Pardiso Returning Wrong Results

wagner_b_1 — Sun, 01 Nov 2015 00:45:09 GMT

Hello dear friends,

I am trying to solve a problem using the finite volume method and I am having some troubles configurating the Pardiso to solve my linear system.

The system that I am trying to solve has 12 elements, and it is given by:

ia = (/ 1, 10, 19, 28, 40, 52, 64, 76, 88, 100, 109, 118, 127 /)

jac = (/ 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 5, 6, 4, 5, 6, &
4, 5, 6, 7, 8, 9, 7, 8, 9, 7, 8, 9, 1, 2, 3, &
1, 2, 3, 1, 2, 3, 4, 5, 6, 4, 5, 6, 4, 5, 6, &
7, 8, 9, 7, 8, 9, 7, 8, 9, 10, 11, 12, 10, 11, 12, &
10, 11, 12, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 5, 6, &
4, 5, 6, 4, 5, 6, 7, 8, 9, 7, 8, 9, 7, 8, 9, &
10, 11, 12, 10, 11, 12, 10, 11, 12, 4, 5, 6, 4, 5, 6, &
4, 5, 6, 7, 8, 9, 7, 8, 9, 7, 8, 9, 10, 11, 12, &
10, 11, 12, 10, 11, 12 /)

a = (/ 4.19829745d-09, -4.66477495d-06, -1.04957436d-07, -7.85398163d-10, &
0.00000000d+00, 3.36766430d-05, 3.92499666d-05, 7.14315468d-18, &
-1.37394825d-03, 0.00000000d+00, 0.00000000d+00, 1.04957436d-07, &
7.85398163d-10, 0.00000000d+00, 0.00000000d+00, 0.00000000d+00, &
0.00000000d+00, 1.37394825d-03, 0.00000000d+00, 0.00000000d+00, &
0.00000000d+00, 0.00000000d+00, 0.00000000d+00, 0.00000000d+00, &
0.00000000d+00, 0.00000000d+00, 0.00000000d+00, 0.00000000d+00, &
0.00000000d+00, -1.04957436d-07, 0.00000000d+00, 0.00000000d+00, &
0.00000000d+00, 0.00000000d+00, 0.00000000d+00, -1.37394825d-03, &
4.19829745d-09, -4.66477495d-06, 6.29744618d-08, -7.85398163d-10, &
0.00000000d+00, 2.02059858d-05, 3.92499666d-05, 7.14315468d-18, &
8.24368947d-04, 0.00000000d+00, 0.00000000d+00, -0.00000000d+00, &
7.85398163d-10, 0.00000000d+00, 0.00000000d+00, 0.00000000d+00, &
0.00000000d+00, 0.00000000d+00, 0.00000000d+00, 0.00000000d+00, &
0.00000000d+00, 0.00000000d+00, 0.00000000d+00, 0.00000000d+00, &
0.00000000d+00, 0.00000000d+00, 0.00000000d+00, 0.00000000d+00, &
0.00000000d+00, 0.00000000d+00, 0.00000000d+00, 0.00000000d+00, &
0.00000000d+00, 0.00000000d+00, 0.00000000d+00, 0.00000000d+00, &
0.00000000d+00, 0.00000000d+00, -6.29744618d-08, 0.00000000d+00, &
0.00000000d+00, 0.00000000d+00, 0.00000000d+00, 0.00000000d+00, &
-8.24368947d-04, 4.19829745d-09, -9.32954989d-07, 2.09914873d-08, &
-7.85398163d-10, 0.00000000d+00, 6.73532860d-06, 3.92499666d-05, &
1.78578867d-18, 2.74789649d-04, 0.00000000d+00, 0.00000000d+00, &
-0.00000000d+00, 7.85398163d-10, 0.00000000d+00, 0.00000000d+00, &
0.00000000d+00, 0.00000000d+00, 0.00000000d+00, 0.00000000d+00, &
0.00000000d+00, 0.00000000d+00, 0.00000000d+00, 0.00000000d+00, &
0.00000000d+00, 0.00000000d+00, 0.00000000d+00, 0.00000000d+00, &
0.00000000d+00, 0.00000000d+00, -2.09914873d-08, -7.85398163d-10, &
0.00000000d+00, 0.00000000d+00, 0.00000000d+00, 0.00000000d+00, &
-2.74789649d-04, 4.19829745d-09, -9.32954989d-07, 2.09914873d-08, &
7.85398163d-10, 0.00000000d+00, 6.73532860d-06, 3.92499666d-05, &
1.78578867d-18, 2.74789649d-04 /)

b = (/ 0.00000000d+00, 0.00000000d+00, 0.00000000d+00, 0.00000000d+00, &
-0.00031416d+00, 0.00000000d+00, 0.00000000d+00, 0.00000000d+00, &
0.00000000d+00, 0.00000000d+00, 0.00000000d+00, 0.00000000d+00 /)

