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# scipy.special.log_expit

scipy.special.log_expit(x, out=None) = <ufunc 'log_expit'>

  Logarithm of the logistic sigmoid function.

  The SciPy implementation of the logistic sigmoid function is `scipy.special.expit`, so this function is called `log_expit`.

  The function is mathematically equivalent to `log(expit(x))`, but is formulated to avoid loss of precision for inputs with large (positive or negative) magnitude.

  Parameters:
    xarray_like

      The values to apply `log_expit` to element-wise.

    outndarray, optional

      Optional output array for the function results

  Returns:
    outscalar or ndarray

      The computed values, an ndarray of the same shape as `x`.

  See also

  `expit`

  Notes

  As a ufunc, `log_expit` takes a number of optional keyword arguments. For more information see ufuncs

  Added in version 1.8.0.

  Examples

      >>> import numpy as np
      >>> from scipy.special import log_expit, expit

      >>> log_expit([-3.0, 0.25, 2.5, 5.0])
      array([-3.04858735, -0.57593942, -0.07888973, -0.00671535])

  Large negative values:

      >>> log_expit([-100, -500, -1000])
      array([ -100.,  -500., -1000.])

  Note that `expit(-1000)` returns 0, so the naive implementation `log(expit(-1000))` return `-inf`.

  Large positive values:

      >>> log_expit([29, 120, 400])
      array([-2.54366565e-013, -7.66764807e-053, -1.91516960e-174])

  Compare that to the naive implementation:

      >>> np.log(expit([29, 120, 400]))
      array([-2.54463117e-13,  0.00000000e+00,  0.00000000e+00])

  The first value is accurate to only 3 digits, and the larger inputs lose all precision and return 0.