Re: Flattening a hypermatrix into an ordinary matrix

• To: mathgroup at smc.vnet.net
• Subject: [mg126728] Re: Flattening a hypermatrix into an ordinary matrix
• From: Ray Koopman <koopman at sfu.ca>
• Date: Sat, 2 Jun 2012 05:46:40 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jqa1j4\$bjd\$1@smc.vnet.net>

```On Jun 1, 2:21 am, car... at colorado.edu wrote:
> I have an n x n hypermatrix, the entries of which are m x m blocks.
> For example A below (m=3, n=2):
>
> A11={{B11,B12,B13},{B21,B22,B23},{B31,B32,B33}};
> A12={{C11,C12,C13},{C21,C22,C23},{C31,C32,C33}};
> A21={{D11,D12,D13},{D21,D22,D23},{D31,D32,D33}};
> A22={{E11,E12,E13},{E21,E22,E23},{E31,E32,E33}};
> A={{ A11,A12},{A21,A22}};
>
> I want to convert this to an ordinary n*m x n*m matrix.
> For the example I want A to become
>
>  {{B11,B12,B13,C11,C12,C13},{B21,B22,B23,C21,C22,C23},
>   {B31,B32,B33,C31,C32,C33},{D11,D12,D13,E11,E12,E13},
>   {D21,D22,D23,E21,E22,E23},{D31,D32,D33,E31,E32,E33}}
>
> This can be easily done with C style loops as
>
> AA=Table[0,{m*n},{m*n}];
> For [i=1,i<=n,i++, For[j=1,j<=n,j++,
>     For [k=1,k<=m,k++, For [l=1,l<=m,l++,
>          AA[[m*(i-1)+k,m*(j-1)+l]]=A[[i,j,k,l]]
>          ]]]];
>
> but is there a more elegant way using Flatten?
> (Flatten[A,1] doesnt do it.)  It should work also for blocks
> of varying size for future use.

In[1]:=
A11 = {{B11,B12,B13},{B21,B22,B23},{B31,B32,B33}};
A12 = {{C11,C12,C13},{C21,C22,C23},{C31,C32,C33}};
A21 = {{D11,D12,D13},{D21,D22,D23},{D31,D32,D33}};
A22 = {{E11,E12,E13},{E21,E22,E23},{E31,E32,E33}};
A   = {{ A11,A12},{A21,A22}};

In[6]:=
Flatten[Map[Flatten,Transpose[A,{1,3,2,4}],{2}],1]

Out[6]=
{{B11,B12,B13,C11,C12,C13},{B21,B22,B23,C21,C22,C23},
{B31,B32,B33,C31,C32,C33},{D11,D12,D13,E11,E12,E13},
{D21,D22,D23,E21,E22,E23},{D31,D32,D33,E31,E32,E33}}

```

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