Production Linpack

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Linpack is a set of bechmarks used to evaluate the speed of a machine or a cluster of machines running as a whole to solve one complex problem.

For the second cluster (gt3):

The cluster configuration to try out was with 232 processes using the 29 dual Xeon QuadCore computing nodes. Under these conditions, this benchmark has reported a speed of 1378 Gflops.

 ================================================================================
 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.
 
 Column=001024 Fraction=0.005 Mflops=1464513.55
Column=002048 Fraction=0.010 Mflops=1528896.47
Column=003072 Fraction=0.015 Mflops=1551433.57
Column=004096 Fraction=0.020 Mflops=1547655.82
Column=005120 Fraction=0.025 Mflops=1553515.70
Column=006016 Fraction=0.030 Mflops=1563080.91
Column=007040 Fraction=0.035 Mflops=1568080.65
Column=008064 Fraction=0.040 Mflops=1561764.53
Column=009088 Fraction=0.045 Mflops=1564233.07
Column=010112 Fraction=0.050 Mflops=1567674.61
Column=011008 Fraction=0.055 Mflops=1570180.91
Column=012032 Fraction=0.060 Mflops=1564210.24
Column=013056 Fraction=0.065 Mflops=1565705.73
Column=014080 Fraction=0.070 Mflops=1566729.81
Column=015104 Fraction=0.075 Mflops=1562692.74
Column=016128 Fraction=0.080 Mflops=1561284.43
Column=017024 Fraction=0.085 Mflops=1563470.14
Column=018048 Fraction=0.090 Mflops=1564261.64
Column=019072 Fraction=0.095 Mflops=1560160.89
Column=020096 Fraction=0.100 Mflops=1560021.98
Column=021120 Fraction=0.105 Mflops=1560699.03
Column=022016 Fraction=0.110 Mflops=1561489.45
Column=023040 Fraction=0.115 Mflops=1557829.44
Column=024064 Fraction=0.120 Mflops=1557188.75
Column=025088 Fraction=0.125 Mflops=1556971.27
Column=026112 Fraction=0.130 Mflops=1557117.95
Column=027008 Fraction=0.135 Mflops=1553671.36
Column=028032 Fraction=0.140 Mflops=1552868.51
Column=029056 Fraction=0.145 Mflops=1552921.66
Column=030080 Fraction=0.150 Mflops=1550135.41
Column=031104 Fraction=0.155 Mflops=1548939.66
Column=032128 Fraction=0.160 Mflops=1549517.84
Column=033024 Fraction=0.165 Mflops=1549134.73
Column=034048 Fraction=0.170 Mflops=1546405.02
Column=035072 Fraction=0.175 Mflops=1545369.47
Column=036096 Fraction=0.180 Mflops=1544983.27
Column=037120 Fraction=0.185 Mflops=1544769.86
Column=038016 Fraction=0.190 Mflops=1542111.25
Column=039040 Fraction=0.195 Mflops=1541073.19
Column=040064 Fraction=0.200 Mflops=1540166.07
Column=041088 Fraction=0.205 Mflops=1537917.89
Column=042112 Fraction=0.210 Mflops=1536658.62
Column=043008 Fraction=0.215 Mflops=1536318.45
Column=044032 Fraction=0.220 Mflops=1535691.70
Column=045056 Fraction=0.225 Mflops=1533448.44
Column=046080 Fraction=0.230 Mflops=1532268.45
Column=047104 Fraction=0.235 Mflops=1531728.49 
Column=048128 Fraction=0.240 Mflops=1531312.36
Column=049024 Fraction=0.245 Mflops=1529062.01
Column=050048 Fraction=0.250 Mflops=1528109.99
Column=051072 Fraction=0.255 Mflops=1527138.80
Column=052096 Fraction=0.260 Mflops=1526087.23
Column=053120 Fraction=0.265 Mflops=1523759.51
Column=054016 Fraction=0.270 Mflops=1523113.70
Column=055040 Fraction=0.275 Mflops=1522614.67
Column=056064 Fraction=0.280 Mflops=1520684.17
Column=057088 Fraction=0.285 Mflops=1519579.14
Column=058112 Fraction=0.290 Mflops=1518743.19
Column=059008 Fraction=0.295 Mflops=1518378.29
Column=060032 Fraction=0.300 Mflops=1516297.43
Column=061056 Fraction=0.305 Mflops=1515407.04
Column=062080 Fraction=0.310 Mflops=1514563.84
Column=063104 Fraction=0.315 Mflops=1514082.46
Column=064128 Fraction=0.320 Mflops=1511468.49
Column=065024 Fraction=0.325 Mflops=1510562.86
Column=066048 Fraction=0.330 Mflops=1509898.73
Column=067072 Fraction=0.335 Mflops=1508293.27
Column=068096 Fraction=0.340 Mflops=1507081.74
Column=069120 Fraction=0.345 Mflops=1506164.45
Column=070016 Fraction=0.350 Mflops=1505495.85
Column=071040 Fraction=0.355 Mflops=1503697.85
Column=072064 Fraction=0.360 Mflops=1502791.16
Column=073088 Fraction=0.365 Mflops=1501597.72
Column=074112 Fraction=0.370 Mflops=1500609.92
Column=075008 Fraction=0.375 Mflops=1498602.58
Column=076032 Fraction=0.380 Mflops=1497656.26
Column=077056 Fraction=0.385 Mflops=1496824.08
Column=078080 Fraction=0.390 Mflops=1496181.00
Column=079104 Fraction=0.395 Mflops=1494061.85
Column=080128 Fraction=0.400 Mflops=1493040.40
Column=081024 Fraction=0.405 Mflops=1492179.83
Column=082048 Fraction=0.410 Mflops=1490526.43
Column=083072 Fraction=0.415 Mflops=1489289.09
Column=084096 Fraction=0.420 Mflops=1488366.60
Column=085120 Fraction=0.425 Mflops=1487605.28
Column=086016 Fraction=0.430 Mflops=1485792.55
Column=087040 Fraction=0.435 Mflops=1484365.41
Column=088064 Fraction=0.440 Mflops=1483779.68
Column=089088 Fraction=0.445 Mflops=1482827.44
Column=090112 Fraction=0.450 Mflops=1481148.13
Column=091008 Fraction=0.455 Mflops=1480201.60
Column=092032 Fraction=0.460 Mflops=1479215.24
Column=093056 Fraction=0.465 Mflops=1477651.56
Column=094080 Fraction=0.470 Mflops=1476433.06
Column=095104 Fraction=0.475 Mflops=1475347.70
Column=096128 Fraction=0.480 Mflops=1474413.50
Column=097024 Fraction=0.485 Mflops=1472972.13
Column=098048 Fraction=0.490 Mflops=1471652.31
Column=099072 Fraction=0.495 Mflops=1470786.47
Column=103040 Fraction=0.515 Mflops=1465931.38
Column=107008 Fraction=0.535 Mflops=1461122.48
Column=111104 Fraction=0.555 Mflops=1456361.12
Column=115072 Fraction=0.575 Mflops=1451592.06
Column=119040 Fraction=0.595 Mflops=1446176.62
Column=123008 Fraction=0.615 Mflops=1441447.81
Column=127104 Fraction=0.635 Mflops=1436657.14
Column=131072 Fraction=0.655 Mflops=1432163.30
Column=135040 Fraction=0.675 Mflops=1427918.50
Column=139008 Fraction=0.695 Mflops=1423897.07
Column=159104 Fraction=0.795 Mflops=1403688.92
Column=179072 Fraction=0.895 Mflops=1387496.05
Column=199040 Fraction=0.995 Mflops=1378255.81
 ================================================================================
 T/V                N    NB     P     Q               Time                 Gflops
 --------------------------------------------------------------------------------
 WR01C2R4      200000   128     8    29            3871.74              1.378e+03
 --------------------------------------------------------------------------------
 ||Ax-b||_oo/(eps*(||A||_oo*||x||_oo+||b||_oo)*N)=        0.0015715 ...... PASSED
 ================================================================================

