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NonDMultilevControlVarSampling Class Reference

Performs multilevel-multifidelity Monte Carlo sampling for uncertainty quantification. More...

Inheritance diagram for NonDMultilevControlVarSampling:
NonDControlVariateSampling NonDMultilevelSampling NonDHierarchSampling NonDHierarchSampling NonDEnsembleSampling NonDEnsembleSampling NonDSampling NonDSampling NonD NonD Analyzer Analyzer Iterator Iterator

Public Member Functions

 NonDMultilevControlVarSampling (ProblemDescDB &problem_db, Model &model)
 standard constructor More...
 
 ~NonDMultilevControlVarSampling ()
 destructor
 
- Public Member Functions inherited from NonDControlVariateSampling
 NonDControlVariateSampling (ProblemDescDB &problem_db, Model &model)
 standard constructor More...
 
 ~NonDControlVariateSampling ()
 destructor
 
- Public Member Functions inherited from NonDHierarchSampling
 NonDHierarchSampling (ProblemDescDB &problem_db, Model &model)
 standard constructor More...
 
virtual ~NonDHierarchSampling ()
 destructor (virtual declaration should be redundant with ~Iterator, but this is top of MLMF diamond so doesn't hurt to be explicit)
 
- Public Member Functions inherited from NonDEnsembleSampling
 NonDEnsembleSampling (ProblemDescDB &problem_db, Model &model)
 standard constructor More...
 
 ~NonDEnsembleSampling ()
 destructor (virtual declaration should be redundant with ~Iterator, but this is top of MLMF diamond so doesn't hurt to be explicit)
 
bool resize ()
 reinitializes iterator based on new variable size
 
- Public Member Functions inherited from NonDSampling
 NonDSampling (Model &model, const RealMatrix &sample_matrix)
 alternate constructor for evaluating and computing statistics for the provided set of samples More...
 
 ~NonDSampling ()
 destructor
 
void compute_statistics (const RealMatrix &vars_samples, const IntResponseMap &resp_samples)
 For the input sample set, computes mean, standard deviation, and probability/reliability/response levels (aleatory uncertainties) or intervals (epsitemic or mixed uncertainties)
 
void compute_intervals (RealRealPairArray &extreme_fns)
 called by compute_statistics() to calculate min/max intervals using allResponses
 
void compute_intervals (const IntResponseMap &samples)
 called by compute_statistics() to calculate extremeValues from samples
 
void compute_intervals (RealRealPairArray &extreme_fns, const IntResponseMap &samples)
 called by compute_statistics() to calculate min/max intervals using samples
 
void compute_moments (const RealVectorArray &fn_samples)
 calculates sample moments from a matrix of observations for a set of QoI
 
void compute_moments (const IntResponseMap &samples)
 calculate sample moments and confidence intervals from a map of response observations
 
void compute_moments (const IntResponseMap &samples, RealMatrix &moment_stats, RealMatrix &moment_grads, RealMatrix &moment_conf_ints, short moments_type, const StringArray &labels)
 convert IntResponseMap to RealVectorArray and invoke helpers
 
void compute_moment_gradients (const RealVectorArray &fn_samples, const RealMatrixArray &grad_samples, const RealMatrix &moment_stats, RealMatrix &moment_grads, short moments_type)
 compute moment_grads from function and gradient samples
 
void compute_moment_confidence_intervals (const RealMatrix &moment_stats, RealMatrix &moment_conf_ints, const SizetArray &sample_counts, short moments_type)
 compute moment confidence intervals from moment values
 
void archive_moments (size_t inc_id=0)
 archive moment statistics in results DB
 
void archive_moment_confidence_intervals (size_t inc_id=0)
 archive moment confidence intervals in results DB
 
void archive_extreme_responses (size_t inc_id=0)
 archive extreme values (epistemic result) in results DB
 
void compute_level_mappings (const IntResponseMap &samples)
 called by compute_statistics() to calculate CDF/CCDF mappings of z to p/beta and of p/beta to z as well as PDFs More...
 
void print_statistics (std::ostream &s) const
 prints the statistics computed in compute_statistics()
 
void print_intervals (std::ostream &s) const
 prints the intervals computed in compute_intervals() with default qoi_type and moment_labels
 
void print_intervals (std::ostream &s, String qoi_type, const StringArray &interval_labels) const
 prints the intervals computed in compute_intervals()
 
void print_moments (std::ostream &s) const
 prints the moments computed in compute_moments() with default qoi_type and moment_labels
 
void print_moments (std::ostream &s, String qoi_type, const StringArray &moment_labels) const
 prints the moments computed in compute_moments()
 
void print_wilks_stastics (std::ostream &s) const
 prints the Wilks stastics
 
void update_final_statistics ()
 update finalStatistics from minValues/maxValues, momentStats, and computedProbLevels/computedRelLevels/computedRespLevels
 
void transform_samples (Pecos::ProbabilityTransformation &nataf, bool x_to_u=true)
 transform allSamples imported by alternate constructor. This is needed since random variable distribution parameters are not updated until run time and an imported sample_matrix is typically in x-space. More...
 
void transform_samples (Pecos::ProbabilityTransformation &nataf, RealMatrix &sample_matrix, size_t num_samples=0, bool x_to_u=true)
 transform the specified samples matrix from x to u or u to x
 
unsigned short sampling_scheme () const
 return sampleType
 
const String & random_number_generator () const
 return rngName
 
- Public Member Functions inherited from NonD
void requested_levels (const RealVectorArray &req_resp_levels, const RealVectorArray &req_prob_levels, const RealVectorArray &req_rel_levels, const RealVectorArray &req_gen_rel_levels, short resp_lev_tgt, short resp_lev_tgt_reduce, bool cdf_flag, bool pdf_output)
 set requestedRespLevels, requestedProbLevels, requestedRelLevels, requestedGenRelLevels, respLevelTarget, cdfFlag, and pdfOutput (used in combination with alternate ctors)
 
void print_level_mappings (std::ostream &s) const
 prints the z/p/beta/beta* mappings reflected in {requested,computed}{Resp,Prob,Rel,GenRel}Levels for default qoi_type and qoi_labels
 
void print_level_mappings (std::ostream &s, String qoi_type, const StringArray &qoi_labels) const
 prints the z/p/beta/beta* mappings reflected in {requested,computed}{Resp,Prob,Rel,GenRel}Levels More...
 
void print_level_mappings (std::ostream &s, const RealVector &level_maps, bool moment_offset, const String &prepend="")
 print level mapping statistics using optional pre-pend More...
 
bool pdf_output () const
 get pdfOutput
 
void pdf_output (bool output)
 set pdfOutput
 
short final_moments_type () const
 get finalMomentsType
 
void final_moments_type (short type)
 set finalMomentsType
 
- Public Member Functions inherited from Analyzer
const VariablesArray & all_variables ()
 return the complete set of evaluated variables
 
const RealMatrix & all_samples ()
 return the complete set of evaluated samples
 
const IntResponseMap & all_responses () const
 return the complete set of computed responses
 
- Public Member Functions inherited from Iterator
 Iterator (std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
 default constructor More...
 
 Iterator (ProblemDescDB &problem_db, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
 standard envelope constructor, which constructs its own model(s) More...
 
 Iterator (ProblemDescDB &problem_db, Model &model, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
 alternate envelope constructor which uses the ProblemDescDB but accepts a model from a higher level (meta-iterator) context, instead of constructing its own More...
 
 Iterator (const String &method_string, Model &model, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
 alternate envelope constructor for instantiations by name without the ProblemDescDB More...
 
 Iterator (const Iterator &iterator)
 copy constructor More...
 
virtual ~Iterator ()
 destructor
 
Iterator operator= (const Iterator &iterator)
 assignment operator
 
virtual void derived_free_communicators (ParLevLIter pl_iter)
 derived class contributions to freeing the communicators associated with this Iterator instance
 
virtual void post_input ()
 read tabular data for post-run mode
 
virtual void reset ()
 restore initial state for repeated sub-iterator executions
 
virtual void nested_variable_mappings (const SizetArray &c_index1, const SizetArray &di_index1, const SizetArray &ds_index1, const SizetArray &dr_index1, const ShortArray &c_target2, const ShortArray &di_target2, const ShortArray &ds_target2, const ShortArray &dr_target2)
 set primaryA{CV,DIV,DRV}MapIndices, secondaryA{CV,DIV,DRV}MapTargets within derived Iterators; supports computation of higher-level sensitivities in nested contexts (e.g., derivatives of statistics w.r.t. inserted design variables)
 
virtual void initialize_iterator (int job_index)
 used by IteratorScheduler to set the starting data for a run
 
virtual void pack_parameters_buffer (MPIPackBuffer &send_buffer, int job_index)
 used by IteratorScheduler to pack starting data for an iterator run
 
virtual void unpack_parameters_buffer (MPIUnpackBuffer &recv_buffer, int job_index)
 used by IteratorScheduler to unpack starting data for an iterator run
 
virtual void unpack_parameters_initialize (MPIUnpackBuffer &recv_buffer, int job_index)
 used by IteratorScheduler to unpack starting data and initialize an iterator run
 
virtual void pack_results_buffer (MPIPackBuffer &send_buffer, int job_index)
 used by IteratorScheduler to pack results data from an iterator run
 
virtual void unpack_results_buffer (MPIUnpackBuffer &recv_buffer, int job_index)
 used by IteratorScheduler to unpack results data from an iterator run
 
virtual void update_local_results (int job_index)
 used by IteratorScheduler to update local results arrays
 
virtual bool accepts_multiple_points () const
 indicates if this iterator accepts multiple initial points. Default return is false. Override to return true if appropriate.
 
virtual void initial_point (const Variables &pt)
 sets the initial point for this iterator (user-functions mode for which Model updating is not used)
 
virtual void initial_point (const RealVector &pt)
 sets the initial point (active continuous variables) for this iterator (user-functions mode for which Model updating is not used)
 
virtual void initial_points (const VariablesArray &pts)
 sets the multiple initial points for this iterator. This should only be used if accepts_multiple_points() returns true.
 
