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from __future__ import annotations
import functools
from typing import Callable, Dict, List, Sequence, Tuple, Union
import torch
from functorch._C import dim as _C
from ._parsing import (
_ellipsis,
AnonymousAxis,
comma_separate,
parse_pattern,
validate_rearrange_expressions,
)
__all__ = ["rearrange"]
dims = _C.dims
@functools.lru_cache(256)
def _create_rearrange_callable(
tensor_ndim: int, pattern: str, **axes_lengths: int
) -> Callable[[torch.Tensor], torch.Tensor]:
r"""Translate an `einops`-style pattern into a callable that performs the rearrange using first-class dimensions.
Since the an equivalent result is computed for tensors with the same number of dimensions, with the same pattern and
specified axes lengths, this function can be memoized.
Args:
tensor_ndim (int): the number of dimensions in the tensor to rearrange
pattern (str): the `einops`-style rearrangement pattern
axes_lengths (int): any additional length specifications for dimensions
Returns:
Callable[[torch.Tensor], torch.Tensor]: a callable that performs the rearrangement
"""
left, right = parse_pattern(pattern, axes_lengths)
validate_rearrange_expressions(left, right, axes_lengths)
n_anon_dims = sum(not dim for dim in left.composition)
if left.has_ellipsis:
n_ellipsis_dims = tensor_ndim - (len(left.composition) - 1)
n_named_dims = len(left.identifiers) - 1
if (pattern_ndim := n_anon_dims + n_named_dims) > tensor_ndim:
raise ValueError(
f"Number of dimensions in pattern ({pattern_ndim}) must be less than or equal to the number of "
f"dimensions in the tensor ({tensor_ndim})"
)
else:
n_ellipsis_dims = 0
n_named_dims = len(left.identifiers)
if (pattern_ndim := len(left.composition)) != tensor_ndim:
raise ValueError(
f"Number of dimensions in pattern ({pattern_ndim}) must be equal to the number of dimensions in "
f"the tensor ({tensor_ndim})"
)
n_dims = n_named_dims + n_ellipsis_dims + n_anon_dims
if n_dims == 0:
# an identity rearrangement on a 0-dimension tensor
return lambda tensor: tensor
first_class_dims: Tuple[str, ...] = tuple(f"d{i}" for i in range(n_dims))
identifier_dim_map: Dict[Union[str, AnonymousAxis], Tuple[str, ...]] = {}
anon_axes: List[AnonymousAxis] = []
# map the left-hand side identifiers to strings representing first class dims
dims_i = 0
for dimension in left.composition:
if isinstance(dimension, list):
for identifier in dimension:
# non-unitary anon axes are not allowed in rearrange & unitary anon axes are represented as empty lists
assert isinstance(identifier, str)
identifier_dim_map[identifier] = (first_class_dims[dims_i],)
dims_i += 1
if not dimension:
# unitary anonymous axis
anon_axis = AnonymousAxis("1")
identifier_dim_map[anon_axis] = (first_class_dims[dims_i],)
anon_axes.append(anon_axis)
dimension.append(anon_axis)
dims_i += 1
elif dimension == _ellipsis:
identifier = _ellipsis
identifier_dim_map[identifier] = tuple(
first_class_dims[dims_i + j] for j in range(n_ellipsis_dims)
)
dims_i += n_ellipsis_dims
else:
raise ValueError(f"Unexpected dimension: {dimension}")
def composition_to_dims(
composition: Sequence[Union[List[Union[str, AnonymousAxis]], str]]
) -> List[Union[str, Tuple[str, ...]]]:
"""Convert a `ParsedExpression.composition` into a `Tensor.__getitem__` index of strings representing first
class dims."""
dim_composition: List[Union[str, Tuple[str, ...]]] = []
for dimension in composition:
if isinstance(dimension, list):
dim_composition.append(
tuple(
dim
for identifier in dimension
for dim in identifier_dim_map[identifier]
)
)
elif dimension == _ellipsis:
dim_composition.extend(identifier_dim_map[_ellipsis])
else:
raise ValueError(f"Unexpected dimension: {dimension}")
return dim_composition
left_dims = composition_to_dims(left.composition)
right_dims = composition_to_dims(right.composition)
anon_dims = tuple(identifier_dim_map[axis][0] for axis in anon_axes)
specified_lengths = tuple(
(identifier_dim_map[axis][0], length) for axis, length in axes_lengths.items()
)
custom_rearrange_callable_name = "do_rearrange"
custom_rearrange_callable_code = (
(
f"def {custom_rearrange_callable_name}(tensor):\n"
f" {comma_separate(first_class_dims)} = dims({n_dims})\n"
)
+ (
"".join(
f" {dim}.size = {length}\n" for (dim, length) in specified_lengths
)
if specified_lengths
else ""
)
+ f" tensor = tensor[{comma_separate(left_dims)}].order({comma_separate(right_dims)})\n"
+ (
f" return tensor.sum({comma_separate([anon_dims])}, keepdim=False)\n"
if anon_dims
else " return tensor\n"
)
)
exec(custom_rearrange_callable_code)
return locals()[custom_rearrange_callable_name]
def rearrange(
tensor: Union[torch.Tensor, List[torch.Tensor], Tuple[torch.Tensor, ...]],
pattern: str,
**axes_lengths: int,
) -> torch.Tensor:
r"""A native implementation of `einops.rearrange`, a reader-friendly smart element reordering for multidimensional
tensors. This operation includes functionality of transpose (axes permutation), reshape (view), squeeze, unsqueeze,
stack, concatenate and other operations.
See: https://einops.rocks/api/rearrange/
Args:
tensor (Tensor or sequence of Tensor): the tensor(s) to rearrange
pattern (str): the rearrangement pattern
axes_lengths (int): any additional length specifications for dimensions
Returns:
Tensor: the rearranged tensor
Examples:
>>> # suppose we have a set of 32 images in "h w c" format (height-width-channel)
>>> images = torch.randn((32, 30, 40, 3))
>>> # stack along first (batch) axis, output is a single array
>>> rearrange(images, 'b h w c -> b h w c').shape
torch.Size([32, 30, 40, 3])
>>> # concatenate images along height (vertical axis), 960 = 32 * 30
>>> rearrange(images, 'b h w c -> (b h) w c').shape
torch.Size([960, 40, 3])
>>> # concatenated images along horizontal axis, 1280 = 32 * 40
>>> rearrange(images, 'b h w c -> h (b w) c').shape
torch.Size([30, 1280, 3])
>>> # reordered axes to "b c h w" format for deep learning
>>> rearrange(images, 'b h w c -> b c h w').shape
torch.Size([32, 3, 30, 40])
>>> # flattened each image into a vector, 3600 = 30 * 40 * 3
>>> rearrange(images, 'b h w c -> b (c h w)').shape
torch.Size([32, 3600])
>>> # split each image into 4 smaller (top-left, top-right, bottom-left, bottom-right), 128 = 32 * 2 * 2
>>> rearrange(images, 'b (h1 h) (w1 w) c -> (b h1 w1) h w c', h1=2, w1=2).shape
torch.Size([128, 15, 20, 3])
>>> # space-to-depth operation
>>> rearrange(images, 'b (h h1) (w w1) c -> b h w (c h1 w1)', h1=2, w1=2).shape
torch.Size([32, 15, 20, 12])
"""
if not isinstance(tensor, torch.Tensor):
tensor = torch.stack(tensor)
rearrange_callable = _create_rearrange_callable(
tensor.ndim, pattern, **axes_lengths
)
return rearrange_callable(tensor)
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