Hamiltonian Fitting Class

class galport.HFitting(potential=None, Omega=0, axisym_potential=None, reverse=False)[source]

Bases: object

Parameters:

potential (agama.potential()) – Potential of model
axisymmetric_potential (agama.potential(symmetry='a' or 's')) – Axisymmetric or Spherical-symmetric potential for action-angle calculation
Omega (float) – Angular velocity of non-axisymmetric pattern (a bar or spirals) Default: 0
reverse (bool, optional) – Integrate orbit in both direct and reverse direction Default: False

Fitting Workflow

The fitting process follows these steps:

1. Orbit Generation – Use galport.OrbitGenerator to find initial conditions for orbits with given Jacobi integral.

2. Phase Space Calculation – Integrate orbits and compute averaged action-angle variables \((J, \dot{J}, \theta, \dot{\theta})\).

3. Hamiltonian Optimization – Fit the specified Hamiltonian model to the phase space data using least squares optimization.

Hamiltonian types

The following Hamiltonian models are available for fitting:

`Htype`	Description	Default Parameters
`'bar_2d'`	Flat bar and near-bar orbits in the xy-plane. Suitable for studying in-plane bar dynamics.	`n=[0,1,2,3]`, `deg=8`, `weight_dthetadat=10`
`'vertical_bar'`	Orbits along the major axis of a bar, including vertical motion. Assumes potential is symmetric about the z-axis.	`n=[0,2,4,-2,-4]`, `deg=4`, `weight_dthetadat=0.5`
`'buckling'`	Similar to `'vertical_bar'` but includes asymmetric terms for studying bar buckling modes.	`n=[0,1,2,3,-1,-2,-3]`, `deg=4`, `weight_dthetadat=0.5`

Example

>>> import galport
>>> HF = galport.HFitting(potential=pot, axisym_potential=pot_sym, Omega=omega)
>>> H_vilr = HF.fit(H=H, Htype='buckling', Norb=15, Tint=100, Nint=20000)

Notes

The fitting uses scipy.optimize.least_squares() with the Levenberg-Marquardt method. The residual is computed from both dJ/dt and dθ/dt terms

DEFAULT_PARAMS = {'bar_2d': {'deg': 8, 'n': [0, 1, 2, 3], 'otype': 'bar_2d', 'weight_dthetadt': 10}, 'buckling': {'deg': 4, 'n': [0, 1, 2, 3, -1, -2, -3], 'otype': 'x1v', 'weight_dthetadt': 0.5}, 'vertical_bar': {'deg': 4, 'n': [0, 2, 4, -2, -4], 'otype': 'x1v', 'weight_dthetadt': 0.5}}

__init__(potential=None, Omega=0, axisym_potential=None, reverse=False)[source]

Initialise HFitting

Parameters:

potential (agama.potential()) – Potential of model
axisymmetric_potential (agama.potential(symmetry='a' or 's')) – Axisymmetric or Spherical-symmetric potential for action-angle calculation
Omega (float) – Angular velocity of non-axisymmetric pattern (a bar or spirals) Default: 0
reverse (bool, optional) – Integrate orbit in both direct and reverse direction Default: False

fit(H, Htype, Norb=10, Tint=200, Nint=None, max_delta=1, coef_fix=None, coef_0=None, **kwargs)[source]

Fit hamiltonian

Parameters:

H (float) – Jacobi integral
Htype (str) –
- bar_2d : flat orbits on xy plane
- vertical_bar : orbits along major axis of a bar
- buckling : the same as ‘vertical_bar’, but other
Norb (int, optional) – number of orbits for fitting Default : 10
Tint (float, optional) – time of integrating orbit Default : 200
Nint (int, optional) – number of points on every orbit Default : int(Tint*100)
**kwargs (additional parameters) –
n, deg, weight_dthetadt

Default :
- 'bar_2d' : n=[0,1,2,3], weight_dthetadt=10, deg=4
- 'vertical_bar' : n=[0,2,4,-2,-4], weight_dthetadt=0.5, deg=4
- 'buckling' : n=[0,1,2,3,-1,-2,-3], weight_dthetadt=0.5, deg=4
coef_fix (2D numpy array or None) – Matrix for the Hamiltonian, where Nan correspond to coefficients, which are required to find, other - fix Default: None

Returns:

hamiltonian – Allow calculate H and derivatives of phase coordinates

Return type:

class Hamiltonian