Re: Do-loop conversion

*To*: mathgroup at smc.vnet.net*Subject*: [mg50247] Re: [mg50211] Do-loop conversion*From*: DrBob <drbob at bigfoot.com>*Date*: Mon, 23 Aug 2004 06:34:08 -0400 (EDT)*References*: <200408210704.DAA24758@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

Do loops are not always the wrong way to go and, in this case, the real problem could be this statement: newc = AppendTo[newc, newdata] In the first place, it can be replaced with simply AppendTo[newc, newdata] The Set statement isn't necessary, since AppendTo already changes the value of its first argument. Secondly, AppendTo is slow. Consider these three timings: n=10000 SeedRandom[1] new1={}; Timing@Do[AppendTo[new1,Random[]],{i,1,n}] 10000 {0.938 Second,Null} SeedRandom[1] new2={}; Timing[Do[new2={new2,Random[]},{i,1,n}];new2=Flatten@new2;] {0.031 Second,Null} SeedRandom[1] Timing[new3=Reap[Do[Sow@Random[],{i,1,n}]][[-1,1]];] {0.016 Second,Null} new1 == new2 == new2 True The second method only works for you if "newdata" is a scalar (not a List). The speed difference gets much MORE dramatic as n gets larger. But, if n=200, there may or may not be a noticeable difference. In that case, other Mathgroupers may have ideas for you. Offhand, I doubt that getting rid of the Do loop will speed things up for you in this case. Bobby > Mathematica colleagues, > > I have a problem that involves converting a Do-loop structure into > faster-executing version using functional programming. This is an optics > problem -- specifically, calculating the angle dependence of the X-ray > reflectivity of an n-layered medium on an infinitely thick substrate. The > calculation relies on a well-known recursion relation: > > X(j) = [ r(j) + X(j+1) p^2(j+1) ]/[1+ r(j) X(j+1) p^2(j+1)] > > where X(j) is the ratio of the reflected and transmitted X-ray amplitudes > at the bottom of layer j, p(j+1) is a phase factor (given below), and r(j) > is the Fresnel coefficient for reflection at the interface between layers j > and j+1: > > r(j) = [k(z,j) - k(z,j+1)]/[k(z,j) + k(z,j+1)] > > where the wavevector k(z,j) = (2*Pi/wavelength)Sqrt[n^2(j) - Cos(phi)^2], > n(j) is the complex index of refraction for X-rays for the layer n(j) = 1 - > delta(j) + I*beta(j), and phi is incident angle of the X-rays. The phase > factor mentioned above is given by > > p(j) = r(j) exp[-2 (k(j) k(j+1)) s(j+1)] with s being the roughness at > interface j+1. > > The recursion layer works because with an infinitely thick substrate, the > reflected amplitude coming up from the substrate = 0, so at a given angle > of incidence, you work from the bottom up starting with X(bottom) = 0 and > add the amplitudes at each interface until you get to the top surface. The > Mathematica code that works just fine as a Do-loop is: > > Do[ > wavevectmap := wavetabc[revdelta, revbeta, phi]; > leftvectmap := leftvectmapc[wavevectmap]; > thtest := thtestcomp[revrough, leftvectmap, wavevectmap]; > maproughrev := roughrevcomp[thtest]; > coeffmap := coeffcomp[wavevectmap, leftvectmap, maproughrev]; > phasemap := phasecomp[wavevectmap, revthick]; > coeffs := fcoeffcomp[coeffmap, phasemap]; > recurr[prior_, {fc_, pf_}] := (fc + (prior*pf^2))/(1 + > (fc*prior*pf^2)); > intensity := intensitycomp[Fold[recurr, 0, coeffs ]]; > newdata = newdatacomp[phi, intensity, params]; > newc = AppendTo[newc, newdata], > {phi, phistart, phiend, phiinc}] > > The various functions above -- wavetabc, leftvectmapc, thtestcomp, > roughrevcomp, coeffcomp, phasecomp, fcoeffcomp, intensitycomp, and > newdatacomp -- are complied functions that take structural parameters for > each layer (index of refraction parameters delta and beta, layer thickness, > interfacial roughness) by reading them out of a list {params} that is input > at the start of the program. I've left out these functions for brevity; if > needed, I'll post them as well. > > As I said, the above Do-loop works just fine by calculating at each angle > phi the final intensity at that angle, normalizing it with a background and > maximum peak factor (also in the {params} list and applied by the > newdatacomp line) and appending it to the intensity datafile > newc. Executing this loop for a five-layer system and a couple of hundred > angular points takes around 0.2 seconds -- not bad, except that I need to > use this in a genetic algorithm minimization routine which needs many > hundreds of these curves to be calculated with GA- dictated changes to the > initial parameter matrix. So: if anyone can give me some guidance on how to > eliminate the Do-loop over the angular range so I can speed things up, I > would be very grateful. > > Thanks in advance, > Rich Matyi > rjmatyi at comcast.net > > > > > -- DrBob at bigfoot.com www.eclecticdreams.net

**References**:**Do-loop conversion***From:*"Rich Matyi" <rjmatyi@comcast.net>

**Re: Do-loop conversion**

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