virtual void variable_bounds (const RealVector &cv_lower_bnds, const RealVector &cv_upper_bnds)
 assign nonlinear inequality and equality constraint allowables for this iterator (user-functions mode for which Model updating is not used)
 
virtual void linear_constraints (const RealMatrix &lin_ineq_coeffs, const RealVector &lin_ineq_lb, const RealVector &lin_ineq_ub, const RealMatrix &lin_eq_coeffs, const RealVector &lin_eq_tgt)
 assign linear inequality and linear equality constraints for this iterator (user-functions mode for which Model updating is not used)
 
virtual void nonlinear_constraints (const RealVector &nln_ineq_lb, const RealVector &nln_ineq_ub, const RealVector &nln_eq_tgt)
 assign nonlinear inequality and equality constraint allowables for this iterator (user-functions mode for which Model updating is not used)
 
virtual void initialize_graphics (int iterator_server_id=1)
 initialize the 2D graphics window and the tabular graphics data More...
 
virtual void check_sub_iterator_conflict ()
 detect any conflicts due to recursive use of the same Fortran solver More...
 
virtual unsigned short uses_method () const
 return name of any enabling iterator used by this iterator
 
virtual void method_recourse ()
 perform a method switch, if possible, due to a detected conflict
 
virtual void sampling_increment ()
 increment to next in sequence of refinement samples
 
virtual IntIntPair estimate_partition_bounds ()
 estimate the minimum and maximum partition sizes that can be utilized by this Iterator
 
virtual void declare_sources ()
 Declare sources to the evaluations database.
 
void init_communicators (ParLevLIter pl_iter)
 initialize the communicators associated with this Iterator instance
 
void set_communicators (ParLevLIter pl_iter)
 set the communicators associated with this Iterator instance
 
void free_communicators (ParLevLIter pl_iter)
 free the communicators associated with this Iterator instance
 
void resize_communicators (ParLevLIter pl_iter, bool reinit_comms)
 Resize the communicators. This is called from the letter's resize()
 
void parallel_configuration_iterator (ParConfigLIter pc_iter)
 set methodPCIter
 
ParConfigLIter parallel_configuration_iterator () const
 return methodPCIter
 
void parallel_configuration_iterator_map (std::map< size_t, ParConfigLIter > pci_map)
 set methodPCIterMap
 
std::map< size_t, ParConfigLIter > parallel_configuration_iterator_map () const
 return methodPCIterMap
 
void run (ParLevLIter pl_iter)
 invoke set_communicators(pl_iter) prior to run()
 
void run ()
 orchestrate initialize/pre/core/post/finalize phases More...
 
void assign_rep (std::shared_ptr< Iterator > iterator_rep)
 replaces existing letter with a new one More...
 
void iterated_model (const Model &model)
 set the iteratedModel (iterators and meta-iterators using a single model instance)
 
Modeliterated_model ()
 return the iteratedModel (iterators & meta-iterators using a single model instance)
 
ProblemDescDBproblem_description_db () const
 return the problem description database (probDescDB)
 
ParallelLibraryparallel_library () const
 return the parallel library (parallelLib)
 
void method_name (unsigned short m_name)
 set the method name to an enumeration value
 
unsigned short method_name () const
 return the method name via its native enumeration value
 
void method_string (const String &m_str)
 set the method name by string
 
String method_string () const
 return the method name by string
 
String method_enum_to_string (unsigned short method_enum) const
 convert a method name enumeration value to a string
 
unsigned short method_string_to_enum (const String &method_str) const
 convert a method name string to an enumeration value
 
String submethod_enum_to_string (unsigned short submethod_enum) const
 convert a sub-method name enumeration value to a string
 
const String & method_id () const
 return the method identifier (methodId)
 
int maximum_evaluation_concurrency () const
 return the maximum evaluation concurrency supported by the iterator
 
void maximum_evaluation_concurrency (int max_conc)
 set the maximum evaluation concurrency supported by the iterator
 
size_t maximum_iterations () const
 return the maximum iterations for this iterator
 
void maximum_iterations (size_t max_iter)
 set the maximum iterations for this iterator
 
void convergence_tolerance (Real conv_tol)
 set the method convergence tolerance (convergenceTol)
 
Real convergence_tolerance () const
 return the method convergence tolerance (convergenceTol)
 
void output_level (short out_lev)
 set the method output level (outputLevel)
 
short output_level () const
 return the method output level (outputLevel)
 
void summary_output (bool summary_output_flag)
 Set summary output control; true enables evaluation/results summary.
 
size_t num_final_solutions () const
 return the number of solutions to retain in best variables/response arrays
 
void num_final_solutions (size_t num_final)
 set the number of solutions to retain in best variables/response arrays
 
void active_set (const ActiveSet &set)
 set the default active set (for use with iterators that employ evaluate_parameter_sets())
 
const ActiveSetactive_set () const
 return the default active set (used by iterators that employ evaluate_parameter_sets())
 
void active_set_request_vector (const ShortArray &asv)
 return the default active set request vector (used by iterators that employ evaluate_parameter_sets())
 
const ShortArray & active_set_request_vector () const
 return the default active set request vector (used by iterators that employ evaluate_parameter_sets())
 
void active_set_request_values (short asv_val)
 return the default active set request vector (used by iterators that employ evaluate_parameter_sets())
 
void sub_iterator_flag (bool si_flag)
 set subIteratorFlag (and update summaryOutputFlag if needed)
 
bool is_null () const
 function to check iteratorRep (does this envelope contain a letter?)
 
std::shared_ptr< Iteratoriterator_rep () const
 returns iteratorRep for access to derived class member functions that are not mapped to the top Iterator level
 
virtual void eval_tag_prefix (const String &eval_id_str)
 set the hierarchical eval ID tag prefix More...
 
std::shared_ptr< TraitsBasetraits () const
 returns methodTraits for access to derived class member functions that are not mapped to the top TraitsBase level
 
bool top_level ()
 Return whether the iterator is the top level iterator.
 
void top_level (bool tflag)
 Set the iterator's top level flag.
 
- Public Member Functions inherited from NonDMultilevelSampling
 NonDMultilevelSampling (ProblemDescDB &problem_db, Model &model)
 standard constructor More...
 
 ~NonDMultilevelSampling ()
 destructor
 

Protected Member Functions

void pre_run ()
 pre-run portion of run (optional); re-implemented by Iterators which can generate all Variables (parameter sets) a priori More...
 
void core_run ()
 
void print_variance_reduction (std::ostream &s)
 
- Protected Member Functions inherited from NonDControlVariateSampling
bool lf_increment (const RealVector &eval_ratios, const SizetArray &N_lf, Real hf_target, size_t iter, size_t lev)
 perform LF sample increment as indicated by the evaluation ratio More...
 
bool lf_increment (const Pecos::ActiveKey &lf_key, const RealVector &eval_ratios, const SizetArray &N_lf, const RealVector &hf_targets, size_t iter, size_t lev)
 perform final LF sample increment as indicated by the evaluation ratio More...
 
void compute_mf_correlation (Real sum_L, Real sum_H, Real sum_LL, Real sum_LH, Real sum_HH, size_t N_shared, Real &var_H, Real &rho2_LH)
 compute scalar variance and correlation parameters for control variates
 
void apply_mf_control (Real sum_H, Real sum_L_shared, size_t N_shared, Real sum_L_refined, size_t N_refined, Real beta, Real &H_raw_mom)
 apply scalar control variate parameter (beta) to approximate HF moment
 
void apply_mf_control (const RealMatrix &sum_H, const RealMatrix &sum_L_shared, const SizetArray &N_shared, const RealMatrix &sum_L_refined, const SizetArray &N_refined, size_t lev, const RealVector &beta, RealVector &H_raw_mom)
 apply matrix control variate parameter (beta) to approximate HF moment
 
- Protected Member Functions inherited from NonDHierarchSampling
void uncorrected_surrogate_mode ()
 synchronize iteratedModel and activeSet on UNCORRECTED_SURROGATE mode
 
void average_online_cost (const RealVector &accum_cost, const SizetArray &num_cost, RealVector &seq_cost)
 average costs once accumulations are complete
 
void accumulate_paired_online_cost (RealVector &accum_cost, SizetArray &num_cost, size_t step)
 recover partial estimates of simulation cost using aggregated (paired) response metadata
 
void recover_paired_online_cost (RealVector &seq_cost, size_t step)
 accumulate cost and counts and then perform averaging
 
- Protected Member Functions inherited from NonDEnsembleSampling
void post_run (std::ostream &s)
 post-run portion of run (optional); verbose to print results; re-implemented by Iterators that can read all Variables/Responses and perform final analysis phase in a standalone way More...
 
void print_results (std::ostream &s, short results_state=FINAL_RESULTS)
 print the final iterator results More...
 
void initialize_final_statistics ()
 initializes finalStatistics for storing NonD final results More...
 
void update_final_statistics ()
 update finalStatistics::functionValues
 
bool seed_updated ()
 
void active_set_mapping ()
 in the case of sub-iteration, map from finalStatistics.active_set() requests to activeSet used in evaluate_parameter_sets() More...
 
void aggregated_models_mode ()
 synchronize iteratedModel and activeSet on AGGREGATED_MODELS mode
 
void bypass_surrogate_mode ()
 synchronize iteratedModel and activeSet on BYPASS_SURROGATE mode
 
void assign_specification_sequence (size_t index)
 advance any sequence specifications
 
int seed_sequence (size_t index)
 extract current random seed from randomSeedSeqSpec More...
 
