🆕 December 1, 2024: The original [`lap`](https://github.com/gatagat/lap) and [`lapx`](https://github.com/rathaROG/lapx) have been merged.
---
<details><summary>See more</summary><br>
[](https://github.com/rathaROG/lapx/actions/workflows/test_simple.yaml)
[](https://github.com/rathaROG/lapx/actions/workflows/benchmark.yaml)
[](https://github.com/rathaROG/lapx/actions/workflows/prepublish.yaml)
[](https://github.com/rathaROG/lapx/actions/workflows/publish.yaml)
# Linear Assignment Problem Solver
`lapx` basically is Tomas Kazmar's [`gatagat/lap`](https://github.com/gatagat/lap) with support for all Windows/Linux/macOS and Python 3.7-3.13.
<details><summary>About <code>lap</code></summary><br>
Tomas Kazmar's [`lap`](https://github.com/gatagat/lap) is a [linear assignment problem](https://en.wikipedia.org/wiki/Assignment_problem) solver using Jonker-Volgenant algorithm for dense LAPJV ¹ or sparse LAPMOD ² matrices. Both algorithms are implemented from scratch based solely on the papers ¹˒² and the public domain Pascal implementation provided by A. Volgenant ³. The LAPMOD implementation seems to be faster than the LAPJV implementation for matrices with a side of more than ~5000 and with less than 50% finite coefficients.
<sup>¹ R. Jonker and A. Volgenant, "A Shortest Augmenting Path Algorithm for Dense and Sparse Linear Assignment Problems", Computing 38, 325-340 (1987) </sup><br>
<sup>² A. Volgenant, "Linear and Semi-Assignment Problems: A Core Oriented Approach", Computer Ops Res. 23, 917-932 (1996) </sup><br>
<sup>³ http://www.assignmentproblems.com/LAPJV.htm | [[archive.org](https://web.archive.org/web/20220221010749/http://www.assignmentproblems.com/LAPJV.htm)] </sup><br>
</details>
## 💽 Installation
### Install from [PyPI](https://pypi.org/project/lapx/):
[](https://badge.fury.io/py/lapx)
[](https://pepy.tech/project/lapx)
[](https://pepy.tech/project/lapx)
```
pip install lapx
```
| **Pre-built Wheels** 🛞 | **Windows** ✅ | **Linux** ✅ | **macOS** ✅ |
|:---:|:---:|:---:|:---:|
| Python 3.7 | AMD64 | x86_64/aarch64 | x86_64 |
| Python 3.8 | AMD64 | x86_64/aarch64 | x86_64/arm64 |
| Python 3.9-3.13 ¹ | AMD64/ARM64 ² | x86_64/aarch64 | x86_64/arm64 |
<sup>¹ v0.5.10+ supports both numpy 1.x and 2.x for Python 3.8-3.13. 🆕 </sup><br>
<sup>² Windows ARM64 is experimental.</sup><br>
<details><summary>Other options</summary>
### Install from GitHub repo (Require C++ compiler):
```
pip install git+https://github.com/rathaROG/lapx.git
```
### Build and install (Require C++ compiler):
```
git clone https://github.com/rathaROG/lapx.git
cd lapx
pip install "setuptools>=67.8.0"
pip install wheel build
python -m build --wheel
cd dist
```
</details>
## 🧪 Usage
`lapx` is just the name for package distribution. The same as `lap`, use `import lap` to import; for example:
```
import lap
import numpy as np
print(lap.lapjv(np.random.rand(4, 5), extend_cost=True))
```
<details><summary>More details</summary>
### `cost, x, y = lap.lapjv(C)`
The function `lapjv(C)` returns the assignment cost `cost` and two arrays `x` and `y`. If cost matrix `C` has shape NxM, then `x` is a size-N array specifying to which column each row is assigned, and `y` is a size-M array specifying to which row each column is assigned. For example, an output of `x = [1, 0]` indicates that row 0 is assigned to column 1 and row 1 is assigned to column 0. Similarly, an output of `x = [2, 1, 0]` indicates that row 0 is assigned to column 2, row 1 is assigned to column 1, and row 2 is assigned to column 0.
