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# 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:
    amplitude `python:float`

      Model amplitude

    x_0 `python:float`

      Reference point

    alpha `python:float`

      Power law index

    x_cutoff `python: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.