Implementation of OneDOrthogPolyBasis via Pecos. More...

#include <Stokhos_PecosOneDOrthogPolyBasis.hpp>

Inheritance diagram for Stokhos::PecosOneDOrthogPolyBasis< ordinal_type, value_type >:

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

Public Member Functions
	PecosOneDOrthogPolyBasis (const Teuchos::RCP< Pecos::OrthogonalPolynomial > &pecosPoly, const std::string &name, ordinal_type p)
	Constructor. More...

virtual	~PecosOneDOrthogPolyBasis ()
	Destructor.

virtual void	evaluateBasesAndDerivatives (const value_type &point, Teuchos::Array< value_type > &vals, Teuchos::Array< value_type > &derivs) const
	Evaluate basis polynomials and their derivatives at given point `point`.

Public Member Functions inherited from Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >
	OneDOrthogPolyBasis ()
	Default constructor.

virtual	~OneDOrthogPolyBasis ()
	Destructor.

virtual void	setSparseGridGrowthRule (LevelToOrderFnPtr ptr)=0
	Set sparse grid rule.

Protected Member Functions
	PecosOneDOrthogPolyBasis (ordinal_type p, const PecosOneDOrthogPolyBasis &basis)
	Copy constructor with specified order.

Protected Attributes
Teuchos::RCP < Pecos::OrthogonalPolynomial >	pecosPoly
	Pointer to Pecos orthgonal polynomial object.

std::string	name
	Name of basis.

ordinal_type	p
	Order of basis.

LevelToOrderFnPtr	sparse_grid_growth_rule
	Sparse grid growth rule (as determined by Pecos)

Teuchos::Array< value_type >	norms
	Norms.

Implementation of Stokhos::OneDOrthogPolyBasis methods
typedef OneDOrthogPolyBasis < ordinal_type, value_type > ::LevelToOrderFnPtr	LevelToOrderFnPtr
	Function pointer needed for level_to_order mappings.

virtual ordinal_type	order () const
	Return order of basis (largest monomial degree ).

virtual ordinal_type	size () const
	Return total size of basis (given by order() + 1).

virtual const Teuchos::Array < value_type > &	norm_squared () const
	Return array storing norm-squared of each basis polynomial. More...

virtual const value_type &	norm_squared (ordinal_type i) const
	Return norm squared of basis polynomial `i`.

virtual Teuchos::RCP < Stokhos::Dense3Tensor < ordinal_type, value_type > >	computeTripleProductTensor () const
	Compute triple product tensor. More...

virtual Teuchos::RCP < Stokhos::Sparse3Tensor < ordinal_type, value_type > >	computeSparseTripleProductTensor (ordinal_type order) const
	Compute triple product tensor. More...

virtual Teuchos::RCP < Teuchos::SerialDenseMatrix < ordinal_type, value_type > >	computeDerivDoubleProductTensor () const
	Compute derivative double product tensor. More...

virtual void	evaluateBases (const value_type &point, Teuchos::Array< value_type > &basis_pts) const
	Evaluate each basis polynomial at given point `point`. More...

virtual value_type	evaluate (const value_type &point, ordinal_type order) const
	Evaluate basis polynomial given by order `order` at given point `point`.

virtual void	print (std::ostream &os) const
	Print basis to stream `os`.

virtual const std::string &	getName () const
	Return string name of basis.

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

virtual ordinal_type	quadDegreeOfExactness (ordinal_type n) const

virtual ordinal_type	coefficientGrowth (ordinal_type n) const
	Evaluate coefficient growth rule for Smolyak-type bases.

virtual ordinal_type	pointGrowth (ordinal_type n) const
	Evaluate point growth rule for Smolyak-type bases.

virtual LevelToOrderFnPtr	getSparseGridGrowthRule () const
	Get sparse grid level_to_order mapping function. More...

virtual void	setSparseGridGrowthRule (LevelToOrderFnPtr ptr)
	Set sparse grid rule.

virtual Teuchos::RCP < OneDOrthogPolyBasis < ordinal_type, value_type > >	cloneWithOrder (ordinal_type p) const
	Clone this object with the option of building a higher order basis. More...

Additional Inherited Members
Public Types inherited from Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >
typedef int(*	LevelToOrderFnPtr )(int level, int growth)
	Function pointer needed for level_to_order mappings.

Detailed Description

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

Implementation of OneDOrthogPolyBasis via Pecos.

Constructor & Destructor Documentation

template<typename ordinal_type , typename value_type >

Stokhos::PecosOneDOrthogPolyBasis< ordinal_type, value_type >::PecosOneDOrthogPolyBasis	(	const Teuchos::RCP< Pecos::OrthogonalPolynomial > &	pecosPoly,
		const std::string &	name,
		ordinal_type	p
	)

Constructor.

name is the name for the basis that will be displayed when printing the basis and p is the order of the basis.

References Stokhos::PecosOneDOrthogPolyBasis< ordinal_type, value_type >::norms, Stokhos::PecosOneDOrthogPolyBasis< ordinal_type, value_type >::p, and Stokhos::PecosOneDOrthogPolyBasis< ordinal_type, value_type >::pecosPoly.

Member Function Documentation

template<typename ordinal_type , typename value_type >

Teuchos::RCP< Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type > > Stokhos::PecosOneDOrthogPolyBasis< ordinal_type, value_type >::cloneWithOrder ( ordinal_type p ) const

virtual

Clone this object with the option of building a higher order basis.

This method is following the Prototype pattern (see Design Pattern's textbook). The slight variation is that it allows the order of the polynomial to be modified, otherwise an exact copy is formed. The use case for this is creating basis functions for column indices in a spatially varying adaptive refinement context.

Implements Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type >

Teuchos::RCP< Teuchos::SerialDenseMatrix< ordinal_type, value_type > > Stokhos::PecosOneDOrthogPolyBasis< ordinal_type, value_type >::computeDerivDoubleProductTensor ( ) const

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.

This method is implemented by computing $B_{ij}$ using Gaussian quadrature.

Implements Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type >

Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > Stokhos::PecosOneDOrthogPolyBasis< ordinal_type, value_type >::computeSparseTripleProductTensor ( ordinal_type order ) const

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.

Implements Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type >

Teuchos::RCP< Stokhos::Dense3Tensor< ordinal_type, value_type > > Stokhos::PecosOneDOrthogPolyBasis< ordinal_type, value_type >::computeTripleProductTensor ( ) const

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.

This method is implemented by computing $C_{ijk}$ using Gaussian quadrature.

Implements Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type >

void Stokhos::PecosOneDOrthogPolyBasis< ordinal_type, value_type >::evaluateBases	(	const value_type &	point,
		Teuchos::Array< value_type > &	basis_pts
	)		const

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().

Implements Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type >

void Stokhos::PecosOneDOrthogPolyBasis< 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

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.

The quadrature points and weights are computed from the three-term recurrence by solving a tri-diagional symmetric eigenvalue problem (see Gene H. Golub and John H. Welsch, "Calculation of Gauss Quadrature Rules", Mathematics of Computation, Vol. 23, No. 106 (Apr., 1969), pp. 221-230).

Implements Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type >

virtual LevelToOrderFnPtr Stokhos::PecosOneDOrthogPolyBasis< ordinal_type, value_type >::getSparseGridGrowthRule ( ) const

inlinevirtual

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

Implements Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >.

References Stokhos::PecosOneDOrthogPolyBasis< ordinal_type, value_type >::sparse_grid_growth_rule.

template<typename ordinal_type , typename value_type >

const Teuchos::Array< value_type > & Stokhos::PecosOneDOrthogPolyBasis< ordinal_type, value_type >::norm_squared ( ) const

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().

Implements Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type >

ordinal_type Stokhos::PecosOneDOrthogPolyBasis< ordinal_type, value_type >::quadDegreeOfExactness ( ordinal_type n ) const

virtual

Return polynomial degree of exactness for a given number of quadrature points.

Implements Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >.

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

Stokhos_PecosOneDOrthogPolyBasis.hpp
Stokhos_PecosOneDOrthogPolyBasisImp.hpp

Public Member Functions

Protected Member Functions

Protected Attributes

Implementation of Stokhos::OneDOrthogPolyBasis methods

Additional Inherited Members

Detailed Description

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

Constructor & Destructor Documentation

Member Function Documentation

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