| /* randist/sphere.c |
| * |
| * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004 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_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; |
| } |
| } |