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NonDPolynomialChaos Class Reference

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

Inheritance diagram for NonDPolynomialChaos:
NonDExpansion NonD Analyzer Iterator

Public Member Functions

 NonDPolynomialChaos (ProblemDescDB &problem_db, Model &model)
 standard constructor More...
 
 NonDPolynomialChaos (Model &model, short exp_coeffs_approach, const UShortArray &num_int_seq, const RealVector &dim_pref, short u_space_type, bool piecewise_basis, bool use_derivs)
 alternate constructor for numerical integration (tensor, sparse, cubature) More...
 
 NonDPolynomialChaos (Model &model, short exp_coeffs_approach, const UShortArray &exp_order_seq, const RealVector &dim_pref, const SizetArray &colloc_pts_seq, Real colloc_ratio, int seed, short u_space_type, bool piecewise_basis, bool use_derivs, bool cv_flag, const String &import_build_points_file, unsigned short import_build_format, bool import_build_active_only)
 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, short u_space_type, bool piecewise_basis, bool use_derivs)
 alternate constructor
 
 ~NonDExpansion ()
 destructor
 
void core_run ()
 perform a forward uncertainty propagation using PCE/SC methods
 
void print_results (std::ostream &s)
 print the final statistics
 
const Modelalgorithm_space_model () const
 
- Public Member Functions inherited from NonD
void initialize_random_variables (short u_space_type)
 initialize natafTransform based on distribution data from iteratedModel More...
 
void initialize_random_variables (const Pecos::ProbabilityTransformation &transform, bool deep_copy=false)
 alternate form: initialize natafTransform based on incoming data More...
 
void initialize_random_variable_transformation ()
 instantiate natafTransform
 
void initialize_random_variable_types ()
 initializes ranVarTypesX within natafTransform (u-space not needed) More...
 
void initialize_random_variable_types (short u_space_type)
 initializes ranVarTypesX and ranVarTypesU within natafTransform More...
 
void initialize_random_variable_parameters ()
 initializes ranVarMeansX, ranVarStdDevsX, ranVarLowerBndsX, ranVarUpperBndsX, and ranVarAddtlParamsX within natafTransform More...
 
void initialize_random_variable_correlations ()
 propagate iteratedModel correlations to natafTransform
 
void verify_correlation_support (short u_space_type)
 verify that correlation warping is supported by Nataf for given variable types
 
void transform_correlations ()
 perform correlation warping for variable types supported by Nataf
 
void requested_levels (const RealVectorArray &req_resp_levels, const RealVectorArray &req_prob_levels, const RealVectorArray &req_rel_levels, const RealVectorArray &req_gen_rel_levels, short resp_lev_tgt, short resp_lev_tgt_reduce, bool cdf_flag, bool pdf_output)
 set requestedRespLevels, requestedProbLevels, requestedRelLevels, requestedGenRelLevels, respLevelTarget, cdfFlag, and pdfOutput (used in combination with alternate ctors)
 
void distribution_parameter_derivatives (bool dist_param_derivs)
 set distParamDerivs
 
void print_level_mappings (std::ostream &s) const
 prints the z/p/beta/beta* mappings reflected in {requested,computed}{Resp,Prob,Rel,GenRel}Levels for default qoi_type and qoi_labels
 
void print_level_mappings (std::ostream &s, String qoi_type, const StringArray &qoi_labels) const
 prints the z/p/beta/beta* mappings reflected in {requested,computed}{Resp,Prob,Rel,GenRel}Levels More...
 
bool pdf_output () const
 get pdfOutput
 
void pdf_output (bool output)
 set pdfOutput
 
Pecos::ProbabilityTransformation & variable_transformation ()
 return natafTransform
 
- Public Member Functions inherited from Analyzer
const VariablesArray & all_variables ()
 return the complete set of evaluated variables
 
const RealMatrix & all_samples ()
 return the complete set of evaluated samples
 
const IntResponseMap & all_responses () const
 return the complete set of computed responses
 
int 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 ()
 default constructor More...
 
