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Public Member Functions | Protected Types | Protected Member Functions | Protected Attributes
Stokhos::StieltjesPCEBasis< ordinal_type, value_type > Class Template Reference

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

#include <Stokhos_StieltjesPCEBasis.hpp>

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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.
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.
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 Cijk_typeCijk
 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:
porder of the basis
pcepolynomial chaos expansion defining new density function
quadquadrature data for basis of PC expansion
use_pce_quad_pointswhether to use quad to define quadrature points for the new basis, or whether to use the Golub-Welsch system.
normalizewhether 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:
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