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Flattening a hypermatrix into an ordinary matrix

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126710] Flattening a hypermatrix into an ordinary matrix
  • From: carlos at colorado.edu
  • Date: Fri, 1 Jun 2012 05:19:24 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

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.



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