HPL is a software package that solves a (random) dense linear system in double precision (64 bits) arithmetic on distributed-memory computers. It can thus be regarded as a portable as well as freely available implementation of the High Performance Computing Linpack Benchmark. The algorithm used by HPL can be summarized by the following keywords: Two-dimensional block-cyclic data distribution - Right-looking variant of the LU factorization with row partial pivoting featuring multiple look-ahead depths - Recursive panel factorization with pivot search and column broadcast combined - Various virtual panel broadcast topologies - bandwidth reducing swap-broadcast algorithm - backward substitution with look-ahead of depth 1. The HPL package provides a testing and timing program to quantify the accuracy of the obtained solution as well as the time it took to compute it. The best performance achievable by this software on your system depends on a large variety of factors. Nonetheless, with some restrictive assumptions on the interconnection network, the algorithm described here and its attached implementation are scalable in the sense that their parallel efficiency is maintained constant with respect to the per processor memory usage.

1. LINPACK Introduction
CSTL HPC IT
Mu Wei

2. Agenda
• LINPACK
• LINPACK & MATRIX
• HPL TEST

3. What’s LINPACK
• A collection of Fortran subroutines that
analyze and sovlve linear equations and linea
least-squares problems
• LINPACK100,LINPACK1000,HPL

4. LINPACK AND
MATRIX
• Based on decompositional approach to
numerical linear algebra
• Divide computational problem into two parts
• Ax=b

5. Organized around matrix decompositions
LINPACK AND MATRIX
LU Cholesky
QR singular value

6. NAME OF LINPACK
• T - Type of arithmetic
• XX - Reflect a fundamental division
• YY - Specifies task the subroutine is to
perform
Name of LINPACK subroutine is divided into a prefix, an
infix, a suffix as follow

7. EFFICIENCY
• Column orientation of the algorithms
• Use of Basic Liear Algebra Subprograms
Effects of two aspects of LINPACK on efficiency

8. How to Setup HPL
• Download Open source HPL
• Prequisites: 1) BLAS; 2)MPI
• Edit Data File
• Compile: $ make arch=Linux_PII_CBLAS
• Execute

9. DATA FILE
$ cat HPL.dat
HPLinpack benchmark input file
Innovative Computing Laboratory, University of Tennessee
HPL.out output file name (if any)
6 device out (6=stdout,7=stderr,file)
4 # of problems sizes (N)
29 30 34 35 Ns
4 # of NBs
1 2 3 4 NBs
0 PMAP process mapping (0=Row-,1=Column-major)
3 # of process grids (P x Q)
2 1 4 Ps
2 4 1 Qs

10. Key Parameters
• Estimate the LARGEST PROBLEM SIZE
• Expected Execution Time
• Expected Gflops
• Sample - Choose N=14k, then Time=52s

11. RESULT

12. Q & A