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

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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`. More...

virtual ordinal_type	index (const MultiIndex< ordinal_type > &term) const =0
	Get index of the multivariate polynomial given orders of each coordinate. More...

virtual Teuchos::Array < Teuchos::RCP< const OneDOrthogPolyBasis < ordinal_type, value_type > > >	getCoordinateBases () const =0
	Return array of coordinate bases. More...

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. More...

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. More...

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`. More...

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

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

Referenced by Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >::ProductLanczosGramSchmidtPCEBasis(), Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >::ProductLanczosPCEBasis(), and Stokhos::TensorProductPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::TensorProductPseudoSpectralOperator().

template<typename ordinal_type, typename value_type>

virtual ordinal_type Stokhos::ProductBasis< ordinal_type, value_type >::index ( const MultiIndex< 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 >, Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >, Stokhos::TensorProductBasis< ordinal_type, value_type, coeff_compare_type >, Stokhos::TotalOrderBasis< ordinal_type, value_type, coeff_compare_type >, and Stokhos::SmolyakBasis< ordinal_type, value_type, coeff_compare_type >.

Referenced by Stokhos::BasisInteractionGraph::initialize().

template<typename ordinal_type, typename value_type>

virtual const MultiIndex<ordinal_type>& Stokhos::ProductBasis< ordinal_type, value_type >::term ( 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 >, Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >, Stokhos::TensorProductBasis< ordinal_type, value_type, coeff_compare_type >, Stokhos::TotalOrderBasis< ordinal_type, value_type, coeff_compare_type >, and Stokhos::SmolyakBasis< ordinal_type, value_type, coeff_compare_type >.

Referenced by Stokhos::BasisInteractionGraph::initialize(), Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::order(), and Stokhos::TensorProductPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::TensorProductPseudoSpectralOperator().

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 >