[Gretl-devel] Re: qrdecomp with column pivoting?

Am 04.06.2022 um 15:51 schrieb Sven Schreiber: > Am 04.06.2022 um 13:11 schrieb Riccardo (Jack) Lucchetti: >> On Fri, 3 Jun 2022, Cottrell, Allin wrote: >>> columns the execution time is not that different. Note: we currently >>> assess rank using regular QR, by counting the R elements greater than >>> some specified "tiny" value. >> >> in Hansl: >> >> <hansl> >> R = {} >> Q = qrdecomp(mnormal(4)~zeros(4)~mnormal(4) , &R) >> scalar r = sumc(abs(diag(R)).>1.0e-12) >> print r >> </hansl> > > OK, thanks, that's what I thought. Hm, but plain QR is not rank-revealing in general, that's why the thing with column-pivoting exists. Trivial example: <hansl> R = {} A = zeros(4,2) ~ I(4,2) print A Q = qrdecomp(A , &R) print rank(A) # correct: 2 scalar r = sumc(abs(diag(R)).>1.0e-12) print r # wrong: 0 </hansl> Now, I guess that in your internal usage this is quite unlikely to happen, but still, if you don't want to use the SVD for that --and I presume it's because of the computational expenses-- then maybe there's a role for the pivoted QR thing?