MATLAB: Error – Failure in initial objective function evaluation. FSOLVE cannot continue.

fsolvefunctionMATLABmatlab function

Hello all,
I am trying to solve a system of non-linear vector equations in MATLAB using fsolve.
Here is my function code:
function F = ekmodelProto(x)
global dni T L theta gam beta
n = 4;
p = ones(1, n);
x_ni = ones(n);
w = ones(1, n);
for i = 1:n
    p(i) = x(i);
end
for i = n+1:n + (n.^2) - 1
    for j = 1:n.^2
    x_ni(j) = x(i);
    end
end
for i = n+n.^2:2.*n+ n.^2
    for j = 1:n
    w(j) = x(i);
    end
end
F = [(((gam.*(((dni.*((((p.^(1-beta)'))*((w.^beta)))))').^(-theta))*T)').^(-1/theta))-p; 
((T'.*((1/p)'.*dni.*(((p.^(1-beta)'))*((w.^beta)))').^(-theta))')- x_ni;
((((x'*((w.*L)'))./L)')')-w];
end
And here is my script for getting the output:
x0 = 0.5.*ones(1, 24);
x0 = x0;
n = 4;
dni = ones(2);
T = ones(4,1);
L = ones(4,1);
theta = 4;
beta = 0.5;
gam = 1;
sol = fsolve(@ekmodelProto, x0);
For context the matrix in function F should be a n+2 x n matrix. For example, if n is 2 I expect to have a 6 x 2. This is because The first row is a vector equation equal to p which is a 1xn. The second row is equal to x_ni, which is an nxn, and the third row is equal to w which is an 1xn. I am getting the following error.
Matrix dimensions must agree.
Error in ekmodelProto (line 21)
F = [((gam.*(((dni.*((((p.^(1-beta)'))*((w.^beta)))))').^-theta)*T)')-p;
Error in fsolve (line 255)
            fuser = feval(funfcn{3},x,varargin{:});
Error in getoutput2 (line 12)
sol = fsolve(@ekmodelProto, x0);
Caused by:
    Failure in initial objective function evaluation. FSOLVE cannot continue.
Two errors are puzzling me. First, MATLAB is telling me that my matrix dimensions don't match up. I double checked and I can't find the error. Obviously, MATLAB is'nt lying. Second, I'm not sure why fsolve is having trouble parsing the initial guess. I am assuming it is shaped incorrectly. How should I shape it? When n = 4 I have 24 unknowns (4 p's, 16 x_ni's, and 4 w's). Is something else causing this error? (The way the function is written?)

Best Answer

Second, I'm not sure why fsolve is having trouble parsing the initial guess.
This is not a separate error. fsolve is simply telling you that it tried to call ekmodelProto(x0) and didn't get a result (because of the matrix dimension mismatch). It is always good to first test your objective function in isolation, and particularly at x0, before feeding it to fsolve, as I have done below.
First, MATLAB is telling me that my matrix dimensions don't match up. I double checked and I can't find the error.
When I execute,
    clear
    
    global dni T L theta gam beta
    
    x0 = 0.5.*ones(1, 24);
    x0 = x0;
    n = 4;
    dni = ones(2);
    T = ones(4,1);
    L = ones(4,1);
    theta = 4;
    beta = 0.5;
    gam = 1;
    
    ekmodelProto(x0)
and stop the code at line 21, I find that this quantity is 4x4
K>> ((((p.^(1-beta)'))*((w.^beta))))
ans =
    0.5000    0.5000    0.5000    0.5000
    0.5000    0.5000    0.5000    0.5000
    0.5000    0.5000    0.5000    0.5000
    0.5000    0.5000    0.5000    0.5000
while dni is 2x2
K>> dni
dni =
     1     1
     1     1
Therefore, you cannot multiply these two matrices together, as you attempt to do in line 21
K>> dni.*((((p.^(1-beta)'))*((w.^beta))))
Matrix dimensions must agree.
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