Arianna

AbstractEuclideanSystem

Base abstract type for Euclidean Hamiltonian systems. All Euclidean systems require a constant positive definite matrix corresponding to the metric on the unconstrained position space. Positive definiteness is enforced by requiring metric to be of type AbstractPDMat.

AbstractRiemannianSystem

Base abstract type for Riemannian systems.

AbstractSystem

Base abstract type for Hamiltonian systems with energy H(q, p) = H₁(q) + H₂(q, p) where q – current position p – current momentum H₁ – energy term depending on state only H₂ – energy term depending on momentum and state (optionally)

In a standard Euclidean System, H₁ and H₂ correspond to potential energy and kinetic energy respectively. However, solving the Hamiltonian dynamics in more complex systems may benefit from a more flexible distinction between (state) and (momentum, state) energy components.

All abstract systems must have fields: neglogdens – function to calculate negative log density of the target function at the current position gradneglog_dens – function to calculate gradient of the negative log density of the target function at the current position

EuclideanSystem

Composite type for an (Unconstrained) Euclidean System, with kinetric energy of the form H₂(q, p) = ½ pᵀ M⁻¹ p where M is a constant positive definite matrix.