import math
import torch
from torch.nn.parameter import Parameter
from .. import functional as F
from .module import Module
from .utils import _single, _pair, _triple


class _ConvNd(Module):

    def __init__(self, in_channels, out_channels, kernel_size, stride,
                 padding, dilation, transposed, output_padding, groups, bias):
        super(_ConvNd, self).__init__()
        if in_channels % groups != 0:
            raise ValueError('in_channels must be divisible by groups')
        if out_channels % groups != 0:
            raise ValueError('out_channels must be divisible by groups')
        self.in_channels = in_channels
        self.out_channels = out_channels
        self.kernel_size = kernel_size
        self.stride = stride
        self.padding = padding
        self.dilation = dilation
        self.transposed = transposed
        self.output_padding = output_padding
        self.groups = groups
        if transposed:
            self.weight = Parameter(torch.Tensor(
                in_channels, out_channels // groups, *kernel_size))
        else:
            self.weight = Parameter(torch.Tensor(
                out_channels, in_channels // groups, *kernel_size))
        if bias:
            self.bias = Parameter(torch.Tensor(out_channels))
        else:
            self.register_parameter('bias', None)
        self.reset_parameters()

    def reset_parameters(self):
        n = self.in_channels
        for k in self.kernel_size:
            n *= k
        stdv = 1. / math.sqrt(n)
        self.weight.data.uniform_(-stdv, stdv)
        if self.bias is not None:
            self.bias.data.uniform_(-stdv, stdv)

    def __repr__(self):
        s = ('{name}({in_channels}, {out_channels}, kernel_size={kernel_size}'
             ', stride={stride}')
        if self.padding != (0,) * len(self.padding):
            s += ', padding={padding}'
        if self.dilation != (1,) * len(self.dilation):
            s += ', dilation={dilation}'
        if self.output_padding != (0,) * len(self.output_padding):
            s += ', output_padding={output_padding}'
        if self.groups != 1:
            s += ', groups={groups}'
        if self.bias is None:
            s += ', bias=False'
        s += ')'
        return s.format(name=self.__class__.__name__, **self.__dict__)


class Conv1d(_ConvNd):
    r"""Applies a 1D convolution 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_{in}, L)`
    and output :math:`(N, C_{out}, L_{out})` can be precisely described as:

    .. math::

        \begin{array}{ll}
        out(N_i, C_{out_j})  = bias(C_{out_j})
                       + \sum_{{k}=0}^{C_{in}-1} weight(C_{out_j}, k)  \star input(N_i, k)
        \end{array}

    where :math:`\star` is the valid `cross-correlation`_ operator

    | :attr:`stride` controls the stride for the cross-correlation.
    | 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.
    | :attr:`groups` controls the connections between inputs and outputs.
    |       At groups=1, all inputs are convolved to all outputs.
    |       At groups=2, the operation becomes equivalent to having two conv layers
                 side by side, each seeing half the input channels,
                 and producing half the output channels, and both subsequently concatenated.

    .. note::

         Depending of the size of your kernel, several (of the last)
         columns of the input might be lost, because it is a valid `cross-correlation`_,
         and not a full `cross-correlation`_.
         It is up to the user to add proper padding.

    Args:
        in_channels (int): Number of channels in the input image
        out_channels (int): Number of channels produced by the convolution
        kernel_size (int or tuple): Size of the convolving kernel
        stride (int or tuple, optional): Stride of the convolution
        padding (int or tuple, optional): Zero-padding added to both sides of the input
        dilation (int or tuple, optional): Spacing between kernel elements
        groups (int, optional): Number of blocked connections from input channels to output channels
        bias (bool, optional): If True, adds a learnable bias to the output

    Shape:
        - Input: :math:`(N, C_{in}, L_{in})`
        - Output: :math:`(N, C_{out}, L_{out})` where
          :math:`L_{out} = floor((L_{in}  + 2 * padding - dilation * (kernel\_size - 1) - 1) / stride + 1)`

    Attributes:
        weight (Tensor): the learnable weights of the module of shape (out_channels, in_channels, kernel_size)
        bias (Tensor):   the learnable bias of the module of shape (out_channels)

