Re: letrec/named let
- To: mathgroup at smc.vnet.net
- Subject: [mg56837] Re: letrec/named let
- From: DrBob <drbob at bigfoot.com>
- Date: Sat, 7 May 2005 04:16:58 -0400 (EDT)
- References: <069a01c55260$afdad760$6400a8c0@Main> <opsqc8fk0aiz9bcq@monster.ma.dl.cox.net> <06cb01c55267$3a6b5930$6400a8c0@Main>
- Reply-to: drbob at bigfoot.com
- Sender: owner-wri-mathgroup at wolfram.com
Oh yeah... I forgot to describe my system: Mathematica 5.1.1, WinXP, 2 GB RAM, with an AMD 3200+ chip. Timing differences could occur (I think) due to AMD versus Intel issues, as well as 5.1.1 versus 4.1. I suppose it could also be the type and amount of RAM we're using, the way our swap files are configured, or even our hard disks. Bobby On Fri, 6 May 2005 14:12:55 -0400, Carl K. Woll <carl at woll2woll.com> wrote: > ----- Original Message ----- > From: "DrBob" <drbob at bigfoot.com> To: mathgroup at smc.vnet.net > To: "Carl K. Woll" <carlw at u.washington.edu>; "MathGroup" > Sent: Friday, May 06, 2005 2:03 PM > Subject: [mg56837] Re: letrec/named let > > >> 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 >> > > Interesting. On my machine, carl is over 5 times faster than treat for the > same test. I have version 4.1 on a Windows XP operating system. What is your > setup? Perhaps you could test each individual line of carl to see where the > bottleneck is. > > Carl Woll > >> 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 >> >> > > > > > -- DrBob at bigfoot.com