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Re: Help with Speeding up a For loop

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  • Subject: [mg98926] Re: Help with Speeding up a For loop
  • From: Szabolcs Horvát <szhorvat at>
  • Date: Wed, 22 Apr 2009 05:09:44 -0400 (EDT)
  • References: <gsivhv$9f6$>

Adam Dally wrote:
> I am using an Intel MacBook with OS X 10.5.6.
> I am trying to create 2 lists: "Ideal" and "Resolution".  This is basically
> a "Monte Carlo Integration" technique. Ideal should simulate the curve.
> Resolution should simulate the curve convoluted with a normal distribution.
> I want to do this for n=10 000 000 or more, but it takes far too long right
> now. I can do n=100 000 in about 1 minute, but 1 000 000 takes more than an
> hour. I haven't waited long enough for 10 000 000 to finish (it has been 5
> days).
> Thank you,
> Adam Dally
> Here is the code:
> ClearAll[E0, Eb1, m, DeltaE, Sigma, k, n, y3, Ideal, Resolution, i,
> normalizer, maxE, minE]
> Eb1 = 0; k = 0; n = 10000; E0 = 2470; m = 0.2; DeltaE = 50; Sigma = 5; maxE
> = E0 - m; minE = E0 - DeltaE; Resolution = {Eb1}; Ideal = {Eb1};  (*Setup
> all constants, lists and ranges*)
> Eb1 = RandomReal[{minE, maxE}, n];  (*create a list of 'n' random Eb1
> values*)
> k = -RandomReal[TriangularDistribution[{-2470, 0}, -0.1], n]; (*create a
> list of 'n' random k values; triangle distribution gives more successful
> results*)
> For[i = 0, i < n, i++,
>  If[k[[i]] < Re[(E0 - Eb1[[i]])^2*Sqrt[1 - m^2/(E0 - Eb1[[i]])^2]], (*check
> if the {k,Eb1} value is under the curve*)
>      AppendTo[Ideal, Eb1[[i]]];  (*Keep events under curve in 'Ideal'*)
>      y3 = Eb1[[i]]; (*cast element to a number*)
>      Eb1[[i]] = RandomReal[NormalDistribution[y3, Sigma], 1]; (*choose a
> random number from a normal distribution about that point*)
>      AppendTo[Resolution, Eb1[[i]]]; ]] (*Keep that event in 'Resolution'*)

This can certainly be sped up (the biggest problem is that AppendTo has 
linear complexity, the larger the list, the longer appending takes.  Use 
Sow/Reap for collecting results).

But I don't see a reason for speeding up the Mathematica version of the 
program.  The program looks like as if it were translated from C/Java or 
some similar language.  So implement it in one of these languages.  I 
think that it is a waste of time waiting 5 days for Mathematica when you 
are not using any of the built in special algorithms.  There are plenty 
of C/C++/Java/Fortran libraries for drawing random numbers from a 
normal/triangular distribution (but implementing the algorithms for it 
yourself takes much less than 5 days too).

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