NAME

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

SYNOPSIS

       SUBROUTINE PDLAWIL( II, JJ, M, A, DESCA, H44, H33, H43H34, V )

           INTEGER         II, JJ, M

           DOUBLE          PRECISION H33, H43H34, H44

           INTEGER         DESCA( * )

           DOUBLE          PRECISION A( * ), V( * )

PURPOSE

       PDLAWIL 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) DOUBLE PRECISION 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) DOUBLE PRECISION These three  values  are  for  the
               double shift QR iteration.  Unchanged on exit.

       V       (global output) DOUBLE PRECISION array of size 3.
               Contains the transform on ouput.

               Implemented by:  G. Henry, November 17, 1996