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Re: Best way to do contractions (arbitrary Tables with a Sum)?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105962] Re: Best way to do contractions (arbitrary Tables with a Sum)?
  • From: "Norbert P." <bertapozar at gmail.com>
  • Date: Mon, 28 Dec 2009 04:56:29 -0500 (EST)
  • References: <hh72a3$kqa$1@smc.vnet.net>

On Dec 26, 11:28 pm, Erik Max Francis <m... at alcyone.com> wrote:
> I'm trying to do arbitrary contractions with tensors, which basically
> amounts to taking an (arbitrarily) large multi-dimensional array,
> iterating over the uncontracted indices, and then summing over the two
> (and only two) indices to be contracted.  If I were dealing with a
> specific case, I'd use Table with Sum:
>
>         Table[
>             Sum[
>                 a[[i1]][[i2]]...[[j]]...[[j]]...[[im]]],
>             {j, n}],
>         {i1, n}, {i2, n}, ... {im, n}]
>
> That is, iterating over the indices i1, i2, through im (all taking on
> values 1 through n) and summing over two of the indices (as j).  I'm
> trying to figure out the most elegant way to do this in Mathematica and
> I'm only coming up with ugly solutions which are basically arbitrary
> reimplementations of Table-like functionality.
>
> I figure there's probably some more elegant way to approach this.
> Anyone have any ideas?
>
> --
> Erik Max Francis && m... at alcyone.com &&http://www.alcyone.com/max/
>   San Jose, CA, USA && 37 18 N 121 57 W && AIM/Y!M/Skype erikmaxfrancis
>    Without love, benevolence becomes egotism.
>     -- Dr. Martin Luther King, Jr.

Hi,

not sure if this is the best way, but you don't need to use Table,
use

Sum[a[[All, ..., All, j, All, ..., All, j, All, ...]], {j,n}]

But it is still a Table-like functionality...

Norbert


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