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NAME

       PZMAX1  -  compute  the global index of the maximum element in absolute
       value of a distributed vector sub( X )

SYNOPSIS

       SUBROUTINE PZMAX1( N, AMAX, INDX, X, IX, JX, DESCX, INCX )

           INTEGER        INDX, INCX, IX, JX, N

           COMPLEX*16     AMAX

           INTEGER        DESCX( * )

           COMPLEX*16     X( * )

PURPOSE

       PZMAX1 computes the global index of the  maximum  element  in  absolute
       value of a distributed vector sub( X ). The global index is returned in
       INDX and the value is returned in AMAX,

       where sub( X ) denotes X(IX:IX+N-1,JX) if INCX = 1,
                              X(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
       ---------------  --------------  --------------------------------------
       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;

       Based on PZAMAX from Level 1 PBLAS. The change is to use the

       The serial version was contributed to LAPACK by  Nick  Higham  for  use
       with ZLACON.

ARGUMENTS

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

       AMAX    (global output) pointer to DOUBLE PRECISION
               The absolute value of the  largest  entry  of  the  distributed
               vector sub( X ) only in the scope of sub( X ).

       INDX    (global output) pointer to INTEGER
               The  global index of the element of the distributed vector sub(
               X ) whose real part has maximum absolute value.

       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) INTEGER
               The row index in the global array X indicating the first row of
               sub( X ).

       JX      (global input) INTEGER
               The  column  index  in  the global array X indicating the first
               column of sub( X ).

       DESCX   (global and local input) INTEGER array of dimension DLEN_.
               The array descriptor for the distributed matrix X.

       INCX    (global input) INTEGER
               The global increment for the elements of X. Only two values  of
               INCX  are  supported  in  this version, namely 1 and M_X.  INCX
               must not be zero.