FittableImageModel#

class photutils.psf.FittableImageModel(data, *, flux=1.0, x_0=0.0, y_0=0.0, normalize=False, normalization_correction=1.0, origin=None, oversampling=1, fill_value=0.0, **kwargs)[source]#

Bases: Fittable2DModel

Deprecated since version 2.0.0: The FittableImageModel class is deprecated and may be removed in a future version. Use ImagePSF instead.

A fittable image model allowing for intensity scaling and translations.

This class takes 2D image data and computes the values of the model at arbitrary locations, including fractional pixel positions, within the image using spline interpolation provided by RectBivariateSpline.

The fittable model provided by this class has three model parameters: an image intensity scaling factor (flux) which is applied to (normalized) image, and two positional parameters (x_0 and y_0) indicating the location of a feature in the coordinate grid on which the model is to be evaluated.

Parameters:

data2D ndarray

Array containing the 2D image.

fluxfloat, optional

Intensity scaling factor for image data. If flux is None, then the normalization constant will be computed so that the total flux of the model’s image data is 1.0.

x_0, y_0float, optional

Position of a feature in the image in the output coordinate grid on which the model is evaluated.

normalizebool, optional

Indicates whether or not the model should be build on normalized input image data. If true, then the normalization constant (N) is computed so that

\[N \cdot C \cdot \sum\limits_{i,j} D_{i,j} = 1,\]

where N is the normalization constant, C is correction factor given by the parameter normalization_correction, and \(D_{i,j}\) are the elements of the input image data array.

normalization_correctionfloat, optional

A strictly positive number that represents correction that needs to be applied to model’s data normalization (see C in the equation in the comments to normalize for more details). A possible application for this parameter is to account for aperture correction. Assuming model’s data represent a PSF to be fitted to some target star, we set normalization_correction to the aperture correction that needs to be applied to the model. That is, normalization_correction in this case should be set to the ratio between the total flux of the PSF (including flux outside model’s data) to the flux of model’s data. Then, best fitted value of the flux model parameter will represent an aperture-corrected flux of the target star. In the case of aperture correction, normalization_correction should be a value larger than one, as the total flux, including regions outside of the aperture, should be larger than the flux inside the aperture, and thus the correction is applied as an inversely multiplied factor.

origintuple, None, optional

A reference point in the input image data array. When origin is None, origin will be set at the middle of the image array.

If origin represents the location of a feature (e.g., the position of an intensity peak) in the input data, then model parameters x_0 and y_0 show the location of this peak in an another target image to which this model was fitted. Fundamentally, it is the coordinate in the model’s image data that should map to coordinate (x_0, y_0) of the output coordinate system on which the model is evaluated.

Alternatively, when origin is set to (0, 0), then model parameters x_0 and y_0 are shifts by which model’s image should be translated in order to match a target image.

oversamplingint or array_like (int)

The integer oversampling factor(s) of the ePSF relative to the input stars along each axis. If oversampling is a scalar then it will be used for both axes. If oversampling has two elements, they must be in (y, x) order.

fill_valuefloat, optional

The value to be returned by the evaluate or astropy.modeling.Model.__call__ methods when evaluation is performed outside the definition domain of the model.

**kwargsdict, optional

Additional optional keyword arguments to be passed directly to the compute_interpolator method. See compute_interpolator for more details.

Deprecated since version 2.0.0: The FittableImageModel class is deprecated and may be removed in a future version. Use ImagePSF instead.

Attributes Summary

`bbox_with_units`
`bounding_box`	A `tuple` of length `n_inputs` defining the bounding box limits, or raise `NotImplementedError` 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`
`cov_matrix`	Fitter should set covariance matrix, if available.
`data`	Get original image data.
`eqcons`	List of parameter equality constraints.
`fill_value`	Fill value to be returned for coordinates outside of the domain of definition of the interpolator.
`fit_deriv`	Function (similar to the model's `evaluate`) to compute the derivatives of the model with respect to its parameters, for use by fitting algorithms.
`fittable`
`fixed`	A `dict` mapping parameter names to their fixed constraint.
`flux`
`has_bounds`	Whether the model has any bounds constraints.
`has_fixed`	Whether the model has any fixed constraints.
`has_tied`	Whether the model has any tied constraints.
`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`
`interpolator_kwargs`	Get current interpolator's arguments used when interpolator was created.
`inverse`	Returns a new `Model` instance which performs the inverse transform, if an analytic inverse is defined for this model.
`linear`
`meta`	A dict-like object to store optional information.
`model_constraints`	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.
`n_inputs`
`n_outputs`
`n_submodels`	Return the number of components in a single model, which is obviously 1.
`name`	User-provided name for this model instance.
`normalization_constant`	Get normalization constant.
`normalization_correction`	Set/Get flux correction factor.
`normalization_status`	Get normalization status.
`normalized_data`	Get normalized and/or intensity-corrected image data.
`nx`	Number of columns in the data array.
`ny`	Number of rows in the data array.
`origin`	A tuple of `x` and `y` coordinates of the origin of the coordinate system in terms of pixels of model's image.
`outputs`
`oversampling`	The factor by which the stored image is oversampled.
`param_names`	Names of the parameters that describe models of this type.
`param_sets`	Return parameters as a pset.
`parameter_constraints`	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.
`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.
`shape`	A tuple of dimensions of the data array in numpy style (ny, nx).
`standard_broadcasting`
`stds`	Standard deviation of parameters, if covariance matrix is available.
`sync_constraints`	This is a boolean property that indicates whether or not accessing constraints automatically check the constituent models current values.
`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.
`x_0`
`x_origin`	X-coordinate of the origin of the coordinate system.
`y_0`
`y_origin`	Y-coordinate of the origin of the coordinate system.

