# Source code for mars.tensor.special.info_theory

# Copyright 1999-2021 Alibaba Group Holding Ltd.
#
# you may not use this file except in compliance with the License.
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# Unless required by applicable law or agreed to in writing, software
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import scipy.special as spspecial

from ..arithmetic.utils import arithmetic_operand
from ..utils import infer_dtype, implement_scipy
from .core import TensorSpecialUnaryOp, TensorSpecialBinOp, _register_special_op

@_register_special_op
@arithmetic_operand(sparse_mode="unary")
class TensorEntr(TensorSpecialUnaryOp):
_func_name = "entr"

[docs]@implement_scipy(spspecial.entr)
@infer_dtype(spspecial.entr)
def entr(x, out=None, where=None, **kwargs):
r"""
Elementwise function for computing entropy.

.. math:: \text{entr}(x) = \begin{cases} - x \log(x) & x > 0  \\ 0 & x = 0 \\ -\infty & \text{otherwise} \end{cases}

Parameters
----------
x : Tensor
Input tensor.

Returns
-------
res : Tensor
The value of the elementwise entropy function at the given points x.

--------
kl_div, rel_entr

Notes
-----
This function is concave.
"""
op = TensorEntr(**kwargs)
return op(x, out=out, where=where)

@_register_special_op
class TensorRelEntr(TensorSpecialBinOp):
_func_name = "rel_entr"

@classmethod
def _is_sparse(cls, x1, x2):
if hasattr(x1, "issparse") and x1.issparse():
return True
return False

[docs]@implement_scipy(spspecial.rel_entr)
@infer_dtype(spspecial.rel_entr)
def rel_entr(x, y, out=None, where=None, **kwargs):
r"""
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

--------
entr, kl_div

Notes
-----
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
"""
op = TensorRelEntr(**kwargs)
return op(x, y, out=out, where=where)

@_register_special_op
class TensorKlDiv(TensorSpecialBinOp):
_func_name = "kl_div"

@classmethod
def _is_sparse(cls, x1, x2):
if hasattr(x1, "issparse") and x1.issparse():
return True
return False

@implement_scipy(spspecial.kl_div)
@infer_dtype(spspecial.kl_div)
def kl_div(x, y, out=None, where=None, **kwargs):
r"""
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

--------
entr, kl_div

Notes
-----
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
"""
op = TensorKlDiv(**kwargs)
return op(x, y, out=out, where=where)