[Gretl-devel] Re: speed of (m)ols with svd

On Fri, 27 Dec 2019, Allin Cottrell wrote: > It appears to be a free lunch, pretty much. The speed-up is significant but > not huge, something like 30 percent. That's now in git. But the primary > source of difference between the gretl and numpy times that you quote must > be due to the respective Blas/Lapack implementations. > > Here's what I'm seeing on a fairly elderly PC running Fedora with gretl > linked against openblas. I reduced the number of replications to 2000 > (impatience) and created a baseline of accuracy by running mpols with > GRETL_MP_BITS=4096. > > # gretl svd on, using DGELSS > gretl (mols): 8.43043 seconds > maxerr (gretl) = 0.000000000000007 > python (linalg.lstsq): 5.63282 seconds > maxerr (python) = 0.000000000000007 > > # gretl svd on, using DGELSD > gretl (mols): 6.00157 seconds > maxerr (gretl) = 0.000000000000007 > python (linalg.lstsq): 5.62002 seconds > maxerr (python) = 0.000000000000007 > > # gretl svd off (Cholesky) > gretl (mols): 0.396789 seconds > maxerr (gretl) = 0.000000000000005 > python (linalg.lstsq): 5.62659 seconds > maxerr (python) = 0.000000000000007 > >> From this, three points are apparent: (1) as stated above, DGELSD is > close to 30% faster than DGELSS; (2) numpy is a little faster than us on > SVD; and (3) you get just as accurate results an order of magnitude faster > via Cholesky (the mols default) provided the regressors (as here) are not > horribly collinear. Hm, I'm seeing something weird here: on my home laptop (an 8-core, 4 real cpus machine) I'm getting results that are fairly consistent with yours. On the other hand, trying the same on my work PC (a 12-core box) I'm seeing this: ---------------------------------------------- Old code (with set svd on): ---------------------------------------------- gretl (mols): 7.09208 seconds maxerr (gretl) = 0.000000000000010 python (linalg.lstsq): 3.92083 seconds maxerr (numpy) = 0.000000000000008 ---------------------------------------------- New code (with set svd on): ---------------------------------------------- gretl (mols): 3.79993 seconds maxerr (gretl) = 0.000000000000008 python (linalg.lstsq): 3.89591 seconds ---------------------------------------------- New code (with set svd on):

---------------------------------------------- gretl (mols): 120.903 seconds maxerr (gretl) = 0.000000000000005 python (linalg.lstsq): 5.63783 seconds It looks as if turning svd off makes mols a good deal slower (by the way: all 12 cpus go at 100% for the whole time). I have no time now to check why this happens, but I'll throw a idea in: perhaps, for some reason, I'm getting the QR decomposition instead of Cholesky?