Nonintrusive polynomial chaos expansion approaches to uncertainty quantification. More...

Inheritance diagram for NonDMultilevelPolynomialChaos:

Public Member Functions
	NonDMultilevelPolynomialChaos (ProblemDescDB &problem_db, Model &model)
	standard constructor More...

	NonDMultilevelPolynomialChaos (Model &model, short exp_coeffs_approach, const UShortArray &num_int_seq, const RealVector &dim_pref, short u_space_type, short refine_type, short refine_control, short covar_control, short ml_alloc_cntl, short ml_discrep, short rule_nest, short rule_growth, bool piecewise_basis, bool use_derivs)
	alternate constructor for numerical integration (tensor, sparse, cubature) More...

	NonDMultilevelPolynomialChaos (unsigned short method_name, Model &model, short exp_coeffs_approach, const UShortArray &exp_order_seq, const RealVector &dim_pref, const SizetArray &colloc_pts_seq, Real colloc_ratio, const SizetArray &seed_seq, short u_space_type, short refine_type, short refine_control, short covar_control, short ml_alloc_cntl, short ml_discrep, bool piecewise_basis, bool use_derivs, bool cv_flag, const String &import_build_pts_file, unsigned short import_build_format, bool import_build_active_only)
	alternate constructor for regression (least squares, CS, OLI) More...

	~NonDMultilevelPolynomialChaos ()
	destructor

Public Member Functions inherited from NonDPolynomialChaos
	NonDPolynomialChaos (ProblemDescDB &problem_db, Model &model)
	standard constructor More...

	NonDPolynomialChaos (Model &model, short exp_coeffs_approach, unsigned short num_int, const RealVector &dim_pref, short u_space_type, short refine_type, short refine_control, short covar_control, short rule_nest, short rule_growth, bool piecewise_basis, bool use_derivs, String exp_expansion_file="")
	alternate constructor for numerical integration (tensor, sparse, cubature) More...

	NonDPolynomialChaos (Model &model, short exp_coeffs_approach, unsigned short exp_order, const RealVector &dim_pref, size_t colloc_pts, Real colloc_ratio, int seed, short u_space_type, short refine_type, short refine_control, short covar_control, bool piecewise_basis, bool use_derivs, bool cv_flag, const String &import_build_pts_file, unsigned short import_build_format, bool import_build_active_only, String exp_expansion_file="")
	alternate constructor for regression (least squares, CS, OLI) More...

	NonDPolynomialChaos (Model &model, const String &exp_import_file, short u_space_type, const ShortShortPair &approx_view)
	alternate constructor for coefficient import More...

	~NonDPolynomialChaos ()
	destructor

bool	resize ()
	reinitializes iterator based on new variable size

Public Member Functions inherited from NonDExpansion
	NonDExpansion (ProblemDescDB &problem_db, Model &model)
	standard constructor

	NonDExpansion (unsigned short method_name, Model &model, const ShortShortPair &approx_view, short exp_coeffs_approach, const RealVector &dim_pref, int seed, short refine_type, short refine_control, short covar_control, Real colloc_ratio, short rule_nest, short rule_growth, bool piecewise_basis, bool use_derivs)
	alternate constructor

	~NonDExpansion ()
	destructor

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)

const Model &	algorithm_space_model () const

virtual void	append_expansion ()
	generate numSamplesOnModel, append to approximation data, and update QoI expansions

size_t	maximum_refinement_iterations () const
	return maxRefineIterations

void	maximum_refinement_iterations (size_t max_refine_iter)
	set maxRefineIterations

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

size_t	num_samples () const

virtual void	vary_pattern (bool pattern_flag)
	sets varyPattern in derived classes that support it

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	post_input ()
	read tabular data for post-run mode

virtual void	reset ()
	restore initial state for repeated sub-iterator executions

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 const RealSymMatrix &	response_error_estimates () const
	return error estimates associated with the final iterator solution

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 unsigned short	uses_method () const
	return name of any enabling iterator used by this iterator

virtual void	method_recourse (unsigned short method_name)
	perform a method switch, if possible, due to a detected conflict with the simultaneous use of method_name at an higher-level

virtual void	sampling_reset (size_t min_samples, bool all_data_flag, bool stats_flag)
	reset sampling iterator to use at least min_samples

virtual void	sampling_reference (size_t samples_ref)
	set reference number of samples, which is a lower bound during reset

virtual void	sampling_increment ()
	increment to next in sequence of refinement samples

virtual void	random_seed (int seed)
	set randomSeed, if present

virtual unsigned short	sampling_scheme () const
	return sampling name

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	initialize_u_space_model ()
	initialize uSpaceModel polynomial approximations with PCE/SC data

void	core_run ()
	perform a forward uncertainty propagation using PCE/SC methods

void	assign_specification_sequence ()
	assign the current values from the input specification sequence

void	increment_specification_sequence ()
	increment the input specification sequence and assign values More...

size_t	collocation_points () const
	return specification for number of collocation points (may be part of a sequence specification)

int	random_seed () const
	return specification for random seed (may be part of a sequence specification)

int	first_seed () const
	return first seed in sequence specification (defaults to random_seed())

void	initialize_ml_regression (size_t num_lev, bool &import_pilot)
	initializations for multilevel_regression()

void	infer_pilot_sample (size_t num_steps, SizetArray &delta_N_l)

void	increment_sample_sequence (size_t new_samp, size_t total_samp, size_t step)
	increment sequence in numSamplesOnModel for multilevel_regression()

void	compute_sample_increment (const RealVector &sparsity, const SizetArray &N_l, SizetArray &delta_N_l)
	compute delta_N_l for {RIP,RANK}_SAMPLING cases

void	print_results (std::ostream &s, short results_state=FINAL_RESULTS)
	print the final statistics

void	assign_allocation_control ()
	assign defaults related to allocation control (currently for ML regression approaches)

Protected Member Functions inherited from NonDPolynomialChaos
	NonDPolynomialChaos (unsigned short method_name, ProblemDescDB &problem_db, Model &model)
	base constructor for DB construction of multilevel/multifidelity PCE (method_name is not necessary, rather it is just a convenient overload allowing the derived ML PCE class to bypass the standard PCE ctor) More...

	NonDPolynomialChaos (unsigned short method_name, Model &model, short exp_coeffs_approach, const RealVector &dim_pref, short u_space_type, short refine_type, short refine_control, short covar_control, short ml_alloc_control, short ml_discrep, short rule_nest, short rule_growth, bool piecewise_basis, bool use_derivs)
	base constructor for lightweight construction of multifidelity PCE using numerical integration More...

	NonDPolynomialChaos (unsigned short method_name, Model &model, short exp_coeffs_approach, const RealVector &dim_pref, short u_space_type, short refine_type, short refine_control, short covar_control, const SizetArray &colloc_pts_seq, Real colloc_ratio, short ml_alloc_control, short ml_discrep, bool piecewise_basis, bool use_derivs, bool cv_flag)
	base constructor for lightweight construction of multilevel PCE using regression More...

void	derived_init_communicators (ParLevLIter pl_iter)
	derived class contributions to initializing the communicators associated with this Iterator instance

void	derived_set_communicators (ParLevLIter pl_iter)
	derived class contributions to setting the communicators associated with this Iterator instance

void	derived_free_communicators (ParLevLIter pl_iter)
	derived class contributions to freeing the communicators associated with this Iterator instance

void	resolve_inputs (short &u_space_type, short &data_order)
	perform error checks and mode overrides

void	initialize_u_space_model ()
	initialize uSpaceModel polynomial approximations with PCE/SC data

size_t	collocation_points () const
	return specification for number of collocation points (may be part of a sequence specification)

void	compute_expansion ()
	form the expansion by calling uSpaceModel.build_approximation()

void	select_refinement_points (const RealVectorArray &candidate_samples, unsigned short batch_size, RealMatrix &best_samples)
	evaluate allSamples for inclusion in the (PCE regression) approximation and retain the best set (well spaced) of size batch_size

void	select_refinement_points_deprecated (const RealVectorArray &candidate_samples, unsigned short batch_size, RealMatrix &best_samples)

void	append_expansion (const RealMatrix &samples, const IntResponseMap &resp_map)
	append new data to uSpaceModel and, when appropriate, update expansion order

void	update_samples_from_order_increment ()
	update numSamplesOnModel after an order increment

void	sample_allocation_metric (Real &sparsity_metric, Real power)
	accumulate one of the level metrics for {RIP,RANK}_SAMPLING cases

virtual void	post_run (std::ostream &s) override
	Inherit to allow on-the-fly instances to customize behavior.

