activation.py

import warnings
from typing import Optional, Tuple

import torch
from torch import Tensor
from .linear import NonDynamicallyQuantizableLinear
from torch.nn.init import constant_, xavier_normal_, xavier_uniform_
from torch.nn.parameter import Parameter
from .module import Module
from .. import functional as F

__all__ = ['Threshold', 'ReLU', 'RReLU', 'Hardtanh', 'ReLU6', 'Sigmoid', 'Hardsigmoid', 'Tanh',
           'SiLU', 'Mish', 'Hardswish', 'ELU', 'CELU', 'SELU', 'GLU', 'GELU', 'Hardshrink', 'LeakyReLU',
           'LogSigmoid', 'Softplus', 'Softshrink', 'MultiheadAttention', 'PReLU', 'Softsign', 'Tanhshrink',
           'Softmin', 'Softmax', 'Softmax2d', 'LogSoftmax']

class Threshold(Module):
    r"""Thresholds each element of the input Tensor.

    Threshold is defined as:

    .. math::
        y =
        \begin{cases}
        x, &\text{ if } x > \text{threshold} \\
        \text{value}, &\text{ otherwise }
        \end{cases}

    Args:
        threshold: The value to threshold at
        value: The value to replace with
        inplace: can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    Examples::

        >>> m = nn.Threshold(0.1, 20)
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['threshold', 'value', 'inplace']

    threshold: float
    value: float
    inplace: bool

    def __init__(self, threshold: float, value: float, inplace: bool = False) -> None:
        super(Threshold, self).__init__()
        self.threshold = threshold
        self.value = value
        self.inplace = inplace
        # TODO: check in THNN (if inplace == True, then assert value <= threshold)

    def forward(self, input: Tensor) -> Tensor:
        return F.threshold(input, self.threshold, self.value, self.inplace)

    def extra_repr(self):
        inplace_str = ', inplace=True' if self.inplace else ''
        return 'threshold={}, value={}{}'.format(
            self.threshold, self.value, inplace_str
        )


class ReLU(Module):
    r"""Applies the rectified linear unit function element-wise:

    :math:`\text{ReLU}(x) = (x)^+ = \max(0, x)`

    Args:
        inplace: can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/ReLU.png

    Examples::

        >>> m = nn.ReLU()
        >>> input = torch.randn(2)
        >>> output = m(input)


      An implementation of CReLU - https://arxiv.org/abs/1603.05201

        >>> m = nn.ReLU()
        >>> input = torch.randn(2).unsqueeze(0)
        >>> output = torch.cat((m(input),m(-input)))
    """
    __constants__ = ['inplace']
    inplace: bool

    def __init__(self, inplace: bool = False):
        super(ReLU, self).__init__()
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.relu(input, inplace=self.inplace)

    def extra_repr(self) -> str:
        inplace_str = 'inplace=True' if self.inplace else ''
        return inplace_str


class RReLU(Module):
    r"""Applies the randomized leaky rectified liner unit function, element-wise,
    as described in the paper:

    `Empirical Evaluation of Rectified Activations in Convolutional Network`_.

    The function is defined as:

    .. math::
        \text{RReLU}(x) =
        \begin{cases}
            x & \text{if } x \geq 0 \\
            ax & \text{ otherwise }
        \end{cases}

    where :math:`a` is randomly sampled from uniform distribution
    :math:`\mathcal{U}(\text{lower}, \text{upper})`.

     See: https://arxiv.org/pdf/1505.00853.pdf

    Args:
        lower: lower bound of the uniform distribution. Default: :math:`\frac{1}{8}`
        upper: upper bound of the uniform distribution. Default: :math:`\frac{1}{3}`
        inplace: can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/RReLU.png

    Examples::

        >>> m = nn.RReLU(0.1, 0.3)
        >>> input = torch.randn(2)
        >>> output = m(input)

    .. _`Empirical Evaluation of Rectified Activations in Convolutional Network`:
        https://arxiv.org/abs/1505.00853
    """
    __constants__ = ['lower', 'upper', 'inplace']

    lower: float
    upper: float
    inplace: bool

    def __init__(
        self,
        lower: float = 1. / 8,
        upper: float = 1. / 3,
        inplace: bool = False
    ):
        super(RReLU, self).__init__()
        self.lower = lower
        self.upper = upper
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.rrelu(input, self.lower, self.upper, self.training, self.inplace)

    def extra_repr(self):
        inplace_str = ', inplace=True' if self.inplace else ''
        return 'lower={}, upper={}{}'.format(self.lower, self.upper, inplace_str)


class Hardtanh(Module):
    r"""Applies the HardTanh function element-wise.

    HardTanh is defined as:

    .. math::
        \text{HardTanh}(x) = \begin{cases}
            \text{max\_val} & \text{ if } x > \text{ max\_val } \\
            \text{min\_val} & \text{ if } x < \text{ min\_val } \\
            x & \text{ otherwise } \\
        \end{cases}

    Args:
        min_val: minimum value of the linear region range. Default: -1
        max_val: maximum value of the linear region range. Default: 1
        inplace: can optionally do the operation in-place. Default: ``False``

    Keyword arguments :attr:`min_value` and :attr:`max_value`
    have been deprecated in favor of :attr:`min_val` and :attr:`max_val`.

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Hardtanh.png

    Examples::

        >>> m = nn.Hardtanh(-2, 2)
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['min_val', 'max_val', 'inplace']

    min_val: float
    max_val: float
    inplace: bool

    def __init__(
        self,
        min_val: float = -1.,
        max_val: float = 1.,
        inplace: bool = False,
        min_value: Optional[float] = None,
        max_value: Optional[float] = None
    ) -> None:
        super(Hardtanh, self).__init__()
        if min_value is not None:
            warnings.warn("keyword argument min_value is deprecated and rename to min_val")
            min_val = min_value
        if max_value is not None:
            warnings.warn("keyword argument max_value is deprecated and rename to max_val")
            max_val = max_value

        self.min_val = min_val
        self.max_val = max_val
        self.inplace = inplace
        assert self.max_val > self.min_val

    def forward(self, input: Tensor) -> Tensor:
        return F.hardtanh(input, self.min_val, self.max_val, self.inplace)

    def extra_repr(self) -> str:
        inplace_str = ', inplace=True' if self.inplace else ''
        return 'min_val={}, max_val={}{}'.format(
            self.min_val, self.max_val, inplace_str
        )


class ReLU6(Hardtanh):
    r"""Applies the element-wise function:

    .. math::
        \text{ReLU6}(x) = \min(\max(0,x), 6)

    Args:
        inplace: can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/ReLU6.png

    Examples::

        >>> m = nn.ReLU6()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """

    def __init__(self, inplace: bool = False):
        super(ReLU6, self).__init__(0., 6., inplace)

    def extra_repr(self) -> str:
        inplace_str = 'inplace=True' if self.inplace else ''
        return inplace_str


class Sigmoid(Module):
    r"""Applies the element-wise function:

    .. math::
        \text{Sigmoid}(x) = \sigma(x) = \frac{1}{1 + \exp(-x)}


    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Sigmoid.png

    Examples::

        >>> m = nn.Sigmoid()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """

    def forward(self, input: Tensor) -> Tensor:
        return torch.sigmoid(input)


class Hardsigmoid(Module):
    r"""Applies the Hardsigmoid function element-wise.

    Hardsigmoid is defined as:

    .. math::
        \text{Hardsigmoid}(x) = \begin{cases}
            0 & \text{if~} x \le -3, \\
            1 & \text{if~} x \ge +3, \\
            x / 6 + 1 / 2 & \text{otherwise}
        \end{cases}

    Args:
        inplace: can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Hardsigmoid.png

    Examples::

        >>> m = nn.Hardsigmoid()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['inplace']

    inplace: bool

    def __init__(self, inplace : bool = False) -> None:
        super(Hardsigmoid, self).__init__()
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.hardsigmoid(input, self.inplace)


class Tanh(Module):
    r"""Applies the Hyperbolic Tangent (Tanh) function element-wise.

    Tanh is defined as:

    .. math::
        \text{Tanh}(x) = \tanh(x) = \frac{\exp(x) - \exp(-x)} {\exp(x) + \exp(-x)}

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Tanh.png

    Examples::

        >>> m = nn.Tanh()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """

    def forward(self, input: Tensor) -> Tensor:
        return torch.tanh(input)

class SiLU(Module):
    r"""Applies the Sigmoid Linear Unit (SiLU) function, element-wise.
    The SiLU function is also known as the swish function.

    .. math::
        \text{silu}(x) = x * \sigma(x), \text{where } \sigma(x) \text{ is the logistic sigmoid.}

    .. note::
        See `Gaussian Error Linear Units (GELUs) <https://arxiv.org/abs/1606.08415>`_
        where the SiLU (Sigmoid Linear Unit) was originally coined, and see
        `Sigmoid-Weighted Linear Units for Neural Network Function Approximation
        in Reinforcement Learning <https://arxiv.org/abs/1702.03118>`_ and `Swish:
        a Self-Gated Activation Function <https://arxiv.org/abs/1710.05941v1>`_
        where the SiLU was experimented with later.

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/SiLU.png

    Examples::

        >>> m = nn.SiLU()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['inplace']
    inplace: bool

    def __init__(self, inplace: bool = False):
        super(SiLU, self).__init__()
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.silu(input, inplace=self.inplace)

    def extra_repr(self) -> str:
        inplace_str = 'inplace=True' if self.inplace else ''
        return inplace_str

class Mish(Module):
    r"""Applies the Mish function, element-wise.
    Mish: A Self Regularized Non-Monotonic Neural Activation Function.

    .. math::
        \text{Mish}(x) = x * \text{Tanh}(\text{Softplus}(x))

    .. note::
        See `Mish: A Self Regularized Non-Monotonic Neural Activation Function <https://arxiv.org/abs/1908.08681>`_

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Mish.png

    Examples::

        >>> m = nn.Mish()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['inplace']
    inplace: bool

    def __init__(self, inplace: bool = False):
        super(Mish, self).__init__()
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.mish(input, inplace=self.inplace)

    def extra_repr(self) -> str:
        inplace_str = 'inplace=True' if self.inplace else ''
        return inplace_str

class Hardswish(Module):
    r"""Applies the Hardswish function, element-wise, as described in the paper:
    `Searching for MobileNetV3 <https://arxiv.org/abs/1905.02244>`_.

    Hardswish is defined as:

    .. math::
        \text{Hardswish}(x) = \begin{cases}
            0 & \text{if~} x \le -3, \\
            x & \text{if~} x \ge +3, \\
            x \cdot (x + 3) /6 & \text{otherwise}
        \end{cases}

    Args:
        inplace: can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Hardswish.png

    Examples::

        >>> m = nn.Hardswish()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['inplace']

    inplace: bool

    def __init__(self, inplace : bool = False) -> None:
        super(Hardswish, self).__init__()
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.hardswish(input, self.inplace)


class ELU(Module):
    r"""Applies the Exponential Linear Unit (ELU) function, element-wise, as described
    in the paper: `Fast and Accurate Deep Network Learning by Exponential Linear
    Units (ELUs) <https://arxiv.org/abs/1511.07289>`__.

