Public Member Functions | Private Member Functions | Private Attributes
NonDPolynomialChaos Class Reference

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

Inheritance diagram for NonDPolynomialChaos:
NonDExpansion NonD Analyzer Iterator

List of all members.

Public Member Functions

 NonDPolynomialChaos (Model &model)
 standard constructor
 NonDPolynomialChaos (Model &model, short exp_coeffs_approach, unsigned short num_int_level, short u_space_type, bool piecewise_basis, bool use_derivs)
 alternate constructor
 ~NonDPolynomialChaos ()
 destructor
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 compute_expansion ()
 form or import an orthogonal polynomial expansion using PCE methods
void increment_expansion ()
 uniformly increment the order of the polynomial chaos expansion
void print_coefficients (std::ostream &s)
 print the PCE coefficient array for the orthogonal basis

Private Member Functions

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

Private Attributes

String expansionImportFile
 filename for import of chaos coefficients
int expansionTerms
 user specification of PCE terms
Real collocRatio
 factor applied to expansionTerms^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
bool tensorRegression
 option for regression PCE using a filtered set tensor-product points
RealMatrix pceGradsMeanX
 derivative of the PCE with respect to the x-space variables evaluated at the means (used as uncertainty importance metrics)

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 ( Model model)

standard constructor

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

References Dakota::abort_handler(), Model::assign_rep(), NonDPolynomialChaos::collocRatio, NonDExpansion::construct_cubature(), NonDExpansion::construct_expansion_sampler(), NonD::construct_lhs(), NonDExpansion::construct_quadrature(), NonDExpansion::construct_sparse_grid(), NonD::construct_u_space_model(), Model::derivative_concurrency(), NonDExpansion::expansionCoeffsApproach, NonDPolynomialChaos::expansionImportFile, NonDPolynomialChaos::expansionTerms, ProblemDescDB::get_dusa(), ProblemDescDB::get_int(), ProblemDescDB::get_rdv(), ProblemDescDB::get_real(), ProblemDescDB::get_short(), ProblemDescDB::get_string(), ProblemDescDB::get_ushort(), Model::init_communicators(), NonDExpansion::initialize(), NonDPolynomialChaos::initialize_u_space_model(), Iterator::iteratedModel, Iterator::iterator_rep(), Iterator::maxConcurrency, NonD::numContDesVars, NonD::numContEpistUncVars, Iterator::numContinuousVars, NonD::numContStateVars, NonDExpansion::numSamplesOnExpansion, NonDExpansion::numSamplesOnModel, Iterator::outputLevel, NonDExpansion::piecewiseBasis, Iterator::probDescDB, NonDExpansion::refineControl, NonDExpansion::refineType, NonDPolynomialChaos::resolve_inputs(), NonDPolynomialChaos::tensorRegression, NonDPolynomialChaos::terms_ratio_to_samples(), NonDPolynomialChaos::terms_samples_to_ratio(), NonDPolynomialChaos::termsOrder, NonDExpansion::uSpaceModel, and Analyzer::vary_pattern().

NonDPolynomialChaos ( Model model,
short  exp_coeffs_approach,
unsigned short  num_int_level,
short  u_space_type,
bool  piecewise_basis,
bool  use_derivs 
)

Member Function Documentation

void increment_expansion ( ) [virtual]

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