How to combine various function files into a single nested function file?

Here are four function files that utilize Newton's method to solve a system of nonlinear equations. Separately, these functions solve for unknowns x1 and x2 just fine. However, I am required to combine these function files together, but I simply don't know how. Either nested functions or one simplified function file are required.

function x = NewtonSol
x0 = [2;3];
x = NewtonMethod(@function_def,@Jacobian_def,100,10^-5,x0);
%using built in function
xsol = fsolve(@function_def,x0);
end

function x = NewtonMethod(funcF,JacobianF,max_iter,epsilon,x0)
f = funcF;
J = JacobianF;
x = x0;
iter = 1;
while iter < max_iter
    y = J(x)\(-f(x));
    x = x + y;
    if norm(y, 2) < epsilon
        break;
    end
    iter = iter + 1;
end
if iter >= max_iter + 1;
    fprintf('No solution found');
end

function A = Jacobian_def(x)
x1 = x(1);
x2 = x(2);
A = zeros(2,2);
A(1,1) = 2*(x1); %df1x1
A(1,2) = 2*(x2); %df1x2
A(2,1) = (16/3)*(x1)^(-1/3); %df2x1
A(2,2) = (1/3)*(x2)^(-2/3); %df2x2
end

function y = function_def(x)
x1 = x(1);
x2 = x(2);
y = zeros(2,1);
y(1) = ((x1)^2) + ((x2)^2) - 17; %f1(x1,x2)
y(2) = (8*(x1)^(2/3)) + (x2)^(1/3) - 4; %f2(x1,x2)
end

Answer 1

[Ameer Hamza]

See Nested functions: https://www.mathworks.com/help/matlab/matlab_prog/nested-functions.html

This can be saved in one file called NewtonSol.m

function x = NewtonSol
x0 = [2;3];
x = NewtonMethod(@function_def,@Jacobian_def,100,10^-5,x0);
%using built in function
xsol = fsolve(@function_def,x0);

function x = NewtonMethod(funcF,JacobianF,max_iter,epsilon,x0)
f = funcF;
J = JacobianF;
x = x0;
iter = 1;
while iter < max_iter
    y = J(x)\(-f(x));
    x = x + y;
    if norm(y, 2) < epsilon
        break;
    end
    iter = iter + 1;
end
if iter >= max_iter + 1;
    fprintf('No solution found');
end
end

function A = Jacobian_def(x)
x1 = x(1);
x2 = x(2);
A = zeros(2,2);
A(1,1) = 2*(x1); %df1x1
A(1,2) = 2*(x2); %df1x2
A(2,1) = (16/3)*(x1)^(-1/3); %df2x1
A(2,2) = (1/3)*(x2)^(-2/3); %df2x2
end

function y = function_def(x)
x1 = x(1);
x2 = x(2);
y = zeros(2,1);
y(1) = ((x1)^2) + ((x2)^2) - 17; %f1(x1,x2)
y(2) = (8*(x1)^(2/3)) + (x2)^(1/3) - 4; %f2(x1,x2)
end

end

[Aaron Zambiasi]

Thank you very much!

[Ameer Hamza]

Glad to be of help.