Legendre polynomial basis. More...

#include <Stokhos_LegendreBasis.hpp>

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

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

Public Member Functions
	LegendreBasis (ordinal_type p, bool normalize=false)
	Constructor.
	~LegendreBasis ()
	Destructor.
Implementation of Stokhos::OneDOrthogPolyBasis methods
virtual int	getSparseGridRule () const
	Get sparse grid rule number 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

Legendre polynomial basis.

Legendre polynomials are defined by the recurrence relationship

$\psi_{k+1}(x) = \frac{2k+1}{k+1}x\psi_{k}(x) - \frac{k}{k+1}\psi_{k-1}(x)$

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

$\rho(x) = \frac{1}{2}, \quad x\in[-1,1].$

This class implements computeRecurrenceCoefficients() using the above formula.

Constructor & Destructor Documentation

template<typename ordinal_type , typename value_type >

Stokhos::LegendreBasis< ordinal_type, value_type >::LegendreBasis	(	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 int Stokhos::LegendreBasis< ordinal_type, value_type >::getSparseGridRule ( ) 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: