Stuck at Gauss-Newton Method code

I am trying to make a code with a formula (𝑦 = 𝑎0 (1 − 𝑒 ^(−𝑎1𝑥 ))).

Help

x=[0.25,0.75,1.25,1.75,2.25];
y=[0.23,0.58,0.70,0.76,0.79];

disp('iterations a0 a1 da0 da1')
tol= 10^-8;
a=[0.5 1];
error=1;
n=length(x);
itermax=100;

for iter=1:itermax
    a0=a(1);
    a1=a(2);
    for i=1:n
        f(i)=a0*(1-exp(-a1.*x(i)));
        j(i,1)=1-exp(-a1.*x(i));
        j(i,2)=a0*a1*exp(-a1.*x(i));
        d(i)=y(i)-f(i);
    end
    da=(j'*j)\(j'*d');
    a=a+da';
    out= [iter a da']
    disp(out);
    if (abs(da(1))<tol && abs(da(2))<tol)
        break
    end
end

x1=min(x);
x2=max(x);
xx=linspace(x1,x2,100);
yy=(a0*xx).*(1-exp(-a1*xx));
p=plot(xx,yy,x,y,'o');

[KSSV]

What is the question? Where are you stuck?

[seoung gi Sin]

the plot does not correctly reflect the data.

Answer 1

[Walter Roberson]

your j 2 is the derivative with respect to x, but you need it to be the derivative with respect to a1 which is a0*x*exp(-a1*x)

[seoung gi Sin]

Your advice is a bit helpful to me, but the graph still don't reflect the data at all.

[Walter Roberson]

da=(j'*j)\(j'*d');

I am clear why you do not factor out the j' giving you

da = j\d';

?

Answer 2

[Torsten]

Change

j(i,2)=a0*a1*exp(-a1.*x(i));

to

j(i,2)=a0*x(i)*exp(-a1.*x(i));

and

xx=linspace(x1,x2,100);
yy=(a0*xx).*(1-exp(-a1*xx));

to

xx=linspace(x1,x2,100);
yy=(a0).*(1-exp(-a1*xx));