NonDACVSampling Class Reference

Perform Approximate Control Variate Monte Carlo sampling for UQ. More...

Inheritance diagram for NonDACVSampling:

Public Member Functions
	NonDACVSampling (ProblemDescDB &problem_db, Model &model)
	standard constructor More...
	~NonDACVSampling ()
	destructor
Public Member Functions inherited from NonDNonHierarchSampling
	NonDNonHierarchSampling (ProblemDescDB &problem_db, Model &model)
	standard constructor More...
	~NonDNonHierarchSampling ()
	destructor
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	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
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	update_callback_data (const RealVector &cv_initial, const RealVector &cv_lower_bnds, const RealVector &cv_upper_bnds, 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, const RealVector &nln_ineq_lb, const RealVector &nln_ineq_ub, const RealVector &nln_eq_tgt)
	assign variable values and bounds and constraint coefficients and bounds for this iterator (user-functions mode for which iteratedModel is null)
virtual const RealMatrix &	callback_linear_ineq_coefficients () const
	return linear constraint coefficients for this iterator (user-functions mode for which iteratedModel is null)
virtual const RealVector &	callback_linear_ineq_lower_bounds () const
	return linear constraint lower bounds for this iterator (user-functions mode for which iteratedModel is null)
virtual const RealVector &	callback_linear_ineq_upper_bounds () const
	return linear constraint upper bounds for this iterator (user-functions mode for which iteratedModel is null)
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 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 ()
	core portion of run; implemented by all derived classes and may include pre/post steps in lieu of separate pre/post More...
Real	estimator_accuracy_metric ()
void	print_variance_reduction (std::ostream &s)
void	estimator_variance_ratios (const RealVector &r_and_N, RealVector &estvar_ratios)
	compute estimator variance ratios from HF samples and oversample ratios
void	initialize_acv_sums (RealMatrix &sum_L, RealVector &sum_H, RealSymMatrixArray &sum_LL, RealMatrix &sum_LH, RealVector &sum_HH)
void	initialize_acv_sums (IntRealMatrixMap &sum_L_baseline, IntRealVectorMap &sum_H, IntRealSymMatrixArrayMap &sum_LL, IntRealMatrixMap &sum_LH, RealVector &sum_HH)
void	evaluate_pilot (RealMatrix &sum_L_pilot, RealVector &sum_H_pilot, RealSymMatrixArray &sum_LL_pilot, RealMatrix &sum_LH_pilot, RealVector &sum_HH_pilot, SizetArray &N_shared_pilot, bool incr_cost)
void	evaluate_pilot (IntRealMatrixMap &sum_L_pilot, IntRealVectorMap &sum_H_pilot, IntRealSymMatrixArrayMap &sum_LL_pilot, IntRealMatrixMap &sum_LH_pilot, RealVector &sum_HH_pilot, SizetArray &N_shared_pilot, bool incr_cost)
void	compute_LH_statistics (RealMatrix &sum_L_pilot, RealVector &sum_H_pilot, RealSymMatrixArray &sum_LL_pilot, RealMatrix &sum_LH_pilot, RealVector &sum_HH_pilot, SizetArray &N_shared_pilot, RealMatrix &var_L, RealVector &var_H, RealSymMatrixArray &cov_LL, RealMatrix &cov_LH)
void	accumulate_acv_sums (IntRealMatrixMap &sum_L_baseline, IntRealVectorMap &sum_H, IntRealSymMatrixArrayMap &sum_LL, IntRealMatrixMap &sum_LH, RealVector &sum_HH, SizetArray &N_shared)
void	accumulate_acv_sums (IntRealMatrixMap &sum_L_refined, Sizet2DArray &N_L_refined, const SizetArray &approx_sequence, size_t approx_start, size_t approx_end)
void	accumulate_acv_sums (IntRealMatrixMap &sum_L, Sizet2DArray &N_L_actual, const RealVector &fn_vals, const ShortArray &asv, size_t approx)
void	compute_acv_control_covariances (const RealMatrix &sum_L, Real sum_H_q, const RealSymMatrix &sum_LL_q, const RealMatrix &sum_LH, size_t N_shared_q, size_t qoi, RealSymMatrix &cov_LL, RealMatrix &cov_LH)
void	update_projected_lf_samples (const MFSolutionData &soln, const UShortArray &approx_set, const SizetArray &N_H_actual, size_t &N_H_alloc, Real &delta_equiv_hf)
void	update_projected_samples (const MFSolutionData &soln, const UShortArray &approx_set, const SizetArray &N_H_actual, size_t &N_H_alloc, size_t &delta_N_H_actual, Real &delta_equiv_hf)
Real	update_hf_target (const RealVector &avg_eval_ratios, Real avg_N_H, const RealVector &var_H, const RealVector &estvar0)
void	print_model_solution (std::ostream &s, const MFSolutionData &soln, const UShortArray &approx_set)
Protected Member Functions inherited from NonDNonHierarchSampling
void	pre_run ()
	pre-run portion of run (optional); re-implemented by Iterators which can generate all Variables (parameter sets) a priori More...
unsigned short	uses_method () const
	return name of active optimizer method
void	method_recourse (unsigned short method_name)
	perform a numerical solver method switch due to a detected conflict
virtual Real	average_estimator_variance (const RealVector &cd_vars)
	helper function that supports optimization APIs passing design variables
virtual void	numerical_solution_counts (size_t &num_cdv, size_t &num_lin_con, size_t &num_nln_con)
	within ensemble_numerical_solution(), define the number of solution variables and constraints
virtual void	numerical_solution_bounds_constraints (const MFSolutionData &soln, RealVector &x0, RealVector &x_lb, RealVector &x_ub, RealVector &lin_ineq_lb, RealVector &lin_ineq_ub, RealVector &lin_eq_tgt, RealVector &nln_ineq_lb, RealVector &nln_ineq_ub, RealVector &nln_eq_tgt, RealMatrix &lin_ineq_coeffs, RealMatrix &lin_eq_coeffs)
	within ensemble_numerical_solution(), define initial values, coefficients, bounds, and targets for solution variables and constraints
virtual void	derived_finite_solution_bounds (const RealVector &x0, RealVector &x_lb, RealVector &x_ub, Real budget)
	portion of finite_solution_bounds() specific to derived class implementations
virtual void	apply_mc_reference (RealVector &mc_targets)
	apply convergenceTol to estVarIter0 to form an estimate of required high-fidelity MC samples
virtual void	augment_linear_ineq_constraints (RealMatrix &lin_ineq_coeffs, RealVector &lin_ineq_lb, RealVector &lin_ineq_ub)
	augment linear inequality constraints as required by derived algorithm
virtual Real	augmented_linear_ineq_violations (const RealVector &cd_vars, const RealMatrix &lin_ineq_coeffs, const RealVector &lin_ineq_lb, const RealVector &lin_ineq_ub)
	return quadratic constraint violation for augmented linear inequality constraints
virtual void	recover_results (const RealVector &cv_star, const RealVector &fn_star, MFSolutionData &soln)
	post-process optimization final results to recover solution data
virtual Real	linear_model_cost (const RealVector &N_vec)
	constraint helper function shared by NPSOL/OPT++ static evaluators
