Solve a numerical equation using for loop

I'm trying to solve a numerical equation with with two variables x,y with for loop that are basically normalized of each other but I get the error below. I would really appreciate if someone could please help me. Here is the code and error message:

A=rand(10,10);
B=rand(10,10);
C=rand(10,10);
xAve=2;
t=0.1;
x = zeros(10,10);
y = zeros(10,10);
S = zeros(10,10);
syms x y
for i=1:10
    for j=1:10
    eqn=(x(i,j)*y(i,j))== (A(i,j)*B(i,j)*t^2)/(xAve*C(i,j));
    S(i,j)=vpasolve(eqn,[x,y]);
    end
end

Error:

Conversion to double from struct is not possible.

Thanks in advance.

Answer 1

[DGM]

This might help:

psize=[10 10];
A=rand(psize);
B=rand(psize);
C=rand(psize);
xAve=2;
t=0.1;

S = struct('x',[],'y',[]); 
syms x y
for i=1:psize(1)
    for j=1:psize(2)
		eqn=(x*y)== (A(i,j)*B(i,j)*t^2)/(xAve*C(i,j));
		S(i,j)=vpasolve(eqn,[x,y]);
    end
end

% look at one result
S(10,10).x
S(10,10).y

You were trying to put structs into a numeric array. That doesn't work. You were also simultaneously trying to use x and y as symbolic variables and numeric arrays. When used as numeric arrays, they'd make eqn1 invalid, since you're asserting that a nonzero constant is equal to zero. Not only is there nothing to solve, it's a false assertion.

Preallocate a struct to put your results in, and just use syms for x and y.

The last issue is that I don't know how you hope to solve the equation x*y=k, where k is a constant. You only have one equation, so the solution is a curve -- the locus of an infinite number of solutions. You might be able to graph these curves and obtain some information about them, but using a solver really doesn't tell you the whole story. For emphasis:

psize=[10 10];
A=rand(psize);
B=rand(psize);
C=rand(psize);
xAve=2;
t=0.1;

% plot the solution locus for the first element
x=linspace(0,1,100);
y=((A(1,1)*B(1,1)*t^2)/(xAve*C(1,1)))./x;
loglog(x,y); hold on; grid on

That's a line, not a point. There are infinitely many solutions to every one of these. vpasolve() will just give you one point on the line. It's lack of uniqueness likely makes the given solution meaningless in any particular application.

[MarshallSc]

That helped a lot. Thank you so much, really appreciate it.

Well, what I'm ultimately looking to solve is the equation below:

I which x and y corrospond to Li and Lk, A,B and C corrospond to Eijkl, Ri, deltaH. While I got you here, could you please take a look at it to see whether there is a method to solve this equation simultaneously? I would really appreciate your advice. The Li,Lj,Lk,Ll are interchangeable. The number of roots of this equation should be 16.

Thank you.

[DGM]

Without breaking out pen and paper and trying to wrap my head around the whole thing, I'm not sure of any best way to solve it.

More generally, see if you can either simplify it to an equation of one variable, or suss out enough information to write two equations of two variables. If you can do the latter, you can just include it in your call to vpasolve().