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Re: evaluations in Plot in Manipulate?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90915] Re: evaluations in Plot in Manipulate?
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Tue, 29 Jul 2008 01:39:53 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <g6kc15$k4d$1@smc.vnet.net>

J Davis wrote:

> I must be overlooking something simple in the way Mathematica handles
> the arguments of Manipulate.
> 
> Could someone expound on the contrast in behavior between the last
> example below and the previous two?
> 
> Clear[a, b, c, h];
> a = 1;
> c = 1;
> h[t_] = InverseLaplaceTransform[1/(a s^2 + b s + c), s, t]
> 
> 
> Manipulate[
>  Plot[Evaluate[
>    InverseLaplaceTransform[1/(a s^2 + b s + c), s, t]], {t, 0, 10},
>   PlotRange -> {{0, 10}, {-1, 1}}], {b, 0, 5}]
> 
> (* works fine *)
> 
> 
> Manipulate[
>  Plot[-((E^((-(b/(2 a)) - Sqrt[b^2 - 4 a c]/(2 a)) t) -
>     E^((-(b/(2 a)) + Sqrt[b^2 - 4 a c]/(2 a)) t))/Sqrt[
>    b^2 - 4 a c]), {t, 0, 10}, PlotRange -> {{0, 10}, {-1, 1}}], {b, 0,
>    5}]
> 
> (* works fine... I just copied and pasted the output of h[t] into the
> Plot[...] *)
> 
> 
> Manipulate[
>  Plot[Evaluate[h[t]], {t, 0, 10},
>   PlotRange -> {{0, 10}, {-1, 1}}], {b, 0, 5}]
> 
> (* nothing... what am I missing? *)
> 
> Doesn't Evaluate[h[t]] hold the evaluated form of h[t] (so that it is
> computed just once) and then Plot simply substitutes a sequence of
> numerical values into that evaluated form? If so, why is there no
> output?

Evaluate does nothing here since the function h[t] is defined with 
immediate assignment ("=" or *Set[]*), i.e. h[t] has already been 
evaluated when you defined it.

(That's why you got an output when you evaluated the function. Contrast 
this behavior with the same definition but using delayed assignment ":=" 
or *SetDelayed[]*).

Manipulate must "see" all the variables it manipulates in its first 
argument. Therefore, when one uses a function, the function must 
explicitly depends on all the variables that are going to be controlled 
by Manipulate[]. One possible way is as follows:

     Clear[a, b, c, h];
     a = 1;
     c = 1;
     h[b_][t_] = InverseLaplaceTransform[1/(a s^2 + b s + c), s, t];

     Manipulate[
      Plot[h[b][t], {t, 0, 10}, PlotRange -> {{0, 10}, {-1, 1}}],
       {b, 0, 5}]

Regards,
-- Jean-Marc


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