topic run pardiso twice on same matrix = not same result in Intel® oneAPI Math Kernel Library

run pardiso twice on same matrix = not same result

apocalx — Fri, 09 Sep 2011 17:23:36 GMT

I test case is attached to this message.I solve exactly the same matrix more than one time and I get different result.I can solve 10 times and get 8 times same result and 2 times another result. The next time, I get 6 times sames result and 4 times another result.Maybe you will need to run the case more than 1 time because sometime I get 10 time the same result.At each solve, it's a new surprise for me :)Here is a example result of X[2] whit 5 solve (fill matrix, facotrization and solve) :x[2] = 3.954994 +j 36.454584x[2] = 4.039025 +j 36.871752x[2] = 4.386890 +j 36.496321x[2] = 4.386890 +j 36.496321x[2] = 4.386890 +j 36.496321Marc

run pardiso twice on same matrix = not same result

Gennady_F_Intel — Sat, 10 Sep 2011 05:00:20 GMT

I just quickly checked the issue - I 've got the different numbers

x[2] = -0.220519 +j 26.730090

x[2] = -0.333848 +j 26.842847

x[2] = -0.220519 +j 26.730090

x[2] = -0.333848 +j 26.842847

x[2] = -0.220519 +j 26.730090

but the similar unrepeated results.

We will investigate the problem and back soon.

Did you check the condition number of this input?

--Gennady

run pardiso twice on same matrix = not same result

styc — Mon, 12 Sep 2011 03:02:16 GMT

Element magnitudes of your matrix vary in a huge range. I saw ones as large as 5000000 and as small as 1e-7. Typically this is not a good sign for numerical stability.

EDIT: Well, it is worse than that. The matrix is singular. The last row is all zeros. Changing the bottom right element to 1 produces a matrix with a 2-condition number of 1.8e27.

run pardiso twice on same matrix = not same result

Konstantin_A_Intel — Mon, 12 Sep 2011 03:50:42 GMT

Hi,

Indeed, if the matrix is singular (or highly ill-conditioned) than the solving process is highly unstable and, generally speaking, the result of computations is unpredictable.

Regards,
Konstantin