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HPL_pdpancrT - Man Page

Crout panel factorization.


#include "hpl.h"
 void HPL_pdpancrT( HPL_T_panel * PANEL, const int M, const int N, const int ICOFF, double * WORK );


HPL_pdpancrT factorizes  a panel of columns that is a sub-array of a larger one-dimensional panel  A using the 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.
 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.


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_pdpanllN (3), HPL_pdpanllT (3), HPL_pdpanrlN (3), HPL_pdpanrlT (3).

Referenced By

HPL_dlocmax(3), HPL_dlocswpN(3), HPL_dlocswpT(3), HPL_pdfact(3), HPL_pdmxswp(3), HPL_pdpancrN(3), HPL_pdpanllN(3), HPL_pdpanllT(3), HPL_pdpanrlN(3), HPL_pdpanrlT(3), HPL_pdrpancrN(3), HPL_pdrpancrT(3), HPL_pdrpanllN(3), HPL_pdrpanllT(3), HPL_pdrpanrlN(3), HPL_pdrpanrlT(3).

February 24, 2016 HPL 2.2 HPL Library Functions