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NAME

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

SYNOPSIS

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

           INTEGER        IX, INCX, JX, N

           REAL           SA

           INTEGER        DESCX( * )

           REAL           SX( * )

PURPOSE

       PSRSCL 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) REAL
               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) REAL 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.