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PZLAWIL(l)                             )                            PZLAWIL(l)

NAME
       PZLAWIL - get the transform given by H44,H33, & H43H34 into V starting
       at row M

SYNOPSIS
       SUBROUTINE PZLAWIL( II, JJ, M, A, DESCA, H44, H33, H43H34, V )
           INTEGER II, JJ, M
           COMPLEX*16 H33, H43H34, H44
           INTEGER DESCA( * )
           COMPLEX*16 A( * ), V( * )

PURPOSE
       PZLAWIL gets the transform given by H44,H33, & H43H34 into V starting
       at row M.  Notes
       =====

       Each global data object is described by an associated description
       vector.  This vector stores the information required to establish the
       mapping between an object element and its corresponding process and
       memory location.

       Let A be a generic term for any 2D block cyclicly distributed array.
       Such a global array has an associated description vector DESCA.  In the
       following comments, the character _ should be read as "of the global
       array".

       NOTATION        STORED IN      EXPLANATION
       --------------- -------------- --------------------------------------
       DTYPE_A(global) DESCA( DTYPE_ )The descriptor type.  In this case,
                                      DTYPE_A = 1.
       CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
                                      the BLACS process grid A is distribu-
                                      ted over. The context itself is glo-
                                      bal, but the handle (the integer
                                      value) may vary.
       M_A    (global) DESCA( M_ )    The number of rows in the global
                                      array A.
       N_A    (global) DESCA( N_ )    The number of columns in the global
                                      array A.
       MB_A   (global) DESCA( MB_ )   The blocking factor used to distribute
                                      the rows of the array.
       NB_A   (global) DESCA( NB_ )   The blocking factor used to distribute
                                      the columns of the array.
       RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
                                      row of the array A is distributed.
       CSRC_A (global) DESCA( CSRC_ ) The process column over which the
                                      first column of the array A is
                                      distributed.
       LLD_A  (local)  DESCA( LLD_ )  The leading dimension of the local
                                      array.  LLD_A >= MAX(1,LOCr(M_A)).

       Let K be the number of rows or columns of a distributed matrix, and
       assume that its process grid has dimension p x q.
       LOCr( K ) denotes the number of elements of K that a process would
       receive if K were distributed over the p processes of its process
       column.
       Similarly, LOCc( K ) denotes the number of elements of K that a process
       would receive if K were distributed over the q processes of its process
       row.
       The values of LOCr() and LOCc() may be determined via a call to the
       ScaLAPACK tool function, NUMROC:
               LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
               LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).  An upper
       bound for these quantities may be computed by:
               LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
               LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A

ARGUMENTS
       II      (global input) INTEGER
               Row owner of H(M+2,M+2)

       JJ      (global input) INTEGER
               Column owner of H(M+2,M+2)

       M       (global input) INTEGER
               On entry, this is where the transform starts (row M.)
               Unchanged on exit.

       A       (global input) COMPLEX*16 array, dimension
               (DESCA(LLD_),*) On entry, the Hessenberg matrix.  Unchanged on
               exit.

       DESCA   (global and local input) INTEGER array of dimension DLEN_.
               The array descriptor for the distributed matrix A.  Unchanged
               on exit.

               H44 H33 H43H34  (global input) COMPLEX*16 These three values
               are for the double shift QR iteration.  Unchanged on exit.

       V       (global output) COMPLEX*16 array of size 3.
               Contains the transform on ouput.

FURTHER DETAILS
       Implemented by:  M. Fahey, May 28, 1999

ScaLAPACK version 1.7           13 August 2001                      PZLAWIL(l)