如何计算Spark MLLib中的γ？

Question

I am trying to implement Log likelihood function of Buytillyoudie model in Spark MLLib.

L(r, α, a, b |X = x, tx, T) = A1 · A2 · (A3 + δx>0 A4)

where

  A1 = Γ(r + x)αr/Γ(r)
  A2 = Γ(a + b)Γ(b + x)/(Γ(b)Γ(a + b + x))
  A3 = ( 1/(α + T))^(r+x)
  A4 = (a/(b+x-1))(1/(α + tx))^(r+x)

For this, I am using L-BFGS algorithm as given here https://spark.apache.org/docs/2.2.0/mllib-optimization.html

I am implementing a custom Gradient class to be passed on to L-BFGS method LBFGS.runLBFGS .

I don't know how to calculate Γ(x) in Spark. Is there any method or another optimization library which I can use to calculate gamma or gamma log? Please suggest.

PS: I got a cue from comment section to use Breeze library of Scala. But since I am using Java, it is not possible. Can I use ND4J or Apache-commons math library in Java?

Answer 1

Reads in a command line input x and prints Gamma(x) and log Gamma(x). The Gamma function is defined by : Gamma(x) = integral( t^(x-1) e^(-t), t = 0 .. infinity)

 public class Gamma {

       static double logGamma(double x) {
          double tmp = (x - 0.5) * Math.log(x + 4.5) - (x + 4.5);
          double ser = 1.0 + 76.18009173    / (x + 0)   - 86.50532033    / (x + 1)
                           + 24.01409822    / (x + 2)   -  1.231739516   / (x + 3)
                           +  0.00120858003 / (x + 4)   -  0.00000536382 / (x + 5);
          return tmp + Math.log(ser * Math.sqrt(2 * Math.PI));
       }
       static double gamma(double x) { return Math.exp(logGamma(x)); }

       public static void main(String[] args) { 
          double x = Double.parseDouble(args[0]);
          StdOut.println("Gamma(" + x + ") = " + gamma(x));
          StdOut.println("log Gamma(" + x + ") = " + logGamma(x));
       }

    }