How can I extract data from fsolve results?

If I use fsolve and ('Display','iter') to display the function count, function value, norm of step, first-order optimality, and trust region radius, is there a way to create a vector containing values from this list?

options = optimoptions('fsolve','Display','iter')
fsolve(fun,x0,options)

Answer 1

[Ameer Hamza]

You can use OutputFcn property to get information from each iteration. The following code shows a simple example. It records the value of the variable and the function value. Check here for more details: https://www.mathworks.com/help/releases/R2020a/optim/ug/output-function.html

opts = optimoptions('fsolve', 'OutputFcn', @myOutFcn, 'Display', 'off');

global X f_val
X = [];
f_val = [];

fsolve(@(x) x.^3-5, rand, opts);

function stop = myOutFcn(x, optimValues, state)
    global X
    global f_val
    
    X = [X; x];
    f_val = [f_val; optimValues.fval];
    stop = 0;
end

I wrote the above code using a global variable for a quick demonstration. Global variables are somewhat unrecommended in MATLAB. You can look at John's answer here for alternate approaches: https://www.mathworks.com/matlabcentral/answers/510713-is-it-possible-to-store-the-intermediate-values-of-fmincon#answer_420002

[Ameer Hamza]

Yes, this is the simplest possible way to get the information for each iteration of the fsolve().