parallel independent iteration of elements in an array - matlab

Question

I want to iterate all the elements independently (same condition for all elements though). I want to stop the iteration when the value stops changing. I will post the part of my code. According to some research, I figured that it can also be done using parfor loop but i don't know how to implement it. Can anyone please correct my code? Thanks in Advance.
probability = (ones(1,2048) .* 1/2048);
Tij = sum(StateTransitionfwd); %gives us an array of 2048 elements.
probability = ((probability * StateTransitionbwd) - (Tij .* probability));
threshold = (ones(1,2048) .* 0.05);
old = zeros(1,2048);
new = zeros(1,2048);
while(1)
probability = ((probability * StateTransitionbwd) - (Tij .* probability));
new = probability;
if old-new <= threshold
break
end
old = probability;
end
So basically I want the steady state probability (where it is not changing anymore)

Answer 1

For one you cannot parallellise while loops.
To implement a parfor loop make sure of the following:
- All variables must be defined before the parfor loop. Thus define output variables before the loop.
- All iterations must be absolutely independent of one another.
The second condition is not fulfilled in your case, since you are constantly updating the variable new, making it not independent.
I'd not even parallellise this code, since it's designed to break up before it went through all elements, but for the sake of argument I'll try this:
parfor ii = 1:length(Tij)
probability{ii} = ((probability * StateTransitionbwd) - (Tij .* probability));
end
Either use a cell or a matrix, whichever is more useful for your work.
Now you can go ahead and use a simple if to find your threshold:
for ii = 1:length(probability)-1
if probability(ii+1)-probability(ii)<threshold
break
end
end
As for your while loop stop condition: it's dangerous to let a loop run uncontrolled to some condition, as you do. It's rather easy to get stuck in an infinite loop. Use an additional condition MaxIt for the maximum number of iterations to do before terminating, regardless of the other condition.
while probability<threshold && MaxIt<someNumber
your code
end
Also you are checking for the validity of a full array.
A = logical([1;0]);
while A
B=1;
end
C = logical([1;1]);
while C
D=1;
end
The first while loop will not run, since one of its entries is not true; the second loop is an infinite loop now. If you want to terminate each row as soon as the condition is met, put the while loop inside a for loop over each row instead. That forloop can be parallellised if you put the while loop into a function, see the parfor documentation for that.