PZLAWIL(3)    ScaLAPACK routine of NEC Numeric Library Collection   PZLAWIL(3)



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 vec-
       tor.  This vector stores the information required to establish the map-
       ping 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  col-
       umn.
       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 routine               31 October 2017                     PZLAWIL(3)