A modified version of Matlab code in
https://theclevermachine.wordpress.com/2012/11/18/mcmc-hamiltonian-monte-carlo-a-k-a-hybrid-monte-carlo/
implementing a second order energy-preserving splitting method.

Brigida Pace, Fasma Diele, Carmela Marangi
Splitting schemes and energy preservation for separable Hamiltonian systems
Mathematics and Computers in Simulation, North-Holland, 2015, pp. 40--52