Re: Re: Help with Speeding up a For loop

*To*: mathgroup at smc.vnet.net*Subject*: [mg99014] Re: [mg98916] Re: Help with Speeding up a For loop*From*: dh <dh at metrohm.com>*Date*: Fri, 24 Apr 2009 03:45:41 -0400 (EDT)*References*: <gsivhv$9f6$1@smc.vnet.net> <200904220907.FAA13170@smc.vnet.net> <49EF3785.7010901@wolfram.com>

Hi Darren, you are right of course. This was easy, but I hope you will not mind if I will ask you occasionally a question I can not get an answer. There are not too many knowledgeable people around. Daniel Darren Glosemeyer wrote: > A smaller additional speedup can be had by using one call to RandomReal > to get the normals, e.g. > > Resolution = RandomReal[NormalDistribution[0, Sigma], Length[Ideal]] + > Ideal > > This uses the fact that if z follows NormalDistribution[0,sigma], mu+z > follows NormalDistribution[mu,sigma]. This is more efficient because it > is faster to get a bunch of random numbers in one call than to get them > one at a time and the addition of Ideal is comparatively very fast. > > Darren Glosemeyer > Wolfram Research > > dh wrote: >> 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'*) >>> >> >> >> >> >> > > > > -- Daniel Huber Metrohm Ltd. Oberdorfstr. 68 CH-9100 Herisau Tel. +41 71 353 8585, Fax +41 71 353 8907 E-Mail:<mailto:dh at metrohm.com> Internet:<http://www.metrohm.com>

**References**:**Re: Help with Speeding up a For loop***From:*dh <dh@metrohm.com>