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 Stokhos::OrthogPolyApprox< ordinal_type, value_type > &pce, const Stokhos::Quadrature< ordinal_type, value_type > &quad, bool use_pce_quad_points, bool normalize=false)
 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 ordinal_type getRule () const
 Get sparse grid rule number as defined by Dakota's webbur package.
virtual value_type getQuadWeightFactor () const
 Get quadrature weight factor as defined by Dakota's webbur package.
virtual value_type getQuadPointFactor () const
 Get quadrature point factor as defined by Dakota's webbur package.

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 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::Array< value_type > pce_vals
 Values of PCE at quadrature points.
Teuchos::Array< value_type > pce_weights
 PCE quadrature weights.
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.

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 Stokhos::OrthogPolyApprox< ordinal_type, value_type > &  pce,
const Stokhos::Quadrature< ordinal_type, value_type > &  quad,
bool  use_pce_quad_points,
bool  normalize = false 
)

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>
value_type Stokhos::StieltjesPCEBasis< ordinal_type, value_type >::getQuadPointFactor (  )  const [virtual]

Get quadrature point factor as defined by Dakota's webbur package.

This method is needed for building Smolyak sparse grids out of this basis.

Implements Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >.

template<typename ordinal_type, typename value_type>
value_type Stokhos::StieltjesPCEBasis< ordinal_type, value_type >::getQuadWeightFactor (  )  const [virtual]

Get quadrature weight factor as defined by Dakota's webbur package.

This method is needed for building Smolyak sparse grids out of this basis.

Implements Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >.

template<typename ordinal_type, typename value_type>
ordinal_type Stokhos::StieltjesPCEBasis< ordinal_type, value_type >::getRule (  )  const [virtual]

Get sparse grid rule number as defined by Dakota's webbur package.

This method is needed for building Smolyak sparse grids out of this basis. A rule number of 10 is not defined by the webbur package, and this rule number is used internally by Stokhos::SparseGridQuadrature to pass an arbitrary one-dimensional basis to that package.

Implements Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >.


The documentation for this class was generated from the following files:
Generated on Tue Jul 13 09:23:21 2010 for Stokhos by  doxygen 1.4.7