problem with integrating a function containing one fitting parameter

Hello all,

I am trying to fit one integral function:

Y(x) = integral ( x ./ (x.^4 + (omega + p(1)).^2) dx)

which has one fitting parameter p(1) inside.

Below is my code. But before reviewing the code, I should mention these points:

x data are "omega"

y data are the measures values "Y"

so in the code, matlab first makes a cell array of functions (one function for every Omega value). Now function contains only 'x' and p(1).

Here is the problem: G(j) = @(p)quad(f_string(p),0,3);

I try to do the integral(for example between 0 and 3), taking 'p' as independant, then do the fitting on p(1).

x=[... some example data ...];

 y=[... some example data ...];

 %estimate of error in the measurement 2%
dy = y*0.02;

 pat = 'omega';

 K_diff = 1.0 / (6.0e-9);

 f = ' x ./ (x.^4 + (omega + p(1)).^2) ';

 %Number of parameters
 Npar = 1;
 %initial parameter guess
 p = [1];

Nrepeat=10;

 sd = 0.08;

 %========================================================
 pList=zeros(Nrepeat,Npar);
 for rep =1:Nrepeat
    rep

    %form the new randomized start vector
    for np = 1:Npar
        p(np) = [p(np)*(1+sd*randn)];
    end

    %do the fit

    w = [1 5 10 15 20];

% makes a cell array of functions (one function for every Omega value)

    f_str ='';
    for i = 1:5
        replace = int2str(w(i));    
        r = regexprep(f,pat,replace);    
        r = cellstr(r);
        f_str = [f_str; r];   
    end

    f_cell = cellstr(f_str);

% integrating and fitting

    for j = 1:5
        f_string = char(f_cell(j)); 
        G(j) = @(p)quad(f_string(p),0,3);
        [p,r,j] = nlinfit(x,y,G(j),p); 
    end

??? Index exceeds matrix dimensions.

Error in ==> quad at 75 if ~isfinite(y(1))

Error in ==> @(p)quad(f_string(p),0,3)

Error in ==> nonlinear_fit_integral at 178 [p,r,j] = nlinfit(x,y,G(j),p);