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Re: Where's the Speed?
Along the same line: I have found the optimization routine "FindMinimum" to be far less reliable and slower than for example the Excel Solver; running repeated trials with quasi-convex functions, FindMinimum slowly converged to the Minima and generally stopped at points that were inferior solutions to those found by Excel's Solver (one would assume that Mathematica is more cutting edge in that respect). However, Mathematica does come in extemely handy when it comes to proving convexity issues..... I bought and installed Mathematica 4.0 due to the hype: I have M3 and M4 - I run 3 on a PPro200, NT4 in the office and Mathematica 4 on a PII 400, W98 at home. Speedwise I have not noticed any significant differences, other than those attributable to the clockspeed difference. But perhaps I didn't use the routines that were improved. The positive thing I did not was that M4 is much more stable (with M3.0 I frequently run into printing problems or problems with the notebook regarding the GUI). I do have to say that it has been only a few days that I have been able to work with M4, so there is the possibility that my impression of M4 will change - in dubio pro reo. All in all M4 does make a very good impression - and got an extremely favourable review by Dr. Kuska of the German computer magazine Ct (<http://www.ix.de/ct/inhverz/search.shtml?T=mathematica> they do thorough analysis of software and hardware - not just the handwaving of so many other mags). I guess I will buy M5 also, when it comes out - Mathematica is a great product after all; but it would be nice if Wolfram would NOT follow the Apple/MS way of producing lots of noise for things that aren't really that much of an improvement. Marc Sachon Industrial Engineering Stanford University "Kevin J. McCann" wrote: > I have read and heard a lot of hype about Mathematica 4.0 > > "featuring a > New Generation of > Fast Numerics" > > e.g. on www.wri.com . > > However, in the real world it is hard to find anything to get excited about. > I have had several disappointing results from 4.0, here are the latest: > > On a P450/NT I ran a very simple Crank-Nicholson integration of a > one-dimensional quantum free-particle wave-packet with x-dimensioned to 1001 > points and time to 401 points - no error checks or adaptive stepsize, just > plug-and-chug. Runtime under 4.0 was 501 seconds, 3.0 was 480 seconds, but > who's quibbling; however, in FORTRAN this ran in 8 seconds. I don't even > consider this to be "fast numerics", but 501 seconds sure isn't. I would > like to know where all this speed is so I can use some of it, or am I > missing something? > > When I ran the FORTRAN code and then read it into Mathematica, it still was faster > than the Mathematica code alone, although the ReadList I used on the ASCII > file did take some time. When I upped the dimensions to 2001 x 1001, the > FORTRAN ran in about 40 s - most of this is for the output; however, when I > tried to read it in to Mathematica, it took forever, and on the subsequent plot it > bombed the Kernel. I then made the mistake of saving the NB which managed > to acquire an error so that I can't open it anymore - 6 Mb of useless NB! > > -- > > Kevin J. McCann > Johns Hopkins University APL