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.

LAPACK version 1.5                                 12 May 1997                                        PCLARFG(l)