ParamTimeKernelExpansion: Kernel expansion class for time and/or parameter dependent kernels. More...

Detailed Description

ParamTimeKernelExpansion: Kernel expansion class for time and/or parameter dependent kernels.

This class represents a function \(f\) in the space induced by given kernels \(\K_{s,t,\mu}\) for state, time and parameter space as

\[f(x,t,\mu) = \sum\limits_{i=1}^N c_i\K_s(x,x_i)\K_t(t,t_i)\K_\mu(\mu,\mu_i)\]

This class is the composition of three different kernels, which are one for time, parameters and state variables. Those kernels are combined using the function handle set by the property SubKernelCombinationFun.

Author: Daniel Wirtz

Date: 2011-07-07

New in 0.5:: (Daniel Wirtz, 2011-07-07) Added this class.

Former changes from old class AKernelCoreFun

New in 0.3:: (Daniel Wirtz, 2011-04-21) Integrated this class to the property default value changed supervision system Property classes and levels. This class now inherits from KerMorObject and has an extended constructor registering any user-relevant properties using KerMorObject.registerProps.

Change in 0.3:: (Syed Ammar, 2011-04-16) Implemented Setter for the property Centers

New in 0.3:: (Daniel Wirtz, 2011-04-15) Added the dscomponents.AKernelCoreFun.evaluateStateNabla method to allow efficient computation of kernel expansion jacobians.

Change in 0.3:: (Daniel Wirtz, 2011-04-6) Set the kernel properties to dependent and introduced private storage members for them. Also improved the setter for the SubKernelCombinationFun (checks for 3 args now)

New in 0.3:: (Daniel Wirtz, 2011-04-04) Added the dscomponents.AKernelCoreFun.getKernelMatrix method

Change in 0.2:

(Daniel Wirtz, 2011-03-21)

Moved the dscomponents.AKernelCoreFun.RotationInvariant property into a local private variable that gets updated only when the kernels are changed. This way a repetitive in-simulation evaluation of the property gets avoided.
Changed & documented the default kernels.
Added set method for dscomponents.AKernelCoreFun.SubKernelCombinationFun property.

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 ParamTimeKernelExpansion.m.

Public Member Functions
	ParamTimeKernelExpansion ()
	Default constructor. More...

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

function phi =	getKernelVector (colvec< double > x,double t,colvec< double > mu)
	Returns the kernel vector \(\varphi(x,t,\mu) = (\K(x,x_i)\K(t,t_i)\K(\mu,\mu_i))_i\). (for the case of a product `SubKernelCombinationFun` More...

function J =	getStateJacobian (colvec< double > x,double t,colvec< double > mu)
	Evaluates the jacobian matrix of this function at the given point. More...

function c =	getGlobalLipschitz (double t,colvec< double > mu)
	Overrides the implementation in KernelExpansion. More...

function K =	getKernelMatrix ()
	Computes the kernel matrix for the currently set center data. More...

function K =	getKernelMatrixColumn (idx,colvec< double > x,double t,colvec< double > mu)
	Computes the kernel matrix for the currently set center data. More...

function	setCentersFromATD (data.ApproxTrainData atd,rowvec< integer > idx)
	Sets the centers according to the indices `idx` of the training data. More...

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

function	clear ()
	Removes all centers and coefficients from the expansion and leaves the associated kernels untouched. More...

Public Member Functions inherited from kernels.KernelExpansion
	KernelExpansion ()
	Default constructor. More...

function fx =	evaluate (matrix x, varargin)
	Evaluates the kernel expansion. More...

function phi =	getKernelVector (matrix x, varargin)
	Evaluates the kernel expansion. More...

function row =	getKernelMatrixColumn (integer idx,matrix x, varargin)
	Evaluates the kernel expansion. More...

function J =	getStateJacobian (x, varargin)
	Evaluates the jacobian matrix of this function at the given point. More...

function K =	getKernelMatrix ()
	Computes the kernel matrix for the currently set center data. More...

function v =	scalarProductWith (f)

function	normalize ()

function	setCentersFromATD (data.ApproxTrainData atd,rowvec< integer > idx)
	Sets the centers according to the indices `idx` of the data.ApproxTrainData. More...

function kernels.KernelExpansion kexp =	toTranslateBase ()
	Returns the same kernel expansion with the canonical translate base used. More...

function subexp =	getSubExpansion (arg)

function target =	project (V, W)

function	clear ()
	Removes all centers and coefficients from the expansion and leaves the associated kernels untouched. More...

function sum =	plus (B)
	Adds two kernel expansions and will clone the frist argument's class as result type. More...

function diff =	minus (B)
	Adds two kernel expansions and will clone the frist argument's class as result type. More...

function neg =	uminus ()

function	exportToDirectory (dir)

function json =	toJSON (filename)

function res =	test_getStateJacobianInstance ()

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 Attributes
kernels.BaseKernel	TimeKernel
	The Kernel to use for time variables. More...

kernels.BaseKernel	ParamKernel
	The Kernel to use for parameter variables. More...

