PODGreedy: Greedy subspace computation over a fixed set of trajectories. More...

Detailed Description

PODGreedy: Greedy subspace computation over a fixed set of trajectories.

This subspace computation method uses the POD-Greedy algorithm to determine a subspace which has a projection error less than the specified tolerance Eps. Therein, subsequently the largest trajectory projection error norm sums are taken for all trajectories, and the one with the largest is chosen. Of that trajectory, a POD of the projection error (orthogonal complement) vectors is performed and the first mode is added to the base, which is orthonormalized afterwards.

See http://www.agh.ians.uni-stuttgart.de/publications/2011/Haa11/ and references therein for details.

Author: Daniel Wirtz

Date: 2011-08-04

Change in 0.5:

(Daniel Wirtz, 2011-10-11)

Renamed this class to PODGreedy from TrajectoryGreedy.
Added another stopping criterion PODGreedy.MinRelImprovement in order to stop subspace computations as soon as the subsequent improvement becomes too small.

Change in 0.5:: (Daniel Wirtz, 2011-09-29) Fixed initial subspace setup when all vectors are identical or even zero. Also added a new alglimit-property PODGreedy.MaxSubspaceSize to have an upper bound to the subspace size.

New in 0.5:: (Daniel Wirtz, 2011-08-04) 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 PODGreedy.m.

Public Member Functions
	PODGreedy ()

function	plotSummary (pm, context)

Public Member Functions inherited from spacereduction.BaseSpaceReducer
function [ V , W ] =	generateReducedSpace (models.BaseFullModel model)
	Generates the reduced linear subspace for the given model. 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 ()

Static Public Member Functions
static function	test_PODGreedy ()

Public Attributes
double	Eps = 1e-6
	The desired accuracy over all training trajectories. More...

double	MinRelImprovement = .005
	The minimum required relative error improvement compared to the previous error. More...

integer	MaxSubspaceSize = 100
	The maximum subspace size, EXCLUDING any non-reducable dimensions. More...

matrix< double >	InitialSpace = "[]"
	An initial space to use. More...

	ErrorImprovements

Public Attributes inherited from spacereduction.BaseSpaceReducer
logical	IncludeTrajectoryFxiData = false
	Flag if to include \(f(x_i)\) values for each \(x_i\) value, too. More...

	IncludeFiniteDifferences = false

	IncludeBSpan = false

	IncludeAxData = false

varargin	TargetDimensions = ":"
	This property determines which dimensions are to be reduced. It is possible to reduce the entire number of DoFs but also only selected ones. More...

	ProjectionError = "[]"

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 IParallelizable
	ComputeParallel = false
	Flag whether the code should be run in parallel or not. More...

Protected Member Functions
function [ V , W ] =	generateReducedSpaceImpl (models.BaseFullModel model, subset)

Protected Member Functions inherited from spacereduction.BaseSpaceReducer
function V =	getInitialSpace (blockdata, pod, subset)
	Computes the initial space, which is the first POD mode of the initial 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)

Additional Inherited Members
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)

Constructor & Destructor Documentation

spacereduction.PODGreedy.PODGreedy ( )

Definition at line 136 of file PODGreedy.m.

References DPCMObject.registerProps().

Here is the call graph for this function:

Member Function Documentation

function [V , W ] = spacereduction.PODGreedy.generateReducedSpaceImpl	(	models.BaseFullModel	model,
			subset
	)

protectedvirtual

function spacereduction.PODGreedy.plotSummary	(	pm,
		context
	)

virtual

Reimplemented from spacereduction.BaseSpaceReducer.

Definition at line 141 of file PODGreedy.m.

References Eps, ErrorImprovements, spacereduction.BaseSpaceReducer.IncludeBSpan, spacereduction.BaseSpaceReducer.IncludeFiniteDifferences, spacereduction.BaseSpaceReducer.IncludeTrajectoryFxiData, PlotManager.LeaveOpen, and MaxSubspaceSize.

static function spacereduction.PODGreedy.test_PODGreedy ( )

static

Definition at line 309 of file PODGreedy.m.

Member Data Documentation

spacereduction.PODGreedy.Eps = 1e-6

The desired accuracy over all training trajectories.

Property class critical:: Ultimately determines the projection error on all training trajectories.

Default: 1e-6

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

Definition at line 60 of file PODGreedy.m.

Referenced by generateReducedSpaceImpl(), and plotSummary().

spacereduction.PODGreedy.ErrorImprovements

Definition at line 131 of file PODGreedy.m.

Referenced by generateReducedSpaceImpl(), and plotSummary().

spacereduction.PODGreedy.InitialSpace = "[]"

An initial space to use.

Optional, otherwise an initial space is computed using the first vectors from the available trajectories.

Must match the system's state space trajectory size.

Property class optional:: Can be useful if a specific choice for initial spaces is available.

Default: []

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

Definition at line 108 of file PODGreedy.m.

Referenced by generateReducedSpaceImpl().

spacereduction.PODGreedy.MaxSubspaceSize = 100

The maximum subspace size, EXCLUDING any non-reducable dimensions.

Property class alglimit:

Default: 100

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

Definition at line 93 of file PODGreedy.m.

Referenced by generateReducedSpaceImpl(), and plotSummary().

spacereduction.PODGreedy.MinRelImprovement = .005

The minimum required relative error improvement compared to the previous error.

Property class important:: Too little minimal improvement causes a too large subspace

Default: 0.005

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

Definition at line 76 of file PODGreedy.m.

Referenced by generateReducedSpaceImpl().

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

core/+spacereduction/PODGreedy.m

Detailed Description

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation