# 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, y array_like

      Input arrays

    out ndarray, optional

      Optional output array for the function results

  Returns
    scalar or ndarray

      Relative entropy of the inputs

  See also

  `entr`, `kl_div`

  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

scipy.special.entr scipy.special.kl_div