PlummerPotential¶
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class
gala.potential.
PlummerPotential
(m, b, units)¶ Bases:
gala.potential.CPotentialBase
Plummer potential for a spheroid.
\[\Phi(r) = -\frac{G M}{\sqrt{r^2 + b^2}}\]Parameters: m : numeric
Mass.
b : numeric
Core concentration.
units :
UnitSystem
(optional)Set of non-reducable units that specify (at minimum) the length, mass, time, and angle units.
Methods Summary
__call__
(q)acceleration
(q[, t])Compute the acceleration due to the potential at the given position(s). density
(q[, t])Compute the density value 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
(w0[, Integrator, ...])Integrate an orbit in the current potential using the integrator class provided. mass_enclosed
(q, t)Estimate the mass enclosed within the given position by assuming the potential is spherical. plot_contours
(grid[, ax, labels, subplots_kw])Plot equipotentials contours. plot_densty_contours
(grid[, ax, labels, ...])Plot density contours. save
(f)Save the potential to a text file. total_energy
(x, v)Compute the total energy (per unit mass) of a point in phase-space in this potential. value
(q[, t])Compute the value of the potential at the given position(s). Methods Documentation
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__call__
(q)¶
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acceleration
(q, t=0.0)¶ Compute the acceleration due to the potential at the given position(s).
Parameters: q : array_like, numeric
Position to compute the acceleration at.
Returns: acc :
ndarray
The acceleration. Will have the same shape as the input position array,
q
.
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density
(q, t=0.0)¶ Compute the density value at the given position(s).
Parameters: q :
Quantity
, array_likeThe 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.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:]
.
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gradient
(q, t=0.0)¶ Compute the gradient of the potential at the given position(s).
Parameters: q :
Quantity
, array_likeThe 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.Returns: grad :
Quantity
The gradient of the potential. Will have the same shape as the input position array,
q
.
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hessian
(q, t=0.0)¶ Compute the Hessian of the potential at the given position(s).
Parameters: q :
Quantity
, array_likeThe 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.Returns: hess :
Quantity
TODO:
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integrate_orbit
(w0, Integrator=<class 'gala.integrate.pyintegrators.leapfrog.LeapfrogIntegrator'>, 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_likeInitial conditions.
Integrator :
Integrator
(optional)Integrator class to use.
Integrator_kwargs : dict (optional)
Any extra keyword argumets to pass to the integrator class when initializing. Only works in non-Cython mode.
cython_if_possible : bool (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
.Returns: orbit :
CartesianOrbit
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mass_enclosed
(q, t)¶ Estimate the mass enclosed within the given position by assuming the potential is spherical. This is not so good!
Parameters: q : array_like, numeric
Position to compute the mass enclosed.
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plot_contours
(grid, ax=None, labels=None, subplots_kw={}, **kwargs)¶ Plot equipotentials contours. Computes the potential value 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: grid : tuple
Coordinate grids or slice value for each dimension. Should be a tuple of 1D arrays or numbers.
ax : matplotlib.Axes (optional)
labels : iterable (optional)
List of axis labels.
subplots_kw : dict
kwargs passed to matplotlib’s subplots() function if an axes object is not specified.
kwargs : dict
kwargs passed to either contourf() or plot().
Returns: fig :
Figure
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plot_densty_contours
(grid, 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: grid : tuple
Coordinate grids or slice value for each dimension. Should be a tuple of 1D arrays or numbers.
ax : matplotlib.Axes (optional)
labels : iterable (optional)
List of axis labels.
subplots_kw : dict
kwargs passed to matplotlib’s subplots() function if an axes object is not specified.
kwargs : dict
kwargs passed to either contourf() or plot().
Returns: fig :
Figure
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save
(f)¶ Save the potential to a text file. See
save()
for more information.Parameters: f : str, file_like
A filename or file-like object to write the input potential object to.
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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: x : array_like, numeric
Position.
v : array_like, numeric
Velocity.
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value
(q, t=0.0)¶ Compute the value of the potential at the given position(s).
Parameters: q :
Quantity
, array_likeThe 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.Returns: E :
Quantity
The potential energy per unit mass or value of the potential. If the input position has shape
q.shape
, the output energy will have shapeq.shape[1:]
.
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