NonDMultilevelSampling Class Reference

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

Inheritance diagram for NonDMultilevelSampling:

Public Member Functions
	NonDMultilevelSampling (ProblemDescDB &problem_db, Model &model)
	standard constructor More...
	~NonDMultilevelSampling ()
	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_std_regress_coeffs ()
	archive standardized regression coefficients 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	print_tolerance_intervals_statistics (std::ostream &s) const
	prints the tolerance intervals stastics
void	archive_tolerance_intervals (size_t inc_id=0)
	archive the tolerance intervals statistics in results DB
void	update_final_statistics ()
	update finalStatistics from minValues/maxValues, momentStats, and computedProbLevels/computedRelLevels/computedRespLevels
void	transform_samples (Model &src_model, Model &tgt_model, bool x_to_u=true)
	transform allSamples using configuration data from the source and target models
void	transform_samples (Pecos::ProbabilityTransformation &nataf, bool x_to_u=true)
	alternate version to transform allSamples. 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, bool x_to_u=true)
	transform the specified samples matrix from x to u or u to x, assuming identical view and ids
void	transform_samples (Pecos::ProbabilityTransformation &nataf, RealMatrix &sample_matrix, SizetMultiArrayConstView src_cv_ids, SizetMultiArrayConstView tgt_cv_ids, 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)
Model &	iterated_model ()
	return the iteratedModel (iterators & meta-iterators using a single model instance)
ProblemDescDB &	problem_description_db () const
	return the problem description database (probDescDB)
ParallelLibrary &	parallel_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 ActiveSet &	active_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< Iterator >	iterator_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< TraitsBase >	traits () 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.

Protected Member Functions
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
bool	discrepancy_sample_counts () const
	flag identifying whether sample counts correspond to level discrepancies
void	evaluate_ml_sample_increment (String prepend, 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, Real &equiv_hf)
	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
Protected Member Functions inherited from NonDHierarchSampling
Real	estimator_accuracy_metric ()
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	pre_run ()
	pre-run portion of run (optional); re-implemented by Iterators which can generate all Variables (parameter sets) a priori More...
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...
Real	estimator_cost_metric ()
	return cost metric for entry into finalStatistics
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	resize_active_set ()
	synchronize activeSet with iteratedModel's response size
void	increment_samples (SizetArray &N_l, size_t incr)
	increment samples array with a shared scalar
void	increment_samples (Sizet2DArray &N_l, const SizetArray &incr)
	increment 2D samples array with a shared 1D array (additional dim is QoI)
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, Model &model, const ShortShortPair &approx_view)
	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 Response &	response_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, short seq_type, const Sizet3DArray &N_l, Sizet2DArray &delta_N_l)
	distribute pilot sample specification across model forms and levels
template<typename ArrayType >
void	inflate_approx_samples (const ArrayType &N_l, bool multilev, size_t secondary_index, std::vector< ArrayType > &N_l_vec)
	update the relevant slice of N_l_3D from the final 2D multilevel or 2D multifidelity sample profile
template<typename ArrayType >
void	inflate_sequence_samples (const ArrayType &N_l, bool multilev, size_t secondary_index, std::vector< ArrayType > &N_l_vec)
	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_m)
	print evaluation summary for multilevel sampling across 1D level profile
void	print_multilevel_evaluation_summary (std::ostream &s, const Sizet2DArray &N_m)
	print evaluation summary for multilevel sampling across 2D level+QoI profile
void	print_multilevel_discrepancy_summary (std::ostream &s, const SizetArray &N_m)
	print evaluation summary for multilevel sampling across 1D level profile for discrepancy across levels
void	print_multilevel_discrepancy_summary (std::ostream &s, const SizetArray &N_m, const SizetArray &N_mp1)
	print evaluation summary for multilevel sampling across 1D level profile for discrepancy across model forms
void	print_multilevel_discrepancy_summary (std::ostream &s, const Sizet2DArray &N_m)
	print evaluation summary for multilevel sampling across 2D level+QoI profile for discrepancy across levels
void	print_multilevel_discrepancy_summary (std::ostream &s, const Sizet2DArray &N_m, const Sizet2DArray &N_mp1)
	print evaluation summary for multilevel sampling across 2D level+QoI profile for discrepancy across model forms
template<typename ArrayType >
void	print_multilevel_model_summary (std::ostream &s, const std::vector< ArrayType > &N_samp, String type, short seq_type, bool discrep_flag)
	print evaluation summary for multilevel sampling across 2D model+level profile (allocations) or 3D model+level+QoI profile (actual)
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
bool	differ (size_t N_alloc_ij, const SizetArray &N_actual_ij) const
	return true if fine-grained reporting differs from coarse-grained
bool	differ (const SizetArray &N_alloc_i, const Sizet2DArray &N_actual_i) const
	return true if fine-grained reporting differs from coarse-grained
bool	differ (const Sizet2DArray &N_alloc, const Sizet3DArray &N_actual) const
	return true if fine-grained reporting differs from coarse-grained
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, Model &model, const ShortShortPair &view_override)
	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 Model &	algorithm_space_model () const
const Variables &	variables_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 Attributes
RealVector	estVar
	final estimator variance for output in print_variance_reduction()
Protected Attributes inherited from NonDHierarchSampling
Real	avgEstVar
	final estimator variance for targeted moment (usually mean), averaged across QoI
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	NLevActual
	total number of successful sample evaluations (excluding faults) for each model form, discretization level, and QoI
Sizet2DArray	NLevAlloc
	total number of allocated sample evaluations (prior to any faults) for each model form and discretization level (same for all 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
bool	backfillFailures
	(inactive) option to backfill simulation failures by comparing targets against successful sample completions rather than sample allocations
Real	equivHFEvals
	equivalent number of high fidelity evaluations accumulated using samples across multiple model forms and/or discretization levels
Real	deltaEquivHF
	for sample projections, the calculated increment in equivHFEvals that would be incurred if full iteration/statistics were needed
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	stdRegressionCoeffs
	flags computation/output of standardized regression coefficients
bool	toleranceIntervalsFlag
	flags of double sided tolerance interval equivalent normal
Real	tiCoverage
	coverage to be used in the calculation of the double sided tolerance interval equivaluent normal
Real	tiConfidenceLevel
	confidence interval to be used in the calculation of the double sided tolerance interval equivalent normal
size_t	tiNumValidSamples
RealVector	tiDstienMus
Real	tiDeltaMultiplicativeFactor
RealVector	tiSampleSigmas
RealVector	tiDstienSigmas
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	backfillDuplicates
	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
NonD *	prevNondInstance
	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
ProblemDescDB &	probDescDB
	class member reference to the problem description database More...
ParallelLibrary &	parallelLib
	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
ResultsManager &	resultsDB
	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< TraitsBase >	methodTraits
	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

