# DiskSpatialModel¶

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

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).