BrokenPowerLaw1D

class astropy.modeling.powerlaws.BrokenPowerLaw1D(amplitude=1, x_break=1, alpha_1=1, alpha_2=1, **kwargs)[source] [edit on github]

Bases: astropy.modeling.Fittable1DModel

One dimensional power law model with a break.

Parameters:

amplitude : float

Model amplitude at the break point.

x_break : float

Break point.

alpha_1 : float

Power law index for x < x_break.

alpha_2 : float

Power law index for x > x_break.

Notes

Model formula (with \(A\) for amplitude and \(\alpha_1\) for alpha_1 and \(\alpha_2\) for alpha_2):

\[\begin{split}f(x) = \left \{ \begin{array}{ll} A (x / x_{break}) ^ {-\alpha_1} & : x < x_{break} \\ A (x / x_{break}) ^ {-\alpha_2} & : x > x_{break} \\ \end{array} \right.\end{split}\]

Attributes Summary

alpha_1
alpha_2
amplitude
input_units
param_names
x_break

Methods Summary

evaluate(x, amplitude, x_break, alpha_1, alpha_2) One dimensional broken power law model function
fit_deriv(x, amplitude, x_break, alpha_1, …) One dimensional broken power law derivative with respect to parameters

Attributes Documentation

alpha_1
alpha_2
amplitude
input_units
param_names = ('amplitude', 'x_break', 'alpha_1', 'alpha_2')
x_break

Methods Documentation

static evaluate(x, amplitude, x_break, alpha_1, alpha_2)[source] [edit on github]

One dimensional broken power law model function

static fit_deriv(x, amplitude, x_break, alpha_1, alpha_2)[source] [edit on github]

One dimensional broken power law derivative with respect to parameters