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MathGroup Archive 2011

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Re: Partition a list based on columns

  • To: mathgroup at smc.vnet.net
  • Subject: [mg119664] Re: Partition a list based on columns
  • From: Ray Koopman <koopman at sfu.ca>
  • Date: Thu, 16 Jun 2011 06:23:23 -0400 (EDT)
  • References: <itcdai$d13$1@smc.vnet.net>

On Jun 16, 1:02 am, StatsMath <stats.ma... at gmail.com> wrote:
> [...]
>
> What would be a good way to line up elements in a list in a diagonal
> fashion, for ex: from Range[9] want to create the follwing matrix:
>
> 1 2 4
> 3 5 7
> 6 8 9

This will give a square matrix of order n whose elements are
the integers 1...n^2 in the positions you asked for:

m[n_] := With[{b=FoldList[Plus,0,Join[Range[n-1],Range[n-1,1,-1]]]},
              Table[Take[b,{i,i+n-1}]+i,{i,n}]]
m[5]

{{ 1,  2,  4,  7, 11},
 { 3,  5,  8, 12, 16},
 { 6,  9, 13, 17, 20},
 {10, 14, 18, 21, 23},
 {15, 19, 22, 24, 25}}


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