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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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