 Iterator (ProblemDescDB &problem_db)
 standard envelope constructor, which constructs its own model(s) More...
 
 Iterator (ProblemDescDB &problem_db, Model &model)
 alternate envelope constructor which uses the ProblemDescDB but accepts a model from a higher level (meta-iterator) context, instead of constructing its own More...
 
 Iterator (const String &method_string, Model &model)
 alternate envelope constructor for instantiations by name without the ProblemDescDB More...
 
 Iterator (const Iterator &iterator)
 copy constructor More...
 
virtual ~Iterator ()
 destructor More...
 
Iterator operator= (const Iterator &iterator)
 assignment operator More...
 
virtual void post_input ()
 read tabular data for post-run mode
 
virtual void reset ()
 restore initial state for repeated sub-iterator executions
 
virtual void initialize_iterator (int job_index)
 used by IteratorScheduler to set the starting data for a run
 
virtual void pack_parameters_buffer (MPIPackBuffer &send_buffer, int job_index)
 used by IteratorScheduler to pack starting data for an iterator run
 
virtual void unpack_parameters_buffer (MPIUnpackBuffer &recv_buffer)
 used by IteratorScheduler to unpack starting data for an iterator run
 
virtual void unpack_parameters_initialize (MPIUnpackBuffer &recv_buffer)
 used by IteratorScheduler to unpack starting data and initialize an iterator run
 
virtual void pack_results_buffer (MPIPackBuffer &send_buffer, int job_index)
 used by IteratorScheduler to pack results data from an iterator run
 
virtual void unpack_results_buffer (MPIUnpackBuffer &recv_buffer, int job_index)
 used by IteratorScheduler to unpack results data from an iterator run
 
virtual void update_local_results (int job_index)
 used by IteratorScheduler to update local results arrays
 
virtual bool accepts_multiple_points () const
 indicates if this iterator accepts multiple initial points. Default return is false. Override to return true if appropriate.
 
virtual void initial_points (const VariablesArray &pts)
 sets the multiple initial points for this iterator. This should only be used if accepts_multiple_points() returns true.
 
virtual void initialize_graphics (int iterator_server_id=1)
 initialize the 2D graphics window and the tabular graphics data More...
 
virtual unsigned short uses_method () const
 return name of any enabling iterator used by this iterator More...
 
virtual void method_recourse ()
 perform a method switch, if possible, due to a detected conflict
 
virtual void sampling_reset (int min_samples, bool all_data_flag, bool stats_flag)
 reset sampling iterator to use at least min_samples
 
virtual void sampling_reference (int 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 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
 
void init_communicators (ParLevLIter pl_iter)
 initialize the communicators associated with this Iterator instance
 
void set_communicators (ParLevLIter pl_iter)
 set the communicators associated with this Iterator instance
 
void free_communicators (ParLevLIter pl_iter)
 free the communicators associated with this Iterator instance
 
void resize_communicators (ParLevLIter pl_iter, bool reinit_comms)
 Resize the communicators. This is called from the letter's resize()
 
void parallel_configuration_iterator (ParConfigLIter pc_iter)
 set methodPCIter
 
ParConfigLIter parallel_configuration_iterator () const
 return methodPCIter
 
void run (ParLevLIter pl_iter)
 invoke set_communicators(pl_iter) prior to run()
 
void run ()
 orchestrate initialize/pre/core/post/finalize phases More...
 
void assign_rep (Iterator *iterator_rep, bool ref_count_incr=true)
 replaces existing letter with a new one More...
 
void iterated_model (const Model &model)
 set the iteratedModel (iterators and meta-iterators using a single model instance)
 
Modeliterated_model ()
 return the iteratedModel (iterators & meta-iterators using a single model instance)
 
ProblemDescDBproblem_description_db () const
 return the problem description database (probDescDB)
 
ParallelLibraryparallel_library () const
 return the parallel library (parallelLib)
 
void method_name (unsigned short m_name)
 set the method name to an enumeration value
 
unsigned short method_name () const
 return the method name via its native enumeration value
 
void method_string (const String &m_str)
 set the method name by string
 
String method_string () const
 return the method name by string
 
String method_enum_to_string (unsigned short method_name) const
 convert a method name enumeration value to a string
 
unsigned short method_string_to_enum (const String &method_name) const
 convert a method name string to an enumeration value
 
