Hi, I am trying to fit some (X0, Y0, error and weight W0=1.error) data with a model composed by three functions.
Two of these functions are also convoluted for a resolution function. Since I have 11 free prameters, I tried to fix two of them, but I get some of the paramters out of the bounds, and so I guess I am making some mistakes. My function model is composed by a first part:
y_t=model1(model1_par,x) + model2(model2_par,x);This part is convoluted for the resolution function, yielding y_conv; I add a constant background and then minimize the following quantity :
y=(y_conv+const_bkg(PAR(1),x)).*w; %(w=1./error).
My three models have the following parameters:
– const_bckg_par = [PAR(1)]
– model1_par = [PAR(2) PAR(3) PAR(4)];
– model2_par = [PAR(5) PAR(6) PAR(7) PAR(8) PAR(9) PAR(10) PAR(11)];
I made a first fit with this model, results are reasonable but not fully satisfying. I tried to reduce the number of parameters, by fixing two of them:
PAR(1): bckg = 5.9135e-04
PAR(4): wD = 11.6
The initial values of the free parameters and lb, ub have now 9 elements corresponding to the previous: [PAR(2) PAR(3) PAR(5) PAR(6) PAR(7) PAR(8) PAR(9) PAR(10) PAR(11)]:
start_val=[ 0.1 2 0.1 0.2 0.2 0.3 0.01 0.1 5.5 ];lower_lim=[ 1e-5 0 0 0 0 0 0 0 0];upper_lim=[ 1e-0 10 2 1 5 1 1 1 10];The model needs 11 parameters, then to keep two of them fixed, I define:
guess=[bckg,start_val(1:2),wD,start_val(3:9)]; and fit with
[ff,resnorm,residual,exitf,out,lam,jac]=lsqcurvefit(@model,... guess,X0,Y0,lower_lim,upper_lim,opt,sigma,1,ones(size(W0))); sigma,1,ones(size(W0)) are needed for the convolution.
I get some reasonable numbers compared with previous results, but also a few non-sense ones, completely out of the bounds:
0.0006 0.1038 0.5392 0.4817 0.4593 0.0502 0.2719 0.0434 3.6068 -260.7999 0.0049 In this case, also one of the two fixed parameters (PAR(4)=11.6) is not returned correctly.
Any idea about the error I'm doing?
Thanks!
Nando
Best Answer