fit function not optimizing parameters
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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!
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采纳的回答
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).
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