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'*) > >

**Follow-Ups**:**Re: Re: Help with Speeding up a For loop***From:*Darren Glosemeyer <darreng@wolfram.com>