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

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  • Subject: [mg88090] Re: Print[Plot] vs Print[text,Plot]? (*now Do and Table*)
  • From: "W_Craig Carter" <ccarter at mit.edu>
  • Date: Thu, 24 Apr 2008 05:57:30 -0400 (EDT)

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


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