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

Rys polynomial basis. More...

#include <Stokhos_RysBasis.hpp>

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List of all members.

Public Member Functions

 RysBasis (ordinal_type p, value_type c, bool normalize, GrowthPolicy growth=SLOW_GROWTH)
 Constructor.
 ~RysBasis ()
 Destructor.
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.

Static Public Member Functions

static value_type rysWeight (const value_type &x)
 The Rys weight function.

Protected Member Functions

 RysBasis (ordinal_type p, const RysBasis &basis)
 Copy constructor with specified order.

Detailed Description

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

Rys polynomial basis.

Rys polynomials are polynomials orthogonal with respect to the weight function

\[ w(x) = e^{\frac{-x^2}{2}} \]

defined on the interval $[-c,c]$, for a given choice of $c$. The corresponding density $\rho(x)$ is obtained by scaling $w(x)$ to unit probability.

The coefficients of the corresponding three-term recursion are generated using the Discretized Stieltjes procedure implemented by Stokhos::DiscretizedStieltjesBasis.


Constructor & Destructor Documentation

template<typename ordinal_type , typename value_type >
Stokhos::RysBasis< ordinal_type, value_type >::RysBasis ( ordinal_type  p,
value_type  c,
bool  normalize,
GrowthPolicy  growth = SLOW_GROWTH 
) [inline]

Constructor.

Parameters:
porder of the basis
cdefines domain of support of weight function
normalizewhether polynomials should be given unit norm

Member Function Documentation

template<typename ordinal_type , typename value_type >
virtual Teuchos::RCP<OneDOrthogPolyBasis<ordinal_type,value_type> > Stokhos::RysBasis< ordinal_type, value_type >::cloneWithOrder ( ordinal_type  p) const [inline, 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.

Reimplemented from Stokhos::DiscretizedStieltjesBasis< ordinal_type, value_type >.


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