Abstract base class for multivariate orthogonal polynomials generated from tensor products of univariate polynomials. More...

#include <Stokhos_ProductBasis.hpp>

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

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List of all members.

Public Member Functions
	ProductBasis ()
	Constructor.
virtual	~ProductBasis ()
	Destructor.
virtual Teuchos::Array < ordinal_type >	getTerm (ordinal_type i) const =0
	Get orders of each coordinate polynomial given an index `i`.
virtual ordinal_type	getIndex (const Teuchos::Array< ordinal_type > &term) const =0
	Get index of the multivariate polynomial given orders of each coordinate.
virtual Teuchos::Array < Teuchos::RCP< const OneDOrthogPolyBasis < ordinal_type, value_type > > >	getCoordinateBases () const =0
	Return array of coordinate bases.

Detailed Description

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

Abstract base class for multivariate orthogonal polynomials generated from tensor products of univariate polynomials.

* The multivariate polynomials are given by

$\Psi_i(x) = \psi_{i_1}(x_1)\dots\psi_{i_d}(x_d)$

where $d$ is the dimension of the basis. This class adds methods for indexing the multivariate polynomial and getting the coordinate bases.

Member Function Documentation

template<typename ordinal_type , typename value_type >

virtual Teuchos::Array< Teuchos::RCP<const OneDOrthogPolyBasis<ordinal_type, value_type> > > Stokhos::ProductBasis< ordinal_type, value_type >::getCoordinateBases ( ) const [pure virtual]

Return array of coordinate bases.

Array is of size dimension().

Implemented in Stokhos::CompletePolynomialBasis< ordinal_type, value_type >, and Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type >

virtual ordinal_type Stokhos::ProductBasis< ordinal_type, value_type >::getIndex ( const Teuchos::Array< ordinal_type > & term ) const [pure virtual]

Get index of the multivariate polynomial given orders of each coordinate.

Given the array term storing $i_1,\dots,\i_d$ , returns the index $i$ such that $\Psi_i(x) = \psi_{i_1}(x_1)\dots\psi_{i_d}(x_d)$ .

Implemented in Stokhos::CompletePolynomialBasis< ordinal_type, value_type >, and Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type >

virtual Teuchos::Array<ordinal_type> Stokhos::ProductBasis< ordinal_type, value_type >::getTerm ( ordinal_type i ) const [pure virtual]

Get orders of each coordinate polynomial given an index i.

The returned array is of size $d$ , where $d$ is the dimension of the basis, and entry $l$ is given by $i_l$ where $\Psi_i(x) = \psi_{i_1}(x_1)\dots\psi_{i_d}(x_d)$ .

Implemented in Stokhos::CompletePolynomialBasis< ordinal_type, value_type >, and Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >.

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

Stokhos_ProductBasis.hpp

Public Member Functions

Detailed Description

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

Member Function Documentation

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