	SubKernelCombinationFun = @("t,s,p")t .* s .* p
	The function that combines the sub (time/system/param) kernels. Must be a function handle that takes three arguments. More...

	StateNablaCombinationFun = @("t,s,p)bsxfun(\@times, s, t.*p")
	The combination function for the nabla of the system/state kernel with the other kernels. More...

Public Attributes inherited from kernels.KernelExpansion
kernels.BaseKernel	Kernel
	The Kernel to use for system variables. More...

rowvec	Ma_norms
	The norms of the coefficient matrix of the kernel expansion. More...

double	NativeNorm
	Returns the norm \(\|\|f\|\|^2_{\H^q}\) of \(f\) in the RKHS \(\H^q,\quad q\in\N\). More...

colvec< double >	ComponentNorms
	Returns the native space norms \(\|\|f_j\|\|^2_\H\) for each component function \(j \equiv\)`size(Ma,1)` More...

	MBnd
	Returns the M upper bound for this KernelExpansion, which is \(M := \max\limits_{j=1}^d\sum\limits_{i=1}^m \|c^d_i\|\). More...

logical	HasCustomBase
	Flag that indicates if a base other than the direct translate base is used for this kernel expansion. More...

	Size
	The size of the kernel expansion. More...

struct	Centers = struct("'xi',[]")
	The kernel centers used in the approximation. More...

matrix< double >	Ma = "[]"
	The coefficient data for each dimension. More...

matrix< double >	Base = 1
	This property lets the user store a custom base, for which the coefficients are set. The custom base tells which linear combinations of center elements belong to which base. More...

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
Static Public Member Functions inherited from kernels.KernelExpansion
static function res =	test_getStateJacobian ()

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 kernels.KernelExpansion
static function this =	loadobj (this, from)
	As the constant properties are transient, they have to be re-computed upon loading. More...

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 kernels.KernelExpansion
kernels.BaseKernel	fSK
	The inner (state) kernel object. More...

Constructor & Destructor Documentation

kernels.ParamTimeKernelExpansion.ParamTimeKernelExpansion ( )

Default constructor.

Initializes default kernels.

Definition at line 160 of file ParamTimeKernelExpansion.m.

References kernels.KernelExpansion.Centers, and DPCMObject.registerProps().

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Member Function Documentation

function kernels.ParamTimeKernelExpansion.clear ( )

Removes all centers and coefficients from the expansion and leaves the associated kernels untouched.

Definition at line 347 of file ParamTimeKernelExpansion.m.

References kernels.KernelExpansion.Centers.

function copy = kernels.ParamTimeKernelExpansion.clone ( target )

virtual

The interface method with returns a copy of the current class instance.

Parameters

target If clone was called for a subclass of this class, target must contain the new instance of the subclass that is to be the cloned result.

Reimplemented from kernels.KernelExpansion.

Definition at line 334 of file ParamTimeKernelExpansion.m.

References StateNablaCombinationFun, and SubKernelCombinationFun.

function fx = kernels.ParamTimeKernelExpansion.evaluate	(	colvec< double >	x,
		double	t,
		colvec< double >	mu
	)

Definition at line 190 of file ParamTimeKernelExpansion.m.

References kernels.KernelExpansion.Ma, and t.

function c = kernels.ParamTimeKernelExpansion.getGlobalLipschitz	(	double	t,
		colvec< double >	mu
	)

virtual

Overrides the implementation in KernelExpansion.

Todo:: validate computation

Parameters

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

Reimplemented from kernels.KernelExpansion.

Definition at line 239 of file ParamTimeKernelExpansion.m.

References kernels.KernelExpansion.Centers, kernels.BaseKernel.evaluate(), kernels.BaseKernel.getGlobalLipschitz(), k, kernels.KernelExpansion.Kernel, kernels.KernelExpansion.Ma_norms, ParamKernel, and TimeKernel.

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function K = kernels.ParamTimeKernelExpansion.getKernelMatrix ( )

Computes the kernel matrix for the currently set center data.

Convenience method, equal to call evaluateAtCenters with passing the center data as arguments. However, this method is (possibly, depends on kernel implementation) faster as it calls the kernels kernels.BaseKernel.evaluate -method with one argument.

