# Moffat2D#

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

Two dimensional Moffat model.

Parameters:
amplitudefloat

Amplitude of the model.

x_0float

x position of the maximum of the Moffat model.

y_0float

y position of the maximum of the Moffat model.

gammafloat

Core width of the Moffat model.

alphafloat

Power index of the Moffat model.

Other Parameters:
fixeda 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.

tieddict, 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.

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 and max properties of a parameter may be used.

eqconslist, optional

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

ineqconslist, optional

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

Notes

Model formula:

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

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)[source]#

Two dimensional Moffat model function.

static fit_deriv(x, y, amplitude, x_0, y_0, gamma, alpha)[source]#

Two dimensional Moffat model derivative with respect to parameters.