void increment_samples (SizetArray &N_l, size_t num_samples)
 increment samples array with a shared scalar
 
void compute_mc_estimator_variance (const RealVector &var_l, const SizetArray &N_l, RealVector &mc_est_var)
 compute the variance of the mean estimator (Monte Carlo sample average)
 
void project_mc_estimator_variance (const RealVector &var_l, const SizetArray &N_l, size_t new_samp, RealVector &mc_est_var)
 compute the variance of the mean estimator (Monte Carlo sample average) after projection with additional samples (var_l remains fixed)
 
void estvar_ratios_to_avg_estvar (const RealVector &estvar_ratios, const RealVector &var_H, const SizetArray &N_H, Real &avg_est_var)
 convert estimator variance ratios to average estimator variance
 
void compute_mf_control (Real sum_L, Real sum_H, Real sum_LL, Real sum_LH, size_t N_shared, Real &beta)
 compute scalar control variate parameters
 
void compute_mf_control (const RealMatrix &sum_L, const RealMatrix &sum_H, const RealMatrix &sum_LL, const RealMatrix &sum_LH, const SizetArray &N_shared, size_t lev, RealVector &beta)
 compute matrix control variate parameters
 
void compute_mf_control (const RealVector &sum_L, const RealVector &sum_H, const RealVector &sum_LL, const RealVector &sum_LH, const SizetArray &N_shared, RealVector &beta)
 compute vector control variate parameters
 
void export_all_samples (String root_prepend, const Model &model, size_t iter, size_t step)
 export allSamples to tagged tabular file
 
void convert_moments (const RealMatrix &raw_mom, RealMatrix &final_mom)
 convert uncentered raw moments (multilevel expectations) to standardized moments
 
Real sum (const Real *vec, size_t vec_len) const
 compute sum of a set of observations
 
Real average (const Real *vec, size_t vec_len) const
 compute average of a set of observations
 
Real average (const RealVector &vec) const
 compute average of a set of observations
 
Real average (const SizetArray &sa) const
 compute average of a set of observations
 
void average (const RealMatrix &mat, size_t avg_index, RealVector &avg_vec) const
 compute row-averages for each column or column-averages for each row
 
- Protected Member Functions inherited from NonDSampling
 NonDSampling (ProblemDescDB &problem_db, Model &model)
 constructor More...
 
 NonDSampling (unsigned short method_name, Model &model, unsigned short sample_type, size_t samples, int seed, const String &rng, bool vary_pattern, short sampling_vars_mode)
 alternate constructor for sample generation and evaluation "on the fly" More...
 
 NonDSampling (unsigned short sample_type, size_t samples, int seed, const String &rng, const RealVector &lower_bnds, const RealVector &upper_bnds)
 alternate constructor for sample generation "on the fly" More...
 
 NonDSampling (unsigned short sample_type, size_t samples, int seed, const String &rng, const RealVector &means, const RealVector &std_devs, const RealVector &lower_bnds, const RealVector &upper_bnds, RealSymMatrix &correl)
 alternate constructor for sample generation of correlated normals "on the fly" More...
 
void pre_run ()
 pre-run portion of run (optional); re-implemented by Iterators which can generate all Variables (parameter sets) a priori More...
 
void core_run ()
 
size_t num_samples () const
 
void sampling_reset (size_t min_samples, bool all_data_flag, bool stats_flag)
 resets number of samples and sampling flags More...
 
void sampling_reference (size_t samples_ref)
 set reference number of samples, which is a lower bound during reset
 
void random_seed (int seed)
 assign randomSeed
 
void vary_pattern (bool pattern_flag)
 set varyPattern
 
void get_parameter_sets (Model &model)
 Uses lhsDriver to generate a set of samples from the distributions/bounds defined in the incoming model. More...
 
void get_parameter_sets (Model &model, const size_t num_samples, RealMatrix &design_matrix)
 Uses lhsDriver to generate a set of samples from the distributions/bounds defined in the incoming model and populates the specified design matrix. More...
 
void get_parameter_sets (Model &model, const size_t num_samples, RealMatrix &design_matrix, bool write_msg)
 core of get_parameter_sets that accepts message print control
 
void get_parameter_sets (const RealVector &lower_bnds, const RealVector &upper_bnds)
 Uses lhsDriver to generate a set of uniform samples over lower_bnds/upper_bnds. More...
 
void get_parameter_sets (const RealVector &means, const RealVector &std_devs, const RealVector &lower_bnds, const RealVector &upper_bnds, RealSymMatrix &correl)
 Uses lhsDriver to generate a set of normal samples. More...
 
void update_model_from_sample (Model &model, const Real *sample_vars)
 Override default update of continuous vars only.
 
void sample_to_variables (const Real *sample_vars, Variables &vars)
 override default mapping of continuous variables only
 
void variables_to_sample (const Variables &vars, Real *sample_vars)
 override default mapping of continuous variables only
 
const RealSymMatrix & response_error_estimates () const
 return error estimates associated with each of the finalStatistics
 
void initialize_sample_driver (bool write_message, size_t num_samples)
 increments numLHSRuns, sets random seed, and initializes lhsDriver
 
void mode_counts (const Variables &vars, size_t &cv_start, size_t &num_cv, size_t &div_start, size_t &num_div, size_t &dsv_start, size_t &num_dsv, size_t &drv_start, size_t &num_drv) const
 compute sampled subsets (all, active, uncertain) within all variables (acv/adiv/adrv) from samplingVarsMode and model More...
 
void mode_bits (const Variables &vars, BitArray &active_vars, BitArray &active_corr) const
 define subset views for sampling modes
 
- Protected Member Functions inherited from NonD
 NonD (ProblemDescDB &problem_db, Model &model)
 constructor
 
 NonD (unsigned short method_name, Model &model)
 alternate constructor for sample generation and evaluation "on the fly"
 
 NonD (unsigned short method_name, const RealVector &lower_bnds, const RealVector &upper_bnds)
 alternate constructor for sample generation "on the fly"
 
 ~NonD ()
 destructor
 
void derived_set_communicators (ParLevLIter pl_iter)
 derived class contributions to setting the communicators associated with this Iterator instance
 
void initialize_run ()
 utility function to perform common operations prior to pre_run(); typically memory initialization; setting of instance pointers More...
 
void finalize_run ()
 utility function to perform common operations following post_run(); deallocation and resetting of instance pointers More...
 
const Responseresponse_results () const
 return the final statistics from the nondeterministic iteration
 
void response_results_active_set (const ActiveSet &set)
 set the active set within finalStatistics
 
virtual void initialize_response_covariance ()
 initializes respCovariance
 
void pull_level_mappings (RealVector &level_maps, size_t offset)
 concatenate computed{Resp,Prob,Rel,GenRel}Levels into level_maps
 
void push_level_mappings (const RealVector &level_maps, size_t offset)
 update computed{Resp,Prob,Rel,GenRel}Levels from level_maps
 
void configure_sequence (size_t &num_steps, size_t &secondary_index, short &seq_type)
 configure fidelity/level counts from model hierarchy More...
 
void configure_cost (unsigned short num_steps, bool multilevel, RealVector &cost)
 extract cost estimates from model hierarchy (forms or resolutions)
 
bool query_cost (unsigned short num_steps, bool multilevel, RealVector &cost)
 extract cost estimates from model hierarchy, if available
 
bool query_cost (unsigned short num_steps, Model &model, RealVector &cost)
 extract cost estimates from model hierarchy, if available
 
bool valid_cost_values (const RealVector &cost)
 test cost for valid values > 0
 
void load_pilot_sample (const SizetArray &pilot_spec, size_t num_steps, SizetArray &delta_N_l)
 distribute pilot sample specification across model forms or levels
 
void load_pilot_sample (const SizetArray &pilot_spec, const Sizet3DArray &N_l, Sizet2DArray &delta_N_l)
 distribute pilot sample specification across model forms and levels
 
void inflate_final_samples (const Sizet2DArray &N_l_2D, bool multilev, size_t secondary_index, Sizet3DArray &N_l_3D)
 update the relevant slice of N_l_3D from the final 2D multilevel or 2D multifidelity sample profile
 
void resize_final_statistics_gradients ()
 resizes finalStatistics::functionGradients based on finalStatistics ASV
 
void update_aleatory_final_statistics ()
 update finalStatistics::functionValues from momentStats and computed{Prob,Rel,GenRel,Resp}Levels
 
void update_system_final_statistics ()
 update system metrics from component metrics within finalStatistics
 
void update_system_final_statistics_gradients ()
 update finalStatistics::functionGradients
 
void initialize_level_mappings ()
 size computed{Resp,Prob,Rel,GenRel}Levels
 
void compute_densities (const RealRealPairArray &min_max_fns, bool prob_refinement=false, bool all_levels_computed=false)
 compute the PDF bins from the CDF/CCDF values and store in computedPDF{Abscissas,Ordinates} More...
 
void print_densities (std::ostream &s) const
 output the PDFs reflected in computedPDF{Abscissas,Ordinates} using default qoi_type and pdf_labels
 
void print_densities (std::ostream &s, String qoi_type, const StringArray &pdf_labels) const
 output the PDFs reflected in computedPDF{Abscissas,Ordinates}
 
void print_system_mappings (std::ostream &s) const
 print system series/parallel mappings for response levels
 
void print_multilevel_evaluation_summary (std::ostream &s, const SizetArray &N_samp)
 print evaluation summary for multilevel sampling across 1D profile
 
void print_multilevel_evaluation_summary (std::ostream &s, const Sizet2DArray &N_samp)
 print evaluation summary for multilevel sampling across 2D profile
 
void print_multilevel_evaluation_summary (std::ostream &s, const Sizet3DArray &N_samp, String type="Final")
 print evaluation summary for multilevel sampling across 3D profile
 
void construct_lhs (Iterator &u_space_sampler, Model &u_model, unsigned short sample_type, int num_samples, int seed, const String &rng, bool vary_pattern, short sampling_vars_mode=ACTIVE)
 assign a NonDLHSSampling instance within u_space_sampler
 
unsigned short sub_optimizer_select (unsigned short requested_sub_method, unsigned short default_sub_method=SUBMETHOD_NPSOL)
 utility for vetting sub-method request against optimizers within the package configuration
 
size_t one_sided_delta (Real current, Real target)
 compute a one-sided sample increment for multilevel methods to move current sampling level to a new target
 
size_t one_sided_delta (const SizetArray &current, const RealVector &targets, size_t power)
 compute a one-sided sample increment for multilevel methods to move current sampling level to a new target
 
size_t one_sided_delta (const SizetArray &current, Real target, size_t power)
 compute a one-sided sample increment for multilevel methods to move current sampling level to a new target
 
void archive_allocate_mappings ()
 allocate results array storage for distribution mappings
 
void archive_from_resp (size_t fn_index, size_t inc_id=0)
 archive the mappings from specified response levels for specified fn
 
void archive_to_resp (size_t fn_index, size_t inc_id=0)
 archive the mappings to computed response levels for specified fn and (optional) increment id.
 