See Also: evaluateAtCenters

Definition at line 255 of file ParamTimeKernelExpansion.m.

References kernels.KernelExpansion.Centers, and SubKernelCombinationFun.

function K = kernels.ParamTimeKernelExpansion.getKernelMatrixColumn	(		idx,
		colvec< double >	x,
		double	t,
		colvec< double >	mu
	)

Computes the kernel matrix for the currently set center data.

Convenience method, equal to call evaluateAtCenters with passing the center data as arguments. However, this method is (possibly, depends on kernel implementation) faster as it calls the kernels kernels.BaseKernel.evaluate -method with one argument.

See Also: evaluateAtCenters

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 279 of file ParamTimeKernelExpansion.m.

References kernels.KernelExpansion.Centers, and SubKernelCombinationFun.

function phi = kernels.ParamTimeKernelExpansion.getKernelVector	(	colvec< double >	x,
		double	t,
		colvec< double >	mu
	)

Returns the kernel vector \(\varphi(x,t,\mu) = (\K(x,x_i)\K(t,t_i)\K(\mu,\mu_i))_i\). (for the case of a product SubKernelCombinationFun

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 195 of file ParamTimeKernelExpansion.m.

References kernels.KernelExpansion.Centers, kernels.BaseKernel.evaluate(), kernels.KernelExpansion.fSK, and SubKernelCombinationFun.

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function J = kernels.ParamTimeKernelExpansion.getStateJacobian	(	colvec< double >	x,
		double	t,
		colvec< double >	mu
	)

Evaluates the jacobian matrix of this function at the given point.

As this is a component-wise kernel expansion, the jacobian is easily computed using the coefficient vectors and the state variable nablas.

See Also: dscomponents.IJacobian kernels.BaseKernel

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 213 of file ParamTimeKernelExpansion.m.

References kernels.KernelExpansion.Centers, kernels.KernelExpansion.fSK, kernels.BaseKernel.getNabla(), kernels.KernelExpansion.Ma, StateNablaCombinationFun, and t.

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function kernels.ParamTimeKernelExpansion.setCentersFromATD	(	data.ApproxTrainData	atd,
		rowvec< integer >	idx
	)

Sets the centers according to the indices idx of the training data.

Parameters

atd	The training data
idx	The indices in the training data for centers

Required fields of atd:

Definition at line 312 of file ParamTimeKernelExpansion.m.

References kernels.KernelExpansion.Centers, data.ApproxTrainData.hasParams, data.ApproxTrainData.hasTime, data.ApproxTrainData.mui, and data.ApproxTrainData.ti.

Member Data Documentation

kernels.ParamTimeKernelExpansion.ParamKernel

The Kernel to use for parameter variables.

Property class critical:: Correct choice of the system kernel greatly influences the function behaviour.

Default: kernels.NoKernel

See Also: TimeKernel Kernel

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 93 of file ParamTimeKernelExpansion.m.

Referenced by getGlobalLipschitz().

kernels.ParamTimeKernelExpansion.StateNablaCombinationFun = @("t,s,p)bsxfun(\@times, s, t.*p")

The combination function for the nabla of the system/state kernel with the other kernels.

Depends directly on the SubKernelCombinationFun

Property class optional:: Adjust this whenever the SubKernelCombinationFun is changed.

See Also: SubKernelCombinationFun

Note: This property has the MATLAB attribute SetObservable set to true.; Matlab documentation of property attributes.
Default: @("t,s,p)bsxfun(\@times, s, t.*p")

Definition at line 133 of file ParamTimeKernelExpansion.m.

Referenced by clone(), and getStateJacobian().

kernels.ParamTimeKernelExpansion.SubKernelCombinationFun = @("t,s,p")t .* s .* p

The function that combines the sub (time/system/param) kernels. Must be a function handle that takes three arguments.

Property class optional:: Standard kernel combination is pointwise multiplication.

Default: @(t,s,p)t .* s .* p @(t,s,p)t .* s .* p

See Also: StateNablaCombinationFun

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 114 of file ParamTimeKernelExpansion.m.

Referenced by clone(), getKernelMatrix(), getKernelMatrixColumn(), and getKernelVector().

kernels.ParamTimeKernelExpansion.TimeKernel

The Kernel to use for time variables.

Property class critical:: Correct choice of the time kernel greatly influences the function behaviour.

Default: kernels.NoKernel

See Also: Kernel ParamKernel

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 ParamTimeKernelExpansion.m.

Referenced by getGlobalLipschitz().

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

core/+kernels/ParamTimeKernelExpansion.m

Detailed Description

Public Member Functions

Public Attributes

Additional Inherited Members

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation