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rbmatlab
1.16.09
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rbmatlab
1.16.09
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Default implementation of a Greedy.Plugin.Interface interface class.
Public Member Functions | |
| 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 | |
| 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... | |
| Greedy.Plugin.Default.Default | ( | SnapshotsGenerator.Cached | generator | ) |
|
virtual |
computes the "true" error between a reduced and a detailed function \(\| v_h(t^k;\mu) - v_{\text{red}}(t^k;\mu) \|\).
| 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. |
| errs | a sequence of errors at every time step \(k=0,\ldots,K\). |
Implements Greedy.Plugin.Interface.
Definition at line 173 of file Default.m.
|
pure virtual |
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
\[\mu_{\max} = \arg \sup_{\mu \in {\cal M}_{\text{train}} } \max_{k=0,\ldots,K} \eta^k(\mu).\]
| 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. |
| M_train | a set of parameter vectors \({\cal M}_{\text{train}}\) as returned by ParameterSampling.Interface.space . |
| 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.set matrix. |
Implemented in Greedy.Plugin.POD, and Greedy.Plugin.PODDune.
| function [ max_errs , max_err_sequence , max_mu_index ] = Greedy.Plugin.Default.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 \({\cal M}_{\text{train}}\).
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
\[\mu_{\max} = \arg \sup_{\mu \in {\cal M}_{\text{train}} } \max_{k=0,\ldots,K} \eta^k(\mu)\]
.
| 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) |
| 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. |
If indicator_mode equals
estimator, the method error_estimators() is callederror, compute_error() is used to compute "true" errors. Definition at line 120 of file Default.m.
| Greedy.Plugin.Default.indicator_mode = "error" |
string specifying which indicators shall be used by the error_indicators() method.
error for an error between the detailed and the reduced computation. estimator for an a posteriori error estimator
Default: "error"
| Greedy.Plugin.Default.needs_preparation |
boolean indicating whether the prepare_reduced_data() method needs to be computed before error_indicators can be computed.
Dependent set to true. Dependent set to true. | Greedy.Plugin.Default.reduced_data = "[]" |
temporary handle to the last object computed by prepare_reduced_data().
Transient set to true. | Greedy.Plugin.Default.relative_error = false |
boolean flag specifying whether we want to use the relative error for error_indicators() and compute_error() methods.
Default: false
| Greedy.Plugin.Default.use_l2_error = true |
boolean flag indicating whether the \(L^2(\Omega)\)-norm is used by compute_error().
Otherwise the \(L^{\infty}(\Omega)\)-norm is applied.
Default: true
1.8.8