How to substitute matrix into function handle

I am trying to make this function work with any number of functions F{} and starting variable xx[]

I have distilled it down to this code:

clearvars
tic

% Needs to be edited regardless
xx = [1;1;1;1];  
% End edit

nx = length(xx);
X = transpose(sym('x',[1;nx]));
F = cell(nx,1);

% Needs to be edited regardless
F{1} = matlabFunction(5*X(1)*X(3) - 2*X(1)*X(2) +4*X(3)^2 - X(2)*X(4)-9.75);
F{2} = matlabFunction(6*X(1) + 3*X(2) + X(3) - X(4)-5.5);
F{3} = matlabFunction(2*X(1)^(2) + X(2)*X(3)-5*X(3)+X(1)*X(4)+3.50);
F{4} = matlabFunction(-3*X(1)*X(4) -2*X(2)^2+6*X(3)*X(4)+X(3)*X(4)-16.00);
% End edit

J = {sym(zeros(nx))};
for i = 1:length(xx)
    for j = 1:length(xx)
        J{i,j} = matlabFunction(diff(F{i},X(j)));
    end
end
for i = 1:nx
    F{i} = matlabFunction(-sym(F{i}));
end

for i = 1:200
% X = transpose(sym('x',[1;nx]));

% Currently needs to be edited if number of x changes
syms x1 x2 x3 x4
x1 = xx(1);
x2 = xx(2);
x3 = xx(3);
x4 = xx(4);
% End edit

JJ = subs(J);
FF = subs(F);
dx = JJ\FF;
xx = xx + dx;
if abs(dx) < 0.0000001
    break
end
% Currently needs to be edited if number of x changes
clear x1 x2
% End edit
end

formatSpec = 'Ans =';
for i = 1:nx
    formatSpec = append(formatSpec,' %#.8g');
end
fprintf(formatSpec,xx);
toc

in the second half, and substiture xx(1) number into X(1) symbolic variable and so on into the function handles?

Is there a way to maybe replace the "Currently needs to be edited if number of x changes" parts?

Edit1: Revised code and formatting

Edit2: Selected MATLAB version

[Torsten]

It's a really bad idea to program Newton's method symbolically since it will perform much too inefficient in higher dimensions.

Answer 1

[Infinite_king]

Hi Phuwanut Pataratawinun,

I understand that you want to make code modifications that minimize the changes needed when the input size varies.

You can achieve this by using the 'subs' function. The 'subs' function takes an array of old symbols and an array of new symbols, replacing the old symbols with the new ones and re-evaluating the expressions. To meet your requirements, you should make the following changes,

Modification 1 : Change the ‘F’ and ‘J’ type to sym arrays.

Modification 2 : Change the shape of X to array of shape [1, size]

Modification 3 : Use the ‘subs(expression_matrx, old_sym, new_sym)’ variant instead of ‘subs(expression)’ and pass X as old symbols and xx’ as new symbols.

Please find the complete code after modifications below,

clearvars
tic

% Needs to be edited regardless
xx = [1;1;1;1];  
% End edit

nx = length(xx);
X = transpose(sym('x',[1;nx]));

% Modification 1
% -------------------------------
F = sym(zeros(4,1));

% Needs to be edited regardless
F(1) = matlabFunction(5*X(1)*X(3) - 2*X(1)*X(2) +4*X(3)^2 - X(2)*X(4)-9.75);
F(2) = matlabFunction(6*X(1) + 3*X(2) + X(3) - X(4)-5.5);
F(3) = matlabFunction(2*X(1)^(2) + X(2)*X(3)-5*X(3)+X(1)*X(4)+3.50);
F(4) = matlabFunction(-3*X(1)*X(4) -2*X(2)^2+6*X(3)*X(4)+X(3)*X(4)-16.00);
% End edit


J = sym(zeros(nx));
for i = 1:length(xx)
    for j = 1:length(xx)
        J(i,j) = matlabFunction(diff(F(i),X(j)));
    end
end
for i = 1:nx
    F(i) = matlabFunction(-sym(F(i)));
end

% -----------------------------


% Modification 2 <----------
X = reshape(X,[1,4]);

for i = 1:200

    % Modification 3
    %-----------------------

    JJ = subs(J,X,xx');
    FF = subs(F,X,xx');

    %-----------------------
    dx = JJ\FF;
    xx = xx + dx;
    if abs(dx) < 0.0000001
        break
    end

end

formatSpec = 'Ans =';
for i = 1:nx
    formatSpec = append(formatSpec,' %#.8g');
end
fprintf(formatSpec,xx);

Ans = 0.67450408 0.75984488 1.3931338 2.2196929

toc

Elapsed time is 2.085016 seconds.

For more information refer the following MATLAB documentation,

1. https://www.mathworks.com/help/symbolic/subs.html
2. https://www.mathworks.com/help/matlab/ref/reshape.html
3. https://www.mathworks.com/help/symbolic/conversion.html

Hope this is helpful.