Beta2D¶

class astropy.modeling.functional_models.Beta2D(amplitude, x_0, y_0, gamma, alpha, **kwargs)[source] [edit on github]¶

Bases: astropy.modeling.Fittable2DModel

Two dimensional Beta model.

Parameters:

amplitude : float

Amplitude of the model.

x_0 : float

x position of the maximum of the Beta model.

y_0 : float

y position of the maximum of the Beta model.

gamma : float

Core width of the Beta model.

alpha : float

Power index of the beta 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`
`input_names`	list() -> new empty list
`param_names`	list() -> new empty list
`x_0`
`y_0`

Methods Summary

`eval`(args, *kwargs)	Deprecated since version 1.0.
`evaluate`(x, y, amplitude, x_0, y_0, gamma, alpha)	Two dimensional Beta model function
`fit_deriv`(x, y, amplitude, x_0, y_0, gamma, ...)	Two dimensional Beta model derivative with respect to parameters

Attributes Documentation

alpha¶

amplitude¶

gamma¶

input_names = ['x', 'y']¶

param_names = ['amplitude', 'x_0', 'y_0', 'gamma', 'alpha']¶

x_0¶

y_0¶

Methods Documentation

static eval(*args, **kwargs) [edit on github]¶: Deprecated since version 1.0: The eval method is deprecated and may be removed in a future version. Use Beta2D.evaluate instead.

Two dimensional Beta model function

static evaluate(x, y, amplitude, x_0, y_0, gamma, alpha)[source] [edit on github]¶: Two dimensional Beta model function

static fit_deriv(x, y, amplitude, x_0, y_0, gamma, alpha)[source] [edit on github]¶: Two dimensional Beta model derivative with respect to parameters

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Beta2D¶

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