create a 2 x 1 variable that contains the current initial guess. Initialize it outside of the loop. Inside of the loop, pass the current guess as the next parameter after the variables: the list of variables tells it which value corresponds to which guess.
Inside the loop test isempty(S). If it is not empty then update the current guess to be the result of the vpasolve and record the solution in the arrays. But if isempty then do not update the current guess and save sym(nan) as the outputs.
Sometimes vpasolve fails because the starting guess it used traps it in a false minimum. Using the previous solution as the initial guess can make the algorithm faster and more likely to find a solution.
But sometimes there just are no solutions. Or the equation might turn very steep and the algorithm cannot converge (if so increasing digits() sometimes helps.)
