SYNOPSIS

SUBROUTINE PDLASMSUB(

A, DESCA, I, L, K, SMLNUM, BUF, LWORK )

    

INTEGER I, K, L, LWORK

    

DOUBLE PRECISION SMLNUM

    

INTEGER DESCA( * )

    

DOUBLE PRECISION A( * ), BUF( * )

PURPOSE

PDLASMSUB 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) 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.

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) DOUBLE PRECISION

On entry, a "small number" for the given matrix. Unchanged on exit.

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 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 DLAHQR:

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 = DLANHS( '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