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MathGroup Archive 2005

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Re: Maxima & Minima

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53736] Re: [mg53703] Maxima & Minima
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Tue, 25 Jan 2005 05:03:58 -0500 (EST)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

data={{0.5,1.30301},{0.51,1.30244},
      {0.52,1.30533},{0.53,1.3059},
      {0.54,1.30544},{0.55,1.30816},
      {0.56,1.30942},{0.57,1.30952},
      {0.58,1.31146},{0.59,1.31105},
      {0.6,1.31357},{0.61,1.31614},
      {0.62,1.31636},{0.63,1.31782},
      {0.64,1.31977},{0.65,1.31993},
      {0.66,1.32175},{0.67,1.32041},
      {0.68,1.32705},{0.69,1.33001},
      {0.7,1.33689},{0.71,1.34665},
      {0.72,1.35868},{0.73,1.37899},
      {0.74,1.40351},{0.75,1.44677},
      {0.76,1.49938},{0.77,1.56417},
      {0.78,1.6265},{0.79,1.68231},
      {0.8,1.73439},{0.81,1.77567},
      {0.82,1.79751},{0.83,1.81008},
      {0.84,1.80272},{0.85,1.78359},
      {0.86,1.74827},{0.87,1.69779},
      {0.88,1.63964},{0.89,1.57302},
      {0.9,1.49157},{0.91,1.40873},
      {0.92,1.32168},{0.93,1.22632},
      {0.94,1.12993},{0.95,1.03509},
      {0.96,0.940307},{0.97,0.843889},
      {0.98,0.750626},{0.99,0.658783},
      {1.,0.571786},{1.01,0.490484},
      {1.02,0.414139},{1.03,0.342955},
      {1.04,0.27755},{1.05,0.219544},
      {1.06,0.169213},{1.07,0.126781},
      {1.08,0.091582},{1.09,0.0642237},
      {1.1,0.0444826},{1.11,0.0324386},
      {1.21,0.17094},{1.31,0.721742},
      {1.41,1.17931},{1.51,1.49921},
      {1.61,1.67064},{1.71,1.72145},
      {1.81,1.69853},{1.91,1.6343},
      {2.01,1.54399},{2.11,1.45614},
      {2.21,1.36254},{2.31,1.27609},
      {2.41,1.19319},{2.51,1.12123},
      {2.61,1.04736},{2.71,0.98465},
      {2.81,0.925526},{2.91,0.871404},
      {3.01,0.821615},{3.11,0.77698},
      {3.21,0.732385},{3.31,0.693622},
      {3.41,0.655827},{3.51,0.623108},
      {3.61,0.591913},{3.71,0.562528},
      {3.81,0.534357},{3.91,0.50876},
      {4.01,0.484918},{4.11,0.463476},
      {4.21,0.441866},{4.31,0.422324},
      {4.41,0.4049},{4.51,0.387806},
      {4.61,0.371429},{4.71,0.356785},
      {4.81,0.3418},{4.91,0.328734}};

xmin=Min[data[[All,1]]];
xmax=Max[data[[All,1]]];

id = Interpolation[data];

Plot[id[x],{x,xmin,xmax},
    PlotRange->{{Floor[xmin],Ceiling[xmax]},Automatic}];

Off[InterpolatingFunction::dmval];

idPeaks=({x,id[x]} /. 
      (FindRoot[D[id[x],x]==0,{x,#}]& /@ 
          {0.9,1.1,2.}))

{{0.8306328862190794, 1.8101192247875528}, 
  {1.123068945962959, 0.027059539216569357}, 
  {1.7218962023425761, 1.721953518594516}}

dataPeaks=Table[Sort[data, 
        Abs[#1[[2]]-idPeaks[[k,2]]]<
            Abs[#2[[2]]-idPeaks[[k,2]]]&][[1]],
    {k,Length[idPeaks]}]

{{0.83, 1.81008}, {1.11, 0.0324386}, {1.71, 1.72145}}


Bob Hanlon

> 
> From: nilaakash at gmail.com (nilaakash)
To: mathgroup at smc.vnet.net
> Date: 2005/01/24 Mon AM 03:37:24 EST
> To: mathgroup at smc.vnet.net
> Subject: [mg53736] [mg53703] Maxima & Minima
> 
> Dear Friends,
>                   Suppose I have some points. If you plot these points
> you will see there are few maxima and minima. I want to find only
> those maxima and minima points. Is there any process to findout only
> those max & min coordinates. (both x & y points).
> 
> data={{0.5, 1.30301}, {0.51, 1.30244}, {0.52, 1.30533}, {0.53,
> 1.3059}, {0.54,
>     1.30544}, {0.55, 1.30816}, {0.56, 1.30942}, {0.57, 1.30952},
> {0.58,
>     1.31146}, {0.59, 1.31105}, {0.6, 1.31357}, {0.61, 1.31614}, {0.62,
>     1.31636}, {0.63, 1.31782}, {0.64, 1.31977}, {0.65, 1.31993},
> {0.66,
>     1.32175}, {0.67, 1.32041}, {0.68, 1.32705}, {0.69, 1.33001}, {0.7,
>     1.33689}, {0.71, 1.34665}, {0.72, 1.35868}, {0.73, 1.37899},
> {0.74,
>     1.40351}, {0.75, 1.44677}, {0.76, 1.49938}, {0.77, 1.56417},
> {0.78,
>     1.6265}, {0.79, 1.68231}, {0.8, 1.73439}, {0.81, 1.77567}, {0.82, 
>     1.79751}, {0.83, 1.81008}, {0.84, 1.80272}, {0.85, 1.78359},
> {0.86,
>     1.74827}, {0.87, 1.69779}, {0.88, 1.63964}, {0.89, 1.57302}, {0.9,
>     1.49157}, {0.91, 1.40873}, {0.92, 1.32168}, {0.93, 1.22632},
> {0.94,
>     1.12993}, {0.95, 1.03509}, {0.96, 0.940307}, {0.97, 0.843889},
> {0.98,
>     0.750626}, {0.99, 0.658783}, {1., 0.571786}, {1.01, 0.490484},
> {1.02,
>     0.414139}, {1.03, 0.342955}, {1.04, 0.27755}, {1.05, 0.219544},
> {1.06,
>     0.169213}, {1.07, 0.126781}, {1.08, 0.091582}, {1.09, 0.0642237},
> {1.1,
>     0.0444826}, {1.11, 0.0324386}, {1.21, 0.17094}, {1.31, 0.721742},
> {1.41,
>     1.17931}, {1.51, 1.49921}, {1.61, 1.67064}, {1.71, 1.72145},
> {1.81,
>     1.69853}, {1.91, 1.6343}, {2.01, 1.54399}, {2.11, 1.45614}, {2.21,
>     1.36254}, {2.31, 1.27609}, {2.41, 1.19319}, {2.51, 1.12123},
> {2.61,
>     1.04736}, {2.71, 0.98465}, {2.81, 0.925526}, {2.91, 0.871404},
> {3.01,
>     0.821615}, {3.11, 0.77698}, {3.21, 0.732385}, {3.31, 0.693622},
> {3.41,
>     0.655827}, {3.51, 0.623108}, {3.61, 0.591913}, {3.71, 0.562528},
> {3.81,
>     0.534357}, {3.91, 0.50876}, {4.01, 0.484918}, {4.11, 0.463476},
> {4.21,
>     0.441866}, {4.31, 0.422324}, {4.41, 0.4049}, {4.51, 0.387806},
> {4.61,
>     0.371429}, {4.71, 0.356785}, {4.81, 0.3418}, {4.91, 0.328734}}
> 
>  Thanks
> 		  
>  nilaakash
> 
> 


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