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- /* 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 "gsl__config.h"
- #include <math.h>
- #include "gsl_math.h"
- #include "gsl_rng.h"
- #include "gsl_randist.h"
- #include "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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