String submethod_enum_to_string (unsigned short submethod_name) const
 convert a method name enumeration value to a string
 
const String & method_id () const
 return the method identifier (methodId)
 
int maximum_evaluation_concurrency () const
 return the maximum evaluation concurrency supported by the iterator
 
void maximum_evaluation_concurrency (int max_conc)
 set the maximum evaluation concurrency supported by the iterator
 
void convergence_tolerance (Real conv_tol)
 set the method convergence tolerance (convergenceTol)
 
Real convergence_tolerance () const
 return the method convergence tolerance (convergenceTol)
 
void output_level (short out_lev)
 set the method output level (outputLevel)
 
short output_level () const
 return the method output level (outputLevel)
 
void summary_output (bool summary_output_flag)
 Set summary output control; true enables evaluation/results summary.
 
size_t num_final_solutions () const
 return the number of solutions to retain in best variables/response arrays
 
void num_final_solutions (size_t num_final)
 set the number of solutions to retain in best variables/response arrays
 
void active_set (const ActiveSet &set)
 set the default active set vector (for use with iterators that employ evaluate_parameter_sets())
 
const ActiveSetactive_set () const
 return the default active set vector (used by iterators that employ evaluate_parameter_sets())
 
void sub_iterator_flag (bool si_flag)
 set subIteratorFlag (and update summaryOutputFlag if needed)
 
void active_variable_mappings (const SizetArray &c_index1, const SizetArray &di_index1, const SizetArray &ds_index1, const SizetArray &dr_index1, const ShortArray &c_target2, const ShortArray &di_target2, const ShortArray &ds_target2, const ShortArray &dr_target2)
 set primaryA{CV,DIV,DRV}MapIndices, secondaryA{CV,DIV,DRV}MapTargets
 
bool is_null () const
 function to check iteratorRep (does this envelope contain a letter?)
 
Iteratoriterator_rep () const
 returns iteratorRep for access to derived class member functions that are not mapped to the top Iterator level
 
virtual void eval_tag_prefix (const String &eval_id_str)
 set the hierarchical eval ID tag prefix More...
 

Protected Member Functions

void 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
 
void increment_specification_sequence ()
 increment the input specification sequence (PCE only) More...
 
void compute_expansion ()
 form or import an orthogonal polynomial expansion using PCE methods
 
void multifidelity_expansion ()
 construct a multifidelity expansion, across model forms or discretization levels
 
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 update expansion order (PCE only)
 
void increment_order_and_grid ()
 
void print_coefficients (std::ostream &s)
 print the PCE coefficient array for the orthogonal basis
 
void archive_coefficients ()
 archive the PCE coefficient array for the orthogonal basis
 
void multilevel_regression (size_t model_form)
 special case of multifidelity_expansion() for multilevel allocation of samples, mirroring NonDMultilevelSampling for least sq/compressed sensing
 
void increment_sample_sequence (size_t new_samp, size_t total_samp)
 increment the sequence in numSamplesOnModel for multilevel_regression()
 
void append_expansion ()
 generate new samples from numSamplesOnModel and update expansion
 
- Protected Member Functions inherited from NonDExpansion
virtual void initialize_expansion ()
 initialize random variable definitions and final stats arrays
 
virtual void update_expansion ()
 update an expansion; avoids overhead in compute_expansion()
 
virtual Real compute_covariance_metric ()
 compute 2-norm of change in response covariance More...
 
virtual Real compute_final_statistics_metric ()
 compute 2-norm of change in final statistics More...
 
