Re: letrec/named let

*To*: mathgroup at smc.vnet.net*Subject*: [mg56829] Re: letrec/named let*From*: DrBob <drbob at bigfoot.com>*Date*: Sat, 7 May 2005 04:16:43 -0400 (EDT)*References*: <069a01c55260$afdad760$6400a8c0@Main>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

That's a very nice "rescue" of the Ordering@Ordering solution. Here's a test with (probably) no repeated elements, however, that shows treat ahead. Perhaps there's an intermediate situation where carl wins, or it matters whether the data is integer or real? data=Table[Random[],{10^6}]; Timing[one=treat@data;] Timing[three=carl@data;] one==three {10.109 Second,Null} {15.938 Second,Null} True Bobby On Fri, 6 May 2005 13:26:03 -0400, Carl K. Woll <carlw at u.washington.edu> wrote: > "DrBob" <drbob at bigfoot.com> wrote in message > news:d5f5ka$6dn$1 at smc.vnet.net... >> Our solutions agree on lists of strictly positive integers, but timings >> depend a great deal on the minimum value: >> >> Clear[treat, andrzej] >> treat[s_List] := Module[{u = Union@s}, s /. Dispatch@Thread[u -> Range@ >> Length@u]] >> andrzej[s_List] := >> First@NestWhile[Apply[If[FreeQ[##], {#1 /. x_ /; >> x > #2 :> x - 1, #2}, {#1, #2 + 1}] &, #] &, {s, 1}, >> Last[#] < Max[First[#]] &] >> >> data=1+RandomArray[PoissonDistribution[2],{10^6}]; >> Timing[one=treat@data;] >> Timing[two=andrzej@data;] >> one == two >> >> {0.593 Second,Null} >> {0.657 Second,Null} >> True >> > > [snip] > > Another possibility modeled after DrBob's first answer is the following: > > carl[s_] := Module[{ord,t}, > ord = Ordering[s]; > t = FoldList[Plus, 1, Sign[Abs[ListCorrelate[{1, -1}, s[[ord]]]]]]; > t[[Ordering[ord]]] > ] > > If there are a lot of repeated elements in the data, then treat seems to be > faster. On the other hand, if there aren't a lot of repeated elements, then > carl seems to be faster. It seems like it ought to be possible to compute > Ordering[Ordering[data]] more quickly since > Ordering[Ordering[Ordering[data]]] equals Ordering[data], but I couldn't > think of a way. > > Carl Woll > > > > > > > -- DrBob at bigfoot.com