Re: ZigZag matrix rearrange

• To: mathgroup at smc.vnet.net
• Subject: [mg99077] Re: ZigZag matrix rearrange
• From: Ray Koopman <koopman at sfu.ca>
• Date: Sun, 26 Apr 2009 01:39:01 -0400 (EDT)
• References: <gsuit1\$dsc\$1@smc.vnet.net>

```On Apr 25, 1:50 am, "Serych Jakub" <Ser... at panska.cz> wrote:
> Dear community,
> I'm trying to rearrange 8 x 8 matrix of numbers in ZigZag manner (as it is
> used in JPEG comprimation algorithmhttp://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

zz[n_Integer?Positive] := Module[{s = If[OddQ@#,1,-1]&},
Abs[Rest/@Sort@Flatten[Table[{i+j,i*s[i+j],j*s[i+j]},{i,n},{j,n}],1]]]

zz[8]

{{1,1},
{1,2},{2,1},
{3,1},{2,2},{1,3},
{1,4},{2,3},{3,2},{4,1},
{5,1},{4,2},{3,3},{2,4},{1,5},
{1,6},{2,5},{3,4},{4,3},{5,2},{6,1},
{7,1},{6,2},{5,3},{4,4},{3,5},{2,6},{1,7},
{1,8},{2,7},{3,6},{4,5},{5,4},{6,3},{7,2},{8,1},
{8,2},{7,3},{6,4},{5,5},{4,6},{3,7},{2,8},
{3,8},{4,7},{5,6},{6,5},{7,4},{8,3},
{8,4},{7,5},{6,6},{5,7},{4,8},
{5,8},{6,7},{7,6},{8,5},
{8,6},{7,7},{6,8},
{7,8},{8,7},
{8,8}}

zz[m_List /; ArrayDepth@m > 1 && Equal@@Take[Dimensions@m,2] ] :=
Extract[m,zz@Length@m]

t = Table["t"<>ToString[10i+j],{i,8},{j,8}]

{{t11,t12,t13,t14,t15,t16,t17,t18},
{t21,t22,t23,t24,t25,t26,t27,t28},
{t31,t32,t33,t34,t35,t36,t37,t38},
{t41,t42,t43,t44,t45,t46,t47,t48},
{t51,t52,t53,t54,t55,t56,t57,t58},
{t61,t62,t63,t64,t65,t66,t67,t68},
{t71,t72,t73,t74,t75,t76,t77,t78},
{t81,t82,t83,t84,t85,t86,t87,t88}}

zz[t]

{t11,
t12,t21,
t31,t22,t13,
t14,t23,t32,t41,
t51,t42,t33,t24,t15,
t16,t25,t34,t43,t52,t61,
t71,t62,t53,t44,t35,t26,t17,
t18,t27,t36,t45,t54,t63,t72,t81,
t82,t73,t64,t55,t46,t37,t28,
t38,t47,t56,t65,t74,t83,
t84,t75,t66,t57,t48,
t58,t67,t76,t85,
t86,t77,t68,
t78,t87,
t88}

```

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