Note that this function *does not* return the assignment matrix (as done by scipy's [`linear_sum_assignment`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.linear_sum_assignment.html) and lapsolver's [`solve dense`](https://github.com/cheind/py-lapsolver)). The assignment matrix can be constructed from `x` as follows:
```
A = np.zeros((N, M))
for i in range(N):
A[i, x[i]] = 1
```
Equivalently, we could construct the assignment matrix from `y`:
```
A = np.zeros((N, M))
for j in range(M):
A[y[j], j] = 1
```
Finally, note that the outputs are redundant: we can construct `x` from `y`, and vise versa:
```
x = [np.where(y == i)[0][0] for i in range(N)]
y = [np.where(x == j)[0][0] for j in range(M)]
```
</details>
</details>
Raw data
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"description": "\ud83c\udd95 December 1, 2024: The original [`lap`](https://github.com/gatagat/lap) and [`lapx`](https://github.com/rathaROG/lapx) have been merged.\n\n---\n\n<details><summary>See more</summary><br>\n\n[](https://github.com/rathaROG/lapx/actions/workflows/test_simple.yaml)\n[](https://github.com/rathaROG/lapx/actions/workflows/benchmark.yaml)\n[](https://github.com/rathaROG/lapx/actions/workflows/prepublish.yaml)\n[](https://github.com/rathaROG/lapx/actions/workflows/publish.yaml)\n\n# Linear Assignment Problem Solver\n\n`lapx` basically is Tomas Kazmar's [`gatagat/lap`](https://github.com/gatagat/lap) with support for all Windows/Linux/macOS and Python 3.7-3.13. \n\n<details><summary>About <code>lap</code></summary><br>\n\nTomas Kazmar's [`lap`](https://github.com/gatagat/lap) is a [linear assignment problem](https://en.wikipedia.org/wiki/Assignment_problem) solver using Jonker-Volgenant algorithm for dense LAPJV \u00b9 or sparse LAPMOD \u00b2 matrices. Both algorithms are implemented from scratch based solely on the papers \u00b9\u02d2\u00b2 and the public domain Pascal implementation provided by A. Volgenant \u00b3. The LAPMOD implementation seems to be faster than the LAPJV implementation for matrices with a side of more than ~5000 and with less than 50% finite coefficients.\n\n<sup>\u00b9 R. Jonker and A. Volgenant, \"A Shortest Augmenting Path Algorithm for Dense and Sparse Linear Assignment Problems\", Computing 38, 325-340 (1987) </sup><br>\n<sup>\u00b2 A. Volgenant, \"Linear and Semi-Assignment Problems: A Core Oriented Approach\", Computer Ops Res. 23, 917-932 (1996) </sup><br>\n<sup>\u00b3 http://www.assignmentproblems.com/LAPJV.htm | [[archive.org](https://web.archive.org/web/20220221010749/http://www.assignmentproblems.com/LAPJV.htm)] </sup><br>\n\n</details>\n\n## \ud83d\udcbd Installation\n\n### Install from [PyPI](https://pypi.org/project/lapx/):\n\n[](https://badge.fury.io/py/lapx)\n[](https://pepy.tech/project/lapx)\n[](https://pepy.tech/project/lapx)\n\n```\npip install lapx\n```\n\n| **Pre-built Wheels** \ud83d\udede | **Windows** \u2705 | **Linux** \u2705 | **macOS** \u2705 |\n|:---:|:---:|:---:|:---:|\n| Python 3.7 | AMD64 | x86_64/aarch64 | x86_64 |\n| Python 3.8 | AMD64 | x86_64/aarch64 | x86_64/arm64 |\n| Python 3.9-3.13 \u00b9 | AMD64/ARM64 \u00b2 | x86_64/aarch64 | x86_64/arm64 |\n\n<sup>\u00b9 v0.5.10+ supports both numpy 1.x and 2.x for Python 3.8-3.13. \ud83c\udd95 </sup><br>\n<sup>\u00b2 Windows ARM64 is experimental.</sup><br>\n\n<details><summary>Other options</summary>\n\n### Install from GitHub repo (Require C++ compiler):\n\n```\npip install git+https://github.com/rathaROG/lapx.git\n```\n\n### Build and install (Require C++ compiler):\n\n```\ngit clone https://github.com/rathaROG/lapx.git\ncd lapx\npip install \"setuptools>=67.8.0\"\npip install wheel build\npython -m build --wheel\ncd dist\n```\n\n</details>\n\n## \ud83e\uddea Usage\n\n`lapx` is just the name for package distribution. The same as `lap`, use `import lap` to import; for example:\n\n```\nimport lap\nimport numpy as np\nprint(lap.lapjv(np.random.rand(4, 5), extend_cost=True))\n```\n\n<details><summary>More details</summary>\n \n### `cost, x, y = lap.lapjv(C)`\n\nThe function `lapjv(C)` returns the assignment cost `cost` and two arrays `x` and `y`. If cost matrix `C` has shape NxM, then `x` is a size-N array specifying to which column each row is assigned, and `y` is a size-M array specifying to which row each column is assigned. For example, an output of `x = [1, 0]` indicates that row 0 is assigned to column 1 and row 1 is assigned to column 0. Similarly, an output of `x = [2, 1, 0]` indicates that row 0 is assigned to column 2, row 1 is assigned to column 1, and row 2 is assigned to column 0.\n\nNote that this function *does not* return the assignment matrix (as done by scipy's [`linear_sum_assignment`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.linear_sum_assignment.html) and lapsolver's [`solve dense`](https://github.com/cheind/py-lapsolver)). The assignment matrix can be constructed from `x` as follows:\n```\nA = np.zeros((N, M))\nfor i in range(N):\n A[i, x[i]] = 1\n```\n\nEquivalently, we could construct the assignment matrix from `y`:\n```\nA = np.zeros((N, M))\nfor j in range(M):\n A[y[j], j] = 1\n```\n\nFinally, note that the outputs are redundant: we can construct `x` from `y`, and vise versa:\n```\nx = [np.where(y == i)[0][0] for i in range(N)]\ny = [np.where(x == j)[0][0] for j in range(M)]\n```\n\n</details>\n\n</details>\n",
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