       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>

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

> 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,

>

> 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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