How can I pass in variables into fsolve()?

Say I have some matrix 3x3 matrix, A, that is defined as:

for ii = 1:length(layers+1)
    A(ii) = [k0^2*eO(ii)-ky^2-kz^2,k0^2*eH(ii)+kx*ky,kx*kz;
             kx*ky-k0^2*eH(ii),k0^2*eO(ii)-kx^2-kz^2,ky*kz;
             kx*kz,ky*kz,k0^2*eE(ii)-kx^2-ky^2];
end

I am defining every variable in this matrix except for "kz". I'm trying to solve where the determinant of A is equal to zero. The catch is i don't want to use some variation of:

syms kz
kz = solve(det(A) == 0,kz);

because this is a function that is called several hundred thousand times through my main code and I would like to avoid using syms as it is slow.

Now, I've read up on a function called fsolve() and can't seem to figure out how to pass in the known variables of A to this section of code:

fun = @det0
x0 = zeros(4,1);
kz = fsolve(fun,x0);

function F = det0(kz)
F = det([k0^2*eO-ky^2-kz^2,k0^2*eH+kx*ky,kx*kz;
        kx*ky-k0^2*eH,k0^2*eO-kx^2-kz^2,ky*kz;
        kx*kz,ky*kz,k0^2*eE-kx^2-ky^2]);

Let me know if you need more information to help solve this problem. Thanks!

[Morgan Blankenship]

Or if there is another method of solving for an unknown variable without using syms, that will help too.

Answer 1

[Stephen23]

"...can't seem to figure out how to pass in the known variables of A to this section of code:"

The MATLAB documentation explains how:

https://www.mathworks.com/help/matlab/math/parameterizing-functions.html

Simply define your function with all of the required inputs:

function F = myfun(k0,kx,ky,kz,eE,eH,eO)
M = [k0^2*eO-ky^2-kz^2, k0^2*eH+kx*ky, kx*kz;
    kx*ky-k0^2*eH, k0^2*eO-kx^2-kz^2, ky*kz;
    kx*kz, ky*kz, k0^2*eE-kx^2-ky^2];
F = det(M);
end

And then use an anonymous function with fzero:

>> k0 = 1.1;
>> kx = 1.2;
>> ky = 1.3;
>> eE = 1.4;
>> eH = 1.5;
>> eO = 1.6;
>> fun = @(kz)myfun(k0,kx,ky,kz,eE,eH,eO);
>> kz = fzero(fun,pi)
kz =
      0.51807

Check the function value is zero (within floating point tolerances):

>> fun(kz)
ans =
   1.4664e-16