Re: Help with Speeding up a For loop

*To*: mathgroup at smc.vnet.net*Subject*: [mg98933] Re: Help with Speeding up a For loop*From*: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>*Date*: Wed, 22 Apr 2009 05:11:03 -0400 (EDT)*References*: <gsivhv$9f6$1@smc.vnet.net>

The following code does 10 million iterations in 4 minutes: Ideal = ConstantArray[0, n + 1]; Resolution = ConstantArray[0, n + 1]; For[i = 0, i < n, i++, If[k[[i]] < Re[(E0 - Eb1[[i]])^2*Sqrt[1 - m^2/(E0 - Eb1[[i]])^2]], Eb1[[i]] = RandomReal[NormalDistribution[(Ideal[[i + 1]] = Eb1[[i]]), Sigma]]; Resolution[[i + 1]] = Eb1[[i]] ]; ] It can be sped up even more, but I think this meets your requirements. Cheers -- Sjoerd On Apr 21, 1:13 am, Adam Dally <ada... at wisc.edu> 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 basic= ally > a "Monte Carlo Integration" technique. Ideal should simulate the curve. > Resolution should simulate the curve convoluted with a normal distributio= n. > I want to do this for n=10 000 000 or more, but it takes far too long r= ight > now. I can do n=100 000 in about 1 minute, but 1 000 000 takes more tha= n 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; S= igma = 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]], (*c= heck > if the {k,Eb1} value is under the curve*) > AppendTo[Ideal, Eb1[[i]]]; (*Keep events under curve in 'Id= eal'*) > y3 = Eb1[[i]]; (*cast element to a number*) > Eb1[[i]] = RandomReal[NormalDistribution[y3, Sigma], 1]; (*c= hoose a > random number from a normal distribution about that point*) > AppendTo[Resolution, Eb1[[i]]]; ]] (*Keep that event in 'Resol= ution'*)