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

**References**:**Re: Mathematica v5 versus v6***From:*Jean-Marc Gulliet <jeanmarc.gulliet@gmail.com>