File size: 8,247 Bytes
375a1cf
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
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)