Re: conditions of fit parameters
- To: mathgroup at smc.vnet.net
- Subject: [mg65655] Re: conditions of fit parameters
- From: "petitsun1" <r.bactavatchalou at mx.uni-saarland.de>
- Date: Wed, 12 Apr 2006 06:00:05 -0400 (EDT)
- References: <e17fdv$ol2$1@smc.vnet.net><e1aguo$si$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
I will try to explain my problem explicitely:
I have first the following data:\!\({{10.24`, 12.611`}, {20.48`,
12.595`}, {40.96`, 12.557`}, {81.92`,
12.463`}, {163.84`, 12.234`}, {327.68`, 11.773`}, {655.36`,
11.054`}, {1310.7`, 10.191`}, {2621.4`, 9.3468`}, {5242.9`,
8.6333`}, {10486.`, 8.0744`}, {20972.`, 7.6556`}, {41943.`,
7.3466`}, {83886.`, 7.1146`}, {167770.`, 6.9339`}, {335540.`,
6.7872`}, {671090.`, 6.6575`}, {1.3422`*^6, 6.5308`},
{2.6844`*^6,
6.4072`}, {5.3687`*^6, 6.3103`}, {1.`*^7, 6.1427`},
{1.000001024`*^7,
0.1344`}, {1.000002048`*^7, 0.17804`}, {1.000004096`*^7,
0.29196`}, {1.000008192`*^7, 0.50528`}, {1.000016384`*^7,
0.83546`}, {1.000032768`*^7, 1.2298`}, {1.000065536`*^7,
1.5477`}, {1.00013107`*^7, 1.6657`}, {1.00026214`*^7,
1.5783`}, {1.00052429`*^7, 1.3658`}, {1.0010486`*^7,
1.1128`}, {1.0020972`*^7, 0.87569`}, {1.0041943`*^7,
0.67967`}, {1.0083886`*^7, 0.53152`}, {1.016777`*^7,
0.42835`}, {1.033554`*^7, 0.36402`}, {1.067109`*^7,
0.3308`}, {1.13422`*^7, 0.32231`}, {1.26844`*^7,
0.33302`}, {1.53687`*^7, 0.37133`}, {2.`*^7, 0.47939`}}\)
You can see that there are a discontinuity of the data points at 10^7.
I have define a function wich is the sum of 2 functions define in
differents x -axes, I mean:
The mathematica programm is following:
Needs["Statistics`Master`"]
Needs["Statistics`NonlinearFit`"]
Clear[f, Eu, Es, alpha, tau, beta, frmax, fr]
frmax = 1*10^7;
f1[fr_] :=
Which[0 <= fr <= frmax,
Eu1 + (Es1 -
Eu1)*(Cos[
beta1*ArcTan[((2*\[Pi]*fr*tau1)^(1 - alpha1))*
Cos[0.5*\[Pi]*
alpha1]/(1 + ((2*\[Pi]*fr*tau1)^(1 -
alpha1))*
Sin[0.5*\[Pi]*alpha1])]])
/((1 +
2*((2*\[Pi]*fr*tau1)^(1 - alpha1))*
Sin[0.5*\[Pi]*
alpha1] + ((2*\[Pi]*fr*
tau1)^(2*(1 - alpha1))))^(beta1/2))
, frmax < fr <=
2*frmax, (Es1 -
Eu1)*(Sin[
beta1*ArcTan[((2*\[Pi]*(fr - frmax)*tau1)^(1 - alpha1))*
Cos[0.5*\[Pi]*
alpha1]/(1 + ((2*\[Pi]*(fr - frmax)*tau1)^(1 -
alpha1))*Sin[0.5*\[Pi]*alpha1])]])
/((1 +
2*((2*\[Pi]*(fr - frmax)*tau1)^(1 - alpha1))*
Sin[0.5*\[Pi]*
alpha1] + ((2*\[Pi]*(fr - frmax)*
tau1)^(2*(1 - alpha1))))^(beta1/2))]
(*f2[fr_] :=
Which[0 <= fr <= frmax,
Eu2 + (Es2 -
Eu2)*(Cos[
beta2*ArcTan[((2*\[Pi]*fr*tau2)^(1alpha2))*
Cos[0.5*\[Pi]*
alpha2]/(1 + ((2*\[Pi]*fr*tau2)^(1 -
alpha2))*
Sin[0.5*\[Pi]*alpha2])]])
/((1 +
2*((2*\[Pi]*fr*tau2)^(1 - alpha2))*
Sin[0.5*\[Pi]*
alpha2] + ((2*\[Pi]*fr*
tau2)^(2*(1 - alpha2))))^(beta2/2))
, frmax < fr <=
2*frmax, (Es2 -
Eu2)*(Sin[
beta2*ArcTan[((2*\[Pi]*(fr - frmax)*tau2)^(1 - alpha2))*
Cos[0.5*\[Pi]*
alpha2]/(1 + ((2*\[Pi]*(fr - frmax)*tau2)^(1
-
alpha2))*Sin[0.5*\[Pi]*alpha2])]])
/((1 +
2*((2*\[Pi]*(fr - frmax)*tau2)^(1 - alpha2))*
Sin[0.5*\[Pi]*
alpha2] + ((2*\[Pi]*(fr - frmax)*
tau2)^(2*(1 - alpha2))))^(beta2/2))]
*)
f[fr_] := f1[fr]
p1 = ListPlot[t1, PlotStyle -> {PointSize[.02], RGBColor[0, 0, 1]}]
lsg = NonlinearRegress[ t1, f[fr],
fr, {{Eu1, 12.6}, {Es1, 6.6}, {alpha1, 0.5}, {beta1, 0.4}, {tau1,
0.0003}}, MaxIterations -> 300,
RegressionReport -> {BestFit, FitResiduals, ParameterTable,
AsymptoticCorrelationMatrix, FitCurvatureTable}, ShowProgress
-> True]
As you can see, first I have define the fnction which is a sum of
function define in different x-domain.
After, I would like to fit it with NonLinearRegress.
The Problem is that I can´t give range of the parameters which I need
to help him to fit the data points.
If you have some idea of what i can do to solve my problem, it will be
helpul..
Thanks a lot,
Ravi