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