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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>

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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.

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.


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:
porder of the basis
pcepolynomial chaos expansions defining new measure
quadquadrature data for basis defining pce
Cijksparse triple product tensor for basis defining pce
sparse_toltolerance for dropping terms in sparse tensors

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 >.


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