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.TH HPL_pdpancrT 3 "September 10, 2008" "HPL 2.0" "HPL Library Functions"
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.SH NAME
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HPL_pdpancrT \- Crout panel factorization.
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.SH SYNOPSIS
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\fB\&#include "hpl.h"\fR
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\fB\&void\fR
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\fB\&HPL_pdpancrT(\fR
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\fB\&HPL_T_panel *\fR
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\fI\&PANEL\fR,
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\fB\&const int\fR
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\fI\&M\fR,
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\fB\&const int\fR
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\fI\&N\fR,
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\fB\&const int\fR
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\fI\&ICOFF\fR,
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\fB\&double *\fR
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\fI\&WORK\fR
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\fB\&);\fR
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.SH DESCRIPTION
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\fB\&HPL_pdpancrT\fR
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factorizes  a panel of columns that is a sub-array of a
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larger one-dimensional panel  A using the Crout variant of the  usual
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one-dimensional algorithm.  The lower triangular N0-by-N0 upper block
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of the panel is stored in transpose form.
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Bi-directional  exchange  is  used  to  perform  the  swap::broadcast
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operations  at once  for one column in the panel.  This  results in a
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lower number of slightly larger  messages than usual.  On P processes
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and assuming bi-directional links,  the running time of this function
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can be approximated by (when N is equal to N0):
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   N0 * log_2( P ) * ( lat + ( 2*N0 + 4 ) / bdwth ) +
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   N0^2 * ( M - N0/3 ) * gam2-3
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where M is the local number of rows of  the panel, lat and bdwth  are
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the latency and bandwidth of the network for  double  precision  real
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words, and  gam2-3  is an  estimate of the  Level 2 and Level 3  BLAS
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rate of execution. The  recursive  algorithm  allows indeed to almost
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achieve  Level 3 BLAS  performance  in the panel factorization.  On a
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large  number of modern machines,  this  operation is however latency
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bound,  meaning  that its cost can  be estimated  by only the latency
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portion N0 * log_2(P) * lat.  Mono-directional links will double this
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communication cost.
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Note that  one  iteration of the the main loop is unrolled. The local
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computation of the absolute value max of the next column is performed
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just after its update by the current column. This allows to bring the
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current column only  once through  cache at each  step.  The  current
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implementation  does not perform  any blocking  for  this sequence of
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BLAS operations, however the design allows for plugging in an optimal
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(machine-specific) specialized  BLAS-like kernel.  This idea has been
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suggested to us by Fred Gustavson, IBM T.J. Watson Research Center.
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.SH ARGUMENTS
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.TP 8
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PANEL   (local input/output)    HPL_T_panel *
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On entry,  PANEL  points to the data structure containing the
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panel information.
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.TP 8
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M       (local input)           const int
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On entry,  M specifies the local number of rows of sub(A).
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.TP 8
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N       (local input)           const int
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On entry,  N specifies the local number of columns of sub(A).
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.TP 8
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ICOFF   (global input)          const int
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On entry, ICOFF specifies the row and column offset of sub(A)
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in A.
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.TP 8
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WORK    (local workspace)       double *
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On entry, WORK  is a workarray of size at least 2*(4+2*N0).
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.SH SEE ALSO
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.BR HPL_dlocmax \ (3),
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.BR HPL_dlocswpN \ (3),
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.BR HPL_dlocswpT \ (3),
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.BR HPL_pdmxswp \ (3),
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.BR HPL_pdpancrN \ (3),
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.BR HPL_pdpanllN \ (3),
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.BR HPL_pdpanllT \ (3),
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.BR HPL_pdpanrlN \ (3),
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.BR HPL_pdpanrlT \ (3).