void archive_allocate_pdf ()
 allocate results array storage for pdf histograms
 
void archive_pdf (size_t fn_index, size_t inc_id=0)
 archive a single pdf histogram for specified function
 
void archive_equiv_hf_evals (const Real equiv_hf_evals)
 archive the equivalent number of HF evals (used by ML/MF methods)
 
- Protected Member Functions inherited from Analyzer
 Analyzer ()
 default constructor
 
 Analyzer (ProblemDescDB &problem_db, Model &model)
 standard constructor
 
 Analyzer (unsigned short method_name, Model &model)
 alternate constructor for instantiations "on the fly" with a Model
 
 Analyzer (unsigned short method_name)
 alternate constructor for instantiations "on the fly" without a Model
 
 ~Analyzer ()
 destructor
 
virtual void update_model_from_variables (Model &model, const Variables &vars)
 update model's current variables with data from vars
 
void update_from_model (const Model &model)
 set inherited data attributes based on extractions from incoming model
 
void pre_output ()
 
const Modelalgorithm_space_model () const
 
const Variablesvariables_results () const
 return a single final iterator solution (variables)
 
const VariablesArray & variables_array_results ()
 return multiple final iterator solutions (variables). This should only be used if returns_multiple_points() returns true.
 
const ResponseArray & response_array_results ()
 return multiple final iterator solutions (response). This should only be used if returns_multiple_points() returns true.
 
bool compact_mode () const
 returns Analyzer::compactMode
 
bool returns_multiple_points () const
 indicates if this iterator returns multiple final points. Default return is false. Override to return true if appropriate.
 
void evaluate_parameter_sets (Model &model, bool log_resp_flag, bool log_best_flag)
 perform function evaluations to map parameter sets (allVariables) into response sets (allResponses) More...
 
void get_vbd_parameter_sets (Model &model, size_t num_samples)
 generate replicate parameter sets for use in variance-based decomposition More...
 
void compute_vbd_stats (const size_t num_samples, const IntResponseMap &resp_samples)
 compute VBD-based Sobol indices More...
 
void archive_sobol_indices () const
 archive VBD-based Sobol indices More...
 
virtual void archive_model_variables (const Model &, size_t idx) const
 archive model evaluation points
 
virtual void archive_model_response (const Response &, size_t idx) const
 archive model evaluation responses
 
void read_variables_responses (int num_evals, size_t num_vars)
 convenience function for reading variables/responses (used in derived classes post_input) More...
 
void print_sobol_indices (std::ostream &s) const
 Printing of VBD results. More...
 
void samples_to_variables_array (const RealMatrix &sample_matrix, VariablesArray &vars_array)
 convert samples array to variables array; e.g., allSamples to allVariables
 
void variables_array_to_samples (const VariablesArray &vars_array, RealMatrix &sample_matrix)
 convert variables array to samples array; e.g., allVariables to allSamples
 
- Protected Member Functions inherited from Iterator
 Iterator (BaseConstructor, ProblemDescDB &problem_db, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
 constructor initializes the base class part of letter classes (BaseConstructor overloading avoids infinite recursion in the derived class constructors - Coplien, p. 139) More...
 
 Iterator (NoDBBaseConstructor, unsigned short method_name, Model &model, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
 alternate constructor for base iterator classes constructed on the fly More...
 
 Iterator (NoDBBaseConstructor, unsigned short method_name, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
 alternate constructor for base iterator classes constructed on the fly More...
 
 Iterator (NoDBBaseConstructor, Model &model, size_t max_iter, size_t max_eval, Real conv_tol, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
 alternate envelope constructor for instantiations without ProblemDescDB More...
 
virtual void derived_init_communicators (ParLevLIter pl_iter)
 derived class contributions to initializing the communicators associated with this Iterator instance
 
virtual const VariablesArray & initial_points () const
 gets the multiple initial points for this iterator. This will only be meaningful after a call to initial_points mutator.
 
StrStrSizet run_identifier () const
 get the unique run identifier based on method name, id, and number of executions
 
void initialize_model_graphics (Model &model, int iterator_server_id)
 helper function that encapsulates initialization operations, modular on incoming Model instance More...
 
void export_final_surrogates (Model &data_fit_surr_model)
 export final surrogates generated, e.g., GP in EGO and friends More...
 
- Protected Member Functions inherited from NonDMultilevelSampling
void core_run ()
 
void print_variance_reduction (std::ostream &s)
 
void nested_response_mappings (const RealMatrix &primary_coeffs, const RealMatrix &secondary_coeffs)
 set primaryResponseCoefficients, secondaryResponseCoefficients within derived Iterators; Necessary for scalarization case in MLMC NonDMultilevelSampling to map scalarization in nested context
 
void evaluate_ml_sample_increment (unsigned short step)
 helper that consolidates sequence advancement, sample generation, sample export, and sample evaluation
 
void increment_ml_equivalent_cost (size_t new_N_l, Real lev_cost, Real ref_cost)
 increment the equivalent number of HF evaluations based on new model evaluations
 
void compute_ml_estimator_variance (const RealMatrix &var_Y, const Sizet2DArray &num_Y, RealVector &ml_est_var)
 compute MLMC estimator variance from level QoI variances
 
void recover_variance (const RealMatrix &moment_stats, RealVector &var_H)
 recover variance from raw moments
 
void accumulate_ml_Ysums (IntRealMatrixMap &sum_Y, RealMatrix &sum_YY, size_t lev, SizetArray &num_Y)
 update accumulators for multilevel telescoping running sums using set of model evaluations within allResponses
 
void accumulate_ml_Ysums (RealMatrix &sum_Y, RealMatrix &sum_YY, size_t lev, SizetArray &num_Y)
 update accumulators for multilevel telescoping running sums using set of model evaluations within allResponses
 
void accumulate_ml_Qsums (IntRealMatrixMap &sum_Q, size_t lev, SizetArray &num_Q)
 update running QoI sums for one model (sum_Q) using set of model evaluations within allResponses; used for level 0 from other accumulators
 
Real variance_Ysum (Real sum_Y, Real sum_YY, size_t Nlq)
 compute variance scalar from sum accumulators
 
void variance_Ysum (const Real *sum_Y, const Real *sum_YY, const SizetArray &N_l, Real *var_Y)
 compute variance column vec (all QoI for one level) from sum accumulators
 
Real variance_Qsum (Real sum_Ql, Real sum_Qlm1, Real sum_QlQl, Real sum_QlQlm1, Real sum_Qlm1Qlm1, size_t Nlq)
 compute variance from sum accumulators
 
Real aggregate_variance_Ysum (const Real *sum_Y, const Real *sum_YY, const SizetArray &N_l)
 sum up variances across QoI (using sum_YY with means from sum_Y)
 
Real aggregate_mse_Yvar (const Real *var_Y, const SizetArray &N_l)
 sum up Monte Carlo estimates for mean squared error (MSE) across QoI using discrepancy variances
 
Real aggregate_mse_Ysum (const Real *sum_Y, const Real *sum_YY, const SizetArray &N_l)
 sum up Monte Carlo estimates for mean squared error (MSE) across QoI using discrepancy sums
 
void ml_raw_moments (const RealMatrix &sum_H1, const RealMatrix &sum_H2, const RealMatrix &sum_H3, const RealMatrix &sum_H4, const Sizet2DArray &N_hf, size_t start, size_t end, RealMatrix &ml_raw_mom)
 accumulate ML-only contributions (levels with no CV) to raw moments
 
void configure_indices (unsigned short group, unsigned short form, size_t lev, short seq_type)
 manage response mode and active model key from {group,form,lev} triplet. seq_type defines the active dimension for a 1D model sequence.
 
void configure_indices (size_t group, size_t form, size_t lev, short seq_type)
 convert group and form and call overload
 
Real level_cost (const RealVector &cost, size_t step)
 return (aggregate) level cost
 

Private Member Functions

void multilevel_control_variate_mc_Qcorr ()
 Perform multilevel Monte Carlo across levels in combination with control variate Monte Carlo across model forms at each level; CV computes correlations for Q (LH correlations for QoI) More...
 
void multilevel_control_variate_mc_offline_pilot ()
 Qcorr approach using a pilot sample treated as separate offline cost.
 
void multilevel_control_variate_mc_pilot_projection ()
 Qcorr approach projecting estimator performance from a pilot sample.
 
