scipy.special.rel_entr#
- scipy.special.rel_entr(x, y, out=None) = <ufunc 'rel_entr'>#
Elementwise function for computing relative entropy.
\[\begin{split}\mathrm{rel\_entr}(x, y) = \begin{cases} x \log(x / y) & x > 0, y > 0 \\ 0 & x = 0, y \ge 0 \\ \infty & \text{otherwise} \end{cases}\end{split}\]- Parameters:
- x, yarray_like
Input arrays
- outndarray, optional
Optional output array for the function results
- Returns:
- scalar or ndarray
Relative entropy of the inputs
See also
Notes
Added in version 0.15.0.
This function is jointly convex in x and y.
The origin of this function is in convex programming; see [1]. Given two discrete probability distributions \(p_1, \ldots, p_n\) and \(q_1, \ldots, q_n\), the definition of relative entropy in the context of information theory is
\[\sum_{i = 1}^n \mathrm{rel\_entr}(p_i, q_i).\]To compute the latter quantity, use
scipy.stats.entropy
.See [2] for details.
References
[1]Boyd, Stephen and Lieven Vandenberghe. Convex optimization. Cambridge University Press, 2004. DOI:https://doi.org/10.1017/CBO9780511804441
[2]Kullback-Leibler divergence, https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence