From my understanding, you have written MATLAB Code to optimize the parameters (a), (b), and (c) to minimize the difference between a 3x3 matrix of functions and a constant matrix (D) using “fminsearch”. However, you are facing difficulty in defining unique functions in each matrix cell and formulating a scaler objective function for optimization.
To resolve the issue, we can uniquely define each element of the function matrix(y) within the loop, preventing overwriting. Also, we can convert symbolic expressions to a function handle using “matlabFunction”, allowing numerical evaluations. Finally, the objective function can be modified to return a scalar by calculating the sum of squared differences between the evaluated function matrix and the constant matrix (D).
Please find below the update MATLAB code with the required changes:
syms a b c;
t = [1; 2; 3];
D = [1 1 1; 1 1 1; 1 2 3];
y = sym(zeros(3, 3));
for i = 1:3
for j = 1:3
if i == 1
y(i, j) = a * t(j) + b + c;
elseif i == 2
y(i, j) = a + b * t(j) + c;
else
y(i, j) = b * t(j) + c * t(j)^2 + a;
end
end
end
% Convert symbolic matrix to function handle
y_func = matlabFunction(y, 'Vars', [a, b, c]);
% Objective function
myfun = @(params) sum(sum((D - y_func(params(1), params(2), params(3))).^2));
f0 = [1, 1, 1];
% Use fminsearch to minimize the objective function
a = fminsearch(myfun, f0);
disp('Optimized parameters:');
disp(a);
Please find attached the documentation of functions used for reference:
I hope this assists in resolving the issue.
