HPL_pdpancrT(3) HPL Library Functions HPL_pdpancrT(3) NAME HPL_pdpancrT - Crout panel factorization. SYNOPSIS #include "hpl.h" void HPL_pdpancrT( HPL_T_panel * PANEL, const int M, const int N, const int ICOFF, double * WORK ); DESCRIPTION HPL_pdpancrT factorizes a panel of columns that is a sub-array of a larger one-dimensional panel A using the Crout variant of the usual one-dimen- sional algorithm. The lower triangular N0-by-N0 upper block of the panel is stored in transpose form. Bi-directional exchange is used to perform the swap::broadcast oper- ations at once for one column in the panel. This results in a lower number of slightly larger messages than usual. On P processes and assum- ing bi-directional links, the running time of this function can be approx- imated by (when N is equal to N0): N0 * log_2( P ) * ( lat + ( 2*N0 + 4 ) / bdwth ) + N0^2 * ( M - N0/3 ) * gam2-3 where M is the local number of rows of the panel, lat and bdwth are the latency and bandwidth of the network for double precision real words, and gam2-3 is an estimate of the Level 2 and Level 3 BLAS rate of exe- cution. The recursive algorithm allows indeed to almost achieve Level 3 BLAS performance in the panel factorization. On a large number of mod- ern machines, this operation is however latency bound, meaning that its cost can be estimated by only the latency portion N0 * log_2(P) * lat. Mono-directional links will double this communication cost. Note that one iteration of the the main loop is unrolled. The local com- putation of the absolute value max of the next column is performed just af- ter its update by the current column. This allows to bring the current col- umn only once through cache at each step. The current implementation does not perform any blocking for this sequence of BLAS operations, how- ever the design allows for plugging in an optimal (machine-specific) spe- cialized BLAS-like kernel. This idea has been suggested to us by Fred Gustavson, IBM T.J. Watson Research Center. ARGUMENTS PANEL (local input/output) HPL_T_panel * On entry, PANEL points to the data structure containing the panel information. M (local input) const int On entry, M specifies the local number of rows of sub(A). N (local input) const int On entry, N specifies the local number of columns of sub(A). ICOFF (global input) const int On entry, ICOFF specifies the row and column offset of sub(A) in A. WORK (local workspace) double * On entry, WORK is a workarray of size at least 2*(4+2*N0). SEE ALSO HPL_dlocmax (3), HPL_dlocswpN (3), HPL_dlocswpT (3), HPL_pdmxswp (3), HPL_pdpancrN (3), HPL_pdpanllN (3), HPL_pdpanllT (3), HPL_pdpanrlN (3), HPL_pdpanrlT (3). HPL 2.3 December 2, 2018 HPL_pdpancrT(3)
NAME | SYNOPSIS | DESCRIPTION | ARGUMENTS | SEE ALSO
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