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 initialize (short u_space_type)
 common constructor code for initialization of natafTransform
 
void check_dimension_preference (const RealVector &dim_pref) const
 check length and content of dimension preference vector
 
void refine_expansion ()
 refine the reference expansion found by compute_expansion() using uniform/adaptive p-/h-refinement strategies
 
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, const UShortArray &quad_order_seq, 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, int filtered_samples, const RealVector &dim_pref)
 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, int random_samples, int seed, const UShortArray &quad_order_seq, const RealVector &dim_pref)
 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, const UShortArray &ssg_level_seq, const RealVector &ssg_dim_pref)
 assign a NonDSparseGrid instance within u_space_sampler
 
void construct_expansion_sampler (const String &import_approx_file, unsigned short import_build_format=TABULAR_ANNOTATED, bool import_build_active_only=false)
 construct the expansionSampler for evaluating samples on uSpaceModel
 
void compute_statistics ()
 calculate analytic and numerical statistics from the expansion More...
 
void archive_moments ()
 archive the central moments (numerical and expansion) to ResultsDB
 
- 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...
 
void size ()
 Size local variables.
 
int generate_system_seed ()
 create a system-generated unique seed (when a seed is unspecified)
 
void initialize_final_statistics_gradients ()
 initializes finalStatistics::functionGradients
 
void update_aleatory_final_statistics ()
 update finalStatistics::functionValues from momentStats and computed{Prob,Rel,GenRel,Resp}Levels
 
void update_system_final_statistics ()
 update system metrics from component metrics within finalStatistics
 
void update_system_final_statistics_gradients ()
 update finalStatistics::functionGradients
 
void initialize_level_mappings ()
 size computed{Resp,Prob,Rel,GenRel}Levels
 
void compute_densities (const RealRealPairArray &min_max_fns, bool prob_refinement=false, bool all_levels_computed=false)
 compute the PDF bins from the CDF/CCDF values and store in computedPDF{Abscissas,Ordinates} More...
 
void print_densities (std::ostream &s) const
 output the PDFs reflected in computedPDF{Abscissas,Ordinates} using default qoi_type and pdf_labels
 
void print_densities (std::ostream &s, String qoi_type, const StringArray &pdf_labels) const
 output the PDFs reflected in computedPDF{Abscissas,Ordinates}
 
void print_system_mappings (std::ostream &s) const
 print system series/parallel mappings for response levels
 
void transform_model (Model &x_model, Model &u_model, bool truncated_bounds=false, Real bound=10.)
 recast x_model from x-space to u-space to create u_model
 
void construct_lhs (Iterator &u_space_sampler, Model &u_model, unsigned short sample_type, int num_samples, int seed, const String &rng, bool vary_pattern, short sampling_vars_mode=ACTIVE)
 assign a NonDLHSSampling instance within u_space_sampler
 
void archive_allocate_mappings ()
 allocate results array storage for distribution mappings
 
void archive_from_resp (size_t fn_index)
 archive the mappings from specified response levels for specified fn
 
void archive_to_resp (size_t fn_index)
 archive the mappings to computed response levels for specified fn
 
void archive_allocate_pdf ()
 allocate results array storage for pdf histograms
 
void archive_pdf (size_t fn_index)
 archive a single pdf histogram for specified function
 
- Protected Member Functions inherited from Analyzer
 Analyzer ()
 default constructor
 
 Analyzer (ProblemDescDB &problem_db, Model &model)
 standard constructor
 
 Analyzer (unsigned short method_name, Model &model)
 alternate constructor for instantiations "on the fly" with a Model
 
 Analyzer (unsigned short method_name)
 alternate constructor for instantiations "on the fly" without a Model
 
 ~Analyzer ()
 destructor
 
virtual void get_parameter_sets (Model &model)
 Returns one block of samples (ndim * num_samples)
 
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 post_run (std::ostream &s)
 post-run portion of run (optional); verbose to print results; re-implemented by Iterators that can read all Variables/Responses and perform final analysis phase in a standalone way More...
 
void 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 variance_based_decomp (int ncont, int ndiscint, int ndiscreal, int num_samples)
 
void read_variables_responses (int num_evals, size_t num_vars)
 convenience function for reading variables/responses (used in derived classes post_input) More...
 
void print_sobol_indices (std::ostream &s) const
 Printing of VBD results. More...
 
void samples_to_variables_array (const RealMatrix &sample_matrix, VariablesArray &vars_array)
 convert samples array to variables array; e.g., allSamples to allVariables
 
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)
 constructor initializes the base class part of letter classes (BaseConstructor overloading avoids infinite recursion in the derived class constructors - Coplien, p. 139) More...
 
