scipy.special.kl_div¶
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scipy.special.kl_div(x, y, out=None) = <ufunc 'kl_div'>¶ Elementwise function for computing Kullback-Leibler divergence.
\[\begin{split}\mathrm{kl\_div}(x, y) = \begin{cases} x \log(x / y) - x + y & x > 0, y > 0 \\ y & x = 0, y \ge 0 \\ \infty & \text{otherwise} \end{cases}\end{split}\]- Parameters
- x, yarray_like
Real arguments
- outndarray, optional
Optional output array for the function results
- Returns
- scalar or ndarray
Values of the Kullback-Liebler divergence.
Notes
New in version 0.15.0.
This function is non-negative and is jointly convex in x and y.
The origin of this function is in convex programming; see [1] for details. This is why the the function contains the extra \(-x + y\) terms over what might be expected from the Kullback-Leibler divergence. For a version of the function without the extra terms, see
rel_entr.References
- 1
Grant, Boyd, and Ye, “CVX: Matlab Software for Disciplined Convex Programming”, http://cvxr.com/cvx/