Dakota  Version Explore and Predict with Confidence
NonDPolynomialChaos Class Reference

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

Inheritance diagram for NonDPolynomialChaos:

## Public Member Functions

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 ()
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, 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)

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

const Modelalgorithm_space_model () const

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

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

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

virtual void assign_discrepancy_mode ()
verify supported and define default discrepancy emulation mode

virtual void assign_hierarchical_response_mode ()
define the surrogate response mode for a hierarchical model in multilevel/multifidelity expansions

virtual void infer_pilot_sample (size_t num_steps, SizetArray &delta_N_l)

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 variable_bounds (const RealVector &cv_lower_bnds, const RealVector &cv_upper_bnds)
assign nonlinear inequality and equality constraint allowables for this iterator (user-functions mode for which Model updating is not used)

virtual void linear_constraints (const RealMatrix &lin_ineq_coeffs, const RealVector &lin_ineq_lb, const RealVector &lin_ineq_ub, const RealMatrix &lin_eq_coeffs, const RealVector &lin_eq_tgt)
assign linear inequality and linear equality constraints for this iterator (user-functions mode for which Model updating is not used)

virtual void nonlinear_constraints (const RealVector &nln_ineq_lb, const RealVector &nln_ineq_ub, const RealVector &nln_eq_tgt)
assign nonlinear inequality and equality constraint allowables for this iterator (user-functions mode for which Model updating is not used)

virtual void initialize_graphics (int iterator_server_id=1)
initialize the 2D graphics window and the tabular graphics data More...

virtual void check_sub_iterator_conflict ()
detect any conflicts due to recursive use of the same Fortran solver More...

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

virtual void method_recourse ()
perform a method switch, if possible, due to a detected conflict

virtual void sampling_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)

Modeliterated_model ()
return the iteratedModel (iterators & meta-iterators using a single model instance)

ProblemDescDBproblem_description_db () const
return the problem description database (probDescDB)

ParallelLibraryparallel_library () const
return the parallel library (parallelLib)

void method_name (unsigned short m_name)
set the method name to an enumeration value

unsigned short method_name () const
return the method name via its native enumeration value

void method_string (const String &m_str)
set the method name by string

String method_string () const
return the method name by string

String method_enum_to_string (unsigned short method_enum) const
convert a method name enumeration value to a string

unsigned short method_string_to_enum (const String &method_str) const
convert a method name string to an enumeration value

String submethod_enum_to_string (unsigned short submethod_enum) const
convert a sub-method name enumeration value to a string

const String & method_id () const
return the method identifier (methodId)

int maximum_evaluation_concurrency () const
return the maximum evaluation concurrency supported by the iterator

void maximum_evaluation_concurrency (int max_conc)
set the maximum evaluation concurrency supported by the iterator

size_t maximum_iterations () const
return the maximum iterations for this iterator

void maximum_iterations (size_t max_iter)
set the maximum iterations for this iterator

void convergence_tolerance (Real conv_tol)
set the method convergence tolerance (convergenceTol)

Real convergence_tolerance () const
return the method convergence tolerance (convergenceTol)

void output_level (short out_lev)
set the method output level (outputLevel)

short output_level () const
return the method output level (outputLevel)

void summary_output (bool summary_output_flag)
Set summary output control; true enables evaluation/results summary.

size_t num_final_solutions () const
return the number of solutions to retain in best variables/response arrays

void num_final_solutions (size_t num_final)
set the number of solutions to retain in best variables/response arrays

void active_set (const ActiveSet &set)
set the default active set (for use with iterators that employ evaluate_parameter_sets())

const ActiveSetactive_set () const
return the default active set (used by iterators that employ evaluate_parameter_sets())

void active_set_request_vector (const ShortArray &asv)
return the default active set request vector (used by iterators that employ evaluate_parameter_sets())

const ShortArray & active_set_request_vector () const
return the default active set request vector (used by iterators that employ evaluate_parameter_sets())

void active_set_request_values (short asv_val)
return the default active set request vector (used by iterators that employ evaluate_parameter_sets())

void sub_iterator_flag (bool si_flag)
set subIteratorFlag (and update summaryOutputFlag if needed)

bool is_null () const
function to check iteratorRep (does this envelope contain a letter?)

std::shared_ptr< Iteratoriterator_rep () const
returns iteratorRep for access to derived class member functions that are not mapped to the top Iterator level

virtual void eval_tag_prefix (const String &eval_id_str)
set the hierarchical eval ID tag prefix More...

std::shared_ptr< TraitsBasetraits () const
returns methodTraits for access to derived class member functions that are not mapped to the top TraitsBase level

bool top_level ()
Return whether the iterator is the top level iterator.

void top_level (bool tflag)
Set the iterator's top level flag.

