How to fit a function with n-parameters

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?

[dpb]

Do you mean to fit an exponential function to 250 sets of data I hope and not a single function with 250 exponential terms???

[Simon Streit]

It really is a function with 250 terms and the plausibility lies in the following steps, where I'm doing a Laplace Transformation, so I get a spectral peak, which is broadnend due to several physical mechanics and therefore I need those many terms as kind of a sampling rate.

[dpb]

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