void	print_results (std::ostream &s, short results_state=FINAL_RESULTS)
	print the final coefficients and final statistics

void	print_coefficients (std::ostream &s)
	print the PCE coefficient array for the orthogonal basis

void	export_coefficients ()
	export the PCE coefficient array to expansionExportFile

void	archive_coefficients ()
	archive the PCE coefficient array for the orthogonal basis

bool	config_integration (unsigned short quad_order, unsigned short ssg_level, unsigned short cub_int, Iterator &u_space_sampler, Model &g_u_model, String &approx_type)
	configure u_space_sampler and approx_type based on numerical integration specification

bool	config_expectation (size_t exp_samples, unsigned short sample_type, int seed, const String &rng, Iterator &u_space_sampler, Model &g_u_model, String &approx_type)
	configure u_space_sampler and approx_type based on expansion_samples specification

bool	config_regression (const UShortArray &exp_orders, size_t colloc_pts, Real colloc_ratio_order, short regress_type, short ls_regress_type, const UShortArray &tensor_grid_order, unsigned short sample_type, int seed, const String &rng, const String &pt_reuse, Iterator &u_space_sampler, Model &g_u_model, String &approx_type)
	configure u_space_sampler and approx_type based on regression specification

void	increment_order_from_grid ()
	define an expansion order that is consistent with an advancement in structured/unstructured grid level/density More...

void	ratio_samples_to_order (Real colloc_ratio, int num_samples, UShortArray &exp_order, bool less_than_or_equal)
	convert collocation ratio and number of samples to expansion order

Protected Member Functions inherited from NonDExpansion
virtual void	initialize_expansion ()
	initialize random variable definitions and final stats arrays

virtual void	finalize_expansion ()
	finalize mappings for the uSpaceModel

virtual void	update_expansion ()
	update an expansion; avoids overhead in compute_expansion() More...

virtual void	combined_to_active ()
	combine coefficients, promote to active, and update statsMetricMode

virtual void	push_increment ()
	helper function to manage different push increment cases

virtual void	pop_increment ()
	helper function to manage different pop increment cases

virtual Real	compute_covariance_metric (bool revert, bool print_metric)
	compute 2-norm of change in response covariance More...

virtual Real	compute_level_mappings_metric (bool revert, bool print_metric)
	compute 2-norm of change in final statistics More...

virtual void	compute_statistics (short results_state=FINAL_RESULTS)
	calculate analytic and numerical statistics from the expansion, supporting {REFINEMENT,INTERMEDIATE,FINAL}_RESULTS modes More...

virtual void	pull_candidate (RealVector &stats_star)
	extract statistics from native stats arrays for a selected candidate

virtual void	push_candidate (const RealVector &stats_star)
	restore statistics into native stats arrays for a selected candidate

virtual void	finalize_ml_regression ()
	finalizations for multilevel_regression()

virtual void	update_samples_from_order_decrement ()
	update (restore previous) numSamplesOnModel after an order decrement More...

virtual void	print_sobol_indices (std::ostream &s)
	print global sensitivity indices

void	initialize_response_covariance ()
	set covarianceControl defaults and shape respCovariance

void	update_final_statistics ()
	update function values within finalStatistics

void	update_final_statistics_gradients ()
	update function gradients within finalStatistics

void	assign_modes ()
	verify supported and define default correction / emulation modes

void	assign_surrogate_response_mode ()
	define the surrogate response mode for an ensemble model in multilevel/multifidelity expansions

void	initialize_u_space_grid ()
	helper for initializing a numerical integration grid

void	check_dimension_preference (const RealVector &dim_pref) const
	check length and content of dimension preference vector

void	construct_cubature (Iterator &u_space_sampler, Model &g_u_model, unsigned short cub_int_order)
	assign a NonDCubature instance within u_space_sampler

void	construct_quadrature (Iterator &u_space_sampler, Model &g_u_model, unsigned short quad_order, const RealVector &dim_pref)
	assign a NonDQuadrature instance within u_space_sampler based on a quad_order specification

void	construct_quadrature (Iterator &u_space_sampler, Model &g_u_model, unsigned short quad_order, const RealVector &dim_pref, int filtered_samples)
	assign a NonDQuadrature instance within u_space_sampler that generates a filtered tensor product sample set

void	construct_quadrature (Iterator &u_space_sampler, Model &g_u_model, unsigned short quad_order, const RealVector &dim_pref, int random_samples, int seed)
	assign a NonDQuadrature instance within u_space_sampler that samples randomly from a tensor product multi-index

void	construct_sparse_grid (Iterator &u_space_sampler, Model &g_u_model, unsigned short ssg_level, const RealVector &dim_pref)
	assign a NonDSparseGrid instance within u_space_sampler

void	configure_expansion_orders (unsigned short exp_order, const RealVector &dim_pref, UShortArray &exp_orders)
	configure exp_orders from inputs

void	configure_pecos_options ()
	configure expansion and basis configuration options for Pecos polynomial approximations

void	construct_expansion_sampler (unsigned short sample_type, const String &rng, unsigned short integration_refine=NO_INT_REFINE, const IntVector &refine_samples=IntVector(), const String &import_approx_file=String(), unsigned short import_approx_format=TABULAR_ANNOTATED, bool import_approx_active_only=false)
	construct the expansionSampler for evaluating samples on uSpaceModel

void	multifidelity_expansion ()
	construct a multifidelity expansion, across model forms or discretization levels

void	multilevel_regression ()
	allocate a multilevel expansion based on some approximation to an optimal resource allocation across model forms/discretization levels

void	configure_indices (size_t group, size_t form, size_t lev, short seq_type)
	configure response mode and active/truth/surrogate model keys within a hierarchical model. seq_type is the type of sequence that defines the active dimension for traversing a model sequence.

Real	sequence_cost (size_t step, const RealVector &cost)
	return aggregate cost (one or more models) for a level sample

void	compute_equivalent_cost (const SizetArray &N_l, const RealVector &cost)
	compute equivHFEvals from samples per level and cost per evaluation

void	compute_sample_increment (const RealVector &agg_var, const RealVector &cost, Real sum_root_var_cost, Real eps_sq_div_2, const SizetArray &N_l, SizetArray &delta_N_l)
	compute increment in samples for multilevel_regression() based on ESTIMATOR_VARIANCE

size_t	collocation_points (size_t index) const
	return number of collocation points for index within model sequence

int	seed_sequence (size_t index) const
	return random seed for index within model sequence More...

void	refine_expansion ()
	refine the reference expansion found by compute_expansion() using uniform/adaptive p-/h-refinement strategies

void	pre_refinement ()
	initialization of expansion refinement, if necessary

size_t	core_refinement (Real &metric, bool revert=false, bool print_metric=true)
	advance the refinement strategy one step

void	post_refinement (Real &metric, bool reverted=false)
	finalization of expansion refinement, if necessary

void	increment_grid (bool update_anisotropy=true)
	helper function to manage different grid increment cases

void	decrement_grid ()
	helper function to manage different grid decrement cases

void	merge_grid ()
	helper function to manage different grid merge cases

void	increment_order_and_grid ()
	uniformly increment the expansion order and structured/unstructured grid (PCE and FT) More...

void	decrement_order_and_grid ()
	uniformly decrement the expansion order and structured/unstructured grid (PCE and FT) More...

void	update_model_from_samples ()
	publish numSamplesOnModel update to the DataFitSurrModel instance

void	update_u_space_sampler (size_t sequence_index, const UShortArray &approx_orders)
	perform sampler updates after a change to numSamplesOnModel (shared code from ML/MF updaters)

void	refinement_statistics_mode (short stats_mode)
	update statsMetricMode, here and in Pecos::ExpansionConfigOptions

void	metric_roll_up (short results_state=FINAL_RESULTS)
	perform any required expansion roll-ups prior to metric computation

void	aggregate_variance (Real &agg_var_l)
	Aggregate variance across the set of QoI for a particular model level.

void	compute_covariance ()
	calculate the response covariance (diagonal or full matrix) for the expansion indicated by statsMetricMode

void	compute_active_covariance ()
	calculate the response covariance of the active expansion

void	compute_combined_covariance ()
	calculate the response covariance of the combined expansion

void	compute_active_diagonal_variance ()
	calculate the diagonal response variance of the active expansion

void	compute_combined_diagonal_variance ()
	calculate the diagonal response variance of the cmbined expansion

void	compute_off_diagonal_covariance ()
	calculate off diagonal terms in respCovariance(i,j) for j<i for the expansion indicated by statsMetricMode

void	compute_active_off_diagonal_covariance ()
	calculate off diagonal terms in respCovariance(i,j) for j<i using the active expansion coefficients

