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/* randist/gausstail.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 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 2 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) ;
}
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