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MathGroup Archive 2005

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NonlinearFit

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57671] NonlinearFit
  • From: "michael" <john at rsc.anu.edu.au>
  • Date: Fri, 3 Jun 2005 05:34:39 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hallo!

I get a series of error messages when trying to do the following
fitting. Does anyone have an explanation for this?

Needs["Statistics`NonlinearFit`"];

dataset = {{1.57, 166796}, {3.13, 136002}, {4.7, 65030}, {6.26, 4521},
{7.83,
      4318}, {9.39, 49000}, {10.96, 60576}, {12.52,
      17297}, {14.09, -18531}, {15.65, 19586}, {17.22, 113782}, {18.78,

      162297}, {20.35, 104847}, {21.91, 21690}, {23.48, 26122}, {25.04,

      124402}, {26.61, 230890}, {28.17, 268847}, {29.74, 265542},
{31.3,
      286730}, {32.87, 347177}, {34.43, 398782}, {36., 405570}, {37.56,

      386662}, {39.13, 378862}, {40.69, 375894}, {42.26, 382073},
{43.82,
      421963}, {45.39, 513252}, {46.95, 623846}, {48.52, 690012},
{50.08,
      717172}, {51.65, 768446}, {53.21, 909624}, {54.78, 1113780},
{56.34,
      1300421}, {57.91, 1468149}, {59.47, 1680055}, {61.04, 1970465},
{62.6,
      2367746}, {64.17, 2809895}, {65.73, 3264465}, {67.3, 3692246},
{68.86,
      4046681}, {70.43, 4277327}, {71.99, 4360413}, {73.56, 4345338},
{75.12,
      4362619}, {76.69, 4547432}, {78.25, 4956316}, {79.82, 5597006},
{81.38,
      6424912}, {82.95, 7086361}, {84.51, 7292635}, {86.08, 6797194},
{87.64,
      5857715}, {89.21, 4739038}, {90.77, 3744384}, {92.34, 2973363},
{93.9,
      2428473}, {95.47, 2062134}, {97.03, 1767899}, {98.6, 1540802},
{100.16,
      1377719}, {101.73, 1267488}, {103.29, 1165008}, {104.86,
      1017071}, {106.42, 862570}, {107.99, 757954}, {109.55, 720299},
{111.12,
       679967}, {112.68, 606439}, {114.25, 518329}, {115.81, 472809},
{117.38,
       481415}, {118.94, 496234}, {120.51, 471529}, {122.07, 404742},
{123.64,
       343763}, {125.2, 312319}, {126.77, 302469}, {128.33, 294309},
{129.9,
      280108}, {131.46, 285452}, {133.03, 323044}, {134.59, 364258},
{136.16,
      350050}, {137.72, 291175}, {139.29, 221524}, {140.85, 184576},
{142.42,
      178082}, {143.98, 168295}, {145.55, 150666}, {147.11, 144994},
{148.68,
      163618}, {150.24, 164462}, {151.81, 126623}, {153.37, 88763},
{154.94,
      96576}, {156.5, 130508}}

Clear[ny, nyzero, rate];
AL[ny_, nyzero_, rate_] = rate/(rate^2 + 4*Pi^2*(ny - nyzero)^2);
DL[ny_, nyzero_, rate_] =
    2*Pi*(ny - nyzero)/(rate^2 + 4*Pi^2*(ny - nyzero)^2);

tmix = 0.006; Imax = 2.9*10^8; freqzero = 78; J = 16; lambda = 45; eta
= 8;

reg = NonlinearRegress[dataset,
        Imax*(AL[freq, freqzero + J/2, lambda - eta]*
                Exp[-(lambda - eta)*tmix] +
              AL[freq, freqzero - J/2, lambda + eta]*
                Exp[-(lambda + eta)*tmix])*Cos[Pi*J*tmix] +
        Imax*(DL[freq, freqzero + J/2, lambda - eta]*
                Exp[-(lambda - eta)*tmix] -
              DL[freq, freqzero - J/2, lambda + eta]*
                Exp[-(lambda + eta)*tmix])*Sin[Pi*J*tmix],
      freq, {{Imax, 3*10^8}, {freqzero, 78}, {J, 16}, {lambda, 45},
{eta,
          10}}];
u = (BestFitParameters /. reg)
Plot[Imax*(AL[freq, freqzero + J/2, lambda - eta]*Exp[-(lambda -
eta)*tmix] +
            AL[freq, freqzero - J/2, lambda + eta]*Exp[-(lambda +
eta)*tmix])*
        Cos[Pi*J*tmix] +
      Imax*(DL[freq, freqzero + J/2, lambda - eta]*Exp[-(lambda -
eta)*tmix] -
             DL[freq, freqzero - J/2, lambda + eta]*
              Exp[-(lambda + eta)*tmix])*Sin[Pi*J*tmix], {freq, 0,
154.94},
    Prolog -> {RGBColor[1, 0, 0], PointSize[0.02], Point /@ dataset}];


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