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 >:

[legend]

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

[legend]

Public Member Functions
	ProductBasis ()
	Constructor.

virtual	~ProductBasis ()
	Destructor.

virtual const MultiIndex< ordinal_type > &	term (ordinal_type i) const =0
	Get orders of each coordinate polynomial given an index `i`.

virtual ordinal_type	index (const MultiIndex< 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.

virtual MultiIndex< ordinal_type >	getMaxOrders () const =0
	Return maximum order allowable for each coordinate basis.

Public Member Functions inherited from Stokhos::OrthogPolyBasis< ordinal_type, value_type >
	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< Stokhos::Sparse3Tensor< ordinal_type, value_type > >	computeTripleProductTensor () const =0
	Compute triple product tensor.

virtual Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > >	computeLinearTripleProductTensor () const =0
	Compute linear triple product tensor where k = 0,1.

virtual value_type	evaluateZero (ordinal_type i) const =0
	Evaluate basis polynomial `i` at zero.

virtual void	evaluateBases (const Teuchos::ArrayView< const 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::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 is the dimension of the basis. This class adds methods for indexing the multivariate polynomial and getting the coordinate bases.

Member Function Documentation

◆ getCoordinateBases()

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 >, Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >, Stokhos::SmolyakBasis< ordinal_type, value_type, coeff_compare_type >, Stokhos::TensorProductBasis< ordinal_type, value_type, coeff_compare_type >, and Stokhos::TotalOrderBasis< ordinal_type, value_type, coeff_compare_type >.

Referenced by Stokhos::TensorProductPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::TensorProductPseudoSpectralOperator().