miscFunc.java

import java.util.*;
/**
 * This class contains a mix of miscellaneous functions used
 * by other routines: stirling's approximation and the log of 
 * the approximation for factorials, the beta function, and the
 * log of the gamma function.
 * 
 * @author Eric Ward 
 * @version August 31, 2006
 */
public class miscFunc
{
    // these are constants
    final double PI = 3.14159265358979;
    final double ROOT2PI = 2.506628274631;
    final double LOGRT2PI = 0.91893853320467;
    // these variables are used for the gammln function
    private double f;
    // these variables are used for the gammln function
    private double x, y, tmp, ser;
    private int j;
    final double cof[]={76.18009172947146,-86.50532032941677,24.01409824083091,
        -1.231739572450155,0.1208650973866179e-2,-0.5395239384953e-5};

    /**
     * Constructor for objects of class misc
     */
    public miscFunc()
    {
    }

    
    /**
     * This function returns the log of the gamma function.
     * 
     * @param  xx, the value to evaluate the function at
     * @return  val, function value
     */
    public double gammln(double xx) {
        y=x=xx;
        tmp=x+5.5;
        ser=1.000000000190015;
        tmp -= (x+0.5)*Math.log(tmp);
        for (j=0;j<=5;j++) ser += cof[j]/++y;
        return (double)(-tmp+Math.log(2.5066282746310005*ser/x));
    }
    
    
    /**
     * This method uses Stirling's approximation to generate Beta
     * random variables.
     * 
     * @param  n1, the first beta parameter
     * @param  n2, the second beta parameter
     * @return  double
     */
    public double betaFunction(int n1, int n2) {
        // beta can be re-written as gamma(n1)*gamma(n2)/gamma(n1+n2)
        return stirling(n1-1)*stirling(n2-1)/stirling(n1+n2-1);
    }   

    
    /**
     * This function returns Stirling's approximation to (n!).
     * 
     * @param  n, the integer to find the factorial of.
     * @return  double
     */
    public double stirling(int n) {
        f = 1.0;
        if(n <= 10) {
            // calculate the actual factorial
            for(j = 1; j <= n; j++) f*=j;
            return f;
        }
        return (ROOT2PI*Math.pow((float)n,(float)n+0.5)*Math.exp(-(double)n));
    }

    
    /**
     * This function returns the log of Stirling's approximation to (n!).
     * 
     * @param  n, the value to find the factorial of.
     * @return  double
     */
    public double logStirling(int n) {
        f = 1.0;
        if(n <= 10) {
            // calculate the actual factorial
            // f = f * j
            for(j = 1; j <= n; j++) f*=j;
            return Math.log(f);
        }
        return (LOGRT2PI + (n+0.5)*Math.log(n) -(double)n);
    }
    
}