       Re: Labelling a plot with maximum

• To: mathgroup at smc.vnet.net
• Subject: [mg105173] Re: Labelling a plot with maximum
• From: dh <dh at metrohm.com>
• Date: Mon, 23 Nov 2009 06:52:34 -0500 (EST)
• References: <heb69h\$abg\$1@smc.vnet.net>

```
Shalin Mehta 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

>

Hi Shalin,

here is an example. I set ContinuousAction -> False due to the delay

cause by NMaximize:

Manipulate[Column[{

Plot[f[x, \[CapitalDelta]], {x, -1.22, 1.22},

PlotRange -> {{-0.5, 0.5}, {0, 1.5}},

Epilog -> {Red,

Point[{x /. #[], peak = #[]}] & @

NMaximize[f[x, \[CapitalDelta]], x]}]

, "Peak=" <> ToString[peak]}]

, {\[CapitalDelta], 0.125, 0.5}, ContinuousAction -> False]

Daniel

```

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