Re: How to "unflatten"?
- To: mathgroup at smc.vnet.net
- Subject: [mg83909] Re: How to "unflatten"?
- From: dh <dh at metrohm.ch>
- Date: Tue, 4 Dec 2007 04:24:21 -0500 (EST)
- References: <fj0rlv$pff$1@smc.vnet.net>
Hi Hauke,
here is an example. We create a 2x2x2x2 tensor,destroy its structure and
restructure it again:
t1=Array[a,{2,2,2,2}]
t=Flatten[t1,3]
t2=Nest[Partition[#,2]&,t,3]
t1==t2
Further, we contract the first with the last index:
Sum[arr[[i, All, All, i]], {i, 2}]
hope this helps, Daniel
Hauke Reddmann wrote:
> Excuse a complete noob's question:
>
> I do calculations with S matrices and need to convert
> the tensor form Sab_cd (which would be e.g. the nested
> list {{{{,},{,}},{{,},{,}}},{{{,},{,}},{{,},{,}}}} -
> I omitted variables a1-a16, since only the structure
> of the list, a 2*2*2*2 nest, is relevant) into a
> matrix Mab_cd: {{,,,},{,,,},{,,,},{,,,}}. That is trivial:
> Mab_cd=Partition[Flatten[Sab_cd],4].
>
> But how to reverse the process? Of course even I already
> can write a quadruple loop S[[,,,]]=M[,] with direct
> handover of elements, but that is so unelegant, especially
> as I have to apply this a hundred times in the computation
> (and can't write subroutines yet, I'm a noob after all :-)
>
> Question 2: I could skip the whole converting if I knew
> how to do an Einstein sum over two indices inside a tensor:
> Sab_cd -> Sab_ca -> sum(a=1,n,Sab_ca) -> Tb_c.
> At the moment I do this whith "blocking" multiple indices
> into a matrix and then do the matrix product, but this is
> more a clever hack.