FaucherKaspi2006¶

class
gammapy.astro.population.
FaucherKaspi2006
(amplitude=1, r_0=7.04, sigma=1.83, **kwargs)[source]¶ Bases:
astropy.modeling.Fittable1DModel
Radial distribution of the birth surface density of pulsars in the galaxy  FaucherGiguere & Kaspi 2006.
\[f(r) = A \frac{1}{\sqrt{2 \pi} \sigma} \exp \left( \frac{(r  r_0)^2}{2 \sigma ^ 2}\right)\]Reference: https://ui.adsabs.harvard.edu/abs/2006ApJ…643..332F (Appendix B)
Parameters:  amplitude : float
See model formula
 r_0 : float
See model formula
 sigma : float
See model formula
See also
Attributes Summary
amplitude
bounding_box
A tuple
of lengthn_inputs
defining the bounding box limits, orNone
for no bounding box.bounds
A dict
mapping parameter names to their upper and lower bounds as(min, max)
tuples or[min, max]
lists.col_fit_deriv
eqcons
List of parameter equality constraints. evolved
fit_deriv
fittable
fixed
A dict
mapping parameter names to their fixed constraint.has_user_bounding_box
A flag indicating whether or not a custom bounding_box has been assigned to this model by a user, via assignment to model.bounding_box
.has_user_inverse
A flag indicating whether or not a custom inverse model has been assigned to this model by a user, via assignment to model.inverse
.ineqcons
List of parameter inequality constraints. input_units
This property is used to indicate what units or sets of units the evaluate method expects, and returns a dictionary mapping inputs to units (or None
if any units are accepted).input_units_allow_dimensionless
Allow dimensionless input (and corresponding output). input_units_equivalencies
input_units_strict
Enforce strict units on inputs to evaluate. inputs
inverse
Returns a new Model
instance which performs the inverse transform, if an analytic inverse is defined for this model.linear
meta
model_constraints
model_set_axis
The index of the model set axis–that is the axis of a parameter array that pertains to which model a parameter value pertains to–as specified when the model was initialized. n_inputs
The number of inputs to this model. n_outputs
The number of outputs from this model. name
Userprovided name for this model instance. outputs
param_names
param_sets
Return parameters as a pset. parameter_constraints
parameters
A flattened array of all parameter values in all parameter sets. r_0
return_units
This property is used to indicate what units or sets of units the output of evaluate should be in, and returns a dictionary mapping outputs to units (or None
if any units are accepted).separable
A flag indicating whether a model is separable. sigma
standard_broadcasting
tied
A dict
mapping parameter names to their tied constraint.uses_quantity
True if this model has been created with Quantity
objects or if there are no parameters.Methods Summary
__call__
(self, x[, model_set_axis, …])Evaluate this model using the given input(s) and the parameter values that were specified when the model was instantiated. copy
(self)Return a copy of this model. deepcopy
(self)Return a deep copy of this model. evaluate
(r, amplitude, r_0, sigma)Evaluate model. n_submodels
()Return the number of components in a single model, which is obviously 1. prepare_inputs
(self, \*inputs[, …])This method is used in __call__
to ensure that all the inputs to the model can be broadcast into compatible shapes (if one or both of them are input as arrays), particularly if there are more than one parameter sets.prepare_outputs
(self, format_info, …)rename
(name)Creates a copy of this model class with a new name. render
(self[, out, coords])Evaluate a model at fixed positions, respecting the bounding_box
.strip_units_from_tree
(self)sum_of_implicit_terms
(self, \*args, \*\*kwargs)Evaluate the sum of any implicit model terms on some input variables. with_units_from_data
(self, \*\*kwargs)Return an instance of the model which has units for which the parameter values are compatible with the data units specified. without_units_for_data
(self, \*\*kwargs)Return an instance of the model for which the parameter values have been converted to the right units for the data, then the units have been stripped away. Attributes Documentation

