MATLAB: Not quite fitting the data using lsqcurvefit

Question

Hello everyone. I'm trying to use lsqcurvefit to get optimal parameter value for K (see code). The fitting looks fine except for 2 things: fitted curves are always shifted down by some amount to respect to the data (see picture), and the values I get for K are complex when it should be a real number (but I guess that's a subproduct of the main problem here). K values for different initial guesses are similar, which is good. I really don't know what is going on, I hope someone can give me a hint.

Here's the code:

R=[0.1:0.1:0.4 0.6:0.2:1.8 2.1 2.4:0.4:3.2 3.8 4.8 6 8.4 12.8 20 36];
pks_locs1 = [114 93.5 144 167 199.5 225.5 275 271.5 282.5 301.5 315.5 319.5 348 356.5 362.5 390.5 408.5 420.5 464.5 449.5 457.5 477 494.5]';
CIS_H2 = 352.6;
H=0.0002529;
G=H./R';
fun_H2=@(K,R) pks_locs1(1)+CIS_H2*(K*G*(1+R)+1-sqrt((K*G*(1+R)+1)^2-R'*(2*K*G').^2))/(2*K*G');
K0_H2=100;
K=lsqcurvefit(fun_H2,K0_H2,R,pks_locs1(2:end))
plot([0 R],pks_locs1,'ko',R,fun_H2(K,R),'b-')
legend('Data','Fitted exponential')
title('Data and Fitted Curve')

The value I get for K is 9.3155e+03 – 1.1463e-01i. I have tried using lsqnonlin with similar results: fitted curve down-shifted and complex K values.

Thanks in advance!

Answer 1

When your model function is fully vectorized, as suggested by Walter, the results are better, but only you can know for sure what your model function is supposed to be.

R=[0.1:0.1:0.4 0.6:0.2:1.8 2.1 2.4:0.4:3.2 3.8 4.8 6 8.4 12.8 20 36].';
pks_locs1 = [114 93.5 144 167 199.5 225.5 275 271.5 282.5 301.5 315.5 319.5 348 356.5 362.5 390.5 408.5 420.5 464.5 449.5 457.5 477 494.5]';
CIS_H2 = 352.6;
H=0.0002529;
G=H./R;
fun_H2= @(K,R)pks_locs1(1)+CIS_H2.*(K.*G.*(1+R)+1-sqrt((K.*G.*(1+R)+1).^2-R.*(2.*K.*G).^2))./(2.*K.*G);
K0_H2=5.0758e+04;
[K,fval]=lsqcurvefit(fun_H2,K0_H2,R,pks_locs1(2:end))
plot([0 R.'],pks_locs1,'ko',R,fun_H2(K,R),'b-')
legend('Data','Fitted exponential','location','southeast')
title('Data and Fitted Curve')