 Iterator (NoDBBaseConstructor, unsigned short method_name, Model &model)
 alternate constructor for base iterator classes constructed on the fly More...
 
 Iterator (NoDBBaseConstructor, unsigned short method_name)
 alternate constructor for base iterator classes constructed on the fly More...
 
virtual const VariablesArray & initial_points () const
 gets the multiple initial points for this iterator. This will only be meaningful after a call to initial_points mutator.
 
StrStrSizet run_identifier () const
 get the unique run identifier based on method name, id, and number of executions
 

Private Member Functions

void increment_grid_from_order ()
 define a grid increment that is consistent with an advancement in expansion order More...
 
void increment_order_from_grid ()
 define an expansion order that is consistent with an advancement in structured/unstructured grid level/density More...
 
int terms_ratio_to_samples (size_t num_exp_terms, Real colloc_ratio)
 convert number of expansion 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 expansion terms and number of collocation samples to a collocation ratio
 
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
 
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

String expansionExportFile
 filename for export of chaos coefficients
 
String expansionImportFile
 filename for import of chaos coefficients
 
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
 
int randomSeed
 seed for random number generator used for regression with LHS and sub-sampled tensor grids
 
bool tensorRegression
 option for regression PCE using a filtered set tensor-product points
 
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
 
RealVector noiseTols
 noise tolerance for compressive sensing algorithms; vector form used in cross-validation
 
Real l2Penalty
 L2 penalty for LASSO algorithm (elastic net variant)
 
unsigned short numAdvance
 number of frontier expansions per iteration with the ADAPTED_BASIS_EXPANDING_FRONT approach
 
UShortArray expOrderSeqSpec
 user specification for expansion_order (array for multifidelity)
 
RealVector dimPrefSpec
 user specification for dimension_preference
 
SizetArray collocPtsSeqSpec
 user specification for collocation_points (array for multifidelity)
 
SizetArray expSamplesSeqSpec
 user specification for expansion_samples (array for multifidelity)
 
size_t sequenceIndex
 sequence index for {expOrder,collocPts,expSamples}SeqSpec
 
RealMatrix pceGradsMeanX
 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
 
short uSpaceType
 user requested expansion type
 
UShortArray quadOrderSeqSpec
 user request of quadrature order
 
UShortArray ssgLevelSeqSpec
 user request of sparse grid level
 
unsigned short cubIntSpec
 cubature integrand
 
String importBuildPointsFile
 user specified import approx. points file
 
unsigned short importBuildFormat
 user specified import file format
 
bool importBuildActiveOnly
 user specified import build active only
 
bool resizedFlag
 local flag to signal a resizing occurred
 
bool callResize
 local flag to signal an explicit call to resize is necessary if resizedFlag is false
 

Additional Inherited Members

- Static Protected Member Functions inherited from NonD
static void vars_u_to_x_mapping (const Variables &u_vars, Variables &x_vars)
 static function for RecastModels used for forward mapping of u-space variables from NonD Iterators to x-space variables for Model evaluations More...
 
static void vars_x_to_u_mapping (const Variables &x_vars, Variables &u_vars)
 static function for RecastModels used for inverse mapping of x-space variables from data import to u-space variables for NonD Iterators More...
 
static void set_u_to_x_mapping (const Variables &u_vars, const ActiveSet &u_set, ActiveSet &x_set)
 static function for RecastModels used to map u-space ActiveSets from NonD Iterators to x-space ActiveSets for Model evaluations More...
 
static void resp_x_to_u_mapping (const Variables &x_vars, const Variables &u_vars, const Response &x_response, Response &u_response)
 static function for RecastModels used to map x-space responses from Model evaluations to u-space responses for return to NonD Iterator.
 
