Iteration Involving 1x4 matrix

Hello... Would like to ask the proper procedure for iteration. Say instance below

Given P: Pgiven = [2.42 4.52 10.01 15.32]
rho=function of eta (1x4 matrix)
Z=function of eta and rho (1x4 matrix)
P=function of eta, rho and  Z (1x4 matrix)-----> the P that should be calculated here needs to be equal the Pgiven

Step 1. Assumption of eta
Step 2. Calculation of rho
Step 3. Calculation of Z
Step 4. calculation of P---> end of iteration 1 

What function in matlab would allow to automatically iterate until it reached an eta that provides the calculated P be equal to Pgiven?

Thank u so much!

Answer 1

[Jan]

while abs(P - Pgiven) > 1e-6
   ...
end

[lvenG]

Hello, thank you for this... In the case that while loop doesn't result to convergence, is there any other way or procedure for iteration on matlab? Thanks.

[Jan]

Yes, of course. As in other programming languages:

maxIter = 1e6;
iter    = 0;
while abs(P - Pgiven) > 1e-6 && iter < maxIter
   ...
   iter = iter + 1;
end

Or:

maxIter   = 1e6;
converged = false;
for k = 1:maxIter
   
    converged = (abs(P - Pgiven) <= 1e-6);
    if converged
        break;
    end
end

[lvenG]

Hello @Jan, thank you so much again for helping... In my below code (with hightlighted steps from my original question above, steps 1-4), I followed your advised procedure:

maxIter = 1e6;

iter = 0;

while abs(P - Pgiven) > 1e-6 && iter < maxIter

...

iter = iter + 1;

end

but when I ran it, I got a "Operands to the logical and (&&) and or (||) operators must be convertible to logical scalar values"

Please note that I have 2 while conditions-----> calculated Pcompliq and Pcompvap must be (almost) equal to Pgiven. Hoping for your help here.

Kind regards,

Pcompliq=1; %assumed only
Pcompvap=1; %assumed only
Pgiven=[2.42*10^6 4.29*10^6 10.01*10^6 12.21*10^6];
maxIter = 1e6;
iter    = 0;
while abs(Pcompliq - Pgiven) > 1e-6 && abs(Pcompvap - Pgiven) > 1e-6 && iter < maxIter


iter = iter + 1;
end

Operands to the logical and (&&) and or (||) operators must be convertible to logical scalar values.

[Jan]

The error message means, that the operands abs(Pcompliq - Pgiven) > 1e-6 and abs(Pcompvap - Pgiven) > 1e-6 are not scalars. && needs scalar operands. What exactly is the criterion for convergence?

• all(abs(Pcompliq - Pgiven) > 1e-6)
• mean(abs(Pcompliq - Pgiven)) > 1e-6
• sum(abs(Pcompliq - Pgiven)) > 1e-6
• norm(abs(Pcompliq - Pgiven)) > 1e-6

All of these methods reply a scalar output and the && operator is working.

By the way: (10^10).^3 are two expensive power operations. 1e30 is a cheap constant.

a and b are constants. Then it saves time to define them once outside the loop.

[lvenG]

Hi Jan, thank you so much for explaining and thank you so much for helping me, there really is so much to learn and am glad this community is in for some enlightenment. Now my code is proceeding to run... Have a good day!

[Jan]

You are welcome.