please refer to this picture for the function to be fitted. everything other than and π is a fitting parameter. is given by: where R is also a fitting parameter. There should be a total pf 6 fitting parameters.
Function with multiple input parameters to be determined through fitting
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Hi, I have a function to be fitted to some experimental data, but this function has multiple fitting parameters (6 parameters). I know that one of the ways to find these fitting parameters is to pass the function, the inital guess to the parameters and the lower and upper bounds into the lsqcurvefit function.
I have already created the function, but it seems like the software doesn't know that the p(1),p(2), p(3)... are parameters. Sorry if the function is very long.
What I wanted was p to be a vector with 6 elements p(1) p(2) p(3) p(4) p(5) p(6) but it seems like the software cant differentiate betwen p and p(1) p(2) p(3) p(4) p(5) p(6). When I try running the code, the error message I got was "Not enough input arguments"
Thank you for helping
function F = EM_SS(p, E_p)
F = p(1)*(2*pi*sqrt(p(4))/E_p)*(1/p(6))*(int(sech(((E_p - E)./p(6)))*(1 + 10*p(5)*(E - p(3)) + 126*p(5)^2*(E - p(3))^2)/(1 - exp(-2*pi*sqrt(p(4)/(E - p(3))))), E, p(3), Inf, 'ArrayValued', 1)) + p(2)*(2*pi*p(4)^3/2)*1/p(6)*((1/1^3)*sech((E_p - p(3) + p(4)/1^2)./p(6)) + (1/2^3)*sech((E_p - p(3) + p(4)/2^2)./p(6)) + (1/3^3)*sech((E_p - p(3) + p(4)/3^2)./p(6)) + (1/4^3)*sech((E_p - p(3) + p(4)/4^2)./p(6)) + (1/5^3)*sech((E_p - p(3) + p(4)/5^2)./p(6)) + (1/6^3)*sech((E_p - p(3) + p(4)/6^2)./p(6)) + (1/7^3)*sech((E_p - p(3) + p(4)/7^2)./p(6)));
end
Accepted Answer
Torsten
on 7 Jun 2024
Edited: Torsten
on 8 Jun 2024
You have to use "integral" instead of "int" and loop over the elements in E_p:
EM_SS([1 1 1 1 1 1],1)
function F = EM_SS(p, e_p)
for i = 1:numel(e_p)
E_p = e_p(i);
F(i) = p(1)*(2*pi*sqrt(p(4))/E_p)*(1/p(6))*...
(integral(@(E)sech(((E_p - E)./p(6)))*(1 + 10*p(5)*(E - p(3)) + ...
126*p(5)^2*(E - p(3))^2)/(1 - exp(-2*pi*sqrt(p(4)/(E - p(3))))), p(3), Inf, 'ArrayValued', 1)) + ...
p(2)*(2*pi*p(4)^3/2)*1/p(6)*(...
(1/1^3)*sech((E_p - p(3) + p(4)/1^2)./p(6)) + ...
(1/2^3)*sech((E_p - p(3) + p(4)/2^2)./p(6)) + ...
(1/3^3)*sech((E_p - p(3) + p(4)/3^2)./p(6)) + ...
(1/4^3)*sech((E_p - p(3) + p(4)/4^2)./p(6)) + ...
(1/5^3)*sech((E_p - p(3) + p(4)/5^2)./p(6)) + ...
(1/6^3)*sech((E_p - p(3) + p(4)/6^2)./p(6)) + ...
(1/7^3)*sech((E_p - p(3) + p(4)/7^2)./p(6)));
end
end
15 Comments
Torsten
on 8 Jun 2024
I think the problems will be too problem-specific to find general ressources. As said: less parameters and good initial guesses for them would be helpful. Did you plot Abs against E_p for the initial guesses you provided to get an impression of the "initial fitting quality" ?
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