LogParabola1D

class astropy.modeling.powerlaws.LogParabola1D(amplitude=1, x_0=1, alpha=1, beta=0, **kwargs)

Bases: Fittable1DModel

One dimensional log parabola model (sometimes called curved power law).

Parameters:

amplitudepython:float

Model amplitude

x_0python:float

Reference point

alphapython:float

Power law index

betapython:float

Power law curvature

See also

PowerLaw1D, BrokenPowerLaw1D, ExponentialCutoffPowerLaw1D

Notes

Model formula (with \(A\) for amplitude and \(\alpha\) for alpha and \(\beta\) for beta):

\[f(x) = A \left( \frac{x}{x_{0}}\right)^{- \alpha - \beta \log{\left (\frac{x}{x_{0}} \right )}}\]

Attributes Summary

alpha
amplitude
beta
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

Methods Summary

evaluate(x, amplitude, x_0, alpha, beta)	One dimensional log parabola model function
fit_deriv(x, amplitude, x_0, alpha, beta)	One dimensional log parabola derivative with respect to parameters

Attributes Documentation

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

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

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

input_units

param_names = ('amplitude', 'x_0', 'alpha', 'beta')

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=1.0)

Methods Documentation

static evaluate(x, amplitude, x_0, alpha, beta)

One dimensional log parabola model function

static fit_deriv(x, amplitude, x_0, alpha, beta)

One dimensional log parabola derivative with respect to parameters