## Protected Member Functions

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

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

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

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

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

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 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)

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, 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 Responseresponse_results () const
return the final statistics from the nondeterministic iteration

void response_results_active_set (const ActiveSet &set)
set the active set within finalStatistics

virtual void initialize_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_sequence (size_t &num_steps, size_t &secondary_index, short &seq_type)
configure fidelity/level counts from model hierarchy More...

void configure_cost (unsigned short num_steps, bool multilevel, RealVector &cost)
extract cost estimates from model hierarchy (forms or resolutions)

bool query_cost (unsigned short num_steps, bool multilevel, RealVector &cost)
extract cost estimates from model hierarchy, if available

bool query_cost (unsigned short num_steps, Model &model, RealVector &cost)
extract cost estimates from model hierarchy, if available

bool valid_cost_values (const RealVector &cost)
test cost for valid values > 0

void load_pilot_sample (const SizetArray &pilot_spec, size_t num_steps, SizetArray &delta_N_l)
distribute pilot sample specification across model forms or levels

void load_pilot_sample (const SizetArray &pilot_spec, short seq_type, const Sizet3DArray &N_l, Sizet2DArray &delta_N_l)
distribute pilot sample specification across model forms and levels

template<typename ArrayType >
void inflate_approx_samples (const ArrayType &N_l, bool multilev, size_t secondary_index, std::vector< ArrayType > &N_l_vec)
update the relevant slice of N_l_3D from the final 2D multilevel or 2D multifidelity sample profile

template<typename ArrayType >
void inflate_sequence_samples (const ArrayType &N_l, bool multilev, size_t secondary_index, std::vector< ArrayType > &N_l_vec)
update the relevant slice of N_l_3D from the final 2D multilevel or 2D multifidelity sample profile

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 initialize_level_mappings ()
size computed{Resp,Prob,Rel,GenRel}Levels

void compute_densities (const RealRealPairArray &min_max_fns, bool prob_refinement=false, bool all_levels_computed=false)
compute the PDF bins from the CDF/CCDF values and store in computedPDF{Abscissas,Ordinates} More...

void print_densities (std::ostream &s) const
output the PDFs reflected in computedPDF{Abscissas,Ordinates} using default qoi_type and pdf_labels

void print_densities (std::ostream &s, String qoi_type, const StringArray &pdf_labels) const
output the PDFs reflected in computedPDF{Abscissas,Ordinates}

void print_system_mappings (std::ostream &s) const
print system series/parallel mappings for response levels

void print_multilevel_evaluation_summary (std::ostream &s, const SizetArray &N_m)
print evaluation summary for multilevel sampling across 1D level profile

void print_multilevel_evaluation_summary (std::ostream &s, const Sizet2DArray &N_m)
print evaluation summary for multilevel sampling across 2D level+QoI profile

void print_multilevel_discrepancy_summary (std::ostream &s, const SizetArray &N_m)
print evaluation summary for multilevel sampling across 1D level profile for discrepancy across levels

void print_multilevel_discrepancy_summary (std::ostream &s, const SizetArray &N_m, const SizetArray &N_mp1)
print evaluation summary for multilevel sampling across 1D level profile for discrepancy across model forms

void print_multilevel_discrepancy_summary (std::ostream &s, const Sizet2DArray &N_m)
print evaluation summary for multilevel sampling across 2D level+QoI profile for discrepancy across levels

void print_multilevel_discrepancy_summary (std::ostream &s, const Sizet2DArray &N_m, const Sizet2DArray &N_mp1)
print evaluation summary for multilevel sampling across 2D level+QoI profile for discrepancy across model forms