Private Types
enum	{ COV_BOOTSTRAP, COV_PEARSON, COV_CORRLIFT }

Private Member Functions
void	multilevel_mc_Qsum ()
	Perform multilevel Monte Carlo across the discretization levels for a particular model form using QoI accumulators (sum_Q) More...
void	multilevel_mc_offline_pilot ()
	Qsum approach using a pilot sample treated as separate offline cost.
void	multilevel_mc_pilot_projection ()
	Qsum approach projecting estimator performance from a pilot sample.
void	evaluate_levels (IntRealMatrixMap &sum_Ql, IntRealMatrixMap &sum_Qlm1, IntIntPairRealMatrixMap &sum_QlQlm1, RealVector &cost, Sizet2DArray &N_actual_pilot, Sizet2DArray &N_actual_online, SizetArray &N_alloc_pilot, SizetArray &N_alloc_online, SizetArray &delta_N_l, RealMatrix &var_Y, RealMatrix &var_qoi, RealVector &eps_sq_div_2, bool increment_cost, bool pilot_estvar)
	helper for shared code among offline-pilot and pilot-projection modes
void	initialize_ml_Qsums (IntRealMatrixMap &sum_Ql, IntRealMatrixMap &sum_Qlm1, IntIntPairRealMatrixMap &sum_QlQlm1, size_t num_lev)
	initialize the ML accumulators for computing means, variances, and covariances across fidelity levels
void	reset_ml_Qsums (IntRealMatrixMap &sum_Ql, IntRealMatrixMap &sum_Qlm1, IntIntPairRealMatrixMap &sum_QlQlm1)
	reset existing ML accumulators to zero for all keys
void	store_evaluations (const size_t step)
	adds the response evaluations for the current step to levQoisamplesmatrixMap.
void	accumulate_ml_Qsums (IntRealMatrixMap &sum_Ql, IntRealMatrixMap &sum_Qlm1, IntIntPairRealMatrixMap &sum_QlQlm1, size_t lev, SizetArray &num_Q)
	update running QoI sums for two models (sum_Ql, sum_Qlm1) using set of model evaluations within allResponses
size_t	allocation_increment (size_t N_l_alloc, const Real *N_l_target)
	increment the allocated samples counter
Real	compute_ml_equivalent_cost (const SizetArray &raw_N_l, const RealVector &cost)
void	compute_error_estimates (const IntRealMatrixMap &sum_Ql, const IntRealMatrixMap &sum_Qlm1, const IntIntPairRealMatrixMap &sum_QlQlm1, const Sizet2DArray &num_Q)
	populate finalStatErrors for MLMC based on Q sums
void	update_projected_samples (const SizetArray &delta_N_l, SizetArray &N_alloc, const RealVector &cost, Real &delta_equiv_hf)
	for pilot projection, advance the sample counts and aggregate cost based on projected rather than actual samples
Real	var_lev_l (Real sum_Ql, Real sum_Qlm1, Real sum_QlQl, Real sum_Qlm1Qlm1, size_t Nlq)
void	aggregate_variance_target_Qsum (const IntRealMatrixMap &sum_Ql, const IntRealMatrixMap &sum_Qlm1, const IntIntPairRealMatrixMap &sum_QlQlm1, const Sizet2DArray &N_l, const size_t step, RealMatrix &agg_var_qoi)
	sum up variances for QoI (using sum_YY with means from sum_Y) based on allocation target
Real	variance_mean_Qsum (const IntRealMatrixMap &sum_Ql, const IntRealMatrixMap &sum_Qlm1, const IntIntPairRealMatrixMap &sum_QlQlm1, const Sizet2DArray &N_l, const size_t step, const size_t qoi)
	wrapper for variance_Qsum
Real	aggregate_variance_Qsum (const Real *sum_Ql, const Real *sum_Qlm1, const Real *sum_QlQl, const Real *sum_QlQlm1, const Real *sum_Qlm1Qlm1, const SizetArray &N_l, const size_t lev)