virtual void	linear_model_cost_gradient (const RealVector &N_vec, RealVector &grad_c)
	constraint gradient helper fn shared by NPSOL/OPT++ static evaluators
virtual Real	linear_group_cost (const RealVector &N_vec)
	constraint helper function shared by NPSOL/OPT++ static evaluators
virtual void	linear_group_cost_gradient (const RealVector &N_vec, RealVector &grad_c)
	constraint gradient helper fn shared by NPSOL/OPT++ static evaluators
virtual Real	nonlinear_model_cost (const RealVector &r_and_N)
	constraint helper function shared by NPSOL/OPT++ static evaluators
virtual void	nonlinear_model_cost_gradient (const RealVector &r_and_N, RealVector &grad_c)
	constraint gradient helper fn shared by NPSOL/OPT++ static evaluators
virtual size_t	num_approximations () const
void	shared_increment (String prepend)
void	shared_increment (String prepend, const UShortArray &approx_set)
void	shared_approx_increment (String prepend)
bool	approx_increment (String prepend, const SizetArray &approx_sequence, size_t start, size_t end)
bool	approx_increment (String prepend, const SizetArray &approx_sequence, size_t start, size_t end, const UShortArray &approx_set)
bool	approx_increment (String prepend, unsigned short root, const UShortSet &reverse_dag)
void	group_increments (SizetArray &delta_N_G, String prepend, bool reverse_order=false)
void	ensemble_sample_increment (const String &prepend, size_t step, bool new_samples=true)
void	ensemble_sample_batch (const String &prepend, size_t step, bool new_samples=true)
size_t	group_approx_increment (const RealVector &soln_vars, const UShortArray &approx_set, const Sizet2DArray &N_L_actual, SizetArray &N_L_alloc, const UShortArray &model_group)
void	export_sample_sets (const String &prepend, size_t step)
	export allSamples for all Models included in ensemble batch evaluation
void	export_all_samples (const String &root_prepend, const Model &model, size_t iter, size_t step)
	export allSamples to a tagged tabular file
void	finite_solution_bounds (const RealVector &x0, RealVector &x_lb, RealVector &x_ub)
	When looping through a minimizer sequence/competition, this function enables per-minimizer updates to the parameter bounds, e.g. for providing a bounded domain for methods that require it, while removing it for those that don't.
void	assign_active_key ()
void	initialize_sums (IntRealMatrixMap &sum_L_baseline, IntRealVectorMap &sum_H, IntRealMatrixMap &sum_LH, RealVector &sum_HH)
void	initialize_counts (Sizet2DArray &num_L_baseline, SizetArray &num_H, Sizet2DArray &num_LH)
void	initialize_group_sums (RealMatrixArray &sum_G, RealSymMatrix2DArray &sum_GG)
void	initialize_group_sums (RealMatrixArray &sum_G)
void	initialize_group_sums (IntRealMatrixArrayMap &sum_G, IntRealSymMatrix2DArrayMap &sum_GG)
void	initialize_group_sums (IntRealMatrixArrayMap &sum_G)
void	initialize_group_counts (Sizet2DArray &num_G)
void	finalize_counts (const Sizet2DArray &N_L_actual, const SizetArray &N_L_alloc)
Real	compute_equivalent_cost (Real avg_hf_target, const RealVector &avg_eval_ratios, const RealVector &cost)
Real	compute_equivalent_cost (Real avg_hf_target, const RealVector &avg_eval_ratios, const RealVector &cost, const UShortArray &approx_set)
void	increment_equivalent_cost (size_t new_samp, const RealVector &cost, size_t index, Real &equiv_hf_evals)
void	increment_equivalent_cost (size_t new_samp, const RealVector &cost, size_t start, size_t end, Real &equiv_hf_evals)
void	increment_equivalent_cost (size_t new_samp, const RealVector &cost, const SizetArray &approx_sequence, size_t start, size_t end, Real &equiv_hf_evals)
void	increment_equivalent_cost (size_t new_samp, const RealVector &cost, const SizetArray &approx_sequence, size_t start, size_t end, const UShortArray &approx_set, Real &equiv_hf_evals)
void	increment_equivalent_cost (size_t new_samp, const RealVector &cost, unsigned short root, const UShortSet &reverse_dag, Real &equiv_hf_evals)
void	increment_equivalent_cost (size_t new_samp, const RealVector &cost, unsigned short root, const UShortArray &approx_set, Real &equiv_hf_evals)
void	increment_equivalent_cost (const SizetArray &delta_N_g, const RealVector &group_cost, Real hf_cost, Real &equiv_hf_evals)
void	increment_sample_range (SizetArray &N_L, size_t incr, const SizetArray &approx_sequence, size_t start, size_t end)
void	increment_sample_range (SizetArray &N_L, size_t incr, const UShortArray &approx_set)
void	increment_sample_range (SizetArray &N_L, size_t incr, const SizetArray &approx_sequence, size_t start, size_t end, const UShortArray &approx_set)
void	increment_sample_range (SizetArray &N_L, size_t incr, unsigned short root, const UShortSet &reverse_dag)
void	accumulate_group_sums (IntRealMatrixArrayMap &sum_G, Sizet2DArray &num_G, const IntIntResponse2DMap &batch_resp_map)
void	accumulate_group_sums (IntRealMatrixArrayMap &sum_G, Sizet2DArray &num_G, size_t group, const IntResponseMap &resp_map)
void	ensemble_active_set (const UShortArray &model_set)
void	hf_indices (size_t &hf_form_index, size_t &hf_lev_index)
	define model form and resolution level indices
void	compute_variance (Real sum_Q, Real sum_QQ, size_t num_Q, Real &var_Q)
void	compute_variance (const RealVector &sum_Q, const RealVector &sum_QQ, const SizetArray &num_Q, RealVector &var_Q)
void	compute_correlation (Real sum_Q1, Real sum_Q2, Real sum_Q1Q1, Real sum_Q1Q2, Real sum_Q2Q2, size_t N_shared, Real &var_Q1, Real &var_Q2, Real &rho2_Q1Q2)
void	compute_covariance (Real sum_Q1, Real sum_Q2, Real sum_Q1Q2, size_t N_shared, Real &cov_Q1Q2)
void	covariance_to_correlation_sq (const RealMatrix &cov_LH, const RealMatrix &var_L, const RealVector &var_H, RealMatrix &rho2_LH)
void	mfmc_analytic_solution (const UShortArray &approx_set, const RealMatrix &rho2_LH, const RealVector &cost, RealVector &avg_eval_ratios, bool lower_bounded_r=true, bool monotonic_r=false)
void	mfmc_reordered_analytic_solution (const UShortArray &approx_set, const RealMatrix &rho2_LH, const RealVector &cost, SizetArray &corr_approx_sequence, RealVector &avg_eval_ratios, bool lower_bounded_r=true, bool monotonic_r=false)
void	mfmc_estvar_ratios (const RealMatrix &rho2_LH, const RealVector &avg_eval_ratios, SizetArray &approx_sequence, RealVector &estvar_ratios)
void	cvmc_ensemble_solutions (const RealMatrix &rho2_LH, const RealVector &cost, RealVector &avg_eval_ratios, bool lower_bounded_r=true)
void	pick_mfmc_cvmc_solution (const MFSolutionData &mf_soln, const MFSolutionData &cv_soln, MFSolutionData &soln)
void	ensemble_numerical_solution (MFSolutionData &soln)
void	process_model_solution (MFSolutionData &soln, size_t &num_samples)
