# LogParabola1D¶

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

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

Parameters: amplitude : float Model amplitude x_0 : float Reference point alpha : float Power law index beta : float 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
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).

Model sub-classes can also use function annotations in evaluate to indicate valid input units, in which case this property should not be overridden since it will return the input units based on the annotations.

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