Write a ros node (say "eigens") in cpp that subscribes to the /amcl_pose topic, extracts the covariance matrix for the pose estimate and computes its eigenvectors and eigenvalues, so that the uncertainty ellipsoid can be determined. Note however that you can stop after you compute the eigenvector and eigenvalues and you do not need to compute the ellipsoid.

To compute the eigenvectors use this function:

http://docs.ros.org/kinetic/api/amcl/html/eig3_8h.html