- Protected Attributes inherited from NonDExpansion
Model uSpaceModel
 Model representing the approximate response function in u-space, after u-space recasting and polynomial data fit recursions.
 
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
 
size_t numUncertainQuant
 number of invocations of core_run()
 
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
 
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...
 
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
 
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 initialPtU
 stores the initial variables data in u-space
 
- 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.

Constructor & Destructor Documentation

NonDPolynomialChaos ( 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(), NonDIntegration::anisotropic_order_to_dimension_preference(), Model::assign_rep(), NonDExpansion::check_dimension_preference(), NonDPolynomialChaos::collocPtsSeqSpec, NonDPolynomialChaos::collocRatio, ParallelLibrary::command_line_check(), NonDExpansion::construct_cubature(), NonDExpansion::construct_expansion_sampler(), NonD::construct_lhs(), NonDExpansion::construct_quadrature(), NonDExpansion::construct_sparse_grid(), NonDPolynomialChaos::cubIntSpec, Model::current_response(), NonDIntegration::dimension_preference_to_anisotropic_order(), NonDPolynomialChaos::dimPrefSpec, NonDExpansion::expansionBasisType, NonDExpansion::expansionCoeffsApproach, NonDPolynomialChaos::expansionImportFile, NonDPolynomialChaos::expOrderSeqSpec, NonDPolynomialChaos::expSamplesSeqSpec, ProblemDescDB::get_real(), ProblemDescDB::get_short(), ProblemDescDB::get_string(), ProblemDescDB::get_usa(), ProblemDescDB::get_ushort(), NonDPolynomialChaos::importBuildActiveOnly, NonDPolynomialChaos::importBuildFormat, NonDPolynomialChaos::importBuildPointsFile, NonDExpansion::initialize(), NonDPolynomialChaos::initialize_u_space_model(), Iterator::iteratedModel, Iterator::maxEvalConcurrency, Analyzer::numContinuousVars, NonDExpansion::numSamplesOnModel, Iterator::outputLevel, Iterator::parallelLib, Iterator::probDescDB, NonDPolynomialChaos::quadOrderSeqSpec, NonDPolynomialChaos::randomSeed, NonDExpansion::refineControl, NonDExpansion::refineType, ActiveSet::request_values(), NonDPolynomialChaos::resolve_inputs(), NonDPolynomialChaos::sequenceIndex, NonDPolynomialChaos::ssgLevelSeqSpec, NonDPolynomialChaos::tensorRegression, NonDPolynomialChaos::terms_ratio_to_samples(), NonDPolynomialChaos::terms_samples_to_ratio(), NonDPolynomialChaos::termsOrder, NonD::transform_model(), NonDExpansion::uSpaceModel, NonDPolynomialChaos::uSpaceType, and Analyzer::vary_pattern().

NonDPolynomialChaos ( Model model,
short  exp_coeffs_approach,
const UShortArray &  num_int_seq,
const RealVector &  dim_pref,
short  u_space_type,
bool  piecewise_basis,
bool  use_derivs 
)
NonDPolynomialChaos ( Model model,
short  exp_coeffs_approach,
const UShortArray &  exp_order_seq,
const RealVector &  dim_pref,
const SizetArray &  colloc_pts_seq,
Real  colloc_ratio,
int  seed,
short  u_space_type,
bool  piecewise_basis,
bool  use_derivs,
bool  cv_flag,
const String &  import_build_points_file,
unsigned short  import_build_format,
bool  import_build_active_only 
)

Member Function Documentation

void increment_specification_sequence ( )
protectedvirtual
void increment_order_and_grid ( )
protectedvirtual
void increment_grid_from_order ( )
private
void increment_order_from_grid ( )
private

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

Used for uniform refinement of regression-based PCE.

References NonDPolynomialChaos::collocRatio, SharedApproxData::data_rep(), SharedPecosApproxData::expansion_order(), NonDExpansion::numSamplesOnModel, NonDPolynomialChaos::ratio_samples_to_order(), Model::shared_approximation(), and NonDExpansion::uSpaceModel.

Referenced by NonDPolynomialChaos::append_expansion().


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