Re: [Meep-discuss] Nonlinear Complex fit
You may want to try lmfit, https://lmfit.github.io/lmfit-py/ On Tue, Dec 17, 2019 at 01:31:29PM +, md mir wrote: > Hello, Steven G. Johnson/Oskooi and meep users, > I post this topic earlier but didn't get reply. So I'm writing it again. In > my Research I have Complex Refractive Index data from an Experiment. Like as > shown below, > Wavelength Re(index) Im(index)0.2041 2.572896.30832E-12 0.2042 > 2.572876.32153E-12 0.2043 2.572856.3348E-12 0.2044 > 2.572846.34812E-12 0.2045 2.572826.3615E-12 --- - > - - --- - - --- > - - --- - - --- - > - --- - - 4.02.572826.3615E-12 > Dr. Steven wrote in here > https://www.mail-archive.com/meep-discuss@ab-initio.mit.edu/msg01001.html > that we have to use a nonlinear optimization program to do the fit. I spent > quite a long time to find a proper code/software. But release that, most > off-the-shelf fitting programs only fit a real-valued function, whereas here > I have to fit a complex-valued function. > > I'm stuck in here for a long time now to find out the parameters (omega, > sigma, gamma) for the Lorentzian model. Does anyone have any program/code to > fit the data?Any help will be highly appreciated. > Thank you in advance.Regards Mir > ___ > meep-discuss mailing list > meep-discuss@ab-initio.mit.edu > http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss -- Andrey V. Panov panov /AT/ iacp.dvo.ru http://canopus.iacp.dvo.ru/~panov/ ___ meep-discuss mailing list meep-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
[Meep-discuss] Nonlinear Complex fit
Hello, Steven G. Johnson/Oskooi and meep users, I post this topic earlier but didn't get reply. So I'm writing it again. In my Research I have Complex Refractive Index data from an Experiment. Like as shown below, Wavelength Re(index) Im(index)0.2041 2.572896.30832E-12 0.2042 2.572876.32153E-12 0.2043 2.572856.3348E-12 0.2044 2.572846.34812E-12 0.2045 2.572826.3615E-12 --- - - - --- - - --- - - --- - - --- - - --- - - 4.02.572826.3615E-12 Dr. Steven wrote in here https://www.mail-archive.com/meep-discuss@ab-initio.mit.edu/msg01001.html that we have to use a nonlinear optimization program to do the fit. I spent quite a long time to find a proper code/software. But release that, most off-the-shelf fitting programs only fit a real-valued function, whereas here I have to fit a complex-valued function. I'm stuck in here for a long time now to find out the parameters (omega, sigma, gamma) for the Lorentzian model. Does anyone have any program/code to fit the data?Any help will be highly appreciated. Thank you in advance.Regards Mir___ meep-discuss mailing list meep-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
Re: [Meep-discuss] nonlinear complex fit
On Tue, 3 Jul 2007, matt wrote:
I have the following data for a lossy material (nylon), and I'd like to
find the parameters for meep's lorentzian model which fit the data:
frequency (hz) real(eps) imag(eps)
60 3.7 -.0666
1e3 3.5 -.0651
1e6 3.14-.068452
1e8 3.0 -.06
3e9 2.84-.033228
2.5e10 2.73-.028665
There was an indication in a previous post that this is simple
[...]
I'm not sure it's quite so simple, because most off-the-shelf fitting
programs only fit a real-valued function, whereas here you have to fit a
complex-valued function. In general, you have to use a nonlinear
optimization program to do the fit (to minimize the sum-of-squares errors
or whatever error criterion you prefer).
I don't have any off-the-shelf code to do this for the Lorentzian problem
(although of course there are lots of off-the-shelf nonlinear optimization
routines), but perhaps someone on the list does.
Steven
Here is a snippet to coax MatLab into fitting a complex valued function (a
single Lorentzian):
--
%Example data:
freq=[1 5 8 10 12 15 20];
epsre=[1.10 1.13 1.19 1.00 0.86 0.93 0.97];
epsim=[0.0031 0.026 0.13 0.33 0.11 0.026 0.0064];
epsilon=epsre+i*epsim;
%Plot it:
plot(freq,real(epsilon),'bo', freq,imag(epsilon),'ro');
lorentzian=inline('p(1)+p(2)*p(3)^2./(p(3)^2-f.^2-i*f*p(4))','p','f');
%p(1) - epsilon_infinity
%p(2) - Delta epsilon_n
%p(3) - w_n
%p(4) - gamma_n
fitfunc=inline('[real(p(1)+p(2)*p(3)^2./(p(3)^2-f.^2-i*f*p(4)))-re,imag(p(1)+p(2)*p(3)^2./(p(3)^2-f.^2-i*f*p(4)))-im]','p','f','re','im');
p=[0.9 0.15 8 2]; %initial guess
p=lsqnonlin(fitfunc,p,[],[],[],freq,real(epsilon),imag(epsilon));
disp(p) %show the answer
%Plot the result:
f=1:0.01:20;
hold on; plot(f,real(lorentzian(p,f)),'b', f,imag(lorentzian(p,f)),'r');
Unfortunately, Matt's data do not look like a Lorentzian, so it won't fit
very well if you try it on his data. Of course it is possible to add more
Lorentzians, but quite a few Lorentzians would be needed to span the wide
frequency range and since there are only few data points in Matt's table, a
multiple Lorentzian fit would start doing funny things in between the data
points (as if fitting a high order polynomial to scant data).