    ELU is defined as:

    .. math::
        \text{ELU}(x) = \begin{cases}
        x, & \text{ if } x > 0\\
        \alpha * (\exp(x) - 1), & \text{ if } x \leq 0
        \end{cases}

    Args:
        alpha: the :math:`\alpha` value for the ELU formulation. Default: 1.0
        inplace: can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/ELU.png

    Examples::

        >>> m = nn.ELU()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['alpha', 'inplace']
    alpha: float
    inplace: bool

    def __init__(self, alpha: float = 1., inplace: bool = False) -> None:
        super(ELU, self).__init__()
        self.alpha = alpha
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.elu(input, self.alpha, self.inplace)

    def extra_repr(self) -> str:
        inplace_str = ', inplace=True' if self.inplace else ''
        return 'alpha={}{}'.format(self.alpha, inplace_str)


class CELU(Module):
    r"""Applies the element-wise function:

    .. math::
        \text{CELU}(x) = \max(0,x) + \min(0, \alpha * (\exp(x/\alpha) - 1))

    More details can be found in the paper `Continuously Differentiable Exponential Linear Units`_ .

    Args:
        alpha: the :math:`\alpha` value for the CELU formulation. Default: 1.0
        inplace: can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/CELU.png

    Examples::

        >>> m = nn.CELU()
        >>> input = torch.randn(2)
        >>> output = m(input)

    .. _`Continuously Differentiable Exponential Linear Units`:
        https://arxiv.org/abs/1704.07483
    """
    __constants__ = ['alpha', 'inplace']
    alpha: float
    inplace: bool

    def __init__(self, alpha: float = 1., inplace: bool = False) -> None:
        super(CELU, self).__init__()
        self.alpha = alpha
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.celu(input, self.alpha, self.inplace)

    def extra_repr(self) -> str:
        inplace_str = ', inplace=True' if self.inplace else ''
        return 'alpha={}{}'.format(self.alpha, inplace_str)


class SELU(Module):
    r"""Applied element-wise, as:

    .. math::
        \text{SELU}(x) = \text{scale} * (\max(0,x) + \min(0, \alpha * (\exp(x) - 1)))

    with :math:`\alpha = 1.6732632423543772848170429916717` and
    :math:`\text{scale} = 1.0507009873554804934193349852946`.

    .. warning::
        When using ``kaiming_normal`` or ``kaiming_normal_`` for initialisation,
        ``nonlinearity='linear'`` should be used instead of ``nonlinearity='selu'``
        in order to get `Self-Normalizing Neural Networks`_.
        See :func:`torch.nn.init.calculate_gain` for more information.

    More details can be found in the paper `Self-Normalizing Neural Networks`_ .

    Args:
        inplace (bool, optional): can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/SELU.png

    Examples::

        >>> m = nn.SELU()
        >>> input = torch.randn(2)
        >>> output = m(input)

    .. _Self-Normalizing Neural Networks: https://arxiv.org/abs/1706.02515
    """
    __constants__ = ['inplace']
    inplace: bool

    def __init__(self, inplace: bool = False) -> None:
        super(SELU, self).__init__()
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.selu(input, self.inplace)

    def extra_repr(self) -> str:
        inplace_str = 'inplace=True' if self.inplace else ''
        return inplace_str


class GLU(Module):
    r"""Applies the gated linear unit function
    :math:`{GLU}(a, b)= a \otimes \sigma(b)` where :math:`a` is the first half
    of the input matrices and :math:`b` is the second half.

    Args:
        dim (int): the dimension on which to split the input. Default: -1

    Shape:
        - Input: :math:`(\ast_1, N, \ast_2)` where `*` means, any number of additional
          dimensions
        - Output: :math:`(\ast_1, M, \ast_2)` where :math:`M=N/2`

    Examples::

        >>> m = nn.GLU()
        >>> input = torch.randn(4, 2)
        >>> output = m(input)
    """
    __constants__ = ['dim']
    dim: int

    def __init__(self, dim: int = -1) -> None:
        super(GLU, self).__init__()
        self.dim = dim

    def forward(self, input: Tensor) -> Tensor:
        return F.glu(input, self.dim)

    def extra_repr(self) -> str:
        return 'dim={}'.format(self.dim)


class GELU(Module):
    r"""Applies the Gaussian Error Linear Units function:

    .. math:: \text{GELU}(x) = x * \Phi(x)

    where :math:`\Phi(x)` is the Cumulative Distribution Function for Gaussian Distribution.

    When the approximate argument is 'tanh', Gelu is estimated with:

    .. math:: \text{GELU}(x) = 0.5 * x * (1 + \text{Tanh}(\sqrt(2 / \pi) * (x + 0.044715 * x^3)))

    Args:
        approximate (str, optional): the gelu approximation algorithm to use:
            ``'none'`` | ``'tanh'``. Default: ``'none'``

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/GELU.png

    Examples::

        >>> m = nn.GELU()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['approximate']
    approximate: str

    def __init__(self, approximate: str = 'none') -> None:
        super(GELU, self).__init__()
        self.approximate = approximate

    def forward(self, input: Tensor) -> Tensor:
        return F.gelu(input, approximate=self.approximate)

    def extra_repr(self) -> str:
        return 'approximate={}'.format(repr(self.approximate))


class Hardshrink(Module):
    r"""Applies the Hard Shrinkage (Hardshrink) function element-wise.

    Hardshrink is defined as:

    .. math::
        \text{HardShrink}(x) =
        \begin{cases}
        x, & \text{ if } x > \lambda \\
        x, & \text{ if } x < -\lambda \\
        0, & \text{ otherwise }
        \end{cases}

    Args:
        lambd: the :math:`\lambda` value for the Hardshrink formulation. Default: 0.5

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Hardshrink.png

    Examples::

        >>> m = nn.Hardshrink()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['lambd']
    lambd: float

    def __init__(self, lambd: float = 0.5) -> None:
        super(Hardshrink, self).__init__()
        self.lambd = lambd

    def forward(self, input: Tensor) -> Tensor:
        return F.hardshrink(input, self.lambd)

    def extra_repr(self) -> str:
        return '{}'.format(self.lambd)


class LeakyReLU(Module):
    r"""Applies the element-wise function:

    .. math::
        \text{LeakyReLU}(x) = \max(0, x) + \text{negative\_slope} * \min(0, x)


    or

    .. math::
        \text{LeakyReLU}(x) =
        \begin{cases}
        x, & \text{ if } x \geq 0 \\
        \text{negative\_slope} \times x, & \text{ otherwise }
        \end{cases}

    Args:
        negative_slope: Controls the angle of the negative slope. Default: 1e-2
        inplace: can optionally do the operation in-place. Default: ``False``

    Shape:
        - Input: :math:`(*)` where `*` means, any number of additional
          dimensions
        - Output: :math:`(*)`, same shape as the input

    .. image:: ../scripts/activation_images/LeakyReLU.png

    Examples::

        >>> m = nn.LeakyReLU(0.1)
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['inplace', 'negative_slope']
    inplace: bool
    negative_slope: float

    def __init__(self, negative_slope: float = 1e-2, inplace: bool = False) -> None:
        super(LeakyReLU, self).__init__()
        self.negative_slope = negative_slope
        self.inplace = inplace

    def forward(self, input: Tensor) -> Tensor:
        return F.leaky_relu(input, self.negative_slope, self.inplace)

    def extra_repr(self) -> str:
        inplace_str = ', inplace=True' if self.inplace else ''
        return 'negative_slope={}{}'.format(self.negative_slope, inplace_str)


class LogSigmoid(Module):
    r"""Applies the element-wise function:

    .. math::
        \text{LogSigmoid}(x) = \log\left(\frac{ 1 }{ 1 + \exp(-x)}\right)

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/LogSigmoid.png

    Examples::

        >>> m = nn.LogSigmoid()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """

    def forward(self, input: Tensor) -> Tensor:
        return F.logsigmoid(input)


class Softplus(Module):
    r"""Applies the Softplus function :math:`\text{Softplus}(x) = \frac{1}{\beta} *
    \log(1 + \exp(\beta * x))` element-wise.

    SoftPlus is a smooth approximation to the ReLU function and can be used
    to constrain the output of a machine to always be positive.

    For numerical stability the implementation reverts to the linear function
    when :math:`input \times \beta > threshold`.

    Args:
        beta: the :math:`\beta` value for the Softplus formulation. Default: 1
        threshold: values above this revert to a linear function. Default: 20

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Softplus.png

    Examples::

        >>> m = nn.Softplus()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['beta', 'threshold']
    beta: int
    threshold: int

    def __init__(self, beta: int = 1, threshold: int = 20) -> None:
        super(Softplus, self).__init__()
        self.beta = beta
        self.threshold = threshold

    def forward(self, input: Tensor) -> Tensor:
        return F.softplus(input, self.beta, self.threshold)

    def extra_repr(self) -> str:
        return 'beta={}, threshold={}'.format(self.beta, self.threshold)


class Softshrink(Module):
    r"""Applies the soft shrinkage function elementwise:

    .. math::
        \text{SoftShrinkage}(x) =
        \begin{cases}
        x - \lambda, & \text{ if } x > \lambda \\
        x + \lambda, & \text{ if } x < -\lambda \\
        0, & \text{ otherwise }
        \end{cases}

    Args:
        lambd: the :math:`\lambda` (must be no less than zero) value for the Softshrink formulation. Default: 0.5

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Softshrink.png

    Examples::

        >>> m = nn.Softshrink()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['lambd']
    lambd: float

    def __init__(self, lambd: float = 0.5) -> None:
        super(Softshrink, self).__init__()
        self.lambd = lambd

    def forward(self, input: Tensor) -> Tensor:
        return F.softshrink(input, self.lambd)

    def extra_repr(self) -> str:
        return str(self.lambd)


class MultiheadAttention(Module):
    r"""Allows the model to jointly attend to information
    from different representation subspaces as described in the paper:
    `Attention Is All You Need <https://arxiv.org/abs/1706.03762>`_.

    Multi-Head Attention is defined as:

    .. math::
        \text{MultiHead}(Q, K, V) = \text{Concat}(head_1,\dots,head_h)W^O

    where :math:`head_i = \text{Attention}(QW_i^Q, KW_i^K, VW_i^V)`.

    ``forward()`` will use a special optimized implementation if all of the following
    conditions are met:

    - self attention is being computed (i.e., ``query``, ``key``, and ``value`` are the same tensor. This
      restriction will be loosened in the future.)
    - inputs are batched (3D) with ``batch_first==True``
    - Either autograd is disabled (using ``torch.inference_mode`` or ``torch.no_grad``) or no tensor argument ``requires_grad``
    - training is disabled (using ``.eval()``)
    - ``add_bias_kv`` is ``False``
    - ``add_zero_attn`` is ``False``
    - ``batch_first`` is ``True`` and the input is batched
    - ``kdim`` and ``vdim`` are equal to ``embed_dim``
    - if a `NestedTensor <https://pytorch.org/docs/stable/nested.html>`_ is passed, neither ``key_padding_mask``
      nor ``attn_mask`` is passed
    - autocast is disabled

    If the optimized implementation is in use, a
    `NestedTensor <https://pytorch.org/docs/stable/nested.html>`_ can be passed for
    ``query``/``key``/``value`` to represent padding more efficiently than using a
    padding mask. In this case, a `NestedTensor <https://pytorch.org/docs/stable/nested.html>`_
    will be returned, and an additional speedup proportional to the fraction of the input
    that is padding can be expected.

    Args:
        embed_dim: Total dimension of the model.
        num_heads: Number of parallel attention heads. Note that ``embed_dim`` will be split
            across ``num_heads`` (i.e. each head will have dimension ``embed_dim // num_heads``).
        dropout: Dropout probability on ``attn_output_weights``. Default: ``0.0`` (no dropout).
        bias: If specified, adds bias to input / output projection layers. Default: ``True``.
        add_bias_kv: If specified, adds bias to the key and value sequences at dim=0. Default: ``False``.
        add_zero_attn: If specified, adds a new batch of zeros to the key and value sequences at dim=1.
            Default: ``False``.
        kdim: Total number of features for keys. Default: ``None`` (uses ``kdim=embed_dim``).
        vdim: Total number of features for values. Default: ``None`` (uses ``vdim=embed_dim``).
        batch_first: If ``True``, then the input and output tensors are provided
            as (batch, seq, feature). Default: ``False`` (seq, batch, feature).

    Examples::

        >>> # xdoctest: +SKIP
        >>> multihead_attn = nn.MultiheadAttention(embed_dim, num_heads)
        >>> attn_output, attn_output_weights = multihead_attn(query, key, value)

    """
    __constants__ = ['batch_first']
    bias_k: Optional[torch.Tensor]
    bias_v: Optional[torch.Tensor]

    def __init__(self, embed_dim, num_heads, dropout=0., bias=True, add_bias_kv=False, add_zero_attn=False,
                 kdim=None, vdim=None, batch_first=False, device=None, dtype=None) -> None:
        factory_kwargs = {'device': device, 'dtype': dtype}
        super(MultiheadAttention, self).__init__()
        self.embed_dim = embed_dim
        self.kdim = kdim if kdim is not None else embed_dim
        self.vdim = vdim if vdim is not None else embed_dim
        self._qkv_same_embed_dim = self.kdim == embed_dim and self.vdim == embed_dim

        self.num_heads = num_heads
        self.dropout = dropout
        self.batch_first = batch_first
        self.head_dim = embed_dim // num_heads
        assert self.head_dim * num_heads == self.embed_dim, "embed_dim must be divisible by num_heads"

        if not self._qkv_same_embed_dim:
            self.q_proj_weight = Parameter(torch.empty((embed_dim, embed_dim), **factory_kwargs))
            self.k_proj_weight = Parameter(torch.empty((embed_dim, self.kdim), **factory_kwargs))
            self.v_proj_weight = Parameter(torch.empty((embed_dim, self.vdim), **factory_kwargs))
            self.register_parameter('in_proj_weight', None)
        else:
            self.in_proj_weight = Parameter(torch.empty((3 * embed_dim, embed_dim), **factory_kwargs))
            self.register_parameter('q_proj_weight', None)
            self.register_parameter('k_proj_weight', None)
            self.register_parameter('v_proj_weight', None)

        if bias:
            self.in_proj_bias = Parameter(torch.empty(3 * embed_dim, **factory_kwargs))
        else:
            self.register_parameter('in_proj_bias', None)
        self.out_proj = NonDynamicallyQuantizableLinear(embed_dim, embed_dim, bias=bias, **factory_kwargs)

        if add_bias_kv:
            self.bias_k = Parameter(torch.empty((1, 1, embed_dim), **factory_kwargs))
            self.bias_v = Parameter(torch.empty((1, 1, embed_dim), **factory_kwargs))
        else:
            self.bias_k = self.bias_v = None

        self.add_zero_attn = add_zero_attn

        self._reset_parameters()

    def _reset_parameters(self):
        if self._qkv_same_embed_dim:
            xavier_uniform_(self.in_proj_weight)
        else:
            xavier_uniform_(self.q_proj_weight)
            xavier_uniform_(self.k_proj_weight)
            xavier_uniform_(self.v_proj_weight)

        if self.in_proj_bias is not None:
            constant_(self.in_proj_bias, 0.)
            constant_(self.out_proj.bias, 0.)
        if self.bias_k is not None:
            xavier_normal_(self.bias_k)
        if self.bias_v is not None:
            xavier_normal_(self.bias_v)

    def __setstate__(self, state):
        # Support loading old MultiheadAttention checkpoints generated by v1.1.0
        if '_qkv_same_embed_dim' not in state:
            state['_qkv_same_embed_dim'] = True

        super(MultiheadAttention, self).__setstate__(state)

    def forward(self, query: Tensor, key: Tensor, value: Tensor, key_padding_mask: Optional[Tensor] = None,
                need_weights: bool = True, attn_mask: Optional[Tensor] = None,
                average_attn_weights: bool = True) -> Tuple[Tensor, Optional[Tensor]]:
        r"""
    Args:
        query: Query embeddings of shape :math:`(L, E_q)` for unbatched input, :math:`(L, N, E_q)` when ``batch_first=False``
            or :math:`(N, L, E_q)` when ``batch_first=True``, where :math:`L` is the target sequence length,
            :math:`N` is the batch size, and :math:`E_q` is the query embedding dimension ``embed_dim``.
            Queries are compared against key-value pairs to produce the output.
            See "Attention Is All You Need" for more details.
        key: Key embeddings of shape :math:`(S, E_k)` for unbatched input, :math:`(S, N, E_k)` when ``batch_first=False``
            or :math:`(N, S, E_k)` when ``batch_first=True``, where :math:`S` is the source sequence length,
            :math:`N` is the batch size, and :math:`E_k` is the key embedding dimension ``kdim``.
            See "Attention Is All You Need" for more details.
        value: Value embeddings of shape :math:`(S, E_v)` for unbatched input, :math:`(S, N, E_v)` when
            ``batch_first=False`` or :math:`(N, S, E_v)` when ``batch_first=True``, where :math:`S` is the source
            sequence length, :math:`N` is the batch size, and :math:`E_v` is the value embedding dimension ``vdim``.
            See "Attention Is All You Need" for more details.
        key_padding_mask: If specified, a mask of shape :math:`(N, S)` indicating which elements within ``key``
            to ignore for the purpose of attention (i.e. treat as "padding"). For unbatched `query`, shape should be :math:`(S)`.
            Binary and byte masks are supported.
            For a binary mask, a ``True`` value indicates that the corresponding ``key`` value will be ignored for
            the purpose of attention. For a float mask, it will be directly added to the corresponding ``key`` value.
        need_weights: If specified, returns ``attn_output_weights`` in addition to ``attn_outputs``.
            Default: ``True``.
        attn_mask: If specified, a 2D or 3D mask preventing attention to certain positions. Must be of shape
            :math:`(L, S)` or :math:`(N\cdot\text{num\_heads}, L, S)`, where :math:`N` is the batch size,
            :math:`L` is the target sequence length, and :math:`S` is the source sequence length. A 2D mask will be
            broadcasted across the batch while a 3D mask allows for a different mask for each entry in the batch.
            Binary, byte, and float masks are supported. For a binary mask, a ``True`` value indicates that the
            corresponding position is not allowed to attend. For a byte mask, a non-zero value indicates that the
            corresponding position is not allowed to attend. For a float mask, the mask values will be added to
            the attention weight.
        average_attn_weights: If true, indicates that the returned ``attn_weights`` should be averaged across
            heads. Otherwise, ``attn_weights`` are provided separately per head. Note that this flag only has an
            effect when ``need_weights=True``. Default: ``True`` (i.e. average weights across heads)