	sum up variances across QoI for given level
Real	variance_Qsum (const Real *sum_Ql, const Real *sum_Qlm1, const Real *sum_QlQl, const Real *sum_QlQlm1, const Real *sum_Qlm1Qlm1, const SizetArray &N_l, const size_t lev, const size_t qoi)
	evaluate variance for given level and QoI (using sum_YY with means from sum_Y)
void	variance_Qsum (const Real *sum_Ql, const Real *sum_Qlm1, const Real *sum_QlQl, const Real *sum_QlQlm1, const Real *sum_Qlm1Qlm1, const SizetArray &N_l, const size_t lev, Real *var_Yl)
	evaluate variances for given level across set of QoI
Real	variance_variance_Qsum (const IntRealMatrixMap &sum_Ql, const IntRealMatrixMap &sum_Qlm1, const IntIntPairRealMatrixMap &sum_QlQlm1, const Sizet2DArray &N_l, const size_t step, const size_t qoi)
	wrapper for var_of_var_ml
Real	variance_sigma_Qsum (const IntRealMatrixMap &sum_Ql, const IntRealMatrixMap &sum_Qlm1, const IntIntPairRealMatrixMap &sum_QlQlm1, const Sizet2DArray &N_l, const size_t step, const size_t qoi)
	wrapper for var_of_sigma_ml
Real	variance_scalarization_Qsum (const IntRealMatrixMap &sum_Ql, const IntRealMatrixMap &sum_Qlm1, const IntIntPairRealMatrixMap &sum_QlQlm1, const Sizet2DArray &N_l, const size_t step, const size_t qoi)
	wrapper for var_of_scalarization_ml More...
void	aggregate_mse_target_Qsum (RealMatrix &agg_var_qoi, const Sizet2DArray &N_l, const size_t step, RealVector &estimator_var0_qoi)
	sum up Monte Carlo estimates for mean squared error (MSE) for QoI using discrepancy sums based on allocation target
void	set_convergence_tol (const RealVector &estimator_var0_qoi, const RealVector &cost, RealVector &eps_sq_div_2_qoi)
	compute epsilon^2/2 term for each qoi based on reference estimator_var0 and relative convergence tolereance
void	compute_sample_allocation_target (const RealMatrix &var_qoi, const RealVector &cost, const Sizet2DArray &N_actual, const SizetArray &N_alloc, SizetArray &delta_N_l)
	compute sample allocation delta based on a budget constraint
void	compute_sample_allocation_target (const IntRealMatrixMap &sum_Ql, const IntRealMatrixMap &sum_Qlm1, const IntIntPairRealMatrixMap &sum_QlQlm1, const RealVector &eps_sq_div_2_in, const RealMatrix &var_qoi, const RealVector &cost, const Sizet2DArray &N_pilot, const Sizet2DArray &N_online, const SizetArray &N_alloc, SizetArray &delta_N_l)
	compute sample allocation delta based on current samples and based on allocation target. Single allocation target for each qoi, aggregated using max operation.
void	compute_moments (const IntRealMatrixMap &sum_Ql, const IntRealMatrixMap &sum_Qlm1, const IntIntPairRealMatrixMap &sum_QlQlm1, const Sizet2DArray &N_l)
void	assign_static_member (const Real &conv_tol, size_t &qoi, const size_t &qoi_aggregation, const size_t &num_functions, const RealVector &level_cost_vec, const IntRealMatrixMap &sum_Ql, const IntRealMatrixMap &sum_Qlm1, const IntIntPairRealMatrixMap &sum_QlQlm1, const RealVector &pilot_samples, const RealMatrix &scalarization_response_mapping)
void	assign_static_member_problem18 (Real &var_L_exact, Real &var_H_exact, Real &mu_four_L_exact, Real &mu_four_H_exact, Real &Ax, RealVector &level_cost_vec) const