void	compute_combined_off_diagonal_covariance ()
	calculate off diagonal terms in respCovariance(i,j) for j<i using the combined expansion coefficients

void	compute_moments ()
	compute expansion moments; this uses a lightweight approach for incremental statistics (no additional moments; no finalStatistics update)

void	compute_level_mappings ()
	compute all analytic/numerical level mappings; this uses a lightweight approach for incremental statistics (no derivatives, no finalStatistics update)

void	compute_numerical_level_mappings ()
	compute only numerical level mappings; this uses a lightweight approach for incremental statistics (no derivatives, no finalStatistics update)

void	compute_sobol_indices ()
	compute Sobol' indices for main, interaction, and total effects; this is intended for incremental statistics

void	print_covariance (std::ostream &s)
	print resp{Variance,Covariance}

void	print_variance (std::ostream &s, const RealVector &resp_var, const String &prepend="")
	print resp_var (response variance vector) using optional pre-pend

void	print_covariance (std::ostream &s, const RealSymMatrix &resp_covar, const String &prepend="")
	print resp_covar (response covariance matrix) using optional pre-pend

void	archive_moments ()
	archive the central moments (numerical and expansion) to ResultsDB

void	archive_sobol_indices ()
	archive the Sobol' indices to the resultsDB

void	pull_reference (RealVector &stats_ref)

void	push_reference (const RealVector &stats_ref)

void	pull_lower_triangle (const RealSymMatrix &mat, RealVector &vec, size_t offset=0)
	pull lower triangle of symmetric matrix into vector

void	push_lower_triangle (const RealVector &vec, RealSymMatrix &mat, size_t offset=0)
	push vector into lower triangle of symmetric matrix

int	terms_ratio_to_samples (size_t num_exp_terms, Real colloc_ratio)
	convert number of regression terms and collocation ratio to a number of collocation samples

Real	terms_samples_to_ratio (size_t num_exp_terms, int samples)
	convert number of regression terms and number of collocation samples to a collocation ratio

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	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_final_statistics ()
	initializes finalStatistics for storing NonD final results More...

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	get_parameter_sets (Model &model)
	Generate one block of numSamples samples (ndim * num_samples), populating allSamples; ParamStudy is the only class that specializes to use allVariables.

virtual void	get_parameter_sets (Model &model, const size_t num_samples, RealMatrix &design_matrix)
	Generate one block of numSamples samples (ndim * num_samples), populating design_matrix.

virtual void	update_model_from_sample (Model &model, const Real *sample_vars)
	update model's current variables with data from sample

virtual void	update_model_from_variables (Model &model, const Variables &vars)
	update model's current variables with data from vars

virtual void	sample_to_variables (const Real *sample_vars, Variables &vars)
	convert column of samples array to variables; derived classes may reimplement for more than active continuous variables More...

void	update_from_model (const Model &model)
	set inherited data attributes based on extractions from incoming model

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

void	pre_output ()

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

virtual void	variables_to_sample (const Variables &vars, Real *sample_c_vars)
	convert the active continuous variables into a column of allSamples More...

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 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...

Private Member Functions
size_t	expansion_samples (size_t index) const

unsigned short	expansion_order (size_t index) const

unsigned short	quadrature_order (size_t index) const

unsigned short	sparse_grid_level (size_t index) const

size_t	expansion_samples () const

unsigned short	expansion_order () const

unsigned short	quadrature_order () const

unsigned short	sparse_grid_level () const

void	update_from_specification (bool update_exp, bool update_sampler, bool update_from_ratio)
	perform specification updates (shared code from

Private Attributes
UShortArray	expOrderSeqSpec
	user specification for expansion_order (array for multifidelity)

SizetArray	expSamplesSeqSpec
	user specification for expansion_samples (array for multifidelity)

UShortArray	quadOrderSeqSpec
	user request of quadrature order

UShortArray	ssgLevelSeqSpec
	user request of sparse grid level

size_t	sequenceIndex
	sequence index for {...}SeqSpec

Additional Inherited Members
Static Protected Member Functions inherited from Iterator
static void	gnewton_set_recast (const Variables &recast_vars, const ActiveSet &recast_set, ActiveSet &sub_model_set)
	conversion of request vector values for the Gauss-Newton Hessian approximation More...

