Full Code of arogozhnikov/einops for AI

Repository: arogozhnikov/einops
Branch: main
Commit: 451e16ff3ebf
Files: 67
Total size: 987.0 KB

Directory structure:
gitextract_7syaalsv/

├── .devcontainer/
│   ├── devcontainer.json
│   └── einops.Dockerfile
├── .github/
│   ├── ISSUE_TEMPLATE/
│   │   ├── bug_report.md
│   │   └── extensions--introducing-new-operation---improve-notion.md
│   └── workflows/
│       ├── deploy_docs.yml
│       ├── deploy_to_pypi.yml
│       ├── run_tests.yml
│       └── test_notebooks.yml
├── .gitignore
├── .pre-commit-config.yaml
├── CITATION.cff
├── LICENSE
├── README.md
├── docs/
│   ├── 1-einops-basics.ipynb
│   ├── 2-einops-for-deep-learning.ipynb
│   ├── 3-einmix-layer.ipynb
│   ├── 4-pack-and-unpack.ipynb
│   ├── README.md
│   ├── pytorch-examples.html
│   ├── resources/
│   │   └── test_images.npy
│   └── utils/
│       └── __init__.py
├── docs_src/
│   ├── CNAME
│   ├── api/
│   │   ├── asnumpy.md
│   │   ├── einsum.md
│   │   ├── pack_unpack.md
│   │   ├── parse_shape.md
│   │   ├── rearrange.md
│   │   ├── reduce.md
│   │   └── repeat.md
│   ├── css/
│   │   ├── codehilite.css
│   │   └── mkdocs.css
│   └── pages/
│       ├── projects.md
│       └── testimonials.md
├── einops/
│   ├── __init__.py
│   ├── _backends.py
│   ├── _torch_specific.py
│   ├── array_api.py
│   ├── einops.py
│   ├── experimental/
│   │   ├── __init__.py
│   │   └── indexing.py
│   ├── layers/
│   │   ├── __init__.py
│   │   ├── _einmix.py
│   │   ├── flax.py
│   │   ├── keras.py
│   │   ├── oneflow.py
│   │   ├── paddle.py
│   │   ├── tensorflow.py
│   │   └── torch.py
│   ├── packing.py
│   ├── parsing.py
│   ├── py.typed
│   └── tests/
│       ├── __init__.py
│       ├── run_tests.py
│       ├── test_einsum.py
│       ├── test_examples.py
│       ├── test_layers.py
│       ├── test_ops.py
│       ├── test_other.py
│       ├── test_packing.py
│       └── test_parsing.py
├── mkdocs.yml
├── pyproject.toml
└── scripts/
    ├── convert_readme.py
    ├── pytorch_examples_source/
    │   ├── Pytorch.ipynb
    │   └── converter.py
    ├── setup.py
    └── test_notebooks.py

================================================
FILE CONTENTS
================================================

================================================
FILE: .devcontainer/devcontainer.json
================================================
{
    "name": "EinopsDev",
    "build": {
        "context": "..",
        "dockerfile": "./einops.Dockerfile",
        "target": "einops-devimage",
    },
    "runArgs": [
        // to use GPUs in container uncomment next line
        // "--gpus=all",
        "--name=einops-devbox",
    ],
    "shutdownAction": "none",
    "postCreateCommand": "uv pip install --system -e . && pre-commit install -f",
    "customizations": {
        "vscode": {
            "settings": {
                "python.defaultInterpreterPath": "/opt/venv/bin/python"
            },
            "extensions": [
                "ms-azuretools.vscode-docker",
                "ms-python.python",
                "ms-python.vscode-pylance",
                "ms-python.mypy-type-checker",
                "charliermarsh.ruff",
                "ms-toolsai.jupyter",
                // very optional git-specific stuff
                "arturock.gitstash",
                "mhutchie.git-graph",
            ]
        }
    }
}

================================================
FILE: .devcontainer/einops.Dockerfile
================================================
FROM python:3.11-bookworm AS einops-devimage
# note this will pull aarch64 or x86 depending on machine it is running on.
RUN pip install uv \
 && uv pip install --system pre-commit hatch

================================================
FILE: .github/ISSUE_TEMPLATE/bug_report.md
================================================
---
name: Bug report
about: Create a report to help us improve
title: "[BUG]"
labels: bug
assignees: ''

---

**Describe the bug**
A clear and concise description of what the bug is.

**Reproduction steps**
Steps to reproduce the behavior:

**Expected behavior**
What you expected to happen.

**Your platform**
Version of einops, python and DL package that you used


================================================
FILE: .github/ISSUE_TEMPLATE/extensions--introducing-new-operation---improve-notion.md
================================================
---
name: 'Extensions: Introducing new operation / improve notion'
about: 'You want to suggest a new operation or extend an existing one? '
title: "[Feature suggestion]"
labels: feature suggestion
assignees: ''

---

Einops sparks a lot of interest to introduce new operations that either meet specific requirements or look like a plausible extension of existing ones.

Einops is not a purely experimental thing, it's already used in a number of large projects, so there are high expectations for any introduced improvement. Let's see which are they and how to check them?

1. Try to collect **use-cases**
2. **Implementation**. (optional) Implementing a sketch of your proposal in a code allows detecting possible conflicts and realize possible caveats.
3. **Integrity** - does it interplay well with existing operations and notation in einops?
4. **Readability**. This is harder to check, but give it a try. A simple but usable test is to write an exercise sheet with several examples of your extension explained, for others meaning of operation should be guessed. Send this test to a couple of your friends to collect the feedback and see how your notion will be understood. This should also help to improve your ideas to make them more digestible.


