NonDPolynomialChaos Class Reference

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

Inheritance diagram for NonDPolynomialChaos:

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)

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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.

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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
	)

alternate constructor

This constructor is used for helper iterator instantiation on the fly.

References Model::assign_rep(), NonDExpansion::construct_cubature(), NonDExpansion::construct_quadrature(), NonDExpansion::construct_sparse_grid(), NonD::construct_u_space_model(), NonDExpansion::expansionCoeffsApproach, NonDExpansion::initialize(), NonDPolynomialChaos::initialize_u_space_model(), Iterator::iteratedModel, NonD::numContDesVars, NonD::numContEpistUncVars, NonD::numContStateVars, Iterator::outputLevel, NonDExpansion::piecewiseBasis, NonDPolynomialChaos::resolve_inputs(), and NonDExpansion::uSpaceModel.

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Member Function Documentation

void increment_expansion

(

)

[virtual]

uniformly increment the order of the polynomial chaos expansion

Used for uniform refinement of regression-based PCE.

Reimplemented from NonDExpansion.

References Model::approximations(), NonDPolynomialChaos::collocRatio, NonDQuadrature::compute_minimum_quadrature_order(), PecosApproximation::expansion_terms(), NonDQuadrature::filtered_samples(), PecosApproximation::increment_order(), Iterator::iterator_rep(), Model::model_rep(), Iterator::numFunctions, NonDExpansion::numSamplesOnModel, NonDSampling::sampling_reference(), Model::subordinate_iterator(), NonDPolynomialChaos::tensorRegression, NonDPolynomialChaos::terms_ratio_to_samples(), NonDPolynomialChaos::termsOrder, DataFitSurrModel::total_points(), and NonDExpansion::uSpaceModel.

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

• NonDPolynomialChaos.H
• NonDPolynomialChaos.C