void evaluate_pilot (RealVector &hf_cost, RealVector &lf_cost, RealVectorArray &eval_ratios, RealMatrix &Lambda, RealMatrix &var_YH, Sizet2DArray &N_shared, RealVector &hf_targets, bool accumulate_cost, bool pilot_estvar)
 helper for shared code among offline-pilot and pilot-projection modes
 
void compute_mlmf_equivalent_cost (const SizetArray &raw_N_hf, const RealVector &hf_cost, const SizetArray &raw_N_lf, const RealVector &lf_cost)
 compute the equivalent number of HF evaluations (includes any sim faults)
 
void increment_mlmf_equivalent_cost (size_t new_N_hf, Real hf_lev_cost, size_t new_N_lf, Real lf_lev_cost, Real hf_ref_cost)
 increment the equivalent number of HF evaluations
 
void compute_mlmf_estimator_variance (const RealMatrix &var_Y, const Sizet2DArray &num_Y, const RealMatrix &Lambda, RealVector &mlmf_est_var)
 compute the variance of the MLMF estimator
 
void compute_eval_ratios (RealMatrix &sum_L_shared, RealMatrix &sum_H, RealMatrix &sum_LL, RealMatrix &sum_LH, RealMatrix &sum_HH, Real cost_ratio, size_t lev, const SizetArray &N_shared, RealMatrix &var_H, RealMatrix &rho2_LH, RealVector &eval_ratios)
 compute the LF/HF evaluation ratio, averaged over the QoI
 
void compute_eval_ratios (RealMatrix &sum_Ll, RealMatrix &sum_Llm1, RealMatrix &sum_Hl, RealMatrix &sum_Hlm1, RealMatrix &sum_Ll_Ll, RealMatrix &sum_Ll_Llm1, RealMatrix &sum_Llm1_Llm1, RealMatrix &sum_Hl_Ll, RealMatrix &sum_Hl_Llm1, RealMatrix &sum_Hlm1_Ll, RealMatrix &sum_Hlm1_Llm1, RealMatrix &sum_Hl_Hl, RealMatrix &sum_Hl_Hlm1, RealMatrix &sum_Hlm1_Hlm1, Real cost_ratio, size_t lev, const SizetArray &N_shared, RealMatrix &var_YHl, RealMatrix &rho_dot2_LH, RealVector &eval_ratios)
 compute the LF/HF evaluation ratio, averaged over the QoI
 
void cv_raw_moments (IntRealMatrixMap &sum_L_shared, IntRealMatrixMap &sum_H, IntRealMatrixMap &sum_LL, IntRealMatrixMap &sum_LH, const SizetArray &N_shared, IntRealMatrixMap &sum_L_refined, const SizetArray &N_refined, size_t lev, RealMatrix &H_raw_mom)
 apply control variate parameters for MLMF MC to estimate raw moment contributions
 
void cv_raw_moments (IntRealMatrixMap &sum_Ll, IntRealMatrixMap &sum_Llm1, IntRealMatrixMap &sum_Hl, IntRealMatrixMap &sum_Hlm1, IntRealMatrixMap &sum_Ll_Ll, IntRealMatrixMap &sum_Ll_Llm1, IntRealMatrixMap &sum_Llm1_Llm1, IntRealMatrixMap &sum_Hl_Ll, IntRealMatrixMap &sum_Hl_Llm1, IntRealMatrixMap &sum_Hlm1_Ll, IntRealMatrixMap &sum_Hlm1_Llm1, IntRealMatrixMap &sum_Hl_Hl, IntRealMatrixMap &sum_Hl_Hlm1, IntRealMatrixMap &sum_Hlm1_Hlm1, const SizetArray &N_shared, IntRealMatrixMap &sum_Ll_refined, IntRealMatrixMap &sum_Llm1_refined, const SizetArray &N_refined, size_t lev, RealMatrix &H_raw_mom)
 apply control variate parameters for MLMF MC to estimate raw moment contributions
 
void compute_mlmf_control (Real sum_Ll, Real sum_Llm1, Real sum_Hl, Real sum_Hlm1, Real sum_Ll_Ll, Real sum_Ll_Llm1, Real sum_Llm1_Llm1, Real sum_Hl_Ll, Real sum_Hl_Llm1, Real sum_Hlm1_Ll, Real sum_Hlm1_Llm1, Real sum_Hl_Hl, Real sum_Hl_Hlm1, Real sum_Hlm1_Hlm1, size_t N_shared, Real &var_YHl, Real &rho_dot2_LH, Real &beta_dot, Real &gamma)
 compute scalar control variate parameters
 
void compute_mlmf_control (const RealMatrix &sum_Ll, const RealMatrix &sum_Llm1, const RealMatrix &sum_Hl, const RealMatrix &sum_Hlm1, const RealMatrix &sum_Ll_Ll, const RealMatrix &sum_Ll_Llm1, const RealMatrix &sum_Llm1_Llm1, const RealMatrix &sum_Hl_Ll, const RealMatrix &sum_Hl_Llm1, const RealMatrix &sum_Hlm1_Ll, const RealMatrix &sum_Hlm1_Llm1, const RealMatrix &sum_Hl_Hl, const RealMatrix &sum_Hl_Hlm1, const RealMatrix &sum_Hlm1_Hlm1, const SizetArray &N_shared, size_t lev, RealVector &beta_dot, RealVector &gamma)
 compute matrix control variate parameters
 
void apply_mlmf_control (Real sum_Hl, Real sum_Hlm1, Real sum_Ll, Real sum_Llm1, size_t N_shared, Real sum_Ll_refined, Real sum_Llm1_refined, size_t N_refined, Real beta_dot, Real gamma, Real &H_raw_mom)
 apply scalar control variate parameter (beta) to approximate HF moment
 
void apply_mlmf_control (const RealMatrix &sum_Hl, const RealMatrix &sum_Hlm1, const RealMatrix &sum_Ll, const RealMatrix &sum_Llm1, const SizetArray &N_shared, const RealMatrix &sum_Ll_refined, const RealMatrix &sum_Llm1_refined, const SizetArray &N_refined, size_t lev, const RealVector &beta_dot, const RealVector &gamma, RealVector &H_raw_mom)
 apply matrix control variate parameter (beta) to approximate HF moment
 
void update_projected_samples (const RealVector &hf_targets, const RealVectorArray &eval_ratios, Sizet2DArray &N_hf, const RealVector &hf_cost, Sizet2DArray &N_lf, const RealVector &lf_cost)
 for pilot projection mode, advance sample counts and accumulated cost
 
void initialize_mlmf_sums (IntRealMatrixMap &sum_L_shared, IntRealMatrixMap &sum_L_refined, IntRealMatrixMap &sum_H, IntRealMatrixMap &sum_LL, IntRealMatrixMap &sum_LH, IntRealMatrixMap &sum_HH, size_t num_ml_lev, size_t num_cv_lev)
 initialize the MLMF accumulators for computing means, variances, and covariances across fidelity levels
 
void initialize_mlmf_sums (IntRealMatrixMap &sum_Ll, IntRealMatrixMap &sum_Llm1, IntRealMatrixMap &sum_Ll_refined, IntRealMatrixMap &sum_Llm1_refined, IntRealMatrixMap &sum_Hl, IntRealMatrixMap &sum_Hlm1, IntRealMatrixMap &sum_Ll_Ll, IntRealMatrixMap &sum_Ll_Llm1, IntRealMatrixMap &sum_Llm1_Llm1, IntRealMatrixMap &sum_Hl_Ll, IntRealMatrixMap &sum_Hl_Llm1, IntRealMatrixMap &sum_Hlm1_Ll, IntRealMatrixMap &sum_Hlm1_Llm1, IntRealMatrixMap &sum_Hl_Hl, IntRealMatrixMap &sum_Hl_Hlm1, IntRealMatrixMap &sum_Hlm1_Hlm1, size_t num_ml_lev, size_t num_cv_lev)
 initialize the MLMF accumulators for computing means, variances, and covariances across fidelity levels
 
void accumulate_mlmf_Qsums (IntRealMatrixMap &sum_Ql, IntRealMatrixMap &sum_Qlm1, size_t lev, SizetArray &num_Q)
 update running QoI sums for one model at two levels (sum_Ql, sum_Qlm1) using set of model evaluations within allResponses
 
void accumulate_mlmf_Ysums (IntRealMatrixMap &sum_Y, size_t lev, SizetArray &num_Y)
 update running discrepancy sums for one model (sum_Y) using set of model evaluations within allResponses
 
void accumulate_mlmf_Qsums (const IntResponseMap &lf_resp_map, const IntResponseMap &hf_resp_map, IntRealMatrixMap &sum_L_shared, IntRealMatrixMap &sum_L_refined, IntRealMatrixMap &sum_H, IntRealMatrixMap &sum_LL, IntRealMatrixMap &sum_LH, IntRealMatrixMap &sum_HH, size_t lev, SizetArray &num_L, SizetArray &num_H)
 update running QoI sums for two models (sum_L, sum_H, sum_LL, sum_LH, and sum_HH) from set of low/high fidelity model evaluations within {lf,hf}_resp_map; used for level 0 from other accumulators
 
void accumulate_mlmf_Qsums (const IntResponseMap &lf_resp_map, const IntResponseMap &hf_resp_map, RealMatrix &sum_L_shared, RealMatrix &sum_L_refined, RealMatrix &sum_H, RealMatrix &sum_LL, RealMatrix &sum_LH, RealMatrix &sum_HH, size_t lev, SizetArray &N_shared)
 update running QoI sums for two models (sum_L, sum_H, sum_LL, sum_LH, and sum_HH) from set of low/high fidelity model evaluations within {lf,hf}_resp_map; used for level 0 from other accumulators
 
void accumulate_mlmf_Ysums (const IntResponseMap &lf_resp_map, const IntResponseMap &hf_resp_map, IntRealMatrixMap &sum_L_shared, IntRealMatrixMap &sum_L_refined, IntRealMatrixMap &sum_H, IntRealMatrixMap &sum_LL, IntRealMatrixMap &sum_LH, IntRealMatrixMap &sum_HH, size_t lev, SizetArray &num_L, SizetArray &num_H)
 update running two-level discrepancy sums for two models (sum_L, sum_H, sum_LL, sum_LH, and sum_HH) from set of low/high fidelity model evaluations within {lf,hf}resp_map
 
void accumulate_mlmf_Qsums (const IntResponseMap &lf_resp_map, const IntResponseMap &hf_resp_map, IntRealMatrixMap &sum_Ll, IntRealMatrixMap &sum_Llm1, IntRealMatrixMap &sum_Ll_refined, IntRealMatrixMap &sum_Llm1_refined, IntRealMatrixMap &sum_Hl, IntRealMatrixMap &sum_Hlm1, IntRealMatrixMap &sum_Ll_Ll, IntRealMatrixMap &sum_Ll_Llm1, IntRealMatrixMap &sum_Llm1_Llm1, IntRealMatrixMap &sum_Hl_Ll, IntRealMatrixMap &sum_Hl_Llm1, IntRealMatrixMap &sum_Hlm1_Ll, IntRealMatrixMap &sum_Hlm1_Llm1, IntRealMatrixMap &sum_Hl_Hl, IntRealMatrixMap &sum_Hl_Hlm1, IntRealMatrixMap &sum_Hlm1_Hlm1, size_t lev, SizetArray &num_L, SizetArray &num_H)
 update running QoI sums for two models and two levels from set of low/high fidelity model evaluations within {lf,hf}_resp_map
 
void accumulate_mlmf_Qsums (const IntResponseMap &lf_resp_map, const IntResponseMap &hf_resp_map, RealMatrix &sum_Ll, RealMatrix &sum_Llm1, RealMatrix &sum_Ll_refined, RealMatrix &sum_Llm1_refined, RealMatrix &sum_Hl, RealMatrix &sum_Hlm1, RealMatrix &sum_Ll_Ll, RealMatrix &sum_Ll_Llm1, RealMatrix &sum_Llm1_Llm1, RealMatrix &sum_Hl_Ll, RealMatrix &sum_Hl_Llm1, RealMatrix &sum_Hlm1_Ll, RealMatrix &sum_Hlm1_Llm1, RealMatrix &sum_Hl_Hl, RealMatrix &sum_Hl_Hlm1, RealMatrix &sum_Hlm1_Hlm1, size_t lev, SizetArray &N_shared)
 update running QoI sums for two models and two levels from set of low/high fidelity model evaluations within {lf,hf}_resp_map
 