================================================
FILE: .github/workflows/deploy_docs.yml
================================================
name: deploy-docs
on:
  push:
    branches:
      # triggers on new commits / merged PRs to main or a special branch
      - main
      - docs-deploy-testing
permissions:
  contents: write
jobs:
  deploy:
    runs-on: ubuntu-latest
    steps:
      - uses: actions/checkout@v5
      - name: Configure Git Credentials
        # credentials of GitHub's public bot, so that commits 'belonged' to bot
        run: |
          git config user.name github-actions[bot]
          git config user.email 41898282+github-actions[bot]@users.noreply.github.com
      - uses: actions/setup-python@v5
        with:
          python-version: 3.12
      ## Switched off cache, deployment is fast anyway.
      # - run: echo "cache_id=$(date --utc '+%V')" >> $GITHUB_ENV
      # - uses: actions/cache@v4
      #   with:
      #     key: mkdocs-material-${{ env.cache_id }}
      #     path: .cache
      #     restore-keys: |
      #       mkdocs-material-
      ## original deploy instruction has --force
      # - run: mkdocs gh-deploy --force
      - run: pip install hatch && hatch run docs:deploy_force


================================================
FILE: .github/workflows/deploy_to_pypi.yml
================================================
name: Deploy to pypi

on:
    release:
        types: [created]

jobs:
    publish:
        runs-on: ubuntu-latest
        steps:
            - name: Checkout sources
              uses: actions/checkout@v5

            - name: Set up Python
              uses: actions/setup-python@v5
              with:
                  python-version: "3.12"

            - name: Install dependencies
              run: |
                  pip install . && pip install hatch
            - name: Publish einops to PyPi
              env:
                  HATCH_INDEX_USER: "__token__"
                  HATCH_INDEX_AUTH: ${{ secrets.PYPI_TOKEN }}
              run: |
                  hatch run pypi:deploy


================================================
FILE: .github/workflows/run_tests.yml
================================================
name: Run tests

on: [push, pull_request]

jobs:
  build:

    runs-on: ubuntu-latest
    strategy:
      # do not fail other jobs if one framework / version misbehaves
      fail-fast: false
      matrix:
        python-version: ['3.10', '3.11', '3.13']
        # there was (and likely still is) conflict between tf, oneflow and paddle in protobuf versions.
        # cupy is not tested because it demands gpu
        # oneflow testing is dropped, see details at https://github.com/Oneflow-Inc/oneflow/issues/10340
        # paddle  testing is dropped because of divergence with numpy in py3.10, paddle==2.6.1
        frameworks: ['numpy pytorch tensorflow jax mlx.core']
        include:
          - python-version: '3.10'
            frameworks: 'pytensor'
          - python-version: '3.13'
            frameworks: 'pytensor'


    steps:
      - uses: actions/checkout@v5
      - name: Set up Python ${{ matrix.python-version }}
        uses: actions/setup-python@v5
        with:
          python-version: ${{ matrix.python-version }}
          cache: pip
      - name: Check for ruff compliance
        run: |
          pip install ruff==0.11.7 && ruff check . && ruff format . --check
      - name: Run tests
        run: |
          pip install -e . && python -m einops.tests.run_tests ${{ matrix.frameworks }} --pip-install


================================================
FILE: .github/workflows/test_notebooks.yml
================================================
name: Test notebooks

on: [push, pull_request]

jobs:
  build:

    runs-on: ubuntu-latest
    strategy:
      matrix:
        python-version: ['3.10', '3.13']

    steps:
      - uses: actions/checkout@v5
      - name: Install uv
        uses: astral-sh/setup-uv@v7

      - run: uv venv --python ${{ matrix.python-version }}

      - name: Install dependencies to run/test notebooks
        run: |
          uv pip install nbformat nbconvert jupyter pillow pytest numpy tensorflow
          uv pip install torch --index-url https://download.pytorch.org/whl/cpu
      - name: Testing notebooks
        run: |
          uv pip install -e . && uv run pytest scripts/test_notebooks.py


================================================
FILE: .gitignore
================================================
# Byte-compiled / optimized / DLL files
__pycache__/
*.py[cod]
*$py.class

# C extensions
*.so

# Distribution / packaging
.Python
build/
develop-eggs/
dist/
downloads/
eggs/
.eggs/
lib/
lib64/
parts/
sdist/
var/
wheels/
*.egg-info/
.installed.cfg
*.egg
MANIFEST

# PyInstaller
#  Usually these files are written by a python script from a template
#  before PyInstaller builds the exe, so as to inject date/other infos into it.
*.manifest
*.spec

# Installer logs
pip-log.txt
pip-delete-this-directory.txt

# Unit test / coverage reports
htmlcov/
.tox/
.coverage
.coverage.*
.cache
nosetests.xml
coverage.xml
*.cover
.hypothesis/
.pytest_cache/

# Translations
*.mo
*.pot

# Django stuff:
*.log
local_settings.py
db.sqlite3

# Flask stuff:
instance/
.webassets-cache

# Scrapy stuff:
.scrapy

# Sphinx documentation
docs/_build/

# PyBuilder
target/

# Jupyter Notebook
.ipynb_checkpoints

# pyenv
.python-version

# celery beat schedule file
celerybeat-schedule

# SageMath parsed files
*.sage.py

# Environments
.env
.venv
env/
venv/
ENV/
env.bak/
venv.bak/

# Spyder project settings
.spyderproject
.spyproject

# Rope project settings
.ropeproject

# mkdocs documentation
/site

# mypy
.mypy_cache/

# pycharm
.idea

# design-document
design-einops.txt

# logo and video generation
logo

# any local explorations
*.personal*

# oneflow's output trash
log

# this file is auto-generated
docs_src/index.md

# vs code 
*.code-workspace

# macos system files
.DS_Store

================================================
FILE: .pre-commit-config.yaml
================================================
---
repos:
  - repo: https://github.com/astral-sh/ruff-pre-commit
    # Ruff version, synced with CI
    rev: v0.11.7
    hooks:
      # Run the linter.
      - id: ruff
        types_or: [ python, pyi, jupyter ]
      # Run the formatter.
      - id: ruff-format
        types_or: [ python, pyi, jupyter ]

================================================
FILE: CITATION.cff
================================================
cff-version: 1.2.0
title: einops
message: >-
  If you use this software, please cite it using the
  metadata from this file.
type: software
authors:
  - given-names: Alex
    family-names: Rogozhnikov
repository-code: 'https://github.com/arogozhnikov/einops'
abstract: >-
  Flexible and powerful tensor operations for readable and reliable code (for pytorch, jax, TF and others)
license: MIT
preferred-citation:
  type: article
  authors:
  - given-names: Alex
    family-names: Rogozhnikov
  journal: "International Conference on Learning Representations"
  title: "Einops: Clear and Reliable Tensor Manipulations with Einstein-like Notation"
  year: 2022
  url: https://openreview.net/forum?id=oapKSVM2bc

================================================
FILE: LICENSE
================================================
MIT License

Copyright (c) 2018 Alex Rogozhnikov

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.


================================================
FILE: README.md
================================================

<!--
<a href='http://arogozhnikov.github.io/images/einops/einops_video.mp4' >
<div align="center">
  <img src="http://arogozhnikov.github.io/images/einops/einops_video.gif" alt="einops package examples" />
  <br>
  <small><a href='http://arogozhnikov.github.io/images/einops/einops_video.mp4'>This video in high quality (mp4)</a></small>
  <br><br>
</div>
</a>
-->

<!-- this link magically rendered as video on github readme, unfortunately not in docs -->

https://user-images.githubusercontent.com/6318811/177030658-66f0eb5d-e136-44d8-99c9-86ae298ead5b.mp4




# einops 
[![Run tests](https://github.com/arogozhnikov/einops/actions/workflows/run_tests.yml/badge.svg)](https://github.com/arogozhnikov/einops/actions/workflows/run_tests.yml)
[![PyPI version](https://badge.fury.io/py/einops.svg)](https://badge.fury.io/py/einops)
[![Documentation](https://img.shields.io/badge/documentation-link-blue.svg)](https://einops.rocks/)
![Supported python versions](https://raw.githubusercontent.com/arogozhnikov/einops/main/docs/resources/python_badge.svg)


Flexible and powerful tensor operations for readable and reliable code. <br />
Supports numpy, pytorch, jax, mlx and [others](#supported-frameworks).

## Recent updates:

- [einops playground](https://arogozhnikov.github.io/jupyterlite/lab/index.html?download_github_folder=arogozhnikov/einops/docs) can run 2 of 4 example notebooks right in your browser
- 0.8.2: MLX backend added
- 0.8.0: tinygrad backend added, small fixes
- 0.7.0: no-hassle `torch.compile`, support of [array api standard](https://data-apis.org/array-api/latest/API_specification/index.html) and more
- 10'000🎉: github reports that more than 10k project use einops
- einops 0.6.1: paddle backend added
- einops 0.6 introduces [packing and unpacking](https://github.com/arogozhnikov/einops/blob/main/docs/4-pack-and-unpack.ipynb)
- einops 0.5: einsum is now a part of einops
- [Einops paper](https://openreview.net/pdf?id=oapKSVM2bcj) is accepted for oral presentation at ICLR 2022 (yes, it worth reading).
  Talk recordings are [available](https://iclr.cc/virtual/2022/oral/6603)


<details markdown="1">
<summary>Previous updates</summary>
- flax and oneflow backend added
- torch.jit.script is supported for pytorch layers
- powerful EinMix added to einops. [Einmix tutorial notebook](https://github.com/arogozhnikov/einops/blob/main/docs/3-einmix-layer.ipynb) 
</details>

<!--<div align="center">
  <img src="http://arogozhnikov.github.io/images/einops/einops_logo_350x350.png" 
  alt="einops package logo" width="250" height="250" />
  <br><br>
</div> -->


## Tweets 

> In case you need convincing arguments for setting aside time to learn about einsum and einops...
[Tim Rocktäschel](https://twitter.com/_rockt/status/1230818967205425152)

> Writing better code with PyTorch and einops 👌
[Andrej Karpathy](https://twitter.com/karpathy/status/1290826075916779520)

> Slowly but surely, einops is seeping in to every nook and cranny of my code. If you find yourself shuffling around bazillion dimensional tensors, this might change your life
[Nasim Rahaman](https://twitter.com/nasim_rahaman/status/1216022614755463169)

[More testimonials](https://einops.rocks/pages/testimonials/)


## Contents

- [Installation](#Installation)
- [Documentation](https://einops.rocks/)
- [Tutorial](#Tutorials)
- [API micro-reference](#API)
- [Why use einops](#Why-use-einops-notation)
- [Supported frameworks](#Supported-frameworks)
- [Citing](#Citing)
- [Repository](https://github.com/arogozhnikov/einops) and [discussions](https://github.com/arogozhnikov/einops/discussions)

## Installation  <a name="Installation"></a>

Plain and simple:
```bash
pip install einops
```

(`uv pip install einops` works as well)

## Tutorials <a name="Tutorials"></a>

Tutorials are the most convenient way to see `einops` in action

- part 1: [einops fundamentals](https://github.com/arogozhnikov/einops/blob/main/docs/1-einops-basics.ipynb)
- part 2: [einops for deep learning](https://github.com/arogozhnikov/einops/blob/main/docs/2-einops-for-deep-learning.ipynb)
- part 3: [packing and unpacking](https://github.com/arogozhnikov/einops/blob/main/docs/4-pack-and-unpack.ipynb)
- part 4: [improve pytorch code with einops](http://einops.rocks/pytorch-examples.html)

Kapil Sachdeva recorded a small [intro to einops](https://www.youtube.com/watch?v=xGy75Pjsqzo).

## API <a name="API"></a>

`einops` has a minimalistic yet powerful API.

Three core operations provided ([einops tutorial](https://github.com/arogozhnikov/einops/blob/main/docs/)
shows those cover stacking, reshape, transposition, squeeze/unsqueeze, repeat, tile, concatenate, view and numerous reductions)

```python
from einops import rearrange, reduce, repeat
# rearrange elements according to the pattern
output_tensor = rearrange(input_tensor, 't b c -> b c t')
# combine rearrangement and reduction
output_tensor = reduce(input_tensor, 'b c (h h2) (w w2) -> b h w c', 'mean', h2=2, w2=2)
# copy along a new axis
output_tensor = repeat(input_tensor, 'h w -> h w c', c=3)
```

Later additions to the family are `pack` and `unpack` functions (better than stack/split/concatenate):

```python
from einops import pack, unpack
# pack and unpack allow reversibly 'packing' multiple tensors into one.
# Packed tensors may be of different dimensionality:
packed,  ps = pack([class_token_bc, image_tokens_bhwc, text_tokens_btc], 'b * c')
class_emb_bc, image_emb_bhwc, text_emb_btc = unpack(transformer(packed), ps, 'b * c')
```

Finally, einops provides einsum with a support of multi-lettered names:

```python
from einops import einsum, pack, unpack
# einsum is like ... einsum, generic and flexible dot-product
# but 1) axes can be multi-lettered  2) pattern goes last 3) works with multiple frameworks
C = einsum(A, B, 'b t1 head c, b t2 head c -> b head t1 t2')
```

### EinMix

`EinMix` is a generic linear layer, perfect for MLP Mixers and similar architectures.

### Layers

Einops provides layers (`einops` keeps a separate version for each framework) that reflect corresponding functions

```python
from einops.layers.torch      import Rearrange, Reduce
from einops.layers.tensorflow import Rearrange, Reduce
from einops.layers.flax       import Rearrange, Reduce
from einops.layers.paddle     import Rearrange, Reduce
```

<details markdown="1">
<summary>Example of using layers within a pytorch model</summary>
Example given for pytorch, but code in other frameworks is almost identical

```python 
from torch.nn import Sequential, Conv2d, MaxPool2d, Linear, ReLU
from einops.layers.torch import Rearrange

model = Sequential(
    ...,
    Conv2d(6, 16, kernel_size=5),
    MaxPool2d(kernel_size=2),
    # flattening without need to write forward
    Rearrange('b c h w -> b (c h w)'),
    Linear(16*5*5, 120),
    ReLU(),
    Linear(120, 10),
)
```

No more flatten needed!

Additionally, torch layers as those are script-able and compile-able.
Operations [are torch.compile-able](https://github.com/arogozhnikov/einops/wiki/Using-torch.compile-with-einops),
 but not script-able due to limitations of torch.jit.script.
</details>




## Naming <a name="Naming"></a>

`einops` stands for Einstein-Inspired Notation for operations 
(though "Einstein operations" is more attractive and easier to remember).

Notation was loosely inspired by Einstein summation (in particular by `numpy.einsum` operation).

## Why use `einops` notation?! <a name="Why-use-einops-notation"></a>


### Semantic information (being verbose in expectations)

```python
y = x.view(x.shape[0], -1)
y = rearrange(x, 'b c h w -> b (c h w)')
```
While these two lines are doing the same job in *some* context,
the second one provides information about the input and output.
In other words, `einops` focuses on interface: *what is the input and output*, not *how* the output is computed.

The next operation looks similar:

```python
y = rearrange(x, 'time c h w -> time (c h w)')
```
but it gives the reader a hint:
this is not an independent batch of images we are processing,
but rather a sequence (video).

Semantic information makes the code easier to read and maintain.

### Convenient checks

Reconsider the same example:

```python
y = x.view(x.shape[0], -1) # x: (batch, 256, 19, 19)
y = rearrange(x, 'b c h w -> b (c h w)')
```
The second line checks that the input has four dimensions,
but you can also specify particular dimensions.
That's opposed to just writing comments about shapes since comments don't prevent mistakes,
not tested, and without code review tend to be outdated
```python
y = x.view(x.shape[0], -1) # x: (batch, 256, 19, 19)
y = rearrange(x, 'b c h w -> b (c h w)', c=256, h=19, w=19)
```

### Result is strictly determined

Below we have at least two ways to define the depth-to-space operation
```python
# depth-to-space
rearrange(x, 'b c (h h2) (w w2) -> b (c h2 w2) h w', h2=2, w2=2)
rearrange(x, 'b c (h h2) (w w2) -> b (h2 w2 c) h w', h2=2, w2=2)
```
There are at least four more ways to do it. Which one is used by the framework?

These details are ignored, since *usually* it makes no difference,
but it can make a big difference (e.g. if you use grouped convolutions in the next stage),
and you'd like to specify this in your code.


### Uniformity

```python
reduce(x, 'b c (x dx) -> b c x', 'max', dx=2)
reduce(x, 'b c (x dx) (y dy) -> b c x y', 'max', dx=2, dy=3)
reduce(x, 'b c (x dx) (y dy) (z dz) -> b c x y z', 'max', dx=2, dy=3, dz=4)
```
These examples demonstrated that we don't use separate operations for 1d/2d/3d pooling,
those are all defined in a uniform way.

Space-to-depth and depth-to space are defined in many frameworks but how about width-to-height? Here you go:

```python
rearrange(x, 'b c h (w w2) -> b c (h w2) w', w2=2)
```


### Framework independent behavior

Even simple functions are defined differently by different frameworks

```python
y = x.flatten() # or flatten(x)
```

Suppose `x`'s shape was `(3, 4, 5)`, then `y` has shape ...

- numpy, pytorch, cupy, chainer, jax: `(60,)`
- keras, tensorflow.layers, gluon: `(3, 20)`

`einops` works the same way in all frameworks.


### Independence of framework terminology

Example: `tile` vs `repeat` causes lots of confusion. To copy image along width:
```python
np.tile(image, (1, 2))    # in numpy
image.repeat(1, 2)        # pytorch's repeat ~ numpy's tile
```

With einops you don't need to decipher which axis was repeated:
```python
repeat(image, 'h w -> h (tile w)', tile=2)  # in numpy
repeat(image, 'h w -> h (tile w)', tile=2)  # in pytorch
repeat(image, 'h w -> h (tile w)', tile=2)  # in tf
repeat(image, 'h w -> h (tile w)', tile=2)  # in jax
repeat(image, 'h w -> h (tile w)', tile=2)  # in cupy
... (etc.)
```

[Testimonials](https://einops.rocks/pages/testimonials/) provide users' perspective on the same question.


## Supported frameworks <a name="Supported-frameworks"></a>

Einops works with ...

- [numpy](http://www.numpy.org/)
- [pytorch](https://pytorch.org/)
- [tensorflow](https://www.tensorflow.org/)
- [jax](https://github.com/google/jax)
- [cupy](https://github.com/cupy/cupy)
- [flax](https://github.com/google/flax) (community)
- [paddle](https://github.com/PaddlePaddle/Paddle) (community)
- [oneflow](https://github.com/Oneflow-Inc/oneflow) (community)
- [tinygrad](https://github.com/tinygrad/tinygrad) (community)
- [pytensor](https://github.com/pymc-devs/pytensor) (community)



```python
from einops import rearrange  
=> from einops.array_api import rearrange
```

But actually it is even better: einops can be used with *any* framework that supports
[Python array API standard](https://data-apis.org/array-api/latest/API_specification/index.html),
to name a few:

- numpy >= 2.0
- [MLX](https://github.com/ml-explore/mlx)  # yes, einops works with apple's framework
- [pydata/sparse](https://github.com/pydata/sparse) >= 0.15 # and works with sparse tensors
- [cubed](https://github.com/cubed-dev/cubed) # and with distributed tensors too
- [quantco/ndonnx](https://github.com/Quantco/ndonnx)
- jax
- cupy
- dask is supported via [array-api-compat](https://github.com/data-apis/array-api-compat)


## Development

Devcontainer is provided, this environment can be used locally, or on your server,
or within github codespaces. 
To start with devcontainers in vs code, clone repo, and click 'Reopen in Devcontainer'. 

