scipy.special.expit

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

Expit (a.k.a. logistic sigmoid) ufunc for ndarrays.

The expit function, also known as the logistic sigmoid function, is defined as expit(x) = 1/(1+exp(-x)). It is the inverse of the logit function.

Parameters

xndarray

The ndarray to apply expit to element-wise.

outndarray, optional

Optional output array for the function values

Returns

scalar or ndarray

An ndarray of the same shape as x. Its entries are expit of the corresponding entry of x.

See also

logit

Notes

As a ufunc expit takes a number of optional keyword arguments. For more information see ufuncs

New in version 0.10.0.

Examples

>>> from scipy.special import expit, logit

>>> expit([-np.inf, -1.5, 0, 1.5, np.inf])
array([ 0.        ,  0.18242552,  0.5       ,  0.81757448,  1.        ])

logit is the inverse of expit:

>>> logit(expit([-2.5, 0, 3.1, 5.0]))
array([-2.5,  0. ,  3.1,  5. ])

Plot expit(x) for x in [-6, 6]:

>>> import matplotlib.pyplot as plt
>>> x = np.linspace(-6, 6, 121)
>>> y = expit(x)
>>> plt.plot(x, y)
>>> plt.grid()
>>> plt.xlim(-6, 6)
>>> plt.xlabel('x')
>>> plt.title('expit(x)')
>>> plt.show()