Class Gamma

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

public class Gamma extends Object
This is a utility class that provides computation methods related to the Gamma family of functions.
Version:
$Revision: 1042510 $ $Date: 2010-12-06 02:54:18 +0100 (lun. 06 déc. 2010) $
  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    static final double
  • Method Summary

    Modifier and Type
    Method
    Description
    static double
    digamma(double x)
    Computes the digamma function of x.
    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).
    static double
    trigamma(double x)
    Computes the trigamma function of x.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
  • Field Details

  • Method Details

    • 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:
      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:
      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:
      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.
    • digamma

      public static double digamma(double x)

      Computes the digamma function of x.

      This is an independently written implementation of the algorithm described in Jose Bernardo, Algorithm AS 103: Psi (Digamma) Function, Applied Statistics, 1976.

      Some of the constants have been changed to increase accuracy at the moderate expense of run-time. The result should be accurate to within 10^-8 absolute tolerance for x >= 10^-5 and within 10^-8 relative tolerance for x > 0.

      Performance for large negative values of x will be quite expensive (proportional to |x|). Accuracy for negative values of x should be about 10^-8 absolute for results less than 10^5 and 10^-8 relative for results larger than that.

      Parameters:
      x - the argument
      Returns:
      digamma(x) to within 10-8 relative or absolute error whichever is smaller
      Since:
      2.0
      See Also:
    • trigamma

      public static double trigamma(double x)

      Computes the trigamma function of x. This function is derived by taking the derivative of the implementation of digamma.

      Parameters:
      x - the argument
      Returns:
      trigamma(x) to within 10-8 relative or absolute error whichever is smaller
      Since:
      2.0
      See Also: