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NonDMultilevelSampling Class Reference

Performs Multilevel Monte Carlo sampling for uncertainty quantification. More...

Inheritance diagram for NonDMultilevelSampling:
NonDSampling NonD Analyzer Iterator

Public Member Functions

 NonDMultilevelSampling (ProblemDescDB &problem_db, Model &model)
 standard constructor More...
 
 ~NonDMultilevelSampling ()
 destructor
 
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...
 
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 IntResponseMap &samples)
 called by compute_statistics() to calculate sample moments and confidence intervals
 
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 update_final_statistics ()
 update finalStatistics from minValues/maxValues, momentStats, and computedProbLevels/computedRelLevels/computedRespLevels
 
void compute_moments (const RealMatrix &samples)
 calculates sample moments for an array of observations for a set of QoI
 
void transform_samples (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.
 
void transform_samples (RealMatrix &sample_matrix, bool x_to_u, int num_samples=0)
 transform the specified samples matrix from x to u or u to x
 
- Public Member Functions inherited from NonD
void initialize_random_variables (short u_space_type)
 initialize natafTransform based on distribution data from iteratedModel More...
 
void initialize_random_variables (const Pecos::ProbabilityTransformation &transform, bool deep_copy=false)
 alternate form: initialize natafTransform based on incoming data More...
 
void initialize_random_variable_transformation ()
 instantiate natafTransform
 
void initialize_random_variable_types ()
 initializes ranVarTypesX within natafTransform (u-space not needed) More...
 
void initialize_random_variable_types (short u_space_type)
 initializes ranVarTypesX and ranVarTypesU within natafTransform More...
 
void initialize_random_variable_parameters ()
 initializes ranVarMeansX, ranVarStdDevsX, ranVarLowerBndsX, ranVarUpperBndsX, and ranVarAddtlParamsX within natafTransform More...
 
void initialize_random_variable_correlations ()
 propagate iteratedModel correlations to natafTransform
 
void verify_correlation_support (short u_space_type)
 verify that correlation warping is supported by Nataf for given variable types
 
void transform_correlations ()
 perform correlation warping for variable types supported by Nataf
 
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 distribution_parameter_derivatives (bool dist_param_derivs)
 set distParamDerivs
 
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...
 
bool pdf_output () const
 get pdfOutput
 
void pdf_output (bool output)
 set pdfOutput
 
Pecos::ProbabilityTransformation & variable_transformation ()
 return natafTransform
 
- 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 ()
 default constructor More...
 
 Iterator (ProblemDescDB &problem_db)
 standard envelope constructor, which constructs its own model(s) More...
 
 Iterator (ProblemDescDB &problem_db, Model &model)
 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)
 alternate envelope constructor for instantiations by name without the ProblemDescDB More...
 
 Iterator (const Iterator &iterator)
 copy constructor More...
 
virtual ~Iterator ()
 destructor More...
 
Iterator operator= (const Iterator &iterator)
 assignment operator More...
 
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 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)
 used by IteratorScheduler to unpack starting data for an iterator run
 
virtual void unpack_parameters_initialize (MPIUnpackBuffer &recv_buffer)
 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_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 initialize_graphics (int iterator_server_id=1)
 initialize the 2D graphics window and the tabular graphics data More...
 
virtual unsigned short uses_method () const
 return name of any enabling iterator used by this iterator More...
 
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
 
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 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 (Iterator *iterator_rep, bool ref_count_incr=true)
 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_name) const
 convert a method name enumeration value to a string
 
unsigned short method_string_to_enum (const String &method_name) const
 convert a method name string to an enumeration value
 
String submethod_enum_to_string (unsigned short submethod_name) const
 convert a 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
 
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 vector (for use with iterators that employ evaluate_parameter_sets())
 
const ActiveSetactive_set () const
 return the default active set vector (used by iterators that employ evaluate_parameter_sets())
 
void sub_iterator_flag (bool si_flag)
 set subIteratorFlag (and update summaryOutputFlag if needed)
 
void active_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
 
bool is_null () const
 function to check iteratorRep (does this envelope contain a letter?)
 
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...
 

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 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)
 print the final iterator results More...
 
- 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, int 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, int 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, int 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...
 