 Finished      1 tests with the following results:
               1 tests completed and passed residual checks,
             0 tests completed and failed residual checks,
             0 tests skipped because of illegal input values.
 ----------------------------------------------------------------------------


For the third cluster (gt):

The cluster configuration to try out was with 64 processes using the 16 dual Xeon HT (Hyperthreading) computing nodes. Under these conditions, this benchmark has reported a speed of 90.46 Gflops.

[root@gt em64t]# /opt/mpich-ch_p4-intel-1.2.7/bin/mpirun -np 64 -nolocal -machinefile machines.LINUX xhpl

============================================================================
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      :   80000 
NB     :     120 
PMAP   : Row-major process mapping
P      :       5 
Q      :       6 
PFACT  :    Left 
NBMIN  :       2 
NDIV   :       2 
RFACT  :   Crout 
BCAST  :   1ring 
DEPTH  :       0 
SWAP   : Mix (threshold = 256)
L1     : no-transposed form
U      : no-transposed form
EQUIL  : no
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
----------------------------------------------------------------------------
W00C2L2        80000   120     5     6            3773.40          9.046e+01
----------------------------------------------------------------------------
||Ax-b||_oo / ( eps * ||A||_1  * N        ) =        0.0251621 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1  * ||x||_1  ) =        0.0150516 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) =        0.0027751 ...... PASSED
============================================================================

Finished      1 tests with the following results:
             1 tests completed and passed residual checks,
             0 tests completed and failed residual checks,
             0 tests skipped because of illegal input values.
----------------------------------------------------------------------------

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