custom logarithmic fit with three coefficients

Hello everyone,

I am trying to fit a custom logarithmic function

logfit2 = fittype('a + b*log(c*x)','dependent',{'y'},'independent',{'x'}, 'coefficients',{'a','b','c'});
fitulog2=fit(urot2,z,logfit2);   plot(fitulog2,'magenta');

and the data are urot2 = [5.1689; 6.2631; 7.1724; 8.1874]; and z=[20;40;60;80]; I get the error:

Error using fit>iFit

Complex value computed by model function, fitting cannot continue.

Try using or tightening upper and lower bounds on coefficients.

Did anyone use the above function for fitting? How do I set lower and upper bounds on coefficients?

Thanks, Petr.

Answer 1

[Torsten]

It doesn't make sense to use three fitting parameters for the function type you supply.

a + b*log(c*x) = a + b*log(c) + b*log(x)

So the fittype should be

u + v*log(x)

This way, you also circumvent the problem of a negative value for c which makes log(c*x) complex-valued (the reason for your error message).