Click here to download a matlab routine to create the bertini input and start file (called constructinputfiles.m). In addition, there is a matlab routine (measurelengths.m) to parse the Bertini output file (nonsingular_solutions), and compute the max-length-vector line of best fit, as in the paper.
Please visit here to download the latest version of Bertini for numerical predictor-corrector methods, as in the paper.
In MLV_supplementary.zip, you will find a series of MATLAB scripts that should be run in one of your directories. Please take care to read the descriptions of the scripts, especially if you want to run your own matrices.
In addition, there are two folders 'smallexample' and 'largeexample' which store the 'input', 'start', and relevant '.mat' files for the two examples in the paper. For each of these, the '.mat' files are needed for the script 'measurelengths.m' to compute the max-length-vector line of best fit.
To summarize how to run with random matrices:
1) First set up the top matter in constructinputfiles.m. (i.e. ambient dimension, subspace dimensions)
2) After running constructinputfiles.m there will be 4 relevant files: input, start, orthomatrices.mat, and relevantdata.mat.
3) Use Bertini with 'input' and 'start'. Bertini will produce an output file 'nonsingular_solutions'. Make sure the proper configurations are set. See [BHSW13] for a reference to relevant configurations.
4) Copy 'nonsingular_solutions' back to the matlab directory.
5) Run measurelengths.m using 'nonsingular_solutions', 'orthomatrices.mat' and 'relevantdata.mat'.
See the comments in 'constructinputfiles.m' on how to modify the code to support user-defined matrices.