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

SUBROUTINE PDLASMSUB(

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

INTEGER I, K, L, LWORK

DOUBLE PRECISION SMLNUM

INTEGER DESCA( * )

DOUBLE PRECISION A( * ), BUF( * )

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

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