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/* randist/lognormal.c
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 James Theiler, Brian Gough
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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#include <config.h>
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#include <math.h>
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_rng.h>
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#include <gsl/gsl_randist.h>
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/* The lognormal distribution has the form
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p(x) dx = 1/(x * sqrt(2 pi sigma^2)) exp(-(ln(x) - zeta)^2/2 sigma^2) dx
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for x > 0. Lognormal random numbers are the exponentials of
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gaussian random numbers */
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double
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gsl_ran_lognormal (const gsl_rng * r, const double zeta, const double sigma)
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{
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double u, v, r2, normal, z;
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do
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{
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/* choose x,y in uniform square (-1,-1) to (+1,+1) */
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u = -1 + 2 * gsl_rng_uniform (r);
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v = -1 + 2 * gsl_rng_uniform (r);
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/* see if it is in the unit circle */
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r2 = u * u + v * v;
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}
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while (r2 > 1.0 || r2 == 0);
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normal = u * sqrt (-2.0 * log (r2) / r2);
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z = exp (sigma * normal + zeta);
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return z;
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}
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double
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gsl_ran_lognormal_pdf (const double x, const double zeta, const double sigma)
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{
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if (x <= 0)
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{
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return 0 ;
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}
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else
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{
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double u = (log (x) - zeta)/sigma;
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double p = 1 / (x * fabs(sigma) * sqrt (2 * M_PI)) * exp (-(u * u) /2);
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return p;
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}
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}
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