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:

amplitudefloat

Model amplitude

x_0float

Reference point

alphafloat

Power law index

betafloat

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.