Nonlinear curve fitting of multiple peaks

Hi,

I have an home-made equation as y=f(x1,x2,x3). I would like to fit peaks using this formula. However, I want to us the same x1,x2,x3 to fit 3 peaks. How can I do it? Also, my equation is kind of comlicated. It contains several home-made functions. In short, the function is not as obvious as a simple formula. I don't know if this matters. Thanks!

Answer 1

[Bjorn Gustavsson]

General question, general answer.

If you have a 1-Dimensional function , f(pars,x), that depends on a couple of parameters and you want to fit a sum of that function with different sets of parameters you can do something like this:

function fx = sum_of_function(f,pars,x)
fx = 0;
for i1 = 1:size(pars,1)
  fx = fx + f(pars(i1,:),x);
end
end

Then you can fit your sum-of-functions something like this:

par0 = [1,2;pi,exp(1);sqrt(2),sqrt(3)]; % whatever suitable initial parameters might be
best_par = fminsearch(@(pars) sum((curve2fit-sum_of_functions(f,pars,x)).^2),par0);

HTH

[Xi]

I am sorry I may be not clear enough. My question is:

My function has three variables, x1,x2,x3, not parameters;

I want to fit at least three curves with the same x1,x2,x3.

best_par = fminsearch(@(pars) sum((curve2fit-sum_of_functions(f,pars,x)).^2),par0); This can only fit one curve at once.

[Bjorn Gustavsson]

So you want to fit one function to three different curves? Something like this?

best_par = fminsearch(@(pars) sum(sum((curves2fit-[1;1;1]*f(pars(1),pars(2),pars(3))).^2)),par0); 

This should work if curves2fit is a [3 x nX] double array and f(p1,p2,p3) returns an [1 x nX] array.

Unfortunately your description is still confusing, if this is not what you want, then I suggest that you make a

clear description of what you want.

Answer 2

[Image Analyst]

See my attached demo that can fit any number of Gaussians to some data. Adapt the formula from Gaussian to your special formulas and it should work. The main part is here:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% HEAVY LIFTING DONE RIGHT HERE:
% Run optimization
[parameter, fval, flag, output] = fminsearch(@(lambda)(fitgauss(lambda, tFit, y)), startingGuesses, options);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%