Protected Attributes inherited from NonDPolynomialChaos
short	uSpaceType
	user requested expansion type

unsigned short	cubIntSpec
	cubature integrand

bool	crossValidation
	flag for use of cross-validation for selection of parameter settings in regression approaches

bool	crossValidNoiseOnly
	flag to restrict cross-validation to only estimate the noise tolerance in order to manage computational cost

unsigned short	maxCVOrderCandidates
	maximum number of expansion order candidates for cross-validation in regression-based PCE

bool	respScaling
	flag for scaling response data to [0,1] for alignment with regression tols

String	importBuildPointsFile
	user-specified file for importing build points

String	expansionImportFile
	filename for import of chaos coefficients

String	expansionExportFile
	filename for export of chaos coefficients

Protected Attributes inherited from NonDExpansion
Model	uSpaceModel
	Model representing the approximate response function in u-space, after u-space recasting and polynomial data fit recursions.

Iterator	expansionSampler
	Iterator used for sampling on the uSpaceModel to generate approximate probability/reliability/response level statistics. Currently this is an LHS sampling instance, but AIS could also be used.

Iterator	importanceSampler
	Iterator used to refine the approximate probability estimates generated by the expansionSampler using importance sampling.

short	expansionCoeffsApproach
	method for collocation point generation and subsequent calculation of the expansion coefficients

short	expansionBasisType
	type of expansion basis: DEFAULT_BASIS or Pecos::{NODAL,HIERARCHICAL}_INTERPOLANT for SC or Pecos::{TENSOR_PRODUCT,TOTAL_ORDER,ADAPTED}_BASIS for PCE regression

short	statsMetricMode
	type of statistical metric roll-up: {NO,ACTIVE,COMBINED}_EXPANSION_STATS

bool	relativeMetric
	flag indicating the use of relative scaling in refinement metrics

RealVector	dimPrefSpec
	user specification for dimension_preference

SizetArray	collocPtsSeqSpec
	user specification of number of initial samples per model instance, including adaptive cases where an optimal sample profile is the target of iteration (e.g., multilevel_regression())

Real	collocRatio
	factor applied to terms^termsOrder in computing number of regression points, either user-specified or inferred

Real	termsOrder
	exponent applied to number of expansion terms for computing number of regression points (usually 1)

int	randomSeed
	seed for random number generator (used for regression with LHS and sub-sampled tensor grids, as well as for expansionSampler)

SizetArray	randomSeedSeqSpec
	user specification for seed_sequence

bool	fixedSeed
	don't continue an existing random number sequence, rather reset seed each time within some sampling-based iteration

size_t	mlmfIter
	top level iteration counter in adaptive NonDExpansion ML/MF algorithms, allowing special updating logic for some sequence handlers

bool	allVars
	flag for combined variable expansions which include a non-probabilistic subset (design, epistemic, state)

bool	tensorRegression
	option for regression FT using a filtered set of tensor-product quadrature points

short	multilevAllocControl
	type of sample allocation scheme for discretization levels / model forms within multilevel / multifidelity methods

short	multilevDiscrepEmulation
	emulation approach for multilevel / multifidelity discrepancy: distinct or recursive

SizetArray	NLev
	number of samples allocated to each level of a discretization/model hierarchy within multilevel/multifidelity methods

Real	equivHFEvals
	equivalent number of high fidelity evaluations accumulated using samples across multiple model forms and/or discretization levels

Real	kappaEstimatorRate
	rate parameter for allocation by ESTIMATOR_VARIANCE in multilevel_regression()

Real	gammaEstimatorScale
	scale parameter for allocation by ESTIMATOR_VARIANCE in multilevel_regression()

int	numSamplesOnModel
	number of truth samples performed on g_u_model to form the expansion

int	numSamplesOnExpansion
	number of approximation samples performed on the polynomial expansion in order to estimate probabilities

bool	nestedRules
	flag for indicating state of `nested` and `non_nested` overrides of default rule nesting, which depends on the type of integration driver; this is defined in construct_{quadrature,sparse_grid}(), such that override attributes (defined in ctors) must be used upstream

short	ruleNestingOverride
	user override of default rule nesting: NO_NESTING_OVERRIDE, NESTED, or NON_NESTED

short	ruleGrowthOverride
	user override of default rule growth: NO_GROWTH_OVERRIDE, RESTRICTED, or UNRESTRICTED

bool	piecewiseBasis
	flag for `piecewise` specification, indicating usage of local basis polynomials within the stochastic expansion

bool	useDerivs
	flag for `use_derivatives` specification, indicating usage of derivative data (with respect to expansion variables) to enhance the calculation of the stochastic expansion. More...

