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 >:

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. More...
virtual	~MonomialProjGramSchmidtPCEBasis ()
	Destructor.
Implementation of Stokhos::OrthogPolyBasis methods
virtual const std::string &	getName () const
	Return string name of basis.
Public Member Functions inherited from Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >
	GSReducedPCEBasisBase (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. More...
virtual	~GSReducedPCEBasisBase ()
	Destructor.
ordinal_type	order () const
	Return order of basis.
ordinal_type	dimension () const
	Return dimension of basis.
virtual ordinal_type	size () const
	Return total size of basis.
virtual const Teuchos::Array < value_type > &	norm_squared () const
	Return array storing norm-squared of each basis polynomial. More...
virtual const value_type &	norm_squared (ordinal_type i) const
	Return norm squared of basis polynomial i.
virtual Teuchos::RCP < Stokhos::Sparse3Tensor < ordinal_type, value_type > >	computeTripleProductTensor () const
	Compute triple product tensor. More...
virtual Teuchos::RCP < Stokhos::Sparse3Tensor < ordinal_type, value_type > >	computeLinearTripleProductTensor () const
	Compute linear triple product tensor where k = 0,1,..,d.
virtual value_type	evaluateZero (ordinal_type i) const
	Evaluate basis polynomial i at zero.
virtual void	evaluateBases (const Teuchos::ArrayView< const value_type > &point, Teuchos::Array< value_type > &basis_vals) const
	Evaluate basis polynomials at given point point. More...
virtual void	print (std::ostream &os) const
	Print basis to stream os.
virtual void	transformToOriginalBasis (const value_type *in, value_type *out, ordinal_type ncol=1, bool transpose=false) const
	Transform coefficients to original basis from this basis.
virtual void	transformFromOriginalBasis (const value_type *in, value_type *out, ordinal_type ncol=1, bool transpose=false) const
	Transform coefficients from original basis to this basis.
virtual Teuchos::RCP< const Stokhos::Quadrature < ordinal_type, value_type > >	getReducedQuadrature () const
	Get reduced quadrature object.
Public Member Functions inherited from Stokhos::ReducedPCEBasis< ordinal_type, value_type >
	ReducedPCEBasis ()
	Default constructor.
virtual	~ReducedPCEBasis ()
	Destructor.
Public Member Functions inherited from Stokhos::OrthogPolyBasis< ordinal_type, value_type >
	OrthogPolyBasis ()
	Constructor.
virtual	~OrthogPolyBasis ()
	Destructor.

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 Types inherited from Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >
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< Stokhos::MultiIndex< 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. More...
Protected Member Functions inherited from Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >
void	setup (ordinal_type p, const Teuchos::Array< Stokhos::OrthogPolyApprox< ordinal_type, value_type > > &pce, const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &quad)

Protected Attributes
std::string	name
	Name of basis.
Protected Attributes inherited from Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >
std::string	name
	Name of basis.
Teuchos::ParameterList	params
	Algorithm parameters.
Teuchos::RCP< const Stokhos::OrthogPolyBasis < ordinal_type, value_type > >	pce_basis
	Original pce basis.
ordinal_type	pce_sz
	Size of original pce basis.
ordinal_type	p
	Total order of basis.
ordinal_type	d
	Total dimension of basis.
ordinal_type	sz
	Total size of basis.
Teuchos::Array < Stokhos::MultiIndex < ordinal_type > >	terms
	2-D array of basis terms
Teuchos::Array< ordinal_type >	num_terms
	Number of terms up to each order.
Teuchos::Array< value_type >	norms
	Norms.
SDM	Q
	Values of transformed basis at quadrature points.
SDM	Qp
	Coefficients of transformed basis in original basis.
Teuchos::RCP< const Stokhos::Quadrature < ordinal_type, value_type > >	reduced_quad
	Reduced quadrature object.
bool	verbose
	Whether to print a bunch of stuff out.
value_type	rank_threshold
	Rank threshold.
std::string	orthogonalization_method
	Orthogonalization method.
Teuchos::BLAS< ordinal_type, value_type >	blas

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

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

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< Stokhos::MultiIndex< ordinal_type > > &  terms_, Teuchos::Array< ordinal_type > &  num_terms_, Teuchos::SerialDenseMatrix< ordinal_type, value_type > &  Qp_, Teuchos::SerialDenseMatrix< ordinal_type, value_type > &  Q_  )

protectedvirtual

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