void	configure_minimizers (RealVector &x0, RealVector &x_lb, RealVector &x_ub, const RealVector &lin_ineq_lb, const RealVector &lin_ineq_ub, const RealVector &lin_eq_tgt, const RealVector &nln_ineq_lb, const RealVector &nln_ineq_ub, const RealVector &nln_eq_tgt, const RealMatrix &lin_ineq_coeffs, const RealMatrix &lin_eq_coeffs)
void	run_minimizers (MFSolutionData &soln)
void	root_reverse_dag_to_group (unsigned short root, const UShortSet &rev_dag, UShortArray &model_group)
void	group_to_root_reverse_dag (const UShortArray &model_group, unsigned short &root, UShortSet &rev_dag)
void	overlay_group_sums (const IntRealMatrixArrayMap &sum_G, const Sizet2DArray &N_G_actual, IntRealMatrixMap &sum_L_shared, Sizet2DArray &N_L_actual_shared, IntRealMatrixMap &sum_L_refined, Sizet2DArray &N_L_actual_refined)
void	mfmc_model_group (size_t last_index, UShortArray &model_group) const
void	mfmc_model_group (size_t last_index, const SizetArray &approx_sequence, UShortArray &model_group) const
void	singleton_model_group (size_t index, UShortArray &model_group) const
void	singleton_model_group (size_t index, const SizetArray &approx_sequence, UShortArray &model_group) const
void	cvmc_model_group (size_t index, UShortArray &model_group) const
void	cvmc_model_group (size_t index, const SizetArray &approx_sequence, UShortArray &model_group) const
void	mlmc_model_group (size_t index, UShortArray &model_group) const
void	mlmc_model_group (size_t index, const SizetArray &approx_sequence, UShortArray &model_group) const
void	update_model_group_costs ()
void	print_group (std::ostream &s, size_t g) const
Real	allocate_budget (const RealVector &avg_eval_ratios, const RealVector &cost, Real budget)
Real	allocate_budget (const RealVector &avg_eval_ratios, const RealVector &cost)
Real	allocate_budget (const UShortArray &approx_set, const RealVector &avg_eval_ratios, const RealVector &cost, Real budget)
Real	allocate_budget (const UShortArray &approx_set, const RealVector &avg_eval_ratios, const RealVector &cost)
Real	update_hf_target (const RealVector &estvar, const SizetArray &N_H, const RealVector &estvar_iter0)
Real	update_hf_target (const RealVector &estvar_ratios, const RealVector &var_H, const RealVector &estvar_iter0)
void	scale_to_target (Real avg_N_H, const RealVector &cost, RealVector &avg_eval_ratios, Real &avg_hf_target, Real budget, Real offline_N_lwr=1.)
void	scale_to_budget_with_pilot (RealVector &avg_eval_ratios, const RealVector &cost, Real avg_N_H, Real budget)
void	cache_mc_reference ()
void	enforce_bounds (RealVector &x0, const RealVector &x_lb, const RealVector &x_ub)
void	print_estimator_performance (std::ostream &s, const MFSolutionData &soln)
	helper function that supports virtual print_variance_reduction(s)
void	r_and_N_to_N_vec (const RealVector &avg_eval_ratios, Real N_H, RealVector &N_vec)
void	r_and_N_to_design_vars (const RealVector &avg_eval_ratios, Real N_H, RealVector &cd_vars)
bool	ordered_approx_sequence (const RealVector &metric, SizetArray &approx_sequence, bool descending_keys=false)
	define approx_sequence in increasing metric order
bool	ordered_approx_sequence (const RealMatrix &metric, SizetArray &approx_sequence, bool descending_keys=false)
	define approx_sequence in increasing metric order
bool	ordered_approx_sequence (const RealMatrix &metric)
	determine whether metric is in increasing order by columns for all rows
bool	ordered_approx_sequence (const RealMatrix &metric, const UShortArray &approx_set)
	determine whether metric is in increasing order by active columns for all rows
void	raw_moments (const IntRealVectorMap &sum_H_baseline, const SizetArray &N_baseline, const IntRealMatrixMap &sum_L_shared, const Sizet2DArray &N_L_shared, const IntRealMatrixMap &sum_L_refined, const Sizet2DArray &N_L_refined, const RealVector2DArray &beta)
void	apply_control (Real sum_L_shared, size_t num_shared, Real sum_L_refined, size_t num_refined, Real beta, Real &H_raw_mom)
bool	active_set_for_model (size_t i)
	identify if there are activeSet requests for model i
void	inflate (size_t N_0D, SizetArray &N_1D)
	promote scalar to 1D array
void	inflate (size_t N_0D, SizetArray &N_1D, const UShortArray &approx_set)
	promote scalar to portion of 1D array
void	inflate (const SizetArray &N_1D, Sizet2DArray &N_2D)
	promote 1D array to 2D array
void	inflate (const SizetArray &N_1D, Sizet2DArray &N_2D, const UShortArray &approx_set)
	promote 1D array to active portion of 2D array
void	inflate (const RealVector &avg_eval_ratios, RealMatrix &eval_ratios)
	promote vector of averaged values to full matrix
void	inflate (Real r_i, size_t num_rows, Real *eval_ratios_col)
	promote scalar to column vector
void	inflate (const RealVector &vec, const BitArray &mask, RealVector &inflated_vec)
	promote active vector subset to full vector based on mask
void	deflate (const RealVector &vec, const BitArray &mask, RealVector &deflated_vec)
	demote full vector to active subset based on mask
void	deflate (const SizetArray &vec, const BitArray &mask, RealVector &deflated_vec)
	demote full vector to active subset based on mask
Real	nh_penalty_merit (const RealVector &c_vars, const RealVector &fn_vals)
	compute a penalty merit function after an optimization solve
Real	nh_penalty_merit (const MFSolutionData &soln)
	compute a penalty merit function after a MFSolutionData instance
Protected Member Functions inherited from NonDEnsembleSampling
virtual void	print_multimodel_summary (std::ostream &s, const String &summary_type, bool projections)
virtual void	print_multigroup_summary (std::ostream &s, const String &summary_type, bool projections)
void	post_run (std::ostream &s)
	post-run portion of run (optional); verbose to print results; re-implemented by Iterators that can read all Variables/Responses and perform final analysis phase in a standalone way More...
void	print_results (std::ostream &s, short results_state=FINAL_RESULTS)
	print the final iterator results More...
void	initialize_final_statistics ()
	initializes finalStatistics for storing NonD final results More...
void	update_final_statistics ()
	update finalStatistics::functionValues
bool	seed_updated ()
void	active_set_mapping ()
	in the case of sub-iteration, map from finalStatistics.active_set() requests to activeSet used in evaluate_parameter_sets() More...
void	recover_online_cost (const IntResponseMap &all_resp)
	recover estimates of simulation cost using aggregated response metadata spanning one batch of samples
void	recover_online_cost (const IntIntResponse2DMap &batch_resp_map)
	recover estimates of simulation cost using aggregated response metadata spanning multiple batches of samples
void	check_cost_options (const BitArray &cost_specs, const SizetSizetPairArray &cost_md_indices, short seq_type)
	enforce either a user cost specification or online cost recovery for each ACTIVE model within the sequence type
