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MathGroup Archive 2007

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Re: Re: Mathematica v5 versus v6

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80117] Re: [mg80075] Re: Mathematica v5 versus v6
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Mon, 13 Aug 2007 04:28:36 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <f9jjnc$2i8$1@smc.vnet.net> <200708121110.HAA27500@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

Just what would "dense" mean in the case of an 8 x 8 matrix, which is 
the case raised?

Jean-Marc Gulliet wrote:
> Jon wrote:
>> Hi
>>
>> I have found that there are some simple problems which can be done quickly in v5 but the new v6 seemingly cannot.
>>
>> For example I am presently doing some work which requires the calculation of the Rank of an 8 by 8 matrix. Using my notebook, 1Gb RAM and 1.73GHz with v5.1, I get the answer in a few seconds. When I installed v6 and ran the same nb file I never got an answer even after running for 1 hour.
>>
>> Is there a bug in v6?
>>
>> If others are also running v6 I would be interested in getting in touch to see if other users have the same experience. If you are running on a 64 bit machine I would really like to see if that solves the problem and can give  an answer with v6.
>>
>> Any comments are very welcome!
> 
> More input is needed. We can assume that you are using dense matrices, 
> but what about the precision of their entries? Do you use exact 
> arithmetic, arbitrary precision, or machine precision? Do you use 
> built-in function or some code of your own? Can you provide an example?
> 
> On my Wintel system (Pentium 4HT 2.6 MHz, 1 Go physical RAM), the 
> built-in function *MatrixRank* is fast enough to compute the rank of a 
> random 100 by 100 matrix in a second or so for machine-precision entries 
> on both versions. For matrices with infinite-precision entries, 
> Mathematica 6 improves the performances by a factor of two or so.
> 
> In[1]:=
> $HistoryLength = 0;
> $Version
> 
> Out[2]=
> 5.2 for Microsoft Windows (June 20, 2005)
> 
> In[3]:=
> m = Table[Random[Real, {$MinMachineNumber, $MaxMachineNumber}], {100},
>      {100}];
> Timing[MatrixRank[m]]
> 
> Out[4]=
> {0.907 Second,100}
> 
> In[5]:=
> m = Table[Random[Integer, {-10000, 10000}], {100}, {100}];
>    Timing[MatrixRank[m]]
> 
> Out[6]=
> {2.047 Second,100}
> 
> In[7]:= $HistoryLength = 0;
> $Version
> 
> Out[8]= "6.0 for Microsoft Windows (32-bit) (June 19, 2007)"
> 
> In[9]:= m =
>    RandomReal[{$MinMachineNumber, $MaxMachineNumber}, {100, 100}];
> Timing[MatrixRank[m]]
> 
> Out[10]= {1.094, 100}
> 
> In[11]:= m = RandomInteger[{-10000, 10000}, {100, 100}];
> Timing[MatrixRank[m]]
> 
> Out[12]= {1.187, 100}
> 

-- 
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


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