Jac might be unused, but I am using the Jac value.

function Test2
    clear
    n=2;
    Jac=zeros(n); fv=zeros(n,1); f=zero(n,1); Cd=zeros(n,1); C=zeros(n,1);
    C=[0.3;0.5];
    Ca0=1;V=100; Q=50; k1=1; k2=1; al=0.5;
    Rel_dx=0.01;
    itr_max=100; tol=10^-4;
    
    for k=1:itr_max
        Jac=J(C);
        fv=fx(C);
        f=-1.*fv';
        d=Jac\f;
        C=C+d;
        Rerr=d./C;
        max_err=max(abs(Rerr));
        
        fprintf('CA1=%f CB=%f, CC=%f, CD=%f max_err=%f\n', C, max_err)
        if max_err<tol; break; end
    end
    
    if k==itr_max
        fprintf('Newtons Method Failed to converge in %d iterations\n', itr_max)
    end
    
    if i<itr_max
        fprintf('The solution is CA1=%f and CA2=%f in %d iterations\n',C,k)
    end
    
    function Jac=J(C)
        fv=fx(C);
        for j=1:n
            C(j)=C(j)*(1+Rel_dx);
            for i=1:n
                Jac(i,j)=(fvd(i)-fv(i))/C(j)/Rel_dx;
            end
            C(j)=C(j)/(1+Rel_dx);
        end
    end
    
    function fv=fx(C)
        fv(1)=Q*Ca0-Q*C(1)-k1*C(1)^2*(al*V);
        fv(2)=Q*C(1)-Q*C(2)-k2*C(2)^2*(1-al)*V;
    end
end

[per isakson]

What's your question?

Your code doesn't run

>> Test2
Undefined function 'zero' for input arguments of type
'double'.
Error in Test2 (line 3)
    Jac=zeros(n); fv=zeros(n,1); f=zero(n,1); Cd=zeros(n,1);
    C=zeros(n,1); 
>> Test2
Undefined function or variable 'fvd'.
Error in Test2/J (line 35)
                Jac(i,j)=(fvd(i)-fv(i))/C(j)/Rel_dx;
Error in Test2 (line 10)
        Jac=J(C); 
>> 

[Victor Jimenez Carrillo]

My code didn't run, but I rewrote the code on another script and it worked!

[Rik]

You also have a function with the same name as a variable.

Answer 1

[Voss]

The reason for the warning "Jac might be unused" is that Jac is initialized and then later overwritten, and it is not used for anything between the time it's initialized and the time it's overwritten.

It is true that Jac is also a variable in a nested function, which ordinarily is seen by the parent function, but in this case Jac is an output argument from the nested function, so the two Jac's are different. That is to say, your thinking would be right (i.e., the warning is mistaken) if Jac were not used as an output argument from the nested function J.

In this case, the warning is correct and initializing Jac to zeros up top has no effect.