Hamiltonian¶
- class gala.potential.hamiltonian.Hamiltonian(potential, frame=None)¶
Bases:
gala.potential.common.CommonBase
Represents a composition of a gravitational potential and a reference frame.
This class is used to integrate orbits and compute quantities when working in non-inertial reference frames. The input potential and frame objects must have the same dimensionality and the same unit system. If both the potential and the frame are implemented in C, numerical orbit integration will use the C-implemented integrators and will be fast (to check if your object is C-enabled, check the
.c_enabled
attribute).- Parameters
- potential
PotentialBase
subclass The gravitational potential.
- frame
FrameBase
subclass (optional) The reference frame.
- potential
Attributes Summary
Methods Summary
__call__
(w)Call self as a function.
energy
(w[, t])Compute the energy (the value of the Hamiltonian) at the given phase-space position(s).
gradient
(w[, t])Compute the gradient of the Hamiltonian at the given phase-space position(s).
hessian
(w[, t])Compute the Hessian of the Hamiltonian at the given phase-space position(s).
integrate_orbit
(w0[, Integrator, ...])Integrate an orbit in the current potential using the integrator class provided.
Attributes Documentation
- units¶
Methods Documentation
- __call__(w)¶
Call self as a function.
- energy(w, t=0.0)¶
Compute the energy (the value of the Hamiltonian) at the given phase-space position(s).
- Parameters
- w
PhaseSpacePosition
, array_like The phase-space position to compute the value of the Hamiltonian. If the input object has no units (i.e. is an
ndarray
), it is assumed to be in the same unit system as the potential class.
- w
- Returns
- H
Quantity
Energy per unit mass or value of the Hamiltonian. If the input phase-space position has shape
w.shape
, the output energy will have shapew.shape[1:]
.
- H
- gradient(w, t=0.0)¶
Compute the gradient of the Hamiltonian at the given phase-space position(s).
- Parameters
- w
PhaseSpacePosition
, array_like The phase-space position to compute the value of the Hamiltonian. If the input object has no units (i.e. is an
ndarray
), it is assumed to be in the same unit system as the potential class.
- w
- Returns
- hessian(w, t=0.0)¶
Compute the Hessian of the Hamiltonian at the given phase-space position(s).
- Parameters
- w
PhaseSpacePosition
, array_like The phase-space position to compute the value of the Hamiltonian. If the input object has no units (i.e. is an
ndarray
), it is assumed to be in the same unit system as the potential class.
- w
- Returns
- # TODO:
see
TODO
about
units
about
- hess
Quantity
The Hessian matrix of second derivatives of the potential. If the input position has shape
w.shape
, the output energy will have shape(w.shape[0],w.shape[0]) + w.shape[1:]
. That is, ann_dim
byn_dim
array (matrix) for each position, where the dimensionality of phase-space isn_dim
.
- # TODO:
- integrate_orbit(w0, Integrator=None, Integrator_kwargs={}, cython_if_possible=True, **time_spec)¶
Integrate an orbit in the current potential using the integrator class provided. Uses same time specification as
Integrator.run()
– see the documentation forgala.integrate
for more information.- Parameters
- w0
PhaseSpacePosition
, array_like Initial conditions.
- Integrator
Integrator
(optional) Integrator class to use. By default, uses
LeapfrogIntegrator
if the frame is static andDOPRI853Integrator
else.- Integrator_kwargs
dict
(optional) Any extra keyword argumets to pass to the integrator class when initializing. Only works in non-Cython mode.
- cython_if_possiblebool (optional)
If there is a Cython version of the integrator implemented, and the potential object has a C instance, using Cython will be much faster.
- **time_spec
Specification of how long to integrate. Most commonly, this is a timestep
dt
and number of stepsn_steps
, or a timestepdt
, initial timet1
, and final timet2
. You may also pass in a time array witht
. See documentation forparse_time_specification
for more information.
- w0
- Returns
- orbit
Orbit
- orbit