RealVector	initialPtU
	stores the initial variables data in u-space

short	refineType
	refinement type: NO_REFINEMENT, P_REFINEMENT, or H_REFINEMENT

short	refineControl
	refinement control: NO_CONTROL, UNIFORM_CONTROL, LOCAL_ADAPTIVE_CONTROL, DIMENSION_ADAPTIVE_CONTROL_SOBOL, DIMENSION_ADAPTIVE_CONTROL_DECAY, or DIMENSION_ADAPTIVE_CONTROL_GENERALIZED

short	refineMetric
	refinement metric: NO_METRIC, COVARIANCE_METRIC, LEVEL_STATS_METRIC, or MIXED_STATS_METRIC

short	covarianceControl
	enumeration for controlling response covariance calculation and output: {DEFAULT,DIAGONAL,FULL}_COVARIANCE

unsigned short	softConvLimit
	number of consecutive iterations within tolerance required to indicate soft convergence

RealSymMatrix	respCovariance
	symmetric matrix of analytic response covariance (full response covariance option)

RealVector	respVariance
	vector of response variances (diagonal response covariance option)

RealVector	statsStar
	stats of the best refinement candidate for the current model indices

size_t	numUncertainQuant
	number of invocations of core_run()

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

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

Nonintrusive polynomial chaos expansion approaches to uncertainty quantification.

The NonDMultilevelPolynomialChaos class uses a polynomial chaos expansion (PCE) approach to approximate the effect of parameter uncertainties on response functions of interest. It utilizes the OrthogPolyApproximation class to manage multiple types of orthogonal polynomials within a Wiener-Askey scheme to PCE. It supports PCE coefficient estimation via sampling, quadrature, point-collocation, and file import.

Constructor & Destructor Documentation

◆ NonDMultilevelPolynomialChaos() [1/3]

NonDMultilevelPolynomialChaos	(	ProblemDescDB &	problem_db,
		Model &	model
	)

standard constructor

This constructor is called for a standard letter-envelope iterator instantiation using the ProblemDescDB.

References Dakota::abort_handler(), Response::active_set(), NonDMultilevelPolynomialChaos::assign_allocation_control(), NonDExpansion::assign_modes(), Model::assign_rep(), NonDMultilevelPolynomialChaos::collocation_points(), ParallelLibrary::command_line_check(), NonDPolynomialChaos::config_expectation(), NonDPolynomialChaos::config_integration(), NonDPolynomialChaos::config_regression(), NonDExpansion::configure_expansion_orders(), NonDExpansion::construct_expansion_sampler(), NonDPolynomialChaos::cubIntSpec, Model::current_response(), Model::current_variables(), ActiveSet::derivative_vector(), NonDExpansion::dimPrefSpec, ProblemDescDB::get_bool(), ProblemDescDB::get_iv(), ProblemDescDB::get_real(), ProblemDescDB::get_short(), ProblemDescDB::get_string(), ProblemDescDB::get_sza(), ProblemDescDB::get_usa(), ProblemDescDB::get_ushort(), NonDPolynomialChaos::importBuildPointsFile, NonDMultilevelPolynomialChaos::initialize_u_space_model(), Iterator::iteratedModel, NonDExpansion::numSamplesOnModel, Iterator::outputLevel, Iterator::parallelLib, Iterator::probDescDB, Model::qoi(), NonDMultilevelPolynomialChaos::random_seed(), NonDExpansion::randomSeedSeqSpec, NonDPolynomialChaos::resolve_inputs(), NonDExpansion::uSpaceModel, NonDPolynomialChaos::uSpaceType, and Variables::view().

◆ NonDMultilevelPolynomialChaos() [2/3]

NonDMultilevelPolynomialChaos	(	Model &	model,
		short	exp_coeffs_approach,
		const UShortArray &	num_int_seq,
		const RealVector &	dim_pref,
		short	u_space_type,
		short	refine_type,
		short	refine_control,
		short	covar_control,
		short	ml_alloc_control,
		short	ml_discrep,
		short	rule_nest,
		short	rule_growth,
		bool	piecewise_basis,
		bool	use_derivs
	)

alternate constructor for numerical integration (tensor, sparse, cubature)

This constructor is used for helper iterator instantiation on the fly that employ numerical integration (quadrature, sparse grid, cubature).

