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

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

#include <Stokhos_OrthogPolyBasis.hpp>

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

◆ computeLinearTripleProductTensor()

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

Compute linear triple product tensor where k = 0,1.

Implemented in Stokhos::CompletePolynomialBasis< ordinal_type, value_type >, Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >, Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >, Stokhos::ProductLanczosGramSchmidtPCEBasis< 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 >.

◆ computeTripleProductTensor()

template<typename ordinal_type , typename value_type >
virtual Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > Stokhos::OrthogPolyBasis< ordinal_type, value_type >::computeTripleProductTensor ( ) 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.

Implemented in Stokhos::CompletePolynomialBasis< ordinal_type, value_type >, Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >, Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >, Stokhos::ProductLanczosGramSchmidtPCEBasis< 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 >.

◆ dimension()

template<typename ordinal_type , typename value_type >
virtual ordinal_type Stokhos::OrthogPolyBasis< ordinal_type, value_type >::dimension ( ) const
pure virtual

Return dimension of basis.

Implemented in Stokhos::CompletePolynomialBasis< ordinal_type, value_type >, Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >, Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >, Stokhos::ProductLanczosGramSchmidtPCEBasis< 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::BasisInteractionGraph::initialize(), and Stokhos::QuadraturePseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::QuadraturePseudoSpectralOperator().

◆ evaluateBases()

template<typename ordinal_type , typename value_type >
virtual void Stokhos::OrthogPolyBasis< ordinal_type, value_type >::evaluateBases ( const Teuchos::ArrayView< const 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 >, Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >, Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >, Stokhos::ProductLanczosGramSchmidtPCEBasis< 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 >.

◆ evaluateZero()

template<typename ordinal_type , typename value_type >
virtual value_type Stokhos::OrthogPolyBasis< ordinal_type, value_type >::evaluateZero ( ordinal_type  i) const
pure virtual

Evaluate basis polynomial i at zero.

Implemented in Stokhos::CompletePolynomialBasis< ordinal_type, value_type >, Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >, Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >, Stokhos::ProductLanczosGramSchmidtPCEBasis< 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 >.

◆ getName()

template<typename ordinal_type , typename value_type >
virtual const std::string & Stokhos::OrthogPolyBasis< ordinal_type, value_type >::getName ( ) const
pure virtual

Return string name of basis.

Implemented in Stokhos::CompletePolynomialBasis< ordinal_type, value_type >, Stokhos::MonomialGramSchmidtPCEBasis< ordinal_type, value_type >, Stokhos::MonomialProjGramSchmidtPCEBasis< ordinal_type, value_type >, Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >, Stokhos::ProductLanczosGramSchmidtPCEBasis< 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 >.

◆ norm_squared() [1/2]

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 >, Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >, Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >, Stokhos::ProductLanczosGramSchmidtPCEBasis< 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::QuadraturePseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::QuadraturePseudoSpectralOperator().

◆ norm_squared() [2/2]

template<typename ordinal_type , typename value_type >
virtual const value_type & Stokhos::OrthogPolyBasis< ordinal_type, value_type >::norm_squared ( ordinal_type  i) const
pure virtual

Return norm squared of basis polynomial i.

Implemented in Stokhos::CompletePolynomialBasis< ordinal_type, value_type >, Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >, Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >, Stokhos::ProductLanczosGramSchmidtPCEBasis< 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 >.

◆ order()

template<typename ordinal_type , typename value_type >
virtual ordinal_type Stokhos::OrthogPolyBasis< ordinal_type, value_type >::order ( ) const
pure virtual

Return order of basis.

Implemented in Stokhos::CompletePolynomialBasis< ordinal_type, value_type >, Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >, Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >, Stokhos::ProductLanczosGramSchmidtPCEBasis< 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 >.

◆ print()

template<typename ordinal_type , typename value_type >
virtual void Stokhos::OrthogPolyBasis< ordinal_type, value_type >::print ( std::ostream &  os) const
pure virtual

Print basis to stream os.

Implemented in Stokhos::CompletePolynomialBasis< ordinal_type, value_type >, Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >, Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >, Stokhos::ProductLanczosGramSchmidtPCEBasis< 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 >.

◆ size()

template<typename ordinal_type , typename value_type >
virtual ordinal_type Stokhos::OrthogPolyBasis< ordinal_type, value_type >::size ( ) const
pure virtual

Return total size of basis.

Implemented in Stokhos::CompletePolynomialBasis< ordinal_type, value_type >, Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >, Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >, Stokhos::ProductLanczosGramSchmidtPCEBasis< 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::BasisInteractionGraph::initialize(), Stokhos::BasisInteractionGraph::initialize(), Stokhos::PCECovarianceOp::PCECovarianceOp(), Stokhos::QuadraturePseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::QuadraturePseudoSpectralOperator(), Stokhos::sparse3Tensor2CrsGraph(), and Stokhos::TensorProductPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::TensorProductPseudoSpectralOperator().

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