LogParabola1D

class astropy.modeling.powerlaws.LogParabola1D(amplitude, x_0, alpha, beta, **constraints)

Bases: astropy.modeling.core.Parametric1DModel

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
param_names	list() -> new empty list
x_0

Methods Summary

deriv(x, amplitude, x_0, alpha, beta)	One dimensional log parabola derivative
eval(x, amplitude, x_0, alpha, beta)	One dimenional log parabola model function

Attributes Documentation

alpha

amplitude

beta

param_names = ['amplitude', 'x_0', 'alpha', 'beta']

x_0

Methods Documentation

static deriv(x, amplitude, x_0, alpha, beta)

One dimensional log parabola derivative

static eval(x, amplitude, x_0, alpha, beta)

One dimenional log parabola model function