A J model of the QR decomposition can be found in http://code.jsoftware.com/wiki/Essays/QR_Decomposition
> He builded better than he knew: it relies on +/ .* for most of the numeric work. (Ahem) actually I knew. It was part of my M.Sc. thesis and is another lemma which shows that %.x has the same order of complexity as +/ .* , at the time O(n*2^.7) (better than the conventional O(n*3)), now down to O(n*2.3728639) according to Wikipedia. The algorithm is also good answer to claims that QR and other matrix decompositions are inherently loopy. See Hui & Iverson, _A Note on Programming Style_, Vector, volume 12, number 13, 1996-01. On Sun, Sep 8, 2019 at 1:14 PM Henry Rich <henryhr...@gmail.com> wrote: > For years Joey Tuttle has used the performance of (%. y) as a simple > measure of the performance of J releases. It has improved pretty steadily. > > This surprised me, because I know where the gaussian-elimination code > is, and that code doesn't do much except C loops that do add and > subtract. I didn't see how improvements to the JE would have any effect > on (%. y). Not wanting to mess up a good story, I kept my doubts to > myself. > > Finally I understand. The code I had been looking at is used only for > rational matrices. The code for general (%. y) is a lovely little > recursive QR decomposition that does lots of memory allocation and calls > to internal J arithmetic functions. In fact, it's a pretty good > exercise of the computational side of the system. It's quite short but > uses general utilities so that it works on all fixed-precision numeric > types. Bravo to Roger. He builded better than he knew: it relies on +/ > . * for most of the numeric work, and that code has now been polished so > well that it is the most efficient code in the system. > > Long live Joey's benchmark! > > Henry Rich > > --- > This email has been checked for viruses by AVG. > https://www.avg.com > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
