[Gretl-devel] Re: qrdecomp with column pivoting?
Am 06.06.2022 um 23:56 schrieb Cottrell, Allin:
On Mon, Jun 6, 2022 at 5:24 PM Sven Schreiber
<svetosch(a)gmx.net> wrote:
>
> OTOH, I ran some very crude and simple speed comparisons between
> qrdecomp with and without pivoting (on Linux, current git), and
> depending on the input the advantage could go either way it seemed,
> which I found a little surprising. But then I also ran SVD on the same
> input (and also grabbing the optional output), and that went even
> faster, so now I'm puzzled... isn't SVD supposed to be the most
> expensive thing of the candidates? What am I missing?
Are you doing enough replications to get good resolution from the timer?
Here's what I see for a 100 x 10 random matrix with 10,000 replications:
SVD 0.324311s
QR 0.094924s
QRP 0.114874s
I think I had 500x12 or so. But interesting that QRP is almost as fast
as QR.
But as I mentioned earlier, big m favors SVD. Here's 800 x 20
with
1000 replications.
SVD 0.137257s
QR 0.231528s
QRP 0.248974s
Apparently I missed that, this is something I was completely unaware of.
I thought that one tries to avoid SVD because of the costs. But here I
see no costs!? For mols() for example, SVD has to be forced explicitly.
OK, you could say that at least in macro T=100 is more common than
T=800. But maybe then a heuristic could help, so SVD is used for some
large enough T (or T-K, or T/K). (Only as a fallback from Cholesky, of
course.)
For the dropcoll() functions and related ones that currently use the R
diagonal internally, I guess a similar argument applies. The cost of QRP
seems negligible, and SVD takes over at some point. The advantage of
plain QR seems to be limited.
thanks
sven