PSLAWIL - get the transform given by H44,H33, & H43H34 into V starting at row M

SUBROUTINE PSLAWIL(

II, JJ, M, A, DESCA, H44, H33, H43H34, V )

INTEGER II, JJ, M

REAL H33, H43H34, H44

INTEGER DESCA( * )

REAL A( * ), V( * )

PSLAWIL gets the transform given by H44,H33, & H43H34 into V starting at row M.

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

II (global input) INTEGER

Row owner of H(M+2,M+2)

JJ (global input) INTEGER

Column owner of H(M+2,M+2)

M (global input) INTEGER

On entry, this is where the transform starts (row M.) Unchanged on exit.

A (global input) REAL array, dimension

(DESCA(LLD_),*) On entry, the Hessenberg matrix. Unchanged on exit.

DESCA (global and local input) INTEGER array of dimension DLEN_.

The array descriptor for the distributed matrix A. Unchanged on exit.

H44 H33 H43H34 (global input) REAL These three values are for the double shift QR iteration. Unchanged on exit.

V (global output) REAL array of size 3.

Contains the transform on output.

Implemented by: G. Henry, November 17, 1996