Detailed Description

Plugin for the Greedy.Algorithm class generating collateral reduced basis space plus interpolation DOFs and a local grid for several different parameterized functions or operators.

This can be used for the empirical interpolation of parametrized functions or operator evaluations.

Definition at line 19 of file SummedEI.m.

Inheritance diagram for Greedy.Plugin.SummedEI:

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Public Member Functions
	SummedEI (Greedy.Plugin.EI varargin)
	constructor "summing together a list of different EI plugin instances. More...

function Greedy.DataTree.Detailed.IdMapNode detailed_data =	init_basis (Greedy.User.IReducedModel rmodel,ModelData model_data, M_train)
	creates an initial detailed data node storing an initial reduced basis More...

function	prepare_reduced_data (Greedy.User.IReducedModel rmodel,Greedy.DataTree.Detailed.IdMapNode detailed_data)
	prepares reduced data that is necessary for the execution of other methods if indicated by needs_preparation. More...

function [ max_errs , max_err_sequence , max_mu_index ] =	error_indicators (Greedy.User.IReducedModel rmodel,Greedy.DataTree.Detailed.IdMapNode detailed_data, parameter_set, reuse_reduced_data)
	this function should never be used. It calls the error_indicators() method for the first wrapped parametrized function/operator. More...

function errs =	compute_error (Greedy.User.IReducedModel rmodel,Greedy.User.ReducedData reduced_data,Greedy.DataTree.Detailed.IdMapNode detailed_data)
	this function should never be used. It calls the compute_error() method for the first wrapped parametrized function/operator. More...

function Uapprox =	generate_reduced (Greedy.User.IReducedModel rmodel,Greedy.User.ReducedData reduced_data,Greedy.DataTree.Detailed.IdMapNode detailed_data, U)
	this function should never be used. It calls the generate_reduced() method for the first wrapped parametrized function/operator. More...

function [ breakloop , reason ] =	pre_check_for_end (Greedy.User.IReducedModel rmodel,Greedy.DataTree.Detailed.IdMapNode detailed_data)
	checks whether the basis generation process has come to an end. More...

function Greedy.DataTree.Detailed.IdMapNode detailed_data =	basis_extension (Greedy.User.IReducedModel rmodel,Greedy.DataTree.Detailed.IdMapNode detailed_data, max_err_seq, mu)
	extends the reduced basis space from a given function \(v_{h}(\mu)\). More...

function Greedy.DataTree.Detailed.IdMapNode detailed_data =	finalize (Greedy.User.IReducedModel rmodel,Greedy.DataTree.Detailed.IdMapNode detailed_data)
	function called after the last extension process More...

function cop =	copy ()
	makes a deep copy of this extension instance More...

Public Member Functions inherited from Greedy.Plugin.EICommon
	EICommon (SnapshotsGenerator.SpaceOpEvals generator)
	constructor for an EICommon instance More...

function [ max_errs , max_err_sequence , max_mu_index ] =	error_estimators (IReducedModel rmodel,Greedy.DataTree.Detailed.EILeafNode detailed_data, M_train)
	computes a posteriori error estimators for the reduced simulations for every parameter vector from a given parameter set \({\cal M}_{\text{train}}\). More...

function Greedy.DataTree.Detailed.EILeafNode detailed_data =	finalize (IReducedModel rmodel,Greedy.DataTree.Detailed.EILeafNode detailed_data)
	function called after the last extension process More...

function Greedy.Plugin.EI merged =	horzcat (varargin)
	combines an arbitrary number of Greedy.Plugin.EI arguments to a big one, with added SnapshotsGenerator.Cached instances. More...

function summed =	vertcat (varargin)
	combines an arbitrary number of Greedy.Plugin.EI arguments to a Greedy.Plugin.SummedEI instance. More...

Public Member Functions inherited from Greedy.Plugin.Default
	Default (SnapshotsGenerator.Cached generator)
	constructor for a greedy extension object More...

function [ max_errs , max_err_sequence , max_mu_index ] =	error_indicators (Greedy.User.IReducedModel rmodel,Greedy.User.IDetailedData detailed_data,ParameterSampling.Interface parameter_set, reuse_reduced_data)
	computes error indicators for the reduced simulations for every parameter vector from a given parameter set \({\cal M}_{\text{train}}\). More...

function errs =	compute_error (Greedy.User.IReducedModel rmodel,Greedy.User.ReducedData reduced_data,Greedy.User.IDetailedData detailed_data)
	computes the "true" error between a reduced and a detailed function \(\\| v_h(t^k;\mu) - v_{\text{red}}(t^k;\mu) \\|\). More...

virtual function [ max_errs , max_err_sequence , max_mu_index ] =	error_estimators (Greedy.User.IReducedModel rmodel,Greedy.User.IDetailedData detailed_data, M_train)
	computes a posteriori error estimators for the reduced simulations for every parameter vector from a given parameter set \({\cal M}_{\text{train}}\). More...

