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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.