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#
# 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
#
#     http://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
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from __future__ import annotations

import math
import numbers
from typing import TYPE_CHECKING

import numpy as np

import paddle
from paddle.base import framework
from paddle.distribution.transformed_distribution import TransformedDistribution

if TYPE_CHECKING:
    from collections.abc import Sequence

    from paddle import Tensor
    from paddle.distribution import Transform, Uniform


class Gumbel(TransformedDistribution):
    r"""The Gumbel distribution with location `loc` and `scale` parameters.

    Mathematical details

    The probability density function (pdf) is

    .. math::

        pdf(x; mu, sigma) = exp(-(x - mu) / sigma - exp(-(x - mu) / sigma)) / sigma


    In the above equation:

    * :math:`loc = \mu`: is the mean.
    * :math:`scale = \sigma`: is the std.

    Args:
        loc(int|float|tensor): The mean of gumbel distribution.The data type is int, float, tensor.
        scale(int|float|tensor): The std of gumbel distribution.The data type is int, float, tensor.

    Examples:
        .. code-block:: python

            >>> import paddle
            >>> from paddle.distribution.gumbel import Gumbel

            >>> # Gumbel distributed with loc=0, scale=1
            >>> dist = Gumbel(paddle.full([1], 0.0), paddle.full([1], 1.0))

            >>> # doctest: +SKIP
            >>> print(dist.sample([2]))
            Tensor(shape=[2, 1], dtype=float32, place=Place(cpu), stop_gradient=True,
            [[0.40484068],
            [3.19400501]])

            >>> print(dist.rsample([2]))
            Tensor(shape=[2, 1], dtype=float32, place=Place(cpu), stop_gradient=True,
            [[-0.95093185],
            [ 0.32422572]])

            >>> # doctest: -SKIP
            >>> value = paddle.full([1], 0.5)
            >>> print(dist.prob(value))
            Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,
            [0.33070430])

            >>> print(dist.log_prob(value))
            Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,
            [-1.10653067])

            >>> print(dist.cdf(value))
            Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,
            [0.54523921])

            >>> print(dist.entropy())
            Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,
            [1.57721567])
    """

    loc: Tensor
    scale: Tensor
    base_dist: Uniform
    transforms: tuple[Transform, ...]

    def __init__(self, loc: float | Tensor, scale: float | Tensor) -> None:
        if not isinstance(
            loc, (numbers.Real, framework.Variable, paddle.pir.Value)
        ):
            raise TypeError(
                f"Expected type of loc is Real|Variable|Value, but got {type(loc)}"
            )
        if not isinstance(
            scale, (numbers.Real, framework.Variable, paddle.pir.Value)
        ):
            raise TypeError(
                f"Expected type of scale is Real|Variable|Value, but got {type(scale)}"
            )

        if isinstance(loc, numbers.Real):
            loc = paddle.full(shape=(), fill_value=loc)

        if isinstance(scale, numbers.Real):
            scale = paddle.full(shape=(), fill_value=scale)

        if loc.shape != scale.shape:
            self.loc, self.scale = paddle.broadcast_tensors([loc, scale])
        else:
            self.loc, self.scale = loc, scale

        finfo = np.finfo(dtype='float32')
        self.base_dist = paddle.distribution.Uniform(
            paddle.full_like(self.loc, float(finfo.tiny)),
            paddle.full_like(self.loc, float(1 - finfo.eps)),
        )

        self.transforms = ()

        super().__init__(self.base_dist, self.transforms)

    @property
    def mean(self) -> Tensor:
        r"""Mean of distribution

        The mean is

        .. math::

            mean = \mu + \sigma * γ

        In the above equation:

        * :math:`loc = \mu`: is the location parameter.
        * :math:`scale = \sigma`: is the scale parameter.
        * :math:`γ`: is the euler's constant.

        Returns:
            Tensor: mean value.

        """
        return self.loc + self.scale * np.euler_gamma

    @property
    def variance(self) -> Tensor:
        r"""Variance of distribution.

        The variance is

        .. math::

            variance = \sigma^2 * \pi^2 / 6

        In the above equation:

        * :math:`scale = \sigma`: is the scale parameter.

        Returns:
            Tensor: The variance value.

        """
        temp = paddle.full(
            shape=self.loc.shape,
            fill_value=math.pi * math.pi,
            dtype=self.scale.dtype,
        )

        return paddle.pow(self.scale, 2) * temp / 6

    @property
    def stddev(self) -> Tensor:
        r"""Standard deviation of distribution

        The standard deviation is

        .. math::

            stddev = \sqrt{\sigma^2 * \pi^2 / 6}

        In the above equation:
        * :math:`scale = \sigma`: is the scale parameter.

        Returns:
            Tensor: std value
        """
        return paddle.sqrt(self.variance)

    def prob(self, value: Tensor) -> Tensor:
        """Probability density/mass function

        Args:
            value (Tensor): The input tensor.

        Returns:
            Tensor: probability.The data type is same with value.

        """
        y = (self.loc - value.astype(self.loc.dtype)) / self.scale.astype(
            self.loc.dtype
        )

        return paddle.exp(y - paddle.exp(y)) / self.scale.astype(y.dtype)

    def log_prob(self, value: Tensor) -> Tensor:
        """Log probability density/mass function.

        Args:
            value (Tensor): The input tensor.

        Returns:
            Tensor: log probability.The data type is same with value.

        """
        return paddle.log(self.prob(value))

    def cdf(self, value: Tensor) -> Tensor:
        """Cumulative distribution function.
        Args:
            value (Tensor): value to be evaluated.

        Returns:
            Tensor: cumulative probability of value.

        """
        return paddle.exp(
            -paddle.exp(
                -(value - self.loc.astype(value.dtype))
                / self.scale.astype(value.dtype)
            )
        )

    def entropy(self) -> Tensor:
        """Entropy of Gumbel distribution.

        Returns:
            Entropy of distribution.

        """
        return paddle.log(self.scale) + 1 + np.euler_gamma

    def sample(self, shape: Sequence[int]) -> Tensor:
        """Sample from ``Gumbel``.

        Args:
            shape (Sequence[int], optional): The sample shape. Defaults to ().

        Returns:
            Tensor: A tensor with prepended dimensions shape.The data type is float32.

        """
        with paddle.no_grad():
            return self.rsample(shape)

    def rsample(self, shape: Sequence[int]) -> Tensor:
        """reparameterized sample
        Args:
            shape (Sequence[int]): 1D `int32`. Shape of the generated samples.

        Returns:
            Tensor: A tensor with prepended dimensions shape.The data type is float32.

        """
        exp_trans = paddle.distribution.ExpTransform()
        affine_trans_1 = paddle.distribution.AffineTransform(
            paddle.full(
                shape=self.scale.shape, fill_value=0, dtype=self.loc.dtype
            ),
            -paddle.ones_like(self.scale),
        )
        affine_trans_2 = paddle.distribution.AffineTransform(
            self.loc, -self.scale
        )

        return affine_trans_2.forward(
            exp_trans.inverse(
                affine_trans_1.forward(
                    exp_trans.inverse(self._base.sample(shape))
                )
            )
        )
