Solving a System of Nonlinear Equations n Times With Different Values

Hi, I am trying to solve a system of nonlinear equations n times, and recording the output values for each time. For simplicity I wrote less complex, random nonlinear equations here rather than what I was working with, but it is the same idea. I have tried a number of things, and this skeleton of code has been the closest, but I cannot get it to return different values for each iteration. I found that I cannot embed a function into a large for loop because of MATLAB syntax, and placing the for loop within the function returns nothing. I believe that fsolve only solves the system of equations for z1(10) and z2(10) and not the first 9 values in the vectors. I can't find any information on how to change this. Any help would be greatly appreciated.

x0 = [1,1];
m = 10; % same length as z1 below, because I want to output 10 values
c = 0; % counting value
for q=1:m
    x = fsolve(@g,x0)
    c = c+1;
    p(:,c) = x; % records each output value
end

function F = g(x)
z1 = [5 6 7 8 9 10 11 12 13 14];
z2 = [1 2 3 4 5 6 7 8 9 10];
n = length(z1)
    for i=1:n
        F(1) = x(1).*x(2) - z1(i)
        F(2) = x(1) + x(2)./x(1) - z2(i) 
    end
end

Answer 1

[Sam Chak]

Hi @Rocky

When fsolve calls the system function g(x), it consistently executes the same number of loops until n reaches 10, and then returns the final solution for the system of double nonlinear equations. You can fix the code as follows:

x0  = [1, 1];   % static initial guess
c   = 0;        % initialize counting parameter
z1  = [5 6 7 8 9 10 11 12 13 14];
z2  = [1 2 3 4 5  6  7  8  9 10];
opt = optimoptions('fsolve','Display', 'none');  % can also choose 'iter'

%% call fsolve
for q = 1:numel(z1)
    x = fsolve(@(x) g(x, z1(q), z2(q)), x0, opt);
    c = c + 1;
    p(:,c) = x; % records each output value
end

%% display results
disp(p)

    2.0817    2.2543    2.3982    3.2361    4.5688    5.6913    6.7592    7.8029    8.8334    9.8559
    2.1666    2.5410    2.8756    2.4721    1.9699    1.7571    1.6274    1.5379    1.4717    1.4205

%% system of double nonlinear equations
function F = g(x, z1, z2)
    F(1) = x(1).*x(2)        - z1;
    F(2) = x(1) + x(2)./x(1) - z2;
end

[Rocky]

Thank you Sam. That makes sense.