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/* randist/bigauss.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 Bivariate Gaussian probability distribution is
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p(x,y) dxdy = (1/(2 pi sigma_x sigma_y sqrt(c)))
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exp(-((x/sigma_x)^2 + (y/sigma_y)^2 - 2 r (x/sigma_x)(y/sigma_y))/2c) dxdy
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where c = 1-r^2
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*/
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void
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gsl_ran_bivariate_gaussian (const gsl_rng * r,
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double sigma_x, double sigma_y, double rho,
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double *x, double *y)
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{
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double u, v, r2, scale;
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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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scale = sqrt (-2.0 * log (r2) / r2);
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*x = sigma_x * u * scale;
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*y = sigma_y * (rho * u + sqrt(1 - rho*rho) * v) * scale;
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}
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double
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gsl_ran_bivariate_gaussian_pdf (const double x, const double y,
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const double sigma_x, const double sigma_y,
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const double rho)
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{
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double u = x / sigma_x ;
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double v = y / sigma_y ;
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double c = 1 - rho*rho ;
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double p = (1 / (2 * M_PI * sigma_x * sigma_y * sqrt(c)))
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* exp (-(u * u - 2 * rho * u * v + v * v) / (2 * c));
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return p;
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}
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