Package org.apache.commons.numbers.gamma

Class Digamma

java.lang.Object
org.apache.commons.numbers.gamma.Digamma
public class Digamma
extends java.lang.Object
Digamma function.

It is defined as the logarithmic derivative of the \( \Gamma \) (Gamma) function: \( \frac{d}{dx}(\ln \Gamma(x)) = \frac{\Gamma^\prime(x)}{\Gamma(x)} \).

See Also:
Gamma

  • Constructor Summary

    Constructors 
    Constructor Description
    Digamma()  

  • Method Summary

    Modifier and Type Method Description
    static double value​(double x)
    Computes the digamma function.

    Methods inherited from class java.lang.Object

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

  • Constructor Details

  • Method Details

    • value

      public static double value​(double x)
      Computes the digamma function. This is an independently written implementation of the algorithm described in Jose Bernardo, Algorithm AS 103: Psi (Digamma) Function, Applied Statistics, 1976. A reflection formula is incorporated to improve performance on negative values. Some of the constants have been changed to increase accuracy at the moderate expense of run-time. The result should be accurate to within 1e-8. relative tolerance for 0 < x < 1e-5 and within 1e-8 absolute tolerance otherwise.
      Parameters:
      x - Argument.
      Returns:
      digamma(x) to within 1e-8 relative or absolute error whichever is larger.