Package org.apache.commons.numbers.gamma

Class 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 Detail

      • Digamma

        public Digamma()

    • Method Detail

      • 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.