fix a bug in the theta0 calculation for a path

This commit fixes a bug in the calculation of the average rms width of the
angular distribution for a path with a KL expansion. I also made a lot of
updates to the test-path program:

- plot the distribution of the KL expansion coefficients
- plot the standard deviation of the angular distribution as a function of
  distance along with the prediction
- plot the simulated and reconstructed path in 3D

1 files changed, 27 insertions, 0 deletions

diff --git a/src/misc.c b/src/misc.c
index 189d49b..6f50033 100644
--- a/src/misc.c
+++ b/src/misc.c
@@ -397,3 +397,30 @@ double norm_cdf(double x, double mu, double sigma)
      * standard deviation `sigma`. */
     return erfc(-(x-mu)/(sqrt(2)*sigma))/2.0;
 }
+
+double mean(const double *x, size_t n)
+{
+    /* Returns the mean of the array `x`. */
+    size_t i;
+    double sum = 0.0;
+
+    for (i = 0; i < n; i++)
+        sum += x[i];
+
+    return sum/n;
+}
+
+double std(const double *x, size_t n)
+{
+    /* Returns the standard deviation of the array `x`. */
+    size_t i;
+    double sum, mu;
+
+    mu = mean(x,n);
+
+    sum = 0.0;
+    for (i = 0; i < n; i++)
+        sum += pow(x[i]-mu,2);
+
+    return sqrt(sum/n);
+}