Hermite polynomial basis. More...

#include <Stokhos_HermiteBasis.hpp>

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

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 Teuchos::RCP < OneDOrthogPolyBasis < ordinal_type, value_type > >	cloneWithOrder (ordinal_type p) const
	Clone this object with the option of building a higher order basis.
Protected Member Functions
	HermiteBasis (ordinal_type p, const HermiteBasis &basis)
	Copy constructor with specified order.
Implementation of Stokhos::RecurrenceBasis methods
virtual bool	computeRecurrenceCoefficients (ordinal_type n, Teuchos::Array< value_type > &alpha, Teuchos::Array< value_type > &beta, Teuchos::Array< value_type > &delta, Teuchos::Array< value_type > &gamma) const
	Compute recurrence coefficients.

Detailed Description

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

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.

Constructor & Destructor Documentation

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

Member Function Documentation

template<typename ordinal_type , typename value_type >

Teuchos::RCP< Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type > > Stokhos::HermiteBasis< 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 >.

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

Stokhos_HermiteBasis.hpp
Stokhos_HermiteBasisImp.hpp

Public Member Functions

Protected Member Functions

Detailed Description

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

Constructor & Destructor Documentation

Member Function Documentation

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