Re: Compiling numerical iterations

*To*: mathgroup at smc.vnet.net*Subject*: [mg129904] Re: Compiling numerical iterations*From*: Dana DeLouis <dana01 at icloud.com>*Date*: Mon, 25 Feb 2013 02:19:17 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

Hello. My ideas are very similar to Ray's ideas. It seems you are doing a random walk 1,000 times, and adding the positions repeatedly. I may be wrong, but I interpret a little differently. Here's what I'm thinking, Your steps are +- 1, but your adding +-.1 each time. (ie /10) tab=Table[0,{1000}]; Do[tab = tab + NestList[#+RandomChoice[{+1,-1}]&,0,1000-1]/10,{1000}]; // Or perhaps without the division tab=Table[0,{1000}]; Do[tab = tab + NestList[#+RandomChoice[{+.1,-.1}]&,0,1000-1],{1000}]; I like the FoldList idea also. Perhaps a different approach: FoldList[Plus,0,RandomInteger[{-1,1},1000-1]] / 10 If I run Ray's excellent code, here are the first 5 items of his corr array using the same Seed Number. num=1000; SeedRandom[1234567890] AbsoluteTiming@Length[ = tab=FoldList[Plus,0,Total@Sign@Table[Most@RandomReal[{-1,1},num],{1000}]] ] = AbsoluteTiming@Length[corr=Table[Take[tab,{k,num*9/10-1+k}],{k,num/10}]. Drop[tab,-num/10]/(num*10*9)] ray = corr[[1;;5]] {3019993/1875, 36211327/22500, 7236173/4500, 4018739/2500, 36160711/22500} I believe the constant is n=1000/10*9 900 Constant = 1/n, or 1/900 Ray uses a constant of 1/ 90000. I may be wrong, but I "think" it should be 1/900. Here's my idea once the tab array is calculated. I'll use Ray solution for comparison. You can skip the initialization of the corr array of all zero's at this point. CorrMe=Partition[tab,1000/10*9,1]//Most; CorrMe=Map[Dot[CorrMe[[1]],#]&,CorrMe] / 90000; me =CorrMe[[1;;5]] {3019993/1875, 36211327/22500, 7236173/4500, 4018739/2500, 36160711/22500} me == ray True = = = = = = = = = = HTH :>) Dana DeLouis Mac & Mathematica 9 = = = = = = = = = = > tab = Table[0, {i, 1, num}]; > > For[l = 1, l <= 1000, l++, > a = 0; > For[i = 1, i <= num, i++, > tab[[i]] = tab[[i]] + a/10; > > If[RandomReal[{-1, 1}] < 0, a = a + 1, a = a - 1]; > > ] > > ] > On Saturday, February 23, 2013 7:01:22 AM UTC-5, firlefranz wrote: > Hi, > > > > to speed up some calculations I'd like to use this relatively new method of compiling equations or export them to C. But since I'm very new in these things, I have really problems to use this c-compiling function. > > Can someone show me on this simple part of code (calculation of a correlation function of a 1D random walk), how it should be implemented? > > > > num = 1000; > > tab = Table[0, {i, 1, num}]; > > corr = Table[0, {i, 1, num/10}]; > > For[l = 1, l <= 1000, l++, > > a = 0; > > For[i = 1, i <= num, i++, > > tab[[i]] = tab[[i]] + a/10; > > If[RandomReal[{-1, 1}] < 0, a = a + 1, a = a - 1]; > > ] > > ] > > For[k = 1, k <= num/10, k++, > > For[n = 1, n <= num/10*9, n++, > > corr[[k]] = corr[[k]] + tab[[n]]*tab[[n + k - 1]]/num*10/9]; > > ] > > ListPlot[{corr}, Joined -> False] > > > > Best regards > > Cornelius