Methods Summary

`__call__`(*inputs[, model_set_axis, ...])	Evaluate this model using the given input(s) and the parameter values that were specified when the model was instantiated.
`coerce_units`([input_units, return_units, ...])	Attach units to this (unitless) model.
`compute_interpolator`(**kwargs)	Compute/define the interpolating spline.
`copy`()	Return a copy of this model.
`deepcopy`()	Return a deep copy of this model.
`evaluate`(x, y, flux, x_0, y_0, *[, ...])	Calculate the value of the image model at the input coordinates for the given model parameters.
`get_bounding_box`([with_bbox])	Return the `bounding_box` of a model if it exists or `None` otherwise.
`has_inverse`()	Returns True if the model has an analytic or user inverse defined.
`input_shape`(inputs)	Get input shape for bounding_box evaluation.
`output_units`(**kwargs)	Return a dictionary of output units for this model given a dictionary of fitting inputs and outputs.
`prepare_inputs`(*inputs[, model_set_axis, ...])	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`(broadcasted_shapes, ...)
`rename`([name, inputs, outputs])	Return a copy of this model with a new name.
`render`([out, coords])	Evaluate a model at fixed positions, respecting the `bounding_box`.
`set_slice_args`(*args)
`strip_units_from_tree`()
`sum_of_implicit_terms`(args, *kwargs)	Evaluate the sum of any implicit model terms on some input variables.
`with_units_from_data`(**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`(**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

bbox_with_units#

bounding_box#

A tuple of length n_inputs defining the bounding box limits, or raise NotImplementedError 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 raises NotImplementedError by default (but may be assigned a custom value by a user). bounding_box can be set manually to an array-like object of shape (model.n_inputs, 2). For further usage, see Efficient Model Rendering with Bounding Boxes

The limits are ordered according to the numpy 'C' 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 user-defined 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 user-defined 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 to None:

>>> 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.

col_fit_deriv = True#

cov_matrix#: Fitter should set covariance matrix, if available.

data#: Get original image data.

eqcons#: List of parameter equality constraints.

fill_value#

Fill value to be returned for coordinates outside of the domain of definition of the interpolator.

If fill_value is None, then values outside of the domain of definition are the ones returned by the interpolator.

fit_deriv = None#: Function (similar to the model’s evaluate) to compute the derivatives of the model with respect to its parameters, for use by fitting algorithms. In other words, this computes the Jacobian matrix with respect to the model’s parameters.

fittable = True#

fixed#: A dict mapping parameter names to their fixed constraint.

flux = Parameter('flux', value=1.0)#

has_bounds#: Whether the model has any bounds constraints.

has_fixed#: Whether the model has any fixed constraints.

has_tied#: Whether the model has any tied constraints.

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 sub-classes 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#

interpolator_kwargs#: Get current interpolator’s arguments used when interpolator was created.

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 manually-defined inverse, such a pre-computed 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 raise NotImplementedError).

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 manually-overridable is added automatically by the base class.

linear = False#

meta = None#: A dict-like 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 = 2#

n_outputs = 1#

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

name#: User-provided name for this model instance.

normalization_constant#: Get normalization constant.

normalization_correction#: Set/Get flux correction factor.

Note

When setting correction factor, model’s flux will be adjusted accordingly such that if this model was a good fit to some target image before, then it will remain a good fit after correction factor change.

normalization_status#

Get normalization status.

Possible status values are:

0: Performed. Model has been successfully normalized at
user’s request.
1: Failed. Attempt to normalize has failed.
2: NotRequested. User did not request model to be normalized.

normalized_data#: Get normalized and/or intensity-corrected image data.

nx#: Number of columns in the data array.

ny#: Number of rows in the data array.

origin#

A tuple of x and y coordinates of the origin of the coordinate system in terms of pixels of model’s image.

