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Curve fitting

From: lionel
Subject: Curve fitting
Date: Sat, 30 Jul 2011 04:36:10 -0700 (PDT)

Hi all,

I am interested in curve fitting techniques in Octave but there is little
information around to tell how to do, so I propose this tread to regroup the
different techniques available. I can start with one that I have developed
from this tread:
They give an interesting way to program curve fitting, but its is a bit
unconvenient to define the fitting function every time you need it. It also
add more probability for copy errors and makes it harder to maintain. So my
idea is to use nested functions so that you can easily change it.

First you will need to define a function for your code so that you can use
nested functions to define your fit function.

Here is a general draft script, any suggestion to make it better, or
propositions for other methods are welcome.

function c = fit_exemple

x=[ ]; % copy your x-data here or take it from the thread above
y= []; % same for y

% here you give the initial guess for the fit. This may be done better
depening on the model
b0 = 3;
a0 = 1/10;
c0 = 1/500;
c_opt = [a0, b0,c0]; % regroup the guesses
tol = 1e-5; % this is not used yet, its just a draft

[c, fval, info, output] =  fsolve (@(c) (infunc(c,x)  - y),c_opt); % here
you use the nested function defined at the end of the script
y2 =  infunc(c,x); % now you can create the fitted curve
 plot(x,y2,'linewidth',2,'r',x,y,'+','markersize',3,'linewidth',2) % and
function p = infunc(c,x)  % here is the nested function. If you want to
change the model, do it here.
        p =(1-exp(-c(1)*x))* c(2).*exp(-c(3)*x) ;


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