How do I fit a nonlinear function correctly in matlab

I have the following table, named "test":

  0.0037071        0.5 
         0.015203          1 
         0.035039        1.5 
         0.062272          2 
         0.093988        2.5 
          0.12776          3 
          0.16291        3.5 
          0.19991          4 
          0.24002        4.5 
          0.28574          5 
          0.34696        5.5 
          0.47879          6 
           1.8882     6.1125 

Now I want do fit a nonlinear function (error function) using matlab:

modelfun = @(b,x)erf(b(1)*x)./b(2) + b(3);
    beta0 = [0, 0, 0];
    mdl = fitnlm(test,modelfun,beta0)

But I get the following error:

  Error using nlinfit (line 247)
    No usable observations after removing NaNs in Y and in the result of evaluating MODELFUN at the initial value BETA0.

How can I solve this ?

(and how can I get the final fitted nonlinear function for plotting ? )

Answer 1

[Rik]

I don't have the toolbox that contains the fitnlm so I'm using fminsearch instead:

data=[...
    0.0037071 0.5
    0.015203  1
    0.035039  1.5
    0.062272  2
    0.093988  2.5
    0.12776   3
    0.16291   3.5
    0.19991   4
    0.24002   4.5
    0.28574   5
    0.34696   5.5
    0.47879   6
    1.8882    6.1125 ];
x=data(:,2);y=data(:,1);
initial_guess=[0 0 0];
modelfun = @(b,x)erf(b(1)*x)./b(2) + b(3);
f=modelfun;

%objective least squares cost function
OLS=@(b,x,y,f) sum((f(b,x) - y).^2);
opts = optimset('MaxFunEvals',50000, 'MaxIter',10000);
% Use 'fminsearch' to minimise the 'OLS' function
fit_val = fminsearch(OLS, initial_guess(:), opts,x,y,f);

Now the fit_val variable contains the estimated values of b. Now you can generate a new x vector and use your modelfun to calculate the corresponding y values.

[dh]

Thanks a lot !!

[Rik]

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