       Re: Labelling a plot with maximum

• To: mathgroup at smc.vnet.net
• Subject: [mg105179] Re: [mg105146] Labelling a plot with maximum
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Mon, 23 Nov 2009 06:53:46 -0500 (EST)

```jinc[x_] := BesselJ[1, 2 *Pi* x]/(2 *Pi* x);

Since you are working with Real functions, you do not need the Abs

f[x_, d_] := 4 (jinc[x + d] - jinc[x - d])^2;

The global maximum is

gmax = NMaximize[f[x, d], {x, d}]

{1.28206,{x->0.40868,d->0.40868}}

gPts = {{gmax[[2, 1, 2]], gmax[]},
{-gmax[[2, 1, 2]], gmax[]}};

Module[{nmax, pts},
Manipulate[
nmax = NMaximize[f[x, d], x];
pts = {{nmax[[2, 1, 2]], nmax[]},
{-nmax[[2, 1, 2]], nmax[]}};
Plot[f[x, d], {x, -1.22, 1.22},
PlotRange -> {{-0.5, 0.5}, {0, 1.5}},
Epilog -> {
Text[NumberForm[nmax, {4, 3}],
{-0.5, 1.5}, {-1, 1}],
AbsolutePointSize,
Red, Point[gPts],
Orange, Point[pts]}],
{d, 0.125, 0.5, 0.005,
Appearance -> "Labeled"}]]

I do not know how to export a movie.

Bob

---- Shalin Mehta <shalin.mehta at gmail.com> wrote:

=============
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}]

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

mobile: +65-90694182
blog: shalin.wordpress.com

Bioimaging Lab, Block-E3A, #7-10
Div of Bioengineering, NUS Singapore 117574
website: http://www.bioeng.nus.edu.sg/optbioimaging/colin/people.asp#shalinm

```

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