Code for solving the standard integer least squares problem$$ \min_{\boldsymbol{x} \in \mathbb{Z}^n}\|\boldsymbol{y}-\boldsymbol{B}\boldsymbol{x}\|_2, $$ where \(\boldsymbol{B}\) is a real matrix with full column rank, and \(\boldsymbol{y}\) is a real vector (December 2022):

• sils.m for a user who wants to view the source code.
• sils.zip (includes three files) for a user who wants to run the code faster (sub-functions are in MEX form)

Contributors: Xiao-Wen Chang, Tianchi Ma, Xiangyu Ren, Xiaohu Xie, Tianyang Zhou

If you use this package in your research work to be published, please include explicit mention of the package in your publication:

X.-W. Chang. MILES: MATLAB package for solving mixed integer least squares problems, School of Computer Science, McGill University, http://www.cs.mcgill.ca/~chang/software/MILES.php. Last updated: December 2022

The routines use the algorithms proposed in the following papers:

[1] X. Xie, X.-W. Chang, and M. Al Borno. Partial LLL reduction, Proceedings of IEEE GLOBECOM 2011, 5 pages.

[2] X.-W. Chang, X. Yang, and T. Zhou. MLAMBDA: A Modified LAMBDA Method for Integer Least-squares Estimation, Journal of Geodesy, 79 (2005), pp. 552-565.

[3] A. Ghasemmehdi and E. Agrell. Faster Recursions in Sphere Decoding, IEEE Transactions on Information Theory, 57 (2011), pp. 3530-3536.