    Outputs:
        - **attn_output** - Attention outputs of shape :math:`(L, E)` when input is unbatched,
          :math:`(L, N, E)` when ``batch_first=False`` or :math:`(N, L, E)` when ``batch_first=True``,
          where :math:`L` is the target sequence length, :math:`N` is the batch size, and :math:`E` is the
          embedding dimension ``embed_dim``.
        - **attn_output_weights** - Only returned when ``need_weights=True``. If ``average_attn_weights=True``,
          returns attention weights averaged across heads of shape :math:`(L, S)` when input is unbatched or
          :math:`(N, L, S)`, where :math:`N` is the batch size, :math:`L` is the target sequence length, and
          :math:`S` is the source sequence length. If ``average_attn_weights=False``, returns attention weights per
          head of shape :math:`(\text{num\_heads}, L, S)` when input is unbatched or :math:`(N, \text{num\_heads}, L, S)`.

        .. note::
            `batch_first` argument is ignored for unbatched inputs.
        """
    def forward(self, query: Tensor, key: Tensor, value: Tensor, key_padding_mask: Optional[Tensor] = None,
                need_weights: bool = True, attn_mask: Optional[Tensor] = None,
                average_attn_weights: bool = True) -> Tuple[Tensor, Optional[Tensor]]:
        r"""
    Args:
        query: Query embeddings of shape :math:`(L, E_q)` for unbatched input, :math:`(L, N, E_q)` when ``batch_first=False``
            or :math:`(N, L, E_q)` when ``batch_first=True``, where :math:`L` is the target sequence length,
            :math:`N` is the batch size, and :math:`E_q` is the query embedding dimension ``embed_dim``.
            Queries are compared against key-value pairs to produce the output.
            See "Attention Is All You Need" for more details.
        key: Key embeddings of shape :math:`(S, E_k)` for unbatched input, :math:`(S, N, E_k)` when ``batch_first=False``
            or :math:`(N, S, E_k)` when ``batch_first=True``, where :math:`S` is the source sequence length,
            :math:`N` is the batch size, and :math:`E_k` is the key embedding dimension ``kdim``.
            See "Attention Is All You Need" for more details.
        value: Value embeddings of shape :math:`(S, E_v)` for unbatched input, :math:`(S, N, E_v)` when
            ``batch_first=False`` or :math:`(N, S, E_v)` when ``batch_first=True``, where :math:`S` is the source
            sequence length, :math:`N` is the batch size, and :math:`E_v` is the value embedding dimension ``vdim``.
            See "Attention Is All You Need" for more details.
        key_padding_mask: If specified, a mask of shape :math:`(N, S)` indicating which elements within ``key``
            to ignore for the purpose of attention (i.e. treat as "padding"). For unbatched `query`, shape should be :math:`(S)`.
            Binary and byte masks are supported.
            For a binary mask, a ``True`` value indicates that the corresponding ``key`` value will be ignored for
            the purpose of attention. For a float mask, it will be directly added to the corresponding ``key`` value.
        need_weights: If specified, returns ``attn_output_weights`` in addition to ``attn_outputs``.
            Default: ``True``.
        attn_mask: If specified, a 2D or 3D mask preventing attention to certain positions. Must be of shape
            :math:`(L, S)` or :math:`(N\cdot\text{num\_heads}, L, S)`, where :math:`N` is the batch size,
            :math:`L` is the target sequence length, and :math:`S` is the source sequence length. A 2D mask will be
            broadcasted across the batch while a 3D mask allows for a different mask for each entry in the batch.
            Binary, byte, and float masks are supported. For a binary mask, a ``True`` value indicates that the
            corresponding position is not allowed to attend. For a byte mask, a non-zero value indicates that the
            corresponding position is not allowed to attend. For a float mask, the mask values will be added to
            the attention weight.
        average_attn_weights: If true, indicates that the returned ``attn_weights`` should be averaged across
            heads. Otherwise, ``attn_weights`` are provided separately per head. Note that this flag only has an
            effect when ``need_weights=True``. Default: ``True`` (i.e. average weights across heads)

    Outputs:
        - **attn_output** - Attention outputs of shape :math:`(L, E)` when input is unbatched,
          :math:`(L, N, E)` when ``batch_first=False`` or :math:`(N, L, E)` when ``batch_first=True``,
          where :math:`L` is the target sequence length, :math:`N` is the batch size, and :math:`E` is the
          embedding dimension ``embed_dim``.
        - **attn_output_weights** - Only returned when ``need_weights=True``. If ``average_attn_weights=True``,
          returns attention weights averaged across heads of shape :math:`(L, S)` when input is unbatched or
          :math:`(N, L, S)`, where :math:`N` is the batch size, :math:`L` is the target sequence length, and
          :math:`S` is the source sequence length. If ``average_attn_weights=False``, returns attention weights per
          head of shape :math:`(\text{num\_heads}, L, S)` when input is unbatched or :math:`(N, \text{num\_heads}, L, S)`.

        .. note::
            `batch_first` argument is ignored for unbatched inputs.
        """
        is_batched = query.dim() == 3
        if key_padding_mask is not None:
            _kpm_dtype = key_padding_mask.dtype
            if _kpm_dtype != torch.bool and not torch.is_floating_point(key_padding_mask):
                raise AssertionError(
                    "only bool and floating types of key_padding_mask are supported")
        why_not_fast_path = F._can_use_fastpath(query,
                                                key,
                                                value,
                                                self.embed_dim,
                                                self.num_heads,
                                                self.in_proj_weight,
                                                self.in_proj_bias,
                                                self.bias_k,
                                                self.bias_v,
                                                self.add_zero_attn,
                                                self.dropout,
                                                self.out_proj.weight,
                                                self.out_proj.bias,
                                                self.training,
                                                key_padding_mask,
                                                attn_mask)
        if not why_not_fast_path:
            if not self.batch_first:
                why_not_fast_path = "batch_first was not True"
            elif not self._qkv_same_embed_dim:
                why_not_fast_path = "_qkv_same_embed_dim was not True"
            else:
                merged_mask, mask_type = F._merge_masks(attn_mask, key_padding_mask, query, self.num_heads)
                return torch._native_multi_head_attention(
                    query,
                    key,
                    value,
                    self.embed_dim,
                    self.num_heads,
                    self.in_proj_weight,
                    self.in_proj_bias,
                    self.out_proj.weight,
                    self.out_proj.bias,
                    merged_mask,
                    need_weights,
                    average_attn_weights,
                    mask_type)

        any_nested = query.is_nested or key.is_nested or value.is_nested
        assert not any_nested, ("MultiheadAttention does not support NestedTensor outside of its fast path. " +
                                f"The fast path was not hit because {why_not_fast_path}")

        if self.batch_first and is_batched:
            # make sure that the transpose op does not affect the "is" property
            if key is value:
                if query is key:
                    query = key = value = query.transpose(1, 0)
                else:
                    query, key = [x.transpose(1, 0) for x in (query, key)]
                    value = key
            else:
                query, key, value = [x.transpose(1, 0) for x in (query, key, value)]

        if not self._qkv_same_embed_dim:
            attn_output, attn_output_weights = F._multi_head_attention_forward_impl(
                query, key, value, self.embed_dim, self.num_heads,
                self.in_proj_weight, self.in_proj_bias,
                self.bias_k, self.bias_v, self.add_zero_attn,
                self.dropout, self.out_proj.weight, self.out_proj.bias,
                training=self.training,
                key_padding_mask=key_padding_mask, need_weights=need_weights,
                attn_mask=attn_mask, use_separate_proj_weight=True,
                q_proj_weight=self.q_proj_weight, k_proj_weight=self.k_proj_weight,
                v_proj_weight=self.v_proj_weight, average_attn_weights=average_attn_weights)
        else:
            attn_output, attn_output_weights = F._multi_head_attention_forward_impl(
                query, key, value, self.embed_dim, self.num_heads,
                self.in_proj_weight, self.in_proj_bias,
                self.bias_k, self.bias_v, self.add_zero_attn,
                self.dropout, self.out_proj.weight, self.out_proj.bias,
                training=self.training,
                key_padding_mask=key_padding_mask, need_weights=need_weights,
                attn_mask=attn_mask, average_attn_weights=average_attn_weights)
        if self.batch_first and is_batched:
            return attn_output.transpose(1, 0), attn_output_weights
        else:
            return attn_output, attn_output_weights


class PReLU(Module):
    r"""Applies the element-wise function:

    .. math::
        \text{PReLU}(x) = \max(0,x) + a * \min(0,x)

    or

    .. math::
        \text{PReLU}(x) =
        \begin{cases}
        x, & \text{ if } x \geq 0 \\
        ax, & \text{ otherwise }
        \end{cases}

    Here :math:`a` is a learnable parameter. When called without arguments, `nn.PReLU()` uses a single
    parameter :math:`a` across all input channels. If called with `nn.PReLU(nChannels)`,
    a separate :math:`a` is used for each input channel.


    .. note::
        weight decay should not be used when learning :math:`a` for good performance.

    .. note::
        Channel dim is the 2nd dim of input. When input has dims < 2, then there is
        no channel dim and the number of channels = 1.

    Args:
        num_parameters (int): number of :math:`a` to learn.
            Although it takes an int as input, there is only two values are legitimate:
            1, or the number of channels at input. Default: 1
        init (float): the initial value of :math:`a`. Default: 0.25

    Shape:
        - Input: :math:`( *)` where `*` means, any number of additional
          dimensions.
        - Output: :math:`(*)`, same shape as the input.

    Attributes:
        weight (Tensor): the learnable weights of shape (:attr:`num_parameters`).

    .. image:: ../scripts/activation_images/PReLU.png

    Examples::

        >>> m = nn.PReLU()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """
    __constants__ = ['num_parameters']
    num_parameters: int

    def __init__(self, num_parameters: int = 1, init: float = 0.25,
                 device=None, dtype=None) -> None:
        factory_kwargs = {'device': device, 'dtype': dtype}
        self.num_parameters = num_parameters
        super(PReLU, self).__init__()
        self.weight = Parameter(torch.empty(num_parameters, **factory_kwargs).fill_(init))

    def forward(self, input: Tensor) -> Tensor:
        return F.prelu(input, self.weight)

    def extra_repr(self) -> str:
        return 'num_parameters={}'.format(self.num_parameters)


class Softsign(Module):
    r"""Applies the element-wise function:

    .. math::
        \text{SoftSign}(x) = \frac{x}{ 1 + |x|}

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Softsign.png

    Examples::

        >>> m = nn.Softsign()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """

    def forward(self, input: Tensor) -> Tensor:
        return F.softsign(input)


class Tanhshrink(Module):
    r"""Applies the element-wise function:

    .. math::
        \text{Tanhshrink}(x) = x - \tanh(x)

    Shape:
        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.
        - Output: :math:`(*)`, same shape as the input.

