How to fit a function with n-parameters
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Hello,
I have Data (x,y) to which I want to fit a series of exponential functions like the following analytical function:
y = sum_i=1 to i=250 (A_i*exp(-x/tau_i))
This i tried to write in Matlab with vectors:
'sum(Ai.*exp(-x./taui),2)'
with Vectors Ai and taui each 1x250. I am not sure if it is possible to write it in this "vectorial" manner, but I don't know how to frame it otherwise.
The taui are known parameters and only the coefficients from Ai need to be fitted, so it is actually only a linear fit.
For the fitting i created a fittype:
myfittype = fittype('sum(Ai.*exp(-x./taui),2)','dependent',{'y'},'problem',{'taui'},'independent',{'x'},'coefficients',{'Ai'});
myfit = fit(x,y,myfittype,'StartPoints',Ai,'problem',taui);
Here occurs the Problem I am stuck with and you hopefully can help me out:
The fittype function seems not to take all vector entries as Parameters, but only the first.
So my question in general is: How can I create a function with n-parameters and fit to these parameters?
3 comentarios
dpb
el 13 de Sept. de 2018
That's totally impractical with the fittype structure; while you can write an m-file to evaluate the equation, coefficients are specified as individual strings so you would have to have and try to dereference 500 separate variables; absolutely unworkable.
The likelihood of being able to estimate that many coefficients is also probably vanishingly small, but the only way I see feasible at all would be to build the model and try to solve with nlinfit
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