W. Zhang, J. Fan, and M. Chen (PRC)
high performance Linpack, linear algebra equations, LU factorization, MPI
HPL is a Linpack benchmark package widely used in massive cluster system performance test. Based on in depth analysis of the blocked parallel solution algorithm of linear algebra equations and HPL implementation mechanics, the restriction factors of the HPL peak performance are probed. The influence of main parameters PQ and NB on computing performance in LU factorization process is discussed especially. Theory analysis and experiment results indicate that, the efficiency factor, defined as the ratio of the matrix operation time and the amount of operations, is relevant to the matrix block size to a great extent, yet little correlate to the matrix size itself. According to this law, the author proposes to determine the block size NB of massively parallel test through scanning the operation efficiency of proper small-scale matrix. Thus it improves the status getting NB through trial-and-error experiment without definite aim. The author's idea has been verified by the real test results, as well as been applicable to the matrix parallel operations of other courses.
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