 ~NonDSampling ()
 destructor
 
void core_run ()
 
int num_samples () const
 
void sampling_reset (int min_samples, bool all_data_flag, bool stats_flag)
 resets number of samples and sampling flags More...
 
void sampling_reference (int samples_ref)
 set reference number of samples, which is a lower bound during reset
 
unsigned short sampling_scheme () const
 return sampleType
 
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 (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)
 
void initialize_lhs (bool write_message)
 increments numLHSRuns, sets random seed, and initializes lhsDriver
 
void view_design_counts (const Model &model, size_t &num_cdv, size_t &num_ddiv, size_t &num_ddsv, size_t &num_ddrv) const
 compute sampled subsets (all, active, uncertain) within all variables (acv/adiv/adrv) from samplingVarsMode and model More...
 
void view_aleatory_uncertain_counts (const Model &model, size_t &num_cauv, size_t &num_dauiv, size_t &num_dausv, size_t &num_daurv) const
 compute sampled subsets (all, active, uncertain) within all variables (acv/adiv/adrv) from samplingVarsMode and model More...
 
void view_epistemic_uncertain_counts (const Model &model, size_t &num_ceuv, size_t &num_deuiv, size_t &num_deusv, size_t &num_deurv) const
 compute sampled subsets (all, active, uncertain) within all variables (acv/adiv/adrv) from samplingVarsMode and model More...
 
void view_uncertain_counts (const Model &model, size_t &num_cuv, size_t &num_duiv, size_t &num_dusv, size_t &num_durv) const
 compute sampled subsets (all, active, uncertain) within all variables (acv/adiv/adrv) from samplingVarsMode and model More...
 
void view_state_counts (const Model &model, size_t &num_csv, size_t &num_dsiv, size_t &num_dssv, size_t &num_dsrv) const
 compute sampled subsets (all, active, uncertain) within all variables (acv/adiv/adrv) from samplingVarsMode and model
 
void mode_counts (const Model &model, 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 get_lhs_samples (const Model &model, int 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...
 
- 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
 
virtual void initialize_final_statistics ()
 initializes finalStatistics for storing NonD final results More...
 
void size ()
 Size local variables.
 
int generate_system_seed ()
 create a system-generated unique seed (when a seed is unspecified)
 
void initialize_final_statistics_gradients ()
 initializes finalStatistics::functionGradients
 
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 transform_model (Model &x_model, Model &u_model, bool truncated_bounds=false, Real bound=10.)
 recast x_model from x-space to u-space to create u_model
 
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
 
void archive_allocate_mappings ()
 allocate results array storage for distribution mappings
 
void archive_from_resp (size_t fn_index)
 archive the mappings from specified response levels for specified fn
 
void archive_to_resp (size_t fn_index)
 archive the mappings to computed response levels for specified fn
 
void archive_allocate_pdf ()
 allocate results array storage for pdf histograms
 
void archive_pdf (size_t fn_index)
 archive a single pdf histogram for specified function
 
- 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 variance_based_decomp (int ncont, int ndiscint, int ndiscreal, int num_samples)
 
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)
 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)
 alternate constructor for base iterator classes constructed on the fly More...
 
 Iterator (NoDBBaseConstructor, unsigned short method_name)
 alternate constructor for base iterator classes constructed on the fly 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
 

Private Member Functions

void multilevel_mc (size_t model_form)
 Perform multilevel Monte Carlo across the discretization levels for a particular model form. More...
 
void control_variate_mc (const SizetSizetPair &lf_form_level, const SizetSizetPair &hf_form_level)
 Perform control variate Monte Carlo across two model forms. More...
 
void multilevel_control_variate_mc (size_t lf_model_form, size_t hf_model_form)
 Perform multilevel Monte Carlo across levels in combination with control variate Monte Carlo across model forms at each level. More...
 