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 (SizetArray &N_l, const SizetArray &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	increment_sums (Real *sum_l, const Real *incr, size_t len)
	increment samples array with a shared scalar
void	compute_mc_estimator_variance (const RealVector &var_l, const SizetArray &N_l, RealVector &mc_est_var)
	compute the variance of the mean estimator (Monte Carlo sample average)
void	project_mc_estimator_variance (const RealVector &var_l, const SizetArray &N_l, size_t new_samp, RealVector &mc_est_var)
	compute the variance of the mean estimator (Monte Carlo sample average) after projection with additional samples (var_l remains fixed)
Real	estvar_ratios_to_avg_estvar (const RealVector &estvar_ratios, const RealVector &var_H, const SizetArray &N_H)
	convert estimator variance ratios to average estimator variance
void	reset_relaxation ()
	initialize relaxFactor prior to iteration
void	advance_relaxation ()
	update relaxFactor based on iteration number
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 (const Model &model, const String &tabular_filename)
	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
void	uncentered_to_centered (const RealMatrix &raw_mom, RealMatrix &cent_mom)
	convert uncentered (raw) moments to centered moments; biased estimators More...
void	centered_to_standard (const RealMatrix &cent_mom, RealMatrix &std_mom)
	convert centered moments to standardized moments 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, 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 samplerDriver 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 samplerDriver 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 samplerDriver 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 samplerDriver 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 samplerDriver
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
virtual bool	discrepancy_sample_counts () const
	flag identifying whether sample counts correspond to level discrepancies
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_1d_sequence (size_t &num_steps, size_t &secondary_index, short &seq_type)
	configure a one-dimensional hierarchical sequence (ML or MF) More...
void	configure_2d_sequence (size_t &num_steps, size_t &secondary_index, short &seq_type)
	configure a two-dimensional hierarchical sequence (MLMF) More...
void	configure_enumeration (size_t &num_combinations, short &seq_type)
	configure the total number of model form/resolution level options More...
short	configure_cost (size_t num_steps, short seq_type, RealVector &cost)
	extract cost estimates from model ensemble, enforcing requirements (case without metadata support)
short	configure_cost (size_t num_steps, short seq_type, RealVector &cost, SizetSizetPairArray &cost_md_indices)
	extract cost estimates from model ensemble, enforcing requirements (case with metadata support)
short	query_cost (size_t num_steps, short seq_type, RealVector &cost)
	optionally extract cost estimates from model ensemble, if available (case without metadata support)
short	query_cost (size_t num_steps, short seq_type, RealVector &cost, BitArray &model_cost_spec, const SizetSizetPairArray &cost_md_indices)
	optionally extract cost estimates from model ensemble, if available (case with metadata support)
void	test_cost (short seq_type, const BitArray &model_cost_spec, SizetSizetPairArray &cost_md_indices)
	check cost specification and metadata indices for each active model
bool	test_cost (bool cost_spec, SizetSizetPair &cost_md_indices, const String &model_id)
	check cost specification and metadata indices for a given model
bool	valid_cost (Real cost) const
	test cost for value > 0
bool	valid_costs (const RealVector &costs) const
	test costs 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_relax_round (Real diff, Real relax_factor=1.)
	compute a one-sided sample increment for multilevel methods to move current sampling level to a new target
size_t	one_sided_delta (Real current, Real target, Real relax_factor=1.)
	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, Real relax_factor=1., size_t power=1)
	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, Real relax_factor=1., size_t power=1)
	compute a one-sided sample increment for multilevel methods to move current sampling level to a new target
void	one_sided_delta (const SizetArray &current, const RealVector &targets, SizetArray &delta_N, Real relax_factor=1.)
	compute a one-sided sample increment vector to move current sampling levels to new targets
void	one_sided_delta (const Sizet2DArray &current, const RealVector &targets, SizetArray &delta_N, Real relax_factor=1.)
	compute a one-sided sample increment vector to move current sampling levels to new targets
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)
bool	zeros (const SizetArray &N_m) const
	return true if N_m is empty or only populated with zeros
bool	zeros (const Sizet2DArray &N_m) const
	return true if N_m is empty or only populated with zeros
bool	zeros (const SizetVector &N_m) const
	return true if N_m is empty or only populated with zeros
bool	homogeneous (const SizetArray &N_l) const
	return true if N_l has consistent values
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=true, bool log_best_flag=false)
	perform function evaluations to map parameter sets (allVariables) into response sets (allResponses) More...
void	evaluate_batch (Model &model, int batch_id, bool log_best_flag=false)
	perform function evaluations to map a keyed batch of parameter sets (allVariablesMap[key]) into a corresponding batch of response sets (allResponsesMap[key])
const IntIntResponse2DMap &	synchronize_batches (Model &model, bool log_best_flag=false)
	perform function evaluations to map a keyed batch of parameter sets (allVariablesMap[key]) into a corresponding batch of response sets (allResponsesMap[key])
void	clear_batches ()
	since synchronize returns the aggregation of all evaluated batches, we use a separate call to indicate when processing of this data is complete and bookkeeping can be cleared
void	get_vbd_parameter_sets (Model &model, size_t num_samples)
	generate replicate parameter sets for use in variance-based decomposition 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	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
RealMatrix	covLH
	covariances between each LF approximation and HF truth (the c vector in ACV); organized numFunctions x numApprox
RealSymMatrixArray	covLL
	covariances among all LF approximations (the C matrix in ACV); organized as a numFunctions array of symmetric numApprox x numApprox matrices
Protected Attributes inherited from NonDNonHierarchSampling
