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Re: Compiling numerical iterations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg129940] Re: Compiling numerical iterations
  • From: Peter Klamser <klamser at googlemail.com>
  • Date: Wed, 27 Feb 2013 03:06:38 -0500 (EST)
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Hi Cornelius,

your code is not slow because you use Mathematica but because you are not
writing in functional and Mathematica style.

Use /@, @@, pure Functions like #1^2& etc. to realize your algorithm.

Plus @@ {a, b, c, d} is much faster then procedural programming.

Kind regards from Peter



2013/2/26 firlefranz <cornelius.franz at gmx.net>:
> Thanks a lot! To be honest, some of the commands Ray is using, I've never seen before. I stopped using mathematica before version 5 came out.
>
> Coming back to Peters statement of exporting the code from Mathematica to C. How this can be done starting from my or Ray's code? There is an automated C-code-gernerator implemented in Mathematica 9, am I right?
>
>
> As a step forward to the first little peace of code, here is another try, which is not really optimized. The be concrete, I try to simulate the autocorrelation function of a random walk, which is doing a step at none equally distant time steps. This has to been done for a long random walk for many particles. Instead of doing an average over many random walks and calculate one autocorrelation function I want to simulate many correlation functions and make an average over them. Since the time steps are non equal, I wrote a sub-function, which creates a new time axis and taking the necessary value for the random walk from the first table.
>
> Here is what I come up with. It's running in a reasonable time for one particle, but for a real statistic ensemble, I have to do it over 1.000.000 particles for a long time. Optimizing this or (probably better) exporting it to C would hopefully help a lot. So how to export it?
>
> Clear["Global`*"]
> SeedRandom[1234567890];
> zeitmax = 100;(* muss ein Integer sein *)
> numteilchen = 1;
> tauj = 1;
> corr = Table[0, {i, 1, zeitmax/10}];
>
> SucheIndex[zeitliste_, zeit_, maxindex_] :=
>   Module[{i},
>    For[i = 1, i <= maxindex, i++,
>     If[zeitliste[[i]] > zeit, Break[]];
>     ];
>    i - 1
>    ];
>
> For[j = 1, j <= numteilchen, j++,
>   (* Zeitachse generieren von 0 bis zeitmax *)
>   t = 0;
>   i = 1;
>   tabzeit = {};
>   time = AbsoluteTiming[While[True,
>       tabzeit = Append[tabzeit, t];
>       dt = -tauj*Log[1 - RandomReal[]];
>       If[t > zeitmax, Break[]];
>       t = t + dt;
>       i++;
>       ];
>     ];
>   Print[time];
>   maxidx = i;
>
>   (* Random Walk *)
>   time = AbsoluteTiming[
>     tabwalk = Table[0, {i, 1, maxidx}];
>     a = 0;
>     For[i = 1, i <= maxidx, i++,
>      tabwalk[[i]] = a;
>      If[RandomReal[{-1, 1}] > 0, a = a + 1, a = a - 1];
>      ];
>     ];
>   Print[time];
>   (*tabwalk=Table[Subscript[b, i],{i,1,maxidx}];*)
>
>   (* Korrelationsfunktion berechnen *)
>   time = AbsoluteTiming[
>     For[k = 1, k <= zeitmax/10, k++,
>       For[n = 1, n <= zeitmax/10*9, n++,
>         corr[[k]] =
>           corr[[k]] +
>            tabwalk[[SucheIndex[tabzeit, n - 1, maxidx]]]*
>             tabwalk[[SucheIndex[tabzeit, n + k - 2, maxidx]]]/
>              zeitmax*10/9/numteilchen;
>         (*Print[corr//N];*)
>         ];
>       ];
>     ];
>   Print[time];
>   Print[corr // N];
>   ];
> Table[{tabzeit[[i]], tabwalk[[i]]}, {i, 1, maxidx}]
> corr // N
>



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