GenLaguerreOrthogPolynomial Class Reference

Derived orthogonal polynomial class for generalized Laguerre polynomials. More...

Inheritance diagram for GenLaguerreOrthogPolynomial:

List of all members.

Public Member Functions
	GenLaguerreOrthogPolynomial ()
	default constructor
	GenLaguerreOrthogPolynomial (const Real &alpha_stat)
	standard constructor
	~GenLaguerreOrthogPolynomial ()
	destructor
Protected Member Functions
const Real &	get_value (const Real &x, unsigned short order)
	parameter x
const Real &	get_gradient (const Real &x, unsigned short order)
	given parameter x
const Real &	norm_squared (unsigned short order)
	return the inner product <L^(alpha)_n,L^(alpha)_n> = ||L^(alpha)_n||^2
const RealVector &	gauss_points (unsigned short order)
	corresponding to polynomial order n
const RealVector &	gauss_weights (unsigned short order)
	corresponding to polynomial order n
void	alpha_stat (const Real &alpha)
	set alphaPoly using the conversion alphaPoly = alpha_stat-1.
Private Attributes
Real	alphaPoly
	by Abramowitz and Stegun (differs from statistical PDF notation)

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Detailed Description

Derived orthogonal polynomial class for generalized Laguerre polynomials.

The GenLaguerreOrthogPolynomial class evaluates a univariate generalized/associated Laguerre polynomial L^(alpha)_n of a particular order. These polynomials are orthogonal with respect to the weight function x^alpha exp(-x) when integrated over the support range of [0,+infinity]. This corresponds to the probability density function f(x) = x^alpha exp(-x) / Gamma(alpha+1) for the standard gamma distribution, although common statistical PDF parameter conventions (see, e.g., the uncertain variables section in the DAKOTA Reference Manual) and the Abramowitz and Stegun orthogonal polynomial parameter conventions require an offset conversion in this case (alpha_poly = alpha_stat - 1 with the poly definition used in both cases above). It enables (mixed) multidimensional orthogonal polynomial basis functions within OrthogPolyApproximation. A special case is the LaguerreOrthogPolynomial (implemented separately), for which alpha_poly = 0 and weight function = exp(-x) (the standard exponential distribution).

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

• GenLaguerreOrthogPolynomial.H
• GenLaguerreOrthogPolynomial.C

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