NAME

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

SYNOPSIS

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

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

           COMPLEX         ALPHA

           INTEGER         DESCX( * )

           COMPLEX         TAU( * ), X( * )

PURPOSE

       PCLARFG 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
               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, 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, 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.