PSLARFG(l)					      LAPACK auxiliary routine (version 1.5)						PSLARFG(l)

NAME

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

SYNOPSIS

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

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

	   REAL 	   ALPHA

	   INTEGER	   DESCX( * )

	   REAL 	   TAU( * ), X( * )

PURPOSE

       PSLARFG generates a real elementary reflector H of order n, such that
			     (	    x	  )   (   0   )

       where alpha is a scalar, and sub( X ) is an (N-1)-element real 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 real scalar and v is a real (N-1)-element
       vector.

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

       Otherwise  1 <= tau <= 2.

       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  col-
       umn.
       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) REAL
	       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) REAL, 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) REAL, 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 							PSLARFG(l)