Model¶

class
astropy.modeling.
Model
(*args, meta=None, name=None, **kwargs)[source]¶ Bases:
object
Base class for all models.
This is an abstract class and should not be instantiated directly.
The following initialization arguments apply to the majority of Model subclasses by default (exceptions include specialized utility models like
Mapping
). Parametric models take all their parameters as arguments, followed by any of the following optional keyword arguments: Parameters
 namestr, optional
A humanfriendly name associated with this model instance (particularly useful for identifying the individual components of a compound model).
 metadict, optional
An optional dict of userdefined metadata to attach to this model. How this is used and interpreted is up to the user or individual use case.
 n_modelsint, optional
If given an integer greater than 1, a model set is instantiated instead of a single model. This affects how the parameter arguments are interpreted. In this case each parameter must be given as a list or array–elements of this array are taken along the first axis (or
model_set_axis
if specified), such that the Nth element is the value of that parameter for the Nth model in the set.See the section on model sets in the documentation for more details.
 model_set_axisint, optional
This argument only applies when creating a model set (i.e.
n_models > 1
). It changes how parameter values are interpreted. Normally the first axis of each input parameter array (properly the 0th axis) is taken as the axis corresponding to the model sets. However, any axis of an input array may be taken as this “model set axis”. This accepts negative integers as well–for example usemodel_set_axis=1
if the last (most rapidly changing) axis should be associated with the model sets. Also,model_set_axis=False
can be used to tell that a given input should be used to evaluate all the models in the model set. fixeddict, optional
Dictionary
{parameter_name: bool}
setting the fixed constraint for one or more parameters.True
means the parameter is held fixed during fitting and is prevented from updates once an instance of the model has been created.Alternatively the
fixed
property of a parameter may be used to lock or unlock individual parameters. tieddict, optional
Dictionary
{parameter_name: callable}
of parameters which are linked to some other parameter. The dictionary values are callables providing the linking relationship.Alternatively the
tied
property of a parameter may be used to set thetied
constraint on individual parameters. boundsdict, optional
A dictionary
{parameter_name: value}
of lower and upper bounds of parameters. Keys are parameter names. Values are a list or a tuple of length 2 giving the desired range for the parameter.Alternatively the
min
andmax
or ~astropy.modeling.Parameter.bounds` properties of a parameter may be used to set bounds on individual parameters. eqconslist, optional
List of functions of length n such that
eqcons[j](x0, *args) == 0.0
in a successfully optimized problem. ineqconslist, optional
List of functions of length n such that
ieqcons[j](x0, *args) >= 0.0
is a successfully optimized problem.
Examples
>>> from astropy.modeling import models >>> def tie_center(model): ... mean = 50 * model.stddev ... return mean >>> tied_parameters = {'mean': tie_center}
Specify that
'mean'
is a tied parameter in one of two ways:>>> g1 = models.Gaussian1D(amplitude=10, mean=5, stddev=.3, ... tied=tied_parameters)
or
>>> g1 = models.Gaussian1D(amplitude=10, mean=5, stddev=.3) >>> g1.mean.tied False >>> g1.mean.tied = tie_center >>> g1.mean.tied <function tie_center at 0x...>
Fixed parameters:
>>> g1 = models.Gaussian1D(amplitude=10, mean=5, stddev=.3, ... fixed={'stddev': True}) >>> g1.stddev.fixed True
or
>>> g1 = models.Gaussian1D(amplitude=10, mean=5, stddev=.3) >>> g1.stddev.fixed False >>> g1.stddev.fixed = True >>> g1.stddev.fixed True
Attributes Summary
A
tuple
of lengthn_inputs
defining the bounding box limits, orNone
for no bounding box.A
dict
mapping parameter names to their upper and lower bounds as(min, max)
tuples or[min, max]
lists.List of parameter equality constraints.
A
dict
mapping parameter names to their fixed constraint.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
.A flag indicating whether or not a custom inverse model has been assigned to this model by a user, via assignment to
model.inverse
.List of parameter inequality constraints.
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).Allow dimensionless input (and corresponding output).
Enforce strict units on inputs to evaluate.
Returns a new
Model
instance which performs the inverse transform, if an analytic inverse is defined for this model.A dictlike object to store optional information.
Primarily for informational purposes, these are the types of constraints that constrain model evaluation.
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.
The number of inputs.
The number of outputs.
Return the number of components in a single model, which is obviously 1.
Userprovided name for this model instance.
Names of the parameters that describe models of this type.
Return parameters as a pset.
Primarily for informational purposes, these are the types of constraints that can be set on a model’s parameters.
A flattened array of all parameter values in all parameter sets.
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).A flag indicating whether a model is separable.
A
dict
mapping parameter names to their tied constraint.True if this model has been created with
Quantity
objects or if there are no parameters.Methods Summary
__call__
(self, *args, **kwargs)Evaluate this model using the given input(s) and the parameter values that were specified when the model was instantiated.
coerce_units
(self[, input_units, …])Attach units to this (unitless) model.
copy
(self)Return a copy of this model.
deepcopy
(self)Return a deep copy of this model.
evaluate
(self, *args, **kwargs)Evaluate the model on some input variables.
has_inverse
(self)Returns True if the model has an analytic or user inverse defined.
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, *outputs, …)rename
([name, inputs, outputs])Creates a copy of this model class with a new name, inputs or outputs.
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

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 Traceback (most recent call last): 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).

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

eqcons
¶ List of parameter equality constraints.

fittable
= False¶

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).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
¶

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
= True¶

meta
¶ A dictlike object to store optional information.

model_constraints
= ('eqcons', 'ineqcons')¶ Primarily for informational purposes, these are the types of constraints that constrain model evaluation.

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.

n_outputs
¶ The number of outputs.

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

name
¶ Userprovided name for this model instance.

outputs
¶

param_names
= ()¶ Names of the parameters that describe models of this type.
The parameters in this tuple are in the same order they should be passed in when initializing a model of a specific type. Some types of models, such as polynomial models, have a different number of parameters depending on some other property of the model, such as the degree.
When defining a custom model class the value of this attribute is automatically set by the
Parameter
attributes defined in the class body.

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')¶ Primarily for informational purposes, these are the types of constraints that can be set on a model’s parameters.

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

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.

standard_broadcasting
= True¶

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.This can be used to determine if this model should be evaluated with
Quantity
or regular floats.
Methods Documentation

__call__
(self, *args, **kwargs)[source]¶ Evaluate this model using the given input(s) and the parameter values that were specified when the model was instantiated.

coerce_units
(self, input_units=None, return_units=None, input_units_equivalencies=None, input_units_allow_dimensionless=False)[source]¶ Attach units to this (unitless) model.
 Parameters
 input_unitsdict or tuple, optional
Input units to attach. If dict, each key is the name of a model input, and the value is the unit to attach. If tuple, the elements are units to attach in order corresponding to
Model.inputs
. return_unitsdict or tuple, optional
Output units to attach. If dict, each key is the name of a model output, and the value is the unit to attach. If tuple, the elements are units to attach in order corresponding to
Model.outputs
. input_units_equivalenciesdict, optional
Default equivalencies to apply to input values. If set, this should be a dictionary where each key is a string that corresponds to one of the model inputs.
 input_units_allow_dimensionlessbool or dict, optional
Allow dimensionless input. 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.
 Returns
CompoundModel
A
CompoundModel
composed of the current model plusUnitsMapping
model(s) that attach the units.
 Raises
 ValueError
If the current model already has units.
Examples
Wrapping a unitless model to require and convert units:
>>> from astropy.modeling.models import Polynomial1D >>> from astropy import units as u >>> poly = Polynomial1D(1, c0=1, c1=2) >>> model = poly.coerce_units((u.m,), (u.s,)) >>> model(u.Quantity(10, u.m)) <Quantity 21. s> >>> model(u.Quantity(1000, u.cm)) <Quantity 21. s> >>> model(u.Quantity(10, u.cm)) <Quantity 1.2 s>
Wrapping a unitless model but still permitting unitless input:
>>> from astropy.modeling.models import Polynomial1D >>> from astropy import units as u >>> poly = Polynomial1D(1, c0=1, c1=2) >>> model = poly.coerce_units((u.m,), (u.s,), input_units_allow_dimensionless=True) >>> model(u.Quantity(10, u.m)) <Quantity 21. s> >>> model(10) <Quantity 21. s>

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

prepare_inputs
(self, *inputs, model_set_axis=None, equivalencies=None, **kwargs)[source]¶ 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.

classmethod
rename
(name=None, inputs=None, outputs=None)[source]¶ Creates a copy of this model class with a new name, inputs or outputs.
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 'astropy.modeling.core.SkyRotation'> Name: SkyRotation (Rotation2D) N_inputs: 2 N_outputs: 2 Fittable parameters: ('angle',) >>> issubclass(SkyRotation, Rotation2D) True >>> r = SkyRotation(90) >>> isinstance(r, Rotation2D) True

render
(self, out=None, coords=None)[source]¶ 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. coordsarray_like, 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
.
 out
 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.
 out
 Raises
 ValueError
If
coords
are not given and the theModel.bounding_box
of this model is not set.
Examples

sum_of_implicit_terms
(self, *args, **kwargs)[source]¶ 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)[source]¶ 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)[source]¶ 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.For compound models this will only work when the expression only involves the addition or subtraction operators.