Using fsolve for solving multiple equations by using loops

I'm starting to get more deeper into equation solving with Matlab and I'm facing some problems. I have multiple equations stored in Eq (here 13, but later on there will be hundreds):

   Eq= 
   X11 + v1_3/2 + X12*v1_2 - 1
     v2_3/2 - 2*X11 + X12*v2_2 + 4
     3*X11 + v3_3/2 + X12*v3_2 + 9
   X21 + X23*v1_3 + v1_2*(X22 - 1)
 X23*v2_3 - 2*X21 + v2_2*(X22 - 2)
 3*X21 + X23*v3_3 + v3_2*(X22 + 3)
   X32*v1_2 + v1_3*(X33 - 1) + 1/2
     X32*v2_2 + v2_3*(X33 - 2) - 1
   X32*v3_2 + v3_3*(X33 + 3) + 3/2

Now, I can specify a function as input to fsolve by writing each function by hand, which works:

x0 = ones(1,13);
options = optimoptions('fsolve', 'Algorithm', 'Levenberg-Marquardt');
result = fsolve(@equations, x0, options)
   
function F = equations(x)

X11=x(1);
X12=x(2);
X21=x(3);
X22=x(4);
X23=x(5);
X32=x(6);
X33=x(7);
v1_2=x(8);
v1_3=x(9);
v2_2=x(10);
v2_3=x(11);
v3_2=x(12);
v3_3=x(13);

F(1) = X11 + v1_3/2 + X12*v1_2 - 1;
F(2) = v2_3/2 - 2*X11 + X12*v2_2 + 4;
F(3) = 3*X11 + v3_3/2 + X12*v3_2 + 9;
F(4) = X21 + X23*v1_3 + v1_2*(X22 - 1);
F(5)=X23*v2_3 - 2*X21 + v2_2*(X22 - 2);
F(6)=3*X21 + X23*v3_3 + v3_2*(X22 + 3);
F(7)= X32*v1_2 + v1_3*(X33 - 1) + 1/2;
F(8)= X32*v2_2 + v2_3*(X33 - 2) - 1;
F(9)= X32*v3_2 + v3_3*(X33 + 3) + 3/2;
end

However, I can't possibly do this for hundreds of equations, so I need to find a way to run a loop. So I thought to first extract all symbolic variables :

allVars=symvar(Eq);

and then run a loop somewhat like this:

x0 = ones(1,13);
options = optimoptions('fsolve', 'Algorithm', 'Levenberg-Marquardt');
result = fsolve(@equations, x0, options)

function F = equations(x,Eq,allVars)

    for v=1:length(allVars)
        allVars(v)=x(v);
    end

    for n=1:length(M2)
        F(n)=Eq(n);
    end

end

This does not work unfortunately. I guess it's because the equations-function needs to have only one input x so that fsolve can handle it. But then I can't assign my equations to F asf.

how could I make this work?

Answer 1

[Matt J]

Use matlabFunction to convert a symbolic implementation of the equations to a numeric one.

[holistic]

Thank you Matt. That seems to work out well, but gets me into more troubles somehow. After using matlabFunction, I get a function handle of the form:

fun=@(X11,X12...)=... 

Trying to input this into fsolve gives me an error:

Failure in initial objective function evaluation. FSOLVE cannot continue.

I assume this is because fsolve wants a function of the form:

fun=@(x) f(x(1)...x(n))

Or maybe I'm doing something wrong.

[Matt J]

Indeed, you should rewrite your symbolic code so that it works with a matrix of unknowns X(i,j) rather than naming the individual variables Xij.