Re: letrec/named let

*To*: mathgroup at smc.vnet.net*Subject*: [mg56838] Re: letrec/named let*From*: DrBob <drbob at bigfoot.com>*Date*: Sat, 7 May 2005 04:17:00 -0400 (EDT)*References*: <069a01c55260$afdad760$6400a8c0@Main> <opsqc8fk0aiz9bcq@monster.ma.dl.cox.net> <06cb01c55267$3a6b5930$6400a8c0@Main> <opsqdiiiixiz9bcq@monster.ma.dl.cox.net> <083a01c5528e$c7e11da0$6400a8c0@Main>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

I was assuming nothing in your code would be slower in the newest version, so I was hoping to identify a component that had gotten faster from version to version in MY code. Perhaps Union is 12 times faster in 5.1.1, for instance. Either way, as I said before, we need timings on both machines to narrow it down. Nevertheless, here are timings for statements in "carl": carlTimed[s_]:=Module[{ord,t,ans}, Print@Timing[ord=Ordering@s;Ordering]; Print@Timing[t=FoldList[Plus,1,Sign[Abs[ListCorrelate[{1,-1},s[[ord]]]]]]; FoldList]; Print@Timing[ans=t[[Ordering[ord]]];Part]] data=1+RandomArray[PoissonDistribution[2],{10^6}]; Timing[three=carlTimed@data;] {0.813 Second,Ordering} {0.281 Second,FoldList} {0.641 Second,Part} {1.735 Second,Null} data=Table[Random[],{10^6}]; Timing[three=carlTimed@data;] {8.031 Second,Ordering} {0.391 Second,FoldList} {7.281 Second,Part} {15.906 Second,Null} Bobby On Fri, 6 May 2005 18:56:03 -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" <carl at woll2woll.com>; "Carl K. Woll" > Sent: Friday, May 06, 2005 5:40 PM > Subject: [mg56838] Re: letrec/named let > > >> I'm guessing Union, ReplaceAll, Dispatch, and/or Thread are better >> optimized in version 5.1.1. We'd have to get relative times for various >> statements on BOTH our machines, to narrow it down. Here they are for my >> machine: >> >> treat2[s_List] := Module[{u, t, d, ans}, >> Print@Timing[u = Union@s; "Union"]; >> Print@Timing[t = Thread[u -> Range@Length@u]; "Thread"]; >> Print@Timing[d = Dispatch@t; "Dispatch"]; >> Print@Timing[ans = s /. d; "ReplaceAll"]; >> ans] >> >> data=1+RandomArray[PoissonDistribution[2],{10^6}]; >> Timing[treat2@data;] >> >> {0.265 Second,Union} >> {0. Second,Thread} >> {0. Second,Dispatch} >> {0.297 Second,ReplaceAll} >> {0.562 Second,Null} >> >> data=Table[Random[],{10^6}]; >> Timing[treat2@data;] >> >> {0.625 Second,Union} >> {2.922 Second,Thread} >> {1.625 Second,Dispatch} >> {3.89 Second,ReplaceAll} >> {10.328 Second,Null} >> >> If your machine has Dispatch (for instance) taking a larger fraction of >> the total time, we'll have a clue to what changed. >> >> I'm actually shocked by how fast this is, considering the relatively naive >> (IMO) method involved. >> >> Bobby >> > > I'm not surprised by the timings you give for treat. I'm surprised by your > timing for my function, carl. On my machine, applying my function to a > million reals takes about 2 times as long as a Union. On your machine, it > apparently takes about 24 times as long as a Union. The 1st and 3rd lines of > my function are basically sorting operations, so the bottleneck on your > machine must be the 2nd line. However, on my machine, the 2nd line is the > fastest operation. The only candidates for a bottleneck seem to be FoldList > and ListCorrelate, or perhaps something funny is going on with packed > arrays. I'd be curious what timings my function would get if you "treat"ed > it like treat2 <grin>. > > Carl Woll > >> 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" >>> <mathgroup at smc.vnet.net> >>> Sent: Friday, May 06, 2005 2:03 PM >>> Subject: [mg56838] 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 >> >> > > > > > -- DrBob at bigfoot.com

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**Re: letrec/named let**

**Re: letrec/named let**