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Re: Re: Eigenvalues in Mathematica 6.0.0 are

• To: mathgroup at smc.vnet.net
• Subject: [mg75782] Re: [mg75706] Re: [mg75648] Eigenvalues in Mathematica 6.0.0 are
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Thu, 10 May 2007 05:19:52 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200705080941.FAA18244@smc.vnet.net> <200705090823.EAA11678@smc.vnet.net>
• Reply-to: murray at math.umass.edu

Oops: I forgot to change to RandomReal for 6.0.  So I ran that again and 
now get timings:

   $Version: 5.2 for Microsoft Windows (June 20, 2005)
   Timings: 1.562, 2.079, 1.547, 1.656, 1.531
   Total: 8.375

   $Version: 6.0 for Microsoft Windows (32-bit) (April 20, 2007)
   Timings: 1.61,1.641,1.656,1.625,1.562
   Total:  8.094

So this run 6.0 was about 3% faster than 5.2.

Murray Eisenberg wrote:
> 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

• References:
  • Eigenvalues in Mathematica 6.0.0 are SLOW
    • From: Roman <rschmied@gmail.com>
  • Re: Eigenvalues in Mathematica 6.0.0 are SLOW
    • From: Murray Eisenberg <murray@math.umass.edu>