Moffat2D

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

Bases: astropy.modeling.Fittable2DModel

Two dimensional Moffat model.

Parameters:

amplitude : float

Amplitude of the model.

x_0 : float

x position of the maximum of the Moffat model.

y_0 : float

y position of the maximum of the Moffat model.

gamma : float

Core width of the Moffat model.

alpha : float

Power index of the Moffat model.

Other Parameters:
 

fixed : a dict

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.

tied : dict

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.

bounds : dict

A dictionary {parameter_name: boolean} of lower and upper bounds of parameters. Keys are parameter names. Values are a list of length 2 giving the desired range for the parameter. Alternatively the min and max properties of a parameter may be used.

eqcons : list

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

ineqcons : list

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:

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

Attributes Summary

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

Methods Documentation

static evaluate(x, y, amplitude, x_0, y_0, gamma, alpha)[source] [edit on github]

Two dimensional Moffat model function

static fit_deriv(x, y, amplitude, x_0, y_0, gamma, alpha)[source] [edit on github]

Two dimensional Moffat model derivative with respect to parameters