scipy.special.expit

scipy.special.expit(x) = <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.

Returns

outndarray

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()