com.numericalmethod.suanshu.analysis.function.special.gamma

Class Lanczos

java.lang.Object

com.numericalmethod.suanshu.analysis.function.special.gamma.Lanczos

All Implemented Interfaces:

java.io.Serializable

public class Lanczos
extends java.lang.Object
implements java.io.Serializable

The Lanczos approximation is a method for computing the Gamma function numerically, published by Cornelius Lanczos in 1964. This implementation is based on the notes of Paul Godfrey and the discussion of Viktor T. Toth.

See Also:

• Wikipedia: Lanczos approximation
• A note on the computation of the convergent Lanczos complex Gamma approximation.
• The Lanczos Approximation

, Serialized Form

Constructor Summary

Constructors

Constructor and Description
Lanczos() Construct a Lanczos approximation instance using default parameters.
Lanczos(double g, int n, int scale) Construct a Lanczos approximation instance.

Method Summary

Modifier and Type	Method and Description
java.math.BigDecimal	logGamma(java.math.BigDecimal x) Compute log-gamma for a positive value x to arbitrary precision.
double	logGamma(double x) Compute log-gamma for a positive value x.
double	logGammaQuick(double x) Compute log-gamma for a positive value x.

Methods inherited from class java.lang.Object

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

Constructor Detail

Lanczos

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

Construct a Lanczos approximation instance.

Recommended settings are

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

Parameters:

g - g

n - n

scale - precision

Lanczos

public Lanczos()

Construct a Lanczos approximation instance using default parameters. The default parameters are:

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

Method Detail

logGammaQuick

public double logGammaQuick(double x)

Compute log-gamma for a positive value x. All operations are in double precision.

Parameters:

x - x in double

Returns:

lgamma(x) in double

logGamma

public double logGamma(double x)

Compute log-gamma for a positive value x. The accuracy of this function is only as good as the precision of double.

Parameters:

x - x in double

Returns:

lgamma(x) in double

logGamma

public java.math.BigDecimal logGamma(java.math.BigDecimal x)

Compute log-gamma for a positive value x to arbitrary precision.

Parameters:

x - x in BigDecimal

Returns:

lgamma(x) in BigDecimal