HPL_pdrpancrN(3)

NAME
HPL_pdrpancrN - Crout recursive panel factorization.

SYNOPSIS
#include "hpl.h"

void HPL_pdrpancrN( HPL_T_panel * PANEL, const int M, const int N, const int ICOFF, double * WORK );

DESCRIPTION
HPL_pdrpancrN HPL_pdrpancrN recursively factorizes a panel of columns using the recursive Crout variant of the usual one-dimensional algorithm. The lower triangular N0-by-N0 upper block of the panel is stored in no-transpose form (i.e. just like the input matrix itself).

Bi-directional exchange is used to perform the swap::broadcast operations at once for one column in the panel. This results in a lower number of slightly larger messages than usual. On P processes and assuming bi-directional links, the running time of this function can be approximated 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 execution. The recursive algorithm allows indeed to almost achieve Level 3 BLAS performance in the panel factorization. On a large number of modern 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.

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_pdpancrT (3), HPL_pdpanllN (3), HPL_pdpanllT (3), HPL_pdpanrlN (3), HPL_pdpanrlT (3), HPL_pdrpancrT (3), HPL_pdrpanllN (3), HPL_pdrpanllT (3), HPL_pdrpanrlN (3), HPL_pdrpanrlT (3), HPL_pdfact (3).