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, 2 insertions, 0 deletions

diff --git a/src/misc.h b/src/misc.h
index f44125a..46931cb 100644
--- a/src/misc.h
+++ b/src/misc.h
@@ -16,5 +16,7 @@ int allclose(double *a, double *b, size_t n, double rel_tol, double abs_tol);
 double logsumexp(double *a, size_t n);
 double norm(double x, double mu, double sigma);
 double norm_cdf(double x, double mu, double sigma);
+double mean(const double *x, size_t n);
+double std(const double *x, size_t n);
 
 #endif