BrokenPowerLaw1D

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

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.

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
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)

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