Public Member Functions inherited from Greedy.Plugin.Interface
	Interface (SnapshotsGenerator.Cached generator)
	constructor for a greedy extension object More...

virtual function Greedy.DataTree.Detailed.INode detailed_data =	init_basis (Greedy.User.IReducedModel rmodel,ModelData model_data,ParameterSampling.Interface M_train)
	creates an initial detailed data node storing an initial reduced basis More...

virtual function	prepare_reduced_data (Greedy.User.IReducedModel rmodel,Greedy.User.IDetailedData detailed_data)
	prepares reduced data that is necessary for the execution of other methods if indicated by needs_preparation. More...

virtual function [ max_errs , max_err_sequence , max_mu_index ] =	error_indicators (Greedy.User.IReducedModel rmodel,Greedy.User.IDetailedData detailed_data, parameter_set, reuse_reduced_data)
	computes error indicators for the reduced simulations for every parameter vector from a given parameter set \({\cal M}_{\text{train}}\). More...

virtual function Uapprox =	generate_reduced (Greedy.User.IReducedModel rmodel,Greedy.User.ReducedData reduced_data,Greedy.User.IDetailedData detailed_data, U)
	generates a reduced function \(v_{\text{red}}(\mu)\). More...

virtual function [ breakloop , reason ] =	pre_check_for_end (Greedy.User.IReducedModel rmodel,Greedy.User.IDetailedData detailed_data)
	checks whether the basis generation process has come to an end. More...

virtual function Greedy.User.IDetailedData detailed_data =	basis_extension (Greedy.User.IReducedModel rmodel,Greedy.User.IDetailedData detailed_data, max_err_seq, mu)
	extends the reduced basis space from a given function \(v_{h}(\mu)\). More...

virtual function Greedy.User.IDetailedData detailed_data =	finalize (Greedy.User.IReducedModel rmodel,Greedy.User.IDetailedData detailed_data)
	function called after the last extension process More...

Public Attributes
	stop_Mmax
	maximum number of generated collateral reduced basis vectors. More...

Public Attributes inherited from Greedy.Plugin.EICommon
	compute_lebesgue = true
	boolean flag specifying whether after the final extension step the Lebesgue constant shall be computed and stored in the Greedy.DataTree.Detailed.EILeafNode info fields. More...

Public Attributes inherited from Greedy.Plugin.Default
Greedy.User.ReducedData	reduced_data = "[]"
	temporary handle to the last object computed by prepare_reduced_data(). More...

	needs_preparation
	boolean indicating whether the prepare_reduced_data() method needs to be computed before error_indicators can be computed. More...

	indicator_mode = "error"
	string specifying which indicators shall be used by the error_indicators() method. More...

	use_l2_error = true
	boolean flag indicating whether the \(L^2(\Omega)\)-norm is used by compute_error(). More...

	relative_error = false
	boolean flag specifying whether we want to use the relative error for error_indicators() and compute_error() methods. More...

Public Attributes inherited from Greedy.Plugin.Interface
	id
	a string identifying the basis extension algorithm, should be unique over all instances of Interface implementations. More...

	relative_error
	boolean flag specifying whether we want to use the relative error for error_indicators() and compute_error() methods. More...

	indicator_mode
	string specifying which indicators shall be used by the error_indicators() method. More...

	needs_preparation
	boolean indicating whether the prepare_reduced_data() method needs to be computed before error_indicators can be computed. More...

::SnapshotsGenerator.Cached	generator
	an object generating possible (high dimension) basis functions

Static Public Attributes
static const	generated_basis_type = "ei"

Static Public Attributes inherited from Greedy.Plugin.Interface
static const	generated_basis_type
	string specifying the detailed data produced by this basis generation algorithm object. More...

Constructor & Destructor Documentation

Greedy.Plugin.SummedEI.SummedEI ( Greedy.Plugin.EI varargin )

constructor "summing together a list of different EI plugin instances.

Parameters

varargin a list of EI plugin objects

Definition at line 61 of file SummedEI.m.

