KernelEI: DEIM approximation using kernel expansions for function/operator evaluations. More...

Detailed Description

KernelEI: DEIM approximation using kernel expansions for function/operator evaluations.

Implements the ideas described in [14] .

Author: Daniel Wirtz

Date: 2012-03-26

New in 0.6:: (Daniel Wirtz, 2012-03-26) 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 KernelEI.m.

Public Member Functions
	KernelEI (sys)

function	approximateSystemFunction (models.BaseFullModel model)

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

function ESP =	computeEmpiricalSparsityPattern ()

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...

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_KernelEI ()

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

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

	Variant = 2
	The variant to use. More...

approx.ABase	Algorithm
	An approx.ABase approximation algorithm that is used to learn the component functions (either simultaneously or component-wise depending on Variant) More...

natural	nJacobians = 5
	nJacobians: number of Jacobian samples to use for empirical sparsity detection i.e. we choose nJacobians many Jacobian samples from trajectories number More...

kernels.KernelExpansion	V1Expansion = "[]"
	The Kernel expansion computed if using Variant 1. More...

rowvec < kernels.KernelExpansion >	V2Expansions = {""}
	The array of kernel expansions of using Variant 2. More...

integer	Order
	The actual order for the current DEIM approximation. More...

	fOrder = 10

	u
	The full approximation base. More...

	pts
	Interpolation points. More...

	U
	The U matrix for the current Order. More...

	S

	f

	jrow

	jend

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.KernelEI.KernelEI ( sys )

Definition at line 199 of file KernelEI.m.

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

Member Function Documentation

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

Definition at line 206 of file KernelEI.m.

References Algorithm, data.ModelData.ApproxTrainData, computeEmpiricalSparsityPattern(), models.BaseFullModel.Data, dscomponents.ACoreFun.evaluateMulti(), models.BaseFirstOrderSystem.f, f, fOrder, jend, jrow, MaxOrder, Order, pts, models.BaseModel.System, t, u, general.AProjectable.V, V1Expansion, V2Expansions, Variant, and general.AProjectable.W.

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function copy = approx.KernelEI.clone ( )

Definition at line 423 of file KernelEI.m.

References kernels.KernelExpansion.clone(), f, fOrder, jend, jrow, MaxOrder, pts, S, dscomponents.ACoreFun.System, u, U, V1Expansion, V2Expansions, and Variant.

Referenced by project().

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function ESP = approx.KernelEI.computeEmpiricalSparsityPattern ( )

Definition at line 322 of file KernelEI.m.

References models.BaseFirstOrderSystem.f, dscomponents.ACoreFun.getStateJacobianFD(), k, models.BaseFirstOrderSystem.Model, dscomponents.ACoreFun.mu, nJacobians, dscomponents.ACoreFun.prepareSimulation(), and dscomponents.ACoreFun.System.

Referenced by approximateSystemFunction().

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function fx = approx.KernelEI.evaluateCoreFun	(	colvec< double >	x,
		double	t
	)

virtual

Actual method used to evaluate the dynamical sytems' core function.

Subclasses might implement this method and set the flag CustomProjection appropriately. However, for speed reasons, if both are true one might as well override the evaluate member directly as it basically cares for the cases when one of the flags is not true. In that case it is still important to set both flags to true as some components rely on them.

Parameters

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

Implements dscomponents.ACoreFun.

Definition at line 301 of file KernelEI.m.

References kernels.KernelExpansion.evaluate(), fOrder, jend, dscomponents.ACoreFun.mu, S, U, V1Expansion, V2Expansions, and Variant.

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

Definition at line 408 of file KernelEI.m.

References clone(), kernels.KernelExpansion.Ma, kernels.KernelExpansion.project(), and V1Expansion.

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static function res = approx.KernelEI.test_KernelEI ( )

static

Definition at line 546 of file KernelEI.m.

References dscomponents.ACoreFun.mu.

Member Data Documentation

approx.KernelEI.Algorithm

An approx.ABase approximation algorithm that is used to learn the component functions (either simultaneously or component-wise depending on Variant)

Default: []

See Also: Variant

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

Definition at line 71 of file KernelEI.m.

Referenced by approximateSystemFunction().

approx.KernelEI.f

Definition at line 190 of file KernelEI.m.

Referenced by approximateSystemFunction(), and clone().

approx.KernelEI.fOrder = 10

Definition at line 153 of file KernelEI.m.

Referenced by approximateSystemFunction(), clone(), and evaluateCoreFun().

approx.KernelEI.jend

Definition at line 194 of file KernelEI.m.

Referenced by approximateSystemFunction(), clone(), and evaluateCoreFun().

approx.KernelEI.jrow

Definition at line 192 of file KernelEI.m.

Referenced by approximateSystemFunction(), and clone().

approx.KernelEI.MaxOrder = 40

The maximum order up to which the DEIM approximation should be computed.

This corresponds to the maximum number \(m\) that can be choosen as approximation order.

Default: 40

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

Definition at line 41 of file KernelEI.m.

Referenced by approximateSystemFunction(), and clone().

approx.KernelEI.nJacobians = 5

nJacobians: number of Jacobian samples to use for empirical sparsity detection i.e. we choose nJacobians many Jacobian samples from trajectories number

Note: This property has the MATLAB attribute SetObservable set to true.; Matlab documentation of property attributes.
Default: 5

Definition at line 88 of file KernelEI.m.

Referenced by computeEmpiricalSparsityPattern().

approx.KernelEI.Order

The actual order for the current DEIM approximation.

See Also: MaxOrder

Default: 10

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 135 of file KernelEI.m.

Referenced by approximateSystemFunction().

approx.KernelEI.pts

Interpolation points.

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

Definition at line 167 of file KernelEI.m.

Referenced by approximateSystemFunction(), and clone().

approx.KernelEI.S

Definition at line 188 of file KernelEI.m.

Referenced by clone(), and evaluateCoreFun().

approx.KernelEI.u

The full approximation base.

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

Definition at line 156 of file KernelEI.m.

Referenced by approximateSystemFunction(), and clone().

approx.KernelEI.U

The U matrix for the current Order.

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

Definition at line 178 of file KernelEI.m.

Referenced by clone(), and evaluateCoreFun().

approx.KernelEI.V1Expansion = "[]"

The Kernel expansion computed if using Variant 1.

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

Definition at line 105 of file KernelEI.m.

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

approx.KernelEI.V2Expansions = {""}

The array of kernel expansions of using Variant 2.

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

Definition at line 119 of file KernelEI.m.

Referenced by approximateSystemFunction(), clone(), and evaluateCoreFun().

approx.KernelEI.Variant = 2

The variant to use.

Possible values are 1 and 2. 1 means that all components are interpolated simultaneously and only the current KernelEI.Order

Note: This property has the MATLAB attribute SetObservable set to true.; Matlab documentation of property attributes.
Default: 2

Definition at line 56 of file KernelEI.m.

Referenced by approximateSystemFunction(), clone(), and evaluateCoreFun().

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

core/+approx/KernelEI.m

Detailed Description

Public Member Functions

Static Public Member Functions

Public Attributes

Additional Inherited Members

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation