com.numericalmethod.suanshu.analysis.function.special
Class LogGamma

java.lang.Object
  com.numericalmethod.suanshu.analysis.function.rn2r1.UnivariateRealFunction
      com.numericalmethod.suanshu.analysis.function.special.LogGamma

All Implemented Interfaces:

Function, RealScalarFunction

public class LogGamma
extends UnivariateRealFunction

This computes an approximation to the log Gamma function, log(Γ(z)), for positive real numbers.

We provide a few ways to compute log(Γ(z)). Each method differs in accuracy and speed. For example,

The full Lanczos approximation can be made arbitrarily precise because it is computed using BigDecimal.

The quick Lanczos approximation is quick but could be less precise because the computations are done in double precision.

See Also:

• Wikipedia: Gamma function
• Wikipedia: Lanczos approximation

Nested Class Summary

static class

LogGamma.Method the methods available to compute log(Γ(z))

Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.analysis.function.Function

Function.EvaluationException

Constructor Summary

LogGamma()
Construct an instance to compute for log Gamma function with default settings.

LogGamma(LogGamma.Method method, double g, int n, int scale)
Construct an instance to compute for log Gamma function.

Method Summary

double

evaluate(double x) Compute for the Gamma function in the positive Real domain.

Methods inherited from class com.numericalmethod.suanshu.analysis.function.rn2r1.UnivariateRealFunction

dimension4Domain, dimension4Range, evaluate

Methods inherited from class java.lang.Object

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

Constructor Detail

LogGamma

public LogGamma()

Construct an instance to compute for log Gamma function with default settings.

LogGamma

public LogGamma(LogGamma.Method method,
                double g,
                int n,
                int scale)

Construct an instance to compute for log Gamma function.

Recommended settings are

g = 607.0 / 128.0 n = 15 scale = 30

Parameters:

method - the algorithm to use, which affects only precision

g - g

n - n

scale - precision

Method Detail

evaluate

public double evaluate(double x)

Compute for the Gamma function in the positive Real domain.

Specified by:

evaluate in class UnivariateRealFunction

Parameters:

x - a real number > 0

Returns:

log(Γ(z))