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Member Function Documentation

function Greedy.DataTree.Detailed.IdMapNode detailed_data = Greedy.Plugin.SummedEI.basis_extension	(	Greedy.User.IReducedModel	rmodel,
		Greedy.DataTree.Detailed.IdMapNode	detailed_data,
			max_err_seq,
			mu
	)

extends the reduced basis space from a given function \(v_{h}(\mu)\).

This generates a new basis function \(\varphi_{n+1} \in {\cal W}_h\) from the sequence of detailed functions \(v_h(t^k,\mu)\) for \(k=0,\ldots,K\) as returned by the SnapshotsGenerator.Cached generator.

Parameters

rmodel	an object specifying the basis generation process.
detailed_data	object defining the basis generation algorithm and storage for storing high dimensional data, i.e. dependent on dimension \(H\). This data is necessary for detailed simulations, construction of online matrices, `reduced_data` and reconstruction of reduced simulations.
max_err_seq	sequence of error indicators as returned as second return argument of error_indicators()
mu	paramter vector \(\mu\).

Return values

detailed_data updated data tree node .

Definition at line 234 of file SummedEI.m.

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function errs = Greedy.Plugin.SummedEI.compute_error	(	Greedy.User.IReducedModel	rmodel,
		Greedy.User.ReducedData	reduced_data,
		Greedy.DataTree.Detailed.IdMapNode	detailed_data
	)

this function should never be used. It calls the compute_error() method for the first wrapped parametrized function/operator.

Note: This function might depend on a previous execution of prepare_reduced_data().

Parameters

rmodel	an object specifying the basis generation process. The parameter \(\mu\) for which the error shall be computed must be set by `set_mu(rmodel, mu)` before.
reduced_data	an object constructing and storing all (low-dimensional) reduced matrices and vectors needed for reduced simulations.
detailed_data	object defining the basis generation algorithm and storage for storing high dimensional data, i.e. dependent on dimension \(H\). This data is necessary for detailed simulations, construction of online matrices, `reduced_data` and reconstruction of reduced simulations.

Return values

errs	a sequence of errors at every time step \(k=0,\ldots,K\).

Definition at line 172 of file SummedEI.m.

function cop = Greedy.Plugin.SummedEI.copy ( )

virtual

makes a deep copy of this extension instance

Return values

cop	a new instance which is a deep copy of this one.

Implements Greedy.Plugin.EICommon.

Definition at line 274 of file SummedEI.m.

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function [ max_errs , max_err_sequence , max_mu_index ] = Greedy.Plugin.SummedEI.error_indicators	(	Greedy.User.IReducedModel	rmodel,
		Greedy.DataTree.Detailed.IdMapNode	detailed_data,
			parameter_set,
			reuse_reduced_data
	)

this function should never be used. It calls the error_indicators() method for the first wrapped parametrized function/operator.

An error indicator estimates an error

\[\eta^k(\mu) \geq \| v_h(t^k;\mu) - v_{\text{red}}(t^k;\mu) \|\]

for every time step \(0\leq t^0, \ldots, t^K = T\) and every parameter \(\mu \in {\cal M}\). The norm is a problem specific norm determined by the options in rmodel.

This function's main use is to find a parameter vector

\[\mu_{\max} = \arg \sup_{\mu \in {\cal M}_{\text{train}} } \max_{k=0,\ldots,K} \eta^k(\mu)\]

.

Parameters

rmodel	an object specifying the basis generation process.
detailed_data	object defining the basis generation algorithm and storage for storing high dimensional data, i.e. dependent on dimension \(H\). This data is necessary for detailed simulations, construction of online matrices, `reduced_data` and reconstruction of reduced simulations.
parameter_set	a set of parameter vectors \({\cal M}_{\text{train}}\) as returned by ParameterSampling.Interface.space .
reuse_reduced_data	optional flag indicating whether the reduced data needed for reduced simulations or computation of error estimators is still valid since its last generation. (default = `false`)

Return values

max_errs	a matrix of size `n_parameters x model.nt+1` storing the error indicator \(\eta^k(\mu)\) for every \(k=0,\ldots,K\) and \(\mu \in {\cal M}_{\text{train}}\).
max_err_sequence	a sequence of error indicators \(\eta^k(\mu_{\max})\) for every \(k=0,\ldots,K\).
max_mu_index	the index of the parameter vector \(\mu_{\max}\) in the `parameter_set` matrix.

Note: This method is controlled by the indicator_mode variable:

If indicator_mode equals

estimator, the method error_estimators() is called
error, compute_error() is used to compute "true" errors.

