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	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

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 = 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