Beta1D

class astropy.modeling.functional_models.Beta1D(amplitude, x_0, gamma, alpha, **constraints)

Bases: astropy.modeling.core.Parametric1DModel

One dimensional Beta model.

Parameters:

amplitude : float

Amplitude of the model.

x_0 : float

x position of the maximum of the Beta model.

gamma : float

Core width of the Beta model.

alpha : float

Power index of the beta model.

See also

Gaussian1D, Box1D

Notes

Model formula:

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

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.

Attributes Summary

alpha
amplitude
gamma
param_names	list() -> new empty list
x_0

Methods Summary

deriv(x, amplitude, x_0, gamma, alpha)	One dimensional Beta model derivative
eval(x, amplitude, x_0, gamma, alpha)	One dimensional Beta model function

Attributes Documentation

alpha

amplitude

gamma

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

x_0

Methods Documentation

static deriv(x, amplitude, x_0, gamma, alpha)

One dimensional Beta model derivative

static eval(x, amplitude, x_0, gamma, alpha)

One dimensional Beta model function