NonDQuadrature Class Reference

Derived nondeterministic class that generates N-dimensional numerical quadrature points for evaluation of expectation integrals over uncorrelated standard normals/uniforms/exponentials/betas/gammas. More...

Inheritance diagram for NonDQuadrature:

List of all members.

Public Member Functions
	NonDQuadrature (Model &model, const UShortArray &quad_order_seq, const RealVector &dim_pref, short driver_mode)
	alternate constructor for instantiations "on the fly" based on a quadrature order specification
	NonDQuadrature (Model &model, int num_filt_samples, const RealVector &dim_pref, short driver_mode)
	alternate constructor for instantiations "on the fly" that generate a filtered tensor product sample set
	NonDQuadrature (Model &model, int num_rand_samples, int seed, const UShortArray &quad_order_seq, const RealVector &dim_pref, short driver_mode)
	alternate constructor for instantiations "on the fly" that sample randomly from a tensor product multi-index
void	increment_grid ()
	increment SSG level/TPQ order
void	update ()
	propagate any numSamples updates and/or grid updates/increments
const Pecos::UShortArray &	quadrature_order () const
	return Pecos::TensorProductDriver::quadOrder
void	quadrature_order (const Pecos::UShortArray &dim_quad_order)
	set dimQuadOrderRef and map to Pecos::TensorProductDriver::quadOrder
void	samples (size_t samples)
	set numSamples
short	mode () const
	return quadMode
Protected Member Functions
	NonDQuadrature (ProblemDescDB &problem_db, Model &model)
	constructor
	~NonDQuadrature ()
	destructor
void	initialize_grid (const std::vector< Pecos::BasisPolynomial > &poly_basis)
void	get_parameter_sets (Model &model)
	Returns one block of samples (ndim * num_samples)
void	reset ()
	restore initial state for repeated sub-iterator executions
void	sampling_reset (int min_samples, bool all_data_flag, bool stats_flag)
void	increment_grid_preference (const RealVector &dim_pref)
	increment SSG level/TPQ order and update anisotropy
void	increment_specification_sequence ()
	increment sequenceIndex and update active orders/levels
int	num_samples () const
Private Member Functions
void	increment_grid (UShortArray &dim_quad_order)
	convenience function used to make increment_grid() more modular
void	increment_grid_preference (const RealVector &dim_pref, UShortArray &dim_quad_order)
	convenience function used to make increment_grid_preference() more modular
void	compute_minimum_quadrature_order (size_t min_samples, const RealVector &dim_pref, UShortArray &dim_quad_order)
	calculate smallest dim_quad_order with at least min_samples
void	filter_parameter_sets ()
	prune allSamples back to size numSamples, retaining points with highest product weight
void	update_anisotropic_order (const RealVector &dim_pref, UShortArray &quad_order_ref)
	update quad_order_ref based on an updated dimension preference, enforcing previous values as a lower bound
void	initialize_dimension_quadrature_order (unsigned short quad_order_spec, const RealVector &dim_pref_spec, UShortArray &dim_quad_order)
	initialize dim_quad_order from quad_order_spec and dim_pref_spec
void	increment_dimension_quadrature_order (UShortArray &dim_quad_order)
	increment each dim_quad_order entry by 1
void	increment_dimension_quadrature_order (const RealVector &dim_pref, UShortArray &dim_quad_order)
	increment the dim_quad_order entry with maximum preference by 1 and then rebalance
Private Attributes
Pecos::TensorProductDriver *	tpqDriver
	convenience pointer to the numIntDriver representation
bool	nestedRules
	for studies involving refinement strategies, allow for use of nested quadrature rules such as Gauss-Patterson
UShortArray	quadOrderSeqSpec
	a sequence of scalar quadrature orders, one per refinement level
UShortArray	dimQuadOrderRef
	reference point for Pecos::TensorProductDriver::quadOrder: the original user specification for the number of Gauss points per dimension, plus any refinements posted by increment_grid()
short	quadMode
	point generation mode: FULL_TENSOR, FILTERED_TENSOR, RANDOM_TENSOR
size_t	numSamples
	size of a subset of tensor quadrature points (filtered based on product weight or sampled uniformly from the tensor multi-index); used by the regression PCE approach known as "probabilistic collocation"
int	randomSeed
	seed for the random number generator used in sampling of the tensor multi-index

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Detailed Description

Derived nondeterministic class that generates N-dimensional numerical quadrature points for evaluation of expectation integrals over uncorrelated standard normals/uniforms/exponentials/betas/gammas.

This class is used by NonDPolynomialChaos, but could also be used for general numerical integration of moments. It employs Gauss-Hermite, Gauss-Legendre, Gauss-Laguerre, Gauss-Jacobi and generalized Gauss-Laguerre quadrature for use with normal, uniform, exponential, beta, and gamma density functions and integration bounds. The abscissas and weights for one-dimensional integration are extracted from the appropriate OrthogonalPolynomial class and are extended to n-dimensions using a tensor product approach.

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Constructor & Destructor Documentation

NonDQuadrature	(	Model &	model,
		const UShortArray &	quad_order_seq,
		const RealVector &	dim_pref,
		short	driver_mode
	)

alternate constructor for instantiations "on the fly" based on a quadrature order specification

This alternate constructor is used for on-the-fly generation and evaluation of numerical quadrature points.

References NonDIntegration::numIntDriver, and NonDQuadrature::tpqDriver.

NonDQuadrature	(	Model &	model,
		int	num_filt_samples,
		const RealVector &	dim_pref,
		short	driver_mode
	)

alternate constructor for instantiations "on the fly" that generate a filtered tensor product sample set

This alternate constructor is used for on-the-fly generation and evaluation of filtered tensor quadrature points.

References NonDIntegration::numIntDriver, and NonDQuadrature::tpqDriver.

NonDQuadrature	(	Model &	model,
		int	num_rand_samples,
		int	seed,
		const UShortArray &	quad_order_seq,
		const RealVector &	dim_pref,
		short	driver_mode
	)

alternate constructor for instantiations "on the fly" that sample randomly from a tensor product multi-index

This alternate constructor is used for on-the-fly generation and evaluation of random sampling from a tensor quadrature multi-index.

References NonDIntegration::numIntDriver, and NonDQuadrature::tpqDriver.

NonDQuadrature	(	ProblemDescDB &	problem_db,
		Model &	model
	)		[protected]

constructor

This constructor is called for a standard letter-envelope iterator instantiation. In this case, set_db_list_nodes has been called and probDescDB can be queried for settings from the method specification. It is not currently used, as there is not yet a separate nond_quadrature method specification.

References NonDIntegration::check_variables(), Iterator::convergenceTol, ProblemDescDB::get_bool(), ProblemDescDB::get_short(), ProblemDescDB::get_ushort(), Iterator::maxEvalConcurrency, Iterator::maxIterations, NonD::natafTransform, NonDQuadrature::nestedRules, NonDIntegration::numIntDriver, Iterator::outputLevel, Iterator::probDescDB, NonDQuadrature::reset(), and NonDQuadrature::tpqDriver.

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Member Function Documentation

void initialize_grid

(

const std::vector< Pecos::BasisPolynomial > &

poly_basis

)

[protected, virtual]

Used in combination with alternate NonDQuadrature constructor.

Implements NonDIntegration.

References Iterator::maxEvalConcurrency, NonDQuadrature::nestedRules, Analyzer::numContinuousVars, NonDQuadrature::numSamples, NonDQuadrature::quadMode, NonDQuadrature::reset(), NonDQuadrature::tpqDriver, and NonDQuadrature::update().

void sampling_reset	(	int	min_samples,
		bool	all_data_flag,
		bool	stats_flag
	)		[protected, virtual]

used by DataFitSurrModel::build_global() to publish the minimum number of points needed from the quadrature routine in order to build a particular global approximation.

Reimplemented from Iterator.

References NonDQuadrature::compute_minimum_quadrature_order(), NonDIntegration::dimPrefSpec, NonDQuadrature::dimQuadOrderRef, NonDQuadrature::nestedRules, Analyzer::numContinuousVars, and NonDQuadrature::tpqDriver.

Referenced by NonDQuadrature::update().

int num_samples

(

)

const [inline, protected, virtual]

Return current number of evaluation points. Since the calculation of samples, collocation points, etc. might be costly, provide a default implementation here that backs out from the maxEvalConcurrency.

Reimplemented from Analyzer.

References NonDQuadrature::numSamples, NonDQuadrature::quadMode, and NonDQuadrature::tpqDriver.

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

• NonDQuadrature.hpp
• NonDQuadrature.cpp