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MathGroup Archive 2007

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Re: Eigenvalues in Mathematica 6.0.0 are SLOW

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75711] Re: Eigenvalues in Mathematica 6.0.0 are SLOW
  • From: Roman <rschmied at gmail.com>
  • Date: Wed, 9 May 2007 04:25:56 -0400 (EDT)
  • References: <f1pgkg$hqc$1@smc.vnet.net>

Update: With 64-bit Linux this is not the case, indeed you get a 30%
speedup from 5.2 to 6.0. Bobby gets a 20% speedup on WinXP from 5.2 to
6.0. Could it be that only the 32-bit PPC version is affected?

Roman.

On May 8, 11:41 am, Roman <rschm... at gmail.com> wrote:
> Hello all,
>
> 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 ;-)
>
> Fortunately, when you use sparse matrices and diagonalize with ARPACK
> (using "Method->Arnoldi"), there is no difference in evaluation time.
>
> Does anyone have an idea about what could have changed? Maybe some
> precision goal specifiers or so whose defaults have changed?
>
> Cheers!
> Roman.




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