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
Notes
New 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 \(q_1, \ldots, q_n\), to get the relative entropy of statistics compute the sum
\[\sum_{i = 1}^n \mathrm{rel\_entr}(p_i, q_i).\]See [2] for details.
References
- 1
Grant, Boyd, and Ye, “CVX: Matlab Software for Disciplined Convex Programming”, http://cvxr.com/cvx/
- 2
Kullback-Leibler divergence, https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence