LogarithmicPotential#
- class gala.potential.potential.LogarithmicPotential(v_c, r_h, q1, q2, q3, phi=0, theta=0, psi=0, units=None, origin=None, R=None)[source]#
Bases:
CPotentialBase
Triaxial logarithmic potential.
- Parameters:
- v_c
Quantity
,numeric
[velocity
] Circular velocity.
- r_h
Quantity
,numeric
[length
] Scale radius.
- q1
numeric
Flattening in X.
- q2
numeric
Flattening in Y.
- q3
numeric
Flattening in Z.
- phi
Quantity
,numeric
First euler angle in the z-x-z convention.
- units
UnitSystem
(optional) Set of non-reducable units that specify (at minimum) the length, mass, time, and angle units.
- origin
Quantity
(optional) The origin of the potential, the default being 0.
- R
Rotation
, array_like (optional) A Scipy
Rotation
object or an array representing a rotation matrix that specifies a rotation of the potential. This is applied after the origin shift. Default is the identity matrix.
- v_c
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).
as_interop
(package, **kwargs)Interoperability with other Galactic dynamics packages
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)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[, t, filled, ax, labels, ...])Plot equipotentials contours.
plot_density_contours
(grid[, t, filled, ax, ...])Plot density contours.
plot_rotation_curve
(R_grid[, t, ax, labels])Plot the rotation curve or circular velocity curve for this potential on the input grid of cylindrical radii.
replace_units
(units)Change the unit system of this potential.
replicate
(**kwargs)Return a copy of the potential instance with some parameter values changed.
save
(f)Save the potential to a text file.
to_galpy_potential
([ro, vo])to_latex
()Return a string LaTeX representation of this potential
to_sympy
(v, p)Return a representation of this potential class as a sympy expression
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
- ndim = 3#
- phi = <PotentialParameter: phi [angle]>#
- q1 = <PotentialParameter: q1 [dimensionless]>#
- q2 = <PotentialParameter: q2 [dimensionless]>#
- q3 = <PotentialParameter: q3 [dimensionless]>#
- r_h = <PotentialParameter: r_h [length]>#
- units#
- v_c = <PotentialParameter: v_c [speed]>#
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
- as_interop(package, **kwargs)#
Interoperability with other Galactic dynamics packages
- Parameters:
- package
str
The package to export the potential to. Currently supported packages are
"galpy"
and"agama"
.- kwargs
Any additional keyword arguments are passed to the interop function.
- package
- 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.
- qarray_like,
- 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)#
Integrate an orbit in the current potential using the integrator class provided. Uses same time specification as
Integrator()
– see the documentation forgala.integrate
for more information.- Parameters:
- w0
PhaseSpacePosition
, array_like Initial 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_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.
- store_allbool (optional)
Controls whether to store the phase-space position at all intermediate timesteps. Set to False to store only the final values (i.e. the phase-space position(s) at the final timestep). Default is True.
- **time_spec
Specification of how long to integrate. See documentation for
parse_time_specification
.
- w0
- Returns:
- orbit
Orbit
- orbit
- mass_enclosed(q, t)#
Estimate the mass enclosed within the given position by assuming the potential is spherical. This is not so good!
- Parameters:
- qarray_like,
numeric
Position to compute the mass enclosed.
- qarray_like,
- plot_contours(grid, t=0.0, 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:
- grid
tuple
Coordinate grids or slice value for each dimension. Should be a tuple of 1D arrays or numbers.
- tquantity-like (optional)
The time to evaluate at.
- filledbool (optional)
Use
contourf()
instead ofcontour()
. Default isTrue
.- ax
matplotlib.Axes
(optional) - labelsiterable (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().
- grid
- Returns:
- fig
Figure
- fig
- plot_density_contours(grid, t=0.0, filled=True, ax=None, labels=None, subplots_kw={}, **kwargs)#
Plot density contours. Computes the density on a grid (specified by the array
grid
).Warning
For 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.
- tquantity-like (optional)
The time to evaluate at.
- filledbool (optional)
Use
contourf()
instead ofcontour()
. Default isTrue
.- ax
matplotlib.Axes
(optional) - labelsiterable (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().
- grid
- Returns:
- fig
Figure
- fig
- plot_rotation_curve(R_grid, t=0.0, ax=None, labels=None, **plot_kwargs)#
Plot the rotation curve or circular velocity curve for this potential on the input grid of cylindrical radii.
- Parameters:
- R_gridarray_like
A grid of radius values to compute the rotation curve at. This should be a one-dimensional grid.
- tquantity-like (optional)
The time to evaluate at.
- ax
matplotlib.Axes
(optional) - labelsiterable (optional)
List of axis labels. Set to False to disable adding labels.
- plot_kwargs
dict
kwargs passed to plot().
- Returns:
- fig
Figure
- ax
Axes
- fig
- replace_units(units)#
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.
- units
- replicate(**kwargs)#
Return a copy of the potential instance with some parameter values changed. This always produces copies of any parameter arrays.
- Parameters:
- **kwargs
All other keyword arguments are used to overwrite parameter values when making the copy.
- Returns:
- replicant
PotentialBase
subclass instance The replicated potential.
- replicant
- 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.
- f
- to_galpy_potential(ro=None, vo=None)#
Deprecated since version v1.8: This has been replaced by a more general interoperability framework.
Convert a Gala potential to a Galpy potential instance
- Parameters:
- roquantity-like (optional)
- voquantity-like (optional)
- classmethod to_latex()#
Return a string LaTeX representation of this potential
- Returns:
- latex_str
str
The latex expression as a Python string.
- latex_str
- classmethod to_sympy(v, p)[source]#
Return a representation of this potential class as a sympy expression
- 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.
- xarray_like,
- value(*args, **kwargs)#