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



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

SYNOPSIS
       SUBROUTINE PCSRSCL( N, SA, SX, IX, JX, DESCX, INCX )

           INTEGER         IX, INCX, JX, N

           REAL            SA

           INTEGER         DESCX( * )

           COMPLEX         SX( * )

PURPOSE
       PCSRSCL multiplies an N-element complex distributed vector sub( X )  by
       the real scalar 1/a. This is done without overflow or underflow as long
       as the final 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  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
       ---------------  --------------  --------------------------------------
       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 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

       Because vectors may be seen as particular matrices, a distributed  vec-
       tor 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) COMPLEX array
               containing  the  local pieces of a distributed matrix of dimen-
               sion 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.



ScaLAPACK routine               31 October 2017                     PCSRSCL(3)