Starting from einops 0.8.1, einops distributes tests as a part of package.

```bash
# pip install einops pytest
python -m einops.tests.run_tests numpy pytorch jax --pip-install
```

`numpy pytorch jax` is an _example_, any subset of testable frameworks can be provided.
Every framework is tested against numpy, so it is a requirement for tests.

Specifying `--pip-install` will install requirements in current virtualenv,
and should be omitted if dependencies are installed locally.

To build/test docs:

```bash
hatch run docs:serve  # Serving on http://localhost:8000/
```


## Citing einops <a name="Citing"></a>

Please use the following bibtex record

```text
@inproceedings{
    rogozhnikov2022einops,
    title={Einops: Clear and Reliable Tensor Manipulations with Einstein-like Notation},
    author={Alex Rogozhnikov},
    booktitle={International Conference on Learning Representations},
    year={2022},
    url={https://openreview.net/forum?id=oapKSVM2bcj}
}
```


## Supported python versions

`einops` works with python 3.10 or later.


================================================
FILE: docs/1-einops-basics.ipynb
================================================
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Einops tutorial, part 1: basics\n",
    "\n",
    "<!-- <img src='http://arogozhnikov.github.io/images/einops/einops_logo_350x350.png' height=\"80\" /> -->\n",
    "\n",
    "## Welcome to einops-land!\n",
    "\n",
    "We don't write \n",
    "```python\n",
    "y = x.transpose(0, 2, 3, 1)\n",
    "```\n",
    "We write comprehensible code\n",
    "```python\n",
    "y = rearrange(x, 'b c h w -> b h w c')\n",
    "```\n",
    "\n",
    "\n",
    "`einops` supports widely used tensor packages (such as `numpy`, `pytorch`, `jax`, `tensorflow`), and extends them.\n",
    "\n",
    "## What's in this tutorial?\n",
    "\n",
    "- fundamentals: reordering, composition and decomposition of axes\n",
    "- operations: `rearrange`, `reduce`, `repeat`\n",
    "- how much you can do with a single operation!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preparations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "# we need some libraries for this demo\n",
    "%pip install einops numpy pillow -q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Examples are given for numpy. This code also setups ipython/jupyter/jupyterlite\n",
    "# so that numpy arrays in the output are displayed as images\n",
    "import numpy\n",
    "from utils import display_np_arrays_as_images\n",
    "\n",
    "display_np_arrays_as_images()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load a batch of images to play with"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(6, 96, 96, 3) float64\n"
     ]
    }
   ],
   "source": [
    "ims = numpy.load(\"./resources/test_images.npy\", allow_pickle=False)\n",
    "# There are 6 images of shape 96x96 with 3 color channels packed into tensor\n",
    "print(ims.shape, ims.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": []
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# display the first image (whole 4d tensor can't be rendered)\n",
    "ims[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": []
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# second image in a batch\n",
    "ims[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# we'll use three operations\n",
    "from einops import rearrange, reduce, repeat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": []
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# rearrange, as the name suggests, rearranges elements\n",
    "# below we swapped height and width.\n",
    "# In other words, transposed first two axes (dimensions)\n",
    "rearrange(ims[0], \"h w c -> w h c\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": []
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we could use more verbose names for axes, and result is the same:\n",
    "rearrange(ims[0], \"height width color -> width height color\")\n",
    "# when you operate on same set of axes many times,\n",
    "# you usually come up with short names.\n",
    "# That's what we do throughout tutorial - we'll use b (for batch), h, w, and c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Composition of axes\n",
    "transposition is very common and useful, but let's move to other capabilities provided by einops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": []
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# einops allows seamlessly composing batch and height to a new height dimension\n",
    "# We just rendered all images by collapsing to 3d tensor!\n",
    "rearrange(ims, \"b h w c -> (b h) w c\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": []
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# or compose a new dimension of batch and width\n",
    "rearrange(ims, \"b h w c -> h (b w) c\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(96, 576, 3)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# resulting dimensions are computed very simply\n",
    "# length of newly composed axis is a product of components\n",
    "# [6, 96, 96, 3] -> [96, (6 * 96), 3]\n",
    "rearrange(ims, \"b h w c -> h (b w) c\").shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(165888,)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we can compose more than two axes.\n",
    "# let's flatten 4d array into 1d, resulting array has as many elements as the original\n",
    "rearrange(ims, \"b h w c -> (b h w c)\").shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Decomposition of axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3, 96, 96, 3)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# decomposition is the inverse process - represent an axis as a combination of new axes\n",
    "# several decompositions possible, so b1=2 is to decompose 6 to b1=2 and b2=3\n",
    "rearrange(ims, \"(b1 b2) h w c -> b1 b2 h w c \", b1=2).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": []
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# finally, combine composition and decomposition:\n",
    "rearrange(ims, \"(b1 b2) h w c -> (b1 h) (b2 w) c \", b1=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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eg/XiAfkEBA1knWqYfT9bJzwH68UDMgmovKxc10+rFD8u1otHeKE6eUAmAZmameq69ZNlQ0udasLBevGATAKCXe5s7XXrkbN3steLR3ihOnlAJgEBpx79ddu7vueAnjrVhIP14gH5BPTuB+/iawhDY+292uPxHKkvD8gnIK9uXgFjAzD1hNbSsnXL8N8dw9jkGIk8IJ+AoALrwtd16tpJc01ge+w1P6zp1qubZhi/SokHZBUQvItF/RH13tT31H0jAhravx77ddyUcZR4h9PQ6gG5p3NUE0pLToORjbOnzuZk5FRUVPw9H6ijh+9w39ETRxsZG2klLSeAT+fQ7G39CEgzJ6qucgFpDoesjzDNVPhVFj3ABcRi1CjizAVEUTBYpMIFxGLUKOKsn1UZFDmAGioVzyrSMtIy8jKyC7OzC7JzinLg36LHRZAOv/LK8orKiqoXVabGpmYmZlaWVk62TvDzbO3p3d7bw83DoL5+QknsLSwvO8/LwYtsOA6ePwj912Rt6mpNurew0vLS80nnL964ePXW1cS0xPt599WtNdDKuaF5w+F9hgcODPTz8VPXx6bViDCAfmQrjOvrkau4tDjst7BDZw9dvnn55auXRCr15OmT7dHb4efm4DZv4rwpw6cYGsi0vI63gYhEUAcjt7NuL9m05ML1C6TUU7NsMP7Ryo86vtvxTMKZmunSHXMBSedbvVm+eedmnw/7LNq4SPAzEU+dCwjvK5aQ8K2+leEr/ef4QwNcUt5cQJK6V8/GD587HPCvAEk1xAWk5xhLXXzMxZgJiydIVwoXkHS+pcXy3lN7v/75a4nYcAFJ5Fi6zC7euPhq6lUpOHEBSeFV6mxCl8GHX30oRccBFxB1wZaIUHxy/I7DO4gbJ9YTDbNRkXtVPXrwqF2zdsRr8voZXBe8zt3R3drK2qqhlbmpubmZuZGhUUlZSXpmOvQTghqS0pN0qjW82E8YMqF+vfo65dIMJiYgzcXwqwI8MM53nE0TG6WMMIzatV1X+M1/f/6ek3tmfD2j8FGhEkbdKQzWHog98E7fd9QBBKTzR5gAp9GSZVT/UfE74mH8C08ofH84HoxBcgFhvEQvxsHa4djGYzAaj6R45NwRmCKCBGNgXEAYL1GNcbFz+WbON0iK8CJ2/MJxJBgD4wLCeIl2zOSAya2cWiFZcgEhHVWHYDAdcdGURcgKn7um21Zxms3yO5Bm/zBzdWS/kSZGJhi6d3PuwmRIDBKD4QLCeIkBDPQS+XX3wxCFmR43bt/AIDEYLiCMl9jA9O3cF0kUpu4jkVphXEBaXcQMwMPdA8kVlnwgkVphXEBaXcQMoL07dkuu/Af5pGrFBUTKk/q3A6McyMUYZRVlpOhyAZHyJBV2LMwsMDwITnLlAsI4nBlMQwvUmEbV8ypSVeICIuVJKuzAKzqGB0wLwcAwGC4gjJeYwTwtf4rhamxkjIFhMFxAGC8xg0G2jhuYNiBVJT0IiO/fSyp4SnZggALZOm7euLlSXsGnehBQ/fokp1QKrvnrlzH1fiqyUs2tWBaQgSF2Hu3LF2Q2r0C6lXVYWmYasgqwsRASqRWmhzuQsQm2BVf2lFh/l1ZHvAYA/I4crZ1ak6qvHgQEjzBzC3NMBR4UPsDAOKbaA4fPHsa4Ajob7ZrbYZAYjB4EBLQaWTXCkEu9gX2oY6y93pi4xLisgixMHbu81QUDQ2L0IyDrFtYYfnGn4zAwjgEPrNi6AukHnw4+SCQGph8BIT8mB99uvn3rNqYadRwDW3DATi5IJ+CnDWEM6kdALu4uGHKAWRa8DImss7D7uffHLRyHrD4sAOrZsScSjIHpR0BtPNpgyAHm5OGTC2cs1PrB3hcvXsQej53/4fwg/yCkZfphn6z55MYdLXNPj50/5j3J++GTh8jqDOs5DDnlA2mQ2Da/yPKqYdkZ2W87v43P4uzqHDQjqGf/ni0cWlg0tKisqCx9UpqTlQOfBk9OSk64kAAPu+p3fgtLi9QnJJvexLf5hU0OukzUoRnb1qXt0B5DO7XpBJtBWzexhlsIjFfkFuVeTr4My+NPXjqJHECt9vbJ70/269IP73mtSP0ICGh5u3pn3CU2M7dmPROyE2zsbGqmiDnWu4DEkFfKC1s1pO5NJTuUpJ9HGFRsUMAgpeqROoWPkZEy9ZrZ+WzSZ2TVA/7Rm4DGvD9GovBwAal0LOzB8P6w91VeEpOoNwG169hOog+jpqeki/HI65o3bEGYFN/T0JuAIE7zls2TIlr8DlTbqxOHTvT19q2dLj5FnwLy6eMDH0kVXwclC1xASg6B17dNCzcpJZI61aeAoA5fbfjKrY0bqcpU23n88PHDImy/CNmiKbTmaON4YN0BglMQleqoZwFZNrSMOBQBvTtKtESe8ptQtQNd7V1jt8Q6t3AW6U8N2fUsIGDm5OIUfT66vRd2VaWGylRfMjQy5BOJwBX+vfxhAzxJ1QOl6F9AQAL6/eDbctCmNjUzrRaBsH/hTjY3ZO7ljMsDhg4QZoGqXAO7DhT23mTb1Dbiywh4cjWyaCR1jfTWE62yYjCD7Mf1P+7ZsScnM0clQGWig7MDKMZvpB+0yol/r0+PPdF5x/Pge01b92+NiolC7ugL4x4zA2cGDQuSrtGjFAK6BFRNDgZ3kq4kXTp7KTE+EYY7crNyn5Y8rSivgF5Uc0tzGO1q2rypSysX19au0ADv+HZH4k2omj7Sr4AU2/zCZLETF04k3EoAJWXmZ8JnD2EJmImxCUwvtLe2f7Plm15veg32GUxwrmpNJ2g4plFAGujKf4kSAclfcWSJVLSBkFw5jEIPcAFRGBSWKHEBsRQtCrlyAVEYFJYocQGxFC0KuXIBURgUlihxAbEULQq5cgFRGBSWKHEBsRQtCrlyAVEYFJYocQGxFC0KuXIBURgUlihxAbEULQq5cgFRGBSWKHEBsRQtCrlyAVEYFJYo8QllWqJFfEKZlvJYu8zvQKxFjDK+Bv/Is6WMEmV0OiVQRoguOvwORFc8mGPDBcRcyOgizAVEVzyYY8MFxFzI6CLMBURXPJhjwwXEXMjoIswFRFc8mGPDBcRcyOgizAVEVzyYY8MFxFzI6CLMBURXPJhjwwXEXMjoIswFRFc8mGPDBcRcyOgizAVEVzyYY8MFxFzI6CLMBURXPJhjwwXEXMjoIswFRFc8mGPDBcRcyOgizAVEVzyYY8MFxFzI6CLMBURXPJhjYyAn44KC3MzMe9nZGTk5mfAv/B4+LKqoKK+srKj+Fw7gQxmmpmYmJqZNmza3t3dydHTx9Ozi5eXt7OwqJ1Uayrp9O+vChevJyXdv3bqfl/egoOBRcXFpZeWzZ8+eGxoaNGhg0gA+qdLA1NzczMnJ1hW+DfZ/v3bt3KytrWTj/0Zu7l8SFQZfmklLS05MvJyUlJCcnJiScr2kpFhwWW5ubUaMGD9+/BRbW3vBRgRktLWVdWEh/P3Exib89tvx6Og/s7MLBBCGLM7OLXr16uTr6+3n59O4saUwI8hc5AUEKtm2bVNc3OkrV84/fVqK5IGEGRoagYbmzVsG9ydkFpEw2QT0/PmL8PD969b9kpqaIZKzIruRkeGQId0/+mj0oEHdiH8xvroU8gJKTIz38+uiqIMUB40bN1m5Mmz48HFSGFeyKY+AYmIuzpq1mqB0lGoRHr508uQApUQip0w2oh8/fjh9+vg1a5YQcYF+jcCD/rPPNgwaNFM69UAF3d0dJaqmrI1osnUIDf3q5cuXCxeuJGtWTmsvXrycMGExtHikLrRdO6leQZi8AyncvWHDqt27tytOmTuYNm2FDOqxt7du1MhCIuewLSBwyuLFH+flZUvkHUnNbtmyD1rNkhZRbVy62w/YZ15ApaUly5bNkyEMZIsoLHwUHPw/ZG2qs8YFpM4z/59+8OCulJQkLSDKLq9eva20tFweUtC1KF1BzN+BwDXQ+RYeHiadj4hbfvas6qefDhA3q84gvwOp88x/0/fv3wmDIf89p/vo1KnLjx+XyMOxXr16bdu6SFeWgXSmtVpevjzU1bW1jU0LK6tmpn//ZwadIg8eFGZl3Y+Jid67NzI/P0erkWoAdHlD33f//kOQeP3CTp++gidgZWU5bpxvz54doS8H3qdgCMzU1AQcVVlZVVpalptblJ1deP367WvXUs+cSXjwoFjJsouLnampsVIiwVN9CiggYGzz5jZKlbGzc4Rft269Zs9evGjRrKioCCWAutPTp4+xIiCIt7paKKVD9/G3386H4VKl9Pr168F4qoWFWYsWzTp3bjtiRB8AwKM8IeHW/v2nf//9tKIISZ9fUKg+BaTkFKVTCwvL0NCfCwvzz5w5oXRJ5en16wkq0ylMzMkpxLAKCOgNQxAYZDUGRru8vN6E3/Ll0+/cyQYl7d8f6+nZGm9BAJJeAUFl4Pm9evX3Pj5u8LeltW4w8q8VQwmgrKwCw+TddwdjYCoxMLVj7twJ8FN5lWAi7W9hTk4u3bv3w1S4uPgRtJ8wSL1jjI2NMBxgPhAGpl8M7QIC7wwYMBTpo/T0FCRSvzDkwMLatTvu3cO+RuirRgwICKYjIr2TkXEHidQvrE0bZwwBeNX39p50/PgFDFhfGAYE9NZbHZDegWENJFK/sK5d2yEJwDRWX9+ZI0YEX7x4A5lFZhgDAoL50TCDDOOXsrKnGJjeMfB6Be8HeBrwPtWtW1DnzhO+/z7q4cMn+IwyIHWohgxs1BVhY2On7lLNdOIzaGsaJ3hsY9Nk7NhBuhq8ciVl+vRVtraD/Pw+3rx5L9ycdLUgBZ4NAVlZoe5A5eVs3IEgkCtXzkQ2pZWiDlOnjx6Ng4lEdna+gwbN+PnngyUlZUoYOU/ZEJCREaoznqHhMFg4sW3bMjET3V++fHXixMXJk7+wth4wevSne/eegjFaOaVTXRYbAjI2NsG4BtPfiLEjDwZaQiEhU8WXBYNie/acHDVqvoPDkKVLv5f50caGgJB3IPHBkNnCF19M27DhUxjYIlJuUdHj5cu3ODkNhQUe8o32E6HOjQj2wKxZY6Oj19vaNhVsQSkjPMg2btzVuvVIeaYckdG+Uh34qU4eGDzYJzV1H4xbwQC7Thk1gOFuNGXKsvffD6mqeq4BJv4SF5B4HxKwABMz1q79V3Jy1MyZgbUnbwguICLiEKw4gxX1gi1ozcgFpNVF8gHc3BzCwhZkZR1ev36+j08HMe9oCtKxsVfGj/9cutcLLiCFq2k5gP6hTz4Zd+5cOCgpNHRe9+5ilQT9RmvWbJOoelxAEjmWgFk7u+azZ48/ezY8O/sI3JkGDOgquJG0ePF3ijmKBJjVMMEFVMMZtB7CvFVoG5048V1R0cnIyBVjxgzQdZozrKGGN3wp6scFJIVXpbLZsKH5+PGDd+1aXVAQs2XLkg4dWuFLghFZKTqHuIDwIaAICW9tH3ww4urVyF9+WYEcU4NBNCmmFnEBUSQLXanAaxrMmz5z5kfkEy0xMU3XIrTiuYC0uog8AFZ1ETTq4eE2bdoojMF793IxMJ0wXEA6uYsM+Pz56+7uI7788seMjDwiFpFrd0pKyE934QIiEkHdjFy/ng4rLkJCNrVs6d+374cwz1DkEHp6eqZuDMihuYDI+RJtSdElAx3EsMwZ5hm2aOHbu/fUb7/dKWApz5Ej50JDIzGFI5vbGFMKDLHRO4VFfqDVA0lJ6UoYaBXBynb4zZ79DWz6DL3P8FSCTREcHKyhEwg2gzYxMXr16i94k4JFiTC2lZ//EB5/0CiGFytYFa9kTd2piwv5HZK5gNR5W8L0Gzc0LT8CZcAvMvIocQZdurQlbpM/woi7VIvBrKwCSYfH1RUPe0b37u2l7qrgdC4gwa4TmFHRABKYX2g2f/9e0JEtNLfafFxAal0j0QV4BZPIsmazCxYEaQYIu8oFJMxvwnPVbkELt4XOCfsMdenyFhquA5ALSAdnEYHK/wiDrmrYpYoI+dpGuIBq+0TCFHgPl/STBrWpQ1/A8ePfEZwmq1QEF5CSQ6Q9ha19dZqDIZINbH13/vzPsJJapB0N2bmANDiH/CXYMfPSpe0XLmyDRgl0D5Iv4D8WHR1tYOrZvn1rLS0b/CdNkv9zAUniVs1GYXsX2PwwL+/4jz8ugS/DEZk8rygRurB/+GFRevrvMPVMkSjdAe+Jls63WizDpLB//nME/DIz83fvjomOPnPuXCI0krRkU3UZ1raCboYO7fHOO32RI/OqzAhJI//BOSEsKM4jzwfnqh0ALaSrV29du5Z28+Yd6LCGzVzhkxrl5fCV1OewPhBUAr3JMCgGY6JNmzaytm7SsmULWAnk4eEOYxSSPhA1xIcLSINz/r4kp4C0UKHyMm8DURkWdkhxAbETKyqZcgFRGRZ2SHEBsRMrKplyAVEZFnZIcQGxEysqmXIBURkWdkhxAbETKyqZcgFRGRZ2SHEBsRMrKplyAVEZFnZIcQGxEysqmXIBURkWdkhxAbETKyqZcgFRGRZ2SHEBsRMrKplyAVEZFnZIcQGxEysqmf4vPLVVQdr85mIAAAAASUVORK5CYII=",
      "text/plain": []
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# slightly different composition: b1 is merged with width, b2 with height\n",
    "# ... so letters are ordered by w then by h\n",
    "rearrange(ims, \"(b1 b2) h w c -> (b2 h) (b1 w) c \", b1=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": []
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# move part of width dimension to height.\n",
    "# we should call this width-to-height as image width shrunk by 2 and height doubled.\n",
    "# but all pixels are the same!\n",
    "# Can you write reverse operation (height-to-width)?\n",
    "rearrange(ims, \"b h (w w2) c -> (h w2) (b w) c\", w2=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Order of axes matters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": []
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compare with the next example\n",
    "rearrange(ims, \"b h w c -> h (b w) c\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": []
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# order of axes in composition is different\n",
    "# rule is just as for digits in the number: leftmost digit is the most significant,\n",
    "# while neighboring numbers differ in the rightmost axis.\n",
    "\n",
    "# you can also think of this as lexicographic sort\n",
    "rearrange(ims, \"b h w c -> h (w b) c\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": []
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# what if b1 and b2 are reordered before composing to width?\n",
    "rearrange(ims, \"(b1 b2) h w c -> h (b1 b2 w) c \", b1=2)  # produces 'einops'\n",
    "rearrange(ims, \"(b1 b2) h w c -> h (b2 b1 w) c \", b1=2)  # produces 'eoipns'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Meet einops.reduce\n",
    "\n",
    "In einops-land you don't need to guess what happened\n",
    "```python\n",
    "x.mean(-1)\n",
    "```\n",
    "Because you write what the operation does\n",
    "```python\n",
    "reduce(x, 'b h w c -> b h w', 'mean')\n",
    "```\n",
    "\n",