template<typename ArrayType >
void print_multilevel_model_summary (std::ostream &s, const std::vector< ArrayType > &N_samp, String type, short seq_type, bool discrep_flag)
print evaluation summary for multilevel sampling across 2D model+level profile (allocations) or 3D model+level+QoI profile (actual)

void construct_lhs (Iterator &u_space_sampler, Model &u_model, unsigned short sample_type, int num_samples, int seed, const String &rng, bool vary_pattern, short sampling_vars_mode=ACTIVE)
assign a NonDLHSSampling instance within u_space_sampler

unsigned short sub_optimizer_select (unsigned short requested_sub_method, unsigned short default_sub_method=SUBMETHOD_NPSOL)
utility for vetting sub-method request against optimizers within the package configuration

size_t one_sided_delta (Real current, Real target)
compute a one-sided sample increment for multilevel methods to move current sampling level to a new target

size_t one_sided_delta (const SizetArray &current, const RealVector &targets, size_t power)
compute a one-sided sample increment for multilevel methods to move current sampling level to a new target

size_t one_sided_delta (const SizetArray &current, Real target, size_t power)
compute a one-sided sample increment for multilevel methods to move current sampling level to a new target

bool differ (size_t N_alloc_ij, const SizetArray &N_actual_ij) const
return true if fine-grained reporting differs from coarse-grained

bool differ (const SizetArray &N_alloc_i, const Sizet2DArray &N_actual_i) const
return true if fine-grained reporting differs from coarse-grained

bool differ (const Sizet2DArray &N_alloc, const Sizet3DArray &N_actual) const
return true if fine-grained reporting differs from coarse-grained

void archive_allocate_mappings ()
allocate results array storage for distribution mappings

void archive_from_resp (size_t fn_index, size_t inc_id=0)
archive the mappings from specified response levels for specified fn

void archive_to_resp (size_t fn_index, size_t inc_id=0)
archive the mappings to computed response levels for specified fn and (optional) increment id.

void archive_allocate_pdf ()
allocate results array storage for pdf histograms

void archive_pdf (size_t fn_index, size_t inc_id=0)
archive a single pdf histogram for specified function

void archive_equiv_hf_evals (const Real equiv_hf_evals)
archive the equivalent number of HF evals (used by ML/MF methods)

Protected Member Functions inherited from Analyzer
Analyzer ()
default constructor

Analyzer (ProblemDescDB &problem_db, Model &model)
standard constructor

Analyzer (unsigned short method_name, Model &model)
alternate constructor for instantiations "on the fly" with a Model

Analyzer (unsigned short method_name)
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 Variablesvariables_results () const
return a single final iterator solution (variables)

const VariablesArray & variables_array_results ()
return multiple final iterator solutions (variables). This should only be used if returns_multiple_points() returns true.

const ResponseArray & response_array_results ()
return multiple final iterator solutions (response). This should only be used if returns_multiple_points() returns true.

bool compact_mode () const
returns Analyzer::compactMode

bool returns_multiple_points () const
indicates if this iterator returns multiple final points. Default return is false. Override to return true if appropriate.

void evaluate_parameter_sets (Model &model, bool log_resp_flag, bool log_best_flag)
perform function evaluations to map parameter sets (allVariables) into response sets (allResponses) More...

void get_vbd_parameter_sets (Model &model, size_t num_samples)
generate replicate parameter sets for use in variance-based decomposition More...

void compute_vbd_stats (const size_t num_samples, const IntResponseMap &resp_samples)
compute VBD-based Sobol indices More...

void archive_sobol_indices () const
archive VBD-based Sobol indices More...

virtual void archive_model_variables (const Model &, size_t idx) const
archive model evaluation points

virtual void archive_model_response (const Response &, size_t idx) const
archive model evaluation responses

void read_variables_responses (int num_evals, size_t num_vars)
convenience function for reading variables/responses (used in derived classes post_input) More...

void print_sobol_indices (std::ostream &s) const
Printing of VBD results. More...

void samples_to_variables_array (const RealMatrix &sample_matrix, VariablesArray &vars_array)
convert samples array to variables array; e.g., allSamples to allVariables

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...