Iterator2DArray	varianceMinimizers
	the minimizer(s) used to optimize the estimator variance over the number of truth model samples and approximation eval_ratios. Minimizers are arranged in a sequence (first dimension) where each step in the sequence may have multiple competitors (second dimension)
SizetSizetPair	varMinIndices
	active indices for numerical solutions: varianceMinimizers[first][second]
unsigned short	mlmfSubMethod
	variance minimization algorithm selection: SUBMETHOD_MFMC or SUBMETHOD_ACV_{IS,MF,RD}
size_t	numGroups
	number of model groupings (pairings, pyramid levels, tensor-product enumerations) used for sample allocations
UShort2DArray	modelGroups
	the set of model groupings used by the estimator, e.g. ML BLUE
RealVector	modelGroupCost
	aggregate cost of a sample for each of a set of model groupings (i.e. modelGroups)
short	optSubProblemForm
	formulation for optimization sub-problem that minimizes R^2 subject to different variable sets and different linear/nonlinear constraints
unsigned short	optSubProblemSolver
	SQP or NIP.
bool	truthFixedByPilot
	user specification to suppress any increments in the number of HF evaluations (e.g., because too expensive and no more can be performed)
size_t	deltaNActualHF
	for sample projections, the calculated increment in HF samples that would be evaluated if full iteration/statistics were pursued
SizetArray	numHIter0
	number of successful pilot evaluations of HF truth model (exclude faults)
Protected Attributes inherited from NonDEnsembleSampling
short	sequenceType
	type of model sequence enumerated with primary MF/ACV loop over steps
RealVector	sequenceCost
	relative costs of model forms/resolution levels within a 1D sequence
size_t	numApprox
	number of approximation models managed by non-hierarchical iteratedModel
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, ONLINE_PILOT_PROJECTION, or OFFLINE_PILOT_PROJECTION
short	costSource
	indicates use of user-specified cost ratios, online cost recovery, or a combination
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
Real	relaxFactor
	the current relaxation factor applied to the predicted sample increment; in typical use, this is an under-relaxation factor to mitigate over-estimation of the sample allocation based on an initial approximation to response covariance data
size_t	relaxIndex
	index into relaxFactorSequence
RealVector	relaxFactorSequence
	a sequence of relaxation factors to use across ML/MF iterations (see DataMethod.hpp for usage notes)
Real	relaxRecursiveFactor
	a recursive relaxation factor (see DataMethod.hpp for usage notes)
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
std::unique_ptr< SamplerDriver >	samplerDriver
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()
IntIntVariables2DMap	batchVariablesMap
	alternate container for Variables samples supporting evaluate_batch() and synchronize_batches(), a 2D map with outer batch_id and inner eval_id
IntIntRealVector2DMap	batchSamplesMap
	alternate container for RealVector samples supporting evaluate_batch() and synchronize_batches(), a 2D map with outer batch_id and inner eval_id
IntIntResponse2DMap	batchResponsesMap
	alternate container for Response samples supporting evaluate_batch() and synchronize_batches(), a 2D map with outer batch_id and inner eval_id
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
bool	vbdFlag
	flag indicating the activation of variance-bsaed decomposition for computing Sobol' indices, via either PCE or sampling
Real	vbdDropTol
	tolerance for omitting output of small VBD indices computed via either PCE or sampling
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 Member Functions
void	approximate_control_variate_online_pilot ()
void	approximate_control_variate_offline_pilot ()
void	approximate_control_variate_pilot_projection ()
void	approx_increments (IntRealMatrixMap &sum_L_baseline, const SizetArray &N_H_actual, size_t N_H_alloc, IntRealMatrixMap &sum_L_refined, Sizet2DArray &N_L_actual_refined, SizetArray &N_L_alloc_refined, const MFSolutionData &soln)
void	overlay_peer_group_sums (const IntRealMatrixArrayMap &sum_G, const Sizet2DArray &N_G_actual, IntRealMatrixMap &sum_L_refined, Sizet2DArray &N_L_actual_refined)
void	update_model_groups ()
void	update_model_groups (const SizetArray &approx_sequence)
void	acv_raw_moments (const IntRealMatrixMap &sum_L_covar, const IntRealVectorMap &sum_H_covar, const IntRealSymMatrixArrayMap &sum_LL_covar, const IntRealMatrixMap &sum_LH_covar, const SizetArray &N_covar, const MFSolutionData &soln, RealVector2DArray &beta)
void	precompute_acv_controls (const RealVector &avg_eval_ratios)
void	compute_acv_control (const RealMatrix &sum_L_m, Real sum_H_mq, const RealSymMatrix &sum_LL_mq, const RealMatrix &sum_LH_m, size_t N_shared_q, size_t mom, size_t qoi, RealVector &beta)
void	analytic_initialization_from_mfmc (const RealMatrix &rho2_LH, Real avg_N_H, MFSolutionData &soln)
void	analytic_initialization_from_ensemble_cvmc (const RealMatrix &rho2_LH, Real avg_N_H, MFSolutionData &soln)
void	initialize_acv_counts (SizetArray &num_H, SizetSymMatrixArray &num_LL)
void	accumulate_acv_sums (RealMatrix &sum_L_baseline, RealVector &sum_H, RealSymMatrixArray &sum_LL, RealMatrix &sum_LH, RealVector &sum_HH, SizetArray &N_shared)
void	accumulate_acv_sums (IntRealMatrixMap &sum_L_baseline, IntRealSymMatrixArrayMap &sum_LL, Sizet2DArray &N_L_shared)
void	compute_LH_covariance (const RealMatrix &sum_L_shared, const RealVector &sum_H, const RealMatrix &sum_LH, const SizetArray &N_shared, RealMatrix &cov_LH)
void	compute_LL_covariance (const RealMatrix &sum_L_shared, const RealSymMatrixArray &sum_LL, const SizetArray &N_shared, RealSymMatrixArray &cov_LL)
void	compute_L_variance (const RealMatrix &sum_L, const RealSymMatrixArray &sum_LL, const SizetArray &num_L, RealMatrix &var_L)
void	compute_F_matrix (const RealVector &avg_eval_ratios, RealSymMatrix &F)
void	compute_C_F_c_f (const RealSymMatrix &C, const RealSymMatrix &F, const RealMatrix &c, size_t qoi, RealSymMatrix &C_F, RealVector &c_f)
void	solve_for_C_F_c_f (RealSymMatrix &C_F, RealVector &c_f, RealVector &lhs, bool copy_C_F=true, bool copy_c_f=true)
Real	solve_for_triple_product (const RealSymMatrix &C, const RealSymMatrix &F, const RealMatrix &c, size_t qoi)
Real	compute_R_sq (const RealSymMatrix &C, const RealSymMatrix &F, const RealMatrix &c, size_t qoi, Real var_H_q)
void	compute_allocations (const RealMatrix &var_L, MFSolutionData &soln)
void	acv_estvar_ratios (const RealSymMatrix &F, RealVector &estvar_ratios)
void	solve_for_acv_control (const RealSymMatrix &cov_LL, const RealSymMatrix &F, const RealMatrix &cov_LH, size_t qoi, RealVector &beta)

