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

Abstract base class for 1-D orthogonal polynomials. More...

#include <Stokhos_OneDOrthogPolyBasis.hpp>

Inheritance diagram for Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >:
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Public Types

typedef int(* LevelToOrderFnPtr) (int level, int growth)
 Function pointer needed for level_to_order mappings. More...
 

Public Member Functions

 OneDOrthogPolyBasis ()
 Default constructor. More...
 
virtual ~OneDOrthogPolyBasis ()
 Destructor. More...
 
virtual ordinal_type order () const =0
 Return order of basis (largest monomial degree $P$). More...
 
virtual ordinal_type size () const =0
 Return total size of basis (given by order() + 1). More...
 
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. More...
 
virtual Teuchos::RCP< Stokhos::Dense3Tensor< ordinal_type, value_type > > computeTripleProductTensor () const =0
 Compute triple product tensor. More...
 
virtual Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > computeSparseTripleProductTensor (ordinal_type order) const =0
 Compute triple product tensor. More...
 
virtual Teuchos::RCP< Teuchos::SerialDenseMatrix< ordinal_type, value_type > > computeDerivDoubleProductTensor () const =0
 Compute derivative double product tensor. More...
 
virtual void evaluateBases (const value_type &point, Teuchos::Array< value_type > &basis_pts) const =0
 Evaluate each basis polynomial at given point point. More...
 
virtual value_type evaluate (const value_type &point, ordinal_type order) const =0
 Evaluate basis polynomial given by order order at given point point. More...
 
virtual void print (std::ostream &os) const
 Print basis to stream os. More...
 
virtual const std::string & getName () const =0
 Return string name of basis. More...
 
virtual void getQuadPoints (ordinal_type quad_order, Teuchos::Array< value_type > &points, Teuchos::Array< value_type > &weights, Teuchos::Array< Teuchos::Array< value_type > > &values) const =0
 Compute quadrature points, weights, and values of basis polynomials at given set of points points. More...
 
virtual ordinal_type quadDegreeOfExactness (ordinal_type n) const =0
 
virtual Teuchos::RCP< OneDOrthogPolyBasis< ordinal_type, value_type > > cloneWithOrder (ordinal_type p) const =0
 Clone this object with the option of building a higher order basis. More...
 
virtual ordinal_type coefficientGrowth (ordinal_type n) const =0
 Evaluate coefficient growth rule for Smolyak-type bases. More...
 
virtual ordinal_type pointGrowth (ordinal_type n) const =0
 Evaluate point growth rule for Smolyak-type bases. More...
 
virtual LevelToOrderFnPtr getSparseGridGrowthRule () const =0
 Get sparse grid level_to_order mapping function. More...
 
virtual void setSparseGridGrowthRule (LevelToOrderFnPtr ptr)=0
 Set sparse grid rule. More...
 

Private Member Functions

 OneDOrthogPolyBasis (const OneDOrthogPolyBasis &)
 
OneDOrthogPolyBasisoperator= (const OneDOrthogPolyBasis &b)
 

Detailed Description

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

Abstract base class for 1-D orthogonal polynomials.

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

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

where $\rho$ is the density function of the measure associated with the orthogonal polynomials. See Stokhos::RecurrenceBasis for a general implementation of this interface based on the three-term recurrence satisfied by these polynomials. Multivariate polynomials can be formed from a collection of univariate polynomials through tensor products (see Stokhos::CompletePolynomialBasis).

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

Definition at line 81 of file Stokhos_OneDOrthogPolyBasis.hpp.

Member Typedef Documentation

◆ LevelToOrderFnPtr

template<typename ordinal_type, typename value_type>
typedef int( * Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >::LevelToOrderFnPtr) (int level, int growth)

Function pointer needed for level_to_order mappings.

Definition at line 204 of file Stokhos_OneDOrthogPolyBasis.hpp.

Constructor & Destructor Documentation

◆ OneDOrthogPolyBasis() [1/2]

template<typename ordinal_type, typename value_type>
Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >::OneDOrthogPolyBasis ( )
inline

Default constructor.

Definition at line 85 of file Stokhos_OneDOrthogPolyBasis.hpp.

◆ ~OneDOrthogPolyBasis()

template<typename ordinal_type, typename value_type>
virtual Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >::~OneDOrthogPolyBasis ( )
inlinevirtual

Destructor.

Definition at line 88 of file Stokhos_OneDOrthogPolyBasis.hpp.

◆ OneDOrthogPolyBasis() [2/2]

template<typename ordinal_type, typename value_type>
Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >::OneDOrthogPolyBasis ( const OneDOrthogPolyBasis< ordinal_type, value_type > &  )
private

Member Function Documentation

◆ order()

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

Return order of basis (largest monomial degree $P$).

Implemented in Stokhos::RecurrenceBasis< ordinal_type, value_type >, and Stokhos::RecurrenceBasis< OrdinalType, ValueType >.

◆ size()

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

◆ norm_squared() [1/2]

template<typename ordinal_type, typename value_type>
virtual const Teuchos::Array<value_type>& Stokhos::OneDOrthogPolyBasis< 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 given by order().

Implemented in Stokhos::RecurrenceBasis< ordinal_type, value_type >, and Stokhos::RecurrenceBasis< OrdinalType, ValueType >.

◆ norm_squared() [2/2]

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

◆ computeTripleProductTensor()

template<typename ordinal_type, typename value_type>
virtual Teuchos::RCP< Stokhos::Dense3Tensor<ordinal_type, value_type> > Stokhos::OneDOrthogPolyBasis< 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 $i,j=0,\dots,P$ where $P$ is size()-1 and $k=0,\dots,p$ where $p$ is the supplied order.

