LegendreOrthogPolynomial Class Reference

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

Inheritance diagram for LegendreOrthogPolynomial:

List of all members.

Public Member Functions
	LegendreOrthogPolynomial ()
	default constructor
	~LegendreOrthogPolynomial ()
	destructor
Protected Member Functions
const Real &	get_value (const Real &x, unsigned short order)
	retrieve the Legendre polynomial value for a given parameter x
const Real &	get_gradient (const Real &x, unsigned short order)
	retrieve the Legendre polynomial gradient for a given parameter x
const Real &	norm_squared (unsigned short order)
	return the inner product <P_n,P_n> = ||P_n||^2
const RealVector &	gauss_points (unsigned short order)
	polynomial order n
const RealVector &	gauss_weights (unsigned short order)
	polynomial order n

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Detailed Description

Derived orthogonal polynomial class for Legendre polynomials.

The LegendreOrthogPolynomial class evaluates a univariate Legendre polynomial of a particular order. These polynomials are orthogonal with respect to the weight function 1 when integrated over the support range of [-1,+1]. This corresponds to the probability density function f(x) = 1/(U-L) = 1/2 for the uniform distribution for [L,U]=[-1,1]. It enables (mixed) multidimensional orthogonal polynomial basis functions within OrthogPolyApproximation. Legendre polynomials are a special case (alpha = beta = 0) of the more general Jacobi polynomials (implemented separately) which correspond to the beta distribution.

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

• LegendreOrthogPolynomial.H
• LegendreOrthogPolynomial.C

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