FANTASY: User-friendly Symplectic Geodesic Integrator for Arbitrary Metrics with Automatic Differentiation

Pierre Christian, Chi Kwan Chan

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We present FANTASY (Finally A Numerical Trajectory Algorithm both Straightforward and sYmplectic), a user-friendly, open-source symplectic geodesic integrator written in Python. FANTASY is designed to work "out of the box"and does not require anything from the user aside from the metric and the initial conditions for the geodesics. FANTASY efficiently computes derivatives up to machine precision using automatic differentiation, allowing the integration of geodesics in arbitrary space(times) without the need for the user to manually input Christoffel symbols or any other metric derivatives. Further, FANTASY utilizes a Hamiltonian integration scheme that doubles the phase space, where two copies of the particle phase space are evolved together. This technique allows for an integration scheme that is both explicit and symplectic, even when the Hamiltonian is not separable. FANTASY comes prebuilt with second- and fourth-order schemes, and is easily extendable to higher-order schemes. FANTASY also includes an automatic Jacobian calculator that allows for coordinate transformations to be done automatically.

Original languageEnglish (US)
Article number67
JournalAstrophysical Journal
Issue number1
StatePublished - Mar 1 2021

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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