BrokenPowerLaw1D

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

Bases: Fittable1DModel

One dimensional power law model with a break.

Parameters:

amplitudepython:float

Model amplitude at the break point.

x_breakpython:float

Break point.

alpha_1python:float

Power law index for x < x_break.

alpha_2python:float

Power law index for x > x_break.

See also

PowerLaw1D, ExponentialCutoffPowerLaw1D, LogParabola1D

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	Names of the parameters that describe models of this type.
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

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

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_break = Parameter('x_break', value=1.0)

Methods Documentation

static evaluate(x, amplitude, x_break, alpha_1, alpha_2)

One dimensional broken power law model function

static fit_deriv(x, amplitude, x_break, alpha_1, alpha_2)

One dimensional broken power law derivative with respect to parameters