PDLACONSB(l)						   LAPACK routine (version 1.5 )					      PDLACONSB(l)

NAME

       PDLACONSB  -  look  for	two consecutive small subdiagonal elements by  seeing the effect of starting a double shift QR iteration  given by
       H44, H33, & H43H34 and see if this would make a	subdiagonal negligible

SYNOPSIS

       SUBROUTINE PDLACONSB( A, DESCA, I, L, M, H44, H33, H43H34, BUF, LWORK )

	   INTEGER	     I, L, LWORK, M

	   DOUBLE	     PRECISION H33, H43H34, H44

	   INTEGER	     DESCA( * )

	   DOUBLE	     PRECISION A( * ), BUF( * )

PURPOSE

       PDLACONSB looks for two consecutive small subdiagonal elements by
	  seeing the effect of starting a double shift QR iteration
	  given by H44, H33, & H43H34 and see if this would make a
	  subdiagonal negligible.

       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  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

       A       (global input) DOUBLE PRECISION 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.

       M       (global output) INTEGER
	       On exit, this yields the starting location of the QR double shift.  This will satisfy: L <= M  <= I-2.

	       H44 H33 H43H34  (global input) DOUBLE PRECISION These three values are for the double shift QR iteration.

       BUF     (local output) DOUBLE PRECISION array of size LWORK.

       LWORK   (global input) INTEGER
	       On exit, LWORK is the size of the work buffer.  This must be at least 7*Ceil( Ceil( (I-L)/HBL ) / LCM(NPROW,NPCOL) )  Here  LCM	is
	       least common multiple, and NPROWxNPCOL is the logical grid size.

	       Logic: ======

	       Two  consecutive  small	subdiagonal elements will stall convergence of a double shift if their product is small relatively even if
	       each is not very small.	Thus it is necessary to scan the "tridiagonal portion of the matrix."  In the LAPACK algorithm	DLAHQR,  a
	       loop  of  M  goes  from	I-2 down to L and examines H(m,m),H(m+1,m+1),H(m+1,m),H(m,m+1),H(m-1,m-1),H(m,m-1), and H(m+2,m-1).  Since
	       these elements may be on separate processors, the first major loop (10) goes over the tridiagonal and has each node store  whatever
	       values  of  the	7 it has that the node owning H(m,m) does not.	This will occur on a border and can happen in no more than 3 loca-
	       tions per block assuming square blocks.	There are 5 buffers that each node stores these values:  a buffer to send diagonally  down
	       and right, a buffer to send up, a buffer to send left, a buffer to send diagonally up and left and a buffer to send right.  Each of
	       these buffers is actually stored in one buffer BUF where BUF(ISTR1+1) starts the first  buffer,	BUF(ISTR2+1)  starts  the  second,
	       etc..  After the values are stored, if there are any values that a node needs, they will be sent and received.  Then the next major
	       loop passes over the data and searches for two consecutive small subdiagonals.

	       Notes:

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

	       Implemented by:	G. Henry, November 17, 1996

LAPACK version 1.5						    12 May 1997 						      PDLACONSB(l)