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Re: Labelling a plot with maximum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105175] Re: [mg105146] Labelling a plot with maximum
  • From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
  • Date: Mon, 23 Nov 2009 06:52:59 -0500 (EST)

Hi, Shalin,
try this. Alexei

jinc[x_] := BesselJ[1, 2 \[Pi] x]/(2 \[Pi] x);
f[x_, \[CapitalDelta]_] :=
  4 Abs[jinc[x + \[CapitalDelta]] - jinc[x - \[CapitalDelta]]]^2;

Manipulate[DynamicModule[{nmx},
 
  nmx = Dynamic[NMaximize[f[x, \[CapitalDelta]], x][[2, 1, 2]]];
 
  Column[{Row[{Style[
       "\!\(\*SubscriptBox[\"x\", \"max\"]\)=\[PlusMinus]", Red, Bold,
        18], Style[nmx, Red, Bold, 18]}],
    Plot[f[x, \[CapitalDelta]], {x, -1.22, 1.22},
     PlotRange -> {{-0.5, 0.5}, {0, 1.5}}]}]], {\[CapitalDelta],
  0.125, 0.5}]

Hi everyone,

 I am very new to Mathematica. I wish to prepare a figure and a movie
where the maximum of the plot is labelled on the figure.

I am using Manipulate to animate a function as shown below:

jinc[x_] := BesselJ[1, 2 \[Pi] x]/(2 \[Pi] x);
f[x_, \[CapitalDelta]_] :=
  4 Abs[jinc[x + \[CapitalDelta]] - jinc[x - \[CapitalDelta]]]^2;
Manipulate[
 Plot[f[x, \[CapitalDelta]], {x, -1.22, 1.22},
  PlotRange -> {{-0.5, 0.5}, {0, 1.5}}], {\[CapitalDelta], 0.125,
  0.5}]

I find the maximum for different values of Delta using:
Manipulate[
 NMaximize[f[x, \[CapitalDelta]], x], {\[CapitalDelta], 0.125,
  0.5}]

Can someone please help with a code that can print the result returned
by NMaximize on (say) top-left of the Plot generated by the first
Manipulate above? The plot will look  neat if I can place a marker at
the X-position of maximum.

Also, I wish to have a Motion-JPEG compressed quicktime mov file
exported from this manipulate. How can that be achieved?

thanks in advance for any help.
Shalin


-- 
Alexei Boulbitch, Dr., habil.
Senior Scientist

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