## Protected Attributes

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

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
NonDprevNondInstance
pointer containing previous value of nondInstance

size_t startCAUV
starting index of continuous aleatory uncertain variables within active continuous variables (convenience for managing offsets)

size_t numCAUV
number of active continuous aleatory uncertain variables

bool epistemicStats
flag for computing interval-type metrics instead of integrated metrics If any epistemic vars are active in a metric evaluation, then flag is set.

RealMatrix momentStats
standardized or central resp moments, as determined by finalMomentsType. Calculated in compute_moments()) and indexed as (moment,fn).

RealVectorArray requestedRespLevels
requested response levels for all response functions

RealVectorArray computedProbLevels
output probability levels for all response functions resulting from requestedRespLevels

RealVectorArray computedRelLevels
output reliability levels for all response functions resulting from requestedRespLevels

RealVectorArray computedGenRelLevels
output generalized reliability levels for all response functions resulting from requestedRespLevels

short respLevelTarget
indicates mapping of z->p (PROBABILITIES), z->beta (RELIABILITIES), or z->beta* (GEN_RELIABILITIES)

short respLevelTargetReduce
indicates component or system series/parallel failure metrics

RealVectorArray requestedProbLevels
requested probability levels for all response functions

RealVectorArray requestedRelLevels
requested reliability levels for all response functions

RealVectorArray requestedGenRelLevels
requested generalized reliability levels for all response functions

RealVectorArray computedRespLevels
output response levels for all response functions resulting from requestedProbLevels, requestedRelLevels, or requestedGenRelLevels

size_t totalLevelRequests
total number of levels specified within requestedRespLevels, requestedProbLevels, and requestedRelLevels

bool cdfFlag
flag for type of probabilities/reliabilities used in mappings: cumulative/CDF (true) or complementary/CCDF (false)

bool pdfOutput
flag for managing output of response probability density functions (PDFs)

RealVectorArray computedPDFAbscissas
sorted response PDF intervals bounds extracted from min/max sample and requested/computedRespLevels (vector lengths = num bins + 1)

RealVectorArray computedPDFOrdinates
response PDF densities computed from bin counts divided by (unequal) bin widths (vector lengths = num bins)

Response finalStatistics
final statistics from the uncertainty propagation used in strategies: response means, standard deviations, and probabilities of failure

short finalMomentsType
type of moments logged within finalStatistics: none, central, standard

size_t miPLIndex
index for the active ParallelLevel within ParallelConfiguration::miPLIters

BitArray pdfComputed
Whether PDF was computed for function i; used to determine whether a pdf should be archived.

Protected Attributes inherited from Analyzer
size_t numFunctions
number of response functions

size_t numContinuousVars
number of active continuous vars

size_t numDiscreteIntVars
number of active discrete integer vars

size_t numDiscreteStringVars
number of active discrete string vars

size_t numDiscreteRealVars
number of active discrete real vars

bool compactMode
switch for allSamples (compact mode) instead of allVariables (normal mode)

VariablesArray allVariables
array of all variables to be evaluated in evaluate_parameter_sets()

RealMatrix allSamples
compact alternative to allVariables

IntResponseMap allResponses
array of all responses to be computed in evaluate_parameter_sets()

array of headers to insert into output while evaluating allVariables

size_t numObjFns
number of objective functions

size_t numLSqTerms
number of least squares terms

RealPairPRPMultiMap bestVarsRespMap
map which stores best set of solutions

Protected Attributes inherited from Iterator
ProblemDescDBprobDescDB
class member reference to the problem description database More...

ParallelLibraryparallelLib
class member reference to the parallel library

ParConfigLIter methodPCIter
the active ParallelConfiguration used by this Iterator instance

Model iteratedModel
the model to be iterated (for iterators and meta-iterators employing a single model instance)

size_t myModelLayers
number of Models locally (in Iterator or derived classes) wrapped around the initially passed in Model

unsigned short methodName
name of the iterator (the user's method spec)

Real convergenceTol
iteration convergence tolerance

size_t maxIterations
maximum number of iterations for the method

size_t maxFunctionEvals
maximum number of fn evaluations for the method

int maxEvalConcurrency
maximum number of concurrent model evaluations More...

