Developing a tuned version of scaLAPACK's linear equation solver

Dongarra, J

Lawrence Livermore National Laboratory

关键词: 99 General And Miscellaneous//Mathematics, Computing, And Information Science;    Computers;    Factorization;    Algorithms;    Benchmarks;   

DOI  :  10.2172/15013126
RP-ID  :  UCRL-CR-141284
RP-ID  :  W-7405-ENG-48
RP-ID  :  15013126

美国|英语

来源: UNT Digital Library

【 摘 要 】

The LINPACK Benchmark has been used as a yardstick in measuring the performance of the Top500 installed high-end computers. This benchmark was chosen because it is widely used and performance numbers are available for almost all relevant systems. The approach used in the LINPACK Benchmark is to solve a dense system of linear equations. For the Top500, the benchmark allows the user to scale the size of the problem and to optimize the software in order to achieve the best performance for a given machine. This performance does not reflect the overall performance of a given system, as no single number ever can. It does, however, reflect the performance of a dedicated system for solving a dense system of linear equations. Since the problem is very regular, the performance achieved is quite high, and the performance numbers give a good check of peak performance of a system. By measuring the actual performance for different problem sizes n, a user can get not only the maximal achieved performance R{sub max} for the problem size N{sub max} but also the problem size N{sub 1/2} where half of the performance R{sub max} is achieved. These numbers together with the theoretical peak performance R{sub peak} are the numbers given in the Top500. In an attempt to obtain uniformity across all computers in performance reporting, the algorithm used in solving the system of equations must confirm to the standard operation count for LU factorization with partial pivoting. In particular, the operation count for the algorithm must be 2/3 n{sup 3} + O(n{sup 2}) floating point operations.