# 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).