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Re: Flattening a hypermatrix into an ordinary matrix

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126717] Re: Flattening a hypermatrix into an ordinary matrix
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Sat, 2 Jun 2012 05:42:51 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

On 6/1/12 at 5:19 AM, carlos 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

<snip>

>but is there a more elegant way using Flatten?

Better would be to use ArrayFlatten which is specifically
designed for this task, i.e.,

In[6]:= ArrayFlatten[a]

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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