fit function not optimizing parameters

I am attempting to fit a superguassian function to step function. With the following code. (In practice the code should be able to handle all regimes from a normal guassian to a step function, I'm just testing an edge case)

output = ones(512, 1);
output(start:stop) = min(outline); %outline is defined earlier in code, min(outline) ~ 0.92
A = 1 - min(output);
g = fittype(@(b,c,x) 1 - A*exp(- ( (x-256)/ c ).^(2*round(b))),... 
            'dependent',{'y'},'independent',{'x'},'coefficients',{'b','c'});
x = reshape(1:numel(output),numel(output),[])
y = reshape(output,numel(output),[])
mdl = fit(x,y,g,'lower',[1 1], 'upper', [1e3 200])
f = figure
scatter(1:numel(output),output)
xlim([0 numel(output)])
hold on
plot(mdl)
hold off

The code produces the following fit:

However, if I arbitrarily constrain c (which controls the width of the graph) to have a minimum value within the following by modifying the fitting code like such:

g = fittype(@(b,c,x) 1 - A*exp(- ( (x-256)/max([120 c]) ).^(2*round(b))),...
            'dependent',{'y'},'independent',{'x'},'coefficients',{'b','c'});

Then I get the following fit:

Clearly the function is capable of producing a better fit with a slightly larger c value, yet it doesn't. Any insights as to where I'm making a mistake here? Thanks!

[Torsten]

The fittype function must be differentiable with respect to the parameters for "fit" to succeed.

Since this is not the case for your function definitions, the results will be unpredictable and poor.

I suggest using "ga" instead of "fit".

Answer 1

[Matt J]

Loop over the discrete variables. Use fit() with respect to the continuous ones.

for b=1:4

    g = fittype(@(b,c,x) 1 - A*exp(- ( (x-256)/ c ).^(2*b),... 
                'dependent',{'y'},'independent',{'x'},'coefficients',{'c'});

    [mdl(b),gof(b)] = fit(x(:),y(:),g,'lower',1, 'upper', 200)

end

Then take b as that which gives the best gof(b).