Moffat2D

class astropy.modeling.functional_models.Moffat2D(amplitude=1, x_0=0, y_0=0, gamma=1, alpha=1, **kwargs)

Bases: Fittable2DModel

Two dimensional Moffat model.

Parameters:

amplitudepython:float

Amplitude of the model.

x_0python:float

x position of the maximum of the Moffat model.

y_0python:float

y position of the maximum of the Moffat model.

gammapython:float

Core width of the Moffat model.

alphapython:float

Power index of the Moffat model.

Other Parameters:

fixedpython:dict, optional

A dictionary {parameter_name: boolean} of parameters to not be varied during fitting. True means the parameter is held fixed. Alternatively the fixed property of a parameter may be used.

tiedpython:dict, optional

A 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.

boundspython:dict, 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 and max properties of a parameter may be used.

eqconspython:list, optional

A list of functions of length n such that eqcons[j](x0,*args) == 0.0 in a successfully optimized problem.

ineqconspython:list, optional

A list of functions of length n such that ieqcons[j](x0,*args) >= 0.0 is a successfully optimized problem.

See also

Gaussian2D, Box2D

Notes

Model formula:

\[f(x, y) = A \left(1 + \frac{\left(x - x_{0}\right)^{2} + \left(y - y_{0}\right)^{2}}{\gamma^{2}}\right)^{- \alpha}\]

Note that if \(\alpha\) is 1, the Moffat2D profile is a Lorentz2D profile. In that case, the integral of the profile is infinite.

Attributes Summary

alpha
amplitude
fwhm	Moffat full width at half maximum.
gamma
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).
param_names	Names of the parameters that describe models of this type.
x_0
y_0

Methods Summary

evaluate(x, y, amplitude, x_0, y_0, gamma, alpha)	Two dimensional Moffat model function.
fit_deriv(x, y, amplitude, x_0, y_0, gamma, ...)	Two dimensional Moffat model derivative with respect to parameters.

Attributes Documentation

alpha = Parameter('alpha', value=1.0)

amplitude = Parameter('amplitude', value=1.0)

fwhm

Moffat full width at half maximum. Derivation of the formula is available in this notebook by Yoonsoo Bach.

gamma = Parameter('gamma', value=1.0)

input_units

param_names = ('amplitude', 'x_0', 'y_0', 'gamma', 'alpha')

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.

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

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

Methods Documentation

static evaluate(x, y, amplitude, x_0, y_0, gamma, alpha)

Two dimensional Moffat model function.

static fit_deriv(x, y, amplitude, x_0, y_0, gamma, alpha)

Two dimensional Moffat model derivative with respect to parameters.