# BrokenPowerLaw1D¶

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

One dimensional power law model with a break.

Parameters
amplitudefloat

Model amplitude at the break point.

x_breakfloat

Break point.

alpha_1float

Power law index for x < x_break.

alpha_2float

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 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_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 = Parameter('alpha_1', value=1.0)
alpha_2 = Parameter('alpha_2', value=1.0)
amplitude = Parameter('amplitude', value=1.0)
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_break', 'alpha_1', 'alpha_2')
x_break = Parameter('x_break', value=1.0)

Methods Documentation

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

One dimensional broken power law model function

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

One dimensional broken power law derivative with respect to parameters