Re: For loop problem in mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg90213] Re: For loop problem in mathematica*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Wed, 2 Jul 2008 05:32:01 -0400 (EDT)

On 7/1/08 at 6:59 AM, skhoshbinfar at gmail.com (PhysNova) 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? The bottom line in Mathematica is using For is one of the surest ways to create slow code. Don't use For in Mathematica without very good reasons. And so far, I've yet to find one very good reason to use For. The specific computation can be done as: In[23]:= Sqrt[6 Sum[1/n^2, {n, k}] /. k -> 10000000.] // Timing Out[23]= {0.016533,3.14159} in far less than a second. Or if you want more precision, In[24]:= Sqrt[6 Sum[1/n^2, {n, k}] /. k -> N[10000000, 25]] // Timing Out[24]= {0.017678,3.141592558096830706654627046981} somewhat slower but still a small fraction of a second