    .. image:: ../scripts/activation_images/Tanhshrink.png

    Examples::

        >>> m = nn.Tanhshrink()
        >>> input = torch.randn(2)
        >>> output = m(input)
    """

    def forward(self, input: Tensor) -> Tensor:
        return F.tanhshrink(input)


class Softmin(Module):
    r"""Applies the Softmin function to an n-dimensional input Tensor
    rescaling them so that the elements of the n-dimensional output Tensor
    lie in the range `[0, 1]` and sum to 1.

    Softmin is defined as:

    .. math::
        \text{Softmin}(x_{i}) = \frac{\exp(-x_i)}{\sum_j \exp(-x_j)}

    Shape:
        - Input: :math:`(*)` where `*` means, any number of additional
          dimensions
        - Output: :math:`(*)`, same shape as the input

    Args:
        dim (int): A dimension along which Softmin will be computed (so every slice
            along dim will sum to 1).

    Returns:
        a Tensor of the same dimension and shape as the input, with
        values in the range [0, 1]

    Examples::

        >>> m = nn.Softmin(dim=1)
        >>> input = torch.randn(2, 3)
        >>> output = m(input)
    """
    __constants__ = ['dim']
    dim: Optional[int]

    def __init__(self, dim: Optional[int] = None) -> None:
        super(Softmin, self).__init__()
        self.dim = dim

    def __setstate__(self, state):
        super().__setstate__(state)
        if not hasattr(self, 'dim'):
            self.dim = None

    def forward(self, input: Tensor) -> Tensor:
        return F.softmin(input, self.dim, _stacklevel=5)

    def extra_repr(self):
        return 'dim={dim}'.format(dim=self.dim)

class Softmax(Module):
    r"""Applies the Softmax function to an n-dimensional input Tensor
    rescaling them so that the elements of the n-dimensional output Tensor
    lie in the range [0,1] and sum to 1.

    Softmax is defined as:

    .. math::
        \text{Softmax}(x_{i}) = \frac{\exp(x_i)}{\sum_j \exp(x_j)}

    When the input Tensor is a sparse tensor then the unspecified
    values are treated as ``-inf``.

    Shape:
        - Input: :math:`(*)` where `*` means, any number of additional
          dimensions
        - Output: :math:`(*)`, same shape as the input

    Returns:
        a Tensor of the same dimension and shape as the input with
        values in the range [0, 1]

    Args:
        dim (int): A dimension along which Softmax will be computed (so every slice
            along dim will sum to 1).

    .. note::
        This module doesn't work directly with NLLLoss,
        which expects the Log to be computed between the Softmax and itself.
        Use `LogSoftmax` instead (it's faster and has better numerical properties).

    Examples::

        >>> m = nn.Softmax(dim=1)
        >>> input = torch.randn(2, 3)
        >>> output = m(input)

    """
    __constants__ = ['dim']
    dim: Optional[int]

    def __init__(self, dim: Optional[int] = None) -> None:
        super(Softmax, self).__init__()
        self.dim = dim

    def __setstate__(self, state):
        super().__setstate__(state)
        if not hasattr(self, 'dim'):
            self.dim = None

    def forward(self, input: Tensor) -> Tensor:
        return F.softmax(input, self.dim, _stacklevel=5)

    def extra_repr(self) -> str:
        return 'dim={dim}'.format(dim=self.dim)


class Softmax2d(Module):
    r"""Applies SoftMax over features to each spatial location.

    When given an image of ``Channels x Height x Width``, it will
    apply `Softmax` to each location :math:`(Channels, h_i, w_j)`

    Shape:
        - Input: :math:`(N, C, H, W)` or :math:`(C, H, W)`.
        - Output: :math:`(N, C, H, W)` or :math:`(C, H, W)` (same shape as input)

    Returns:
        a Tensor of the same dimension and shape as the input with
        values in the range [0, 1]

    Examples::

        >>> m = nn.Softmax2d()
        >>> # you softmax over the 2nd dimension
        >>> input = torch.randn(2, 3, 12, 13)
        >>> output = m(input)
    """

    def forward(self, input: Tensor) -> Tensor:
        assert input.dim() == 4 or input.dim() == 3, 'Softmax2d requires a 3D or 4D tensor as input'
        return F.softmax(input, -3, _stacklevel=5)


class LogSoftmax(Module):
    r"""Applies the :math:`\log(\text{Softmax}(x))` function to an n-dimensional
    input Tensor. The LogSoftmax formulation can be simplified as:

    .. math::
        \text{LogSoftmax}(x_{i}) = \log\left(\frac{\exp(x_i) }{ \sum_j \exp(x_j)} \right)

    Shape:
        - Input: :math:`(*)` where `*` means, any number of additional
          dimensions
        - Output: :math:`(*)`, same shape as the input

    Args:
        dim (int): A dimension along which LogSoftmax will be computed.

    Returns:
        a Tensor of the same dimension and shape as the input with
        values in the range [-inf, 0)

    Examples::

        >>> m = nn.LogSoftmax(dim=1)
        >>> input = torch.randn(2, 3)
        >>> output = m(input)
    """
    __constants__ = ['dim']
    dim: Optional[int]

    def __init__(self, dim: Optional[int] = None) -> None:
        super(LogSoftmax, self).__init__()
        self.dim = dim

    def __setstate__(self, state):
        super().__setstate__(state)
        if not hasattr(self, 'dim'):
            self.dim = None

    def forward(self, input: Tensor) -> Tensor:
        return F.log_softmax(input, self.dim, _stacklevel=5)

    def extra_repr(self):
        return 'dim={dim}'.format(dim=self.dim)