NAME

       PDRSCL - multiplie an N-element real distributed vector sub( X ) by the real scalar 1/a

SYNOPSIS

       SUBROUTINE PDRSCL( N, SA, SX, IX, JX, DESCX, INCX )

           INTEGER        IX, INCX, JX, N

           DOUBLE         PRECISION SA

           INTEGER        DESCX( * )

           DOUBLE         PRECISION SX( * )

PURPOSE

       PDRSCL  multiplies  an  N-element  real  distributed vector sub( X ) by the real scalar 1/a. This is done
       without overflow or underflow as long as the final result sub( X )/a does not overflow or underflow.

       where sub( X ) denotes X(IX:IX+N-1,JX:JX), if INCX = 1,
                              X(IX:IX,JX:JX+N-1), if INCX = M_X.

       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
       ---------------  -------------- -------------------------------------- DT_A   (global) descA[ DT_ ]   The
       descriptor type.  In this case,
                                      DT_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 distribu-
                                      te the rows of the array.
       NB_A   (global) descA[ NB_ ]   The blocking factor used to distribu-
                                      te 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

       Because  vectors  may  be  seen  as  particular  matrices,  a  distributed  vector  is considered to be a
       distributed matrix.

ARGUMENTS

       N       (global input) pointer to INTEGER
               The number of components of the distributed vector sub( X ).  N >= 0.

       SA      (global input) DOUBLE PRECISION
               The scalar a which is used to divide each component of sub( X  ).   SA  must  be  >=  0,  or  the
               subroutine will divide by zero.

       SX      (local input/local output) DOUBLE PRECISION array
               containing  the local pieces of a distributed matrix of dimension of at least ( (JX-1)*M_X + IX +
               ( N - 1 )*abs( INCX ) ) This array contains the entries of the distributed vector sub( X ).

       IX      (global input) pointer to INTEGER
               The global row index of the submatrix of the distributed matrix X to operate on.

       JX      (global input) pointer to INTEGER
               The global column index of the submatrix of the distributed matrix X to operate on.

       DESCX   (global and local input) INTEGER array of dimension 8.
               The array descriptor of the distributed matrix X.

       INCX    (global input) pointer to INTEGER
               The global increment for the elements of X. Only  two  values  of  INCX  are  supported  in  this
               version, namely 1 and M_X.

LAPACK version 1.5                                 12 May 1997                                         PDRSCL(l)