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- /* randist/bigauss.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"
- /* The Bivariate Gaussian probability distribution is
- p(x,y) dxdy = (1/(2 pi sigma_x sigma_y sqrt(c)))
- exp(-((x/sigma_x)^2 + (y/sigma_y)^2 - 2 r (x/sigma_x)(y/sigma_y))/2c) dxdy
- where c = 1-r^2
- */
- void
- gsl_ran_bivariate_gaussian (const gsl_rng * r,
- double sigma_x, double sigma_y, double rho,
- double *x, double *y)
- {
- double u, v, r2, scale;
- do
- {
- /* choose x,y in uniform square (-1,-1) to (+1,+1) */
- u = -1 + 2 * gsl_rng_uniform (r);
- v = -1 + 2 * gsl_rng_uniform (r);
- /* see if it is in the unit circle */
- r2 = u * u + v * v;
- }
- while (r2 > 1.0 || r2 == 0);
- scale = sqrt (-2.0 * log (r2) / r2);
- *x = sigma_x * u * scale;
- *y = sigma_y * (rho * u + sqrt(1 - rho*rho) * v) * scale;
- }
- double
- gsl_ran_bivariate_gaussian_pdf (const double x, const double y,
- const double sigma_x, const double sigma_y,
- const double rho)
- {
- double u = x / sigma_x ;
- double v = y / sigma_y ;
- double c = 1 - rho*rho ;
- double p = (1 / (2 * M_PI * sigma_x * sigma_y * sqrt(c)))
- * exp (-(u * u - 2 * rho * u * v + v * v) / (2 * c));
- return p;
- }
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