Gamma : Math « Development Class « Java






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  3. Math

Gamma

      
/* Copyright (C) 2003 Univ. of Massachusetts Amherst, Computer Science Dept.
   This file is part of "MALLET" (MAchine Learning for LanguagE Toolkit).
   http://www.cs.umass.edu/~mccallum/mallet
   This software is provided under the terms of the Common Public License,
   version 1.0, as published by http://www.opensource.org.  For further
   information, see the file `LICENSE' included with this distribution. */

//package cc.mallet.util;


/**
 * 
 * 
 * @author <a href="mailto:casutton@cs.umass.edu">Charles Sutton</a>
 * @version $Id: ArrayUtils.java,v 1.1 2007/10/22 21:37:40 mccallum Exp $
 */
public class Util {
    public static double gamma (double x) {
        return Math.exp (logGamma(x));
    }
    public static double logBeta (double a, double b) {
      return logGamma(a)+logGamma(b)-logGamma(a+b);
    }

  // From libbow, dirichlet.c
  // Written by Tom Minka <minka@stat.cmu.edu>
  public static final double logGamma (double x)
  {
    double result, y, xnum, xden;
    int i;
    final double d1 = -5.772156649015328605195174e-1;
    final double p1[] = { 
      4.945235359296727046734888e0, 2.018112620856775083915565e2, 
      2.290838373831346393026739e3, 1.131967205903380828685045e4, 
      2.855724635671635335736389e4, 3.848496228443793359990269e4, 
      2.637748787624195437963534e4, 7.225813979700288197698961e3 
    };
    final double q1[] = {
      6.748212550303777196073036e1, 1.113332393857199323513008e3, 
      7.738757056935398733233834e3, 2.763987074403340708898585e4, 
      5.499310206226157329794414e4, 6.161122180066002127833352e4, 
      3.635127591501940507276287e4, 8.785536302431013170870835e3
    };
    final double d2 = 4.227843350984671393993777e-1;
    final double p2[] = {
      4.974607845568932035012064e0, 5.424138599891070494101986e2, 
      1.550693864978364947665077e4, 1.847932904445632425417223e5, 
      1.088204769468828767498470e6, 3.338152967987029735917223e6, 
      5.106661678927352456275255e6, 3.074109054850539556250927e6
    };
    final double q2[] = {
      1.830328399370592604055942e2, 7.765049321445005871323047e3, 
      1.331903827966074194402448e5, 1.136705821321969608938755e6, 
      5.267964117437946917577538e6, 1.346701454311101692290052e7, 
      1.782736530353274213975932e7, 9.533095591844353613395747e6
    };
    final double d4 = 1.791759469228055000094023e0;
    final double p4[] = {
      1.474502166059939948905062e4, 2.426813369486704502836312e6, 
      1.214755574045093227939592e8, 2.663432449630976949898078e9, 
      2.940378956634553899906876e10, 1.702665737765398868392998e11, 
      4.926125793377430887588120e11, 5.606251856223951465078242e11
    };
    final double q4[] = {
      2.690530175870899333379843e3, 6.393885654300092398984238e5, 
      4.135599930241388052042842e7, 1.120872109616147941376570e9, 
      1.488613728678813811542398e10, 1.016803586272438228077304e11, 
      3.417476345507377132798597e11, 4.463158187419713286462081e11
    };
    final double c[] = {
      -1.910444077728e-03, 8.4171387781295e-04, 
      -5.952379913043012e-04, 7.93650793500350248e-04, 
      -2.777777777777681622553e-03, 8.333333333333333331554247e-02, 
      5.7083835261e-03
    };
    final double a = 0.6796875;

    if((x <= 0.5) || ((x > a) && (x <= 1.5))) {
      if(x <= 0.5) {
        result = -Math.log(x);
        /*  Test whether X < machine epsilon. */
        if(x+1 == 1) {
          return result;
        }
      }
      else {
        result = 0;
        x = (x - 0.5) - 0.5;
      }
      xnum = 0;
      xden = 1;
      for(i=0;i<8;i++) {
        xnum = xnum * x + p1[i];
        xden = xden * x + q1[i];
      }
      result += x*(d1 + x*(xnum/xden));
    }
    else if((x <= a) || ((x > 1.5) && (x <= 4))) {
      if(x <= a) {
        result = -Math.log(x);
        x = (x - 0.5) - 0.5;
      }
      else {
        result = 0;
        x -= 2;
      }
      xnum = 0;
      xden = 1;
      for(i=0;i<8;i++) {
        xnum = xnum * x + p2[i];
        xden = xden * x + q2[i];
      }
      result += x*(d2 + x*(xnum/xden));
    }
    else if(x <= 12) {
      x -= 4;
      xnum = 0;
      xden = -1;
      for(i=0;i<8;i++) {
        xnum = xnum * x + p4[i];
        xden = xden * x + q4[i];
      }
      result = d4 + x*(xnum/xden);
    }
    /*  X > 12  */
    else {
      y = Math.log(x);
      result = x*(y - 1) - y*0.5 + .9189385332046727417803297;
      x = 1/x;
      y = x*x;
      xnum = c[6];
      for(i=0;i<6;i++) {
        xnum = xnum * y + c[i];
      }
      xnum *= x;
      result += xnum;
    }
    return result;
  }
  
}








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