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For[] or While[] can't be used inside Manipulate[]?


Here is a code sample that creates a control object which calculates the expressions inside Maniplate again and again and never stop (it's proved by the code in the note):


Sample 1:


Manipulate[date = Table[0, {num}];
For[i = 1, i <= num, i++, date[[i]] = Sin[i]];(*Print@i;*)
ListPlot[{date}], {{num, 2}, 1, 20, 1}]


While has the same problem:


Sample 2:


Manipulate[date = Table[0, {num}]; i = 1;
While[i <= num, date[[i]] = Sin[i]; i++];
ListPlot[{date}], {{num, 2}, 1, 20, 1}]

I know if I choose Do, the problem will no longer exist:


Sample 3:


Manipulate[date = Table[0, {num}];

Do[date[[i]] = Sin[i], {i, 1, num}];
ListPlot[{date}], {{num, 2}, 1, 20, 1}]

Still, I know I can solve the problem if I throw the expression into Module if what I'm using is For:


Sample 4:


Manipulate[Module[{i}, date = Table[0, {num}];
For[i = 1, i <= num, i++, date[[i]] = Sin[i]];
ListPlot[{date}]], {{num, 2}, 1, 20, 1}]

And…yeah, it doesn't work for the code above with While…:



Sample 5:


Manipulate[Module[{j}, date = Table[0, {num}]; j = 1;
While[j <= num, date[[j]] = Sin[j]; j++];
ListPlot[{date}]], {{num, 2}, 1, 20, 1}]
(*This still creates a problematic control object*)

How to solve the problem with While? what actually happens inside Manipulate? what's the exact reason for the endless loop?




OK, the problem with sample 5 turns out to be a collaboration of Sample 4 and Sample 5, before I run sample 5, a control object has been already created by Sample 4 (let's call it Object 4 below, and so we have Object 5 for Sample 5).I think the process should be like this: when date = Table[0, {num}]; in Sample 5 is executed, it's tracked by Object 4, and then For[i = 1, i <= num, i++, date[[i]] = Sin[i]]; in Sample 4 is executed, so it is tracked by Object 5…so this story tells us how important a good programing habit is…



Answer




If you do not tell Manipulate which symbols to track, the default is Full


enter image description here


Hence use TrackedSymbols to explicitly tell it which symbols to track


Manipulate[
date = Table[0, {num}]; i = 1;
While[i <= num, date[[i]] = Sin[i]; i++];
ListPlot[{date}],
{{num, 2}, 1, 20, 1},
TrackedSymbols :> {num}
]


Another solution is to use Module, and add i and date as the local symbols to the internal module. Now Manipulate will not track these as they are not its own symbols.


Manipulate[
Module[{date, i},
date = Table[0, {num}]; i = 1;
While[i <= num, date[[i]] = Sin[i]; i++];
ListPlot[{date}]
],
{{num, 2}, 1, 20, 1}
]

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