Static Private Member Functions
static Real	variance_Ysum_static (Real sum_Y, Real sum_YY, size_t Nlq_pilot, size_t Nlq, bool compute_gradient, Real &grad)
	compute variance from sum accumulators necessary for sample allocation optimization
static Real	variance_Qsum_static (Real sum_Ql, Real sum_Qlm1, Real sum_QlQl, Real sum_QlQlm1, Real sum_Qlm1Qlm1, size_t Nlq_pilot, size_t Nlq, bool compute_gradient, Real &grad)
	compute variance from sum accumulators necessary for sample allocation optimization
static Real	var_lev_l_static (Real sum_Ql, Real sum_Qlm1, Real sum_QlQl, Real sum_Qlm1Qlm1, size_t Nlq_pilot, size_t Nlq, bool compute_gradient, Real &grad)
static Real	compute_bootstrap_covariance (const size_t step, const size_t qoi, const IntRealMatrixMap &lev_qoisamplematrix_map, const Real N, const bool compute_gradient, Real &grad, int *seed)
static Real	compute_cov_mean_sigma (const IntRealMatrixMap &sum_Ql, const IntRealMatrixMap &sum_Qlm1, const IntIntPairRealMatrixMap &sum_QlQlm1, const size_t Nlq_pilot, const Real Nlq, const size_t qoi, const size_t lev, const bool compute_gradient, Real &grad_g)
static RealVector	compute_cov_mean_sigma_fd (const IntRealMatrixMap &sum_Ql, const IntRealMatrixMap &sum_Qlm1, const IntIntPairRealMatrixMap &sum_QlQlm1, const size_t Nlq_pilot, const Real Nlq, const size_t qoi, const size_t lev)
static Real	compute_mean (const RealVector &samples)
static Real	compute_mean (const RealVector &samples, const bool compute_gradient, Real &grad)
static Real	compute_mean (const RealVector &samples, const Real N)
static Real	compute_mean (const RealVector &samples, const Real N, const bool compute_gradient, Real &grad)
static Real	compute_std (const RealVector &samples)
static Real	compute_std (const RealVector &samples, const bool compute_gradient, Real &grad)
static Real	compute_std (const RealVector &samples, const Real N)
static Real	compute_std (const RealVector &samples, const Real N, const bool compute_gradient, Real &grad)
static Real	compute_cov (const RealVector &samples_X, const RealVector &samples_hat)
static Real	unbiased_mean_product_pair (const Real sumQ1, const Real sumQ2, const Real sumQ1Q2, const size_t Nlq)
	compute the unbiased product of two sampling means
static Real	unbiased_mean_product_triplet (const Real sumQ1, const Real sumQ2, const Real sumQ3, const Real sumQ1Q2, const Real sumQ1Q3, const Real sumQ2Q3, const Real sumQ1Q2Q3, const size_t Nlq)
	compute the unbiased product of three sampling means
static Real	unbiased_mean_product_pairpair (const Real sumQ1, const Real sumQ2, const Real sumQ1Q2, const Real sumQ1sq, const Real sumQ2sq, const Real sumQ1sqQ2, const Real sumQ1Q2sq, const Real sumQ1sqQ2sq, const size_t Nlq)
	compute the unbiased product of two pairs of products of sampling means
static Real	var_of_var_ml_l0 (const IntRealMatrixMap &sum_Ql, const IntRealMatrixMap &sum_Qlm1, const IntIntPairRealMatrixMap &sum_QlQlm1, const size_t Nlq_pilot, const Real Nlq, const size_t qoi, const bool compute_gradient, Real &grad_g)
static Real	var_of_var_ml_lmax (const IntRealMatrixMap &sum_Ql, const IntRealMatrixMap &sum_Qlm1, const IntIntPairRealMatrixMap &sum_QlQlm1, const size_t Nlq_pilot, const Real Nlq, const size_t qoi, const bool compute_gradient, Real &grad_g)
static Real	var_of_var_ml_l (const IntRealMatrixMap &sum_Ql, const IntRealMatrixMap &sum_Qlm1, const IntIntPairRealMatrixMap &sum_QlQlm1, const size_t Nlq_pilot, const Real Nlq, const size_t qoi, const size_t lev, const bool compute_gradient, Real &grad_g)
static Real	compute_cov_meanl_varlmone (const IntRealMatrixMap &sum_Ql, const IntRealMatrixMap &sum_Qlm1, const IntIntPairRealMatrixMap &sum_QlQlm1, const size_t Nlq_pilot, const Real Nlq, const size_t qoi, const size_t lev, const bool compute_gradient, Real &grad_g)
static Real	compute_cov_meanlmone_varl (const IntRealMatrixMap &sum_Ql, const IntRealMatrixMap &sum_Qlm1, const IntIntPairRealMatrixMap &sum_QlQlm1, const size_t Nlq_pilot, const Real Nlq, const size_t qoi, const size_t lev, const bool compute_gradient, Real &grad_g)
static Real	compute_grad_cov_meanl_vark (const Real cov_mean_var, const Real var_of_var, const Real var_of_sigma, const Real grad_var_of_var, const Real grad_var_of_sigma, const Real Nlq)
static void	target_cost_objective_eval_optpp (int mode, int n, const RealVector &x, double &f, RealVector &grad_f, int &result_mode)
	OPTPP definition.
