Combining fsolve and lsqcurvefit
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I have a collection of experimental data (xi, yi) called (texp, rexp). I know that 'texp' must be derived from 'rexp' following:
t(i)=k(1)*integral(@(x) exp(-k(2)./(x.*log(x))), 1, r(i))
, being k(1) and k(2) parameters. So 'r(i)' is the upper integration limit. I need to find the values of k(1) and k(2) that best fits my model. My strategy is solving the equations 't(i)-texp=0' in 'r' with fsolve and fitting k(1) and k(2) with lsqcurvefit. I am trying this:
rteor=@(k,r) fsolve(@(r) arrayfun(@(T) k(1).*integral(@(x) exp(-k(2)./(x.*log(x))), 1, r)-T, texp), 1.0001);
k = lsqcurvefit(rteor, x0, texp, rexp)
which results on the following errors:
Error using lsqcurvefit (line 251)
Function value and YDATA sizes are not equal.
Thank you for your help!