1HPL_pdrpancrN(3)             HPL Library Functions            HPL_pdrpancrN(3)
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NAME

6       HPL_pdrpancrN - Crout recursive panel factorization.
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SYNOPSIS

9       #include "hpl.h"
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11       void  HPL_pdrpancrN(  HPL_T_panel  *  PANEL,  const int M, const int N,
12       const int ICOFF, double * WORK );
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DESCRIPTION

15       HPL_pdrpancrN HPL_pdrpancrN recursively  factorizes  a panel of columns
16       using  the recursive  Crout  variant of the usual one-dimensional algo‐
17       rithm. The lower triangular  N0-by-N0  upper block  of  the  panel   is
18       stored in no-transpose form (i.e. just like the input matrix itself).
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20       Bi-directional   exchange   is  used  to  perform  the  swap::broadcast
21       operations  at once  for one column in the panel.  This  results  in  a
22       lower  number  of slightly larger  messages than usual.  On P processes
23       and assuming bi-directional links,  the running time of  this  function
24       can be approximated by (when N is equal to N0):
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26          N0 * log_2( P ) * ( lat + ( 2*N0 + 4 ) / bdwth ) +
27          N0^2 * ( M - N0/3 ) * gam2-3
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29       where  M  is the local number of rows of  the panel, lat and bdwth  are
30       the latency and bandwidth of the network for  double   precision   real
31       words,  and   gam2-3  is  an estimate of the  Level 2 and Level 3  BLAS
32       rate of execution. The  recursive  algorithm  allows indeed  to  almost
33       achieve   Level  3 BLAS  performance  in the panel factorization.  On a
34       large  number of modern machines,  this  operation is  however  latency
35       bound,   meaning   that its cost can  be estimated  by only the latency
36       portion N0 * log_2(P) * lat.  Mono-directional links will  double  this
37       communication cost.
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ARGUMENTS

40       PANEL   (local input/output)    HPL_T_panel *
41               On  entry,   PANEL  points to the data structure containing the
42               panel information.
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44       M       (local input)           const int
45               On entry,  M specifies the local number of rows of sub(A).
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47       N       (local input)           const int
48               On entry,  N specifies the local number of columns of sub(A).
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50       ICOFF   (global input)          const int
51               On entry, ICOFF specifies the row and column offset  of  sub(A)
52               in A.
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54       WORK    (local workspace)       double *
55               On entry, WORK  is a workarray of size at least 2*(4+2*N0).
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SEE ALSO

58       HPL_dlocmax (3),  HPL_dlocswpN (3),  HPL_dlocswpT (3), HPL_pdmxswp (3),
59       HPL_pdpancrN (3), HPL_pdpancrT (3), HPL_pdpanllN (3), HPL_pdpanllT (3),
60       HPL_pdpanrlN (3),   HPL_pdpanrlT (3),   HPL_pdrpancrT (3),  HPL_pdrpan‐
61       llN (3),   HPL_pdrpanllT (3),   HPL_pdrpanrlN (3),   HPL_pdrpanrlT (3),
62       HPL_pdfact (3).
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66HPL 2.2                        February 24, 2016              HPL_pdrpancrN(3)
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