static void	target_cost_constraint_eval_optpp (int mode, int n, const RealVector &x, RealVector &g, RealMatrix &grad_g, int &result_mode)
static void	target_var_constraint_eval_optpp (int mode, int n, const RealVector &x, RealVector &g, RealMatrix &grad_g, int &result_mode)
static void	target_var_constraint_eval_logscale_optpp (int mode, int n, const RealVector &x, RealVector &g, RealMatrix &grad_g, int &result_mode)
static void	target_sigma_constraint_eval_optpp (int mode, int n, const RealVector &x, RealVector &g, RealMatrix &grad_g, int &result_mode)
static void	target_sigma_constraint_eval_logscale_optpp (int mode, int n, const RealVector &x, RealVector &g, RealMatrix &grad_g, int &result_mode)
static void	target_scalarization_constraint_eval_optpp (int mode, int n, const RealVector &x, RealVector &g, RealMatrix &grad_g, int &result_mode)
static void	target_scalarization_constraint_eval_logscale_optpp (int mode, int n, const RealVector &x, RealVector &g, RealMatrix &grad_g, int &result_mode)
static void	target_var_objective_eval_optpp (int mode, int n, const RealVector &x, double &f, RealVector &grad_f, int &result_mode)
static void	target_var_objective_eval_logscale_optpp (int mode, int n, const RealVector &x, double &f, RealVector &grad_f, int &result_mode)
static void	target_sigma_objective_eval_optpp (int mode, int n, const RealVector &x, double &f, RealVector &grad_f, int &result_mode)
static void	target_sigma_objective_eval_logscale_optpp (int mode, int n, const RealVector &x, double &f, RealVector &grad_f, int &result_mode)
static void	target_scalarization_objective_eval_optpp (int mode, int n, const RealVector &x, double &f, RealVector &grad_f, int &result_mode)
static void	target_scalarization_objective_eval_logscale_optpp (int mode, int n, const RealVector &x, double &f, RealVector &grad_f, int &result_mode)
static void	target_scalarization_objective_eval_optpp_fd (int mode, int n, const RealVector &x, double &f, int &result_mode)
static void	target_cost_objective_eval_npsol (int &mode, int &n, double *x, double &f, double *gradf, int &nstate)
	NPSOL definition (Wrapper using OPTPP implementation above under the hood)
static void	target_cost_constraint_eval_npsol (int &mode, int &m, int &n, int &ldJ, int *needc, double *x, double *g, double *grad_g, int &nstate)
static void	target_var_constraint_eval_npsol (int &mode, int &m, int &n, int &ldJ, int *needc, double *x, double *g, double *grad_g, int &nstate)
static void	target_var_constraint_eval_logscale_npsol (int &mode, int &m, int &n, int &ldJ, int *needc, double *x, double *g, double *grad_g, int &nstate)
static void	target_sigma_constraint_eval_npsol (int &mode, int &m, int &n, int &ldJ, int *needc, double *x, double *g, double *grad_g, int &nstate)
static void	target_sigma_constraint_eval_logscale_npsol (int &mode, int &m, int &n, int &ldJ, int *needc, double *x, double *g, double *grad_g, int &nstate)
static void	target_scalarization_constraint_eval_npsol (int &mode, int &m, int &n, int &ldJ, int *needc, double *x, double *g, double *grad_g, int &nstate)
static void	target_scalarization_constraint_eval_logscale_npsol (int &mode, int &m, int &n, int &ldJ, int *needc, double *x, double *g, double *grad_g, int &nstate)
static void	target_var_objective_eval_npsol (int &mode, int &n, double *x, double &f, double *gradf, int &nstate)
static void	target_var_objective_eval_logscale_npsol (int &mode, int &n, double *x, double &f, double *gradf, int &nstate)
static void	target_sigma_objective_eval_npsol (int &mode, int &n, double *x, double &f, double *gradf, int &nstate)
static void	target_sigma_objective_eval_logscale_npsol (int &mode, int &n, double *x, double &f, double *gradf, int &nstate)
static void	target_scalarization_objective_eval_npsol (int &mode, int &n, double *x, double &f, double *gradf, int &nstate)
static void	target_scalarization_objective_eval_logscale_npsol (int &mode, int &n, double *x, double &f, double *gradf, int &nstate)
static void	target_var_constraint_eval_optpp_problem18 (int mode, int n, const RealVector &x, RealVector &g, RealMatrix &grad_g, int &result_mode)
static void	target_sigma_constraint_eval_optpp_problem18 (int mode, int n, const RealVector &x, RealVector &g, RealMatrix &grad_g, int &result_mode)
static double	exact_var_of_var_problem18 (const RealVector &Nl)
static double	exact_var_of_sigma_problem18 (const RealVector &Nl)

