# coding=utf-8
from .module import Module
from .. import functional as F
from torch import Tensor
from ..common_types import _size_any_t
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 within 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 exactly 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., ``output.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.
In general, folding and unfolding operations are related as
follows. Consider :class:`~torch.nn.Fold` and
:class:`~torch.nn.Unfold` instances created with the same
parameters:
>>> fold_params = dict(kernel_size=..., dilation=..., padding=..., stride=...)
>>> fold = nn.Fold(output_size=..., **fold_params)
>>> unfold = nn.Unfold(**fold_params)
Then for any (supported) ``input`` tensor the following
equality holds:
::
fold(unfold(input)) == divisor * input
where ``divisor`` is a tensor that depends only on the shape
and dtype of the ``input``:
>>> input_ones = torch.ones(input.shape, dtype=input.dtype)
>>> divisor = fold(unfold(input_ones))
When the ``divisor`` tensor contains no zero elements, then
``fold`` and ``unfold`` operations are inverses of each
other (up to constant divisor).
.. 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, 12)
>>> output = fold(input)
>>> output.size()
torch.Size([1, 3, 4, 5])
.. _link:
https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md
"""
__constants__ = ['output_size', 'kernel_size', 'dilation', 'padding',
'stride']
output_size: _size_any_t
kernel_size: _size_any_t
dilation: _size_any_t
padding: _size_any_t
stride: _size_any_t
def __init__(
self,
output_size: _size_any_t,
kernel_size: _size_any_t,
dilation: _size_any_t = 1,
padding: _size_any_t = 0,
stride: _size_any_t = 1
) -> None:
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: Tensor) -> Tensor:
return F.fold(input, self.output_size, self.kernel_size, self.dilation,
self.padding, self.stride)
def extra_repr(self) -> str:
return 'output_size={output_size}, kernel_size={kernel_size}, ' \
'dilation={dilation}, padding={padding}, stride={stride}'.format(
**self.__dict__
)
[docs]class Unfold(Module):
r"""Extracts sliding local blocks from a batched input tensor.
Consider a 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
within 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.
In general, folding and unfolding operations are related as
follows. Consider :class:`~torch.nn.Fold` and
:class:`~torch.nn.Unfold` instances created with the same
parameters:
>>> fold_params = dict(kernel_size=..., dilation=..., padding=..., stride=...)
>>> fold = nn.Fold(output_size=..., **fold_params)
>>> unfold = nn.Unfold(**fold_params)
Then for any (supported) ``input`` tensor the following
equality holds:
::
fold(unfold(input)) == divisor * input
where ``divisor`` is a tensor that depends only on the shape
and dtype of the ``input``:
>>> input_ones = torch.ones(input.shape, dtype=input.dtype)
>>> divisor = fold(unfold(input_ones))
When the ``divisor`` tensor contains no zero elements, then
``fold`` and ``unfold`` operations are inverses of each
other (up to constant divisor).
.. 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
"""
__constants__ = ['kernel_size', 'dilation', 'padding', 'stride']
kernel_size: _size_any_t
dilation: _size_any_t
padding: _size_any_t
stride: _size_any_t
def __init__(
self,
kernel_size: _size_any_t,
dilation: _size_any_t = 1,
padding: _size_any_t = 0,
stride: _size_any_t = 1
) -> None:
super(Unfold, self).__init__()
self.kernel_size = kernel_size
self.dilation = dilation
self.padding = padding
self.stride = stride
def forward(self, input: Tensor) -> Tensor:
return F.unfold(input, self.kernel_size, self.dilation,
self.padding, self.stride)
def extra_repr(self) -> str:
return 'kernel_size={kernel_size}, dilation={dilation}, padding={padding},' \
' stride={stride}'.format(**self.__dict__)
