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

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)

Answer 1

[the cyclist]

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]

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]

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]

Thanks, understood