pooling.py

from typing import List, Optional

from torch import Tensor
from .module import Module
from .utils import _single, _pair, _triple
from .. import functional as F

from ..common_types import _size_any_t, _size_1_t, _size_2_t, _size_3_t, _ratio_3_t, _ratio_2_t


class _MaxPoolNd(Module):
    __constants__ = ['kernel_size', 'stride', 'padding', 'dilation',
                     'return_indices', 'ceil_mode']
    return_indices: bool
    ceil_mode: bool

    def __init__(self, kernel_size: _size_any_t, stride: Optional[_size_any_t] = None,
                 padding: _size_any_t = 0, dilation: _size_any_t = 1,
                 return_indices: bool = False, ceil_mode: bool = False) -> None:
        super(_MaxPoolNd, self).__init__()
        self.kernel_size = kernel_size
        self.stride = stride if (stride is not None) else kernel_size
        self.padding = padding
        self.dilation = dilation
        self.return_indices = return_indices
        self.ceil_mode = ceil_mode

    def extra_repr(self) -> str:
        return 'kernel_size={kernel_size}, stride={stride}, padding={padding}' \
            ', dilation={dilation}, ceil_mode={ceil_mode}'.format(**self.__dict__)


class MaxPool1d(_MaxPoolNd):
    r"""Applies a 1D max pooling over an input signal composed of several input
    planes.

    In the simplest case, the output value of the layer with input size :math:`(N, C, L)`
    and output :math:`(N, C, L_{out})` can be precisely described as:

    .. math::
        out(N_i, C_j, k) = \max_{m=0, \ldots, \text{kernel\_size} - 1}
                input(N_i, C_j, stride \times k + m)

    If :attr:`padding` is non-zero, then the input is implicitly padded with negative infinity on both sides
    for :attr:`padding` number of points. :attr:`dilation` is the stride between the elements within the
    sliding window. This `link`_ has a nice visualization of the pooling parameters.

    Note:
        When ceil_mode=True, sliding windows are allowed to go off-bounds if they start within the left padding
        or the input. Sliding windows that would start in the right padded region are ignored.

    Args:
        kernel_size: The size of the sliding window, must be > 0.
        stride: The stride of the sliding window, must be > 0. Default value is :attr:`kernel_size`.
        padding: Implicit negative infinity padding to be added on both sides, must be >= 0 and <= kernel_size / 2.
        dilation: The stride between elements within a sliding window, must be > 0.
        return_indices: If ``True``, will return the argmax along with the max values.
                        Useful for :class:`torch.nn.MaxUnpool1d` later
        ceil_mode: If ``True``, will use `ceil` instead of `floor` to compute the output shape. This
                   ensures that every element in the input tensor is covered by a sliding window.

    Shape:
        - Input: :math:`(N, C, L_{in})`
        - Output: :math:`(N, C, L_{out})`, where

          .. math::
              L_{out} = \left\lfloor \frac{L_{in} + 2 \times \text{padding} - \text{dilation}
                    \times (\text{kernel\_size} - 1) - 1}{\text{stride}} + 1\right\rfloor

    Examples::

        >>> # pool of size=3, stride=2
        >>> m = nn.MaxPool1d(3, stride=2)
        >>> input = torch.randn(20, 16, 50)
        >>> output = m(input)

    .. _link:
        https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md
    """

    kernel_size: _size_1_t
    stride: _size_1_t
    padding: _size_1_t
    dilation: _size_1_t

    def forward(self, input: Tensor) -> Tensor:
        return F.max_pool1d(input, self.kernel_size, self.stride,
                            self.padding, self.dilation, self.ceil_mode,
                            self.return_indices)


class MaxPool2d(_MaxPoolNd):
    r"""Applies a 2D max pooling over an input signal composed of several input
    planes.

    In the simplest case, the output value of the layer with input size :math:`(N, C, H, W)`,
    output :math:`(N, C, H_{out}, W_{out})` and :attr:`kernel_size` :math:`(kH, kW)`
    can be precisely described as:

    .. math::
        \begin{aligned}
            out(N_i, C_j, h, w) ={} & \max_{m=0, \ldots, kH-1} \max_{n=0, \ldots, kW-1} \\
                                    & \text{input}(N_i, C_j, \text{stride[0]} \times h + m,
                                                   \text{stride[1]} \times w + n)
        \end{aligned}

    If :attr:`padding` is non-zero, then the input is implicitly zero-padded on both sides
    for :attr:`padding` number of points. :attr:`dilation` controls the spacing between the kernel points.
    It is harder to describe, but this `link`_ has a nice visualization of what :attr:`dilation` does.

    Note:
        When ceil_mode=True, sliding windows are allowed to go off-bounds if they start within the left padding
        or the input. Sliding windows that would start in the right padded region are ignored.

    The parameters :attr:`kernel_size`, :attr:`stride`, :attr:`padding`, :attr:`dilation` can either be:

        - a single ``int`` -- in which case the same value is used for the height and width dimension
        - a ``tuple`` of two ints -- in which case, the first `int` is used for the height dimension,
          and the second `int` for the width dimension

    Args:
        kernel_size: the size of the window to take a max over
        stride: the stride of the window. Default value is :attr:`kernel_size`
        padding: implicit zero padding to be added on both sides
        dilation: a parameter that controls the stride of elements in the window
        return_indices: if ``True``, will return the max indices along with the outputs.
                        Useful for :class:`torch.nn.MaxUnpool2d` later
        ceil_mode: when True, will use `ceil` instead of `floor` to compute the output shape

    Shape:
        - Input: :math:`(N, C, H_{in}, W_{in})`
        - Output: :math:`(N, C, H_{out}, W_{out})`, where

          .. math::
              H_{out} = \left\lfloor\frac{H_{in} + 2 * \text{padding[0]} - \text{dilation[0]}
                    \times (\text{kernel\_size[0]} - 1) - 1}{\text{stride[0]}} + 1\right\rfloor

          .. math::
              W_{out} = \left\lfloor\frac{W_{in} + 2 * \text{padding[1]} - \text{dilation[1]}
                    \times (\text{kernel\_size[1]} - 1) - 1}{\text{stride[1]}} + 1\right\rfloor

    Examples::

        >>> # pool of square window of size=3, stride=2
        >>> m = nn.MaxPool2d(3, stride=2)
        >>> # pool of non-square window
        >>> m = nn.MaxPool2d((3, 2), stride=(2, 1))
        >>> input = torch.randn(20, 16, 50, 32)
        >>> output = m(input)

    .. _link:
        https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md
    """

    kernel_size: _size_2_t
    stride: _size_2_t
    padding: _size_2_t
    dilation: _size_2_t

    def forward(self, input: Tensor) -> Tensor:
        return F.max_pool2d(input, self.kernel_size, self.stride,
                            self.padding, self.dilation, self.ceil_mode,
                            self.return_indices)


class MaxPool3d(_MaxPoolNd):
    r"""Applies a 3D max pooling over an input signal composed of several input
    planes.

