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Re: Partition a list based on columns

  • To: mathgroup at smc.vnet.net
  • Subject: [mg119683] Re: Partition a list based on columns
  • From: Ray Koopman <koopman at sfu.ca>
  • Date: Fri, 17 Jun 2011 00:09:45 -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
>
> Thanks in advance!

This will give an r x c matrix whose elements are
the integers 1...r*c in the positions you asked for:

m[r_,c_] := With[{d = Which[
  r < c-1, Join[Range[ r ],Table[r,{c-2-r}],Range[ r ,1,-1]],
  r > c-1, Join[Range[c-1],Table[c-1,{r-c}],Range[c-1,1,-1]],
   True  , Join[Range[c-2],                 Range[c-1,1,-1]]]},
  Partition[FoldList[Plus,0,d],c,1] + Range@r]

m[3,5] //TableForm

 1  2  4  7 10
 3  5  8 11 13
 6  9 12 14 15


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