ExponentialCutoffPowerLaw1D

class astropy.modeling.powerlaws.ExponentialCutoffPowerLaw1D(amplitude=1, x_0=1, alpha=1, x_cutoff=1, **kwargs)

Bases: Fittable1DModel

One dimensional power law model with an exponential cutoff.

Parameters:

amplitudepython:float

Model amplitude

x_0python:float

Reference point

alphapython:float

Power law index

x_cutoffpython:float

Cutoff point

See also

PowerLaw1D, BrokenPowerLaw1D, LogParabola1D

Notes

Model formula (with \(A\) for amplitude and \(\alpha\) for alpha):

\[f(x) = A (x / x_0) ^ {-\alpha} \exp (-x / x_{cutoff})\]

Attributes Summary

alpha
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_0
x_cutoff

Methods Summary

evaluate(x, amplitude, x_0, alpha, x_cutoff)	One dimensional exponential cutoff power law model function
fit_deriv(x, amplitude, x_0, alpha, x_cutoff)	One dimensional exponential cutoff power law derivative with respect to parameters

Attributes Documentation

alpha = Parameter('alpha', value=1.0)

amplitude = Parameter('amplitude', value=1.0)

input_units

param_names = ('amplitude', 'x_0', 'alpha', 'x_cutoff')

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_0 = Parameter('x_0', value=1.0)

x_cutoff = Parameter('x_cutoff', value=1.0)

Methods Documentation

static evaluate(x, amplitude, x_0, alpha, x_cutoff)

One dimensional exponential cutoff power law model function

static fit_deriv(x, amplitude, x_0, alpha, x_cutoff)

One dimensional exponential cutoff power law derivative with respect to parameters