NAME

       PSLASMSUB - look for a small subdiagonal element from the bottom  of the matrix that it can safely set to
       zero

SYNOPSIS

       SUBROUTINE PSLASMSUB( A, DESCA, I, L, K, SMLNUM, BUF, LWORK )

           INTEGER           I, K, L, LWORK

           REAL              SMLNUM

           INTEGER           DESCA( * )

           REAL              A( * ), BUF( * )

PURPOSE

       PSLASMSUB looks for a small subdiagonal element from the bottom
          of the matrix that it can safely set to zero.

       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

       A       (global input) REAL array, dimension
               (DESCA(LLD_),*)  On  entry,  the  Hessenberg  matrix  whose  tridiagonal  part  is being scanned.
               Unchanged on exit.

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

       I       (global input) INTEGER
               The global location of the bottom of the unreduced submatrix of A.  Unchanged on exit.

       L       (global input) INTEGER
               The global location of the top of the unreduced submatrix of A.  Unchanged on exit.

       K       (global output) INTEGER
               On exit, this yields the bottom portion of the unreduced submatrix.  This will satisfy:  L  <=  M
               <= I-1.

       SMLNUM  (global input) REAL
               On entry, a "small number" for the given matrix.  Unchanged on exit.

       BUF     (local output) REAL array of size LWORK.

       LWORK   (global input) INTEGER
               On exit, LWORK is the size of the work buffer.  This must be at least 2*Ceil( Ceil( (I-L)/HBL ) /
               LCM(NPROW,NPCOL) ) Here LCM is least common multiple, and NPROWxNPCOL is the logical grid size.

               Notes:

               This routine does a global maximum and must be called by all processes.

               This code is basically a parallelization of the following snip of LAPACK code from SLAHQR:

               Look for a single small subdiagonal element.

               DO  20  K  =  I,  L  +  1, -1 TST1 = ABS( H( K-1, K-1 ) ) + ABS( H( K, K ) ) IF( TST1.EQ.ZERO ) $
               TST1 = SLANHS( '1', I-L+1, H( L, L ), LDH, WORK ) IF( ABS( H( K, K-1 ) ).LE.MAX( ULP*TST1, SMLNUM
               ) ) $         GO TO 30 20    CONTINUE 30    CONTINUE

               Implemented by:  G. Henry, November 17, 1996

LAPACK version 1.5                                 12 May 1997                                      PSLASMSUB(l)