MBG wiki | RecentChanges | Blog | 2024-03-29 | 2024-03-28

Final test with respect to problem size

============================================================================
HPLinpack 1.0a  --  High-Performance Linpack benchmark  --   January 20, 2004
Written by A. Petitet and R. Clint Whaley,  Innovative Computing Labs.,  UTK
============================================================================

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      :   15000    14000    13000    12000    11000    10000     9000     8000 
            7000     6000     5000     4000     3000     2000     1000 
NB     :      60 
PMAP   : Row-major process mapping
P      :       3 
Q      :       3 
PFACT  :   Crout 
NBMIN  :       8 
NDIV   :       2 
RFACT  :   Right 
BCAST  :  BlongM 
DEPTH  :       0 
SWAP   : Mix (threshold = 60)
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 checks will be computed:
   1) ||Ax-b||_oo / ( eps * ||A||_1  * N        )
   2) ||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  )
   3) ||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo )
- 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
----------------------------------------------------------------------------
WR05R2C8       15000    60     3     3             235.11          9.571e+00
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        0.0062770 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0207517 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0044990 ...... PASSED
============================================================================
T/V                N    NB     P     Q               Time             Gflops
----------------------------------------------------------------------------
WR05R2C8       14000    60     3     3             207.70          8.809e+00
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        0.0625598 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0216866 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0039856 ...... PASSED
============================================================================
T/V                N    NB     P     Q               Time             Gflops
----------------------------------------------------------------------------
WR05R2C8       13000    60     3     3             165.58          8.847e+00
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        0.0145176 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0220823 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0047984 ...... PASSED
============================================================================
T/V                N    NB     P     Q               Time             Gflops
----------------------------------------------------------------------------
WR05R2C8       12000    60     3     3             136.88          8.418e+00
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        0.0111995 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0218696 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0044124 ...... PASSED
============================================================================
T/V                N    NB     P     Q               Time             Gflops
----------------------------------------------------------------------------
WR05R2C8       11000    60     3     3             113.90          7.792e+00
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        0.2599581 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0258505 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0053514 ...... PASSED
============================================================================
T/V                N    NB     P     Q               Time             Gflops
----------------------------------------------------------------------------
WR05R2C8       10000    60     3     3              89.90          7.417e+00
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        0.0940512 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0222553 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0049745 ...... PASSED
============================================================================
T/V                N    NB     P     Q               Time             Gflops
----------------------------------------------------------------------------
WR05R2C8        9000    60     3     3              78.10          6.225e+00
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        0.0116730 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0209866 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0037363 ...... PASSED
============================================================================
T/V                N    NB     P     Q               Time             Gflops
----------------------------------------------------------------------------
WR05R2C8        8000    60     3     3              55.76          6.123e+00
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        0.0366222 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0214132 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0043016 ...... PASSED
============================================================================
T/V                N    NB     P     Q               Time             Gflops
----------------------------------------------------------------------------
WR05R2C8        7000    60     3     3              41.69          5.486e+00
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        0.4895670 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0247585 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0044716 ...... PASSED
============================================================================
T/V                N    NB     P     Q               Time             Gflops
----------------------------------------------------------------------------
WR05R2C8        6000    60     3     3              29.68          4.854e+00
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        0.0116541 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0243047 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0047868 ...... PASSED
============================================================================
T/V                N    NB     P     Q               Time             Gflops
----------------------------------------------------------------------------
WR05R2C8        5000    60     3     3              20.35          4.097e+00
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        0.0333293 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0220024 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0042948 ...... PASSED
============================================================================
T/V                N    NB     P     Q               Time             Gflops
----------------------------------------------------------------------------
WR05R2C8        4000    60     3     3              12.81          3.332e+00
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        0.0258982 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0239165 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0054359 ...... PASSED
============================================================================
T/V                N    NB     P     Q               Time             Gflops
----------------------------------------------------------------------------
WR05R2C8        3000    60     3     3               7.29          2.470e+00
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        0.0208900 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0220915 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0045155 ...... PASSED
============================================================================
T/V                N    NB     P     Q               Time             Gflops
----------------------------------------------------------------------------
WR05R2C8        2000    60     3     3               3.46          1.544e+00
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        0.0959997 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0233347 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0050699 ...... PASSED
============================================================================
T/V                N    NB     P     Q               Time             Gflops
----------------------------------------------------------------------------
WR05R2C8        1000    60     3     3               1.15          5.829e-01
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        1.4432780 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0350303 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0084631 ...... PASSED
============================================================================

Finished     15 tests with the following results:
             15 tests completed and passed residual checks,
              0 tests completed and failed residual checks,
              0 tests skipped because of illegal input values.
----------------------------------------------------------------------------

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