ReducedSystem: A KerMor reduced dynamical system. More...

Detailed Description

ReducedSystem: A KerMor reduced dynamical system.

Any state space scaling is included into the reduced model upon creation, as scaling is possibly of the large systems' dimension. See Scaling of KerMor models for more information.

Author: Daniel Wirtz

Date: 17.03.2010

Change in 0.6:

(Daniel Wirtz, 2012-05-29)

New direct methods for ODE handles (selection once per call more effective than if clauses every evaluation)
fixed cases with A component
fixed setting of A component upon setReducedModel

Change in 0.5:: (Daniel Wirtz, 2011-10-15) Fixed the computation of reduced systems. Previously, the scaling was not included in the reduced model if no subspace projection was used. Now, scaling is included if set and independently from any subspace projection.

Change in 0.5:: (Daniel Wirtz, 2011-08-05) Fixed the use of state space scaling in reduced simulations. Now the scaling and reduction is performed as described in State space scaling.

Change in 0.4:: (Daniel Wirtz, 2011-05-13) Removed the old getODEFun function and replaced it by a direct implementation ODEFun. This enables to avoid nested function handles with in turn allow for a speedup of reduced simulations by almost a factor of 2.

See Also: models.BaseFirstOrderSystem

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 ReducedSystem.m.

Public Member Functions
	ReducedSystem (rmodel)
	Creates a new ReducedSystem instance. More...

function	build ()
	Creates a reduced system from BaseFullModel child system. As default, all system's components are copied as-is and any reduction changes are performed in the BaseFullModel.buildReducedModel method. More...

function	updateSparsityPattern ()
	Reduced systems are not sparse anymore. More...

function	plot (models.BaseFullModel model,double t,matrix< double > y)
	Unless overridden for specific reduced system plots this method just calls the plot method of the original full system. More...

function dx =	ODEFun (double t,colvec< double > x)

function J =	getJacobian (double t, xc)

function x0 =	getX0 (colvec< double > mu)
	Gets the initial value of \(x_0(\mu)\). More...

Public Member Functions inherited from models.BaseFirstOrderSystem
	BaseFirstOrderSystem (models.BaseFullModel model)
	Creates a new base dynamical system class instance. More...

function rsys =	getReducedSystemInstance (models.ReducedModel rmodel)
	Creates a reduced system given the current system and the reduced model. More...

function	setConfig (mu, inputidx)
	Sets the dynamical system's configuration. More...

function	prepareSimulation (colvec< double > mu,integer inputidx)

function dx =	ODEFun (double t,colvec< double > x)
	Debug variant for single evaluation. Commented in function above. More...

function y =	computeOutput (matrix< double > x,colvec< double > mu)
	Computes the output \(y(t) = C(t,\mu)Sx(t)\) from a given state result vector \(x(t)\), using the system's time and current mu (if given). More...

function	updateSparsityPattern ()

function J =	getJacobian (double t, xc)
	Computes the global jacobian of the current system. More...

function matrix < double > x0 =	getX0 (rowvec< double > mu)
	Gets the initial state variable at \(t=0\). More...

function M =	getMassMatrix ()
	For first order systems, only algebraic constraints need to be catered for. More...

function ModelParam p =	addParam (char name, default, varargin)
	Adds a parameter with the given values to the parameter collection of the current dynamical system. More...

function pidx =	getParamIndexFromName (paramname)
	Gets the index within the parameter vector \(\mu\) for a given parameter name. More...

function pt =	getParamInfo (colvec< double > mu)

function	plotInputs (pm)

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 Attributes
	R
	The reduced dof to full dof reconstruction matrix. More...

Public Attributes inherited from models.BaseFirstOrderSystem
dscomponents.ACoreFun	f
	The core f function from the dynamical system. More...

dscomponents.LinearCoreFun	A = "[]"
	Represents a linear or affine-linear component of the dynamical system. More...

dscomponents.AInputConv	B = "[]"
	The input conversion. More...

dscomponents.LinearOutputConv	C
	The output conversion Defaults to an LinearOutputConv instance using a 1-matrix, which just forwards the state variables and supports projection. More...

dscomponents.AInitialValue	x0 = "[]"
	Function handle to initial state evaluation. More...

dscomponents.AMassMatrix	M = "[]"
	The system's mass matrix. More...

dscomponents.ACoreFun	g = "[]"
	The system's algebraic constraints function. More...

	Inputs = {""}
	The system's possible input functions. A cell array of function handles, each taking a time argument t. More...

	Params = data.ModelParam.empty
	The parameters usable for the dynamical system. More...

integer	DependentParamIndices = -1
	Indices of the parameter vector that are effectively used in the system's core function. More...

double	MaxTimestep = "[]"
	The maximum timestep allowed for any ODE solvers. More...

colvec	StateScaling = 1
	The scaling for the state vectors. More...

