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

#include <Stokhos_StieltjesPCEBasis.hpp>

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

[legend]

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

[legend]

List of all members.

Public Member Functions
	StieltjesPCEBasis (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 use_pce_quad_points, bool normalize=false, bool project_integrals=false, const Teuchos::RCP< const Stokhos::Sparse3Tensor< ordinal_type, value_type > > &Cijk=Teuchos::null)
	Constructor.
	~StieltjesPCEBasis ()
	Destructor.
void	transformCoeffsFromStieltjes (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 Stokhos::Sparse3Tensor < ordinal_type, value_type >	Cijk_type
	Short-hand for triple product.
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 $\int\psi^2_k(t) d\lambda(t)$ and $\int t\psi^2_k(t) d\lambda(t)$ .
void	integrateBasisSquaredProj (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 $\int\psi^2_k(t) d\lambda(t)$ and $\int t\psi^2_k(t) d\lambda(t)$ by projecting onto original PCE basis.
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.
	StieltjesPCEBasis (ordinal_type p, const StieltjesPCEBasis &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
	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 >	pce_vals
	Values of PCE 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.
Teuchos::SerialDenseMatrix < ordinal_type, value_type >	fromStieltjesMat
	Matrix mapping coefficients in Stieltjes basis back to original basis.
bool	project_integrals
	Project Stieltjes integrals to original PCE basis.
Teuchos::RCP< const Stokhos::OrthogPolyBasis < ordinal_type, value_type > >	basis
	PCE basis (needed for integral projection method)
Teuchos::RCP< const Cijk_type >	Cijk
	Triple product tensor (needed for integral projection method)
Teuchos::Array< value_type >	phi_pce_coeffs
	Array store PC expansion of generated orthogonal polynomials.

Detailed Description

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

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

Constructor & Destructor Documentation

template<typename ordinal_type , typename value_type >

Stokhos::StieltjesPCEBasis< ordinal_type, value_type >::StieltjesPCEBasis	(	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	use_pce_quad_points,
		bool	normalize = `false`,
		bool	project_integrals = `false`,
		const Teuchos::RCP< const Stokhos::Sparse3Tensor< ordinal_type, value_type > > &	Cijk = `Teuchos::null`
	)

Constructor.

Parameters:

p	order of the basis
pce	polynomial chaos expansion 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

Member Function Documentation

template<typename ordinal_type , typename value_type >

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

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

Stokhos_StieltjesPCEBasis.hpp
Stokhos_StieltjesPCEBasisImp.hpp

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Detailed Description

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

Constructor & Destructor Documentation

Member Function Documentation

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