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Re: Help with Speeding up a For loop
*To*: mathgroup at smc.vnet.net
*Subject*: [mg98916] Re: Help with Speeding up a For loop
*From*: dh <dh at metrohm.com>
*Date*: Wed, 22 Apr 2009 05:07:50 -0400 (EDT)
*References*: <gsivhv$9f6$1@smc.vnet.net>
Hi Adam,
first note that indices in Mathematica start at 1, not 0.
Then I set the start value of Ideal and Resolution to an empty list.
With this changes, your loop can be replaced by:
Ideal = Pick[Eb1,
Thread@Less[k, Re[(E0 - Eb1)^2*Sqrt[1 - m^2/(E0 - Eb1)^2]]] ];
Resolution = RandomReal[NormalDistribution[#, Sigma]] & /@ Ideal;
For n=10^7, this takes 7.5 sec.
Daniel
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'*)
>
>
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