why the caculation results is different for parfor-loop and for-loop?

load('matlab.mat')
for i =1:1
    b_OLS(i) = X_*y;
end
parfor i =1:1
    b_OLS_(i) = X_*y;
end
error = b_OLS_-b_OLS

The results is:

error =

1.8190e-11

why the caculation results is different for parfor-loop and for-loop?

[Stephen23]

Because the associative laws of algebra do not generally hold for floating-point numbers.

Answer 1

[Matt J]

Probably because, with a parpool active, the matrix multiplication code cannot multithread the operation in precisely the same way. The vectors are split into parallel blocks of one size if a parpool is open and another size if not.

[Edric Ellis]

In particular, by default for process-based parpool, the workers run in single-computational-thread mode. This can definitely result in slightly different results compared to multithreaded mode. You can use maxNumCompThreads(1) to put the client in single-computational-thread mode to check. Like this:

A = rand(1,10000);
B = rand(10000,1);
maxNumCompThreads(4);
c1 = A*B;
maxNumCompThreads(1);
c2 = A*B;
c1-c2

ans = -4.5475e-13