Stokhos::OrthogPolyBasis

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

Abstract base class for multivariate orthogonal polynomials. More...

#include <Stokhos_OrthogPolyBasis.hpp>

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

Inheritance graph
[legend]
List of all members.

Public Member Functions

 OrthogPolyBasis ()
 Constructor.
virtual ~OrthogPolyBasis ()
 Destructor.
virtual ordinal_type order () const =0
 Return order of basis.
virtual ordinal_type dimension () const =0
 Return dimension of basis.
virtual ordinal_type size () const =0
 Return total size of basis.
virtual const Teuchos::Array<
value_type > & 		norm_squared () const =0
 Return array storing norm-squared of each basis polynomial.
virtual const value_type & norm_squared (ordinal_type i) const =0
 Return norm squared of basis polynomial i.
virtual Teuchos::RCP< const
Stokhos::Sparse3Tensor< ordinal_type,
value_type > > 		getTripleProductTensor () const =0
 Compute triple product tensor.
virtual Teuchos::RCP< const
Stokhos::Sparse3Tensor< ordinal_type,
value_type > > 		getLowOrderTripleProductTensor (ordinal_type order) const =0
virtual value_type evaluateZero (ordinal_type i) const =0
 Evaluate basis polynomial i at zero.
virtual void evaluateBases (const Teuchos::Array< value_type > &point, Teuchos::Array< value_type > &basis_vals) const =0
 Evaluate basis polynomials at given point point.
virtual void print (std::ostream &os) const =0
 Print basis to stream os.
virtual const std::string & getName () const =0
 Return string name of basis.

Detailed Description

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

Abstract base class for multivariate orthogonal polynomials.

This class provides an abstract interface for multivariate orthogonal polynomials. Orthogonality is defined by the inner product

\[ (f,g) = \langle fg \rangle = \int_{R^d} f(x)g(x) \rho(x) dx \]

where $\rho$ is the density function of the measure associated with the orthogonal polynomials and $d$ is the dimension of the domain.

Like most classes in Stokhos, the class is templated on the ordinal and value types. Typically ordinal_type = int and value_type = double.

Member Function Documentation

template<typename ordinal_type, typename value_type>
virtual void Stokhos::OrthogPolyBasis< ordinal_type, value_type >::evaluateBases ( const Teuchos::Array< value_type > &  point,
Teuchos::Array< value_type > &  basis_vals 
) const [pure virtual]

Evaluate basis polynomials at given point point.

Size of returned array is given by size(), and coefficients are ordered from order 0 up to size size()-1.

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

template<typename ordinal_type, typename value_type>
virtual Teuchos::RCP< const Stokhos::Sparse3Tensor<ordinal_type, value_type> > Stokhos::OrthogPolyBasis< ordinal_type, value_type >::getLowOrderTripleProductTensor ( ordinal_type  order  )  const [pure virtual]

The $(i,j,k)$ entry of the tensor $C_{ijk}$ is given by $C_{ijk} = \langle\Psi_i\Psi_j\Psi_k\rangle$ where $\Psi_l$ represents basis polynomial $l$ and $i,j=0,\dots,P$ where $P$ is size()-1 and $k=0,\dots,p$ where $p$ is the supplied order.

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

template<typename ordinal_type, typename value_type>
virtual Teuchos::RCP< const Stokhos::Sparse3Tensor<ordinal_type, value_type> > Stokhos::OrthogPolyBasis< ordinal_type, value_type >::getTripleProductTensor (  )  const [pure virtual]

Compute triple product tensor.

The $(i,j,k)$ entry of the tensor $C_{ijk}$ is given by $C_{ijk} = \langle\Psi_i\Psi_j\Psi_k\rangle$ where $\Psi_l$ represents basis polynomial $l$ and $i,j,k=0,\dots,P$ where $P$ is size()-1 of the basis.

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

template<typename ordinal_type, typename value_type>
virtual const Teuchos::Array<value_type>& Stokhos::OrthogPolyBasis< ordinal_type, value_type >::norm_squared (  )  const [pure virtual]

Return array storing norm-squared of each basis polynomial.

Entry $l$ of returned array is given by $\langle\Psi_l^2\rangle$ for $l=0,\dots,P$ where $P$ is size()-1.

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

The documentation for this class was generated from the following file:
Generated on Wed May 12 21:25:04 2010 for Stokhos by  doxygen 1.4.7