References Dakota::abort_handler(), Response::active_set(), NonDMultilevelPolynomialChaos::assign_allocation_control(), NonDExpansion::assign_modes(), Model::assign_rep(), NonDPolynomialChaos::config_integration(), NonDPolynomialChaos::cubIntSpec, Model::current_response(), Model::current_variables(), ActiveSet::derivative_vector(), NonDMultilevelPolynomialChaos::initialize_u_space_model(), Iterator::iteratedModel, Iterator::outputLevel, Model::qoi(), NonDMultilevelPolynomialChaos::quadOrderSeqSpec, NonDPolynomialChaos::resolve_inputs(), NonDMultilevelPolynomialChaos::sequenceIndex, NonDMultilevelPolynomialChaos::ssgLevelSeqSpec, NonDExpansion::uSpaceModel, NonDPolynomialChaos::uSpaceType, and Variables::view().

◆ NonDMultilevelPolynomialChaos() [3/3]

NonDMultilevelPolynomialChaos	(	unsigned short	method_name,
		Model &	model,
		short	exp_coeffs_approach,
		const UShortArray &	exp_order_seq,
		const RealVector &	dim_pref,
		const SizetArray &	colloc_pts_seq,
		Real	colloc_ratio,
		const SizetArray &	seed_seq,
		short	u_space_type,
		short	refine_type,
		short	refine_control,
		short	covar_control,
		short	ml_alloc_control,
		short	ml_discrep,
		bool	piecewise_basis,
		bool	use_derivs,
		bool	cv_flag,
		const String &	import_build_pts_file,
		unsigned short	import_build_format,
		bool	import_build_active_only
	)

alternate constructor for regression (least squares, CS, OLI)

This constructor is used for helper iterator instantiation on the fly that employ regression (least squares, CS, OLI).

References Response::active_set(), NonDMultilevelPolynomialChaos::assign_allocation_control(), NonDExpansion::assign_modes(), Model::assign_rep(), NonDMultilevelPolynomialChaos::collocation_points(), NonDPolynomialChaos::config_regression(), NonDExpansion::configure_expansion_orders(), Model::current_response(), Model::current_variables(), ActiveSet::derivative_vector(), NonDExpansion::dimPrefSpec, NonDMultilevelPolynomialChaos::initialize_u_space_model(), Iterator::iteratedModel, Iterator::outputLevel, Model::qoi(), NonDMultilevelPolynomialChaos::random_seed(), NonDExpansion::randomSeedSeqSpec, NonDPolynomialChaos::resolve_inputs(), NonDExpansion::uSpaceModel, NonDPolynomialChaos::uSpaceType, and Variables::view().

Member Function Documentation

◆ increment_specification_sequence()

void increment_specification_sequence ( )

protectedvirtual

increment the input specification sequence and assign values

Default implementation redefined by Multilevel derived classes.

Reimplemented from NonDExpansion.

References Dakota::abort_handler(), NonDExpansion::collocPtsSeqSpec, NonDExpansion::expansionCoeffsApproach, NonDMultilevelPolynomialChaos::expOrderSeqSpec, NonDMultilevelPolynomialChaos::expSamplesSeqSpec, Iterator::iterator_rep(), NonDExpansion::numSamplesOnModel, NonDMultilevelPolynomialChaos::quadOrderSeqSpec, NonDExpansion::randomSeedSeqSpec, NonDMultilevelPolynomialChaos::sequenceIndex, NonDMultilevelPolynomialChaos::ssgLevelSeqSpec, Model::subordinate_iterator(), NonDMultilevelPolynomialChaos::update_from_specification(), and NonDExpansion::uSpaceModel.

◆ infer_pilot_sample()

void infer_pilot_sample	(	size_t	num_steps,
		SizetArray &	delta_N_l
	)

protectedvirtual

Default implementation redefined by Multilevel derived classes.

Reimplemented from NonDExpansion.

References NonDExpansion::collocRatio, NonDExpansion::configure_expansion_orders(), NonDExpansion::dimPrefSpec, NonDExpansion::expansionBasisType, and NonDExpansion::terms_ratio_to_samples().

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

NonDMultilevelPolynomialChaos.hpp
NonDMultilevelPolynomialChaos.cpp

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members