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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)