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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.