Private Attributes

short delegateMethod
 core_run() can delegate execution to either ML or CV if hierarchy does not support MLCV; in this case output must also be delegated
 

Additional Inherited Members

- Static Public Member Functions inherited from NonDSampling
static void compute_moments (const RealVectorArray &fn_samples, SizetArray &sample_counts, RealMatrix &moment_stats, short moments_type, const StringArray &labels)
 core compute_moments() implementation with all data as inputs
 
static void compute_moments (const RealVectorArray &fn_samples, RealMatrix &moment_stats, short moments_type)
 core compute_moments() implementation with all data as inputs
 
static void compute_moments (const RealMatrix &fn_samples, RealMatrix &moment_stats, short moments_type)
 alternate RealMatrix samples API for use by external clients
 
static void print_moments (std::ostream &s, const RealMatrix &moment_stats, const RealMatrix moment_cis, String qoi_type, short moments_type, const StringArray &moment_labels, bool print_cis)
 core print moments that can be called without object
 
static int compute_wilks_sample_size (unsigned short order, Real alpha, Real beta, bool twosided=false)
 calculates the number of samples using the Wilks formula Static so I can test without instantiating a NonDSampling object - RWH
 
static Real compute_wilks_residual (unsigned short order, int nsamples, Real alpha, Real beta, bool twosided)
 Helper function - calculates the Wilks residual.
 
static Real compute_wilks_alpha (unsigned short order, int nsamples, Real beta, bool twosided=false)
 calculates the alpha paramter given number of samples using the Wilks formula Static so I can test without instantiating a NonDSampling object - RWH
 
static Real compute_wilks_beta (unsigned short order, int nsamples, Real alpha, bool twosided=false)
 calculates the beta paramter given number of samples using the Wilks formula Static so I can test without instantiating a NonDSampling object - RWH
 
static Real get_wilks_alpha_min ()
 Get the lower and upper bounds supported by Wilks bisection solves.
 
static Real get_wilks_alpha_max ()
 
static Real get_wilks_beta_min ()
 
static Real get_wilks_beta_max ()
 
- Static Protected Member Functions inherited from NonDEnsembleSampling
static void uncentered_to_centered (Real rm1, Real rm2, Real rm3, Real rm4, Real &cm1, Real &cm2, Real &cm3, Real &cm4, size_t Nlq)
 convert uncentered (raw) moments to centered moments; biased estimators More...
 
static void uncentered_to_centered (Real rm1, Real rm2, Real rm3, Real rm4, Real &cm1, Real &cm2, Real &cm3, Real &cm4)
 convert uncentered (raw) moments to centered moments; unbiased estimators More...
 
static void centered_to_standard (Real cm1, Real cm2, Real cm3, Real cm4, Real &sm1, Real &sm2, Real &sm3, Real &sm4)
 convert centered moments to standardized moments
 
static void check_negative (Real &cm)
 detect, warn, and repair a negative central moment (for even orders)
 
- Static Protected Member Functions inherited from Iterator
static void gnewton_set_recast (const Variables &recast_vars, const ActiveSet &recast_set, ActiveSet &sub_model_set)
 conversion of request vector values for the Gauss-Newton Hessian approximation More...
 
- Protected Attributes inherited from NonDEnsembleSampling
size_t numSteps
 number of model forms/resolution in the (outer) sequence
 
short sequenceType
 type of model sequence enumerated with primary MF/ACV loop over steps
 
size_t secondaryIndex
 setting for the inactive model dimension not traversed by primary MF/ACV loop over steps
 
RealVector sequenceCost
 relative costs of model forms/resolution levels within a 1D sequence
 
Sizet3DArray NLev
 total number of successful sample evaluations (excluding faults) for each model form, discretization level, and QoI
 
SizetArray pilotSamples
 store the pilot_samples input specification, prior to run-time invocation of load_pilot_sample()
 
short pilotMgmtMode
 enumeration for pilot management modes: ONLINE_PILOT (default), OFFLINE_PILOT, PILOT_PROJECTION
 
bool onlineCost
 indicates use of online cost recovery rather than offline user-specified cost ratios
 
SizetSizetPairArray costMetadataIndices
 indices of cost data within response metadata, one per model form
 
SizetArray randomSeedSeqSpec
 user specification for seed_sequence
 
size_t mlmfIter
 major iteration counter
 
Real avgEstVar
 final estimator variance for targeted moment (usually mean), averaged across QoI
 
Real equivHFEvals
 equivalent number of high fidelity evaluations accumulated using samples across multiple model forms and/or discretization levels
 
RealVector varH
 variances for HF truth (length numFunctions)
 
RealVector estVarIter0
 initial estimator variance from shared pilot (no CV reduction)
 
short finalStatsType
 QOI_STATISTICS (moments, level mappings) or ESTIMATOR_PERFORMANCE (for model tuning of estVar,equivHFEvals by an outer loop)
 
bool exportSampleSets
 if defined, export each of the sample increments in ML, CV, MLCV using tagged tabular files
 
unsigned short exportSamplesFormat
 format for exporting sample increments using tagged tabular files
 
- Protected Attributes inherited from NonDSampling
int seedSpec
 the user seed specification (default is 0)
 
int randomSeed
 the current seed
 
const int samplesSpec
 initial specification of number of samples
 
size_t samplesRef
 reference number of samples updated for refinement
 
size_t numSamples
 the current number of samples to evaluate
 
String rngName
 name of the random number generator
 
unsigned short sampleType
 
 the sample type: default, random, lhs,

< incremental random, or incremental lhs

 
bool wilksFlag
 flags use of Wilks formula to calculate num samples
 
unsigned short wilksOrder
 
Real wilksAlpha
 
Real wilksBeta
 
short wilksSidedness
 
RealMatrix momentGrads
 gradients of standardized or central moments of response functions, as determined by finalMomentsType. Calculated in compute_moments() and indexed as (var,moment) when moment id runs from 1:2*numFunctions.
 
RealSymMatrix finalStatErrors
 standard errors (estimator std deviation) for each of the finalStatistics
 
int samplesIncrement
 current increment in a sequence of samples
 
Pecos::LHSDriver lhsDriver
 the C++ wrapper for the F90 LHS library
 
size_t numLHSRuns
 counter for number of sample set generations
 
bool statsFlag
 flags computation/output of statistics
 
bool allDataFlag
 
 flags update of allResponses

< (allVariables or allSamples already defined)

 
short samplingVarsMode
 the sampling mode: ALEATORY_UNCERTAIN{,_UNIFORM}, EPISTEMIC_UNCERTAIN{,_UNIFORM}, UNCERTAIN{,_UNIFORM}, ACTIVE{,_UNIFORM}, or ALL{,_UNIFORM}. This is a secondary control on top of the variables view that allows sampling over subsets of variables that may differ from the view.
 
short sampleRanksMode
 mode for input/output of LHS sample ranks: IGNORE_RANKS, GET_RANKS, SET_RANKS, or SET_GET_RANKS
 
bool varyPattern
 flag for generating a sequence of seed values within multiple get_parameter_sets() calls so that these executions (e.g., for SBO/SBNLS) are not repeated, but are still repeatable
 
RealMatrix sampleRanks
 data structure to hold the sample ranks
 
SensAnalysisGlobal nonDSampCorr
 initialize statistical post processing
 
bool backfillFlag
 flags whether to use backfill to enforce uniqueness of discrete LHS samples
 
RealRealPairArray extremeValues
 Minimum and maximum values of response functions for epistemic calculations (calculated in compute_intervals()),.
 
bool functionMomentsComputed
 Function moments have been computed; used to determine whether to archive the moments.
 
- Protected Attributes inherited from NonD
NonDprevNondInstance
 pointer containing previous value of nondInstance
 
size_t startCAUV
 starting index of continuous aleatory uncertain variables within active continuous variables (convenience for managing offsets)
 
size_t numCAUV
 number of active continuous aleatory uncertain variables
 
bool epistemicStats
 flag for computing interval-type metrics instead of integrated metrics If any epistemic vars are active in a metric evaluation, then flag is set.
 
RealMatrix momentStats
 standardized or central resp moments, as determined by finalMomentsType. Calculated in compute_moments()) and indexed as (moment,fn).
 
RealVectorArray requestedRespLevels
 requested response levels for all response functions
 
RealVectorArray computedProbLevels
 output probability levels for all response functions resulting from requestedRespLevels
 
RealVectorArray computedRelLevels
 output reliability levels for all response functions resulting from requestedRespLevels
 
RealVectorArray computedGenRelLevels
 output generalized reliability levels for all response functions resulting from requestedRespLevels
 
short respLevelTarget
 indicates mapping of z->p (PROBABILITIES), z->beta (RELIABILITIES), or z->beta* (GEN_RELIABILITIES)
 
short respLevelTargetReduce
 indicates component or system series/parallel failure metrics
 
RealVectorArray requestedProbLevels
 requested probability levels for all response functions
 
RealVectorArray requestedRelLevels
 requested reliability levels for all response functions
 
RealVectorArray requestedGenRelLevels
 requested generalized reliability levels for all response functions
 
RealVectorArray computedRespLevels
 output response levels for all response functions resulting from requestedProbLevels, requestedRelLevels, or requestedGenRelLevels
 
size_t totalLevelRequests
 total number of levels specified within requestedRespLevels, requestedProbLevels, and requestedRelLevels
 
bool cdfFlag
 flag for type of probabilities/reliabilities used in mappings: cumulative/CDF (true) or complementary/CCDF (false)
 
bool pdfOutput
 flag for managing output of response probability density functions (PDFs)
 
RealVectorArray computedPDFAbscissas
 sorted response PDF intervals bounds extracted from min/max sample and requested/computedRespLevels (vector lengths = num bins + 1)
 
RealVectorArray computedPDFOrdinates
 response PDF densities computed from bin counts divided by (unequal) bin widths (vector lengths = num bins)
 
Response finalStatistics
 final statistics from the uncertainty propagation used in strategies: response means, standard deviations, and probabilities of failure
 
short finalMomentsType
 type of moments logged within finalStatistics: none, central, standard
 
size_t miPLIndex
 index for the active ParallelLevel within ParallelConfiguration::miPLIters
 
BitArray pdfComputed
 Whether PDF was computed for function i; used to determine whether a pdf should be archived.
 
- Protected Attributes inherited from Analyzer
size_t numFunctions
 number of response functions
 
size_t numContinuousVars
 number of active continuous vars
 
size_t numDiscreteIntVars
 number of active discrete integer vars
 
size_t numDiscreteStringVars
 number of active discrete string vars
 
size_t numDiscreteRealVars
 number of active discrete real vars
 
bool compactMode
 switch for allSamples (compact mode) instead of allVariables (normal mode)
 
VariablesArray allVariables
 array of all variables to be evaluated in evaluate_parameter_sets()
 
RealMatrix allSamples
 compact alternative to allVariables
 
IntResponseMap allResponses
 array of all responses to be computed in evaluate_parameter_sets()
 
StringArray allHeaders
 array of headers to insert into output while evaluating allVariables
 
size_t numObjFns
 number of objective functions
 
size_t numLSqTerms
 number of least squares terms
 
RealPairPRPMultiMap bestVarsRespMap
 map which stores best set of solutions
 
- Protected Attributes inherited from Iterator
ProblemDescDBprobDescDB
 class member reference to the problem description database More...
 
ParallelLibraryparallelLib
 class member reference to the parallel library
 
ParConfigLIter methodPCIter
 the active ParallelConfiguration used by this Iterator instance
 
Model iteratedModel
 the model to be iterated (for iterators and meta-iterators employing a single model instance)
 
size_t myModelLayers
 number of Models locally (in Iterator or derived classes) wrapped around the initially passed in Model
 
unsigned short methodName
 name of the iterator (the user's method spec)
 
Real convergenceTol
 iteration convergence tolerance
 
size_t maxIterations
 maximum number of iterations for the method
 
size_t maxFunctionEvals
 maximum number of fn evaluations for the method
 
int maxEvalConcurrency
 maximum number of concurrent model evaluations More...
 
ActiveSet activeSet
 the response data requirements on each function evaluation
 
size_t numFinalSolutions
 number of solutions to retain in best variables/response arrays
 
VariablesArray bestVariablesArray
 collection of N best solution variables found during the study; always in context of Model originally passed to the Iterator (any in-flight Recasts must be undone)
 
ResponseArray bestResponseArray
 collection of N best solution responses found during the study; always in context of Model originally passed to the Iterator (any in-flight Recasts must be undone)
 
bool subIteratorFlag
 flag indicating if this Iterator is a sub-iterator (NestedModel::subIterator or DataFitSurrModel::daceIterator)
 
short outputLevel
 output verbosity level: {SILENT,QUIET,NORMAL,VERBOSE,DEBUG}_OUTPUT
 
bool summaryOutputFlag
 flag for summary output (evaluation stats, final results); default true, but false for on-the-fly (helper) iterators and sub-iterator use cases
 
ResultsManagerresultsDB
 reference to the global iterator results database
 
EvaluationStore & evaluationsDB
 reference to the global evaluation database
 
EvaluationsDBState evaluationsDBState
 State of evaluations DB for this iterator.
 
ResultsNames resultsNames
 valid names for iterator results
 
std::shared_ptr< TraitsBasemethodTraits
 pointer that retains shared ownership of a TraitsBase object, or child thereof
 
bool topLevel
 Whether this is the top level iterator.
 
bool exportSurrogate = false
 whether to export final surrogates
 
String surrExportPrefix
 base filename for exported surrogates
 
unsigned short surrExportFormat = NO_MODEL_FORMAT
 (bitwise) format(s) to export
 
- Protected Attributes inherited from NonDMultilevelSampling
RealVector estVar
 final estimator variance for output in print_variance_reduction()
 
- Static Protected Attributes inherited from NonD
static NonDnondInstance
 pointer to the active object instance used within static evaluator functions in order to avoid the need for static data
 

Detailed Description

Performs multilevel-multifidelity Monte Carlo sampling for uncertainty quantification.

Multilevel-multifidelity Monte Carlo (MLMFMC) combines variance decay across model resolutions with variance reduction from a control variate across model fidelities.

Constructor & Destructor Documentation

NonDMultilevControlVarSampling ( ProblemDescDB problem_db,
Model model 
)

standard constructor

This constructor is called for a standard letter-envelope iterator instantiation. In this case, set_db_list_nodes has been called and probDescDB can be queried for settings from the method specification.

References Iterator::iteratedModel, and Model::multilevel_multifidelity().

Member Function Documentation

void pre_run ( )
protectedvirtual

pre-run portion of run (optional); re-implemented by Iterators which can generate all Variables (parameter sets) a priori

pre-run phase, which a derived iterator may optionally reimplement; when not present, pre-run is likely integrated into the derived run function. This is a virtual function; when re-implementing, a derived class must call its nearest parent's pre_run(), if implemented, typically before performing its own implementation steps.

Reimplemented from NonDEnsembleSampling.

References NonDEnsembleSampling::NLev, Analyzer::numFunctions, and NonDEnsembleSampling::pre_run().

void core_run ( )
protectedvirtual
void multilevel_control_variate_mc_Qcorr ( )
private

Perform multilevel Monte Carlo across levels in combination with control variate Monte Carlo across model forms at each level; CV computes correlations for Q (LH correlations for QoI)

This function performs "geometrical" MLMC across discretization
levels for the high fidelity model form where CVMC si employed
across two model forms to exploit correlation in the discrepancies
at each level (Y_l).

void NonDMultilevControlVarSampling::multilevel_control_variate_mc_Ycorr() { Model& truth_model = iteratedModel.truth_model(); Model& surr_model = iteratedModel.surrogate_model(); size_t qoi, lev, num_mf = NLev.size(), num_hf_lev = truth_model.solution_levels(), num_cv_lev = std::min(num_hf_lev, surr_model.solution_levels()); bool budget_constrained = (maxFunctionEvals != SZ_MAX);

retrieve cost estimates across solution levels for HF model RealVector hf_targets(num_hf_lev), agg_var_hf(num_hf_lev), hf_cost = truth_model.solution_level_costs(), lf_cost = surr_model.solution_level_costs(); Real eps_sq_div_2, sum_sqrt_var_cost, agg_estvar_iter0 = 0., budget, r_lq, lf_lev_cost, hf_lev_cost, hf_ref_cost = hf_cost[num_hf_lev-1]; if (budget_constrained) budget = (Real)maxFunctionEvals * hf_ref_cost; RealVectorArray eval_ratios(num_cv_lev); For moment estimation, we accumulate telescoping sums for Q^i using discrepancies Yi = Q^i_{lev} - Q^i_{lev-1} (Y_diff_Qpow[i] for i=1:4). For computing N_l from estimator variance, we accumulate square of Y1 estimator (YY[1] = (Y^i)^2 for i=1). IntRealMatrixMap sum_L_refined, sum_L_shared, sum_H, sum_LL, sum_LH, sum_HH; initialize_mlmf_sums(sum_L_shared, sum_L_refined, sum_H, sum_LL, sum_LH, sum_HH, num_hf_lev, num_cv_lev); RealMatrix var_YH(numFunctions, num_hf_lev, false), rho2_LH(numFunctions, num_cv_lev, false), Lambda(numFunctions, num_cv_lev, false); RealVector avg_rho2_LH(num_cv_lev, false), avg_lambda(num_cv_lev, false);

Initialize for pilot sample unsigned short group, lf_form = 0, hf_form = num_mf - 1;// 2 models @ extremes Sizet2DArray& N_lf = NLev[lf_form]; Sizet2DArray& N_hf = NLev[hf_form]; Sizet2DArray delta_N_l; load_pilot_sample(pilotSamples, NLev, delta_N_l); SizetArray& delta_N_lf = delta_N_l[lf_form]; SizetArray& delta_N_hf = delta_N_l[hf_form];

now converge on sample counts per level (N_hf) while (Pecos::l1_norm(delta_N_hf) && mlmfIter <= maxIterations) {

sum_sqrt_var_cost = 0.; for (lev=0, group=0; lev<num_hf_lev; ++lev, ++group) {

configure_indices(group, hf_form, lev, sequenceType); hf_lev_cost = level_cost(hf_cost, lev);

set the number of current samples from the defined increment numSamples = delta_N_hf[lev];

aggregate variances across QoI for estimating N_hf (justification: for independent QoI, sum of QoI variances = variance of QoI sum) Real& agg_var_hf_l = agg_var_hf[lev];//carried over from prev iter if!samp if (numSamples) {

assign sequence, get samples, export, evaluate evaluate_ml_sample_increment(lev);

control variate betwen LF and HF for this discretization level: if unequal number of levels, loop over all HF levels for MLMC and apply CVMC when LF levels are available. LF levels are assigned as control variates to the leading set of HF levels, since these will tend to have larger variance. if (lev < num_cv_lev) {

store allResponses used for sum_H (and sum_HH) IntResponseMap hf_resp = allResponses; // shallow copy activate LF response (lev 0) or LF response discrepancy (lev > 0) within the hierarchical surrogate model. Level indices & surrogate response mode are same as HF above, only the model form changes. However, we must pass the unchanged level index to update the corresponding variable values for the new model form. configure_indices(group, lf_form, lev, sequenceType); lf_lev_cost = level_cost(lf_cost, lev); compute allResp w/ LF model form reusing allVars from MLMC step evaluate_parameter_sets(iteratedModel, true, false); process previous and new set of allResponses for CV sums accumulate_mlmf_Ysums(allResponses, hf_resp, sum_L_shared, sum_L_refined, sum_H, sum_LL, sum_LH, sum_HH, lev, N_lf[lev], N_hf[lev]); if (outputLevel == DEBUG_OUTPUT) Cout << "Accumulated sums (L_shared[1,2], L_refined[1,2], LH[1,2])" << ":\n" << sum_L_shared[1] << sum_L_shared[2] << sum_L_refined[1]<< sum_L_refined[2]<< sum_LH[1]<< sum_LH[2]; increment_mlmf_equivalent_cost(numSamples, hf_lev_cost, numSamples, lf_lev_cost, hf_ref_cost);

compute the average evaluation ratio and Lambda factor RealVector& eval_ratios_l = eval_ratios[lev]; compute_eval_ratios(sum_L_shared[1], sum_H[1], sum_LL[1], sum_LH[1], sum_HH[1], hf_lev_cost/lf_lev_cost, lev, N_hf[lev], var_YH, rho2_LH, eval_ratios_l);

retain Lambda per QoI and level, but apply QoI-average where needed for (qoi=0; qoi<numFunctions; ++qoi) { r_lq = eval_ratios_l[qoi]; Lambda(qoi,lev) = 1. - rho2_LH(qoi,lev) * (r_lq - 1.) / r_lq; } avg_lambda[lev] = average(Lambda[lev], numFunctions); avg_rho2_LH[lev] = average(rho2_LH[lev], numFunctions); } else { // no LF model for this level; accumulate only multilevel sums RealMatrix& sum_HH1 = sum_HH[1]; accumulate H sums for lev = 0, Y sums for lev > 0 accumulate_ml_Ysums(sum_H, sum_HH1, lev, N_hf[lev]); if (outputLevel == DEBUG_OUTPUT) Cout << "Accumulated sums (H[1], H[2], HH):\n" << sum_H[1] << sum_H[2] << sum_HH1; increment_ml_equivalent_cost(numSamples, hf_lev_cost, hf_ref_cost); compute Y variances for this level and aggregate across QoI: variance_Ysum(sum_H[1][lev], sum_HH1[lev], N_hf[lev], var_YH[lev]); } agg_var_hf_l = sum(var_YH[lev], numFunctions); }

accumulate sum of sqrt's of estimator var * cost used in N_target if (lev < num_cv_lev) { Real om_rho2 = 1. - avg_rho2_LH[lev]; sum_sqrt_var_cost += (budget_constrained) ? std::sqrt(agg_var_hf_l / hf_lev_cost * om_rho2) * (hf_lev_cost + (1. + average(eval_ratios[lev])) * lf_lev_cost) : std::sqrt(agg_var_hf_l * hf_lev_cost / om_rho2) * avg_lambda[lev]; } else sum_sqrt_var_cost += std::sqrt(agg_var_hf_l * hf_lev_cost);

MSE reference is MLMF MC applied to {HF,LF} pilot sample aggregated across qoi. Note: if the pilot sample for LF is not shaped, then r=1 will result in no additional variance reduction beyond MLMC. if (mlmfIter == 0 && !budget_constrained) agg_estvar_iter0 += aggregate_mse_Yvar(var_YH[lev], N_hf[lev]); } compute epsilon target based on relative tolerance: total MSE = eps^2 which is equally apportioned (eps^2 / 2) among discretization MSE and estimator variance ( var_Y_l / N_l). Since we do not know the discretization error, we compute an initial estimator variance and then seek to reduce it by a relative_factor <= 1. if (mlmfIter == 0) { MLMC estimator variance for final estvar reporting is not aggregated (reduction from control variate is applied subsequently) compute_ml_estimator_variance(var_YH, N_hf, estVarIter0);//numHIter0=numH; compute eps^2 / 2 = aggregated estvar0 * rel tol if (!budget_constrained) { eps_sq_div_2 = agg_estvar_iter0 * convergenceTol; if (outputLevel == DEBUG_OUTPUT) Cout << "Epsilon squared target = " << eps_sq_div_2 << std::endl; } }

update sample targets based on variance estimates Note: sum_sqrt_var_cost is defined differently for the two cases Real fact = (budget_constrained) ? budget / sum_sqrt_var_cost : // budget constraint sum_sqrt_var_cost / eps_sq_div_2; // error balance constraint for (lev=0; lev<num_hf_lev; ++lev) { hf_lev_cost = (lev) ? hf_cost[lev] + hf_cost[lev-1] : hf_cost[lev]; hf_targets[lev] = (lev < num_cv_lev) ? fact * std::sqrt(agg_var_hf[lev] / hf_lev_cost * (1. - avg_rho2_LH[lev])) : fact * std::sqrt(agg_var_hf[lev] / hf_lev_cost); delta_N_hf[lev] = one_sided_delta(average(N_hf[lev]), hf_targets[lev]); }

++mlmfIter; Cout << "\nMLMF MC iteration " << mlmfIter << " sample increments:\n" << delta_N_hf << std::endl; }

All CV lf_increment() calls now follow convergence of ML iteration: for (lev=0, group=0; lev<num_cv_lev; ++lev, ++group) { configure_indices(group, lf_form, lev, sequenceType); execute additional LF sample increment if (lf_increment(eval_ratios[lev], N_lf[lev], hf_targets[lev], mlmfIter, lev)) { accumulate_mlmf_Ysums(sum_L_refined, lev, N_lf[lev]); increment_ml_equivalent_cost(numSamples, level_cost(lf_cost, lev), hf_ref_cost); if (outputLevel == DEBUG_OUTPUT) Cout << "Accumulated sums (L_refined[1,2]):\n" << sum_L_refined[1] << sum_L_refined[2]; } }

Roll up raw moments from MLCVMC and MLMC levels RealMatrix Y_mom(numFunctions, 4), Y_cvmc_mom(numFunctions, 4, false); for (lev=0; lev<num_cv_lev; ++lev) { cv_raw_moments(sum_L_shared, sum_H, sum_LL, sum_LH, N_hf[lev], sum_L_refined, N_lf[lev], //rho2_LH, lev, Y_cvmc_mom); Y_mom += Y_cvmc_mom; } if (num_hf_lev > num_cv_lev) ml_raw_moments(sum_H[1], sum_H[2], sum_H[3], sum_H[4], N_hf, num_cv_lev, num_hf_lev, Y_mom); convert_moments(Y_mom, momentStats); // raw to final (central or std) recover_variance(momentStats, varH);

compute_mlmf_estimator_variance(var_YH, N_hf, Lambda, estVar); avgEstVar = average(estVar); }This function performs "geometrical" MLMC across discretization levels for the high fidelity model form where CVMC is employed across two model forms. It generalizes the Y_l correlation case to separately target correlations for each QoI level embedded within the level discrepancies.

References NonDMultilevelSampling::accumulate_ml_Ysums(), NonDMultilevControlVarSampling::accumulate_mlmf_Qsums(), NonDHierarchSampling::accumulate_paired_online_cost(), NonDMultilevelSampling::aggregate_mse_Yvar(), Analyzer::allResponses, NonDEnsembleSampling::average(), NonDHierarchSampling::average_online_cost(), NonDEnsembleSampling::avgEstVar, NonDMultilevControlVarSampling::compute_eval_ratios(), NonDMultilevelSampling::compute_ml_estimator_variance(), NonDMultilevControlVarSampling::compute_mlmf_estimator_variance(), NonDMultilevelSampling::configure_indices(), Iterator::convergenceTol, NonDEnsembleSampling::convert_moments(), NonDMultilevControlVarSampling::cv_raw_moments(), NonDMultilevelSampling::estVar, NonDEnsembleSampling::estVarIter0, NonDMultilevelSampling::evaluate_ml_sample_increment(), Analyzer::evaluate_parameter_sets(), NonDEnsembleSampling::finalStatsType, NonDMultilevelSampling::increment_ml_equivalent_cost(), NonDMultilevControlVarSampling::increment_mlmf_equivalent_cost(), NonDMultilevControlVarSampling::initialize_mlmf_sums(), Iterator::iteratedModel, NonDMultilevelSampling::level_cost(), NonDControlVariateSampling::lf_increment(), NonD::load_pilot_sample(), Iterator::maxFunctionEvals, Iterator::maxIterations, NonDMultilevelSampling::ml_raw_moments(), NonDEnsembleSampling::mlmfIter, NonD::momentStats, NonDEnsembleSampling::NLev, Analyzer::numFunctions, NonDSampling::numSamples, NonD::one_sided_delta(), Iterator::outputLevel, NonDEnsembleSampling::pilotSamples, NonD::query_cost(), NonDMultilevelSampling::recover_variance(), NonDEnsembleSampling::sequenceType, Model::solution_levels(), NonDEnsembleSampling::sum(), Model::surrogate_model(), Dakota::SZ_MAX, Model::truth_model(), NonDMultilevControlVarSampling::update_projected_samples(), NonDEnsembleSampling::varH, and NonDMultilevelSampling::variance_Ysum().

Referenced by NonDMultilevControlVarSampling::core_run().


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