Private Attributes
unsigned short	seq_index
short	allocationTarget
	store the allocation_target input specification, prior to run-time Options right now: More...
bool	useTargetVarianceOptimizationFlag
	option to switch on numerical optimization for solution of sample alloation of allocationTarget Variance
short	qoiAggregation
	store the qoi_aggregation_norm input specification, prior to run-time Options right now: More...
short	convergenceTolType
	store the convergence_tolerance_type input specification, prior to run-time Options right now: More...
short	convergenceTolTarget
	store the convergence_tolerance_target input specification, prior to run-time Options right now: More...
RealVector	convergenceTolVec
RealMatrix	scalarizationCoeffs
	"scalarization" response_mapping matrix applied to the mlmc sample allocation when a scalarization, i.e. alpha_1 * mean + alpha_2 * sigma, is the target.
RealMatrix	NTargetQoI
	Helper data structure to store intermedia sample allocations.
IntRealMatrixMap	levQoisamplesmatrixMap
bool	storeEvals
int	bootstrapSeed
short	cov_approximation_type

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 parameter 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...
Static Protected Attributes inherited from NonD
static NonD *	nondInstance
	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()

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(), NonDMultilevelSampling::allocationTarget, NonD::finalMomentsType, ProblemDescDB::get_rv(), Iterator::iteratedModel, Model::multifidelity_precedence(), Analyzer::numFunctions, Iterator::probDescDB, NonDMultilevelSampling::qoiAggregation, and NonDMultilevelSampling::scalarizationCoeffs.

Member Function Documentation

core_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 Dakota::abort_handler(), NonDMultilevelSampling::allocationTarget, NonD::configure_sequence(), Iterator::convergenceTol, NonDMultilevelSampling::multilevel_mc_offline_pilot(), NonDMultilevelSampling::multilevel_mc_pilot_projection(), NonDMultilevelSampling::multilevel_mc_Qsum(), Analyzer::numFunctions, NonDEnsembleSampling::numSteps, NonDEnsembleSampling::onlineCost, NonDEnsembleSampling::pilotMgmtMode, NonD::query_cost(), NonDMultilevelSampling::scalarizationCoeffs, NonDEnsembleSampling::secondaryIndex, NonDEnsembleSampling::sequenceCost, and NonDEnsembleSampling::sequenceType.

Referenced by NonDMultilevControlVarSampling::core_run().

multilevel_mc_Qsum()

void multilevel_mc_Qsum ( )

private

Perform multilevel Monte Carlo across the discretization levels for a particular model form using QoI accumulators (sum_Q)

This function performs MLMC on a model sequence, either defined by model forms or discretization levels. void NonDMultilevelSampling::multilevel_mc_Ysum() { Formulate as a coordinated progression towards convergence, where, e.g., time step is inferred from the spatial discretization (NOT an additional solution control) based on stability criteria, e.g. CFL condition. Can we reliably capture runtime estimates as part of pilot run w/i Dakota? Ultimately seems desirable to support either online or offline cost estimates, to allow more accurate resource allocation when possible or necessary (e.g., combustion processes with expense that is highly parameter dependent). model id_model = 'LF' simulation

point to state vars; ordered based on set values for h, delta-t

solution_level_control = 'dssiv1'

relative cost estimates in same order as state set values

--> re-sort into map keyed by increasing cost

solution_level_cost = 10 2 200

How to manage the set of MLMC statistics:

1. Simplest: proposal is to use the mean estimator to drive the algorithm, but carry along other estimates.
2. Later: could consider a refinement for converging the estimator of the variance after convergence of the mean estimator.

How to manage the vector of QoI:

1. Worst case: select N_l based only on QoI w/ highest total variance from pilot run --> fix for all levels and don't allow switching across major iterations (possible oscillation? Or simple overlay of resolution reqmts?)
2. Better: select N_l based on convergence in aggregated variance.

