HPL_plindx0(3)

NAME
HPL_plindx0 - Compute local swapping index arrays.

SYNOPSIS
#include "hpl.h"

void HPL_plindx0( HPL_T_panel * PANEL, const int K, int * IPID, int * LINDXA, int * LINDXAU, int * LLEN );

DESCRIPTION
HPL_plindx0 computes two local arrays LINDXA and LINDXAU containing the local source and final destination position resulting from the application of row interchanges.

On entry, the array IPID of length K is such that the row of global index IPID(i) should be mapped onto row of global index IPID(i+1). Let IA be the global index of the first row to be swapped. 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). The question then, is to determine which rows should ultimately be part of U.

First, some rows of the process ICURROW may be swapped locally. One of this row belongs to U, the other one belongs to my local piece of A. The other rows of the current block are swapped with remote rows and are thus not part of U. These rows however should be sent along, and grabbed by the other processes as we progress in the exchange phase.

So, assume that I am ICURROW and consider a row of index IPID(2*i) that I own. If I own IPID(2*i+1) as well and IPID(2*i+1) - IA is less than N, this row is locally swapped and should be copied into U at the position IPID(2*i+1) - IA. No row will be exchanged for this one. If IPID(2*i+1)-IA is greater than N, then the row IPID(2*i) should be locally copied into my local piece of A at the position corresponding to the row of global index IPID(2*i+1).

If the process ICURROW does not own IPID(2*i+1), then row IPID(2*i) is to be swapped away and strictly speaking does not belong to U, but to A remotely. Since this process will however send this array U, this row is copied into U, exactly where the row IPID(2*i+1) should go. For this, we search IPID for k1, such that IPID(2*k1) is equal to IPID(2*i+1); and row IPID(2*i) is to be copied in U at the position IPID(2*k1+1)-IA.

It is thus important to put the rows that go into U, i.e., such that IPID(2*i+1) - IA is less than N at the begining of the array IPID. By doing so, U is formed, and the local copy is performed in just one sweep.

Two lists LINDXA and LINDXAU are built. LINDXA contains the local index of the rows I have that should be copied. LINDXAU contains the local destination information: if LINDXAU(k) >= 0, row LINDXA(k) of A is to be copied in U at position LINDXAU(k). Otherwise, row LINDXA(k) of A should be locally copied into A(-LINDXAU(k),:). In the process ICURROW, the initial packing algorithm proceeds as follows.

  for all entries in IPID,
     if IPID(2*i) is in ICURROW,
        if IPID(2*i+1) is in ICURROW,
           if( IPID(2*i+1) - IA < N )
            save corresponding local position
            of this row (LINDXA);
            save local position (LINDXAU) in U
            where this row goes;
            [copy row IPID(2*i) in U at position
            IPID(2*i+1)-IA; ];
           else
            save corresponding local position of
            this row (LINDXA);
            save local position (-LINDXAU) in A
            where this row goes;
            [copy row IPID(2*i) in my piece of A
            at IPID(2*i+1);]
           end if
        else
           find k1 such that IPID(2*k1) = IPID(2*i+1);
           copy row IPID(2*i) in U at position
           IPID(2*k1+1)-IA;
           save corresponding local position of this
           row (LINDXA);
           save local position (LINDXAU) in U where
           this row goes;
        end if
     end if
  end for

Second, if I am not the current row process ICURROW, all source rows in IPID that I own are part of U. Indeed, they are swapped with one row of the current block of rows, and the main factorization algorithm proceeds one row after each other. The processes different from ICURROW, should exchange and accumulate those rows until they receive some data previously owned by the process ICURROW.

In processes different from ICURROW, the initial packing algorithm proceeds as follows. Consider a row of global index IPID(2*i) that I own. When I will be receiving data previously owned by ICURROW, i.e., U, row IPID(2*i) should replace the row in U at pos. IPID(2*i+1)-IA, and this particular row of U should be first copied into my piece of A, at A(il,:), where il is the local row index corresponding to IPID(2*i). Now,initially, this row will be packed into workspace, say as the kth row of that work array. The following algorithm sets LINDXAU[k] to IPID(2*i+1)-IA, that is the position in U where the row should be copied. LINDXA(k) stores the local index in A where this row of U should be copied, i.e il.

  for all entries in IPID,
     if IPID(2*i) is not in ICURROW,
        copy row IPID(2*i) in work array;
        save corresponding local position
        of this row (LINDXA);
        save position (LINDXAU) in U where
        this row should be copied;
     end if
  end for

Since we are at it, we also globally figure out how many rows every process has. That is necessary, because it would rather be cumbersome to figure it on the fly during the bi-directional exchange phase. This information is kept in the array LLEN of size NPROW. Also note that the arrays LINDXA and LINDXAU are of max length equal to 2*N.

ARGUMENTS

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

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

IPID    (global input)          int *
    On entry, IPID is an array of length K. The first K entries of that array contain the src and final destination resulting from the application of the interchanges.

LINDXA  (local output)          int *
    On entry, LINDXA is an array of dimension 2*N. On exit, this array contains the local indexes of the rows of A I have that should be copied into U.

LINDXAU (local output)          int *
    On exit, LINDXAU is an array of dimension 2*N. On exit, this array contains the local destination information encoded as follows. If LINDXAU(k) >= 0, row LINDXA(k) of A is to be copied in U at position LINDXAU(k). Otherwise, row LINDXA(k) of A should be locally copied into A(-LINDXAU(k),:).

LLEN    (global output)         int *
    On entry, LLEN is an array of length NPROW. On exit, it contains how many rows every process has.

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