    "if axis is not present in the output — you guessed it — axis was reduced."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": []
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# average over batch\n",
    "reduce(ims, \"b h w c -> h w c\", \"mean\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": []
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the previous is identical to familiar:\n",
    "ims.mean(axis=0)\n",
    "# but is so much more readable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": []
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example of reducing of several axes\n",
    "# besides mean, there are also min, max, sum, prod\n",
    "reduce(ims, \"b h w c -> h w\", \"min\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": []
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# this is mean-pooling with 2x2 kernel\n",
    "# image is split into 2x2 patches, each patch is averaged\n",
    "reduce(ims, \"b (h h2) (w w2) c -> h (b w) c\", \"mean\", h2=2, w2=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": []
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# max-pooling is similar\n",
    "# result is not as smooth as for mean-pooling\n",
    "reduce(ims, \"b (h h2) (w w2) c -> h (b w) c\", \"max\", h2=2, w2=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": []
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# yet another example. Can you compute result shape?\n",
    "reduce(ims, \"(b1 b2) h w c -> (b2 h) (b1 w)\", \"mean\", b1=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "source": [
    "## Stack and concatenate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'list'> with 6 tensors of shape (96, 96, 3)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(6, 96, 96, 3)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# rearrange can also take care of lists of arrays with the same shape\n",
    "x = list(ims)\n",
    "print(type(x), \"with\", len(x), \"tensors of shape\", x[0].shape)\n",
    "# that's how we can stack inputs\n",
    "# \"list axis\" becomes first (\"b\" in this case), and we left it there\n",
    "rearrange(x, \"b h w c -> b h w c\").shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(96, 96, 3, 6)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# but new axis can appear in the other place:\n",
    "rearrange(x, \"b h w c -> h w c b\").shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# that's equivalent to numpy stacking, but written more explicitly\n",
    "numpy.array_equal(rearrange(x, \"b h w c -> h w c b\"), numpy.stack(x, axis=3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(96, 576, 3)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ... or we can concatenate along axes\n",
    "rearrange(x, \"b h w c -> h (b w) c\").shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# which is equivalent to concatenation\n",
    "numpy.array_equal(rearrange(x, \"b h w c -> h (b w) c\"), numpy.concatenate(x, axis=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Addition or removal of axes\n",
    "\n",
    "You can write 1 to create a new axis of length 1. Similarly you can remove such axis.\n",
    "\n",
    "There is also a synonym `()` that you can use. That's a composition of zero axes and it also has a unit length."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(6, 1, 96, 96, 1, 3)\n",
      "(6, 96, 96, 3)\n"
     ]
    }
   ],
   "source": [
    "x = rearrange(ims, \"b h w c -> b 1 h w 1 c\")  # functionality of numpy.expand_dims\n",
    "print(x.shape)\n",
    "print(rearrange(x, \"b 1 h w 1 c -> b h w c\").shape)  # functionality of numpy.squeeze"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": []
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute max in each image individually, then show a difference\n",
    "x = reduce(ims, \"b h w c -> b () () c\", \"max\") - ims\n",
    "rearrange(x, \"b h w c -> h (b w) c\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Repeating elements\n",
    "\n",
    "Third operation we introduce is `repeat`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(96, 5, 96, 3)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# repeat along a new axis. New axis can be placed anywhere\n",
    "repeat(ims[0], \"h w c -> h new_axis w c\", new_axis=5).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(96, 5, 96, 3)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# shortcut\n",
    "repeat(ims[0], \"h w c -> h 5 w c\").shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": []
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# repeat along w (existing axis)\n",
    "repeat(ims[0], \"h w c -> h (repeat w) c\", repeat=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": []
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# repeat along two existing axes\n",
    "repeat(ims[0], \"h w c -> (2 h) (2 w) c\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
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