Re: Matrix multiplication speed up

*To*: mathgroup at smc.vnet.net*Subject*: [mg83088] Re: Matrix multiplication speed up*From*: Yaroslav Bulatov <yaroslavvb at gmail.com>*Date*: Sat, 10 Nov 2007 03:41:44 -0500 (EST)*References*: <fgs87d$3uh$1@smc.vnet.net><fh1co5$cus$1@smc.vnet.net>

One issue is that Mathematica automatically simplifies/rearranges certain expressions (like Times), so defining a custom multiplication operation (like dh's response) is one solution. If you just want index sets, perhaps you could do the following: Compute product of 3 2x2 matrices m = 3; n = 2; mats = Array[x[#1][#2, #3] &, {m, n, n}]; product = Dot @@ mats; Replace all heads with List, calling Expand to undo automatic factoring tuples = Apply[List, product[[1, 1]] // Expand, {0, 2}]; To get into format you specified, merge the last 2 levels of the tree indices = Flatten[tuples, {{1}, {2, 3}}] You should get {{1, 1, 1, 1, 1, 1}, {1, 2, 2, 1, 1, 1}, {1, 1, 1, 2, 2, 1}, {1, 2, 2, 2, 2, 1}} A question for mathgroup -- Mathematica will automatically factor equations involving Plus/Times. Why doesn't clearing definitions for Plus/Times prevent this? Is there anything I can do to override the default handling of these operators? Yaroslav On Nov 9, 2:28 am, Frank Brand <frank.br... at t-online.de> wrote: > Hi all, > > thanks for responding! > I should be more precise in what I'm looking for. > What I'm especially interested in is the preserved order of FACTORS in > the sums of the components of the resulting product of the two matrices, > so e.g. > I'd like to have a[2,1]*a[27,3]*a[1,5] instead of a[1,5]*a[2,1]*a[27,3] > (Mathematica's natural order), because I'm interested in the resulting > index sets like {2, 1, 27, 3, 1, 5}. > Do you have any idea how to realize this? > > Greetings > Frank