    Examples::

        >>> m = nn.Conv1d(16, 33, 3, stride=2)
        >>> input = autograd.Variable(torch.randn(20, 16, 50))
        >>> output = m(input)

    .. _cross-correlation:
        https://en.wikipedia.org/wiki/Cross-correlation

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

    def __init__(self, in_channels, out_channels, kernel_size, stride=1,
                 padding=0, dilation=1, groups=1, bias=True):
        kernel_size = _single(kernel_size)
        stride = _single(stride)
        padding = _single(padding)
        dilation = _single(dilation)
        super(Conv1d, self).__init__(
            in_channels, out_channels, kernel_size, stride, padding, dilation,
            False, _single(0), groups, bias)

    def forward(self, input):
        return F.conv1d(input, self.weight, self.bias, self.stride,
                        self.padding, self.dilation, self.groups)


class Conv2d(_ConvNd):
    r"""Applies a 2D convolution 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_{in}, H, W)`
    and output :math:`(N, C_{out}, H_{out}, W_{out})` can be precisely described as:

    .. math::

        \begin{array}{ll}
        out(N_i, C_{out_j})  = bias(C_{out_j})
                       + \sum_{{k}=0}^{C_{in}-1} weight(C_{out_j}, k)  \star input(N_i, k)
        \end{array}

    where :math:`\star` is the valid 2D `cross-correlation`_ operator

    | :attr:`stride` controls the stride for the cross-correlation.
    | 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.
    | :attr:`groups` controls the connections between inputs and outputs.
    |       At groups=1, all inputs are convolved to all outputs.
    |       At groups=2, the operation becomes equivalent to having two conv layers
                 side by side, each seeing half the input channels,
                 and producing half the output channels, and both subsequently concatenated.

    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

    .. note::

         Depending of the size of your kernel, several (of the last)
         columns of the input might be lost, because it is a valid `cross-correlation`_,
         and not a full `cross-correlation`_.
         It is up to the user to add proper padding.

    Args:
        in_channels (int): Number of channels in the input image
        out_channels (int): Number of channels produced by the convolution
        kernel_size (int or tuple): Size of the convolving kernel
        stride (int or tuple, optional): Stride of the convolution
        padding (int or tuple, optional): Zero-padding added to both sides of the input
        dilation (int or tuple, optional): Spacing between kernel elements
        groups (int, optional): Number of blocked connections from input channels to output channels
        bias (bool, optional): If True, adds a learnable bias to the output

    Shape:
        - Input: :math:`(N, C_{in}, H_{in}, W_{in})`
        - Output: :math:`(N, C_{out}, H_{out}, W_{out})` where
          :math:`H_{out} = floor((H_{in}  + 2 * padding[0] - dilation[0] * (kernel\_size[0] - 1) - 1) / stride[0] + 1)`
          :math:`W_{out} = floor((W_{in}  + 2 * padding[1] - dilation[1] * (kernel\_size[1] - 1) - 1) / stride[1] + 1)`

    Attributes:
        weight (Tensor): the learnable weights of the module of shape
                         (out_channels, in_channels, kernel_size[0], kernel_size[1])
        bias (Tensor):   the learnable bias of the module of shape (out_channels)

    Examples::

        >>> # With square kernels and equal stride
        >>> m = nn.Conv2d(16, 33, 3, stride=2)
        >>> # non-square kernels and unequal stride and with padding
        >>> m = nn.Conv2d(16, 33, (3, 5), stride=(2, 1), padding=(4, 2))
        >>> # non-square kernels and unequal stride and with padding and dilation
        >>> m = nn.Conv2d(16, 33, (3, 5), stride=(2, 1), padding=(4, 2), dilation=(3, 1))
        >>> input = autograd.Variable(torch.randn(20, 16, 50, 100))
        >>> output = m(input)

    .. _cross-correlation:
        https://en.wikipedia.org/wiki/Cross-correlation

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

    def __init__(self, in_channels, out_channels, kernel_size, stride=1,
                 padding=0, dilation=1, groups=1, bias=True):
        kernel_size = _pair(kernel_size)
        stride = _pair(stride)
        padding = _pair(padding)
        dilation = _pair(dilation)
        super(Conv2d, self).__init__(
            in_channels, out_channels, kernel_size, stride, padding, dilation,
            False, _pair(0), groups, bias)

    def forward(self, input):
        return F.conv2d(input, self.weight, self.bias, self.stride,
                        self.padding, self.dilation, self.groups)


class Conv3d(_ConvNd):
    r"""Applies a 3D convolution 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_{in}, D, H, W)`
    and output :math:`(N, C_{out}, D_{out}, H_{out}, W_{out})` can be precisely described as:

    .. math::

        \begin{array}{ll}
        out(N_i, C_{out_j})  = bias(C_{out_j})
                       + \sum_{{k}=0}^{C_{in}-1} weight(C_{out_j}, k)  \star input(N_i, k)
        \end{array}

    where :math:`\star` is the valid 3D `cross-correlation`_ operator

    | :attr:`stride` controls the stride for the cross-correlation.
    | 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.
    | :attr:`groups` controls the connections between inputs and outputs.
    |       At groups=1, all inputs are convolved to all outputs.
    |       At groups=2, the operation becomes equivalent to having two conv layers
                 side by side, each seeing half the input channels,
                 and producing half the output channels, and both subsequently concatenated.

    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 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

    .. note::

         Depending of the size of your kernel, several (of the last)
         columns of the input might be lost, because it is a valid `cross-correlation`_,
         and not a full `cross-correlation`_.
         It is up to the user to add proper padding.

    Args:
        in_channels (int): Number of channels in the input image
        out_channels (int): Number of channels produced by the convolution
        kernel_size (int or tuple): Size of the convolving kernel
        stride (int or tuple, optional): Stride of the convolution
        padding (int or tuple, optional): Zero-padding added to both sides of the input
        dilation (int or tuple, optional): Spacing between kernel elements
        groups (int, optional): Number of blocked connections from input channels to output channels
        bias (bool, optional): If True, adds a learnable bias to the output

    Shape:
        - Input: :math:`(N, C_{in}, D_{in}, H_{in}, W_{in})`
        - Output: :math:`(N, C_{out}, D_{out}, H_{out}, W_{out})` where
          :math:`D_{out} = floor((D_{in}  + 2 * padding[0] - dilation[0] * (kernel\_size[0] - 1) - 1) / stride[0] + 1)`
          :math:`H_{out} = floor((H_{in}  + 2 * padding[1] - dilation[1] * (kernel\_size[1] - 1) - 1) / stride[1] + 1)`
          :math:`W_{out} = floor((W_{in}  + 2 * padding[2] - dilation[2] * (kernel\_size[2] - 1) - 1) / stride[2] + 1)`

    Attributes:
        weight (Tensor): the learnable weights of the module of shape
                         (out_channels, in_channels, kernel_size[0], kernel_size[1], kernel_size[2])
        bias (Tensor):   the learnable bias of the module of shape (out_channels)

    Examples::

        >>> # With square kernels and equal stride
        >>> m = nn.Conv3d(16, 33, 3, stride=2)
        >>> # non-square kernels and unequal stride and with padding
        >>> m = nn.Conv3d(16, 33, (3, 5, 2), stride=(2, 1, 1), padding=(4, 2, 0))
        >>> input = autograd.Variable(torch.randn(20, 16, 10, 50, 100))
        >>> output = m(input)

    .. _cross-correlation:
        https://en.wikipedia.org/wiki/Cross-correlation

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

    def __init__(self, in_channels, out_channels, kernel_size, stride=1,
                 padding=0, dilation=1, groups=1, bias=True):
        kernel_size = _triple(kernel_size)
        stride = _triple(stride)
        padding = _triple(padding)
        dilation = _triple(dilation)
        super(Conv3d, self).__init__(
            in_channels, out_channels, kernel_size, stride, padding, dilation,
            False, _triple(0), groups, bias)

    def forward(self, input):
        return F.conv3d(input, self.weight, self.bias, self.stride,
                        self.padding, self.dilation, self.groups)


class _ConvTransposeMixin(object):

    def forward(self, input, output_size=None):
        output_padding = self._output_padding(input, output_size)
        func = self._backend.ConvNd(
            self.stride, self.padding, self.dilation, self.transposed,
            output_padding, self.groups)
        if self.bias is None:
            return func(input, self.weight)
        else:
            return func(input, self.weight, self.bias)

    def _output_padding(self, input, output_size):
        if output_size is None:
            return self.output_padding

        output_size = list(output_size)
        k = input.dim() - 2
        if len(output_size) == k + 2:
            output_size = output_size[-2:]
        if len(output_size) != k:
            raise ValueError(
                "output_size must have {} or {} elements (got {})"
                .format(k, k + 2, len(output_size)))

        def dim_size(d):
            return ((input.size(d + 2) - 1) * self.stride[d] -
                    2 * self.padding[d] + self.kernel_size[d])

        min_sizes = [dim_size(d) for d in range(k)]
        max_sizes = [min_sizes[d] + self.stride[d] - 1 for d in range(k)]
        for size, min_size, max_size in zip(output_size, min_sizes, max_sizes):
            if size < min_size or size > max_size:
                raise ValueError((
                    "requested an output size of {}, but valid sizes range "
                    "from {} to {} (for an input of {})").format(
                        output_size, min_sizes, max_sizes, input.size()[2:]))

        return tuple([output_size[d] - min_sizes[d] for d in range(k)])


class ConvTranspose1d(_ConvTransposeMixin, _ConvNd):
    """Applies a 1D transposed convolution operator over an input image
    composed of several input planes.

    This module can be seen as the gradient of Conv1d with respect to its input.
    It is sometimes (but incorrectly) refered to as a deconvolutional operation.

    .. note::

         Depending of the size of your kernel, several (of the last)
         columns of the input might be lost, because it is a valid `cross-correlation`_,
         and not a full `cross-correlation`_.
         It is up to the user to add proper padding.

    Args:
        in_channels (int): Number of channels in the input image
        out_channels (int): Number of channels produced by the convolution
        kernel_size (int or tuple): Size of the convolving kernel
        stride (int or tuple, optional): Stride of the convolution
        padding (int or tuple, optional): Zero-padding added to both sides of the input
        output_padding (int or tuple, optional): Zero-padding added to one side of the output
        groups (int, optional): Number of blocked connections from input channels to output channels
        bias (bool, optional): If True, adds a learnable bias to the output

    Shape:
        - Input: :math:`(N, C_{in}, L_{in})`
        - Output: :math:`(N, C_{out}, L_{out})` where
          :math:`L_{out} = (L_{in} - 1) * stride - 2 * padding + kernel\_size + output\_padding`

    Attributes:
        weight (Tensor): the learnable weights of the module of shape
                         (in_channels, out_channels, kernel_size[0], kernel_size[1])
        bias (Tensor):   the learnable bias of the module of shape (out_channels)
    """

    def __init__(self, in_channels, out_channels, kernel_size, stride=1,
                 padding=0, output_padding=0, groups=1, bias=True, dilation=1):
        kernel_size = _single(kernel_size)
        stride = _single(stride)
        padding = _single(padding)
        dilation = _single(dilation)
        output_padding = _single(output_padding)
        super(ConvTranspose1d, self).__init__(
            in_channels, out_channels, kernel_size, stride, padding, dilation,
            True, output_padding, groups, bias)

    def forward(self, input, output_size=None):
        output_padding = self._output_padding(input, output_size)
        return F.conv_transpose1d(
            input, self.weight, self.bias, self.stride, self.padding,
            output_padding, self.groups, self.dilation)


class ConvTranspose2d(_ConvTransposeMixin, _ConvNd):
    r"""Applies a 2D transposed convolution operator over an input image
    composed of several input planes.

    This module can be seen as the gradient of Conv2d with respect to its input.
    It is sometimes (but incorrectly) refered to as a deconvolutional operation.

    | :attr:`stride` controls the stride for the cross-correlation.
    | If :attr:`padding` is non-zero, then the input is implicitly zero-padded on both sides
      for :attr:`padding` number of points
    | If :attr:`output_padding` is non-zero, then the output is implicitly zero-padded on one side
      for :attr:`output_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.
    | :attr:`groups` controls the connections between inputs and outputs.
    |       At groups=1, all inputs are convolved to all outputs.
    |       At groups=2, the operation becomes equivalent to having two conv layers
                 side by side, each seeing half the input channels,
                 and producing half the output channels, and both subsequently concatenated.

    The parameters :attr:`kernel_size`, :attr:`stride`, :attr:`padding`, :attr:`output_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

    .. note::

         Depending of the size of your kernel, several (of the last)
         columns of the input might be lost, because it is a valid `cross-correlation`_,
         and not a full `cross-correlation`_.
         It is up to the user to add proper padding.

    Args:
        in_channels (int): Number of channels in the input image
        out_channels (int): Number of channels produced by the convolution
        kernel_size (int or tuple): Size of the convolving kernel
        stride (int or tuple, optional): Stride of the convolution
        padding (int or tuple, optional): Zero-padding added to both sides of the input
        output_padding (int or tuple, optional): Zero-padding added to one side of the output
        groups (int, optional): Number of blocked connections from input channels to output channels
        bias (bool, optional): If True, adds a learnable bias to the output
        dilation (int or tuple, optional): Spacing between kernel elements

    Shape:
        - Input: :math:`(N, C_{in}, H_{in}, W_{in})`
        - Output: :math:`(N, C_{out}, H_{out}, W_{out})` where
          :math:`H_{out} = (H_{in} - 1) * stride[0] - 2 * padding[0] + kernel\_size[0] + output\_padding[0]`
          :math:`W_{out} = (W_{in} - 1) * stride[1] - 2 * padding[1] + kernel\_size[1] + output\_padding[1]`

    Attributes:
        weight (Tensor): the learnable weights of the module of shape
                         (in_channels, out_channels, kernel_size[0], kernel_size[1])
        bias (Tensor):   the learnable bias of the module of shape (out_channels)

    Examples::

        >>> # With square kernels and equal stride
        >>> m = nn.ConvTranspose2d(16, 33, 3, stride=2)
        >>> # non-square kernels and unequal stride and with padding
        >>> m = nn.ConvTranspose2d(16, 33, (3, 5), stride=(2, 1), padding=(4, 2))
        >>> input = autograd.Variable(torch.randn(20, 16, 50, 100))
        >>> output = m(input)
        >>> # exact output size can be also specified as an argument
        >>> input = autograd.Variable(torch.randn(1, 16, 12, 12))
        >>> downsample = nn.Conv2d(16, 16, 3, stride=2, padding=1)
        >>> upsample = nn.ConvTranspose2d(16, 16, 3, stride=2, padding=1)
        >>> h = downsample(input)
        >>> h.size()
        torch.Size([1, 16, 6, 6])
        >>> output = upsample(h, output_size=input.size())
        >>> output.size()
        torch.Size([1, 16, 12, 12])

    .. _cross-correlation:
        https://en.wikipedia.org/wiki/Cross-correlation

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

    def __init__(self, in_channels, out_channels, kernel_size, stride=1,
                 padding=0, output_padding=0, groups=1, bias=True, dilation=1):
        kernel_size = _pair(kernel_size)
        stride = _pair(stride)
        padding = _pair(padding)
        dilation = _pair(dilation)
        output_padding = _pair(output_padding)
        super(ConvTranspose2d, self).__init__(
            in_channels, out_channels, kernel_size, stride, padding, dilation,
            True, output_padding, groups, bias)

    def forward(self, input, output_size=None):
        output_padding = self._output_padding(input, output_size)
        return F.conv_transpose2d(
            input, self.weight, self.bias, self.stride, self.padding,
            output_padding, self.groups, self.dilation)


class ConvTranspose3d(_ConvTransposeMixin, _ConvNd):
    r"""Applies a 3D transposed convolution operator over an input image composed of several input
    planes.
    The transposed convolution operator multiplies each input value element-wise by a learnable kernel,
    and sums over the outputs from all input feature planes.

