# coding=utf-8 from .module import Module from .. import functional as F class Fold(Module): r"""Combines an array of sliding local blocks into a large containing tensor. Consider a batched :attr:`input` tensor containing sliding local blocks, e.g., patches of images, of shape :math:`(N, C \times \prod(\text{kernel\_size}), L)`, where :math:`N` is batch dimension, :math:`C \times \prod(\text{kernel\_size})` is the number of values with in a block (a block has :math:`\prod(\text{kernel\_size})` spatial locations each containing a :math:`C`-channeled vector), and :math:`L` is the total number of blocks. (This is exacly the same specification as the output shape of :class:`~torch.nn.Unfold`.) This operation combines these local blocks into the large :attr:`output` tensor of shape :math:`(N, C, \text{output\_size}[0], \text{output\_size}[1], \dots)` by summing the overlapping values. Similar to :class:`~torch.nn.Unfold`, the arguments must satisfy .. math:: L = \prod_d \left\lfloor\frac{\text{output\_size}[d] + 2 \times \text{padding}[d] % - \text{dilation}[d] \times (\text{kernel\_size}[d] - 1) - 1}{\text{stride}[d]} + 1\right\rfloor, where :math:`d` is over all spatial dimensions. * :attr:`output_size` describes the spatial shape of the large containing tensor of the sliding local blocks. It is useful to resolve the ambiguity when multiple input shapes map to same number of sliding blocks, e.g., with ``stride > 0``. The :attr:`padding`, :attr:`stride` and :attr:`dilation` arguments specify how the sliding blocks are retrieved. * :attr:`stride` controls the stride for the sliding blocks. * :attr:`padding` controls the amount of implicit zero-paddings on both sides for :attr:`padding` number of points for each dimension before reshaping. * :attr:`dilation` controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this `link`_ has a nice visualization of what :attr:`dilation` does. Args: output_size (int or tuple): the shape of the spatial dimensions of the output (i.e., ``input.sizes()[2:]``) kernel_size (int or tuple): the size of the sliding blocks stride (int or tuple): the stride of the sliding blocks in the input spatial dimensions. Default: 1 padding (int or tuple, optional): implicit zero padding to be added on both sides of input. Default: 0 dilation (int or tuple, optional): a parameter that controls the stride of elements within the neighborhood. Default: 1 * If :attr:`output_size`, :attr:`kernel_size`, :attr:`dilation`, :attr:`padding` or :attr:`stride` is an int or a tuple of length 1 then their values will be replicated across all spatial dimensions. * For the case of two output spatial dimensions this operation is sometimes called ``col2im``. .. note:: :class:`~torch.nn.Fold` calculates each combined value in the resulting large tensor by summing all values from all containing blocks. :class:`~torch.nn.Unfold` extracts the values in the local blocks by copying from the large tensor. So, if the blocks overlap, they are not inverses of each other. .. warning:: Currently, only 4-D output tensors (batched image-like tensors) are supported. Shape: - Input: :math:`(N, C \times \prod(\text{kernel\_size}), L)` - Output: :math:`(N, C, \text{output\_size}[0], \text{output\_size}[1], \dots)` as described above Examples:: >>> fold = nn.Fold(output_size=(4, 5), kernel_size=(2, 2)) >>> input = torch.randn(1, 3 * 2 * 2, 1) >>> output = fold(input) >>> output.size() .. _link: https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md """ def __init__(self, output_size, kernel_size, dilation=1, padding=0, stride=1): super(Fold, self).__init__() self.output_size = output_size self.kernel_size = kernel_size self.dilation = dilation self.padding = padding self.stride = stride def forward(self, input): return F.fold(input, self.output_size, self.kernel_size, self.dilation, self.padding, self.stride) def extra_repr(self): return 'output_size={output_size}, kernel_size={kernel_size}, ' \ 'dilation={dilation}, padding={padding}, stride={stride}'.format( **self.