DiskSpatialModel¶

class gammapy.modeling.models.DiskSpatialModel(**kwargs)[source]¶

Bases: gammapy.modeling.models.SpatialModel

Constant disk model.

By default, the model is symmetric, i.e. a disk:

\[\begin{split}\phi(lon, lat) = \frac{1}{2 \pi (1 - \cos{r_0}) } \cdot \begin{cases} 1 & \text{for } \theta \leq r_0 \\ 0 & \text{for } \theta > r_0 \end{cases}\end{split}\]

where \(\theta\) is the sky separation. To improve fit convergence of the model, the sharp edges is smoothed using erf.

In case an eccentricity (e) and rotation angle (\(\phi\)) are passed, then the model is an elongated disk (i.e. an ellipse), with a major semiaxis of length \(r_0\) and position angle \(\phi\) (increaing counter-clockwise from the North direction).

The model is defined on the celestial sphere, with a normalization defined by:

\[\int_{4\pi}\phi(\text{lon}, \text{lat}) \,d\Omega = 1\,.\]

Parameters

lon_0, lat_0Angle: Center position
r_0Angle: \(a\): length of the major semiaxis, in angular units.
efloat: Eccentricity of the ellipse (\(0< e< 1\)).
phiAngle: Rotation angle \(\phi\): of the major semiaxis. Increases counter-clockwise from the North direction.
edgeAngle: Width of the edge. The width is defined as the range within the smooth edges of the model drops from 95% to 5% of its amplitude.
frame{“icrs”, “galactic”}: Center position coordinate frame

Attributes Summary

`default_parameters`
`e`	A model parameter.
`edge`	A model parameter.
`evaluation_radius`	Evaluation radius (`Angle`).
`lat_0`	A model parameter.
`lon_0`	A model parameter.
`parameters`	Parameters (`Parameters`)
`phi`	A model parameter.
`phi_0`
`position`	Spatial model center position
`position_error`	Get 95% containment position error as (`EllipseSkyRegion`)
`r_0`	A model parameter.
`tag`

Methods Summary

`__call__`(self, lon, lat)	Call evaluate method
`copy`(self)	A deep copy.
`create`(tag, \args, \\*kwargs)	Create a model instance.
`evaluate`(lon, lat, lon_0, lat_0, r_0, e, …)	Evaluate model.
`evaluate_geom`(self, geom)	Evaluate model on `Geom`.
`from_dict`(data)
`to_dict`(self)	Create dict for YAML serilisation
`to_region`(self, \\kwargs)	Model outline (`EllipseSkyRegion`).

Attributes Documentation

default_parameters = <gammapy.modeling.parameter.Parameters object>¶

e¶

A model parameter.

Note that the parameter value has been split into a factor and scale like this:

value = factor x scale

Users should interact with the value, quantity or min and max properties and consider the fact that there is a factor` and scale an implementation detail.

That was introduced for numerical stability in parameter and error estimation methods, only in the Gammapy optimiser interface do we interact with the factor, factor_min and factor_max properties, i.e. the optimiser “sees” the well-scaled problem.

Parameters

namestr: Name
factorfloat or Quantity: Factor
scalefloat, optional: Scale (sometimes used in fitting)
unitUnit or str, optional: Unit
minfloat, optional: Minimum (sometimes used in fitting)
maxfloat, optional: Maximum (sometimes used in fitting)
frozenbool, optional: Frozen? (used in fitting)

edge¶

A model parameter.

Note that the parameter value has been split into a factor and scale like this:

value = factor x scale

Users should interact with the value, quantity or min and max properties and consider the fact that there is a factor` and scale an implementation detail.

That was introduced for numerical stability in parameter and error estimation methods, only in the Gammapy optimiser interface do we interact with the factor, factor_min and factor_max properties, i.e. the optimiser “sees” the well-scaled problem.

Parameters

namestr: Name
factorfloat or Quantity: Factor
scalefloat, optional: Scale (sometimes used in fitting)
unitUnit or str, optional: Unit
minfloat, optional: Minimum (sometimes used in fitting)
maxfloat, optional: Maximum (sometimes used in fitting)
frozenbool, optional: Frozen? (used in fitting)

evaluation_radius¶

Evaluation radius (Angle).