ActiveSet activeSet
the response data requirements on each function evaluation

size_t numFinalSolutions
number of solutions to retain in best variables/response arrays

VariablesArray bestVariablesArray
collection of N best solution variables found during the study; always in context of Model originally passed to the Iterator (any in-flight Recasts must be undone)

ResponseArray bestResponseArray
collection of N best solution responses found during the study; always in context of Model originally passed to the Iterator (any in-flight Recasts must be undone)

bool subIteratorFlag
flag indicating if this Iterator is a sub-iterator (NestedModel::subIterator or DataFitSurrModel::daceIterator)

short outputLevel
output verbosity level: {SILENT,QUIET,NORMAL,VERBOSE,DEBUG}_OUTPUT

bool summaryOutputFlag
flag for summary output (evaluation stats, final results); default true, but false for on-the-fly (helper) iterators and sub-iterator use cases

ResultsManagerresultsDB
reference to the global iterator results database

EvaluationStore & evaluationsDB
reference to the global evaluation database

EvaluationsDBState evaluationsDBState
State of evaluations DB for this iterator.

ResultsNames resultsNames
valid names for iterator results

std::shared_ptr< TraitsBasemethodTraits
pointer that retains shared ownership of a TraitsBase object, or child thereof

bool topLevel
Whether this is the top level iterator.

bool exportSurrogate = false
whether to export final surrogates

String surrExportPrefix
base filename for exported surrogates

unsigned short surrExportFormat = NO_MODEL_FORMAT
(bitwise) format(s) to export

## Private Member Functions

void order_to_dim_preference (const UShortArray &order, unsigned short &p, RealVector &dim_pref)
convert an isotropic/anisotropic expansion_order vector into a scalar plus a dimension preference vector

## Private Attributes

RealVector noiseTols
noise tolerance for compressive sensing algorithms; vector form used in cross-validation

Real l2Penalty
L2 penalty for LASSO algorithm (elastic net variant)

number of frontier expansions per iteration with the ADAPTED_BASIS_EXPANDING_FRONT approach

unsigned short expOrderSpec
user specification for expansion_order (array for multifidelity)

size_t collocPtsSpec
user specification for collocation_points (array for multifidelity)

size_t expSamplesSpec
user specification for expansion_samples (array for multifidelity)

unsigned short ssgLevelSpec
user request of sparse grid level

derivative of the PCE with respect to the x-space variables evaluated at the means (used as uncertainty importance metrics)

bool normalizedCoeffOutput
user request for use of normalization when outputting PCE coefficients

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 NonDnondInstance
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 NonDPolynomialChaos 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.

## ◆ NonDPolynomialChaos() [1/6]

 NonDPolynomialChaos ( ProblemDescDB & problem_db, Model & model )

## ◆ NonDPolynomialChaos() [2/6]

 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)

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

## ◆ NonDPolynomialChaos() [3/6]

 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)

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

## ◆ NonDPolynomialChaos() [4/6]

 NonDPolynomialChaos ( unsigned short method_name, ProblemDescDB & problem_db, Model & model )
protected

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)

This constructor is called by derived class constructors that customize the object construction.

## ◆ NonDPolynomialChaos() [5/6]

 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 )
protected

base constructor for lightweight construction of multifidelity PCE using numerical integration

This constructor is called by derived class constructors for lightweight instantiations that employ numerical integration (quadrature, sparse grid, cubature).

## ◆ NonDPolynomialChaos() [6/6]

 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 )
protected

base constructor for lightweight construction of multilevel PCE using regression

This constructor is called by derived class constructors for lightweight instantiations that employ regression (least squares, CS, OLI).

## ◆ increment_order_from_grid()

 void increment_order_from_grid ( )
protected

define an expansion order that is consistent with an advancement in structured/unstructured grid level/density

Used for uniform refinement of regression-based PCE.

Referenced by NonDPolynomialChaos::append_expansion().

The documentation for this class was generated from the following files:
• NonDPolynomialChaos.hpp
• NonDPolynomialChaos.cpp