MATLAB beginning having difficulty with function handles [closed] - matlab

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I'm working on a project for school that basically involves iteratively solving a cubic equation. I'm using MATLAB for it, but I've never really done much with MATLAB so I'm having some trouble with the logic of it.
Here's my code:
% Redlich/Kwong EOS
sigma = 1;
epsilon = 0;
omega = 0.08664;
psi = 0.42748;
beta = #(Psat_RK) omega*PsatRK/Pc/Tr(1); % Pc is in bar, may need a unit conversion later
alpha = (Tr(1))^(-1/2);
q = psi*alpha/omega/Tr(1);
A = #(beta) (sigma + epsilon - 1)*beta - 1;
B = #(beta) (sigma*epsilon - sigma - epsilon)*(beta^2) + (q - sigma - epsilon)*beta;
C = #(beta) -(sigma*epsilon*(1+beta) + q)*(beta^2);
Q = #(A,B) ((A^2) - 3*B)/9;
R = #(A,B,C) (2*(A^3) - 9*A*B + 27*C)/54;
M = #(R,Q) R^2 - Q^3;
if M > 0
Z_single = ((-R+(M^0.5))^(1/3)) + ((-R-(M^0.5))^(1/3)) - (A/3);
I = (1/(sigma-epsilon))*log((Z_single+sigma*beta)/(Z_single+epsilon*beta));
end
if M < 0
theta = acos(R/(Q^(1/3)));
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));
end
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);
Psat_RK_solved = fsolve(objfun,10);
Basically, I'm trying to iterate on the value of Psat_RK until the objfun equals 0. I can post more details of the math if needed, but I figured this would be enough to get started. Thanks.
Edit: Sorry, forgot to actually mention the problem.
Here's the error I'm getting.
Undefined operator '>' for input arguments of type 'function_handle'.
Error in Proj2 (line 73)
if M > 0
I can't figure out how to establish in this line that M is being calculated off an anonymous function.
EDIT:
sigma = 1;
epsilon = 0;
omega = 0.08664;
psi = 0.42748;
beta = #(Psat_RK) omega*PsatRK/Pc/Tr(1); % Pc is in bar, may need a unit conversion later
alpha = (Tr(1))^(-1/2);
q = psi*alpha/omega/Tr(1);
A = #(Psat_RK) (sigma + epsilon - 1)*beta(Psat_RK) - 1;
B = #(Psat_RK) (sigma*epsilon - sigma - epsilon)*(beta(Psat_RK)^2) + (q - sigma - epsilon)*beta(Psat_RK);
C = #(Psat_RK) -(sigma*epsilon*(1+beta(Psat_RK)) + q)*(beta(Psat_RK)^2);
Q = #(Psat_RK) ((A(Psat_RK)^2) - 3*B(Psat_RK))/9;
R = #(Psat_RK) (2*(A(Psat_RK)^3) - 9*A(Psat_RK)*B(Psat_RK) + 27*C(Psat_RK))/54;
M = #(Psat_RK) R(Psat_RK)^2 - Q(Psat_RK)^3;
if M(Psat_RK) > 0
Z_single = ((-R+(M^0.5))^(1/3)) + ((-R-(M^0.5))^(1/3)) - (A/3);
I = (1/(sigma-epsilon))*log((Z_single+sigma*beta)/(Z_single+epsilon*beta));
end
if M(Psat_RK) < 0
theta = acos(R/(Q^(1/3)));
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));
end
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);
Psat_RK_solved = fsolve(objfun,10);
I know the code needs some work further down, but the code below shouldn't affect why it hangs at the first if statement, right? The error is:
Undefined function or variable 'Psat_RK'.
Error in Proj2 (line 122)
if M(Psat_RK) > 0

