Details on the HPL Linpack benchmark run on the amd32 (32 cores/node, total 34 nodes or 1088 cores) nodes

The HPL Linpack benchmark version was 1.0. It was compiled against OpenMPI version 1.4.2 and linked with GotoBLAS2 library.
The benchmark was run using the OpenMPI 1.4.4rc2 mpirun launcher since this version has the --loadbalance option which
provides uniform distribution of ranks across all nodes.
The best Linpack performance recorded was 6.2 TFlop/second. The
benchmark was launched from the job head node as follows


$> /usr/local/openmpi/bin/mpirun -np 1088 --loadbalance ./xhpl

Contents of HPL.dat file follow


HPLinpack benchmark input file
Innovative Computing Laboratory, University of Tennessee
HPL.out      output file name (if any)
8            device out (6=stdout,7=stderr,file)
4            # of problems sizes (N)
10000 20000 40000 483072         Ns
1            # of NBs
128           NBs
0            PMAP process mapping (0=Row-,1=Column-major)
1            # of process grids (P x Q)
32            Ps
34            Qs
16.0         threshold
1            # of panel fact
2            PFACTs (0=left, 1=Crout, 2=Right)
1            # of recursive stopping criterium
4            NBMINs (>= 1)
1            # of panels in recursion
2            NDIVs
1            # of recursive panel fact.
1            RFACTs (0=left, 1=Crout, 2=Right)
1            # of broadcast
1            BCASTs (0=1rg,1=1rM,2=2rg,3=2rM,4=Lng,5=LnM)
1            # of lookahead depth
1            DEPTHs (>=0)
2            SWAP (0=bin-exch,1=long,2=mix)
64           swapping threshold
0            L1 in (0=transposed,1=no-transposed) form
0            U  in (0=transposed,1=no-transposed) form
1            Equilibration (0=no,1=yes)
8            memory alignment in double (> 0)
##### This line (no. 32) is ignored (it serves as a separator). ######
0                               Number of additional problem sizes for PTRANS
1200 10000 30000                values of N
0                               number of additional blocking sizes for PTRANS
40 9 8 13 13 20 16 32 64        values of NB

Contents of HPL.out file follow



============================================================================
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      :   10000    20000    40000   483072
NB     :     128
PMAP   : Row-major process mapping
P      :      32
Q      :      34
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 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
----------------------------------------------------------------------------
WR11C2R4       10000   128    32    34               2.03          3.278e+02
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        0.0324856 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0076871 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0017182 ...... PASSED
============================================================================
T/V                N    NB     P     Q               Time             Gflops
----------------------------------------------------------------------------
WR11C2R4       20000   128    32    34               6.35          8.397e+02
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        0.0058409 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0056532 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0010774 ...... PASSED
============================================================================
T/V                N    NB     P     Q               Time             Gflops
----------------------------------------------------------------------------
WR11C2R4       40000   128    32    34              23.14          1.844e+03
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        0.0042686 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0039030 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0007664 ...... PASSED
============================================================================
T/V                N    NB     P     Q               Time             Gflops
----------------------------------------------------------------------------
WR11C2R4      483072   128    32    34           11997.38          6.264e+03
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        0.0015761 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0011265 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0001925 ...... PASSED
============================================================================

Finished      4 tests with the following results:
              4 tests completed and passed residual checks,
              0 tests completed and failed residual checks,
              0 tests skipped because of illegal input values.
----------------------------------------------------------------------------

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


Last Updated: 11/22/2011

Contact: Amitoj Singh
Last modified: Nov 6, 2017