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

Added in version 0.10.0.

expit has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	✅
PyTorch	✅	✅
JAX	✅	✅
Dask	✅	n/a

See Support for the array API standard for more information.

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()