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Stokhos::ProductBasis< ordinal_type, value_type > Class Template Reference

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

#include <Stokhos_ProductBasis.hpp>

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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]
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::MonomialGramSchmidtSimplexPCEBasis< 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::MonomialGramSchmidtSimplexPCEBasis< ordinal_type, value_type >.


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