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What is the point of having Initializations in DynamicModule and Manipulate?


I'd be interested in feedback from other users about the way in which
Initializations works within DynamicModule (and Manipulate?). It is
fair to say that I expected an initialization to occur "initially."
That is to say I expected Initialization content to be evaluated prior
to the body of the DynamicModule. I have exchanged emails with tech
support about this. Attached is an example sent to me by tech support.

ClearAll[plot, g];

(* and in a separate cell *)
DynamicModule[{c}, {plot, Slider[Dynamic[c]], g[Dynamic@c]},
 Initialization :> (g[x_] := Cos[x]; plot = Plot[g[x], {x, 1, 10}]),
 UntrackedVariables -> {g}]

It is important for this example to keep the ClearAll line in a
separate cell so that the global variables are only cleared once. On
my system (OS X 10.6.8, Mma 8.0.4) the output is a list

 {plot, "slider", g[0.]}

where "slider" is the actual rendered slider but plot is the word
(unset variable) plot. In other words Global`plot has no value at the
time the body of the DynamicModule is evaluated. Ditto Global`g.

If you evaluated the cell (the second cell with the DynamicModule) a
second time a plot graphic appears in the list and g[0.] becomes
Cos[0.]. This is not surprising because Global`plot and Global`g now
have a value.

Wolfram have indicated that this is working as designed -- which is
presumably why this example was sent to me of how this should work. If
that is the case it seems poorly designed because (and it is here I
would like feedback) users would expect initializations to be
evaluated prior to the body of the DynamicModule -- otherwise what is
the point?

I'd appreciate the thoughts of other users about this.

Additionally I have been told by Wolfram that wrapping Dynamic around
the variable(s) that are not being evaluated will trigger the
evaluation. But why would a user want to make plot or g Dynamic? It
seems to me that the entire purpose of having an Initialization is to
evaluate this "one off" variable/functions.

thanks

Mike



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