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

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.
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 $d$ 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 >, Stokhos::TensorProductBasis< ordinal_type, value_type, LexographicLess< coeff_type > >, and Stokhos::TotalOrderBasis< ordinal_type, value_type, coeff_compare_type >.

Referenced by Stokhos::TensorProductPseudoSpectralOperator< ordinal_type, value_type >::TensorProductPseudoSpectralOperator().

◆ getMaxOrders()

template<typename ordinal_type, typename value_type>
virtual MultiIndex< ordinal_type > Stokhos::ProductBasis< ordinal_type, value_type >::getMaxOrders ( ) const
pure virtual

Return maximum order allowable for each coordinate basis.

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

References ProductBasis().

Referenced by Stokhos::TensorProductPseudoSpectralOperator< ordinal_type, value_type >::TensorProductPseudoSpectralOperator().

◆ index()

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

References term().

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

◆ term()

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

Referenced by index(), Stokhos::BasisInteractionGraph::initialize(), and Stokhos::TensorProductPseudoSpectralOperator< ordinal_type, value_type >::TensorProductPseudoSpectralOperator().

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