Wrapper for KerMor dynamical systems of the general.DEIM class.

Author: Daniel Wirtz

Date: 2012-03-26

New in 0.6:: (Daniel Wirtz, 2012-05-30) Added a custom implementation of the getStateJacobian method

Change in 0.6:: (Daniel Wirtz, 2012-05-29) Besides many work-in-progress changes, now the evaluate function is implemented directly. further, some matrices needed for the DEIMEstimator have been included and are being computed.

New in 0.6:: (Daniel Wirtz, 2012-03-26) Added this class.

Todo:: think of exporting the jrow, jend, S properties to ACompEvalCoreFun and precompute stuff there; projection happens at that stage

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 DEIM.m.

Public Member Functions
	DEIM (sys)

function	approximateSystemFunction (models.BaseFullModel model)

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

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

function	prepareSimulation (colvec< double > mu)

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

function fx =	evaluateCoreFun ()
	do nothing as evaluate is overridden directly More...

function projected =	project (V, W)

function copy =	clone ()

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...

Public Member Functions inherited from general.DEIM
function	computeDEIM (dscomponents.ACompEvalCoreFun f,matrix< double > fxi)
	Implementation of the DEIM algorithm. 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)

function pts =	getInterpolationPoints (matrix< double > u)
	Computes the interpolation indices according to the DEIM algorithm. More...

function err =	getEstimatedError (colvec< double > x,double t,colvec< double > mu)

function DEIM target =	project (matrix< double > V,matrix< double > W,DEIM target)
	Pojects instance according to the projection biorthogonal matrices \(V,W\). More...

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

function	plotSummary (pm, context)

Static Public Member Functions
static function res =	test_DEIM ()

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

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

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

Additional Inherited Members
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...

Public Attributes inherited from general.DEIM
integer	MaxOrder = 40
	The maximum order up to which the DEIM approximation should be computed. More...

rowvec< integer >	Order
	The actual order \(M\) for the current DEIM approximation. More...

rowvec< double >	SingularValues = "[]"
	The singular values returned by the SVD decomposition to compute the DEIM POD basis. More...

matrix< double >	U
	The U matrix for the current Order. More...

matrix< double >	U_nonproj
	If projection is applied, this contains the non-projected full \(d \times m\) matrix \(U_m(P_m^tU_m)^{-1}\) for use in subclasses. More...

matrix< double >	Uerr1
	Some matrices for M+M' error estimation. More...

	Uerr2

	M1

	M2

dscomponents.ACompEvalCoreFun	f
	The function which DEIM is applied to. More...

rowvec< double >	Residuals
	The maximum residuals obtained along the magic points computation. More...

EVENT	OrderUpdated
	Gets fired whenever this DEIM instance has updated it's order matrices. 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)

Protected Member Functions inherited from general.DEIM
function	updateOrderData ()
	Update approximation order as specified in fOrder. As a consequence some matrices have to be recalculated. More...

Protected Attributes inherited from general.DEIM
matrix< double >	u
	The full approximation base. More...

rowvec< double >	pts
	Interpolation points. More...