Re: For loop problem in mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg90205] Re: For loop problem in mathematica*From*: Bob F <deepyogurt at gmail.com>*Date*: Wed, 2 Jul 2008 05:30:30 -0400 (EDT)*References*: <g4d2qf$emo$1@smc.vnet.net>

On Jul 1, 5:01 am, PhysNova <skhoshbin... at gmail.com> wrote: > Hi, > i wrote a simple program of evaluating Pi number in M6 to test cpu > computation timing, to do this a simple for loop > > was used: > > x=0;For[i = 1, i < 10,000,000, i++, x = x + 1/(i^2)];N[Sqrt(6*x),25= ]// > Timing > > the result was catastrophe! it take few minuates. but i first expect > to do this very simple job in few > > seconds.computation time is just satisfactory up to 100000 cycle. > > could anyone interperet this falut? > our get an idea to improve the result? > > Tanks I think you have a couple of typo's. The Sqrt(6*x) should be Sqrt[6*x], and the comma's in the 10,000,000 should not be there (should be 10000000 instead) so it thinks you are adding more arguments to the function than is allowed. Also the //Timing you have will only be for the Sqrt[] function, not the loop. Is that what you wanted? Try Timing[...] I am guessing that you were just typing something in rather than pasting a Mathematica expression. This is a little more than the built in way to compute Pi -- compare this to N[Pi, 25]//Timing which only took about 0.000032 seconds on my computer. On my system doing it your way for 100000 (one-hundred thousand) iterations took about 15.2 seconds and it's square root took an additional about 2.2 seconds, for 1000000 (one million) the numbers were about 1379.1 and 34.5 seconds -- I would guess the 10000000 (ten million) would take about 100 times longe which was a bit longer than I was willing to wait ;) Am curious why this takes so long -- anyone got any ideas? Try using the Mathematica Benchmark program to get an idea of your relative CPU speed - do a menu command of "Mathematica/About Mathematica/System Information/Benchmark with MathematicaMark" on a Mac or "Help/About Mathematica/System Information/Benchmark with MathematicaMark" on a Windows system - this runs 15 different tests and shows how your system compares with about 10 other different systems (Windows, Linux and Mac systems with various CPU's). A very efficient and fast converging algorithm for computing Pi is the Chudnovsky algorithm (see Wikipedia article at http://en.wikipedia.org/wiki/Chudnovsky_algorithm -- for more details). Mathematica itself uses a Chudnovsky algorithm, but not sure it it's the same as the Wikipedia or another one? I did this in Mathematica and since it converges so fast only did 1 terms of the sum and was within -3.08x10^-28 which took only .000303 seconds and 5 terms which took .000576 seconds and was within -3.6x10^-85, and 100 terms took 0.015829 seconds and was within 5.05x10^-1433 so you can see how much faster converging and better this is ... Here is the Chudnovsky algorithm in Mathematica: Timing[\[Pi] - N[1/(12*Sum[((-1)^k * Factorial[6*k] * (13591409 + 545140134 * k)) / (Factorial[ 3 * k] * Factorial[k]^3 * 640320 ^(3*k + 3/2)), {k, 0, 5}]), 1000]] Have fun... -Bob

**Re: For loop problem in mathematica**

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**Re: For loop problem in mathematica**

**Re: For loop problem in mathematica**