ImagePSF#

class photutils.psf.ImagePSF(data, *, flux=1, x_0=0, y_0=0, origin=None, oversampling=1, fill_value=0.0, **kwargs)[source]#

Bases: Fittable2DModel

A model for a 2D image PSF.

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 model has three model parameters: an image intensity scaling factor (flux) which is applied to the input 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 evaluated.

Parameters:

data2D ndarray

Array containing the 2D image. The length of the x and y axes must both be at least 4. All elements of the input image data must be finite. By default, the PSF peak is assumed to be located at the center of the input image (see the origin keyword). The array must be normalized so that the total flux of a source is 1.0. This means that the sum of the values in the input image PSF over an infinite grid is 1.0. In practice, the sum of the data values in the input image may be less than 1.0 if the input image only covers a finite region of the PSF. These correction factors can be estimated from the ensquared or encircled energy of the PSF based on the size of the input image.

fluxfloat, optional

The total flux of the source, assuming the input image was properly normalized.

x_0, y_0float

The x and y positions of a feature in the image in the output coordinate grid on which the model is evaluated. Typically, this refers to the position of the PSF peak, which is assumed to be located at the center of the input image (see the origin keyword).

origintuple of 2 float or None, optional

The (x, y) coordinate with respect to the input image data array that represents the reference pixel of the input data.

The reference origin pixel will be placed at the model x_0 and y_0 coordinates in the output coordinate system on which the model is evaluated.

Most typically, the input PSF should be centered in the input image, and thus the origin should be set to the central pixel of the data array.

If the origin is set to None, then the origin will be set to the center of the data array ((npix - 1) / 2.0).

oversamplingint or array_like (int), optional

The integer oversampling factor(s) of the input PSF image. 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 use for points outside of the input pixel grid. The default is 0.0.

**kwargsdict, optional

Additional optional keyword arguments to be passed to the astropy.modeling.Model base class.

See also

GriddedPSFModel: A model for a grid of ePSF models.

Examples

In this simple example, we create a PSF image model from a Circular Gaussian PSF. In this case, one should use the CircularGaussianPSF model directly as a PSF model. However, this example demonstrates how to create an image PSF model from an input image.

import matplotlib.pyplot as plt
import numpy as np
from photutils.psf import CircularGaussianPSF, ImagePSF
gaussian_psf = CircularGaussianPSF(x_0=12, y_0=12, fwhm=3.2)
yy, xx = np.mgrid[:25, :25]
psf_data = gaussian_psf(xx, yy)
psf_model = ImagePSF(psf_data, x_0=12, y_0=12, flux=10)
data = psf_model(xx, yy)
plt.imshow(data, origin='lower')

(Source code, png, hires.png, pdf, svg)

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.
`eqcons`	List of parameter equality constraints.
`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`	The interpolating spline function.
`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.
`origin`	A 1D `ndarray` (x, y) pixel coordinates within the model's 2D image of the origin of the coordinate system.
`outputs`
`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.
`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`
`y_0`

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.
`copy`()	Return a copy of this model where only the model parameters are copied.
`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.

eqcons#: List of parameter equality constraints.

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#

The interpolating spline function.

The interpolator is computed with a 3rd-degree RectBivariateSpline (kx=3, ky=3, s=0) using the input image data. The interpolator is used to evaluate the model at arbitrary locations, including fractional pixel positions.

Notes

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

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.

origin#

A 1D ndarray (x, y) pixel coordinates within the model’s 2D image of the origin of the coordinate system.

The reference origin pixel will be placed at the model x_0 and y_0 coordinates in the output coordinate system on which the model is evaluated.

Most typically, the input PSF should be centered in the input image, and thus the origin should be set to the central pixel of the data array.

If the origin is set to None, then the origin will be set to the center of the data array ((npix - 1) / 2.0).

outputs#

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.

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)#

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

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>

copy()[source]#

Return a copy of this model where only the model parameters are copied.

All other copied model attributes are references to the original model. This prevents copying the image data, which may be a large array.

This method is useful if one is interested in only changing the model parameters in a model copy. It is used in the PSF photometry classes during model fitting.

Use the deepcopy method if you want to copy all of the model attributes, including the PSF image data.

Returns:

resultImagePSF: A copy of this model with only the model parameters copied.

deepcopy()[source]#

Return a deep copy of this model.

Returns:

resultImagePSF: A deep copy of this model.

evaluate(x, y, flux, x_0, y_0)[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, assuming the input image was properly normalized.
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.

Returns:

resultndarray: The value of the model evaluated at the input coordinates.

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.