    **This module can be seen as the exact reverse of Conv3d**.
    It is sometimes (but incorrectly) refered to as a deconvolutional operation.

    | :attr:`stride` controls the stride for the cross-correlation.
    | If :attr:`padding` is non-zero, then the input is implicitly zero-padded on both sides
      for :attr:`padding` number of points
    | If :attr:`output_padding` is non-zero, then the output is implicitly zero-padded on one side
      for :attr:`output_padding` number of points
    | :attr:`groups` controls the connections between inputs and outputs.
    |       At groups=1, all inputs are convolved to all outputs.
    |       At groups=2, the operation becomes equivalent to having two conv layers
                 side by side, each seeing half the input channels,
                 and producing half the output channels, and both subsequently concatenated.

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

        - a single ``int`` -- in which case the same value is used for the 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 width dimension and the third `int` for the width dimension

    .. note::

         Depending of the size of your kernel, several (of the last)
         columns of the input might be lost, because it is a valid `cross-correlation`_,
         and not a full `cross-correlation`_.
         It is up to the user to add proper padding.

    Args:
        in_channels (int): Number of channels in the input image
        out_channels (int): Number of channels produced by the convolution
        kernel_size (int or tuple): Size of the convolving kernel
        stride (int or tuple, optional): Stride of the convolution
        padding (int or tuple, optional): Zero-padding added to both sides of the input
        output_padding (int or tuple, optional): Zero-padding added to one side of the output
        groups (int, optional): Number of blocked connections from input channels to output channels
        bias (bool, optional): If True, adds a learnable bias to the output
        dilation (int or tuple, optional): Spacing between kernel elements

    Shape:
        - Input: :math:`(N, C_{in}, D_{in}, H_{in}, W_{in})`
        - Output: :math:`(N, C_{out}, D_{out}, H_{out}, W_{out})` where
          :math:`D_{out} = (D_{in} - 1) * stride[0] - 2 * padding[0] + kernel\_size[0] + output\_padding[0]`
          :math:`H_{out} = (H_{in} - 1) * stride[1] - 2 * padding[1] + kernel\_size[1] + output\_padding[1]`
          :math:`W_{out} = (W_{in} - 1) * stride[2] - 2 * padding[2] + kernel\_size[2] + output\_padding[2]`

    Attributes:
        weight (Tensor): the learnable weights of the module of shape
                         (in_channels, out_channels, kernel_size[0], kernel_size[1], kernel_size[2])
        bias (Tensor):   the learnable bias of the module of shape (out_channels)

    Examples::

        >>> # With square kernels and equal stride
        >>> m = nn.ConvTranspose3d(16, 33, 3, stride=2)
        >>> # non-square kernels and unequal stride and with padding
        >>> m = nn.Conv3d(16, 33, (3, 5, 2), stride=(2, 1, 1), padding=(0, 4, 2))
        >>> input = autograd.Variable(torch.randn(20, 16, 10, 50, 100))
        >>> output = m(input)

    .. _cross-correlation:
        https://en.wikipedia.org/wiki/Cross-correlation

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

    def __init__(self, in_channels, out_channels, kernel_size, stride=1,
                 padding=0, output_padding=0, groups=1, bias=True, dilation=1):
        kernel_size = _triple(kernel_size)
        stride = _triple(stride)
        padding = _triple(padding)
        dilation = _triple(dilation)
        output_padding = _triple(output_padding)
        super(ConvTranspose3d, self).__init__(
            in_channels, out_channels, kernel_size, stride, padding, dilation,
            True, output_padding, groups, bias)

    def forward(self, input, output_size=None):
        output_padding = self._output_padding(input, output_size)
        return F.conv_transpose3d(
            input, self.weight, self.bias, self.stride, self.padding,
            output_padding, self.groups, self.dilation)


# TODO: Conv2dLocal
# TODO: Conv2dMap
# TODO: ConvTranspose2dMap
