Centre Blaise Pascal » HPL sur GPU

.TH HPL_pdfact 3 "September 10, 2008" "HPL 2.0" "HPL Library Functions"

.SH NAME

HPL_pdfact \- recursive panel factorization.

.SH SYNOPSIS

\fB\&#include "hpl.h"\fR

\fB\&void\fR

\fB\&HPL_pdfact(\fR

\fB\&HPL_T_panel *\fR

\fI\&PANEL\fR

\fB\&);\fR

.SH DESCRIPTION

\fB\&HPL_pdfact\fR

recursively factorizes a  1-dimensional  panel of columns.

The  RPFACT  function pointer specifies the recursive algorithm to be

used, either Crout, Left- or Right looking.  NBMIN allows to vary the

recursive stopping criterium in terms of the number of columns in the

panel, and  NDIV  allow to specify the number of subpanels each panel

should be divided into. Usuallly a value of 2 will be chosen. Finally

PFACT is a function pointer specifying the non-recursive algorithm to

to be used on at most NBMIN columns. One can also choose here between

Crout, Left- or Right looking.  Empirical tests seem to indicate that

values of 4 or 8 for NBMIN give the best results.

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.

.SH ARGUMENTS

.TP 8

PANEL   (local input/output)    HPL_T_panel *

On entry,  PANEL  points to the data structure containing the

panel information.

.SH SEE ALSO

.BR HPL_dlocmax \ (3),

.BR HPL_dlocswpN \ (3),

.BR HPL_dlocswpT \ (3),

.BR HPL_pdmxswp \ (3),

.BR HPL_pdpancrN \ (3),

.BR HPL_pdpancrT \ (3),

.BR HPL_pdpanllN \ (3),

.BR HPL_pdpanllT \ (3),

.BR HPL_pdpanrlN \ (3),

.BR HPL_pdpanrlT \ (3),

.BR HPL_pdrpancrN \ (3),

.BR HPL_pdrpancrT \ (3),

.BR HPL_pdrpanllN \ (3),

.BR HPL_pdrpanllT \ (3),

.BR HPL_pdrpanrlN \ (3),

.BR HPL_pdrpanrlT \ (3).