1 files changed, 119 insertions, 0 deletions
diff --git a/gsl-1.9/randist/sphere.c b/gsl-1.9/randist/sphere.c
new file mode 100644
index 0000000..f60c3e4
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+++ b/gsl-1.9/randist/sphere.c
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+/* 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;
+    }
+}