According with wikipedia, LINPACK represents a software library for performing numerical linear algebra on digital computers and it is used as a measure of a system's floating point computing power on different computing systems. In is used as a performance measure for ranking supercomputers in the TOP500 list of the world's fastest computers.

When we performed the HPLinpack test we use the following parameters: - the P x Q: we used 32 x 42. - the NB size: we used 128. - the N size was varied from 50000 to 600576. - We used the default gcc compiler with openmpi/gcc.

cat /HPL.out

================================================================================
HPLinpack 2.0 -- High-Performance Linpack benchmark -- September 10, 2008
Written by A. Petitet and R. Clint Whaley, Innovative Computing Laboratory, UTK
Modified by Piotr Luszczek, Innovative Computing Laboratory, UTK
Modified by Julien Langou, University of Colorado Denver
================================================================================

An explanation of the input/output parameters follows:
T/V : Wall time / encoded variant.
N : The order of the coefficient matrix A.
NB : The partitioning blocking factor.
P : The number of process rows.
Q : The number of process columns.
Time : Time in seconds to solve the linear system.
Gflops : Rate of execution for solving the linear system.
The following parameter values will be used:

N : 5000 10000 25000 50000 100000 150000 200000 250000
300000 350000 400000 450000 500000
NB : 128
PMAP : Row-major process mapping
P : 32
Q : 42
PFACT : Right
NBMIN : 4
NDIV : 2
RFACT : Crout
BCAST : 1ringM
DEPTH : 1
SWAP : Mix (threshold = 64)
L1 : transposed form
U : transposed form
EQUIL : yes
ALIGN : 8 double precision words

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

- The matrix A is randomly generated for each test.
- The following scaled residual check will be computed:
||Ax-b||_oo / ( eps * ( || x ||_oo * || A ||_oo + || b ||_oo ) * N )
- The relative machine precision (eps) is taken to be 1.110223e-16
- Computational tests pass if scaled residuals are less than 16.0

================================================================================
T/V N NB P Q Time Gflops
--------------------------------------------------------------------------------
WR11C2R4 5000 128 32 42 0.54 1.555e+02
--------------------------------------------------------------------------------
||Ax-b||_oo/(eps*(||A||_oo*||x||_oo+||b||_oo)*N)= 0.0060145 ...... PASSED
================================================================================
T/V N NB P Q Time Gflops
--------------------------------------------------------------------------------
WR11C2R4 10000 128 32 42 1.19 5.614e+02
--------------------------------------------------------------------------------
||Ax-b||_oo/(eps*(||A||_oo*||x||_oo+||b||_oo)*N)= 0.0047549 ...... PASSED
================================================================================
T/V N NB P Q Time Gflops
--------------------------------------------------------------------------------
WR11C2R4 25000 128 32 42 5.11 2.041e+03
--------------------------------------------------------------------------------
||Ax-b||_oo/(eps*(||A||_oo*||x||_oo+||b||_oo)*N)= 0.0026793 ...... PASSED
================================================================================
T/V N NB P Q Time Gflops
--------------------------------------------------------------------------------
WR11C2R4 50000 128 32 42 25.24 3.302e+03
--------------------------------------------------------------------------------
||Ax-b||_oo/(eps*(||A||_oo*||x||_oo+||b||_oo)*N)= 0.0021174 ...... PASSED
================================================================================
T/V N NB P Q Time Gflops
--------------------------------------------------------------------------------
WR11C2R4 100000 128 32 42 118.63 5.620e+03
--------------------------------------------------------------------------------
||Ax-b||_oo/(eps*(||A||_oo*||x||_oo+||b||_oo)*N)= 0.0013179 ...... PASSED
================================================================================
T/V N NB P Q Time Gflops
--------------------------------------------------------------------------------
WR11C2R4 150000 128 32 42 340.94 6.600e+03
--------------------------------------------------------------------------------
||Ax-b||_oo/(eps*(||A||_oo*||x||_oo+||b||_oo)*N)= 0.0013197 ...... PASSED
================================================================================
T/V N NB P Q Time Gflops
--------------------------------------------------------------------------------
WR11C2R4 200000 128 32 42 755.58 7.059e+03
--------------------------------------------------------------------------------
||Ax-b||_oo/(eps*(||A||_oo*||x||_oo+||b||_oo)*N)= 0.0013280 ...... PASSED
================================================================================
T/V N NB P Q Time Gflops
--------------------------------------------------------------------------------
WR11C2R4 250000 128 32 42 1407.96 7.398e+03
--------------------------------------------------------------------------------
||Ax-b||_oo/(eps*(||A||_oo*||x||_oo+||b||_oo)*N)= 0.0011130 ...... PASSED
================================================================================
T/V N NB P Q Time Gflops
--------------------------------------------------------------------------------
WR11C2R4 300000 128 32 42 2376.51 7.574e+03
--------------------------------------------------------------------------------
||Ax-b||_oo/(eps*(||A||_oo*||x||_oo+||b||_oo)*N)= 0.0012504 ...... PASSED
================================================================================
T/V N NB P Q Time Gflops
--------------------------------------------------------------------------------
WR11C2R4 350000 128 32 42 3887.73 7.352e+03
--------------------------------------------------------------------------------
||Ax-b||_oo/(eps*(||A||_oo*||x||_oo+||b||_oo)*N)= 0.0011484 ...... PASSED
================================================================================
T/V N NB P Q Time Gflops
--------------------------------------------------------------------------------
WR11C2R4 400000 128 32 42 7229.80 5.902e+03
--------------------------------------------------------------------------------
||Ax-b||_oo/(eps*(||A||_oo*||x||_oo+||b||_oo)*N)= 0.0009979 ...... PASSED
================================================================================
T/V N NB P Q Time Gflops
--------------------------------------------------------------------------------
WR11C2R4 450000 128 32 42 15687.89 3.872e+03
--------------------------------------------------------------------------------
||Ax-b||_oo/(eps*(||A||_oo*||x||_oo+||b||_oo)*N)= 0.0011418 ...... PASSED
================================================================================
T/V N NB P Q Time Gflops
--------------------------------------------------------------------------------
WR11C2R4 500000 128 32 42 30137.08 2.765e+03
--------------------------------------------------------------------------------
||Ax-b||_oo/(eps*(||A||_oo*||x||_oo+||b||_oo)*N)= 0.0010122 ...... PASSED
================================================================================

Finished 13 tests with the following results:
13 tests completed and passed residual checks,
0 tests completed and failed residual checks,
0 tests skipped because of illegal input values.

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

End of Tests.
================================================================================

The performance of the entire HPCC system is 7.6 Tflops (out of 11.3 Tflops). (67% efficiency).
All the hardware was stable during the 12 hours HPLinpack test, which was the main goal/purpose of this HPL run. [no symbol errors on the infiniband network].