PDZSUM1(3)    ScaLAPACK routine of NEC Numeric Library Collection   PDZSUM1(3)



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 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
       --------------- -------------- --------------------------------------
       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  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 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 opera-
       tion 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 pro-
       cess 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 col-
       umn. 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.



ScaLAPACK routine               31 October 2017                     PDZSUM1(3)