Name
HPL_pdpanllT Left-looking panel factorization.
Synopsis
#include "hpl.h"
void
HPL_pdpanllT(
HPL_T_panel *
PANEL,
const int
M,
const int
N,
const int
ICOFF,
double *
WORK
);
Description
HPL_pdpanllT
factorizes  a panel of columns that is a sub-array of a
larger one-dimensional panel A  using the Left-looking 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.
 
Note that  one  iteration of the the main loop is unrolled. The local
computation of the absolute value max of the next column is performed
just after its update by the current column. This allows to bring the
current column only  once through  cache at each  step.  The  current
implementation  does not perform  any blocking  for  this sequence of
BLAS operations, however the design allows for plugging in an optimal
(machine-specific) specialized  BLAS-like kernel.  This idea has been
suggested to us by Fred Gustavson, IBM T.J. Watson Research Center.
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,
HPL_dlocswpN,
HPL_dlocswpT,
HPL_pdmxswp,
HPL_pdpancrN,
HPL_pdpancrT,
HPL_pdpanllN,
HPL_pdpanrlN,
HPL_pdpanrlT.