HermiteOrthogPolynomial Class Reference

Derived orthogonal polynomial class for Hermite polynomials. More...

Inheritance diagram for HermiteOrthogPolynomial:

List of all members.

Public Member Functions
	HermiteOrthogPolynomial ()
	default constructor
	~HermiteOrthogPolynomial ()
	destructor
Protected Member Functions
const Real &	get_value (const Real &x, unsigned short order)
	retrieve the Hermite polynomial value for a given parameter x
const Real &	get_gradient (const Real &x, unsigned short order)
	retrieve the Hermite polynomial gradient for a given parameter x
const Real &	norm_squared (unsigned short order)
	return the inner product <He_n,He_n> = ||He_n||^2
const RealVector &	gauss_points (unsigned short order)
	polynomial order
const RealVector &	gauss_weights (unsigned short order)
	polynomial order
Static Private Attributes
static const Real	Pi
	numerical value of Pi

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Detailed Description

Derived orthogonal polynomial class for Hermite polynomials.

The HermiteOrthogPolynomial class evaluates a univariate Hermite polynomial of a particular order. It uses the "probabilist's" formulation for which the polynomials are orthogonal with respect to the weight function 1/sqrt(2*Pi) exp(-x^2/2) when integrated over the support range of [-infinity,+infinity]. It enables (mixed) multidimensional orthogonal polynomial basis functions within OrthogPolyApproximation.

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

• HermiteOrthogPolynomial.H
• HermiteOrthogPolynomial.C

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