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

Generates three-term recurrence using the Lanczos procedure applied to a polynomial chaos expansion in another basis. More...

#include <Stokhos_LanczosPCEBasis.hpp>

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

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

List of all members.

Public Member Functions
	LanczosPCEBasis (ordinal_type p, const Teuchos::RCP< const Stokhos::OrthogPolyApprox< ordinal_type, value_type > > &pce, const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &quad, bool normalize, bool limit_integration_order)
	Constructor.
	~LanczosPCEBasis ()
	Destructor.
value_type	getNewCoeffs (ordinal_type i) const
	Get new coefficients in this new basis.
void	transformCoeffsFromLanczos (const value_type *in, value_type *out) const
	Map expansion coefficients from this basis to original.
Implementation of Stokhos::OneDOrthogPolyBasis methods
virtual void	getQuadPoints (ordinal_type quad_order, Teuchos::Array< value_type > &points, Teuchos::Array< value_type > &weights, Teuchos::Array< Teuchos::Array< value_type > > &values) const
	Get Gauss quadrature points, weights, and values of basis at points.
virtual Teuchos::RCP < OneDOrthogPolyBasis < ordinal_type, value_type > >	cloneWithOrder (ordinal_type p) const
	Clone this object with the option of building a higher order basis.
Protected Types
typedef WeightedVectorSpace < ordinal_type, value_type >	vectorspace_type
typedef DiagonalOperator < ordinal_type, value_type >	operator_type
typedef Stokhos::Lanczos < vectorspace_type, operator_type >	lanczos_type
typedef lanczos_type::matrix_type	matrix_type
typedef lanczos_type::vector_type	vector_type
Protected Member Functions
	LanczosPCEBasis (ordinal_type p, const LanczosPCEBasis &basis)
	Copy constructor with specified order.
Implementation of Stokhos::RecurrenceBasis methods
virtual bool	computeRecurrenceCoefficients (ordinal_type n, Teuchos::Array< value_type > &alpha, Teuchos::Array< value_type > &beta, Teuchos::Array< value_type > &delta, Teuchos::Array< value_type > &gamma) const
	Compute recurrence coefficients.
virtual void	setup ()
	Setup basis after computing recurrence coefficients.
Protected Attributes
Teuchos::RCP< const Stokhos::OrthogPolyApprox < ordinal_type, value_type > >	pce
	PCE Lanczos procedure is based on.
Teuchos::RCP< const Stokhos::Quadrature < ordinal_type, value_type > >	quad
	Quadrature object.
bool	limit_integration_order
	Flag indicating whether to limit the integration order.
ordinal_type	nqp
	Number of quadrature points.
vector_type	pce_weights
	Quadrature weights.
vector_type	pce_vals
	Values of PCE at quadrature points.
vector_type	u0
	Initial Lanczos vector.
matrix_type	lanczos_vecs
	Lanczos vectors.
matrix_type	fromStieltjesMat
	Matrix mapping coefficients in Stieltjes basis back to original basis.
vector_type	new_pce
	Projection of pce in new basis.

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Detailed Description

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

Generates three-term recurrence using the Lanczos procedure applied to a polynomial chaos expansion in another basis.

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Constructor & Destructor Documentation

template<typename ordinal_type , typename value_type >

Stokhos::LanczosPCEBasis< ordinal_type, value_type >::LanczosPCEBasis	(	ordinal_type	p,
		const Teuchos::RCP< const Stokhos::OrthogPolyApprox< ordinal_type, value_type > > &	pce,
		const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &	quad,
		bool	normalize,
		bool	limit_integration_order
	)

Constructor.

Parameters:

p	order of the basis
pce	polynomial chaos expansion defining new density function
quad	quadrature data for basis of PC expansion

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Member Function Documentation

template<typename ordinal_type , typename value_type >

Teuchos::RCP< Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type > > Stokhos::LanczosPCEBasis< ordinal_type, value_type >::cloneWithOrder

(

ordinal_type

p

)

const [virtual]

Clone this object with the option of building a higher order basis.

This method is following the Prototype pattern (see Design Pattern's textbook). The slight variation is that it allows the order of the polynomial to be modified, otherwise an exact copy is formed. The use case for this is creating basis functions for column indices in a spatially varying adaptive refinement context.

Implements Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >.

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

• Stokhos_LanczosPCEBasis.hpp
• Stokhos_LanczosPCEBasisImp.hpp