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Re: Eigenvalues in Mathematica 6.0.0 are SLOW

• To: mathgroup at smc.vnet.net
• Subject: [mg75706] Re: [mg75648] Eigenvalues in Mathematica 6.0.0 are SLOW
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Wed, 9 May 2007 04:23:10 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200705080941.FAA18244@smc.vnet.net>
• Reply-to: murray at math.umass.edu

That dramatic difference is not invariant across platforms.  On my 
32-bit Windows XP PC, and in each case with a fresh kernel:

$Version: 6.0 for Microsoft Windows (32-bit) (April 20, 2007)
Timings: 2.062, 1.625, 1.594, 1.563, 1.672
Total: 8.516

$Version: 5.2 for Microsoft Windows (June 20, 2005)
Timings: 1.656 Second, 1.86 Second, 1.562 Second, 1.579 Second, 1.531 Second
Total: 8.188

Roman wrote:
> 
> I just installed Mathematica 6.0.0 on my old PowerBook to try it out,
> before upgrading my work horse machine. Doing a few benchmarks, I
> noticed that the Eigenvalues command has slowed down significantly,
> although the help on Eigenvalues says "Last modified in 5".
> 
> In particular, compare this code for repeatedly computing the
> eigenvalues of a full 1000x1000 random symmetric matrix:
> 
> A[n_] := (# + Transpose[#]) &[Table[Random[], {n}, {n}]]
> With[{n = 1000, p = 5},
>  Table[M = A[n]; Timing[Eigenvalues[M];][[1]], {p}]]
> 
> Using $Version = "5.2 for Mac OS X (February 24, 2006)" I get
> 
> {5.38169 Second, 5.38112 Second, 5.39718 Second, 5.38392 Second,
>    5.38465 Second}
> 
> But using $Version = "6.0 for Mac OS X PowerPC (32-bit) (April 20,
> 2007)" I get
> 
> {32.2618, 32.2137, 31.7375, 32.9869, 31.8762}
> 
> which is about 6 times slower! (and has no units ;-)

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

• Follow-Ups:
  • Re: Re: Eigenvalues in Mathematica 6.0.0 are
    • From: Murray Eisenberg <murray@math.umass.edu>

• References:
  • Eigenvalues in Mathematica 6.0.0 are SLOW
    • From: Roman <rschmied@gmail.com>