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 >:

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

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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.
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.
Implementation of Stokhos::RecurrenceBasis methods
virtual void	computeRecurrenceCoefficients (ordinal_type n, Teuchos::Array< value_type > &alpha, Teuchos::Array< value_type > &beta, Teuchos::Array< value_type > &delta) const
	Compute 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 Stokhos::Sparse3Tensor < ordinal_type, value_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

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

Stokhos_StieltjesPCEBasis.hpp
Stokhos_StieltjesPCEBasisImp.hpp

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

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

Constructor & Destructor Documentation

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