Perhaps you can interpolate the table a bit to alleviate this, and fix the
w_n at the original frequency ordinates, only fitting the Delta epsilons and
gammas?
Best regards,
m.
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Re: [Meep-discuss] nonlinear complex fit
--- there's two ways i've done this. first was to use nl2sol fortran routine which is a non-linear optimization routine (http://www.csit.fsu.edu/~brkardt/f_src/nl2sol/ nl2sol.f90- original fortran is at netlib.org as ACM TOMS 573). the second is to use Excel's Solver. in either case you are trying to adjust the parameters in one or more Lorentzians to minimize the difference between the data points and the fit. the obvious metric to use is something like sum over data points i of | eps_data(w_i) - eps_fit(w_i) |, where eps_data(w_i) are your data points (complex numbers) and eps_fit(w_i) is from your sum of Lorentzians (also complex numbrs). In the literature, some claim to first do the imaginary fit first and then use that to do the full fit. it really depends on the data. using nl2sol this is straight forward. in Excel, use ToolsAdd- ins...ToolPak Analysis so you have support of complex numbers. after some excel drudgery, you can set up Solver (also an Add-in) to vary the parameters in your Lorentzians to minimize the metric you have decided on. Steven is right, though, almost every time the schemes fail. you tend to have to help them along usually by giving them some reasonable values of the starting values. that is why i tend to do fits in Excel- it's easy to quickly adjust the parameters to be almost correct values and let Solver (hopefully) find the final solution. for your problem, Matt, i see: 1) too few points. one Lorentz has three parameters. you have seven data points. fitting to such a small data set is problematic (in a statistical meaningful sense). 2) the sign of Im(eps) is correct? gp -- On Jul 8, 2007, at 1:20 PM, Steven G. Johnson wrote: On Tue, 3 Jul 2007, matt wrote: I have the following data for a lossy material (nylon), and I'd like to find the parameters for meep's lorentzian model which fit the data: frequency (hz) real(eps) imag(eps) 60 3.7 -.0666 1e3 3.5 -.0651 1e6 3.14-.068452 1e8 3.0 -.06 3e9 2.84-.033228 2.5e10 2.73-.028665 There was an indication in a previous post that this is simple: G.J. Parker original patch posted by Steven, this does reduce memory requirements when using Lorentzians. i have no problems using five Lorentzians w/ this patch. one can write a stupid excel spread sheet to fit N lorentzians to a table of (experimental) complex epsilons... I'm not sure it's quite so simple, because most off-the-shelf fitting programs only fit a real-valued function, whereas here you have to fit a complex-valued function. In general, you have to use a nonlinear optimization program to do the fit (to minimize the sum-of-squares errors or whatever error criterion you prefer). I don't have any off-the-shelf code to do this for the Lorentzian problem (although of course there are lots of off-the-shelf nonlinear optimization routines), but perhaps someone on the list does. Steven ___ meep-discuss mailing list meep-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss ___ meep-discuss mailing list meep-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
Re: [Meep-discuss] nonlinear complex fit
Hello, Thanks for your suggestion. It seems that a fitting complex data is not possible with grace. It's possible to fit one curve at a time (real, or imaginary, separately). Best Regards, Matt On Tue, 3 Jul 2007, Andreas Wilde wrote: matt wrote: Hello, I have the following data for a lossy material (nylon), and I'd like to find the parameters for meep's lorentzian model which fit the data: frequency (hz) real(eps) imag(eps) 60 3.7 -.0666 1e3 3.5 -.0651 1e6 3.14-.068452 1e8 3.0 -.06 3e9 2.84-.033228 2.5e10 2.73-.028665 There was an indication in a previous post that this is simple: G.J. Parker original patch posted by Steven, this does reduce memory requirements when using Lorentzians. i have no problems using five Lorentzians w/ this patch. one can write a stupid excel spread sheet to fit N lorentzians to a table of (experimental) complex epsilons... Best Regards, Matt ___ meep-discuss mailing list meep-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss Hello, under Unix/Linux you could use xmgrace to fit the parameters of the model. I don´t know if this is better or worse than using a spreadsheet, but it should be one possibility. andreas ___ meep-discuss mailing list meep-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
[Meep-discuss] nonlinear complex fit
Hello, I have the following data for a lossy material (nylon), and I'd like to find the parameters for meep's lorentzian model which fit the data: frequency (hz) real(eps) imag(eps) 60 3.7 -.0666 1e3 3.5 -.0651 1e6 3.14-.068452 1e8 3.0 -.06 3e9 2.84-.033228 2.5e10 2.73-.028665 There was an indication in a previous post that this is simple: G.J. Parker original patch posted by Steven, this does reduce memory requirements when using Lorentzians. i have no problems using five Lorentzians w/ this patch. one can write a stupid excel spread sheet to fit N lorentzians to a table of (experimental) complex epsilons... Best Regards, Matt ___ meep-discuss mailing list meep-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
