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HPLinpack 1.0a -- High-Performance Linpack benchmark -- January 20, 2004
Written by A. Petitet and R. Clint Whaley, Innovative Computing Labs., UTK
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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 : 8000 9000 10000 11000 12000 13000 14000
NB : 60
PMAP : Row-major process mapping
P : 3
Q : 3
PFACT : Crout
NBMIN : 4
NDIV : 2
RFACT : Right
BCAST : 1ring
DEPTH : 1
SWAP : Mix (threshold = 64)
L1 : transposed form
U : transposed form
EQUIL : yes
ALIGN : 8 double precision words
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- 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
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T/V N NB P Q Time Gflops
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WR10R2C4 8000 60 3 3 60.77 5.618e+00
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||Ax-b||_oo / ( eps * ||A||_1 * N ) = 0.0352518 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1 * ||x||_1 ) = 0.0206120 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) = 0.0041406 ...... PASSED
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T/V N NB P Q Time Gflops
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WR10R2C4 9000 60 3 3 78.58 6.186e+00
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||Ax-b||_oo / ( eps * ||A||_1 * N ) = 0.0150937 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1 * ||x||_1 ) = 0.0271364 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) = 0.0048312 ...... PASSED
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T/V N NB P Q Time Gflops
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WR10R2C4 10000 60 3 3 97.99 6.805e+00
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||Ax-b||_oo / ( eps * ||A||_1 * N ) = 0.0916895 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1 * ||x||_1 ) = 0.0216965 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) = 0.0048496 ...... PASSED
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T/V N NB P Q Time Gflops
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WR10R2C4 11000 60 3 3 124.21 7.145e+00
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||Ax-b||_oo / ( eps * ||A||_1 * N ) = 0.2189801 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1 * ||x||_1 ) = 0.0217756 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) = 0.0045078 ...... PASSED
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T/V N NB P Q Time Gflops
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WR10R2C4 12000 60 3 3 151.55 7.603e+00
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||Ax-b||_oo / ( eps * ||A||_1 * N ) = 0.0110107 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1 * ||x||_1 ) = 0.0215008 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) = 0.0043380 ...... PASSED
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T/V N NB P Q Time Gflops
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WR10R2C4 13000 60 3 3 184.89 7.923e+00
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||Ax-b||_oo / ( eps * ||A||_1 * N ) = 0.0130823 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1 * ||x||_1 ) = 0.0198991 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) = 0.0043240 ...... PASSED
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T/V N NB P Q Time Gflops
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WR10R2C4 14000 60 3 3 223.38 8.191e+00
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||Ax-b||_oo / ( eps * ||A||_1 * N ) = 0.0592622 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_1 * ||x||_1 ) = 0.0205435 ...... PASSED
||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) = 0.0037756 ...... PASSED
============================================================================
Finished 7 tests with the following results:
7 tests completed and passed residual checks,
0 tests completed and failed residual checks,
0 tests skipped because of illegal input values.
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End of Tests.
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