Allow either model forms or discretization levels, but not both size_t form, lev; bool multilev = (sequenceType == Pecos::RESOLUTION_LEVEL_SEQUENCE), budget_constrained = (maxFunctionEvals != SZ_MAX); either lev varies and form is fixed, or vice versa: size_t& step = (multilev) ? lev : form; if (multilev) form = secondaryIndex; else lev = secondaryIndex;

retrieve cost estimates across soln levels for a particular model form RealVector agg_var(numSteps); Real eps_sq_div_2, sum_sqrt_var_cost, agg_estvar0 = 0., lev_cost, budget, ref_cost = sequenceCost[numSteps-1]; // HF cost (1 level)

if (budget_constrained) budget = (Real)maxFunctionEvals * ref_cost; For moment estimation, we accumulate telescoping sums for Q^i using discrepancies Yi = Q^i_{lev} - Q^i_{lev-1} (sum_Y[i] for i=1:4). For computing N_l from estimator variance, we accumulate square of Y1 estimator (YY[i] = (Y^i)^2 for i=1). IntRealMatrixMap sum_Y; RealMatrix sum_YY(numFunctions, numSteps); initialize_ml_Ysums(sum_Y, numSteps); RealMatrix var_Y(numFunctions, numSteps, false);

Initialize for pilot sample SizetArray delta_N_l; load_pilot_sample(pilotSamples, numSteps, delta_N_l);

Sizet2DArray& N_l = NLevActual[form]; // slice only valid for ML define a new 2D array and then post back to NLevActual at end Sizet2DArray N_l(numSteps); for (step=0; step<numSteps; ++step) N_l[step].assign(numFunctions, 0);

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

sum_sqrt_var_cost = 0.; for (step=0; step<numSteps; ++step) { // step is reference to lev

configure_indices(step, form, lev, sequenceType); lev_cost = level_cost(sequenceCost, step); // raw cost (not equiv HF)

set the number of current samples from the defined increment numSamples = delta_N_l[step];

aggregate variances across QoI for estimating N_l (justification: for independent QoI, sum of QoI variances = variance of QoI sum) Real& agg_var_l = agg_var[step]; // carried over from prev iter if no samp if (numSamples) {

assign sequence, get samples, export, evaluate evaluate_ml_sample_increment("ml_", step);

process allResponses: accumulate new samples for each qoi and update number of successful samples for each QoI accumulate_ml_Ysums(sum_Y, sum_YY, lev, N_l[step]); increment_ml_equivalent_cost(numSamples, lev_cost, ref_cost, equivHFEvals);

compute estimator variance from current sample accumulation: variance_Ysum(sum_Y[1][step], sum_YY[step], N_l[step], var_Y[step]); agg_var_l = sum(var_Y[lev], numFunctions); }

sum_sqrt_var_cost += std::sqrt(agg_var_l * lev_cost); MSE reference is MLMC with pilot sample, prior to any N_l adaptation: if (mlmfIter == 0 && !budget_constrained) agg_estvar0 += aggregate_mse_Yvar(var_Y[step], N_l[step]); } compute epsilon target based on relative tolerance: total MSE = eps^2 which is equally apportioned (eps^2 / 2) among residual bias and estimator variance (\Sum var_Y_l / N_l). Since we usually do not know the bias error, we compute an initial estimator variance from MLMC on the pilot sample and then seek to reduce it by a relative_factor <= 1. if (mlmfIter == 0) { MLMC estimator variance for final estvar reporting is not aggregated compute_ml_estimator_variance(var_Y, N_l, estVarIter0); compute eps^2 / 2 = aggregated estvar0 * rel tol if (!budget_constrained) // eps^2 / 2 = estvar0 * rel tol eps_sq_div_2 = agg_estvar0 * convergenceTol; }

update sample targets based on latest variance estimates Real N_target, fact = (budget_constrained) ? budget / sum_sqrt_var_cost : // budget constraint sum_sqrt_var_cost / eps_sq_div_2; // error balance constraint for (step=0; step<numSteps; ++step) { Equation 3.9 in CTR Annual Research Briefs: "A multifidelity control variate approach for the multilevel Monte Carlo technique," Geraci, Eldred, Iaccarino, 2015. N_target = std::sqrt(agg_var[step]/level_cost(sequenceCost, step)) * fact; delta_N_l[step] = one_sided_delta(average(N_l[step]), N_target); } ++mlmfIter; Cout << "\nMLMC iteration " << mlmfIter << " sample increments:\n" << delta_N_l << std::endl; }

switch (pilotMgmtMode) { case ONLINE_PILOT: case OFFLINE_PILOT: { aggregate expected value of estimators for Y, Y^2, Y^3, Y^4. Final expectation is sum of expectations from telescopic sum. Note: raw moments have no bias correction (no additional variance from estimated center). RealMatrix Q_raw_mom(numFunctions, 4); ml_raw_moments(sum_Y[1], sum_Y[2], sum_Y[3], sum_Y[4], N_l, 0, numSteps, Q_raw_mom); convert_moments(Q_raw_mom, momentStats); // raw to final (central or std) recover_variance(momentStats, varH); break; } case PILOT_PROJECTION: update_projected_samples(delta_N_l, sequenceCost, deltaEquivHF); break; }

compute_ml_estimator_variance(var_Y, N_l, estVar); avgEstVar = average(estVar); post final N_l back to NLevActual (needed for final eval summary) inflate_sequence_samples(N_l, multilev, secondaryIndex, NLevActual); } This function performs "geometrical" MLMC on a single model form with multiple discretization levels.

