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