amplitude
¶

bounding_box
¶ A
tuple
of lengthn_inputs
defining the bounding box limits, orNone
for no bounding box.The default limits are given by a
bounding_box
property or method defined in the class body of a specific model. If not defined then this property just raisesNotImplementedError
by default (but may be assigned a custom value by a user).bounding_box
can be set manually to an arraylike object of shape(model.n_inputs, 2)
. For further usage, see Efficient Model Rendering with Bounding BoxesThe limits are ordered according to the
numpy
indexing convention, and are the reverse of the model input order, e.g. for inputs('x', 'y', 'z')
,bounding_box
is defined: for 1D:
(x_low, x_high)
 for 2D:
((y_low, y_high), (x_low, x_high))
 for 3D:
((z_low, z_high), (y_low, y_high), (x_low, x_high))
Examples
Setting the
bounding_box
limits for a 1D and 2D model:>>> from astropy.modeling.models import Gaussian1D, Gaussian2D >>> model_1d = Gaussian1D() >>> model_2d = Gaussian2D(x_stddev=1, y_stddev=1) >>> model_1d.bounding_box = (5, 5) >>> model_2d.bounding_box = ((6, 6), (5, 5))
Setting the bounding_box limits for a userdefined 3D
custom_model
:>>> from astropy.modeling.models import custom_model >>> def const3d(x, y, z, amp=1): ... return amp ... >>> Const3D = custom_model(const3d) >>> model_3d = Const3D() >>> model_3d.bounding_box = ((6, 6), (5, 5), (4, 4))
To reset
bounding_box
to its default limits just delete the userdefined value–this will reset it back to the default defined on the class:>>> del model_1d.bounding_box
To disable the bounding box entirely (including the default), set
bounding_box
toNone
:>>> model_1d.bounding_box = None >>> model_1d.bounding_box # doctest: +IGNORE_EXCEPTION_DETAIL Traceback (most recent call last): File "<stdin>", line 1, in <module> File "astropy\modeling\core.py", line 980, in bounding_box "No bounding box is defined for this model (note: the " NotImplementedError: No bounding box is defined for this model (note: the bounding box was explicitly disabled for this model; use `del model.bounding_box` to restore the default bounding box, if one is defined for this model).
 for 1D:

bounds
¶ A
dict
mapping parameter names to their upper and lower bounds as(min, max)
tuples or[min, max]
lists.

col_fit_deriv
= True¶

eqcons
¶ List of parameter equality constraints.

evolved
= False¶

fit_deriv
= None¶

fittable
= True¶

has_user_bounding_box
¶ A flag indicating whether or not a custom bounding_box has been assigned to this model by a user, via assignment to
model.bounding_box
.

has_user_inverse
¶ A flag indicating whether or not a custom inverse model has been assigned to this model by a user, via assignment to
model.inverse
.

ineqcons
¶ List of parameter inequality constraints.

input_units
¶ This property is used to indicate what units or sets of units the evaluate method expects, and returns a dictionary mapping inputs to units (or
None
if any units are accepted).Model subclasses can also use function annotations in evaluate to indicate valid input units, in which case this property should not be overridden since it will return the input units based on the annotations.

input_units_allow_dimensionless
¶ Allow dimensionless input (and corresponding output). If this is True, input values to evaluate will gain the units specified in input_units. If this is a dictionary then it should map input name to a bool to allow dimensionless numbers for that input. Only has an effect if input_units is defined.

input_units_equivalencies
= None¶

input_units_strict
¶ Enforce strict units on inputs to evaluate. If this is set to True, input values to evaluate will be in the exact units specified by input_units. If the input quantities are convertible to input_units, they are converted. If this is a dictionary then it should map input name to a bool to set strict input units for that parameter.

inputs
= ('x',)¶

inverse
¶ Returns a new
Model
instance which performs the inverse transform, if an analytic inverse is defined for this model.Even on models that don’t have an inverse defined, this property can be set with a manuallydefined inverse, such a precomputed or experimentally determined inverse (often given as a
PolynomialModel
, but not by requirement).A custom inverse can be deleted with
del model.inverse
. In this case the model’s inverse is reset to its default, if a default exists (otherwise the default is to raiseNotImplementedError
).Note to authors of
Model
subclasses: To define an inverse for a model simply override this property to return the appropriate model representing the inverse. The machinery that will make the inverse manuallyoverridable is added automatically by the base class.

linear
= False¶

meta
¶

model_constraints
= ('eqcons', 'ineqcons')¶

model_set_axis
¶ The index of the model set axis–that is the axis of a parameter array that pertains to which model a parameter value pertains to–as specified when the model was initialized.
See the documentation on Model Sets for more details.

n_inputs
¶ The number of inputs to this model.
Equivalent to
len(model.inputs)
.

n_outputs
¶ The number of outputs from this model.
Equivalent to
len(model.outputs)
.

name
¶ Userprovided name for this model instance.

outputs
= ('y',)¶

param_names
= ('amplitude', 'r_0', 'sigma')¶

param_sets
¶ Return parameters as a pset.
This is a list with one item per parameter set, which is an array of that parameter’s values across all parameter sets, with the last axis associated with the parameter set.

parameter_constraints
= ('fixed', 'tied', 'bounds', 'prior', 'posterior')¶

parameters
¶ A flattened array of all parameter values in all parameter sets.
Fittable parameters maintain this list and fitters modify it.

r_0
¶

return_units
¶ This property is used to indicate what units or sets of units the output of evaluate should be in, and returns a dictionary mapping outputs to units (or
None
if any units are accepted).Model subclasses can also use function annotations in evaluate to indicate valid output units, in which case this property should not be overridden since it will return the return units based on the annotations.

