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NAME

       PDZSUM1  -  return  the sum of absolute values of a complex distributed vector sub( X ) in
       ASUM,

SYNOPSIS

       SUBROUTINE PDZSUM1( N, ASUM, X, IX, JX, DESCX, INCX )

           INTEGER         IX, INCX, JX, N

           DOUBLE          PRECISION ASUM

           INTEGER         DESCX( * )

           COMPLEX*16      X( * )

PURPOSE

       PDZSUM1 returns the sum of absolute values of a complex distributed vector  sub(  X  )  in
       ASUM,

       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.

       Based on PDZASUM from the Level 1 PBLAS. The change is
       to use the 'genuine' absolute value.

       The  serial version of this routine was originally contributed by Nick Higham for use with
       ZLACON.

       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
       ---------------  --------------   --------------------------------------   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 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  viewed  as  a  subclass  of  matrices,  a distributed vector is
       considered to be a distributed matrix.

       When the result of a vector-oriented PBLAS call is a scalar, it  will  be  made  available
       only within the scope which owns the vector(s) being operated on.  Let X be a generic term
       for the input vector(s).  Then, the processes which receive the answer will be (note  that
       if  an  operation  involves more than one vector, the processes which re- ceive the result
       will be the union of the following calculation for each vector):

       If N = 1, M_X = 1 and INCX = 1, then one can't determine  if  a  process  row  or  process
       column  owns the vector operand, therefore only the process of coordinate {RSRC_X, CSRC_X}
       receives the result;

       If INCX = M_X, then sub( X ) is a vector distributed over a process row. Each process part
       of this row receives the result;

       If  INCX  =  1,  then sub( X ) is a vector distributed over a process column. Each process
       part of this column receives the result;

PARAMETERS

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

       ASUM    (local output) pointer to DOUBLE PRECISION
               The sum of absolute values of the distributed vector sub( X ) only in its scope.

       X       (local input) COMPLEX*16 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.