Re: Print[Plot] vs Print[text,Plot]? (*now Do and Table*)

*To*: mathgroup at smc.vnet.net*Subject*: [mg88151] Re: Print[Plot] vs Print[text,Plot]? (*now Do and Table*)*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Sat, 26 Apr 2008 03:45:06 -0400 (EDT)

On 4/25/08 at 5:29 AM, popkov at gmail.com (Alexey Popkov) wrote: >And I was surprised much more when I have tried the more simple form >of the first expression: >Timing[icount = 0; >Do[icount += i, {i, 1, 10000000, 1}]; icount] >(*this returns {36.042, 50000005000000} on my machine*) >It means that using the "+=" operator takes about 50% more time than >the usual form icount = icount + i; It is sad and very surprising! I understand why you might consider this surprising if you come from a C/C++ background. But why sad? You simply need to realize Mathematica is not C/C++. What is most efficient in such languages cannot be assumed to be most efficient in Mathematica. My experience indicates using Mathematica's functional constructs (Map, Apply etc) are almost always faster than the procedural constructs (Do, For etc.). Since I have no access to the source code, I've no real idea why this is so. I simply accept it as so and write code accordingly. Another rule of thumb seems to be, things run faster when the minimum amount of information needed is given rather than a more complete specification. For example, on my machine: In[251]:= Timing[Total@Table[n, {n, 1, 1000000, 1}]] Out[251]= {1.2309,500000500000} In[252]:= Timing[Total@Table[n, {n, 1, 1000000}]] Out[252]= {1.16736,500000500000} In[253]:= Timing[Total@Table[n, {n, 1000000}]] Out[253]= {1.16389,500000500000} There are other benefits to the functional style over the procedural style in addition to performance. With C/C++ loops probably one of the more common errors is to be one off at the end of a loop. This could happen as a result of using say n < limit versus n <= limit for the stopping criteria or failing to have the stopping test in the right sequence with the step incrementing the loop counter. These kind of problems are eliminated with functional programming constructs since you never need worry about the size on an array.