Stokhos::MonomialProjGramSchmidtPCEBasis< ordinal_type, value_type > Class Template Reference

Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions. More...

#include <Stokhos_MonomialProjGramSchmidtPCEBasis.hpp>

Inheritance diagram for Stokhos::MonomialProjGramSchmidtPCEBasis< ordinal_type, value_type >:

Collaboration diagram for Stokhos::MonomialProjGramSchmidtPCEBasis< ordinal_type, value_type >:

List of all members.

Public Member Functions
	MonomialProjGramSchmidtPCEBasis (ordinal_type p, const Teuchos::Array< Stokhos::OrthogPolyApprox< ordinal_type, value_type > > &pce, const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &quad, const Teuchos::ParameterList &params=Teuchos::ParameterList())
	Constructor.
virtual	~MonomialProjGramSchmidtPCEBasis ()
	Destructor.
Implementation of Stokhos::OrthogPolyBasis methods
virtual const std::string &	getName () const
	Return string name of basis.
Protected Types
typedef Stokhos::CompletePolynomialBasisUtils < ordinal_type, value_type >	CPBUtils
typedef Teuchos::SerialDenseVector < ordinal_type, value_type >	SDV
typedef Teuchos::SerialDenseMatrix < ordinal_type, value_type >	SDM
Protected Member Functions
virtual ordinal_type	buildReducedBasis (ordinal_type max_p, value_type threshold, const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &A, const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &F, const Teuchos::Array< value_type > &weights, Teuchos::Array< Teuchos::Array< ordinal_type > > &terms_, Teuchos::Array< ordinal_type > &num_terms_, Teuchos::SerialDenseMatrix< ordinal_type, value_type > &Qp_, Teuchos::SerialDenseMatrix< ordinal_type, value_type > &Q_)
	Build the reduced basis, parameterized by total order max_p.
Protected Attributes
std::string	name
	Name of basis.

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Detailed Description

template<typename ordinal_type, typename value_type>
class Stokhos::MonomialProjGramSchmidtPCEBasis< ordinal_type, value_type >

Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions.

Given the PCE expansions, first build a non-orthogonal monomial basis. Orthogonalize this basis using Gram-Schmidt, then build a quadrature rule using the simplex method.

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Constructor & Destructor Documentation

template<typename ordinal_type , typename value_type >

Stokhos::MonomialProjGramSchmidtPCEBasis< ordinal_type, value_type >::MonomialProjGramSchmidtPCEBasis	(	ordinal_type	p,
		const Teuchos::Array< Stokhos::OrthogPolyApprox< ordinal_type, value_type > > &	pce,
		const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &	quad,
		const Teuchos::ParameterList &	params = Teuchos::ParameterList()
	)

Constructor.

Parameters:

p	order of the basis
pce	polynomial chaos expansions defining new measure
quad	quadrature data for basis defining pce
Cijk	sparse triple product tensor for basis defining pce
sparse_tol	tolerance for dropping terms in sparse tensors

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Member Function Documentation

template<typename ordinal_type , typename value_type >

ordinal_type Stokhos::MonomialProjGramSchmidtPCEBasis< ordinal_type, value_type >::buildReducedBasis	(	ordinal_type	max_p,
		value_type	threshold,
		const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &	A,
		const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &	F,
		const Teuchos::Array< value_type > &	weights,
		Teuchos::Array< Teuchos::Array< ordinal_type > > &	terms_,
		Teuchos::Array< ordinal_type > &	num_terms_,
		Teuchos::SerialDenseMatrix< ordinal_type, value_type > &	Qp_,
		Teuchos::SerialDenseMatrix< ordinal_type, value_type > &	Q_
	)		[protected, virtual]

Build the reduced basis, parameterized by total order max_p.

Returns resulting size of reduced basis

Implements Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >.

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

• Stokhos_MonomialProjGramSchmidtPCEBasis.hpp
• Stokhos_MonomialProjGramSchmidtPCEBasisImp.hpp