/* randist/gausstail.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_erf.h>

double

gsl_ran_gaussian_tail (const gsl_rng * r, const double a, const double sigma)

{

  /* Returns a gaussian random variable larger than a

   * This implementation does one-sided upper-tailed deviates.

   */

  double s = a / sigma;

  if (s < 1)

    {

      /* For small s, use a direct rejection method. The limit s < 1

         can be adjusted to optimise the overall efficiency */

      double x;

      do

        {

          x = gsl_ran_gaussian (r, 1.0);

        }

      while (x < s);

      return x * sigma;

    }

  else

    {

      /* Use the "supertail" deviates from the last two steps

       * of Marsaglia's rectangle-wedge-tail method, as described

       * in Knuth, v2, 3rd ed, pp 123-128.  (See also exercise 11, p139,

       * and the solution, p586.)

       */

      double u, v, x;

      do

        {

          u = gsl_rng_uniform (r);

          do

            {

              v = gsl_rng_uniform (r);

            }

          while (v == 0.0);

          x = sqrt (s * s - 2 * log (v));

        }

      while (x * u > s);

      return x * sigma;

    }

}

double

gsl_ran_gaussian_tail_pdf (const double x, const double a, const double sigma)

{

  if (x < a)

    {

      return 0;

    }

  else

    {

      double N, p;

      double u = x / sigma ;

      double f = gsl_sf_erfc (a / (sqrt (2.0) * sigma));

      N = 0.5 * f;

      p = (1 / (N * sqrt (2 * M_PI) * sigma)) * exp (-u * u / 2);

      return p;

    }

}

double

gsl_ran_ugaussian_tail (const gsl_rng * r, const double a)

{

  return gsl_ran_gaussian_tail (r, a, 1.0) ;

}

double

gsl_ran_ugaussian_tail_pdf (const double x, const double a)

{

  return gsl_ran_gaussian_tail_pdf (x, a, 1.0) ;

}