Private Attributes
UShortArray	approxSet
	ACV uses all approximations with in numApprox; this array supports this case for functions that are generalized to support approx subsets.
RealSymMatrix	FMat
	the "F" matrix from Gorodetsky JCP paper
MFSolutionData	acvSolnData
	final solution data for ACV (default DAG = {numApprox,...,numApprox})

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)
	convert uncentered (raw) moments to centered moments; unbiased estimators More...
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 (const Real *rm, Real *cm, size_t num_mom)
	convert uncentered (raw) moments to centered moments; biased 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	centered_to_standard (const Real *cm, Real *sm, size_t num_mom)
	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

Perform Approximate Control Variate Monte Carlo sampling for UQ.

Approximate Control Variate (ACV) 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

NonDACVSampling()

NonDACVSampling	(	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 NonDACVSampling::approxSet, ProblemDescDB::get_sza(), ProblemDescDB::get_ushort(), NonD::load_pilot_sample(), Iterator::maxEvalConcurrency, Iterator::maxFunctionEvals, NonDNonHierarchSampling::mlmfSubMethod, NonDEnsembleSampling::numApprox, NonDNonHierarchSampling::numGroups, NonDNonHierarchSampling::optSubProblemForm, NonDNonHierarchSampling::optSubProblemSolver, Iterator::outputLevel, NonDEnsembleSampling::pilotMgmtMode, NonDEnsembleSampling::pilotSamples, Dakota::SZ_MAX, and NonDNonHierarchSampling::truthFixedByPilot.

Member Function Documentation

core_run()

void core_run ( )

protectedvirtual

core portion of run; implemented by all derived classes and may include pre/post steps in lieu of separate pre/post

Virtual run function for the iterator class hierarchy. All derived classes need to redefine it.

Reimplemented from Iterator.

Reimplemented in NonDGenACVSampling.

References Dakota::abort_handler(), NonDACVSampling::approximate_control_variate_offline_pilot(), NonDACVSampling::approximate_control_variate_online_pilot(), NonDACVSampling::approximate_control_variate_pilot_projection(), NonDEnsembleSampling::costSource, NonDEnsembleSampling::finalStatsType, NonDNonHierarchSampling::mlmfSubMethod, NonDEnsembleSampling::numApprox, NonDSampling::numSamples, NonDEnsembleSampling::pilotMgmtMode, and NonDEnsembleSampling::pilotSamples.

accumulate_acv_sums() [1/5]

void accumulate_acv_sums ( IntRealMatrixMap &  sum_L_baseline, IntRealVectorMap &  sum_H, IntRealSymMatrixArrayMap &  sum_LL, IntRealMatrixMap &  sum_LH, RealVector &  sum_HH, SizetArray &  N_shared  )

protected

Multi-moment map-based version used by ACV following shared_increment()

References Response::active_set_request_vector(), Analyzer::allResponses, Response::function_values(), NonDEnsembleSampling::numApprox, and Analyzer::numFunctions.

Referenced by NonDACVSampling::accumulate_acv_sums(), NonDACVSampling::approximate_control_variate_offline_pilot(), NonDACVSampling::approximate_control_variate_online_pilot(), NonDGenACVSampling::generalized_acv_offline_pilot(), and NonDGenACVSampling::generalized_acv_online_pilot().

accumulate_acv_sums() [2/5]

void accumulate_acv_sums ( IntRealMatrixMap &  sum_L_refined, Sizet2DArray &  N_L_refined, const SizetArray &  approx_sequence, size_t  sequence_start, size_t  sequence_end  )

protected

This version used by ACV following approx_increment()

References NonDACVSampling::accumulate_acv_sums(), Response::active_set_request_vector(), Analyzer::allResponses, and Response::function_values().

accumulate_acv_sums() [3/5]

void accumulate_acv_sums ( IntRealMatrixMap &  sum_L, Sizet2DArray &  N_L_actual, const RealVector &  fn_vals, const ShortArray &  asv, size_t  approx  )

protected

This version used by ACV, GenACV following approx_increment()

References Analyzer::numFunctions.

update_projected_lf_samples()

void update_projected_lf_samples ( const MFSolutionData &  soln, const UShortArray &  approx_set, const SizetArray &  N_H_actual, size_t &  N_H_alloc, Real &  delta_equiv_hf  )

protected

LF only

References Dakota::average(), NonDEnsembleSampling::backfillFailures, NonDNonHierarchSampling::inflate(), NonD::one_sided_delta(), NonDEnsembleSampling::pilotMgmtMode, and NonDEnsembleSampling::sequenceCost.

