After the community bonding period and before starting today the coding period, I will briefly list the transformation that has undergone my initial proposal: from just implementing new algorithms and then add them to GNU Octave, to various modifications of GNU Octave itself so that Higham's toolboxes run smoothly and in the end add the new algorithms. Sticking to what I said before, I expect to be doing the modifications (e.g. new bugs, patches, toolboxes) most of the first half of the coding period. From there we aim to go as far as we can about matrix functions, I will do so. These changes are noted in the new time line.
During the community bonding period I have been setting up, you might have seen me at freenode. I have been becoming more and more acquainted with GNU Octave, and found out that the gallery function was broken, with unassigned variables and missing auxiliary functions. This function will prove useful to test matrix functions, because the eigenvalue decomposition strategy (if $A=VDV^{-1}$ then $f\left(A\right) = V f\left( D \right) V^{-1}$) yields a big error using the ill conditioned matrices gallery provides. Another example are the useful positive definite matrices that have a computable principal p-th root. gallery is indeed interesting for anyone looking for a matrix with a special characteristic to test an edge case of a function.
Besides, I also have had the chance to see a plethora of Matlab-style short circuit operators, looping with infinite ranges, and even weird undocumented functions like superiorfloat (it returns either "single" or "double" strings depending on the input). What let Carnë to point me to Undocumented Matlab blog, where they document its unsupported hidden underbelly. More quirks (and their solutions) on the next post.
A final thank goes to The Project in general and my mentors (Carnë and Mario) in particular for this opportunity. I hope everyone pleasantly codes their summer away!
