# lap
**Repository Path**: zhangming8/lap
## Basic Information
- **Project Name**: lap
- **Description**: https://github.com/gatagat/lap.git
- **Primary Language**: Unknown
- **License**: BSD-2-Clause
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No
## Statistics
- **Stars**: 0
- **Forks**: 0
- **Created**: 2021-12-02
- **Last Updated**: 2021-12-02
## Categories & Tags
**Categories**: Uncategorized
**Tags**: None
## README
[](https://travis-ci.org/gatagat/lap/)
[](https://ci.appveyor.com/project/gatagat/lap/history)
lap: Linear Assignment Problem solver
=====================================
**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].
In my tests 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.
[1] R. Jonker and A. Volgenant, "A Shortest Augmenting Path Algorithm for Dense
and Sparse Linear Assignment Problems", Computing 38, 325-340 (1987)
[2] A. Volgenant, "Linear and Semi-Assignment Problems: A Core Oriented
Approach", Computer Ops Res. 23, 917-932 (1996)
[3] http://www.assignmentproblems.com/LAPJV.htm
Installation
------------
#### Runtime dependencies
Running lap requires:
* Python (2.7, 3.7, 3.8, 3.9)
* NumPy (>=1.10.1)
In addition to above, running the tests requires:
* SciPy, pytest, pytest-timeout
#### Install using pip
You can install the latest release of lap from PyPI (recommended):
pip install lap
Alternatively, you can install lap directly from the repository:
pip install git+git://github.com/gatagat/lap.git
#### Install from source
1. Install a C++ compiler (e.g., g++)
2. Python headers (e.g., python-dev package on Debian/Ubuntu)
3. Install Cython (>=0.21)
4. Clone
git clone https://github.com/gatagat/lap.git
5. Under the root of the repo
python setup.py build
python setup.py install
Tested under Linux, OS X, Windows.
### Usage
```
cost, x, y = lap.lapjv(C)
```
The function `lapjv(C)` returns the assignment cost (`cost`) and two arrays, `x, y`. If cost matrix `C` has shape N x M, then `x` is a size-N array specifying to which column is 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-0.18.1/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)]
```
License
-------
Released under the 2-clause BSD license, see `LICENSE`.
Copyright (C) 2012-2017, Tomas Kazmar