Set to the length of the semi-major axis.

lat_0¶

A model parameter.

Note that the parameter value has been split into a factor and scale like this:

value = factor x scale

Users should interact with the value, quantity or min and max properties and consider the fact that there is a factor` and scale an implementation detail.

That was introduced for numerical stability in parameter and error estimation methods, only in the Gammapy optimiser interface do we interact with the factor, factor_min and factor_max properties, i.e. the optimiser “sees” the well-scaled problem.

Parameters

namestr: Name
factorfloat or Quantity: Factor
scalefloat, optional: Scale (sometimes used in fitting)
unitUnit or str, optional: Unit
minfloat, optional: Minimum (sometimes used in fitting)
maxfloat, optional: Maximum (sometimes used in fitting)
frozenbool, optional: Frozen? (used in fitting)

lon_0¶

A model parameter.

Note that the parameter value has been split into a factor and scale like this:

value = factor x scale

Users should interact with the value, quantity or min and max properties and consider the fact that there is a factor` and scale an implementation detail.

That was introduced for numerical stability in parameter and error estimation methods, only in the Gammapy optimiser interface do we interact with the factor, factor_min and factor_max properties, i.e. the optimiser “sees” the well-scaled problem.

Parameters

namestr: Name
factorfloat or Quantity: Factor
scalefloat, optional: Scale (sometimes used in fitting)
unitUnit or str, optional: Unit
minfloat, optional: Minimum (sometimes used in fitting)
maxfloat, optional: Maximum (sometimes used in fitting)
frozenbool, optional: Frozen? (used in fitting)

parameters¶: Parameters (Parameters)

phi¶

A model parameter.

Note that the parameter value has been split into a factor and scale like this:

value = factor x scale

Users should interact with the value, quantity or min and max properties and consider the fact that there is a factor` and scale an implementation detail.

That was introduced for numerical stability in parameter and error estimation methods, only in the Gammapy optimiser interface do we interact with the factor, factor_min and factor_max properties, i.e. the optimiser “sees” the well-scaled problem.

Parameters

namestr: Name
factorfloat or Quantity: Factor
scalefloat, optional: Scale (sometimes used in fitting)
unitUnit or str, optional: Unit
minfloat, optional: Minimum (sometimes used in fitting)
maxfloat, optional: Maximum (sometimes used in fitting)
frozenbool, optional: Frozen? (used in fitting)

phi_0¶

position¶: Spatial model center position

position_error¶: Get 95% containment position error as (EllipseSkyRegion)

r_0¶

A model parameter.

Note that the parameter value has been split into a factor and scale like this:

value = factor x scale

Users should interact with the value, quantity or min and max properties and consider the fact that there is a factor` and scale an implementation detail.

That was introduced for numerical stability in parameter and error estimation methods, only in the Gammapy optimiser interface do we interact with the factor, factor_min and factor_max properties, i.e. the optimiser “sees” the well-scaled problem.

Parameters

namestr: Name
factorfloat or Quantity: Factor
scalefloat, optional: Scale (sometimes used in fitting)
unitUnit or str, optional: Unit
minfloat, optional: Minimum (sometimes used in fitting)
maxfloat, optional: Maximum (sometimes used in fitting)
frozenbool, optional: Frozen? (used in fitting)

tag = 'DiskSpatialModel'¶

Methods Documentation

__call__(self, lon, lat)¶: Call evaluate method

copy(self)¶: A deep copy.

static create(tag, *args, **kwargs)¶

Create a model instance.

Examples

>>> from gammapy.modeling import Model
>>> spectral_model = Model.create("PowerLaw2SpectralModel", amplitude="1e-10 cm-2 s-1", index=3)
>>> type(spectral_model)
gammapy.modeling.models.spectral.PowerLaw2SpectralModel

static evaluate(lon, lat, lon_0, lat_0, r_0, e, phi, edge)[source]¶: Evaluate model.

evaluate_geom(self, geom)¶: Evaluate model on Geom.

classmethod from_dict(data)¶

to_dict(self)¶: Create dict for YAML serilisation

to_region(self, **kwargs)[source]¶: Model outline (EllipseSkyRegion).