Definition at line 144 of file SummedEI.m.

function Greedy.DataTree.Detailed.IdMapNode detailed_data = Greedy.Plugin.SummedEI.finalize	(	Greedy.User.IReducedModel	rmodel,
		Greedy.DataTree.Detailed.IdMapNode	detailed_data
	)

function called after the last extension process

Parameters

rmodel	an object specifying the basis generation process.
detailed_data	object defining the basis generation algorithm and storage for storing high dimensional data, i.e. dependent on dimension \(H\). This data is necessary for detailed simulations, construction of online matrices, `reduced_data` and reconstruction of reduced simulations.

Return values

detailed_data updated data tree node .

Definition at line 255 of file SummedEI.m.

function Uapprox = Greedy.Plugin.SummedEI.generate_reduced	(	Greedy.User.IReducedModel	rmodel,
		Greedy.User.ReducedData	reduced_data,
		Greedy.DataTree.Detailed.IdMapNode	detailed_data,
			U
	)

this function should never be used. It calls the generate_reduced() method for the first wrapped parametrized function/operator.

Note: This function might depend on a previous execution of prepare_reduced_data().

Parameters

rmodel	an object specifying the basis generation process. The parameter \(\mu\) for which the error shall be computed must be set by `set_mu(rmodel, mu)` before.
reduced_data	an object storing all (low-dimensional) reduced matrices and vectors needed for reduced simulations.
detailed_data	object defining the basis generation algorithm and storage for storing high dimensional data, i.e. dependent on dimension \(H\). This data is necessary for detailed simulations, construction of online matrices, `reduced_data` and reconstruction of reduced simulations.
U	optional DOF vector, for example operator evaluations.

Return values

Uapprox A sequence of Dof vectors of the functions \(v_{\text{red}}(\cdot;t^k,\mu)\).

Definition at line 193 of file SummedEI.m.

function Greedy.DataTree.Detailed.IdMapNode detailed_data = Greedy.Plugin.SummedEI.init_basis	(	Greedy.User.IReducedModel	rmodel,
		ModelData	model_data,
			M_train
	)

creates an initial detailed data node storing an initial reduced basis

Parameters

rmodel	an object specifying the basis generation process.
M_train	an object specifying the parameter vector set \({\cal M}_{\text{train}}\) from which the basis functions are obtained.
model_data	Matlab structure storing (possibly) high dimensional data needed by IDetailedModel.detailed_simulation().

Return values

detailed_data an object storing the initial reduced basis vectors.

This method initializes the detailed data node for all parametrized functions/operator evaluations.

Definition at line 108 of file SummedEI.m.

function [ breakloop , reason ] = Greedy.Plugin.SummedEI.pre_check_for_end	(	Greedy.User.IReducedModel	rmodel,
		Greedy.DataTree.Detailed.IdMapNode	detailed_data
	)

checks whether the basis generation process has come to an end.

Global break conditions (error_tolerance, timeout and validation ratio) are handled by Greedy.Algorithm .

Parameters

rmodel	object specifying how the reduced simulations can be computed.
detailed_data	object defining the basis generation algorithm and storage for storing high dimensional data, i.e. dependent on dimension \(H\). This data is necessary for detailed simulations, construction of online matrices, `reduced_data` and reconstruction of reduced simulations.

Return values

breakloop	boolean flag indicating whether the basis generation process is finished for this reduced basis space.
reason	descriptive text telling about the reasons why, the extension process needs to break.

This method only stop when ALL parts are ready.

Definition at line 214 of file SummedEI.m.

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function Greedy.Plugin.SummedEI.prepare_reduced_data	(	Greedy.User.IReducedModel	rmodel,
		Greedy.DataTree.Detailed.IdMapNode	detailed_data
	)

prepares reduced data that is necessary for the execution of other methods if indicated by needs_preparation.

Methods that might depend on the execution of this method are

Parameters

rmodel	an object specifying the basis generation process.
detailed_data	object defining the basis generation algorithm and storage for storing high dimensional data, i.e. dependent on dimension \(H\). This data is necessary for detailed simulations, construction of online matrices, `reduced_data` and reconstruction of reduced simulations.

Definition at line 125 of file SummedEI.m.

Member Data Documentation

Greedy.Plugin.SummedEI.stop_Mmax

maximum number of generated collateral reduced basis vectors.

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

Definition at line 35 of file SummedEI.m.

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

rbasis/basisgen/oop/+Greedy/+Plugin/SummedEI.m

Detailed Description

Public Member Functions

Public Attributes

Static Public Attributes

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation