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

Hermite polynomial basis. More...

#include <Stokhos_HermiteBasis.hpp>

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List of all members.

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

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>
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.

Implements Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >.

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.

Implements Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >.

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.

Implements Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >.


The documentation for this class was generated from the following files:
Generated on Tue Jul 13 09:23:21 2010 for Stokhos by  doxygen 1.4.7