__dict__ ) class Unfold(Module): r"""Extracts sliding local blocks from a batched input tensor. Consider an batched :attr:`input` tensor of shape :math:`(N, C, *)`, where :math:`N` is the batch dimension, :math:`C` is the channel dimension, and :math:`*` represent arbitrary spatial dimensions. This operation flattens each sliding :attr:`kernel_size`-sized block within the spatial dimensions of :attr:`input` into a column (i.e., last dimension) of a 3-D :attr:`output` tensor of shape :math:`(N, C \times \prod(\text{kernel\_size}), L)`, where :math:`C \times \prod(\text{kernel\_size})` is the total number of values with in each block (a block has :math:`\prod(\text{kernel\_size})` spatial locations each containing a :math:`C`-channeled vector), and :math:`L` is the total number of such blocks: .. math:: L = \prod_d \left\lfloor\frac{\text{spatial\_size}[d] + 2 \times \text{padding}[d] % - \text{dilation}[d] \times (\text{kernel\_size}[d] - 1) - 1}{\text{stride}[d]} + 1\right\rfloor, where :math:`\text{spatial\_size}` is formed by the spatial dimensions of :attr:`input` (:math:`*` above), and :math:`d` is over all spatial dimensions. Therefore, indexing :attr:`output` at the last dimension (column dimension) gives all values within a certain block. The :attr:`padding`, :attr:`stride` and :attr:`dilation` arguments specify how the sliding blocks are retrieved. * :attr:`stride` controls the stride for the sliding blocks. * :attr:`padding` controls the amount of implicit zero-paddings on both sides for :attr:`padding` number of points for each dimension before reshaping. * :attr:`dilation` controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this `link`_ has a nice visualization of what :attr:`dilation` does. Args: kernel_size (int or tuple): the size of the sliding blocks stride (int or tuple, optional): the stride of the sliding blocks in the input spatial dimensions. Default: 1 padding (int or tuple, optional): implicit zero padding to be added on both sides of input. Default: 0 dilation (int or tuple, optional): a parameter that controls the stride of elements within the neighborhood. Default: 1 * If :attr:`kernel_size`, :attr:`dilation`, :attr:`padding` or :attr:`stride` is an int or a tuple of length 1, their values will be replicated across all spatial dimensions. * For the case of two input spatial dimensions this operation is sometimes called ``im2col``. .. note:: :class:`~torch.nn.Fold` calculates each combined value in the resulting large tensor by summing all values from all containing blocks. :class:`~torch.nn.Unfold` extracts the values in the local blocks by copying from the large tensor. So, if the blocks overlap, they are not inverses of each other. .. warning:: Currently, only 4-D input tensors (batched image-like tensors) are supported. Shape: - Input: :math:`(N, C, *)` - Output: :math:`(N, C \times \prod(\text{kernel\_size}), L)` as described above Examples:: >>> unfold = nn.Unfold(kernel_size=(2, 3)) >>> input = torch.randn(2, 5, 3, 4) >>> output = unfold(input) >>> # each patch contains 30 values (2x3=6 vectors, each of 5 channels) >>> # 4 blocks (2x3 kernels) in total in the 3x4 input >>> output.size() torch.Size([2, 30, 4]) >>> # Convolution is equivalent with Unfold + Matrix Multiplication + Fold (or view to output shape) >>> inp = torch.randn(1, 3, 10, 12) >>> w = torch.randn(2, 3, 4, 5) >>> inp_unf = torch.nn.functional.unfold(inp, (4, 5)) >>> out_unf = inp_unf.transpose(1, 2).matmul(w.view(w.size(0), -1).t()).transpose(1, 2) >>> out = torch.nn.functional.fold(out_unf, (7, 8), (1, 1)) >>> # or equivalently (and avoiding a copy), >>> # out = out_unf.view(1, 2, 7, 8) >>> (torch.nn.functional.conv2d(inp, w) - out).abs().max() tensor(1.9073e-06) .. _link: https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md """ def __init__(self, kernel_size, dilation=1, padding=0, stride=1): super(Unfold, self).__init__() self.kernel_size = kernel_size self.dilation = dilation self.padding = padding self.stride = stride def forward(self, input): return F.unfold(input, self.kernel_size, self.dilation, self.padding, self.stride) def extra_repr(self): return 'kernel_size={kernel_size}, dilation={dilation}, padding={padding},' \ ' stride={stride}'.format(**self.__dict__)