	SparsityPattern
	The global sparsity pattern for the entire RHS. More...

	mu = "[]"
	The current parameter \(\mu\) for simulations, [] is none used. More...

	u = "[]"
	The current input function \(u(t)\) as function handle, [] if none used. More...

	inputidx = "[]"
	The current inputindex of the function \(u(t)\). More...

	NumStateDofs = "[]"

	NumAlgebraicDofs = 0

	NumTotalDofs = "[]"

	InputCount
	The number of inputs available. More...

	ParamCount
	The number of the system's parameters. More...

	Model
	The Model this System is attached to. 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...

Protected Member Functions
function R =	compileReconstructionMatrix (V)

function	updateDimensions ()

function	validateModel (models.BaseFullModel model)
	Overrides the validateModel function in BaseFirstOrderSystem. More...

Protected Member Functions inherited from models.BaseFirstOrderSystem
function	updateDimensions ()

function ad_ic =	getAlgebraicDofsInitialConditions ()
	The default is to return all zeros. More...

function	validateModel (models.BaseFullModel model)
	Validates if the model to be set is a valid BaseModel at least. Extracting this function out of the setter enables subclasses to further restrict the objects that may be passed, as is being done in models.ReducedSystem, for example. 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

models.ReducedSystem.ReducedSystem ( rmodel )

Creates a new ReducedSystem instance.

Parameters

rmodel [Optional] The reduced model to create the reduced system from.

Definition at line 77 of file ReducedSystem.m.

Member Function Documentation

function models.ReducedSystem.build ( )

Creates a reduced system from BaseFullModel child system. As default, all system's components are copied as-is and any reduction changes are performed in the BaseFullModel.buildReducedModel method.

Important: The reduced model must have set all reduced data (i.e. V,W) that will be used during this constructor; references to variables/properties from the full model will result in large reduced models as references to the full models properties also save the full model with all data.

See Also: models.BaseFullModel.buildReducedModel

Parameters

rmodel The instance of the reduced model that will contain this instance as System property.

Definition at line 89 of file ReducedSystem.m.

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function R = models.ReducedSystem.compileReconstructionMatrix ( V )

protected

Definition at line 305 of file ReducedSystem.m.

References R.

Referenced by build().

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function J = models.ReducedSystem.getJacobian	(	double	t,
			xc
	)

Definition at line 269 of file ReducedSystem.m.

References models.BaseFirstOrderSystem.Model.

function x0 = models.ReducedSystem.getX0 ( colvec< double > mu )

Gets the initial value of \(x_0(\mu)\).

If the estimator is enabled, x0 is extended by the e0 components of the error estimator.

Parameters

mu	The currently used parameter \(\vmu\). Set to \([]\) if not used.

Definition at line 282 of file ReducedSystem.m.

References models.BaseFirstOrderSystem.Model, and models.BaseFirstOrderSystem.x0.

function dx = models.ReducedSystem.ODEFun	(	double	t,
		colvec< double >	x
	)

Definition at line 253 of file ReducedSystem.m.

References models.BaseFirstOrderSystem.Model, and models.BaseFirstOrderSystem.u.

function models.ReducedSystem.plot	(	models.BaseFullModel	model,
		double	t,
		matrix< double >	y
	)

Unless overridden for specific reduced system plots this method just calls the plot method of the original full system.

Parameters

model	A KerMor full model
t	The current time(s) \(t \in [0, T]\)
y	The output variable vector \(\vy(t) = \vC(t,\vmu)\vx(t),~t=0\ldots T\) (general notation)

Definition at line 239 of file ReducedSystem.m.

function models.ReducedSystem.updateDimensions ( )

protected

Definition at line 310 of file ReducedSystem.m.

References models.BaseFirstOrderSystem.Model, models.BaseFirstOrderSystem.NumAlgebraicDofs, models.BaseFirstOrderSystem.NumStateDofs, and models.BaseFirstOrderSystem.NumTotalDofs.

Referenced by build().

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function models.ReducedSystem.updateSparsityPattern ( )

Reduced systems are not sparse anymore.

Definition at line 230 of file ReducedSystem.m.

References models.BaseFirstOrderSystem.SparsityPattern.

function models.ReducedSystem.validateModel ( models.BaseFullModel model )

protected

Overrides the validateModel function in BaseFirstOrderSystem.

No need to call the superclass here as ReducedModel is a child of BaseModel.

Parameters

model A KerMor full model

Definition at line 324 of file ReducedSystem.m.

Member Data Documentation

models.ReducedSystem.R

The reduced dof to full dof reconstruction matrix.

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

Definition at line 59 of file ReducedSystem.m.

Referenced by build(), models.ReducedSecondOrderSystem.compileReconstructionMatrix(), and compileReconstructionMatrix().

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

core/+models/ReducedSystem.m

Detailed Description

Public Member Functions

Public Attributes

Protected Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation