# Copyright 2018 The JAX Authors.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

from __future__ import annotations

from typing import overload, Literal

import jax
from jax import lax
from jax import numpy as jnp
from jax._src.numpy.reductions import _reduction_dims, Axis
from jax._src.numpy.util import promote_args_inexact
from jax._src.typing import Array, ArrayLike
import numpy as np

# The definition of logsumexp is shared between jax.nn and jax.scipy, and
# although it matches scipy's definition, we put it here to avoid having
# unnecessary scipy dependencies.

@overload
def logsumexp(a: ArrayLike, axis: Axis = None, b: ArrayLike | None = None,
              keepdims: bool = False, return_sign: Literal[False] = False, where: ArrayLike | None = None) -> Array: ...

@overload
def logsumexp(a: ArrayLike, axis: Axis = None, b: ArrayLike | None = None,
              keepdims: bool = False, *, return_sign: Literal[True], where: ArrayLike | None = None) -> tuple[Array, Array]: ...

@overload
def logsumexp(a: ArrayLike, axis: Axis = None, b: ArrayLike | None = None,
              keepdims: bool = False, return_sign: bool = False, where: ArrayLike | None = None) -> Array | tuple[Array, Array]: ...

def logsumexp(a: ArrayLike, axis: Axis = None, b: ArrayLike | None = None,
              keepdims: bool = False, return_sign: bool = False, where: ArrayLike | None = None) -> Array | tuple[Array, Array]:
  r"""Log-sum-exp reduction.

  JAX implementation of :func:`scipy.special.logsumexp`.

  .. math::
    \mathrm{logsumexp}(a) = \mathrm{log} \sum_j b \cdot \mathrm{exp}(a_{ij})

  where the :math:`j` indices range over one or more dimensions to be reduced.

  Args:
    a: the input array
    axis: the axis or axes over which to reduce. May be either ``None``, an
      int, or a tuple of ints.
    b: scaling factors for :math:`\mathrm{exp}(a)`. Must be broadcastable to the
      shape of `a`.
    keepdims: If ``True``, the axes that are reduced are left in the output as
      dimensions of size 1.
    return_sign: If ``True``, the output will be a ``(result, sign)`` pair,
      where ``sign`` is the sign of the sums and ``result`` contains the
      logarithms of their absolute values. If ``False`` only ``result`` is
      returned and it will contain NaN values if the sums are negative.
    where: Elements to include in the reduction.

  Returns:
    Either an array ``result`` or a pair of arrays ``(result, sign)``, depending
    on the value of the ``return_sign`` argument.
  """
  if b is not None:
    a_arr, b_arr = promote_args_inexact("logsumexp", a, b)
    a_arr = jnp.where(b_arr != 0, a_arr, -jnp.inf)
  else:
    a_arr, = promote_args_inexact("logsumexp", a)
    b_arr = a_arr  # for type checking
  pos_dims, dims = _reduction_dims(a_arr, axis)
  amax = jnp.max(a_arr.real, axis=dims, keepdims=keepdims, where=where, initial=-jnp.inf)
  amax = lax.stop_gradient(lax.select(jnp.isfinite(amax), amax, lax.full_like(amax, 0)))
  amax_with_dims = amax if keepdims else lax.expand_dims(amax, pos_dims)

  exp_a = lax.exp(lax.sub(a_arr, amax_with_dims.astype(a_arr.dtype)))
  if b is not None:
    exp_a = lax.mul(exp_a, b_arr)
  sumexp = exp_a.sum(axis=dims, keepdims=keepdims, where=where)
  sign = lax.sign(sumexp)
  if return_sign or not np.issubdtype(a_arr.dtype, np.complexfloating):
    sumexp = abs(sumexp)
  out = lax.add(lax.log(sumexp), amax.astype(sumexp.dtype))

  if return_sign:
    return (out, sign)
  if b is not None and not np.issubdtype(out.dtype, np.complexfloating):
    with jax.debug_nans(False):
      out = jnp.where(sign < 0, jnp.array(np.nan, dtype=out.dtype), out)
  return out