void shared_increment (size_t iter, const SizetSizetPair &lf_form_level, const SizetSizetPair &hf_form_level)
 perform a shared increment of LF and HF samples for purposes of computing/updating the evaluation ratio and the MSE ratio
 
bool lf_increment (Real avg_eval_ratio, size_t N_hf, size_t &delta_N_lf, size_t &N_lf)
 perform final LF sample increment as indicated by the evaluation ratio
 
void initialize_ml_sums (IntRealMatrixMap &sum_Y, size_t num_lev)
 initialize the CV bookkeeping for sums, means, variances, and covariances across fidelity levels
 
void initialize_cv_sums_moments (IntRealVectorMap &sum_L_shared, IntRealVectorMap &sum_L_refined, IntRealVectorMap &sum_H, IntRealVectorMap &sum_LL, IntRealVectorMap &sum_LH)
 initialize the CV bookkeeping for sums, means, variances, and covariances across fidelity levels
 
void initialize_cv_sums_moments (IntRealMatrixMap &sum_L_shared, IntRealMatrixMap &sum_L_refined, IntRealMatrixMap &sum_LL, IntRealMatrixMap &sum_LH, size_t num_lev)
 initialize the CV bookkeeping for sums, means, variances, and covariances across fidelity levels
 
void accumulate_cv_sums (IntRealVectorMap &sum_map)
 update running sums for one model (sum_map) using set of model evaluations within allResponses
 
void accumulate_cv_sums (IntRealVectorMap &sum_L_shared, IntRealVectorMap &sum_L_refined, IntRealVectorMap &sum_H, IntRealVectorMap &sum_LL, RealVector &sum_HH, IntRealVectorMap &sum_LH)
 update running sums for two models (sum_L, sum_H, and sum_LH) from set of low/high fidelity model evaluations within allResponses
 
void accumulate_cv_sums (IntRealMatrixMap &sum_map, size_t lev)
 update running sums for one model (sum_map) using set of model evaluations within allResponses
 
void accumulate_cv_sums (const IntResponseMap &lf_resp_map, const IntResponseMap &hf_resp_map, IntRealMatrixMap &sum_L_shared, IntRealMatrixMap &sum_L_refined, IntRealMatrixMap &sum_LL, IntRealMatrixMap &sum_LH, size_t lev)
 update running sums for two models (sum_L, sum_H, and sum_LH) from set of low/high fidelity model evaluations within lf/hf_resp_map
 
void accumulate_ml_sums (IntRealMatrixMap &sum_Y, RealMatrix &sum_YY, size_t lev)
 update accumulators for multilevel telescoping running sums using set of model evaluations within allResponses
 
Real eval_ratio (const RealVector &sum_L_shared, const RealVector &sum_H, const RealVector &sum_LL, const RealVector &sum_HH, const RealVector &sum_LH, Real cost_ratio, RealVector &var_H, RealVector &rho2_LH, size_t N_shared)
 compute the LF/HF evaluation ratio, averaged over the QoI
 
Real eval_ratio (RealMatrix &sum_L_shared, RealMatrix &sum_H, RealMatrix &sum_LL, RealMatrix &sum_HH, RealMatrix &sum_LH, Real cost_ratio, size_t lev, RealMatrix &var_H, RealMatrix &rho2_LH, size_t N_shared)
 compute the LF/HF evaluation ratio, averaged over the QoI
 
Real MSE_ratio (Real avg_eval_ratio, const RealVector &var_H, const RealVector &rho2_LH, size_t iter, size_t N_hf)
 compute ratio of MC and CVMC mean squared errors, averaged over the QoI
 
void cv_raw_moments (IntRealVectorMap &sum_L_shared, IntRealVectorMap &sum_L_refined, IntRealVectorMap &sum_H, IntRealVectorMap &sum_LL, IntRealVectorMap &sum_LH, const RealVector &rho2_LH, size_t N_shared, size_t N_refined, RealMatrix &H_raw_mom)
 compute control variate parameter and estimate raw moments
 
void cv_raw_moments (IntRealMatrixMap &sum_L_shared, IntRealMatrixMap &sum_L_refined, IntRealMatrixMap &sum_H, IntRealMatrixMap &sum_LL, IntRealMatrixMap &sum_LH, const RealMatrix &rho2_LH, size_t lev, size_t N_shared, size_t N_refined, RealMatrix &H_raw_mom)
 compute control variate parameter and estimate raw moments
 
Real average (const RealVector &vec) const
 compute average of a set of observations
 
Real average (const Real *vec, size_t vec_len) const
 compute average of a set of observations
 
void convert_moments (const RealMatrix &raw_moments, RealMatrix &standard_moments)
 convert uncentered raw moments (multilevel expectations) to standardized moments
 

Private Attributes

Sizet2DArray NLev
 total number of samples performed per model form, per discretization level, or both
 
Sizet2DArray deltaNLev
 increment in number of samples required for each model form, discretization level, or both
 
