LogParabola1D

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

Bases: astropy.modeling.Fittable1DModel

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

Parameters
amplitudefloat

Model amplitude

x_0float

Reference point

alphafloat

Power law index

betafloat

Power law curvature

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

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')
x_0 = Parameter('x_0', value=1.0)

Methods Documentation

static evaluate(x, amplitude, x_0, alpha, beta)[source]

One dimensional log parabola model function

static fit_deriv(x, amplitude, x_0, alpha, beta)[source]

One dimensional log parabola derivative with respect to parameters