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

*To*: mathgroup at smc.vnet.net*Subject*: [mg88140] Re: Print[Plot] vs Print[text,Plot]? (*now Do and Table*)*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Sat, 26 Apr 2008 03:43:07 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <fupm2j$s4a$1@smc.vnet.net> <fus8ij$862$1@smc.vnet.net>

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! FWIW, Speaking about speed, as a rule of thumb -- or best practice -- one should try to use the functional programming paradigm rather than the procedural one and, above all, use mathematical knowledge and insight. n = 10000000; Timing[icount = 0; Do[icount += i, {i, n}]; icount] (* {18.2542, 50000005000000} *) Timing[icount = 0; Do[icount = icount + i, {i, n}]; icount] (* {11.8114, 50000005000000} *) Timing[Fold[Plus, 0, Range[n]]] (* {5.21385, 50000005000000} *) Timing[Total@Table[i, {i, n}]] (* {3.47212, 50000005000000} *) Timing[Last@Accumulate[Range[n]]] (* {2.89324, 50000005000000} *) Timing[Sum[i, {i, n}]] (* {0.0312, 50000005000000} *) Timing[i (i + 1)/2 /. i -> n] (* {0.000049, 50000005000000} *) Regards, Jean-Marc > 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 > >

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

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