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Re: ZigZag matrix rearrange

• To: mathgroup at smc.vnet.net
• Subject: [mg99085] Re: [mg99055] ZigZag matrix rearrange
• From: danl at wolfram.com
• Date: Sun, 26 Apr 2009 01:40:29 -0400 (EDT)
• References: <200904250851.EAA14256@smc.vnet.net>

> Dear community,
> I'm trying to rearrange 8 x 8 matrix of numbers in ZigZag manner (as it is
> used in JPEG comprimation algorithm http://en.wikipedia.org/wiki/Jpeg).
>
> I have created function which does it without problems, but it does it "by
> hand" and it seems to me, that it could be done by some more elegant
> algorithm.
> Does somebody have any idea, how to do it more elegantly?
>
> My attempt:
> zigzag[t_] := {
>    t[[1, 1]],
>    t[[1, 2]], t[[2, 1]],
>    t[[3, 1]], t[[2, 2]], t[[1, 3]],
>    t[[1, 4]], t[[2, 3]], t[[3, 2]], t[[4, 1]],
>    t[[5, 1]], t[[4, 2]], t[[3, 3]], t[[2, 4]], t[[1, 5]],
>    t[[1, 6]], t[[2, 5]], t[[3, 4]], t[[4, 3]], t[[5, 2]], t[[6, 1]],
>    t[[7, 1]], t[[6, 2]], t[[5, 3]], t[[4, 4]], t[[3, 5]], t[[2, 6]],
>    t[[1, 7]],
>    t[[1, 8]], t[[2, 7]], t[[3, 6]], t[[4, 5]], t[[5, 4]], t[[6, 3]],
>    t[[7, 2]], t[[8, 1]],
>    t[[8, 2]], t[[7, 3]], t[[6, 4]], t[[5, 5]], t[[4, 6]], t[[3, 7]],
>    t[[2, 8]],
>    t[[3, 8]], t[[4, 7]], t[[5, 6]], t[[6, 5]], t[[7, 4]], t[[8, 3]],
>    t[[8, 4]], t[[7, 5]], t[[6, 6]], t[[5, 7]], t[[4, 8]],
>    t[[5, 8]], t[[6, 7]], t[[7, 6]], t[[8, 5]],
>    t[[8, 6]], t[[7, 7]], t[[6, 8]],
>    t[[7, 8]], t[[8, 7]],
>    t[[8, 8]]};
>
> Thanks for any idea
>
> Jakub

Can be done algorithmically using Reverse and Diagonal.

mat = Array[t, {8, 8}];

Table[If[EvenQ[j], Identity, Reverse][
  Diagonal[Reverse[mat, 2], j]], {j,
  Length[mat] - 1, -Length[mat] + 1, -1}]

{{t[1, 1]}, {t[1, 2], t[2, 1]}, {t[3, 1], t[2, 2], t[1, 3]}, {t[1, 4],
   t[2, 3], t[3, 2], t[4, 1]}, {t[5, 1], t[4, 2], t[3, 3], t[2, 4],
  t[1, 5]}, {t[1, 6], t[2, 5], t[3, 4], t[4, 3], t[5, 2],
  t[6, 1]}, {t[7, 1], t[6, 2], t[5, 3], t[4, 4], t[3, 5], t[2, 6],
  t[1, 7]}, {t[1, 8], t[2, 7], t[3, 6], t[4, 5], t[5, 4], t[6, 3],
  t[7, 2], t[8, 1]}, {t[8, 2], t[7, 3], t[6, 4], t[5, 5], t[4, 6],
  t[3, 7], t[2, 8]}, {t[3, 8], t[4, 7], t[5, 6], t[6, 5], t[7, 4],
  t[8, 3]}, {t[8, 4], t[7, 5], t[6, 6], t[5, 7], t[4, 8]}, {t[5, 8],
  t[6, 7], t[7, 6], t[8, 5]}, {t[8, 6], t[7, 7], t[6, 8]}, {t[7, 8],
  t[8, 7]}, {t[8, 8]}}

Daniel Lichtblau
Wolfram Research

• References:
  • ZigZag matrix rearrange
    • From: "Serych Jakub" <Serych@panska.cz>