# ExponentialCutoffPowerLaw1D¶

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

One dimensional power law model with an exponential cutoff.

Parameters
amplitudefloat

Model amplitude

x_0float

Reference point

alphafloat

Power law index

x_cutofffloat

Cutoff point

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 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

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_0', 'alpha', 'x_cutoff')
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)[source]

One dimensional exponential cutoff power law model function

static fit_deriv(x, amplitude, x_0, alpha, x_cutoff)[source]

One dimensional exponential cutoff power law derivative with respect to parameters