NAME

       PZLARFG - generate a complex elementary reflector H of order n, such that   H * sub( X ) =
       H * ( x(iax,jax) ) = ( alpha ), H' * H = I

SYNOPSIS

       SUBROUTINE PZLARFG( N, ALPHA, IAX, JAX, X, IX, JX, DESCX, INCX, TAU )

           INTEGER         IAX, INCX, IX, JAX, JX, N

           COMPLEX*16      ALPHA

           INTEGER         DESCX( * )

           COMPLEX*16      TAU( * ), X( * )

PURPOSE

       PZLARFG generates a complex elementary reflector H of order n, such that
                             (      x     )   (   0   )

       where alpha is a real scalar, and sub( X ) is an (N-1)-element complex distributed  vector
       X(IX:IX+N-2,JX)  if INCX = 1 and X(IX,JX:JX+N-2) if INCX = DESCX(M_).  H is represented in
       the form

             H = I - tau * ( 1 ) * ( 1 v' ) ,
                           ( v )

       where tau is a complex scalar and v is a complex (N-1)-element vector. Note that H is  not
       Hermitian.

       If  the  elements  of  sub( X ) are all zero and X(IAX,JAX) is real, then tau = 0 and H is
       taken to be the unit matrix.

       Otherwise  1 <= real(tau) <= 2 and abs(tau-1) <= 1.

       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.

ARGUMENTS

       N       (global input) INTEGER
               The global order of the elementary reflector. N >= 0.

       ALPHA   (local output) COMPLEX*16
               On exit, alpha is computed in the process scope having the vector sub( X ).

       IAX     (global input) INTEGER
               The global row index in X of X(IAX,JAX).

       JAX     (global input) INTEGER
               The global column index in X of X(IAX,JAX).

       X       (local input/local output) COMPLEX*16, pointer into the
               local memory to an array of dimension (LLD_X,*). This  array  contains  the  local
               pieces  of  the  distributed vector sub( X ).  Before entry, the incremented array
               sub( X ) must contain the vector x. On exit, it is overwritten with the vector v.

       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.

       TAU     (local output) COMPLEX*16, array, dimension  LOCc(JX)
               if  INCX  = 1, and LOCr(IX) otherwise. This array contains the Householder scalars
               related to the Householder vectors.  TAU is tied to the distributed matrix X.