| /* randist/bigauss.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> |
| |
| /* 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; |
| } |