PDLASMSUB(3)  ScaLAPACK routine of NEC Numeric Library Collection PDLASMSUB(3)



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

SYNOPSIS
       SUBROUTINE PDLASMSUB( A, DESCA, I, L, K, SMLNUM, BUF, LWORK )

           INTEGER           I, K, L, LWORK

           DOUBLE            PRECISION SMLNUM

           INTEGER           DESCA( * )

           DOUBLE            PRECISION A( * ), BUF( * )

PURPOSE
       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 vec-
       tor.  This vector stores the information required to establish the map-
       ping 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  col-
       umn.
       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 tridiago-
               nal 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 subma-
               trix.  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



ScaLAPACK routine               31 October 2017                   PDLASMSUB(3)