Stokhos::HermiteBasis< ordinal_type, value_type > Class Template Reference

Hermite polynomial basis. More...

#include <Stokhos_HermiteBasis.hpp>

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

[legend]Collaboration diagram for Stokhos::HermiteBasis< ordinal_type, value_type >:


Public Member Functions
	HermiteBasis (ordinal_type p, bool normalize=false)
	Constructor.
	~HermiteBasis ()
	Destructor.
Implementation of Stokhos::OneDOrthogPolyBasis methods
virtual ordinal_type	getRule () const
	Get sparse grid rule number as defined by Dakota's `webbur` package.
virtual value_type	getQuadWeightFactor () const
	Get quadrature weight factor as defined by Dakota's `webbur` package.
virtual value_type	getQuadPointFactor () const
	Get quadrature point factor as defined by Dakota's `webbur` package.
Protected Member Functions
Implementation of Stokhos::RecurrenceBasis methods
virtual void	computeRecurrenceCoefficients (ordinal_type n, Teuchos::Array< value_type > &alpha, Teuchos::Array< value_type > &beta, Teuchos::Array< value_type > &delta) const
	Compute recurrence coefficients.

Detailed Description

Hermite polynomial basis.

Hermite polynomials are defined by the recurrence relationship

$\psi_{k+1}(x) = x\psi_{k}(x) - k\psi_{k-1}(x)$

with $\psi_{-1}(x) = 0$ and $\psi_{0}(x) = 1$ . The corresponding density function is

$\rho(x) = \frac{1}{\sqrt{2\pi}}e^{\frac{-x^2}{2}}.$

This class implements computeRecurrenceCoefficients() using the above formula.

template<typename ordinal_type, typename value_type>

Stokhos::HermiteBasis< ordinal_type, value_type >::HermiteBasis	(	ordinal_type	p,
		bool	normalize = `false`
	)

Constructor.

Parameters:

	p	order of the basis
	normalize	whether polynomials should be given unit norm

template<typename ordinal_type, typename value_type>

virtual value_type Stokhos::HermiteBasis< ordinal_type, value_type >::getQuadPointFactor ( ) const [inline, virtual]

Get quadrature point factor as defined by Dakota's webbur package.

This method is needed for building Smolyak sparse grids out of this basis.

template<typename ordinal_type, typename value_type>

virtual value_type Stokhos::HermiteBasis< ordinal_type, value_type >::getQuadWeightFactor ( ) const [inline, virtual]

Get quadrature weight factor as defined by Dakota's webbur package.

This method is needed for building Smolyak sparse grids out of this basis.

template<typename ordinal_type, typename value_type>

virtual ordinal_type Stokhos::HermiteBasis< ordinal_type, value_type >::getRule ( ) const [inline, virtual]

Get sparse grid rule number as defined by Dakota's webbur package.

This method is needed for building Smolyak sparse grids out of this basis.

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

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