Implemented in Stokhos::RecurrenceBasis< ordinal_type, value_type >, and Stokhos::RecurrenceBasis< OrdinalType, ValueType >.

◆ computeSparseTripleProductTensor()

template<typename ordinal_type, typename value_type>
virtual Teuchos::RCP< Stokhos::Sparse3Tensor<ordinal_type, value_type> > Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >::computeSparseTripleProductTensor ( ordinal_type  order) 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 $i,j=0,\dots,P$ where $P$ is size()-1 and $k=0,\dots,p$ where $p$ is the supplied order.

Implemented in Stokhos::RecurrenceBasis< ordinal_type, value_type >, and Stokhos::RecurrenceBasis< OrdinalType, ValueType >.

◆ computeDerivDoubleProductTensor()

template<typename ordinal_type, typename value_type>
virtual Teuchos::RCP< Teuchos::SerialDenseMatrix<ordinal_type, value_type> > Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >::computeDerivDoubleProductTensor ( ) const
pure virtual

Compute derivative double product tensor.

The $(i,j)$ entry of the tensor $B_{ij}$ is given by $B_{ij} = \langle\psi_i'\psi_j\rangle$ where $\psi_l$ represents basis polynomial $l$ and $i,j=0,\dots,P$ where $P$ is the order of the basis.

Implemented in Stokhos::RecurrenceBasis< ordinal_type, value_type >, and Stokhos::RecurrenceBasis< OrdinalType, ValueType >.

◆ evaluateBases()

template<typename ordinal_type, typename value_type>
virtual void Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >::evaluateBases ( const value_type &  point,
Teuchos::Array< value_type > &  basis_pts 
) const
pure virtual

Evaluate each basis polynomial at given point point.

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

Implemented in Stokhos::RecurrenceBasis< ordinal_type, value_type >, and Stokhos::RecurrenceBasis< OrdinalType, ValueType >.

◆ evaluate()

template<typename ordinal_type, typename value_type>
virtual value_type Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >::evaluate ( const value_type &  point,
ordinal_type  order 
) const
pure virtual

Evaluate basis polynomial given by order order at given point point.

Implemented in Stokhos::RecurrenceBasis< ordinal_type, value_type >, and Stokhos::RecurrenceBasis< OrdinalType, ValueType >.

◆ print()

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

◆ getName()

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

◆ getQuadPoints()

template<typename ordinal_type, typename value_type>
virtual void Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >::getQuadPoints ( ordinal_type  quad_order,
Teuchos::Array< value_type > &  points,
Teuchos::Array< value_type > &  weights,
Teuchos::Array< Teuchos::Array< value_type > > &  values 
) const
pure virtual

Compute quadrature points, weights, and values of basis polynomials at given set of points points.

quad_order specifies the order to which the quadrature should be accurate, not the number of quadrature points. The number of points is given by (quad_order + 1) / 2. Note however the passed arrays do NOT need to be sized correctly on input as they will be resized appropriately.

Implemented in Stokhos::RecurrenceBasis< ordinal_type, value_type >, Stokhos::RecurrenceBasis< OrdinalType, ValueType >, Stokhos::LanczosPCEBasis< ordinal_type, value_type >, Stokhos::LanczosProjPCEBasis< ordinal_type, value_type >, Stokhos::StieltjesPCEBasis< ordinal_type, value_type >, Stokhos::HouseTriDiagPCEBasis< ordinal_type, value_type >, Stokhos::MonoProjPCEBasis< ordinal_type, value_type >, Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >, Stokhos::ClenshawCurtisLegendreBasis< ordinal_type, value_type >, and Stokhos::GaussPattersonLegendreBasis< ordinal_type, value_type >.

◆ quadDegreeOfExactness()

template<typename ordinal_type, typename value_type>
virtual ordinal_type Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >::quadDegreeOfExactness ( ordinal_type  n) const
pure virtual

◆ cloneWithOrder()

template<typename ordinal_type, typename value_type>
virtual Teuchos::RCP<OneDOrthogPolyBasis<ordinal_type,value_type> > Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >::cloneWithOrder ( ordinal_type  p) const
pure virtual

◆ coefficientGrowth()

template<typename ordinal_type, typename value_type>
virtual ordinal_type Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >::coefficientGrowth ( ordinal_type  n) const
pure virtual

◆ pointGrowth()

template<typename ordinal_type, typename value_type>
virtual ordinal_type Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >::pointGrowth ( ordinal_type  n) const
pure virtual

◆ getSparseGridGrowthRule()

template<typename ordinal_type, typename value_type>
virtual LevelToOrderFnPtr Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >::getSparseGridGrowthRule ( ) const
pure virtual

Get sparse grid level_to_order mapping function.

Predefined functions are: webbur::level_to_order_linear_wn Symmetric Gaussian linear growth webbur::level_to_order_linear_nn Asymmetric Gaussian linear growth webbur::level_to_order_exp_cc Clenshaw-Curtis exponential growth webbur::level_to_order_exp_gp Gauss-Patterson exponential growth webbur::level_to_order_exp_hgk Genz-Keister exponential growth webbur::level_to_order_exp_f2 Fejer-2 exponential growth

Implemented in Stokhos::RecurrenceBasis< ordinal_type, value_type >, and Stokhos::RecurrenceBasis< OrdinalType, ValueType >.

◆ setSparseGridGrowthRule()

template<typename ordinal_type, typename value_type>
virtual void Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >::setSparseGridGrowthRule ( LevelToOrderFnPtr  ptr)
pure virtual

Set sparse grid rule.

◆ operator=()

template<typename ordinal_type, typename value_type>
OneDOrthogPolyBasis& Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >::operator= ( const OneDOrthogPolyBasis< ordinal_type, value_type > &  b)
private

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