    In the simplest case, the output value of the layer with input size :math:`(N, C, D, H, W)`,
    output :math:`(N, C, D_{out}, H_{out}, W_{out})` and :attr:`kernel_size` :math:`(kD, kH, kW)`
    can be precisely described as:

    .. math::
        \begin{aligned}
            \text{out}(N_i, C_j, d, h, w) ={} & \max_{k=0, \ldots, kD-1} \max_{m=0, \ldots, kH-1} \max_{n=0, \ldots, kW-1} \\
                                              & \text{input}(N_i, C_j, \text{stride[0]} \times d + k,
                                                             \text{stride[1]} \times h + m, \text{stride[2]} \times w + n)
        \end{aligned}

    If :attr:`padding` is non-zero, then the input is implicitly zero-padded on both sides
    for :attr:`padding` number of points. :attr:`dilation` controls the spacing between the kernel points.
    It is harder to describe, but this `link`_ has a nice visualization of what :attr:`dilation` does.

    Note:
        When ceil_mode=True, sliding windows are allowed to go off-bounds if they start within the left padding
        or the input. Sliding windows that would start in the right padded region are ignored.

    The parameters :attr:`kernel_size`, :attr:`stride`, :attr:`padding`, :attr:`dilation` can either be:

        - a single ``int`` -- in which case the same value is used for the depth, height and width dimension
        - a ``tuple`` of three ints -- in which case, the first `int` is used for the depth dimension,
          the second `int` for the height dimension and the third `int` for the width dimension

    Args:
        kernel_size: the size of the window to take a max over
        stride: the stride of the window. Default value is :attr:`kernel_size`
        padding: implicit zero padding to be added on all three sides
        dilation: a parameter that controls the stride of elements in the window
        return_indices: if ``True``, will return the max indices along with the outputs.
                        Useful for :class:`torch.nn.MaxUnpool3d` later
        ceil_mode: when True, will use `ceil` instead of `floor` to compute the output shape

    Shape:
        - Input: :math:`(N, C, D_{in}, H_{in}, W_{in})`
        - Output: :math:`(N, C, D_{out}, H_{out}, W_{out})`, where

          .. math::
              D_{out} = \left\lfloor\frac{D_{in} + 2 \times \text{padding}[0] - \text{dilation}[0] \times
                (\text{kernel\_size}[0] - 1) - 1}{\text{stride}[0]} + 1\right\rfloor

          .. math::
              H_{out} = \left\lfloor\frac{H_{in} + 2 \times \text{padding}[1] - \text{dilation}[1] \times
                (\text{kernel\_size}[1] - 1) - 1}{\text{stride}[1]} + 1\right\rfloor

          .. math::
              W_{out} = \left\lfloor\frac{W_{in} + 2 \times \text{padding}[2] - \text{dilation}[2] \times
                (\text{kernel\_size}[2] - 1) - 1}{\text{stride}[2]} + 1\right\rfloor

    Examples::

        >>> # pool of square window of size=3, stride=2
        >>> m = nn.MaxPool3d(3, stride=2)
        >>> # pool of non-square window
        >>> m = nn.MaxPool3d((3, 2, 2), stride=(2, 1, 2))
        >>> input = torch.randn(20, 16, 50,44, 31)
        >>> output = m(input)

    .. _link:
        https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md
    """  # noqa: E501

    kernel_size: _size_3_t
    stride: _size_3_t
    padding: _size_3_t
    dilation: _size_3_t

    def forward(self, input: Tensor) -> Tensor:
        return F.max_pool3d(input, self.kernel_size, self.stride,
                            self.padding, self.dilation, self.ceil_mode,
                            self.return_indices)


class _MaxUnpoolNd(Module):

    def extra_repr(self) -> str:
        return 'kernel_size={}, stride={}, padding={}'.format(
            self.kernel_size, self.stride, self.padding
        )


class MaxUnpool1d(_MaxUnpoolNd):
    r"""Computes a partial inverse of :class:`MaxPool1d`.

    :class:`MaxPool1d` is not fully invertible, since the non-maximal values are lost.

    :class:`MaxUnpool1d` takes in as input the output of :class:`MaxPool1d`
    including the indices of the maximal values and computes a partial inverse
    in which all non-maximal values are set to zero.

    .. note:: :class:`MaxPool1d` can map several input sizes to the same output
              sizes. Hence, the inversion process can get ambiguous.
              To accommodate this, you can provide the needed output size
              as an additional argument :attr:`output_size` in the forward call.
              See the Inputs and Example below.

    Args:
        kernel_size (int or tuple): Size of the max pooling window.
        stride (int or tuple): Stride of the max pooling window.
            It is set to :attr:`kernel_size` by default.
        padding (int or tuple): Padding that was added to the input

    Inputs:
        - `input`: the input Tensor to invert
        - `indices`: the indices given out by :class:`~torch.nn.MaxPool1d`
        - `output_size` (optional): the targeted output size

    Shape:
        - Input: :math:`(N, C, H_{in})`
        - Output: :math:`(N, C, H_{out})`, where

          .. math::
              H_{out} = (H_{in} - 1) \times \text{stride}[0] - 2 \times \text{padding}[0] + \text{kernel\_size}[0]

          or as given by :attr:`output_size` in the call operator

    Example::

        >>> pool = nn.MaxPool1d(2, stride=2, return_indices=True)
        >>> unpool = nn.MaxUnpool1d(2, stride=2)
        >>> input = torch.tensor([[[1., 2, 3, 4, 5, 6, 7, 8]]])
        >>> output, indices = pool(input)
        >>> unpool(output, indices)
        tensor([[[ 0.,  2.,  0.,  4.,  0.,  6.,  0., 8.]]])

        >>> # Example showcasing the use of output_size
        >>> input = torch.tensor([[[1., 2, 3, 4, 5, 6, 7, 8, 9]]])
        >>> output, indices = pool(input)
        >>> unpool(output, indices, output_size=input.size())
        tensor([[[ 0.,  2.,  0.,  4.,  0.,  6.,  0., 8.,  0.]]])

        >>> unpool(output, indices)
        tensor([[[ 0.,  2.,  0.,  4.,  0.,  6.,  0., 8.]]])
    """

    kernel_size: _size_1_t
    stride: _size_1_t
    padding: _size_1_t

    def __init__(self, kernel_size: _size_1_t, stride: Optional[_size_1_t] = None, padding: _size_1_t = 0) -> None:
        super(MaxUnpool1d, self).__init__()
        self.kernel_size = _single(kernel_size)
        self.stride = _single(stride if (stride is not None) else kernel_size)
        self.padding = _single(padding)

    def forward(self, input: Tensor, indices: Tensor, output_size: Optional[List[int]] = None) -> Tensor:
        return F.max_unpool1d(input, indices, self.kernel_size, self.stride,
                              self.padding, output_size)


class MaxUnpool2d(_MaxUnpoolNd):
    r"""Computes a partial inverse of :class:`MaxPool2d`.

    :class:`MaxPool2d` is not fully invertible, since the non-maximal values are lost.

    :class:`MaxUnpool2d` takes in as input the output of :class:`MaxPool2d`
    including the indices of the maximal values and computes a partial inverse
    in which all non-maximal values are set to zero.

    .. note:: :class:`MaxPool2d` can map several input sizes to the same output
              sizes. Hence, the inversion process can get ambiguous.
              To accommodate this, you can provide the needed output size
              as an additional argument :attr:`output_size` in the forward call.
              See the Inputs and Example below.

    Args:
        kernel_size (int or tuple): Size of the max pooling window.
        stride (int or tuple): Stride of the max pooling window.
            It is set to :attr:`kernel_size` by default.
        padding (int or tuple): Padding that was added to the input

    Inputs:
        - `input`: the input Tensor to invert
        - `indices`: the indices given out by :class:`~torch.nn.MaxPool2d`
        - `output_size` (optional): the targeted output size

    Shape:
        - Input: :math:`(N, C, H_{in}, W_{in})`
        - Output: :math:`(N, C, H_{out}, W_{out})`, where

          .. math::
            H_{out} = (H_{in} - 1) \times \text{stride[0]} - 2 \times \text{padding[0]} + \text{kernel\_size[0]}

          .. math::
            W_{out} = (W_{in} - 1) \times \text{stride[1]} - 2 \times \text{padding[1]} + \text{kernel\_size[1]}

          or as given by :attr:`output_size` in the call operator

    Example::

        >>> pool = nn.MaxPool2d(2, stride=2, return_indices=True)
        >>> unpool = nn.MaxUnpool2d(2, stride=2)
        >>> input = torch.tensor([[[[ 1.,  2,  3,  4],
                                    [ 5,  6,  7,  8],
                                    [ 9, 10, 11, 12],
                                    [13, 14, 15, 16]]]])
        >>> output, indices = pool(input)
        >>> unpool(output, indices)
        tensor([[[[  0.,   0.,   0.,   0.],
                  [  0.,   6.,   0.,   8.],
                  [  0.,   0.,   0.,   0.],
                  [  0.,  14.,   0.,  16.]]]])

        >>> # specify a different output size than input size
        >>> unpool(output, indices, output_size=torch.Size([1, 1, 5, 5]))
        tensor([[[[  0.,   0.,   0.,   0.,   0.],
                  [  6.,   0.,   8.,   0.,   0.],
                  [  0.,   0.,   0.,  14.,   0.],
                  [ 16.,   0.,   0.,   0.,   0.],
                  [  0.,   0.,   0.,   0.,   0.]]]])
    """

    kernel_size: _size_2_t
    stride: _size_2_t
    padding: _size_2_t

    def __init__(self, kernel_size: _size_2_t, stride: Optional[_size_2_t] = None, padding: _size_2_t = 0) -> None:
        super(MaxUnpool2d, self).__init__()
        self.kernel_size = _pair(kernel_size)
        self.stride = _pair(stride if (stride is not None) else kernel_size)
        self.padding = _pair(padding)

    def forward(self, input: Tensor, indices: Tensor, output_size: Optional[List[int]] = None) -> Tensor:
        return F.max_unpool2d(input, indices, self.kernel_size, self.stride,
                              self.padding, output_size)


class MaxUnpool3d(_MaxUnpoolNd):
    r"""Computes a partial inverse of :class:`MaxPool3d`.

    :class:`MaxPool3d` is not fully invertible, since the non-maximal values are lost.
    :class:`MaxUnpool3d` takes in as input the output of :class:`MaxPool3d`
    including the indices of the maximal values and computes a partial inverse
    in which all non-maximal values are set to zero.

    .. note:: :class:`MaxPool3d` can map several input sizes to the same output
              sizes. Hence, the inversion process can get ambiguous.
              To accommodate this, you can provide the needed output size
              as an additional argument :attr:`output_size` in the forward call.
              See the Inputs section below.

    Args:
        kernel_size (int or tuple): Size of the max pooling window.
        stride (int or tuple): Stride of the max pooling window.
            It is set to :attr:`kernel_size` by default.
        padding (int or tuple): Padding that was added to the input

    Inputs:
        - `input`: the input Tensor to invert
        - `indices`: the indices given out by :class:`~torch.nn.MaxPool3d`
        - `output_size` (optional): the targeted output size

    Shape:
        - Input: :math:`(N, C, D_{in}, H_{in}, W_{in})`
        - Output: :math:`(N, C, D_{out}, H_{out}, W_{out})`, where

          .. math::
              D_{out} = (D_{in} - 1) \times \text{stride[0]} - 2 \times \text{padding[0]} + \text{kernel\_size[0]}

          .. math::
              H_{out} = (H_{in} - 1) \times \text{stride[1]} - 2 \times \text{padding[1]} + \text{kernel\_size[1]}

          .. math::
              W_{out} = (W_{in} - 1) \times \text{stride[2]} - 2 \times \text{padding[2]} + \text{kernel\_size[2]}

          or as given by :attr:`output_size` in the call operator

    Example::

        >>> # pool of square window of size=3, stride=2
        >>> pool = nn.MaxPool3d(3, stride=2, return_indices=True)
        >>> unpool = nn.MaxUnpool3d(3, stride=2)
        >>> output, indices = pool(torch.randn(20, 16, 51, 33, 15))
        >>> unpooled_output = unpool(output, indices)
        >>> unpooled_output.size()
        torch.Size([20, 16, 51, 33, 15])
    """

    kernel_size: _size_3_t
    stride: _size_3_t
    padding: _size_3_t

    def __init__(self, kernel_size: _size_3_t, stride: Optional[_size_3_t] = None, padding: _size_3_t = 0) -> None:
        super(MaxUnpool3d, self).__init__()
        self.kernel_size = _triple(kernel_size)
        self.stride = _triple(stride if (stride is not None) else kernel_size)
        self.padding = _triple(padding)

    def forward(self, input: Tensor, indices: Tensor, output_size: Optional[List[int]] = None) -> Tensor:
        return F.max_unpool3d(input, indices, self.kernel_size, self.stride,
                              self.padding, output_size)


class _AvgPoolNd(Module):
    __constants__ = ['kernel_size', 'stride', 'padding', 'ceil_mode', 'count_include_pad']

    def extra_repr(self) -> str:
        return 'kernel_size={}, stride={}, padding={}'.format(
            self.kernel_size, self.stride, self.padding
        )


class AvgPool1d(_AvgPoolNd):
    r"""Applies a 1D average pooling over an input signal composed of several
    input planes.

    In the simplest case, the output value of the layer with input size :math:`(N, C, L)`,
    output :math:`(N, C, L_{out})` and :attr:`kernel_size` :math:`k`
    can be precisely described as:

    .. math::

        \text{out}(N_i, C_j, l) = \frac{1}{k} \sum_{m=0}^{k-1}
                               \text{input}(N_i, C_j, \text{stride} \times l + m)

    If :attr:`padding` is non-zero, then the input is implicitly zero-padded on both sides
    for :attr:`padding` number of points.

    Note:
        When ceil_mode=True, sliding windows are allowed to go off-bounds if they start within the left padding
        or the input. Sliding windows that would start in the right padded region are ignored.

    The parameters :attr:`kernel_size`, :attr:`stride`, :attr:`padding` can each be
    an ``int`` or a one-element tuple.

    Args:
        kernel_size: the size of the window
        stride: the stride of the window. Default value is :attr:`kernel_size`
        padding: implicit zero padding to be added on both sides
        ceil_mode: when True, will use `ceil` instead of `floor` to compute the output shape
        count_include_pad: when True, will include the zero-padding in the averaging calculation

    Shape:
        - Input: :math:`(N, C, L_{in})`
        - Output: :math:`(N, C, L_{out})`, where

          .. math::
              L_{out} = \left\lfloor \frac{L_{in} +
              2 \times \text{padding} - \text{kernel\_size}}{\text{stride}} + 1\right\rfloor

    Examples::

        >>> # pool with window of size=3, stride=2
        >>> m = nn.AvgPool1d(3, stride=2)
        >>> m(torch.tensor([[[1.,2,3,4,5,6,7]]]))
        tensor([[[ 2.,  4.,  6.]]])
    """

    kernel_size: _size_1_t
    stride: _size_1_t
    padding: _size_1_t
    ceil_mode: bool
    count_include_pad: bool

    def __init__(self, kernel_size: _size_1_t, stride: _size_1_t = None, padding: _size_1_t = 0, ceil_mode: bool = False,
                 count_include_pad: bool = True) -> None:
        super(AvgPool1d, self).__init__()
        self.kernel_size = _single(kernel_size)
        self.stride = _single(stride if stride is not None else kernel_size)
        self.padding = _single(padding)
        self.ceil_mode = ceil_mode
        self.count_include_pad = count_include_pad

    def forward(self, input: Tensor) -> Tensor:
        return F.avg_pool1d(
            input, self.kernel_size, self.stride, self.padding, self.ceil_mode,
            self.count_include_pad)


class AvgPool2d(_AvgPoolNd):
    r"""Applies a 2D average pooling over an input signal composed of several input
    planes.

    In the simplest case, the output value of the layer with input size :math:`(N, C, H, W)`,
    output :math:`(N, C, H_{out}, W_{out})` and :attr:`kernel_size` :math:`(kH, kW)`
    can be precisely described as:

    .. math::

        out(N_i, C_j, h, w)  = \frac{1}{kH * kW} \sum_{m=0}^{kH-1} \sum_{n=0}^{kW-1}
                               input(N_i, C_j, stride[0] \times h + m, stride[1] \times w + n)

    If :attr:`padding` is non-zero, then the input is implicitly zero-padded on both sides
    for :attr:`padding` number of points.

    Note:
        When ceil_mode=True, sliding windows are allowed to go off-bounds if they start within the left padding
        or the input. Sliding windows that would start in the right padded region are ignored.

    The parameters :attr:`kernel_size`, :attr:`stride`, :attr:`padding` can either be:

        - a single ``int`` -- in which case the same value is used for the height and width dimension
        - a ``tuple`` of two ints -- in which case, the first `int` is used for the height dimension,
          and the second `int` for the width dimension

    Args:
        kernel_size: the size of the window
        stride: the stride of the window. Default value is :attr:`kernel_size`
        padding: implicit zero padding to be added on both sides
        ceil_mode: when True, will use `ceil` instead of `floor` to compute the output shape
        count_include_pad: when True, will include the zero-padding in the averaging calculation
        divisor_override: if specified, it will be used as divisor, otherwise :attr:`kernel_size` will be used

    Shape:
        - Input: :math:`(N, C, H_{in}, W_{in})`
        - Output: :math:`(N, C, H_{out}, W_{out})`, where

          .. math::
              H_{out} = \left\lfloor\frac{H_{in}  + 2 \times \text{padding}[0] -
                \text{kernel\_size}[0]}{\text{stride}[0]} + 1\right\rfloor

          .. math::
              W_{out} = \left\lfloor\frac{W_{in}  + 2 \times \text{padding}[1] -
                \text{kernel\_size}[1]}{\text{stride}[1]} + 1\right\rfloor

    Examples::

        >>> # pool of square window of size=3, stride=2
        >>> m = nn.AvgPool2d(3, stride=2)
        >>> # pool of non-square window
        >>> m = nn.AvgPool2d((3, 2), stride=(2, 1))
        >>> input = torch.randn(20, 16, 50, 32)
        >>> output = m(input)
    """
    __constants__ = ['kernel_size', 'stride', 'padding', 'ceil_mode', 'count_include_pad', 'divisor_override']

    kernel_size: _size_2_t
    stride: _size_2_t
    padding: _size_2_t
    ceil_mode: bool
    count_include_pad: bool

    def __init__(self, kernel_size: _size_2_t, stride: Optional[_size_2_t] = None, padding: _size_2_t = 0,
                 ceil_mode: bool = False, count_include_pad: bool = True, divisor_override: int = None) -> None:
        super(AvgPool2d, self).__init__()
        self.kernel_size = kernel_size
        self.stride = stride if (stride is not None) else kernel_size
        self.padding = padding
        self.ceil_mode = ceil_mode
        self.count_include_pad = count_include_pad
        self.divisor_override = divisor_override

    def forward(self, input: Tensor) -> Tensor:
        return F.avg_pool2d(input, self.kernel_size, self.stride,
                            self.padding, self.ceil_mode, self.count_include_pad, self.divisor_override)


class AvgPool3d(_AvgPoolNd):
    r"""Applies a 3D average pooling over an input signal composed of several input
    planes.

    In the simplest case, the output value of the layer with input size :math:`(N, C, D, H, W)`,
    output :math:`(N, C, D_{out}, H_{out}, W_{out})` and :attr:`kernel_size` :math:`(kD, kH, kW)`
    can be precisely described as:

    .. math::
        \begin{aligned}
            \text{out}(N_i, C_j, d, h, w) ={} & \sum_{k=0}^{kD-1} \sum_{m=0}^{kH-1} \sum_{n=0}^{kW-1} \\
                                              & \frac{\text{input}(N_i, C_j, \text{stride}[0] \times d + k,
                                                      \text{stride}[1] \times h + m, \text{stride}[2] \times w + n)}
                                                     {kD \times kH \times kW}
        \end{aligned}

    If :attr:`padding` is non-zero, then the input is implicitly zero-padded on all three sides
    for :attr:`padding` number of points.

    Note:
        When ceil_mode=True, sliding windows are allowed to go off-bounds if they start within the left padding
        or the input. Sliding windows that would start in the right padded region are ignored.

    The parameters :attr:`kernel_size`, :attr:`stride` can either be:

        - a single ``int`` -- in which case the same value is used for the depth, height and width dimension
        - a ``tuple`` of three ints -- in which case, the first `int` is used for the depth dimension,
          the second `int` for the height dimension and the third `int` for the width dimension

    Args:
        kernel_size: the size of the window
        stride: the stride of the window. Default value is :attr:`kernel_size`
        padding: implicit zero padding to be added on all three sides
        ceil_mode: when True, will use `ceil` instead of `floor` to compute the output shape
        count_include_pad: when True, will include the zero-padding in the averaging calculation
        divisor_override: if specified, it will be used as divisor, otherwise :attr:`kernel_size` will be used

    Shape:
        - Input: :math:`(N, C, D_{in}, H_{in}, W_{in})`
        - Output: :math:`(N, C, D_{out}, H_{out}, W_{out})`, where

          .. math::
              D_{out} = \left\lfloor\frac{D_{in} + 2 \times \text{padding}[0] -
                    \text{kernel\_size}[0]}{\text{stride}[0]} + 1\right\rfloor

          .. math::
              H_{out} = \left\lfloor\frac{H_{in} + 2 \times \text{padding}[1] -
                    \text{kernel\_size}[1]}{\text{stride}[1]} + 1\right\rfloor

          .. math::
              W_{out} = \left\lfloor\frac{W_{in} + 2 \times \text{padding}[2] -
                    \text{kernel\_size}[2]}{\text{stride}[2]} + 1\right\rfloor

    Examples::

        >>> # pool of square window of size=3, stride=2
        >>> m = nn.AvgPool3d(3, stride=2)
        >>> # pool of non-square window
        >>> m = nn.AvgPool3d((3, 2, 2), stride=(2, 1, 2))
        >>> input = torch.randn(20, 16, 50,44, 31)
        >>> output = m(input)
    """
    __constants__ = ['kernel_size', 'stride', 'padding', 'ceil_mode', 'count_include_pad', 'divisor_override']

    kernel_size: _size_3_t
    stride: _size_3_t
    padding: _size_3_t
    ceil_mode: bool
    count_include_pad: bool

    def __init__(self, kernel_size: _size_3_t, stride: Optional[_size_3_t] = None, padding: _size_3_t = 0,
                 ceil_mode: bool = False, count_include_pad: bool = True, divisor_override: int = None) -> None:
        super(AvgPool3d, self).__init__()
        self.kernel_size = kernel_size
        self.stride = stride if (stride is not None) else kernel_size
        self.padding = padding
        self.ceil_mode = ceil_mode
        self.count_include_pad = count_include_pad
        self.divisor_override = divisor_override

    def forward(self, input: Tensor) -> Tensor:
        return F.avg_pool3d(input, self.kernel_size, self.stride,
                            self.padding, self.ceil_mode, self.count_include_pad, self.divisor_override)

    def __setstate__(self, d):
        super(AvgPool3d, self).__setstate__(d)
        self.__dict__.setdefault('padding', 0)
        self.__dict__.setdefault('ceil_mode', False)
        self.__dict__.setdefault('count_include_pad', True)


class FractionalMaxPool2d(Module):
    r"""Applies a 2D fractional max pooling over an input signal composed of several input planes.

    Fractional MaxPooling is described in detail in the paper `Fractional MaxPooling`_ by Ben Graham

    The max-pooling operation is applied in :math:`kH \times kW` regions by a stochastic
    step size determined by the target output size.
    The number of output features is equal to the number of input planes.

    Args:
        kernel_size: the size of the window to take a max over.
                     Can be a single number k (for a square kernel of k x k) or a tuple `(kh, kw)`
        output_size: the target output size of the image of the form `oH x oW`.
                     Can be a tuple `(oH, oW)` or a single number oH for a square image `oH x oH`
        output_ratio: If one wants to have an output size as a ratio of the input size, this option can be given.
                      This has to be a number or tuple in the range (0, 1)
        return_indices: if ``True``, will return the indices along with the outputs.
                        Useful to pass to :meth:`nn.MaxUnpool2d`. Default: ``False``

    Examples:
        >>> # pool of square window of size=3, and target output size 13x12
        >>> m = nn.FractionalMaxPool2d(3, output_size=(13, 12))
        >>> # pool of square window and target output size being half of input image size
        >>> m = nn.FractionalMaxPool2d(3, output_ratio=(0.5, 0.5))
        >>> input = torch.randn(20, 16, 50, 32)
        >>> output = m(input)

    .. _Fractional MaxPooling:
        https://arxiv.org/abs/1412.6071
    """
    __constants__ = ['kernel_size', 'return_indices', 'output_size',
                     'output_ratio']

    kernel_size: _size_2_t
    return_indices: bool
    output_size: _size_2_t
    output_ratio: _ratio_2_t

    def __init__(self, kernel_size: _size_2_t, output_size: Optional[_size_2_t] = None,
                 output_ratio: Optional[_ratio_2_t] = None,
                 return_indices: bool = False, _random_samples=None) -> None:
        super(FractionalMaxPool2d, self).__init__()
        self.kernel_size = _pair(kernel_size)
        self.return_indices = return_indices
        self.register_buffer('_random_samples', _random_samples)
        self.output_size = _pair(output_size) if output_size is not None else None
        self.output_ratio = _pair(output_ratio) if output_ratio is not None else None
        if output_size is None and output_ratio is None:
            raise ValueError("FractionalMaxPool2d requires specifying either "
                             "an output size, or a pooling ratio")
        if output_size is not None and output_ratio is not None:
            raise ValueError("only one of output_size and output_ratio may be specified")
        if self.output_ratio is not None:
            if not (0 < self.output_ratio[0] < 1 and 0 < self.output_ratio[1] < 1):
                raise ValueError("output_ratio must be between 0 and 1 (got {})"
                                 .format(output_ratio))

    def forward(self, input: Tensor) -> Tensor:
        return F.fractional_max_pool2d(
            input, self.kernel_size, self.output_size, self.output_ratio,
            self.return_indices,
            _random_samples=self._random_samples)


class FractionalMaxPool3d(Module):
    r"""Applies a 3D fractional max pooling over an input signal composed of several input planes.

    Fractional MaxPooling is described in detail in the paper `Fractional MaxPooling`_ by Ben Graham

    The max-pooling operation is applied in :math:`kTxkHxkW` regions by a stochastic
    step size determined by the target output size.
    The number of output features is equal to the number of input planes.

    Args:
        kernel_size: the size of the window to take a max over.
                     Can be a single number k (for a square kernel of k x k x k) or a tuple `(kt x kh x kw)`
        output_size: the target output size of the image of the form `oT x oH x oW`.
                     Can be a tuple `(oT, oH, oW)` or a single number oH for a square image `oH x oH x oH`
        output_ratio: If one wants to have an output size as a ratio of the input size, this option can be given.
                      This has to be a number or tuple in the range (0, 1)
        return_indices: if ``True``, will return the indices along with the outputs.
                        Useful to pass to :meth:`nn.MaxUnpool3d`. Default: ``False``

    Examples:
        >>> # pool of cubic window of size=3, and target output size 13x12x11
        >>> m = nn.FractionalMaxPool3d(3, output_size=(13, 12, 11))
        >>> # pool of cubic window and target output size being half of input size
        >>> m = nn.FractionalMaxPool3d(3, output_ratio=(0.5, 0.5, 0.5))
        >>> input = torch.randn(20, 16, 50, 32, 16)
        >>> output = m(input)

    .. _Fractional MaxPooling:
        https://arxiv.org/abs/1412.6071
    """
    __constants__ = ['kernel_size', 'return_indices', 'output_size',
                     'output_ratio']
    kernel_size: _size_3_t
    return_indices: bool
    output_size: _size_3_t
    output_ratio: _ratio_3_t

    def __init__(self, kernel_size: _size_3_t, output_size: Optional[_size_3_t] = None,
                 output_ratio: Optional[_ratio_3_t] = None,
                 return_indices: bool = False, _random_samples=None) -> None:
        super(FractionalMaxPool3d, self).__init__()
        self.kernel_size = _triple(kernel_size)
        self.return_indices = return_indices
        self.register_buffer('_random_samples', _random_samples)
        self.output_size = _triple(output_size) if output_size is not None else None
        self.output_ratio = _triple(output_ratio) if output_ratio is not None else None
        if output_size is None and output_ratio is None:
            raise ValueError("FractionalMaxPool3d requires specifying either "
                             "an output size, or a pooling ratio")
        if output_size is not None and output_ratio is not None:
            raise ValueError("only one of output_size and output_ratio may be specified")
        if self.output_ratio is not None:
            if not (0 < self.output_ratio[0] < 1 and 0 < self.output_ratio[1] < 1 and 0 < self.output_ratio[2] < 1):
                raise ValueError("output_ratio must be between 0 and 1 (got {})"
                                 .format(output_ratio))

    def forward(self, input: Tensor) -> Tensor:
        return F.fractional_max_pool3d(
            input, self.kernel_size, self.output_size, self.output_ratio,
            self.return_indices,
            _random_samples=self._random_samples)


class _LPPoolNd(Module):
    __constants__ = ['norm_type', 'kernel_size', 'stride', 'ceil_mode']

    norm_type: float
    ceil_mode: bool

    def __init__(self, norm_type: float, kernel_size: _size_any_t, stride: Optional[_size_any_t] = None,
                 ceil_mode: bool = False) -> None:
        super(_LPPoolNd, self).__init__()
        self.norm_type = norm_type
        self.kernel_size = kernel_size
        self.stride = stride
        self.ceil_mode = ceil_mode

    def extra_repr(self) -> str:
        return 'norm_type={norm_type}, kernel_size={kernel_size}, stride={stride}, ' \
            'ceil_mode={ceil_mode}'.format(**self.__dict__)


class LPPool1d(_LPPoolNd):
    r"""Applies a 1D power-average pooling over an input signal composed of several input
    planes.

    On each window, the function computed is:

    .. math::
        f(X) = \sqrt[p]{\sum_{x \in X} x^{p}}

    - At p = :math:`\infty`, one gets Max Pooling
    - At p = 1, one gets Sum Pooling (which is proportional to Average Pooling)

    .. note:: If the sum to the power of `p` is zero, the gradient of this function is
              not defined. This implementation will set the gradient to zero in this case.

    Args:
        kernel_size: a single int, the size of the window
        stride: a single int, the stride of the window. Default value is :attr:`kernel_size`
        ceil_mode: when True, will use `ceil` instead of `floor` to compute the output shape

    Shape:
        - Input: :math:`(N, C, L_{in})`
        - Output: :math:`(N, C, L_{out})`, where

          .. math::
              L_{out} = \left\lfloor\frac{L_{in} - \text{kernel\_size}}{\text{stride}} + 1\right\rfloor

    Examples::
        >>> # power-2 pool of window of length 3, with stride 2.
        >>> m = nn.LPPool1d(2, 3, stride=2)
        >>> input = torch.randn(20, 16, 50)
        >>> output = m(input)
    """

    kernel_size: _size_1_t
    stride: _size_1_t

    def forward(self, input: Tensor) -> Tensor:
        return F.lp_pool1d(input, float(self.norm_type), self.kernel_size,
                           self.stride, self.ceil_mode)


class LPPool2d(_LPPoolNd):
    r"""Applies a 2D power-average pooling over an input signal composed of several input
    planes.

    On each window, the function computed is:

    .. math::
        f(X) = \sqrt[p]{\sum_{x \in X} x^{p}}

    - At p = :math:`\infty`, one gets Max Pooling
    - At p = 1, one gets Sum Pooling (which is proportional to average pooling)

    The parameters :attr:`kernel_size`, :attr:`stride` can either be:

        - a single ``int`` -- in which case the same value is used for the height and width dimension
        - a ``tuple`` of two ints -- in which case, the first `int` is used for the height dimension,
          and the second `int` for the width dimension

    .. note:: If the sum to the power of `p` is zero, the gradient of this function is
              not defined. This implementation will set the gradient to zero in this case.

    Args:
        kernel_size: the size of the window
        stride: the stride of the window. Default value is :attr:`kernel_size`
        ceil_mode: when True, will use `ceil` instead of `floor` to compute the output shape

    Shape:
        - Input: :math:`(N, C, H_{in}, W_{in})`
        - Output: :math:`(N, C, H_{out}, W_{out})`, where

          .. math::
              H_{out} = \left\lfloor\frac{H_{in} - \text{kernel\_size}[0]}{\text{stride}[0]} + 1\right\rfloor

          .. math::
              W_{out} = \left\lfloor\frac{W_{in} - \text{kernel\_size}[1]}{\text{stride}[1]} + 1\right\rfloor

    Examples::

        >>> # power-2 pool of square window of size=3, stride=2
        >>> m = nn.LPPool2d(2, 3, stride=2)
        >>> # pool of non-square window of power 1.2
        >>> m = nn.LPPool2d(1.2, (3, 2), stride=(2, 1))
        >>> input = torch.randn(20, 16, 50, 32)
        >>> output = m(input)

    """

    kernel_size: _size_2_t
    stride: _size_2_t

    def forward(self, input: Tensor) -> Tensor:
        return F.lp_pool2d(input, float(self.norm_type), self.kernel_size,
                           self.stride, self.ceil_mode)


class _AdaptiveMaxPoolNd(Module):
    __constants__ = ['output_size', 'return_indices']
    return_indices: bool

    def __init__(self, output_size: _size_any_t, return_indices: bool = False) -> None:
        super(_AdaptiveMaxPoolNd, self).__init__()
        self.output_size = output_size
        self.return_indices = return_indices

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

# FIXME (by @ssnl): Improve adaptive pooling docs: specify what the input and
#   output shapes are, and how the operation computes output.


class AdaptiveMaxPool1d(_AdaptiveMaxPoolNd):
    r"""Applies a 1D adaptive max pooling over an input signal composed of several input planes.

    The output size is H, for any input size.
    The number of output features is equal to the number of input planes.

    Args:
        output_size: the target output size H
        return_indices: if ``True``, will return the indices along with the outputs.
                        Useful to pass to nn.MaxUnpool1d. Default: ``False``

    Examples:
        >>> # target output size of 5
        >>> m = nn.AdaptiveMaxPool1d(5)
        >>> input = torch.randn(1, 64, 8)
        >>> output = m(input)

    """

    output_size: _size_1_t

    def forward(self, input: Tensor) -> Tensor:
        return F.adaptive_max_pool1d(input, self.output_size, self.return_indices)


class AdaptiveMaxPool2d(_AdaptiveMaxPoolNd):
    r"""Applies a 2D adaptive max pooling over an input signal composed of several input planes.

    The output is of size H x W, for any input size.
    The number of output features is equal to the number of input planes.

    Args:
        output_size: the target output size of the image of the form H x W.
                     Can be a tuple (H, W) or a single H for a square image H x H.
                     H and W can be either a ``int``, or ``None`` which means the size will
                     be the same as that of the input.
        return_indices: if ``True``, will return the indices along with the outputs.
                        Useful to pass to nn.MaxUnpool2d. Default: ``False``

    Examples:
        >>> # target output size of 5x7
        >>> m = nn.AdaptiveMaxPool2d((5,7))
        >>> input = torch.randn(1, 64, 8, 9)
        >>> output = m(input)
        >>> # target output size of 7x7 (square)
        >>> m = nn.AdaptiveMaxPool2d(7)
        >>> input = torch.randn(1, 64, 10, 9)
        >>> output = m(input)
        >>> # target output size of 10x7
        >>> m = nn.AdaptiveMaxPool2d((None, 7))
        >>> input = torch.randn(1, 64, 10, 9)
        >>> output = m(input)

    """

    output_size: _size_2_t

    def forward(self, input: Tensor) -> Tensor:
        return F.adaptive_max_pool2d(input, self.output_size, self.return_indices)


class AdaptiveMaxPool3d(_AdaptiveMaxPoolNd):
    r"""Applies a 3D adaptive max pooling over an input signal composed of several input planes.

    The output is of size D x H x W, for any input size.
    The number of output features is equal to the number of input planes.

    Args:
        output_size: the target output size of the image of the form D x H x W.
                     Can be a tuple (D, H, W) or a single D for a cube D x D x D.
                     D, H and W can be either a ``int``, or ``None`` which means the size will
                     be the same as that of the input.

        return_indices: if ``True``, will return the indices along with the outputs.
                        Useful to pass to nn.MaxUnpool3d. Default: ``False``

    Examples:
        >>> # target output size of 5x7x9
        >>> m = nn.AdaptiveMaxPool3d((5,7,9))
        >>> input = torch.randn(1, 64, 8, 9, 10)
        >>> output = m(input)
        >>> # target output size of 7x7x7 (cube)
        >>> m = nn.AdaptiveMaxPool3d(7)
        >>> input = torch.randn(1, 64, 10, 9, 8)
        >>> output = m(input)
        >>> # target output size of 7x9x8
        >>> m = nn.AdaptiveMaxPool3d((7, None, None))
        >>> input = torch.randn(1, 64, 10, 9, 8)
        >>> output = m(input)

    """

    output_size: _size_3_t

    def forward(self, input: Tensor) -> Tensor:
        return F.adaptive_max_pool3d(input, self.output_size, self.return_indices)


class _AdaptiveAvgPoolNd(Module):
    __constants__ = ['output_size']

    def __init__(self, output_size: _size_any_t) -> None:
        super(_AdaptiveAvgPoolNd, self).__init__()
        self.output_size = output_size

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


class AdaptiveAvgPool1d(_AdaptiveAvgPoolNd):
    r"""Applies a 1D adaptive average pooling over an input signal composed of several input planes.

    The output size is H, for any input size.
    The number of output features is equal to the number of input planes.

    Args:
        output_size: the target output size H

    Examples:
        >>> # target output size of 5
        >>> m = nn.AdaptiveAvgPool1d(5)
        >>> input = torch.randn(1, 64, 8)
        >>> output = m(input)

    """

    output_size: _size_1_t

    def forward(self, input: Tensor) -> Tensor:
        return F.adaptive_avg_pool1d(input, self.output_size)


class AdaptiveAvgPool2d(_AdaptiveAvgPoolNd):
    r"""Applies a 2D adaptive average pooling over an input signal composed of several input planes.

    The output is of size H x W, for any input size.
    The number of output features is equal to the number of input planes.

    Args:
        output_size: the target output size of the image of the form H x W.
                     Can be a tuple (H, W) or a single H for a square image H x H.
                     H and W can be either a ``int``, or ``None`` which means the size will
                     be the same as that of the input.

    Examples:
        >>> # target output size of 5x7
        >>> m = nn.AdaptiveAvgPool2d((5,7))
        >>> input = torch.randn(1, 64, 8, 9)
        >>> output = m(input)
        >>> # target output size of 7x7 (square)
        >>> m = nn.AdaptiveAvgPool2d(7)
        >>> input = torch.randn(1, 64, 10, 9)
        >>> output = m(input)
        >>> # target output size of 10x7
        >>> m = nn.AdaptiveAvgPool2d((None, 7))
        >>> input = torch.randn(1, 64, 10, 9)
        >>> output = m(input)

    """

    output_size: _size_2_t

    def forward(self, input: Tensor) -> Tensor:
        return F.adaptive_avg_pool2d(input, self.output_size)


class AdaptiveAvgPool3d(_AdaptiveAvgPoolNd):
    r"""Applies a 3D adaptive average pooling over an input signal composed of several input planes.

    The output is of size D x H x W, for any input size.
    The number of output features is equal to the number of input planes.

    Args:
        output_size: the target output size of the form D x H x W.
                     Can be a tuple (D, H, W) or a single number D for a cube D x D x D.
                     D, H and W can be either a ``int``, or ``None`` which means the size will
                     be the same as that of the input.

    Examples:
        >>> # target output size of 5x7x9
        >>> m = nn.AdaptiveAvgPool3d((5,7,9))
        >>> input = torch.randn(1, 64, 8, 9, 10)
        >>> output = m(input)
        >>> # target output size of 7x7x7 (cube)
        >>> m = nn.AdaptiveAvgPool3d(7)
        >>> input = torch.randn(1, 64, 10, 9, 8)
        >>> output = m(input)
        >>> # target output size of 7x9x8
        >>> m = nn.AdaptiveAvgPool3d((7, None, None))
        >>> input = torch.randn(1, 64, 10, 9, 8)
        >>> output = m(input)

    """

    output_size: _size_3_t

    def forward(self, input: Tensor) -> Tensor:
        return F.adaptive_avg_pool3d(input, self.output_size)