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

*To*: mathgroup at smc.vnet.net*Subject*: [mg88143] RE: [mg88122] Re: Print[Plot] vs Print[text,Plot]? (*now Do and Table*)*From*: "Jose Luis Gomez" <jose.luis.gomez at itesm.mx>*Date*: Sat, 26 Apr 2008 03:43:40 -0400 (EDT)*References*: <fupm2j$s4a$1@smc.vnet.net> <200804250929.FAA08198@smc.vnet.net>

Dear Alexey I am Not surprised that a functional-programming and list-oriented language like Mathematica is much slower if you force it to Not to construct a list. Mathematica is made for working with lists, and structures similar to lists, for example evaluate FullForm[{a,b,c}] After that evaluate FullForm[a+b+c] Then you will see the kind of structures that Mathematica uses internally. Therefore the natural behavior of Mathematica is to create lists (and similar structures) Forcing Mathematica to NOT create a list, can make it SLOWER. >From the point of view of a functional-programming and list-oriented language (like Mathematica) the Do[] loop IS NOT THE SIMPLEST, as you called it. Perhaps the document in the following links can be interesting for you: http://homepage.cem.itesm.mx/lgomez/matecmatica/funcionalprog.nb http://homepage.cem.itesm.mx/lgomez/matecmatica/fp/fp.html Hope that helps Jose Mexico -----Mensaje original----- De: Alexey Popkov [mailto:popkov at gmail.com] Enviado el: Viernes, 25 de Abril de 2008 04:30 a.m. Para: mathgroup at smc.vnet.net Asunto: [mg88122] Re: Print[Plot] vs Print[text,Plot]? (*now Do and Table*) I should notice that it is VERY strange behavour that the simplest Do[] loop takes MUCH more time than constructing a list of elements and summing them. I do not understand the reason. It looks like a defect. W_Craig Carter: > On Wed, Apr 23, 2008 at 3:09 PM, AES <siegman 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. > > > > > Thanks for comments. > > > > _Why_ (or, in what circumstances?) would Table be a better choice than Do? > > > > I 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. And they (Table > and Do) are just about interchangeable, except in a few unusual (and > technical) cases. Table'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 main kernel's > evaluation loop, and "Table" doesn't). > > I'll try to demonstrate this as an example. I'll try to explain my > steps carefully, and I'll avoid the use of #&/.^= syntax. It 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[ > icount = 0; > Do[icount = icount + i, {i, 1, 10000000, 1}]; > icount > ] > > (*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[ > Total[Table[i, {i, 1, 10000000, 1}]] > ] > > (*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. Table 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 in the mind of a beginner who has neither > seen Do, For, While, or Table. Which style would you recommend based > on speed alone? Which style would you recommend on readability alone? > > So, a typical beginning user might find themselves tending to use > Lists. They 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...). They 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 anyway*) > > (*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 brackets,*) > (* 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. Sometimes, 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

**References**:**Re: Print[Plot] vs Print[text,Plot]? (*now Do and Table*)***From:*Alexey Popkov <popkov@gmail.com>