Setting Stop Conditions for Iteration Loop in Matlab - matlab

Question

I am trying to solve some equations using a while loop. I have a known and fixed output. Workflow is as follows:
P = 100; %Desired output
x = 1; %Initial guess
while abs(something) > 1e-6
x1 = (25 * x)/2
x2 = 10x - x1
x3 = 20x - (x - x1 - x2)*2
x4 = (x - x1 - x2 -x3)*12
x5 = (x - x1 - x2 -x3) * 10 + x4
P1 = 2005x3
P2 = 1500x5
Pnew = P1 + P2
end
I was hoping to calculate x1, x2, ..., x5 and stop looping when the condition P = Pnew is reached. Due to my modest knowledge of MATLAB any help would be appreciated.
Many thanks in advance.
APPENDIX: Perhaps i didn't explained well. My goal was to stop looping when the condition P = Pnew is achieved. I have a known value P and initial value of x. Pnew should be generated through a given series of equations. When the condition is met x, x1, x2, ..., x5 will have their values. So x is not only the initial value for calculating other unknowns (x1, x2, ..., x5). I tried to modify it but got NaN Pnew, P1, error and inf for P2, x, ...
P = 100; %Desired output
x = 1; %Initial guess
Pnew = P + 1
while abs(P - Pnew) > 1e-6
x1 = (25 * x)/2;
x2 = 10*x - x1;
x3 = 20*x - (x - x1 - x2)*2;
x4 = (x - x1 - x2 -x3)*12;
x5 = (x - x1 - x2 -x3) * 10 + x4
P1 = 2005 * x3;
P2 = 150 * x5;
Pnew = P1 - P2;
error = abs(P - Pnew);
x_new = x - .001 * error;
x = x_new;
end

Answer 1

Your code will error out if you don't use * to multiply. I have fixed the code below for you. The something you are looking for is P - Pnew. This is because you are trying to find the difference and making sure it is over 1e-6 to continue the loop.
Since you need Pnew, you should also do an initial calculation for it. You should note that your calculation doesn't actually make Pnew converge to P.
P = 100; %Desired output
x = 1; %Initial guess
x1 = ( 25 * x ) / 2
x2 = 10 * x - x1
x3 = 20 * x - ( x - x1 - x2 ) * 2
x4 = ( x - x1 - x2 -x3 ) * 12
x5 = ( x - x1 - x2 -x3 ) * 10 + x4
P1 = 2005 * x3
P2 = 1500 * x5
Pnew = P1 + P2
while abs( P - Pnew ) > 1e-6
x1 = ( 25 * x ) / 2
x2 = 10 * x - x1
x3 = 20 * x - ( x - x1 - x2 ) * 2
x4 = ( x - x1 - x2 -x3 ) * 12
x5 = ( x - x1 - x2 -x3 ) * 10 + x4
P1 = 2005 * x3
P2 = 1500 * x5
Pnew = P1 + P2
end
You should probably also put ; to terminate the line to suppress the output of the calculation.
A do-while loop here would work, but Matlab doesn't have one. You can use encapsulation to hide the code duplication or use a for loop as follows as well.
P = 100; %Desired output
x = 1; %Initial guess
for i = 1:Inf
x1 = ( 25 * x ) / 2
x2 = 10 * x - x1
x3 = 20 * x - ( x - x1 - x2 ) * 2
x4 = ( x - x1 - x2 -x3 ) * 12
x5 = ( x - x1 - x2 -x3 ) * 10 + x4
P1 = 2005 * x3
P2 = 1500 * x5
Pnew = P1 + P2
if abs( P - Pnew ) < 1e-6
break;
end
end
To set a predefined iteration termination in case you have an infinite loop, you can replace i = 1:Inf with i = 1:iterMax where iterMax is the number of max iterations.

Answer 2

Usually in numeric calculations one does not test for equality as the computers cannot distinguish all real numbers. Your condition is actually satisfying for something == P - Pnew
In code it would look like this
P = 100; % Desired output
x = 1; % Initial guess
Pnew = P + 1; % Something far off, just to get through the first check
MAX_ITERATION_COUNT = 10000; % a reasonable upper bound to your loop
loopCount = 0;
while abs(P - Pnew) > 1e-6 && loopCount < MAX_ITERATION_COUNT
loopCount = loopCount + 1;
x1 = (25 * x) / 2;
x2 = 10 * x - x1;
x3 = 20 * x - (x - x1 - x2) * 2;
x4 = (x - x1 - x2 - x3) * 12;
x5 = (x - x1 - x2 - x3) * 10 + x4;
P1 = 2005 * x3;
P2 = 1500 * x5;
Pnew = P1 + P2;
end
This should work for your problem.
EDIT: I added a loop counter in case you're loop does not finish regularly.