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



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

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

           INTEGER           I, K, L, LWORK

           DOUBLE            PRECISION SMLNUM

           INTEGER           DESCA( * )

           COMPLEX*16        A( * ), BUF( * )

PURPOSE
       PZLASMSUB 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) COMPLEX*16 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 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) COMPLEX*16 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 ZLAHQR:

               Look for a single small subdiagonal element.

               DO  20  K = I, L + 1, -1 TST1 = CABS1( H( K-1, K-1 ) ) + CABS1(
               H( K, K ) ) IF( TST1.EQ.ZERO ) $         TST1 = ZLANHS( '1', I-
               L+1,  H(  L,  L ), LDH, WORK ) IF( CABS1( H( K, K-1 ) ).LE.MAX(
               ULP*TST1, SMLNUM ) ) $          GO  TO  30  20     CONTINUE  30
               CONTINUE

FURTHER DETAILS
       Implemented by:  M. Fahey, May 28, 1999




ScaLAPACK routine               31 October 2017                   PZLASMSUB(3)