Tweety <ftjp <at> gmx.de> writes:
Dear group,
I am trying to fit measured data with a function using this example:
http://fweb.wallawalla.edu/class-wiki/index.php/How_to_use_Octave_to_Fit_an_Arbitrary_Function_with_fmins
Problem is, the fitting parameters all remain 1 except for the last one
so my fitting function values all become INF.
In my understanding, a more complex function may require more time to
converge but may not cause a fundamental issue? I also tried a "tanh"
function, but could not get the files to work.
What am I missing? Do I need to run some kind of update (similar to
"texhash"?) so that octave knows the "model.m" file exists? It is
located in the same folder as the data and the fitting file. Thanks for
your remarks!
Jan
My model.m looks like this:
function sum_square_errors = model(p,x,y)
y_trial = p(1) + p(2)*exp(x.*p(3)) + p(4)*exp(x.*p(5));
difference = y-y_trial;
sum_square_errors = sum(difference.^2);
The file which I am trying to fit my data with looks like this:
clear; clc;
E = dlmread('data.txt');
x = E(:,1);
y_data = E(:,2);
p0 = [1 1 1 1 1];
p = fmins('model', p0, [], [], x, y_data);
y_fit = p(1) + p(2)*e.^(x*p(3)) + p(4)*e.^(x*p(5));
figure(1)
plot(x,y_data,'.', x,y_fit)
The data.txt file looks like this (typical saturation curve):
1329 0.1480062623
3981 0.4818839118
6711 0.691154131
9363 0.805889982
12093 0.8781710629
14745 0.9218823009
17475 0.9490571055
20127 0.9649592347
22857 0.975116832
25509 0.9815304812
28161 0.9857597316
30891 0.9887945353
33543 0.9910305769
36273 0.9927147068
38925 0.9939278847
41655 0.9951150653
44307 0.9961515922
47037 0.9970010438
49689 0.9977598722
52341 0.9983067517
55071 0.9987808017
57723 0.9990164135
60453 0.9992141382
63105 0.9993880715
65835 0.9995269449
68487 0.9996117692
71217 0.9996160582
73869 0.9995567346
76599 0.9994854522
Octave 3.8.1 on LinuxMint
Dear Jan
You approch is fine, but the data does not fit well to a double exponential.
May I suggest to use the funtion leasqr() from the optimization package.
Find illustative example for this type of problems in my lectures notes
in Section 2.2.13 on nonlinear regression, startin on page 167 in
https://web.ti.bfh.ch/~sha1/Labs/PWF/Documentation/OctaveAtBFH.pdf
The code below might illustrate the problem.
Hope this helps
Andreas
============
clear;
%clc;
E = dlmread('data.txt');
x = E(:,1);
y_data = E(:,2);
if 0
p0 = [1 1 1 1 1];
p = fmins('model', p0, [], [], x, y_data)
y_fit = p(1) + p(2)*e.^(x*p(3)) + p(4)*e.^(x*p(5));
figure(1)
plot(x,y_data,'.', x,y_fit)
endif
function res = f1(x,p)
res = p(1) + p(2)*exp(p(3)*x);
endfunction
[fr,p,kvg,iter,corp,covp] = leasqr(x,y_data,[1,-1,-1e-4],'f1');
parameters = [p';sqrt(diag(covp))']
y_fit = f1(x,p);
figure(1)
plot(x,y_data,'.',x,y_fit)
xlabel('x'); ylabel('values')
figure(2)
plot(x,y_data-y_fit)
xlabel('x'); ylabel('difference')
%% now with two exponential, which will fail miserably
function res = f2(x,p)
res = p(1) + p(2)*exp(p(3)*x) + p(4)*exp(p(4)*x);
endfunction
fr,p,kvg,iter,corp,covp] = leasqr(x,y_data,[1,-1,-1e-4,0,0],'f2');
parameters = [p';sqrt(diag(covp))']
y_fit = f2(x,p);
figure(3)
plot(x,y_data,'.',x,y_fit)
xlabel('x'); ylabel('values')
figure(4)
plot(x,y_data-y_fit)
xlabel('x'); ylabel('difference')
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