/* randist/sphere.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004, 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 <config.h>
#include <math.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
void
gsl_ran_dir_2d (const gsl_rng * r, double *x, double *y)
{
/* This method avoids trig, but it does take an average of 8/pi =
* 2.55 calls to the RNG, instead of one for the direct
* trigonometric method. */
double u, v, s;
do
{
u = -1 + 2 * gsl_rng_uniform (r);
v = -1 + 2 * gsl_rng_uniform (r);
s = u * u + v * v;
}
while (s > 1.0 || s == 0.0);
/* This is the Von Neumann trick. See Knuth, v2, 3rd ed, p140
* (exercise 23). Note, no sin, cos, or sqrt ! */
*x = (u * u - v * v) / s;
*y = 2 * u * v / s;
/* Here is the more straightforward approach,
* s = sqrt (s); *x = u / s; *y = v / s;
* It has fewer total operations, but one of them is a sqrt */
}
void
gsl_ran_dir_2d_trig_method (const gsl_rng * r, double *x, double *y)
{
/* This is the obvious solution... */
/* It ain't clever, but since sin/cos are often hardware accelerated,
* it can be faster -- it is on my home Pentium -- than von Neumann's
* solution, or slower -- as it is on my Sun Sparc 20 at work
*/
double t = 6.2831853071795864 * gsl_rng_uniform (r); /* 2*PI */
*x = cos (t);
*y = sin (t);
}
void
gsl_ran_dir_3d (const gsl_rng * r, double *x, double *y, double *z)
{
double s, a;
/* This is a variant of the algorithm for computing a random point
* on the unit sphere; the algorithm is suggested in Knuth, v2,
* 3rd ed, p136; and attributed to Robert E Knop, CACM, 13 (1970),
* 326.
*/
/* Begin with the polar method for getting x,y inside a unit circle
*/
do
{
*x = -1 + 2 * gsl_rng_uniform (r);
*y = -1 + 2 * gsl_rng_uniform (r);
s = (*x) * (*x) + (*y) * (*y);
}
while (s > 1.0);
*z = -1 + 2 * s; /* z uniformly distributed from -1 to 1 */
a = 2 * sqrt (1 - s); /* factor to adjust x,y so that x^2+y^2
* is equal to 1-z^2 */
*x *= a;
*y *= a;
}
void
gsl_ran_dir_nd (const gsl_rng * r, size_t n, double *x)
{
double d;
size_t i;
/* See Knuth, v2, 3rd ed, p135-136. The method is attributed to
* G. W. Brown, in Modern Mathematics for the Engineer (1956).
* The idea is that gaussians G(x) have the property that
* G(x)G(y)G(z)G(...) is radially symmetric, a function only
* r = sqrt(x^2+y^2+...)
*/
d = 0;
do
{
for (i = 0; i < n; ++i)
{
x[i] = gsl_ran_gaussian (r, 1.0);
d += x[i] * x[i];
}
}
while (d == 0);
d = sqrt (d);
for (i = 0; i < n; ++i)
{
x[i] /= d;
}
}
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