void HPL_pdrpanllN( HPL_T_panel * PANEL, const int M, const int N, const int ICOFF, double * WORK );
HPL_pdrpanllN recursively factorizes a panel of columns using the recursive Left-looking variant of the 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.
- 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).
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_pdrpancrN (3), HPL_pdrpancrT (3), HPL_pdrpanllT (3), HPL_pdrpanrlN (3), HPL_pdrpanrlT (3), HPL_pdfact (3).
HPL_dlocmax(3), HPL_dlocswpN(3), HPL_dlocswpT(3), HPL_pdfact(3), HPL_pdmxswp(3), HPL_pdrpancrN(3), HPL_pdrpancrT(3), HPL_pdrpanllT(3), HPL_pdrpanrlN(3), HPL_pdrpanrlT(3).