How to do covariance analysis

From scratch

1. Get coordinates using MDTraj
2. Align the structures
3. Subtract by mean
4. Divided by SDs
5. Combine residual fluctuations (3Nx3N > NxN)

The key computation is to compute the covariances:

X = sel_traj.reshape(traj.n_frames, sel.shape[0] * 3)
X -= X.mean(axis=0)
X /= X.std(axis=0)
emp_cov = np.dot(X.T, X)/traj.n_frames

and to combine intra-residue covariances:

for ii in range(0, sel.shape[0]):
   for jj in range(0, sel.shape[0]):
       emp_cov_residue[ii][jj] = ( emp_cov[ii*3][jj*3] + emp_cov[ii*3+1][jj*3+1] + emp_cov[ii*3+2][jj*3+2] ) / 3