Referenced by NonDACVSampling::approximate_control_variate_online_pilot(), NonDGenACVSampling::generalized_acv_online_pilot(), and NonDACVSampling::update_projected_samples().

update_projected_samples()

void update_projected_samples ( const MFSolutionData &  soln, const UShortArray &  approx_set, const SizetArray &  N_H_actual, size_t &  N_H_alloc, size_t &  delta_N_H_actual, Real &  delta_equiv_hf  )

protected

LF and HF

References Dakota::average(), NonDEnsembleSampling::backfillFailures, NonDEnsembleSampling::numApprox, NonD::one_sided_delta(), NonDEnsembleSampling::sequenceCost, and NonDACVSampling::update_projected_lf_samples().

Referenced by NonDACVSampling::approximate_control_variate_pilot_projection(), and NonDGenACVSampling::generalized_acv_pilot_projection().

approximate_control_variate_online_pilot()

void approximate_control_variate_online_pilot ( )

private

This function performs control variate MC across two combinations of model form and discretization level.

References NonDACVSampling::accumulate_acv_sums(), NonDACVSampling::acvSolnData, NonDEnsembleSampling::advance_relaxation(), Analyzer::allResponses, NonDACVSampling::approxSet, NonDEnsembleSampling::backfillFailures, NonDEnsembleSampling::costSource, NonDACVSampling::covLH, NonDACVSampling::covLL, NonDEnsembleSampling::deltaEquivHF, NonDEnsembleSampling::equivHFEvals, NonDEnsembleSampling::finalStatsType, NonDNonHierarchSampling::hf_indices(), NonDNonHierarchSampling::inflate(), Iterator::maxIterations, NonDEnsembleSampling::mlmfIter, NonDEnsembleSampling::NLevActual, NonDEnsembleSampling::NLevAlloc, Analyzer::numFunctions, NonDNonHierarchSampling::numGroups, NonDSampling::numSamples, NonD::one_sided_delta(), NonDEnsembleSampling::recover_online_cost(), NonDEnsembleSampling::relaxFactor, NonDEnsembleSampling::sequenceCost, NonDACVSampling::update_projected_lf_samples(), and NonDEnsembleSampling::varH.

Referenced by NonDACVSampling::core_run().

approximate_control_variate_offline_pilot()

void approximate_control_variate_offline_pilot ( )

private

This function performs control variate MC across two combinations of model form and discretization level.

References NonDACVSampling::accumulate_acv_sums(), NonDACVSampling::acvSolnData, NonDEnsembleSampling::costSource, NonDACVSampling::covLH, NonDACVSampling::covLL, NonDEnsembleSampling::equivHFEvals, NonDNonHierarchSampling::hf_indices(), NonDNonHierarchSampling::inflate(), NonDEnsembleSampling::mlmfIter, NonDEnsembleSampling::NLevActual, NonDEnsembleSampling::NLevAlloc, Analyzer::numFunctions, NonDNonHierarchSampling::numGroups, NonDSampling::numSamples, NonDEnsembleSampling::sequenceCost, and NonDEnsembleSampling::varH.

Referenced by NonDACVSampling::core_run().

approximate_control_variate_pilot_projection()

void approximate_control_variate_pilot_projection ( )

private

This function performs control variate MC across two combinations of model form and discretization level.

References NonDACVSampling::acvSolnData, NonDACVSampling::approxSet, NonDEnsembleSampling::costSource, NonDACVSampling::covLH, NonDACVSampling::covLL, NonDEnsembleSampling::deltaEquivHF, NonDNonHierarchSampling::deltaNActualHF, NonDNonHierarchSampling::hf_indices(), NonDEnsembleSampling::mlmfIter, NonDEnsembleSampling::NLevActual, NonDEnsembleSampling::NLevAlloc, Analyzer::numFunctions, NonDSampling::numSamples, NonDEnsembleSampling::pilotMgmtMode, NonDACVSampling::update_projected_samples(), and NonDEnsembleSampling::varH.

Referenced by NonDACVSampling::core_run().

accumulate_acv_sums() [4/5]

void accumulate_acv_sums ( RealMatrix &  sum_L_baseline, RealVector &  sum_H, RealSymMatrixArray &  sum_LL, RealMatrix &  sum_LH, RealVector &  sum_HH, SizetArray &  N_shared  )

private

Single moment version used by offline-pilot and pilot-projection ACV following shared_increment()

References Response::active_set_request_vector(), Analyzer::allResponses, Response::function_values(), NonDEnsembleSampling::numApprox, and Analyzer::numFunctions.

accumulate_acv_sums() [5/5]

void accumulate_acv_sums ( IntRealMatrixMap &  sum_L_shared, IntRealSymMatrixArrayMap &  sum_LL, Sizet2DArray &  N_L_shared  )

private

Multi-moment map-based version with fine-grained fault tolerance, used by ACV following shared_increment() void NonDACVSampling:: accumulate_acv_sums(IntRealMatrixMap& sum_L_baseline, IntRealVectorMap& sum_H, IntRealSymMatrixArrayMap& sum_LL, // L w/ itself + other L IntRealMatrixMap& sum_LH, // each L with H RealVector& sum_HH, Sizet2DArray& num_L_baseline, SizetArray& num_H, SizetSymMatrixArray& num_LL, Sizet2DArray& num_LH) { uses one set of allResponses with QoI aggregation across all Models, ordered by unorderedModels[i-1], i=1:numApprox --> truthModel

using std::isfinite; Real lf_fn, lf2_fn, hf_fn, lf_prod, lf2_prod, hf_prod; IntRespMCIter r_it; IntRVMIter h_it; IntRMMIter lb_it, lr_it, lh_it; IntRSMAMIter ll_it; int lb_ord, lr_ord, h_ord, ll_ord, lh_ord, active_ord, m; size_t qoi, approx, approx2, lf_index, lf2_index, hf_index; bool hf_is_finite;

