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

*To*: mathgroup at smc.vnet.net*Subject*: [mg88123] Re: Print[Plot] vs Print[text,Plot]? (*now Do and Table*)*From*: Alexey Popkov <popkov at gmail.com>*Date*: Fri, 25 Apr 2008 05:29:58 -0400 (EDT)*References*: <fupm2j$s4a$1@smc.vnet.net>

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! On 24 =C1=D0=D2, 14:06, "W_Craig Carter" <ccar... at mit.edu> wrote: > On Wed, Apr 23, 2008 at 3:09 PM, AES <sieg... at stanford.edu> wrote: > > > > Table is usually a better choice than Do, but that is a choice and the= > > > language is accommodating enough to allow you to make that choice; and= > > > if you should be curious, to explore. > > > =9AThanks for comments. > > > =9A_Why_ (or, in what circumstances?) would Table be a better choice tha= n Do? > > > =9AI appreciate that their logical behavior is similar, and indeed they = can be > > coded very similarly. > > Dear AES, > I am happy to try to answer. > > I'll take the time to answer at length, because I find that many > people that I try to help out have similar viewpoints as yours. > Perhaps, I may have something useful to contribute. > > Primarily, it is a matter of choice and familiarity. =9AAnd they (Table > and Do) are just about interchangeable, except in a few unusual (and > technical) cases. =9ATable's advantage is speed and efficiency. (Once I > asked someone at Wolfram how I should explain this to my students, and > the kind answer was because "Do" has to access the =9Amain kernel's > evaluation loop, and "Table" doesn't). > > =9AI'll try to demonstrate this as an example. I'll try to explain my > steps carefully, and I'll avoid the use of #&/.^= syntax. =9AIt took me > a while to cook this up--I hope that my example doesn't go amiss. > > This is problem with a known simple result, but it will serve: let's > find the sum of the first 10000000 integers. > > (*let's use a do loop*) > Timing[ > =9Aicount = 0; > =9ADo[icount = icount + i, {i, 1, 10000000, 1}]; > =9Aicount > =9A] > > (*this returns {10.2826, 50000005000000} on my machine.*) > (*10.28 being a measure of how long the computation took to run*) > > (*lets try a table*) > Timing[ > =9ATotal[Table[i, {i, 1, 10000000, 1}]] > =9A] > > (*This returns {3.25516, 50000005000000} on my machine*) > > This is a simple example, but it illustrates the difference nicely. ( > Personally, I've yet to > find a case for which I can replace a Do with a Table or similar list > construct, although I am sure readers of this group could easily > construct one as a challenge.) > > Another way to think of this is that Mathematica is very good at > operating on lists. =9ATable and Lists work together nicely, and many of > the functions like Total are designed to help you make your > programming easier. > > Now, if you put yourself =9Ain the mind of a beginner who has neither > seen Do, For, While, or Table. Which style would you recommend based > on speed alone? =9AWhich style would you recommend on readability alone? > > So, a typical beginning user might find themselves tending to use > Lists. =9AThey are content for a couple years, but soon master the idea > so that begin to do what is natural, abbreviate (ASAP, RJ46, LOL, > AWOL, PM. FM...). =9AThey find shortcuts and optimize their time: > > First attempt may be something like this: > (*create a list*) > > Table[i,{i,1,10000000}] > > (*horrors, the output is too long, and I know what it might look like anyw= ay*) > > (*they graduate to this*) > mytable= Table[i,{i,1,1000000}]; > Total[mytable] > > (* soon they get tired of typing and find an abbreviated version *) > > Total[Table[i,{i,1,1000000}]] > > (* soon they get tired of moving around the screen to type the two bracket= s,*) > (* so they find another way to do the same thing, no better, arguably > less readable > (*at first*) > Total@Total[Table[i,{i,1,1000000}] > (*or, depending on where your cursor tends to be sitting*) > Table[i, {i, 1, 1000000}] // Total > > (*thus they learn a semaphore for analogous constructs*) > (*but there's more, with ever more symbols, the efficiency and power goes*= ) > (*up rapidly, but the readability goes down for beginners*) > (*where you find the happy medium is entirely up to you*) > > In my opinion, this is the fun part of mathematica. I get to decide > how to share the labor with mathematica, and I get to decide how > obscure to make my code. =9ASometimes, for my own pleasure, I write it > as obscurely as possible (and I am no master at this by a long shot). > If I am writing code that I hope someone else will use and modify, or > learn from, I try to write as readable as possible. > > -- > > W. Craig Carter