A MATLAB software for SVLS algorithm
Authors: Avishai Wagner and Or Zuk

The software package solves the problem of low-rank matrix recovery from rows and columns affine measurements 
using the Singular-Value-Least-Squares (SVLS) algorithm.

Installation:
=============

Download the SVLS directory from https://github.com/avishaiwa/SVLS. 
Use the "Download ZIP" button on the right hand side of the page. 
Once done, uncompress it, and follow the introductory files listed below.

You will have to change the path variable to your SVLS location. For example, if SVLS was saved under your home directory then enter the following in each introductory file: 
userDir = '~/SVLS/';


Dependencies: 
=============
The SVLS algorithm uses the PROPACKmod package for computing fast singular value decomposition. You can download PROPACKmod from here:  http://sun.stanford.edu/~rmunk/PROPACK/

Some of the files in the Simulations directory use other packages, since we compare SVLS to other algorithms. 
To be able to run all of these comparisons, you will have to download and install the following packages: 

1. optSpace, from : http://web.engr.illinois.edu/~swoh/software/optspace/code.html

2. SVT, from : http://svt.stanford.edu/code.html

3. APGL, from :http://www.math.nus.edu.sg/~mattohkc/NNLS.html

4. The package uses a few Matlab commands available in latest versions: isrow, strsplit

5. The Simulations directory also uses the MatUtils package with different useful basic functions, available from here: 
https://github.com/orzuk/MatUtils

Getting Started: 
================

An example running the SVLS algorithm is available in the file: test_SVLS

Directories: 
=============

(*) algorithms_SVLS - recovery algorithms, including the SVLS algorithm

(*) simulations - Scripts for running and testing the package

(*) sampleMatrix - functions for sampling both the unknown matrix and the measurements matrices under different models 

(*) result_pic - directory with figures generating during the running of functions

(*) result_vec - simulation results saved to files 

(*) fig_paper - the figures present in the paper [1].

(*) Additional directories contains needed packages and other algorithms for comparison 


Files:
======
SVLS - implementation of the SVLS  algorithm 

SVLS_p - implementation of the SVLS_p  algorithm 

Symmetric_SVLS - implement algorithm SVLS for symmetric matrices

gradient_descent - minimize the loss function (||Ar(X)-Br||_F)^2+(||(X)Ac-Bc||_F)^2

Symmetric_gradientDescent - minimize the loss function (||Ar(X)-Br||_F)^2

AffineMatrixRecovery - a 'Master' recovery function, recovers a matrix from affine measurements by calling the appropriate algorithm

RRMSE - calculating RRMSE

samp_matrix - sample a random low-rank matrix 

All_Simulations - Generate random matrices and random measurements, estimate the original matrix using 
recovery algorithms and evaluate results 

make_SVLS_paper_figures - a script for producing and plotting all the figures shown in paper [1].


Acknowledgment:
===============

SVLS was developed by Avishai Wagner and Or Zuk, as part of work on the paper:

[1] Low-Rank Matrix Recovery from Row-and-Column Affine Measurements", A. Wagner and O. Zuk, ICML 2015

Please cite the above paper if using the package.

For support, any questions or comments, please contact:

Avishai Wagner: avishaiwa@gmail.com

Or Zuk: or.zuk@mail.huji.ac.il