I have analyzed and solved this system with Matlab and the conditioning number is about 1E3, in others words, it is not too high that cannot be solvedd using direct solvers.

I am setting the Pardiso with this parameters:

maxfct=1
mnum=1
mtype=11 ! real and nonsymmetric
msglvl=1 ! NOT prints statistical information to the screen.
perm = 1

iparm=0
iparm(1) = 1 ! no solver default
iparm(2) = 2 ! fill-in reordering from METIS
iparm(3) = 1 ! numbers of processors
iparm(4) = 0 ! no iterative-direct algorithm
iparm(5) = 0 ! no user fill-in reducing permutation
iparm(6) = 0 ! =0 solution on the first n compoments of x
iparm(7) = 0 ! not in use
iparm(8) = 9 ! numbers of iterative refinement steps
iparm(9) = 0 ! not in use
iparm(10) = 13 ! perturbe the pivot elements with 1E-13
iparm(11) = 1 ! use nonsymmetric permutation and scaling MPS
iparm(12) = 0 ! not in use
iparm(13) = 0 ! maximum weighted matching algorithm is switched-off (default for symmetric). Try iparm(13) = 1 in case of inappropriate ccuracy
iparm(14) = 0 ! Output: number of perturbed pivots
iparm(15) = 0 ! not in use
iparm(16) = 0 ! not in use
iparm(17) = 0 ! not in use
iparm(18) = -1 ! Output: number of nonzeros in the factor LU
iparm(19) = -1 ! Output: Mflops for LU factorization
iparm(20) = 0 ! Output: Numbers of CG Iterations
iparm(27) = 1

phase=13 ! Analysis, numerical factorization, solve, iterative refinement
call pardiso(pt, maxfct, mnum, mtype, phase, m, a, ia, jac, perm, 1, iparm, msglvl, b, x, error)

phase=-1
call pardiso(pt, maxfct, mnum, mtype, phase, m, A, rown, col_n, perm, 1, iparm, msglvl, b, x, error)
call mkl_free_buffers

The thing is that when I compare the Pardiso result with the Matlab one, the results does not match because Pardiso is returning strange values.

Please Help me, I cannot continue my reserach without solving this problem.

Thanks,

Wagner Barros

I think that your matrix data

mecej4 — Sun, 01 Nov 2015 01:28:00 GMT

I think that your matrix data are wrong. For instance, in row-1 you should have nine entries. The column indices of these entries should be distinct and in ascending order. What you have, however, are the values [1, 2, 3, 1, 2, 3, 1, 2, 3]. Similar errors exist in the data for subsequent rows.

You may find it helpful to set iparm(27) = 1 so that Pardiso can run some checks on the data.

Your matrix is not sparse (126 out of 144 entries are not zero). Have you considered using a dense matrix routine such as GESV?

Thanks a lot Mecej4,

wagner_b_1 — Sun, 01 Nov 2015 03:48:07 GMT

Thanks a lot Mecej4,

Our matrix entries are really wrong, it is because we are using a routine to change the triplets entries to compressed row format, and this routine was not working very well.

About these matrix, it is a model created with only four discrete cells, used to configurate the solver. The real model will have more than 1.000 cells generating a real sparse matrix with more than 10.000 rows.

I would like to thank you for your patience, and inform that I finally made the Pardiso work.

Thanks, Wagner Barros.

MKL contains a routine for

mecej4 — Sun, 01 Nov 2015 14:48:16 GMT

MKL contains a routine for converting between the COO and CSR representations: https://software.intel.com/en-us/node/468628 .

topic Pardiso Returning Wrong Results in Intel® oneAPI Math Kernel Library

Pardiso Returning Wrong Results

I think that your matrix data

Thanks a lot Mecej4,

MKL contains a routine for