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