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