KuzminPotential¶
-
class
gala.potential.potential.
KuzminPotential
(m, a, units)[source]¶ Bases:
gala.potential.potential.PotentialBase
The Kuzmin flattened disk potential.
\[\Phi = -\frac{Gm}{\sqrt{x^2 + y^2 + (a + |z|)^2}}\]- Parameters
- mnumeric
Mass.
- anumeric
Flattening parameter.
- unitsiterable
Unique list of non-reducable units that specify (at minimum) the length, mass, time, and angle units.
Attributes Summary
Methods Summary
__call__
(q)Call self as a function.
acceleration
(q[, t])Compute the acceleration due to the potential at the given position(s).
circular_velocity
(q[, t])Estimate the circular velocity at the given position assuming the potential is spherical.
density
(q[, t])Compute the density value at the given position(s).
energy
(q[, t])Compute the potential energy at the given position(s).
gradient
(q[, t])Compute the gradient of the potential at the given position(s).
hessian
(q[, t])Compute the Hessian of the potential at the given position(s).
integrate_orbit
(*args, **kwargs)Warning
This is now deprecated. Convenient orbit integration should
mass_enclosed
(q[, t])Estimate the mass enclosed within the given position by assuming the potential is spherical.
plot_contours
(grid[, filled, ax, labels, …])Plot equipotentials contours.
plot_density_contours
(grid[, filled, ax, …])Plot density contours.
replace_units
(units[, copy])Change the unit system of this potential.
save
(f)Save the potential to a text file.
to_latex
()total_energy
(x, v)Compute the total energy (per unit mass) of a point in phase-space in this potential.
value
(*args, **kwargs)Attributes Documentation
-
units
¶
Methods Documentation
-
__call__
(q)¶ Call self as a function.
-
acceleration
(q, t=0.0)¶ Compute the acceleration due to the potential at the given position(s).
- Parameters
- q
PhaseSpacePosition
,Quantity
, array_like Position to compute the acceleration at.
- q
- Returns
- acc
Quantity
The acceleration. Will have the same shape as the input position array,
q
.
- acc
-
circular_velocity
(q, t=0.0)¶ Estimate the circular velocity at the given position assuming the potential is spherical.
- Parameters
- qarray_like, numeric
Position(s) to estimate the circular velocity.
- Returns
- vcirc
Quantity
Circular velocity at the given position(s). If the input position has shape
q.shape
, the output energy will have shapeq.shape[1:]
.
- vcirc
-
density
(q, t=0.0)¶ Compute the density value at the given position(s).
- Parameters
- q
PhaseSpacePosition
,Quantity
, array_like The position to compute the value of the potential. If the input position object has no units (i.e. is an
ndarray
), it is assumed to be in the same unit system as the potential.
- q
- Returns
- dens
Quantity
The potential energy or value of the potential. If the input position has shape
q.shape
, the output energy will have shapeq.shape[1:]
.
- dens
-
energy
(q, t=0.0)¶ Compute the potential energy at the given position(s).
- Parameters
- q
PhaseSpacePosition
,Quantity
, array_like The position to compute the value of the potential. If the input position object has no units (i.e. is an
ndarray
), it is assumed to be in the same unit system as the potential.
- q
- Returns
- E
Quantity
The potential energy per unit mass or value of the potential.
- E
-
gradient
(q, t=0.0)¶ Compute the gradient of the potential at the given position(s).
- Parameters
- q
PhaseSpacePosition
,Quantity
, array_like The position to compute the value of the potential. If the input position object has no units (i.e. is an
ndarray
), it is assumed to be in the same unit system as the potential.
- q
- Returns
- grad
Quantity
The gradient of the potential. Will have the same shape as the input position.
- grad
-
hessian
(q, t=0.0)¶ Compute the Hessian of the potential at the given position(s).
- Parameters
- q
PhaseSpacePosition
,Quantity
, array_like The position to compute the value of the potential. If the input position object has no units (i.e. is an
ndarray
), it is assumed to be in the same unit system as the potential.
- q
- Returns
- hess
Quantity
The Hessian matrix of second derivatives of the potential. If the input position has shape
q.shape
, the output energy will have shape(q.shape[0],q.shape[0]) + q.shape[1:]
. That is, ann_dim
byn_dim
array (matrix) for each position.
- hess
-
integrate_orbit
(*args, **kwargs)¶ Warning
This is now deprecated. Convenient orbit integration should happen using the
gala.potential.Hamiltonian
class. With a static reference frame, you just need to pass your potential in to theHamiltonian
constructor.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.
- Integrator_kwargsdict (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. See documentation for
parse_time_specification
.
- w0
- Returns
- orbit
Orbit
- orbit
-
mass_enclosed
(q, t=0.0)¶ Estimate the mass enclosed within the given position by assuming the potential is spherical.
- Parameters
- q
PhaseSpacePosition
,Quantity
, array_like Position(s) to estimate the enclossed mass.
- q
- Returns
- menc
Quantity
Mass enclosed at the given position(s). If the input position has shape
q.shape
, the output energy will have shapeq.shape[1:]
.
- menc
-
plot_contours
(grid, filled=True, ax=None, labels=None, subplots_kw={}, **kwargs)¶ Plot equipotentials contours. Computes the potential energy on a grid (specified by the array
grid
).Warning
Right now the grid input must be arrays and must already be in the unit system of the potential. Quantity support is coming…
- Parameters
- gridtuple
Coordinate grids or slice value for each dimension. Should be a tuple of 1D arrays or numbers.
- filledbool (optional)
Use
contourf()
instead ofcontour()
. Default isTrue
.- axmatplotlib.Axes (optional)
- labelsiterable (optional)
List of axis labels.
- subplots_kwdict
kwargs passed to matplotlib’s subplots() function if an axes object is not specified.
- kwargsdict
kwargs passed to either contourf() or plot().
- Returns
- fig
Figure
- fig
-
plot_density_contours
(grid, filled=True, ax=None, labels=None, subplots_kw={}, **kwargs)¶ Plot density contours. Computes the density on a grid (specified by the array
grid
).Warning
Right now the grid input must be arrays and must already be in the unit system of the potential. Quantity support is coming…
- Parameters
- gridtuple
Coordinate grids or slice value for each dimension. Should be a tuple of 1D arrays or numbers.
- filledbool (optional)
Use
contourf()
instead ofcontour()
. Default isTrue
.- axmatplotlib.Axes (optional)
- labelsiterable (optional)
List of axis labels.
- subplots_kwdict
kwargs passed to matplotlib’s subplots() function if an axes object is not specified.
- kwargsdict
kwargs passed to either contourf() or plot().
- Returns
- fig
Figure
- fig
-
replace_units
(units, copy=True)¶ Change the unit system of this potential.
- Parameters
- units
UnitSystem
Set of non-reducable units that specify (at minimum) the length, mass, time, and angle units.
- copybool (optional)
If True, returns a copy, if False, changes this object.
- units
-
save
(f)¶ Save the potential to a text file. See
save()
for more information.- Parameters
- fstr, file_like
A filename or file-like object to write the input potential object to.
-
to_latex
()¶
-
total_energy
(x, v)¶ Compute the total energy (per unit mass) of a point in phase-space in this potential. Assumes the last axis of the input position / velocity is the dimension axis, e.g., for 100 points in 3-space, the arrays should have shape (100,3).
- Parameters
- xarray_like, numeric
Position.
- varray_like, numeric
Velocity.
-
value
(*args, **kwargs)¶