Module « scipy.special »

Fonction rel_entr - module scipy.special

Signature de la fonction rel_entr

Description

rel_entr.__doc__

rel_entr(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

rel_entr(x, y, out=None)

Elementwise function for computing relative entropy.

.. math::

    \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}

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
-----
.. versionadded:: 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 :math:`p_1,
\ldots, p_n` and :math:`q_1, \ldots, q_n`, to get the relative
entropy of statistics compute the sum

.. math::

    \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