actionAngleTorus.xvJacobianFreqs(jr, jphi, jz, angler, anglephi, anglez, **kwargs)[source]

Return [R,vR,vT,z,vz,phi], the Jacobian d [R,vR,vT,z,vz,phi] / d (J,angle), the Hessian dO/dJ, and frequencies Omega corresponding to a torus at multiple sets of angles

  • jr (float) – Radial action

  • jphi (float) – Azimuthal action

  • jz (float) – Vertical action

  • angler (numpy.ndarray) – Radial angle

  • anglephi (numpy.ndarray) – Azimuthal angle

  • anglez (numpy.ndarray) – Vertical angle

  • tol (float, optional) – Goal for |dJ|/|J| along the torus (default is object-wide value)

  • dJ (float, optional) – Action difference when computing derivatives (Hessian or Jacobian) (default is object-wide value)

  • nosym (bool, optional) – If True, don’t explicitly symmetrize the Hessian (good to check errors) (default is False)


Tuple containing: - ([R,vR,vT,z,vz,phi], [N,6] array - d[R,vR,vT,z,vz,phi]/d[J,angle], –> (N,6,6) array - dO/dJ, –> (3,3) array - Omegar,Omegaphi,Omegaz, [N] arrays - Autofit error message)

Return type:



  • 2016-07-19 - Written - Bovy (UofT)