for (r_it=allResponses.begin(); r_it!=allResponses.end(); ++r_it) { const Response& resp = r_it->second; const RealVector& fn_vals = resp.function_values(); const ShortArray& asv = resp.active_set_request_vector(); hf_index = numApprox * numFunctions;

for (qoi=0; qoi<numFunctions; ++qoi, ++hf_index) { hf_fn = fn_vals[hf_index]; hf_is_finite = isfinite(hf_fn); High accumulations: if (hf_is_finite) { // neither NaN nor +/-Inf ++num_H[qoi]; High-High: sum_HH[qoi] += hf_fn * hf_fn; // a single vector for ord 1 High: h_it = sum_H.begin(); h_ord = (h_it == sum_H.end()) ? 0 : h_it->first; hf_prod = hf_fn; active_ord = 1; while (h_ord) { if (h_ord == active_ord) { // support general key sequence h_it->second[qoi] += hf_prod; ++h_it; h_ord = (h_it == sum_H.end()) ? 0 : h_it->first; } hf_prod *= hf_fn; ++active_ord; } }

SizetSymMatrix& num_LL_q = num_LL[qoi]; for (approx=0; approx<numApprox; ++approx) { lf_index = approx * numFunctions + qoi; lf_fn = fn_vals[lf_index];

Low accumulations: if (isfinite(lf_fn)) { ++num_L_baseline[approx][qoi]; ++num_LL_q(approx,approx); // Diagonal of C matrix if (hf_is_finite) ++num_LH[approx][qoi]; // pull out of moment loop

lb_it = sum_L_baseline.begin(); ll_it = sum_LL.begin(); lh_it = sum_LH.begin(); lb_ord = (lb_it == sum_L_baseline.end()) ? 0 : lb_it->first; ll_ord = (ll_it == sum_LL.end()) ? 0 : ll_it->first; lh_ord = (lh_it == sum_LH.end()) ? 0 : lh_it->first; lf_prod = lf_fn; active_ord = 1; while (lb_ord || ll_ord || lh_ord) {

Low baseline if (lb_ord == active_ord) { // support general key sequence lb_it->second(qoi,approx) += lf_prod; ++lb_it; lb_ord = (lb_it == sum_L_baseline.end()) ? 0 : lb_it->first; } Low-Low if (ll_ord == active_ord) { // support general key sequence ll_it->second[qoi](approx,approx) += lf_prod * lf_prod; Off-diagonal of C matrix: look back (only) for single capture of each combination for (approx2=0; approx2<approx; ++approx2) { lf2_index = approx2 * numFunctions + qoi; lf2_fn = fn_vals[lf2_index];

if (isfinite(lf2_fn)) { // both are finite if (active_ord == 1) ++num_LL_q(approx,approx2); lf2_prod = lf2_fn; for (m=1; m<active_ord; ++m) lf2_prod *= lf2_fn; ll_it->second[qoi](approx,approx2) += lf_prod * lf2_prod; } } ++ll_it; ll_ord = (ll_it == sum_LL.end()) ? 0 : ll_it->first; } Low-High (c vector for each QoI): if (lh_ord == active_ord) { if (hf_is_finite) { hf_prod = hf_fn; for (m=1; m<active_ord; ++m) hf_prod *= hf_fn; lh_it->second(qoi,approx) += lf_prod * hf_prod; } ++lh_it; lh_ord = (lh_it == sum_LH.end()) ? 0 : lh_it->first; }

lf_prod *= lf_fn; ++active_ord; } } } } } }

Single moment version with fine-grained fault tolerance, used by offline-pilot and pilot-projection ACV following shared_increment() void NonDACVSampling:: accumulate_acv_sums(RealMatrix& sum_L_baseline, RealVector& sum_H, RealSymMatrixArray& sum_LL, // L w/ itself + other L RealMatrix& sum_LH, // each L with H RealVector& sum_HH, Sizet2DArray& num_L_baseline, SizetArray& num_H, SizetSymMatrixArray& num_LL, Sizet2DArray& num_LH) { uses one set of allResponses with QoI aggregation across all Models, ordered by unorderedModels[i-1], i=1:numApprox --> truthModel

using std::isfinite; Real lf_fn, lf2_fn, hf_fn; IntRespMCIter r_it; size_t qoi, approx, approx2, lf_index, lf2_index, hf_index; bool hf_is_finite;

for (r_it=allResponses.begin(); r_it!=allResponses.end(); ++r_it) { const Response& resp = r_it->second; const RealVector& fn_vals = resp.function_values(); const ShortArray& asv = resp.active_set_request_vector(); hf_index = numApprox * numFunctions;

for (qoi=0; qoi<numFunctions; ++qoi, ++hf_index) { hf_fn = fn_vals[hf_index]; hf_is_finite = isfinite(hf_fn); High accumulations: if (hf_is_finite) { // neither NaN nor +/-Inf ++num_H[qoi]; sum_H[qoi] += hf_fn; // High sum_HH[qoi] += hf_fn * hf_fn; // High-High }

SizetSymMatrix& num_LL_q = num_LL[qoi]; RealSymMatrix& sum_LL_q = sum_LL[qoi]; for (approx=0; approx<numApprox; ++approx) { lf_index = approx * numFunctions + qoi; lf_fn = fn_vals[lf_index];

Low accumulations: if (isfinite(lf_fn)) { ++num_L_baseline[approx][qoi]; sum_L_baseline(qoi,approx) += lf_fn; // Low

++num_LL_q(approx,approx); // Diagonal of C matrix sum_LL_q(approx,approx) += lf_fn * lf_fn; // Low-Low Off-diagonal of C matrix: look back (only) for single capture of each combination for (approx2=0; approx2<approx; ++approx2) { lf2_index = approx2 * numFunctions + qoi; lf2_fn = fn_vals[lf2_index]; if (isfinite(lf2_fn)) { // both are finite ++num_LL_q(approx,approx2); sum_LL_q(approx,approx2) += lf_fn * lf2_fn; } }

if (hf_is_finite) { ++num_LH[approx][qoi]; sum_LH(qoi,approx) += lf_fn * hf_fn;// Low-High (c vector)
} } } } } } This version used by ACV following shared_approx_increment()

References Response::active_set_request_vector(), Analyzer::allResponses, Response::function_values(), NonDEnsembleSampling::numApprox, and Analyzer::numFunctions.

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

• NonDACVSampling.hpp
• NonDACVSampling.cpp