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Examples of Block Algorithms in LAPACK

Having discussed in detail the derivation of one particular block algorithm, we now describe examples of the performance that has been achieved with a variety of block algorithms. Tables 3.2, 3.3, 3.4, 3.5, and 3.6 describe the hardware and software characteristics of the machines.

Table 3.2: Characteristics of the Compaq/Digital computers timed
| Dec Alpha Miata | Compaq AlphaServer DS-20
Model | LX164 | DS-20 (21264)
Processor | EV56 | EV6
Clock speed (MHz) | 533 | 500
Processors per node | 1 | 1
Operating system | Linux 2.2.7 | OSF1 V4.0 1091
BLAS | ATLAS (version 1.0) | DXML (version 3.5)
Fortran compiler | g77 (egcs 2.91.60) | f77 (version 5.2)
Fortran flags | -funroll-all-loops -fno-f2c -O3 | -O4 -fpe1
Precision | double (64-bit) | double (64-bit)

Table 3.3: Characteristics of the IBM computers timed
| IBM Power 3 | IBM PowerPC
Model | Winterhawk |
Processor | 630 | 604e
Clock speed (MHz) | 200 | 190
Processors per node | 1 | 1
Operating system | AIX 4.3 | Linux 2.2.7
BLAS | ESSL (3.1.1.0) | ATLAS (version 1.0)
Fortran compiler | xlf (6.1.0.0) | g77 (egcs 2.91.66)
Fortran flags | -O4 -qmaxmem=-1 | -funroll-all-loops -fno-f2c -O3
Precision | double (64-bit) | double (64-bit)

Table 3.4: Characteristics of the Intel computers timed
| Intel Pentium II | Intel Pentium III
Model |  |
Processor | Pentium II | Pentium III
Clock speed (MHz) | 450 | 550
Processors per node | 1 | 1
Operating system | Linux 2.2.7 | Linux 2.2.5-15
BLAS | ATLAS (version 1.0) | ATLAS (version 1.0)
Fortran compiler | g77 (egcs 2.91.60) | g77 (egcs 2.91.66)
Fortran flags | -funroll-all-loops -fno-f2c -O3 | -funroll-all-loops -fno-f2c -O3
Precision | double (64-bit) | double (64-bit)

Table 3.5: Characteristics of the SGI computer timed
| SGI Origin 2000
Model | IP27
Processor | MIPS R12000
Clock speed (MHz) | 300
Processors per node | 64
Operating system | IRIX 6.5
BLAS | SGI BLAS
Fortran compiler | f77 (7.2.1.2m)
Fortran flags | -O3 -64 -mips4 -r10000 -OPT:IEEE_NaN_inf=ON
Precision | double (64-bit)

Table 3.6: Characteristics of the Sun computers timed
| Sun Ultra 2 | Sun Enterprise 450
Model | Ultra 2 Model 2200 | Model 1300
Processor | Sun UltraSPARC | Sun UltraSPARC-II
Clock speed (MHz) | 200 | 300
Processors per node | 1 | 1
Operating system | SunOS 5.5.1 | SunOS 5.5.7
BLAS | Sun Performance Library | Sun Performance Library
Fortran compiler | f77 (SC5.0) | f77 (SC5.0)
Fortran flags | -f -dalign -native -xO5 -xarch=v8plusa | -f -dalign -native -xO5 -xarch=v8plusa
Precision | double (64-bit) | double (64-bit)

See Gallivan et al. [52] and Dongarra et al. [43] for an alternative survey of algorithms for dense linear algebra on high-performance computers.

- Factorizations for Solving Linear Equations
- QR Factorization
- Eigenvalue Problems

Next: Factorizations for Solving Linear Up: Performance of LAPACK Previous: Block Algorithms and their Contents Index