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HPL_pipid(3)                 HPL Library Functions                HPL_pipid(3)

NAME
       HPL_pipid - Simplify the pivot vector.

SYNOPSIS
       #include "hpl.h"

       void HPL_pipid( HPL_T_panel * PANEL, int * K, int * IPID );

DESCRIPTION
       HPL_pipid computes an array  IPID  that contains the source and final
       destination  of  matrix rows  resulting  from  the  application  of N
       interchanges  as computed by the  LU  factorization  with row partial
       pivoting. The array IPID is such that the row of global index IPID(i)
       should be mapped onto the row of global index IPID(i+1). Note that we
       cannot really know the length of IPID a priori. However, we know that
       this array is at least 2*N long,  since  there are N rows to swap and
       broadcast. The length of this array  must be smaller than or equal to
       4*N, since every row is swapped with at most a single distinct remote
       row. The algorithm constructing  IPID  goes as follows: Let IA be the
       global index of the first row to be swapped.

       For every row src IA + i with i in [0..N) to be swapped with row  dst
       such that dst is given by DPIV[i]:

       Is row  src  the destination  of a previous row of the current block,
       that is, is there k odd such that IPID(k) is equal to src ?
           Yes:  update  this destination  with dst.  For  example,  if  the
       pivot array is  (0,2)(1,1)(2,5) ... , then when we swap rows 2 and 5,
       we swap in fact row 0 and 5,  i.e.,  row 0 goes to 5 and not 2  as it
       was thought so far ...
           No :  add  the pair (src,dst) at the end of IPID; row src has not
       been moved yet.

       Is row  dst  different  from src the destination of a previous row of
       the current block, i.e., is there k odd such that IPID(k) is equal to
       dst ?
           Yes:  update  IPID(k) with src.  For example,  if the pivot array
       is (0,5)(1,1)(2,5) ... , then when  we swap rows  2 and 5, we swap in
       fact row 2 and 0,  i.e.,  row 0 goes to 2 and not 5 as it was thought
       so far ...
           No : add  the  pair (dst,src) at the end of IPID; row dst has not
       been moved yet.

       Note that when src is equal to dst, the pair (dst,src)  should not be
       added to  IPID  in  order  to avoid duplicated entries in this array.
       During  the construction of the array  IPID,  we  make  sure that the
       first N entries are such that IPID(k) with k odd is equal to  IA+k/2.
       For k in  [0..K/2),  the  row  of global index  IPID(2*k)  should  be
       mapped onto the row of global index IPID(2*k+1).

ARGUMENTS
       PANEL   (local input/output)    HPL_T_panel *
               On entry,  PANEL  points to the data structure containing the
               panel information.

       K       (global output)         int *
               On exit, K specifies the number of entries in  IPID.  K is at
               least 2*N, and at most 4*N.

       IPID    (global output)         int *
               On entry, IPID is an array of length 4*N.  On exit, the first K
               entries of that array contain the src and final destination
               resulting  from  the  application of the  N  interchanges  as
               specified by  DPIV.  The  pairs  (src,dst)  are  contiguously
               stored and sorted so that IPID(2*i+1) is equal to IA+i with i
               in [0..N)

SEE ALSO
       HPL_pdlaswp00N (3), HPL_pdlaswp00T (3), HPL_pdlaswp01N (3),
       HPL_pdlaswp01T (3).

HPL 2.1                        October 26, 2012                   HPL_pipid(3)