org.apache.commons.math.special
Class Gamma

java.lang.Object
  org.apache.commons.math.special.Gamma

All Implemented Interfaces:

java.io.Serializable

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

This is a utility class that provides computation methods related to the Gamma family of functions.

Version:

$Revision: 233121 $ $Date: 2005-08-16 21:41:02 -0700 (Tue, 16 Aug 2005) $

See Also:

Serialized Form

Field Summary

private static double	DEFAULT_EPSILON Maximum allowed numerical error.
private static double	HALF_LOG_2_PI Avoid repeated computation of log of 2 PI in logGamma
private static double[]	lanczos Lanczos coefficients

Constructor Summary

private

Gamma() Default constructor.

Method Summary

static double	logGamma(double x) Returns the natural logarithm of the gamma function Γ(x).
static double	regularizedGammaP(double a, double x) Returns the regularized gamma function P(a, x).
static double	regularizedGammaP(double a, double x, double epsilon, int maxIterations) Returns the regularized gamma function P(a, x).
static double	regularizedGammaQ(double a, double x) Returns the regularized gamma function Q(a, x) = 1 - P(a, x).
static double	regularizedGammaQ(double a, double x, double epsilon, int maxIterations) Returns the regularized gamma function Q(a, x) = 1 - P(a, x).

Methods inherited from class java.lang.Object

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

Field Detail

DEFAULT_EPSILON

private static final double DEFAULT_EPSILON

Maximum allowed numerical error.

See Also:

Constant Field Values

lanczos

private static double[] lanczos

Lanczos coefficients

HALF_LOG_2_PI

private static final double HALF_LOG_2_PI

Avoid repeated computation of log of 2 PI in logGamma

Constructor Detail

Gamma

private Gamma()

Default constructor. Prohibit instantiation.

Method Detail

logGamma

public static double logGamma(double x)

Returns the natural logarithm of the gamma function Γ(x). The implementation of this method is based on:

• Gamma Function, equation (28).
• Lanczos Approximation, equations (1) through (5).
• Paul Godfrey, A note on the computation of the convergent Lanczos complex Gamma approximation

Parameters:

x - the value.

Returns:

log(Γ(x))

regularizedGammaP

public static double regularizedGammaP(double a,
                                       double x)
                                throws MathException

Returns the regularized gamma function P(a, x).

Parameters:

a - the a parameter.

x - the value.

Returns:

the regularized gamma function P(a, x)

Throws:

MathException - if the algorithm fails to converge.

regularizedGammaP

public static double regularizedGammaP(double a,
                                       double x,
                                       double epsilon,
                                       int maxIterations)
                                throws MathException

Returns the regularized gamma function P(a, x). The implementation of this method is based on:

• Regularized Gamma Function, equation (1).
• Incomplete Gamma Function, equation (4).
• Confluent Hypergeometric Function of the First Kind, equation (1).

Parameters:

a - the a parameter.

x - the value.

epsilon - When the absolute value of the nth item in the series is less than epsilon the approximation ceases to calculate further elements in the series.

maxIterations - Maximum number of "iterations" to complete.

Returns:

the regularized gamma function P(a, x)

Throws:

MathException - if the algorithm fails to converge.

regularizedGammaQ

public static double regularizedGammaQ(double a,
                                       double x)
                                throws MathException

Returns the regularized gamma function Q(a, x) = 1 - P(a, x).

Parameters:

a - the a parameter.

x - the value.

Returns:

the regularized gamma function Q(a, x)

Throws:

MathException - if the algorithm fails to converge.

regularizedGammaQ

public static double regularizedGammaQ(double a,
                                       double x,
                                       double epsilon,
                                       int maxIterations)
                                throws MathException

Returns the regularized gamma function Q(a, x) = 1 - P(a, x). The implementation of this method is based on:

• Regularized Gamma Function, equation (1).
• Regularized incomplete gamma function: Continued fraction representations (formula 06.08.10.0003)

Parameters:

a - the a parameter.

x - the value.

epsilon - When the absolute value of the nth item in the series is less than epsilon the approximation ceases to calculate further elements in the series.

maxIterations - Maximum number of "iterations" to complete.

Returns:

the regularized gamma function P(a, x)

Throws:

MathException - if the algorithm fails to converge.