Stokhos::StieltjesBasis< ordinal_type, value_type, func_type > Class Template Reference

Generates three-term recurrence using the Discretized Stieltjes procedure applied to a functional mapping another basis. More...

#include <Stokhos_StieltjesBasis.hpp>

Inheritance diagram for Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >:

Collaboration diagram for Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >:

List of all members.

Public Member Functions
	StieltjesBasis (ordinal_type p, const Teuchos::RCP< const func_type > &func, const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &quad, bool use_pce_quad_points, bool normalize=false)
	Constructor.
	~StieltjesBasis ()
	Destructor.
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 Member Functions
void	stieltjes (ordinal_type nstart, ordinal_type nfinish, const Teuchos::Array< value_type > &weights, const Teuchos::Array< value_type > &points, Teuchos::Array< value_type > &a, Teuchos::Array< value_type > &b, Teuchos::Array< value_type > &nrm, Teuchos::Array< Teuchos::Array< value_type > > &phi_vals) const
	Compute 3-term recurrence using Stieljtes procedure.
void	integrateBasisSquared (ordinal_type k, const Teuchos::Array< value_type > &a, const Teuchos::Array< value_type > &b, const Teuchos::Array< value_type > &weights, const Teuchos::Array< value_type > &points, Teuchos::Array< Teuchos::Array< value_type > > &phi_vals, value_type &val1, value_type &val2) const
	Compute and .
void	evaluateRecurrence (ordinal_type k, const Teuchos::Array< value_type > &a, const Teuchos::Array< value_type > &b, const Teuchos::Array< value_type > &points, Teuchos::Array< Teuchos::Array< value_type > > &values) const
	Evaluate polynomials via 3-term recurrence.
	StieltjesBasis (ordinal_type p, const StieltjesBasis &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 func_type >	func
	PC expansion.
Teuchos::RCP< const Stokhos::Quadrature < ordinal_type, value_type > >	quad
	Quadrature object.
const Teuchos::Array < value_type > &	pce_weights
	PCE quadrature weights.
const Teuchos::Array < Teuchos::Array< value_type > > &	basis_values
	Values of PCE basis functions at quadrature points.
Teuchos::Array< value_type >	func_vals
	Values of func at quadrature points.
Teuchos::Array< Teuchos::Array < value_type > >	phi_vals
	Values of generated polynomials at PCE quadrature points.
bool	use_pce_quad_points
	Use underlying pce's quadrature data.

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Detailed Description

template<typename ordinal_type, typename value_type, typename func_type>
class Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >

Generates three-term recurrence using the Discretized Stieltjes procedure applied to a functional mapping another basis.

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Constructor & Destructor Documentation

template<typename ordinal_type , typename value_type , typename func_type >

Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >::StieltjesBasis	(	ordinal_type	p,
		const Teuchos::RCP< const func_type > &	func,
		const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &	quad,
		bool	use_pce_quad_points,
		bool	normalize = false
	)

Constructor.

Parameters:

p	order of the basis
func	mapping defining new density function
quad	quadrature data for basis of PC expansion
use_pce_quad_points	whether to use quad to define quadrature points for the new basis, or whether to use the Golub-Welsch system.
normalize	whether polynomials should be given unit norm

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Member Function Documentation

template<typename ordinal_type , typename value_type , typename func_type >

Teuchos::RCP< Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type > > Stokhos::StieltjesBasis< ordinal_type, value_type, func_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_StieltjesBasis.hpp
• Stokhos_StieltjesBasisImp.hpp