add code to expand the track of a particle using a KL expansion

To fit the path of muons and electrons I use the Karhunen-Loeve expansion of a
random 2D walk in the polar angle in x and y. This allows you to decompose the
path into a sum over sine functions whose coefficients become random variables.
The nice thing about fitting the path in this way is that you can capture
*most* of the variation in the path using a small number of variables by only
summing over the first N terms in the expansion and it is easy to calculate the
probability of the coefficients since they are all uncorrelated.

1 files changed, 16 insertions, 0 deletions

diff --git a/src/random.c b/src/random.c
index f6cf85e..e2e5641 100644
--- a/src/random.c
+++ b/src/random.c
@@ -12,3 +12,19 @@ double randn(void)
 
     return sqrt(-2*log(u1))*cos(2*M_PI*u2);
 }
+
+void rand_sphere(double *dir)
+{
+    /* Generates a random point on the unit sphere. */
+    double u, v, theta, phi;
+
+    u = genrand_real1();
+    v = genrand_real1();
+
+    phi = 2*M_PI*u;
+    theta = acos(2*v-1);
+
+    dir[0] = sin(theta)*cos(phi);
+    dir[1] = sin(theta)*sin(phi);
+    dir[2] = cos(theta);
+}