/*
* GammaFunction.java
*
* Copyright (c) 2002-2015 Alexei Drummond, Andrew Rambaut and Marc Suchard
*
* This file is part of BEAST.
* See the NOTICE file distributed with this work for additional
* information regarding copyright ownership and licensing.
*
* BEAST is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as
* published by the Free Software Foundation; either version 2
* of the License, or (at your option) any later version.
*
* BEAST is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with BEAST; if not, write to the
* Free Software Foundation, Inc., 51 Franklin St, Fifth Floor,
* Boston, MA 02110-1301 USA
*/
package dr.math.functionEval;
/**
* Gamma function (Euler's integral).
*
* @author Didier H. Besset
*/
public final class GammaFunction
{
static double sqrt2Pi = Math.sqrt( 2 * Math.PI);
static double[] coefficients = { 76.18009172947146,
-86.50532032941677,
24.01409824083091,
-1.231739572450155,
0.1208650973866179e-2,
-0.5395239384953e-5};
/**
* @return double beta function of the arguments
* @param x double
* @param y double
*/
public static double beta ( double x, double y)
{
return Math.exp( logGamma( x) + logGamma( y) - logGamma( x + y));
}
/**
* @return long factorial of n
* @param n long
*/
public static long factorial ( long n)
{
return n < 2 ? 1 : n * factorial( n - 1);
}
/**
* @return double gamma function
* @param x double
*/
public static double gamma ( double x)
{
return x > 1
? Math.exp( leadingFactor(x)) * series(x) * sqrt2Pi / x
: ( x > 0 ? gamma(x + 1) / x
: Double.NaN);
}
/**
* @return double
* @param x double
*/
private static double leadingFactor ( double x)
{
double temp = x + 5.5;
return Math.log( temp) * ( x + 0.5) - temp;
}
/**
* @return double logarithm of the beta function of the arguments
* @param x double
* @param y double
*/
public static double logBeta ( double x, double y)
{
return logGamma( x) + logGamma( y) - logGamma( x + y);
}
/**
* @return double log of the gamma function
* @param x double
*/
public static double logGamma ( double x)
{
return x > 1
? leadingFactor(x) + Math.log( series(x) * sqrt2Pi / x)
: ( x > 0 ? logGamma(x + 1) - Math.log( x)
: Double.NaN);
}
/**
* @return double value of the series in Lanczos formula.
* @param x double
*/
private static double series( double x)
{
double answer = 1.000000000190015;
double term = x;
for ( int i = 0; i < 6; i++)
{
term += 1;
answer += coefficients[i] / term;
}
return answer;
}
}