Minimize array of functions witn multiple variables

Hello, I am new in Matlab. I have array y with size 3 x 3, and in each cell of this array I have function y(i, j) ( i = 1, 2, 3; j = 1, 2, 3) that depends on 3 variables: a, b, c

I would like minimize function myfun=@(a, b, c)(D - y); D is numerical array like D = [ 1 1 1; 1 1 1; 1 1 1;]

I tried that:

syms a b c;
y=zeros(3,3);
y=sym(y);
t = [ 1 ; 2; 3;];
D = [ 1 1 1; 1 1 1; 1 2 3; ]
for i=1:1:3
    for j=1:1:3
        y(i,j)=@(a, b, c)a.*t(j)+ b + c;
        y(i,j)=@(a, b, c)a + b.*t(j) + c;
        y(i,j)=@(a, b, c)b.*t(j) + c.*t(j).*t(j) + a;
    end
end
f0 = [1, 1, 1];
myfun=@(a, b, c)(D - y);
a = fminsearch(@myfun,f0)

But fminsearch doesn't work in this case

Thanks for the help!

Answer 1

[Deepak]

Hi @Marina Timakova,

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:

sym - www.mathworks.com/help/symbolic/sym.html

matlabFunction - www.mathworks.com/help/symbolic/sym.matlabfunction.html

I hope this assists in resolving the issue.

[Walter Roberson]

If you use

y_func = matlabFunction(y, 'Vars', {[a, b, c]}); 

then you can use

myfun = @(params) sum(sum((D - y_func(params)).^2));