RealVector mcMSEIter0
 mean squared error of mean estimator from pilot sample MC on HF model
 
Real equivHFEvals
 equivalent number of high fidelity evaluations accumulated using samples across multiple model forms and/or discretization levels
 

Additional Inherited Members

- Static Public Member Functions inherited from NonDSampling
static void print_moments (std::ostream &s, const RealMatrix &moment_stats, const RealMatrix moment_cis, String qoi_type, const StringArray &moment_labels, bool print_cis)
 core print moments that can be called without object
 
static void compute_moments (const RealMatrix &samples, RealMatrix &moment_stats)
 core compute 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 for now so I can test without instantiating a NonDSampling object - RWH
 
- Static Protected Member Functions inherited from NonD
static void vars_u_to_x_mapping (const Variables &u_vars, Variables &x_vars)
 static function for RecastModels used for forward mapping of u-space variables from NonD Iterators to x-space variables for Model evaluations More...
 
static void vars_x_to_u_mapping (const Variables &x_vars, Variables &u_vars)
 static function for RecastModels used for inverse mapping of x-space variables from data import to u-space variables for NonD Iterators More...
 
static void set_u_to_x_mapping (const Variables &u_vars, const ActiveSet &u_set, ActiveSet &x_set)
 static function for RecastModels used to map u-space ActiveSets from NonD Iterators to x-space ActiveSets for Model evaluations More...
 
static void resp_x_to_u_mapping (const Variables &x_vars, const Variables &u_vars, const Response &x_response, Response &u_response)
 static function for RecastModels used to map x-space responses from Model evaluations to u-space responses for return to NonD Iterator.
 
- Protected Attributes inherited from NonDSampling
const int seedSpec
 the user seed specification (default is 0)
 
int randomSeed
 the current seed
 
const int samplesSpec
 initial specification of number of samples
 
int samplesRef
 reference number of samples updated for refinement
 
int 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
 
int samplesIncrement
 flags use of Wilks formula to calculate num samples More...
 
Pecos::LHSDriver lhsDriver
 the C++ wrapper for the F90 LHS library
 
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()),.
 
- 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 Monte Carlo sampling for uncertainty quantification.

Multilevel Monte Carlo (MLMC) is a variance-reduction technique that utilitizes lower fidelity simulations that have response QoI that are correlated with the high-fidelity response QoI.

Constructor & Destructor Documentation

NonDMultilevelSampling ( 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 Dakota::abort_handler(), Dakota::copy_data_partial(), NonDMultilevelSampling::deltaNLev, ProblemDescDB::get_sza(), Iterator::iteratedModel, Iterator::maxEvalConcurrency, NonDMultilevelSampling::NLev, Iterator::probDescDB, NonDSampling::sampleType, Model::solution_levels(), Model::subordinate_models(), Model::surrogate_model(), Model::surrogate_response_mode(), Model::surrogate_type(), and Model::truth_model().

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 Analyzer.

References Analyzer::pre_run().

void core_run ( )
protectedvirtual

The primary run function manages the general case: a hierarchy of model forms (from the ordered model fidelities within a HierarchSurrModel), each of which may contain multiple discretization levels.

Reimplemented from Iterator.

References NonDMultilevelSampling::control_variate_mc(), NonDMultilevelSampling::multilevel_control_variate_mc(), NonDMultilevelSampling::multilevel_mc(), and NonDMultilevelSampling::NLev.

void post_run ( std::ostream &  s)
protectedvirtual

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

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

Reimplemented from Analyzer.

References Analyzer::post_run().

void print_results ( std::ostream &  s)
protectedvirtual

print the final iterator results

This virtual function provides additional iterator-specific final results outputs beyond the function evaluation summary printed in finalize_run().

Reimplemented from Analyzer.

References NonDMultilevelSampling::equivHFEvals, Iterator::iteratedModel, NonDMultilevelSampling::NLev, NonDSampling::print_moments(), Model::response_labels(), NonDSampling::statsFlag, and Model::truth_model().

void multilevel_mc ( size_t  model_form)
private
void control_variate_mc ( const SizetSizetPair &  lf_form_level,
const SizetSizetPair &  hf_form_level 
)
private
void multilevel_control_variate_mc ( size_t  lf_model_form,
size_t  hf_model_form 
)
private

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