# 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.

Notes

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

Examples

```>>> import numpy as np
>>> 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()
```