topic Hi, in Intel® oneAPI Math Kernel Library

Pardiso does not scale well in reordering step

li__wei — Sat, 21 Apr 2018 02:00:39 GMT

Hi eveyrone,

I have been solving a large symmetric indefinite sparse matrix using Pardiso symmetric solver, with property as below:

< Linear system Ax = b > (Upper half)

number of equations: 107694

number of non-zeros in A: 714952

number of non-zeros in A (%): 0.006164

number of right-hand sides: 1

However, it does not scale well in reorder step. Could anyone help?

thread = 1

reorder: 0.410754 s

factorize: 0.159544 s

solution: 0.047355 s

thread = 2

reorder: 0.404389 s

factorize: 0.073979 s

solution: 0.049030 s

thread = 4

reorder: 0.417474 s

factorize: 0.054813 s

solution: 0.038233 s

--------------

My laptop has 8 CPU, with details as below:

Architecture: x86_64

CPU op-mode(s): 32-bit, 64-bit

Byte Order: Little Endian

CPU(s): 8

On-line CPU(s) list: 0-7

Thread(s) per core: 2

Core(s) per socket: 4

Socket(s): 1

Vendor ID: GenuineIntel

CPU family: 6

Model: 60

Stepping: 3

CPU MHz: 2594.000

BogoMIPS: 5188.00

Virtualization: VT-x

Detailed information is in attachment.

Thanks for help!

Hi,

Alexander_K_Intel2 — Mon, 23 Apr 2018 14:58:01 GMT

Hi, Is your matrix have blocked structure? Can you try set iparm[36] to -90 and rerun your test? Thanks, Alex

Hi Alexander,

li__wei — Tue, 24 Apr 2018 04:32:34 GMT

Hi Alexander,

Thanks for reply.

The matrix is a KKT system from FEM stiffness matrix and lagrange mutipliers. It has structure as below:

in which A is the n x n stiffness matrix from a FEM structure, Λ is a m x n lagrange multipliers matrix, usually m << n, ε is a very small perturbation.

When I set the iparm[36] to -90,

thread = 1

reorder time: 0.205429 s

thread = 2

reorder time: 0.141978 s

thread = 4

reorder time: 0.127079 s

It does scale somehow. Is this desired scalability for Pardiso?

The Pardiso manual does not mention what iparm[36] is for. What does setting it to -90 mean?

The output files are in attachment.

Btw, the residual is computed from ||Ax - b||₂ / ||b||₂,

iparm[36] = 0

residual = 4.208551e-15

iparm[36] = -90

residual = 5.733099e-12

Thanks!

Hi Li Wei,

Ying_H_Intel — Fri, 27 Apr 2018 02:44:01 GMT

Hi Li Wei,
It looks a problem. Could you provide us your test matrix and command line, a test code will be better.

and FYI, as i mentioned in topic: https://software.intel.com/en-us/forums/intel-math-kernel-library/topic/777236

MKL 2018 update 2 have some update about Pardiso routine, you may try it .

https://software.intel.com/en-us/articles/intel-math-kernel-library-intel-mkl-2018-bug-fixes-list

MKLD-2776

Improved the performance of Intel MKL Pardiso routine in the case of multiple RHS and linking with Intel® Threaded Building Blocks (Intel® TBB) threading layer.

Best Regards,
Ying

Quote:Ying H. (Intel) wrote:

li__wei — Fri, 27 Apr 2018 05:21:32 GMT

Ying H. (Intel) wrote:

Hi Li Wei,
It looks a problem. Could you provide us your test matrix and command line, a test code will be better.

and FYI, as i mentioned in topic: https://software.intel.com/en-us/forums/intel-math-kernel-library/topic/...

MKL 2018 update 2 have some update about Pardiso routine, you may try it .

https://software.intel.com/en-us/articles/intel-math-kernel-library-inte...

MKLD-2776
Improved the performance of Intel MKL Pardiso routine in the case of multiple RHS and linking with Intel® Threaded Building Blocks (Intel® TBB) threading layer.

Best Regards,
Ying

Thanks for your reply!

Here is the matrix in CSR format. bs is right-hand side vector, row-ptr and col-ind are row and column vectors, val is matrix value.

testPardisoSym.cpp is the code I used to test Pardiso, and makefile.txt(remove .txt) is the makefile I used to compile.

I will try the update 2 to see if scalability improves.

Best,

Ying_H_Intel — Sat, 28 Apr 2018 06:56:55 GMT

Hi Wei,

Thank you for the test code. I can reproduce the problem with latest version. Will look into details.

Thanks
Ying

the problem has been fixed

Gennady_F_Intel — Wed, 20 Mar 2019 05:48:07 GMT

the problem has been fixed into version 2019 u3.