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}]
>
> 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
>
> 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 /. #[[2]], peak = #[[1]]}] & @
NMaximize[f[x, \[CapitalDelta]], x]}]
, "Peak=" <> ToString[peak]}]
, {\[CapitalDelta], 0.125, 0.5}, ContinuousAction -> False]
Daniel