# How to write a custom non linear function for data fitting?

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Jacopo Tabaglio on 23 Mar 2020
Commented: Jacopo Tabaglio on 23 Mar 2020
I wrote this script to fit some data with a custom nonlinear function, but I'm getting an almost flat line instead than an exponential.
myfittype=fittype('(N/(1 + exp((-N)*(b)*(t - tf))))','dependent',{'n'},'independent',{'t'},'coefficients',{'N','b','tf'});
h=fit(t,n,myfittype)
plot(h,t,n)

the cyclist on 23 Mar 2020
Edited: the cyclist on 23 Mar 2020
I don't have the Curve Fitting Toolbox, so I can't really comment on your current code. But, if you also have the Statistics and Machine Learning Toolbox, you could try the fitnlm function.
% Some pretend data
t_data = (-2 : 0.1 : 10)';
f_data = 8 ./ (1 + exp(-2*(t_data - 5))) + 0.2*randn(size(t_data));
% Fitting function
f = @(F,t) F(1)./(1 + exp(-F(2).*(t - F(3))));
% Initial guess at parameters
beta0 = [1 1 1];
% Fit the model
mdl = fitnlm(t_data,f_data,f,beta0);
% Plot the fit against the data
figure
hold on
plot(t_data,f_data,'.')
plot(t_data,predict(mdl,t_data)) John D'Errico on 23 Mar 2020
Answer by Jacopo moved to a comment:
"Thanks, it gives a decent graph only if I type in as initial guesses values extremely close to the solution, may be the nature of the problem. If you know a better way to do it let me know"
John D'Errico on 23 Mar 2020
Note that nonlinear fits often require an intelligent choice of starting values. The curvefitting toolbox uses random choice of initial values for general models if you give it nothing.
Jacopo Tabaglio on 23 Mar 2020
Thanks, understood