scipy.special.entr

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

Elementwise function for computing entropy.

\[\begin{split}\text{entr}(x) = \begin{cases} - x \log(x) & x > 0 \\ 0 & x = 0 \\ -\infty & \text{otherwise} \end{cases}\end{split}\]

Parameters:

xndarray

Input array.

outndarray, optional

Optional output array for the function values

Returns:

resscalar or ndarray

The value of the elementwise entropy function at the given points x.

See also

kl_div, rel_entr, scipy.stats.entropy

Notes

Added in version 0.15.0.

This function is concave.

The origin of this function is in convex programming; see [1]. Given a probability distribution \(p_1, \ldots, p_n\), the definition of entropy in the context of information theory is

\[\sum_{i = 1}^n \mathrm{entr}(p_i).\]

To compute the latter quantity, use scipy.stats.entropy.

References

[1]

Boyd, Stephen and Lieven Vandenberghe. Convex optimization. Cambridge University Press, 2004. DOI:https://doi.org/10.1017/CBO9780511804441