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

Legendre polynomial basis. More...

#include <Stokhos_LegendreBasis.hpp>

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List of all members.

Public Member Functions

 LegendreBasis (ordinal_type p, bool normalize=false, GrowthPolicy growth=SLOW_GROWTH)
 Constructor.
 ~LegendreBasis ()
 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

 LegendreBasis (ordinal_type p, const LegendreBasis &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::LegendreBasis< ordinal_type, value_type >

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,
Stokhos::GrowthPolicy  growth = SLOW_GROWTH 
)

Constructor.

Parameters:
porder of the basis
normalizewhether 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::LegendreBasis< 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 >.

Reimplemented in Stokhos::ClenshawCurtisLegendreBasis< ordinal_type, value_type >, and Stokhos::GaussPattersonLegendreBasis< ordinal_type, value_type >.


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