When setting the coordinate system origin, a tuple of two integers or floats may be used. If origin is set to None, the origin of the coordinate system will be set to the middle of the data array ((npix-1)/2.0).

Warning

Modifying origin will not adjust (modify) model’s parameters x_0 and y_0.

outputs#

oversampling#

The factor by which the stored image is oversampled.

An input to this model is multiplied by this factor to yield the index into the stored image.

param_names = ('flux', 'x_0', 'y_0')#

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 sub-classes 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.

shape#: A tuple of dimensions of the data array in numpy style (ny, nx).

standard_broadcasting = True#

stds#: Standard deviation of parameters, if covariance matrix is available.

sync_constraints#: This is a boolean property that indicates whether or not accessing constraints automatically check the constituent models current values. It defaults to True on creation of a model, but for fitting purposes it should be set to False for performance reasons.

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.

x_0 = Parameter('x_0', value=0.0)#

x_origin#: X-coordinate of the origin of the coordinate system.

y_0 = Parameter('y_0', value=0.0)#

y_origin#: Y-coordinate of the origin of the coordinate system.

Methods Documentation

__call__(*inputs, model_set_axis=None, with_bounding_box=False, fill_value=nan, equivalencies=None, inputs_map=None, **new_inputs)#: Evaluate this model using the given input(s) and the parameter values that were specified when the model was instantiated.

coerce_units(input_units=None, return_units=None, input_units_equivalencies=None, input_units_allow_dimensionless=False)#

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 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 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 plus UnitsMapping 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>

compute_interpolator(**kwargs)[source]#

Compute/define the interpolating spline.

This function can be overridden in a subclass to define custom interpolators.

Parameters:

**kwargsdict, optional

Additional optional keyword arguments:

degreeint, tuple, optional
Degree of the interpolating spline. A tuple can be used to provide different degrees for the X- and Y-axes. Default value is degree=3.
sfloat, optional
Non-negative smoothing factor. Default value s=0 corresponds to interpolation. See RectBivariateSpline for more details.

Notes

When subclassing FittableImageModel for the purpose of overriding compute_interpolator(), the evaluate() may need to overridden as well depending on the behavior of the new interpolator. In addition, for improved future compatibility, make sure that the overriding method stores keyword arguments kwargs by calling _store_interpolator_kwargs method.
Use caution when modifying interpolator’s degree or smoothness in a computationally intensive part of the code as it may decrease code performance due to the need to recompute interpolator.

copy()#

Return a copy of this model.

Uses a deep copy so that all model attributes, including parameter values, are copied as well.

deepcopy()#: Return a deep copy of this model.

evaluate(x, y, flux, x_0, y_0, *, use_oversampling=True)[source]#

Calculate the value of the image model at the input coordinates for the given model parameters.

Parameters:

x, yfloat or array_like: The x and y coordinates at which to evaluate the model.
fluxfloat: The total flux of the source.
x_0, y_0float: The x and y positions of the feature in the image in the output coordinate grid on which the model is evaluated.
use_oversamplingbool, optional: Whether to use the oversampling factor to calculate the model pixel indices. The default is True, which means the input indices will be multiplied by this factor.

Returns:

evaluated_modelndarray: The evaluated model.

get_bounding_box(with_bbox=True)#

Return the bounding_box of a model if it exists or None otherwise.

Parameters:

with_bbox: The value of the with_bounding_box keyword argument when calling the model. Default is True for usage when looking up the model’s bounding_box without risk of error.

has_inverse()#: Returns True if the model has an analytic or user inverse defined.

input_shape(inputs)#: Get input shape for bounding_box evaluation.

output_units(**kwargs)#

Return a dictionary of output units for this model given a dictionary of fitting inputs and outputs.

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).

This method will force extra model evaluations, which maybe computationally expensive. To avoid this, one can add a return_units property to the model, see return_units.

prepare_inputs(*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(broadcasted_shapes, *outputs, **kwargs)#

classmethod rename(name=None, inputs=None, outputs=None)#: Return a copy of this model with a new name.

render(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 bounding_box attribute is set.

Parameters:

outnumpy.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 that self(coords) yields the same shape as out. If out 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 by bounding_box.

Returns:

outnumpy.ndarray: The model added to out if out is not None, or else a new array from evaluating the model over coords. If out and coords are both None, the returned array is limited to the bounding_box limits. If bounding_box is None, arr or coords must be passed.

Raises:

ValueError: If coords are not given and the bounding_box of this model is not set.

Examples

Efficient Model Rendering with Bounding Boxes

set_slice_args(*args)#

strip_units_from_tree()#

sum_of_implicit_terms(*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(**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(**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.