HPL_pdrpancrT - Crout recursive panel factorization.

**#include "hpl.h"**
**void** **HPL_pdrpancrT(** **HPL_T_panel *** *PANEL*,

**const
int** *M*,

**const int** *N*,

**const int** *ICOFF*,

**double *** *WORK* **);**
**HPL_pdrpancrT** 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 transpose form.

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_pdrpanllN** (3),

**HPL_pdrpanllT** (3),

**HPL_pdrpanrlN** (3),

**HPL_pdrpanrlT** (3),

**HPL_pdfact** (3).