Provided by: scalapack-doc_1.5-10_all 
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 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.
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 locations 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