Giving a constant input to a function through fsolve - matlab

Question

I have a function that seems to be working correctly when I give it single inputs to test, but I need it to work on a lot of different variables. Right now at the bottom it's evaluating the function with the initial guess of 25, and the index of 50. In playing around with it, I noticed that the index is actually chanding as fsolve runs, so I figure that I have an incomplete understanding of how fsolve is actually running here, but I can't fix it. My end goal is that I'll be able to cycle the index from 1 to 54 in a for loop, and inside that loop, the initial guess will change based on an algorith I already have running. So pretty much I just need to sort out this function input problem.
Here's my code:
function [objfun] = RK_solver( RK_solver_input )
% Redlich/Kwong EOS
index = RK_solver_input(2)
sigma = 1;
epsilon = 0;
omega = 0.08664;
psi = 0.42748;
beta = omega * RK_solver_input(1) / (Input_Data(2)/1.01325) / Tr(index);
alpha = (Tr(index))^(-1/2);
q = psi*alpha/omega/Tr(index);
A = (sigma + epsilon - 1)*beta - 1;
B = (sigma*epsilon - sigma - epsilon)*(beta^2) + (q - sigma - epsilon)*beta;
C = -(sigma*epsilon*(1+beta) + q)*(beta^2);
Q = ((A^2) - 3*B)/9;
R = (2*(A^3) - 9*A*B + 27*C)/54;
M = R^2 - Q^3;
if M < 0
theta = acos(R/(sqrt(Q*Q*Q)));
Z(1) = -2*(Q^0.5)*(cos(theta/3)) - (A/3);
Z(2) = -2*(Q^0.5)*(cos((theta + 2*pi)/3)) - (A/3);
Z(3) = -2*(Q^0.5)*(cos((theta - 2*pi)/3)) - (A/3);
Z_liquid = min(Z);
Z_vapor = max(Z);
I_liquid = (1/(sigma-epsilon))*log((Z_liquid+sigma*beta)/(Z_liquid+epsilon*beta));
I_vapor = (1/(sigma-epsilon))*log((Z_vapor+sigma*beta)/(Z_vapor+epsilon*beta));
ln_phi_liquid = Z_liquid - 1 - log(Z_liquid - beta) - q*I_liquid;
ln_phi_vapor = Z_vapor - 1 - log(Z_vapor - beta) - q*I_vapor;
objfun = (ln_phi_liquid - ln_phi_vapor);
end
end
RK_solver_guess = [25 50];
Psat_RK_solved = fsolve(#RK_solver, RK_solver_guess)

Answer 1

The issue that you are seeing is because fsolve assumes that it can change any of the parameters specified as the second input to fsolve. In your example you pass the index as part of this initial guess, so fsolve includes the index in the optimization. As a result, fsolve is attempting to modify your real parameter (as you intended) as well as the index in an attempt to minimize the function.
Instead, you will want to specify the index as an input to just the function but not as a parameter for fsolve to use in the minimization.
You can accomplish this by modifying your anonymous function
% Can be whatever you want them to be
guesses = rand(54, 1);
for index = 1:numel(guesses)
solution(index) = fsolve(#(guess)RK_solver(guess, index), guesses(index));
end
If you break down that anonymous function, you'll see that fsolve will supplies the guess variable and then I will add the index variable myself to the function call to RK_solver.
Obviously, you would also need to modify your function definition slightly to handle the parameters and index as two parameters rather than a vector.
function objfun = RK_solver(RK_solver_input, index)