LogParabola1D

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

Bases: astropy.modeling.Fittable1DModel

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

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
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

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

x_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