Package dev.nm.analysis.function.special.gamma

Class GammaLanczos

java.lang.Object

dev.nm.analysis.function.rn2r1.AbstractRealScalarFunction

dev.nm.analysis.function.rn2r1.univariate.AbstractUnivariateRealFunction

dev.nm.analysis.function.special.gamma.GammaLanczos

All Implemented Interfaces:

Function<Vector,Double>, RealScalarFunction, UnivariateRealFunction, Gamma

public class GammaLanczos
extends AbstractUnivariateRealFunction
implements Gamma

Lanczos approximation provides a way to compute the Gamma function such that the accuracy can be made arbitrarily precise. Yet, the computations can be time-consuming if done in, e.g., BigDecimal.

See Also:

• Wikipedia: Lanczos approximation

Nested Class Summary

Nested classes/interfaces inherited from interface dev.nm.analysis.function.Function

Function.EvaluationException

Constructor Summary

Constructors

Constructor	Description
GammaLanczos()	Construct an instance of a Gamma function, computed using the Lanczos approximation.
GammaLanczos(double g, int n, int scale)	Construct an instance of a Gamma function, computed using the Lanczos approximation.

Method Summary

Modifier and Type	Method	Description
double	evaluate(double x)	Evaluate \(\Gamma(z) = \int_0^\infty e^{-t} t^{z-1} dt\).

Methods inherited from class dev.nm.analysis.function.rn2r1.univariate.AbstractUnivariateRealFunction

evaluate

Methods inherited from class dev.nm.analysis.function.rn2r1.AbstractRealScalarFunction

dimensionOfDomain, dimensionOfRange

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface dev.nm.analysis.function.Function

dimensionOfDomain, dimensionOfRange

Constructor Details

GammaLanczos

public GammaLanczos()

Construct an instance of a Gamma function, computed using the Lanczos approximation.

GammaLanczos

public GammaLanczos(double g,
 int n,
 int scale)

Construct an instance of a Gamma function, computed using the Lanczos approximation.

Recommended settings are

g = 607.0 / 128.0; n = 15; scale = 30;

Parameters:

g - g

n - n

scale - precision

Method Details

evaluate

public double evaluate(double x)

Description copied from interface: Gamma

Evaluate \(\Gamma(z) = \int_0^\infty e^{-t} t^{z-1} dt\).

Specified by:

evaluate in interface Gamma

Specified by:

evaluate in interface UnivariateRealFunction

Parameters:

x - x

Returns:

\(\Gamma(z)\)