Answer 1

It looks like you are trying to use anonymous functions incorrectly.
If we take a look at one of them:
Q = #(A,B) ((A^2) - 3*B)/9;
To MATLAB, this is the equivalent of this function:
function C = Q(A, B)
C = ((A^2) - 3*B) / 9;
end
Q is the name of the function and doesn't represent a value. If, however, you pass Q the two arguments that it needs (A and B), then it will yield a value.
Obviously, you would want to call this in the following way:
value = Q(a,b);
If you look at your own code, you try to use Q directly as if it were a value rather than a function handle.
Z(1) = -2*(Q^0.5)*(cos(theta/3)) - (A/3);
If we break down this single line a little more, we realize that A (one of the inputs to Q) is also an anonymous function. Same actually goes for B.
Then further down the rabbit hole, A and B depend upon the output of the anonymous function beta which is finally defined at the top.
beta = #(Psat_RK) omega*PsatRK/Pc/Tr(1);
So assuming we have a value for Psat_RK, this whole chain would look like this.
betaValue = beta(Psat_RK);
aValue = A(betaValue);
bValue = B(betaValue);
qValue = A(aValue, bValue);
Now you can use qValue as a value and the statement above would become
Z(1) = -2 * (qValue ^ 0.5) * (cos(theta / 3)) - (aValue / 3);
If you wanted to simplify this, you could redefine Q to be:
Q = #(Psat_RK)(A(beta(Psat_RK))^2 - 3 * B(beta(Psat_RK))) / 9;
This applies to all anonymous functions you have defined (including M which is giving you your first error).
Summary
Anonymous functions are useful for a number of things and functional programmers love them. For your case, I would probably recommend that you just write a simple function that is a function of Psat_RK and create a single anonymous function for that and pass it to fsolve.
fsolve(#objectiveFUnction, x0);
function value = objectiveFunction(Psat_RK)
% Do all your calculations here to get objfun given Psat_RK
% No anonymous functions needed here!
end
Addendum
If we wanted to convert all of your anonymous functions to be a function of Psat_RK they would look like this.
A = #(Psat_RK) (sigma + epsilon - 1) * beta(Psat_RK) - 1;
B = #(Psat_RK) (sigma * epsilon - sigma - epsilon)*(beta(Psat_RK)^2) + (q - sigma - epsilon)*beta(Psat_RK);
C = #(Psat_RK) -(sigma*epsilon*(1+beta(Psat_RK)) + q)*(beta(Psat_RK)^2);
Q = #(Psat_RK) ((A(Psat_RK)^2) - 3*B(Psat_RK))/9;
R = #(Psat_RK) (2*(A(Psat_RK)^3) - 9*A(Psat_RK)*B(Psat_RK) + 27*C(Psat_RK))/54;
M = #(Psat_RK) R(Psat_RK)^2 - Q(Psat_RK)^3;
Example
Here is how I would write this as a separate function without all of those anonymous functions.
objectiveFunction.m
function value = objectiveFunction(psat)
% Redlich/Kwong EOS
sigma = 1;
epsilon = 0;
omega = 0.08664;
psi = 0.42748;
% Pc is in bar, may need a unit conversion later
beta = omega * psat / Pc / Tr(1); % NOT SURE WHAT Tr or Pc ARE
alpha = (Tr(1))^(-1/2);
q = psi*alpha/omega/Tr(1);
A = (sigma + epsilon - 1)*beta - 1;
B = (sigma*epsilon - sigma - epsilon)*(beta^2) + (q - sigma - epsilon)*beta;
C = beta -(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
Z_single = ((-R+(M^0.5))^(1/3)) + ((-R-(M^0.5))^(1/3)) - (A/3);
I = (1/(sigma-epsilon))*log((Z_single+sigma*beta)/(Z_single+epsilon*beta));
end
if M < 0
theta = acos(R/(Q^(1/3)));
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));
end
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;
value = (ln_phi_liquid - ln_phi_vapor);
end
Then from the MATLAB command window, you could type the following to get your solution.
Psat_RK_solved = fsolve(#objectiveFunction, 10);
This way, the only anonymous function is the one that you use to point fsolve to your actual objective function.