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HPL_pdrpancrT(3)             HPL Library Functions            HPL_pdrpancrT(3)


NAME

       HPL_pdrpancrT - Crout recursive panel factorization.


SYNOPSIS

       #include "hpl.h"

       void HPL_pdrpancrT( HPL_T_panel * PANEL, const int M, const int N,
       const int ICOFF, double * WORK );


DESCRIPTION

       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.


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 (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).

HPL 2.1                        October 26, 2012               HPL_pdrpancrT(3)

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