References NonDEnsembleSampling::average(), NonDHierarchSampling::avgEstVar, NonDMultilevelSampling::compute_error_estimates(), NonDMultilevelSampling::compute_ml_estimator_variance(), NonDMultilevelSampling::estVar, NonDMultilevelSampling::evaluate_levels(), NonDEnsembleSampling::finalStatsType, NonD::inflate_sequence_samples(), NonDMultilevelSampling::initialize_ml_Qsums(), NonD::load_pilot_sample(), Iterator::maxIterations, NonDEnsembleSampling::mlmfIter, NonD::momentStats, NonDEnsembleSampling::NLevActual, NonDEnsembleSampling::NLevAlloc, NonDEnsembleSampling::numSteps, NonDEnsembleSampling::pilotSamples, NonDMultilevelSampling::recover_variance(), NonDEnsembleSampling::secondaryIndex, NonDEnsembleSampling::sequenceCost, NonDEnsembleSampling::sequenceType, and NonDEnsembleSampling::varH.

Referenced by NonDMultilevelSampling::core_run().

variance_scalarization_Qsum()

Real variance_scalarization_Qsum ( const IntRealMatrixMap &  sum_Ql, const IntRealMatrixMap &  sum_Qlm1, const IntIntPairRealMatrixMap &  sum_QlQlm1, const Sizet2DArray &  N_l, const size_t  step, const size_t  qoi  )

private

wrapper for var_of_scalarization_ml

For TARGET_SCALARIZATION we have the special case that we can also combine scalarization over multiple qoi This is respresented in the scalarization response mapping stored in scalarizationCoeffs This is for now neglecting cross terms for covariance terms inbetween different qois, e.g. V[mu_1 + 2 sigma_1 + 3 mu_2] = V[mu_1] + V[2 sigma_1] + 2 Cov[mu_1, 2 sigma_1] + V[3 mu_2] + 2 Cov[2 mu_1, 3 mu_2] + 2 Cov[2 sigma_1, 3 mu_2] \approx V[mu_1] + V[2 sigma_1] + 2 Cov[mu_1, 2 sigma_1] + V[3 mu_2] (What we do)

References NonDEnsembleSampling::check_negative(), Analyzer::numFunctions, NonDMultilevelSampling::scalarizationCoeffs, NonDMultilevelSampling::variance_mean_Qsum(), and NonDMultilevelSampling::variance_sigma_Qsum().

Referenced by NonDMultilevelSampling::aggregate_variance_target_Qsum().

Member Data Documentation

allocationTarget

short allocationTarget

private

store the allocation_target input specification, prior to run-time Options right now:

• Mean = First moment (Mean)
• Variance = Second moment (Variance or standard deviation depending on moments central or standard)

Referenced by NonDMultilevelSampling::aggregate_variance_target_Qsum(), NonDMultilevelSampling::compute_sample_allocation_target(), NonDMultilevelSampling::core_run(), and NonDMultilevelSampling::NonDMultilevelSampling().

qoiAggregation

short qoiAggregation

private

store the qoi_aggregation_norm input specification, prior to run-time Options right now:

• sum = aggregate the variance over all QoIs, compute samples from that
• max = take maximum sample allocation over QoIs for each level

Referenced by NonDMultilevelSampling::allocation_increment(), NonDMultilevelSampling::compute_sample_allocation_target(), and NonDMultilevelSampling::NonDMultilevelSampling().

convergenceTolType

short convergenceTolType

private

store the convergence_tolerance_type input specification, prior to run-time Options right now:

• relative = computes reference tolerance in first iteration and sets convergence_tolerance as reference tolerance * convergence_tol
• absolute = sets convergence tolerance from input

Referenced by NonDMultilevelSampling::set_convergence_tol().

convergenceTolTarget

short convergenceTolTarget

private

store the convergence_tolerance_target input specification, prior to run-time Options right now:

• variance_constraint = minimizes cost for equality constraint on variance of estimator (rhs of constraint from convergenceTol)
• cost_constraint = minizes variance of estimator for equality constraint on cost (rhs of constraint from convergenceTol)

Referenced by NonDMultilevelSampling::compute_sample_allocation_target(), and NonDMultilevelSampling::set_convergence_tol().

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

• NonDMultilevelSampling.hpp
• NonDMultilevelSampling.cpp