text: /* 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., 675 Mass Ave, Cambridge, MA 02139, 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(r))) 
                      exp(-(x^2 + y^2 - 2 r x y)/(2c)) dxdy     
  
  */
  
  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;
  }
  