/* randist/beta.c

 * 

 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 James Theiler, Brian Gough

 * 

 * This program is free software; you can redistribute it and/or modify

 * it under the terms of the GNU General Public License as published by

 * the Free Software Foundation; either version 3 of the License, or (at

 * your option) any later version.

 * 

 * This program 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

 * General Public License for more details.

 * 

 * You should have received a copy of the GNU General Public License

 * along with this program; if not, write to the Free Software

 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.

 */

#include <config.h>

#include <math.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_rng.h>

#include <gsl/gsl_randist.h>

#include <gsl/gsl_sf_gamma.h>

/* The beta distribution has the form

   p(x) dx = (Gamma(a + b)/(Gamma(a) Gamma(b))) x^(a-1) (1-x)^(b-1) dx

   The method used here is the one described in Knuth */

double

gsl_ran_beta (const gsl_rng * r, const double a, const double b)

{

  if ( (a <= 1.0) && (b <= 1.0) )

    {

      double U, V, X, Y;

      while (1)

        {

          U = gsl_rng_uniform_pos(r);

          V = gsl_rng_uniform_pos(r);

          X = pow(U, 1.0/a);

          Y = pow(V, 1.0/b);

          if ((X + Y ) <= 1.0)

            {

              if (X + Y > 0)

                {

                  return X/ (X + Y);

                }

              else

                {

                  double logX = log(U)/a;

                  double logY = log(V)/b;

                  double logM = logX > logY ? logX: logY;

                  logX -= logM;

                  logY -= logM;

                  return exp(logX - log(exp(logX) + exp(logY)));

                }

            }

        }

    }

  else

    {

      double x1 = gsl_ran_gamma (r, a, 1.0);

      double x2 = gsl_ran_gamma (r, b, 1.0);

      return x1 / (x1 + x2);

    }

}

double

gsl_ran_beta_pdf (const double x, const double a, const double b)

{

  if (x < 0 || x > 1)

    {

      return 0 ;

    }

  else 

    {

      double p;

      double gab = gsl_sf_lngamma (a + b);

      double ga = gsl_sf_lngamma (a);

      double gb = gsl_sf_lngamma (b);

      if (x == 0.0 || x == 1.0) 

        {

	  if (a > 1.0 && b > 1.0)

	    {

	      p = 0.0;

	    }

	  else

	    {

	      p = exp (gab - ga - gb) * pow (x, a - 1) * pow (1 - x, b - 1);

	    }

        }

      else

        {

          p = exp (gab - ga - gb + log(x) * (a - 1)  + log1p(-x) * (b - 1));

        }

      return p;

    }

}