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Greedy.Plugin.EICommon Class Referenceabstract

Detailed Description

interface for Greedy.Plugin.Interface implementations generating an empirical interpolation basis

Definition at line 19 of file EICommon.m.

Inheritance diagram for Greedy.Plugin.EICommon:
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Public Member Functions

 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...
 
virtual function EICommon cop = copy ()
 makes a deep copy of this extension 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

 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
 

Additional Inherited Members

- 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.EICommon.EICommon ( SnapshotsGenerator.SpaceOpEvals  generator)

constructor for an EICommon instance

Parameters
generatorobject generating the (high dimensional) basis functions, i.e. operator or function evaluations.

Definition at line 46 of file EICommon.m.

Member Function Documentation

function EICommon cop = Greedy.Plugin.EICommon.copy ( )
pure virtual

makes a deep copy of this extension instance

Return values
copa new instance which is a deep copy of this one.

Implemented in Greedy.Plugin.EI, Greedy.Plugin.SummedEI, and Greedy.Plugin.EIPOD.

function [ max_errs , max_err_sequence , max_mu_index ] = Greedy.Plugin.EICommon.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 \({\cal M}_{\text{train}}\).

An a posteriori error estimator 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

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

Note
The estimator must only depend on low dimensional data as computed by the prepare_reduced_data() method such that it is efficiently computable.
Parameters
rmodelan object specifying the basis generation process.
detailed_dataobject 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.
M_traina set of parameter vectors \({\cal M}_{\text{train}}\) as returned by ParameterSampling.Interface.space .
Return values
max_errsa 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_sequencea sequence of error indicators \(\eta^k(\mu_{\max})\) for every \(k=0,\ldots,K\).
max_mu_indexthe index of the parameter vector \(\mu_{\max}\) in the parameter_set.set matrix.
Note
This method is not implemented for empirical interpolation. There is no known a posteriori error estimator.

Definition at line 60 of file EICommon.m.

function Greedy.DataTree.Detailed.EILeafNode detailed_data = Greedy.Plugin.EICommon.finalize ( IReducedModel  rmodel,
Greedy.DataTree.Detailed.EILeafNode  detailed_data 
)

function called after the last extension process

Parameters
rmodelan object specifying the basis generation process.
detailed_dataobject 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_dataupdated data tree node .

This function actually computes the Lebesgue constant if indicated by compute_lebesgue and stores it in info fields.

Definition at line 77 of file EICommon.m.

function Greedy.Plugin.EI merged = Greedy.Plugin.EICommon.horzcat (   varargin)

combines an arbitrary number of Greedy.Plugin.EI arguments to a big one, with added SnapshotsGenerator.Cached instances.

See also
SnapshotsGenerator.Cached.plus()
Usage is like this
ei_ext_merged = [ ei_ext1, ei_ext2, ei_ext3 ];
Parameters
varargina list of Greedy.Plugin.EI instances to be combined.
Return values
mergeda new object with combined generator member.

Definition at line 98 of file EICommon.m.

function summed = Greedy.Plugin.EICommon.vertcat (   varargin)

combines an arbitrary number of Greedy.Plugin.EI arguments to a Greedy.Plugin.SummedEI instance.

See also
Greedy.Plugin.SummedEI
Usage is like this
ei_ext_sum = [ ei_ext1; ei_ext2; ei_ext3 ];
Parameters
varargina list of Greedy.Plugin.EI instances to be combined.
Return values
summedsummed
mergeda new object

Definition at line 124 of file EICommon.m.

Member Data Documentation

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.


Default: true

Definition at line 33 of file EICommon.m.


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