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Re: Compiling numerical iterations

• To: mathgroup at smc.vnet.net
• Subject: [mg129926] Re: Compiling numerical iterations
• From: firlefranz <cornelius.franz at gmx.net>
• Date: Tue, 26 Feb 2013 01:11:34 -0500 (EST)
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• Delivered-to: l-mathgroup@wolfram.com
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• References: <kgab2i$c7f$1@smc.vnet.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