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

Generates three-term recurrence using the Discretized Stieltjes procedure. More...

#include <Stokhos_DiscretizedStieltjesBasis.hpp>

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

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

List of all members.

Public Member Functions
	DiscretizedStieltjesBasis (const std::string &name, const ordinal_type &p, value_type(*weightFn)(const value_type &), const value_type &leftEndPt, const value_type &rightEndPt, bool normalize)
	Constructor.
	~DiscretizedStieltjesBasis ()
	Destructor.
value_type	eval_inner_product (const ordinal_type &order1, const ordinal_type &order2) const
	Evaluate inner product of two basis functions to test orthogonality.
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 Member Functions
value_type	evaluateRecurrence (const value_type &point, ordinal_type order, const Teuchos::Array< value_type > &alpha, const Teuchos::Array< value_type > &beta) const
	Evaluate 3-term recurrence formula using supplied coefficients.
value_type	evaluateWeight (const value_type &x) const
	Evaluates the scaled weight function.
value_type	expectedValue_tJ_nsquared (const ordinal_type &order, const Teuchos::Array< value_type > &alpha, const Teuchos::Array< value_type > &beta) const
	Approximates where = order.
value_type	expectedValue_J_nsquared (const ordinal_type &order, const Teuchos::Array< value_type > &alpha, const Teuchos::Array< value_type > &beta) const
	Approximates where = order.
	DiscretizedStieltjesBasis (const ordinal_type &p, const DiscretizedStieltjesBasis &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.
Protected Attributes
value_type	scaleFactor
	Scale for the weight.
const value_type	leftEndPt_
	Left end point of domain.
const value_type	rightEndPt_
	Right end point of domain.
value_type(*	weightFn_ )(const value_type &)
	Weight function.
Teuchos::Array< value_type >	quad_points
	Quadrature points for discretized stieltjes procedure.
Teuchos::Array< value_type >	quad_weights
	Quadrature points for discretized stieltjes procedure.
Teuchos::Array< Teuchos::Array < value_type > >	quad_values
	Quadrature values for discretized stieltjes procedure.

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Detailed Description

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

Generates three-term recurrence using the Discretized Stieltjes procedure.

Class generates an orthogonal polynomial basis for a given weight function and interval. The Discretized Stiltjes procedure described in "On the Calculation of Rys Polynomials and Quadratures", Robin P. Sagar, Vedene H. Smith is used to generate the recurrence coefficients.

Please be aware that this method is not fullproof and that it appears to encounter trouble with strongly singular weights since Gaussan quadrature is used to compute the relevant integrals. For 'nice' weight functions the method seems relatively robust.

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Constructor & Destructor Documentation

template<typename ordinal_type , typename value_type >

Stokhos::DiscretizedStieltjesBasis< ordinal_type, value_type >::DiscretizedStieltjesBasis	(	const std::string &	name,
		const ordinal_type &	p,
		value_type(*)(const value_type &)	weightFn,
		const value_type &	leftEndPt,
		const value_type &	rightEndPt,
		bool	normalize
	)

Constructor.

Parameters:

name	name of the basis displayed when printing
p	order of the basis
weightFn	function pointer defining weight function
leftEndPt	left end point of the domain of the weight function
rightEndPt	right end point of the domain of the weight function
normalize	whether polynomials should be given unit norm

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Member Function Documentation

template<typename ordinal_type , typename value_type >

Teuchos::RCP< Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type > > Stokhos::DiscretizedStieltjesBasis< 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 >.

Reimplemented in Stokhos::RysBasis< ordinal_type, value_type >.

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

• Stokhos_DiscretizedStieltjesBasis.hpp
• Stokhos_DiscretizedStieltjesBasisImp.hpp