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.

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