separable
¶ A flag indicating whether a model is separable.

sigma
¶

standard_broadcasting
= True¶

uses_quantity
¶ True if this model has been created with
Quantity
objects or if there are no parameters.This can be used to determine if this model should be evaluated with
Quantity
or regular floats.
Methods Documentation

__call__
(self, x, model_set_axis=None, with_bounding_box=False, fill_value=nan, equivalencies=None)¶ Evaluate this model using the given input(s) and the parameter values that were specified when the model was instantiated.

copy
(self)¶ Return a copy of this model.
Uses a deep copy so that all model attributes, including parameter values, are copied as well.

deepcopy
(self)¶ Return a deep copy of this model.

classmethod
n_submodels
()¶ Return the number of components in a single model, which is obviously 1.

prepare_inputs
(self, *inputs, model_set_axis=None, equivalencies=None, **kwargs)¶ This method is used in
__call__
to ensure that all the inputs to the model can be broadcast into compatible shapes (if one or both of them are input as arrays), particularly if there are more than one parameter sets. This also makes sure that (if applicable) the units of the input will be compatible with the evaluate method.

prepare_outputs
(self, format_info, *outputs, **kwargs)¶

classmethod
rename
(name)¶ Creates a copy of this model class with a new name.
The new class is technically a subclass of the original class, so that instance and type checks will still work. For example:
>>> from astropy.modeling.models import Rotation2D >>> SkyRotation = Rotation2D.rename('SkyRotation') >>> SkyRotation <class '__main__.SkyRotation'> Name: SkyRotation (Rotation2D) Inputs: ('x', 'y') Outputs: ('x', 'y') Fittable parameters: ('angle',) >>> issubclass(SkyRotation, Rotation2D) True >>> r = SkyRotation(90) >>> isinstance(r, Rotation2D) True

render
(self, out=None, coords=None)¶ Evaluate a model at fixed positions, respecting the
bounding_box
.The key difference relative to evaluating the model directly is that this method is limited to a bounding box if the
Model.bounding_box
attribute is set.Parameters:  out :
numpy.ndarray
, optional An array that the evaluated model will be added to. If this is not given (or given as
None
), a new array will be created. coords : arraylike, optional
An array to be used to translate from the model’s input coordinates to the
out
array. It should have the property thatself(coords)
yields the same shape asout
. Ifout
is not specified,coords
will be used to determine the shape of the returned array. If this is not provided (or None), the model will be evaluated on a grid determined byModel.bounding_box
.
Returns:  out :
numpy.ndarray
The model added to
out
ifout
is notNone
, or else a new array from evaluating the model overcoords
. Ifout
andcoords
are bothNone
, the returned array is limited to theModel.bounding_box
limits. IfModel.bounding_box
isNone
,arr
orcoords
must be passed.
Raises:  ValueError
If
coords
are not given and the theModel.bounding_box
of this model is not set.
Examples
 out :

strip_units_from_tree
(self)¶

sum_of_implicit_terms
(self, *args, **kwargs)¶ Evaluate the sum of any implicit model terms on some input variables. This includes any fixed terms used in evaluating a linear model that do not have corresponding parameters exposed to the user. The prototypical case is
astropy.modeling.functional_models.Shift
, which corresponds to a function y = a + bx, where b=1 is intrinsically fixed by the type of model, such that sum_of_implicit_terms(x) == x. This method is needed by linear fitters to correct the dependent variable for the implicit term(s) when solving for the remaining terms (ie. a = y  bx).

with_units_from_data
(self, **kwargs)¶ Return an instance of the model which has units for which the parameter values are compatible with the data units specified.
The input and output Quantity objects should be given as keyword arguments.
Notes
This method is needed in order to be able to fit models with units in the parameters, since we need to temporarily strip away the units from the model during the fitting (which might be done by e.g. scipy functions).
The units that the parameters will gain are not necessarily the units of the input data, but are derived from them. Model subclasses that want fitting to work in the presence of quantities need to define a _parameter_units_for_data_units method that takes the input and output units (as two dictionaries) and returns a dictionary giving the target units for each parameter.

without_units_for_data
(self, **kwargs)¶ Return an instance of the model for which the parameter values have been converted to the right units for the data, then the units have been stripped away.
The input and output Quantity objects should be given as keyword arguments.
Notes
This method is needed in order to be able to fit models with units in the parameters, since we need to temporarily strip away the units from the model during the fitting (which might be done by e.g. scipy functions).
The units that the parameters should be converted to are not necessarily the units of the input data, but are derived from them. Model subclasses that want fitting to work in the presence of quantities need to define a _parameter_units_for_data_units method that takes the input and output units (as two dictionaries) and returns a dictionary giving the target units for each parameter.