Re: ZigZag matrix rearrange

• To: mathgroup at smc.vnet.net
• Subject: [mg99080] Re: [mg99055] ZigZag matrix rearrange
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Sun, 26 Apr 2009 01:39:34 -0400 (EDT)
• References: <200904250851.EAA14256@smc.vnet.net>
• Reply-to: drmajorbob at bigfoot.com

```Elegance isn't always fast, but here's a possibility:

Clear[next]
next[{1, 8}] = {2, 8};
next[{8, 1}] = {7, 2};
next[{x_, 1}] := next[{x, 1}] = If[OddQ@x, {x + 1, 1}, {x - 1, 2}]
next[{1, y_}] := next[{1, y}] = If[EvenQ@y, {1, y + 1}, {2, y - 1}]
next[{8, y_}] := next[{8, y}] = If[OddQ@y, {7, y + 1}, {8, y + 1}]
next[{x_, 8}] := next[{x, 8}] = If[EvenQ@x, {x + 1, 7}, {x + 1, 8}]
next[{x_, y_}] :=
next[{x, y}] = If[OddQ[x + y], {x - 1, y + 1}, {x + 1, y - 1}]

Clear[zigzag, t]
zigzag[t_] = t @@@ NestList[next, {1, 1}, 8*8 - 1]

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

or this:

Clear[bounce, next]
bounce[{x_, 9}] := {x + 2, 8}
bounce[{9, y_}] := {8, y + 2}
bounce[{x_, 0}] := {x, 1}
bounce[{0, y_}] := {1, y}
bounce[{x_, y_}] := {x, y}
next[{x_, y_}] :=
next[{x, y}] = bounce@If[OddQ[x + y], {x - 1, y + 1}, {x + 1, y - 1}]

Clear[zigzag, t]
zigzag[t_] = t @@@ NestList[next, {1, 1}, 8*8 - 1]

I've switched x and y so that x is horizontal and y is vertical.

Bobby

On Sat, 25 Apr 2009 03:51:18 -0500, Serych Jakub <Serych 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 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
>

--
DrMajorBob at bigfoot.com

```

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