SLARFG(3f)          LAPACK auxiliary routine (version 3.1)          SLARFG(3f)



NAME
       SLARFG - a real elementary reflector H of order n, such that   H * (
       alpha ) = ( beta ), H' * H = I

SYNOPSIS
       SUBROUTINE SLARFG( N, ALPHA, X, INCX, TAU )

           INTEGER        INCX, N

           REAL           ALPHA, TAU

           REAL           X( * )

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

       where alpha and beta are scalars, and x is an (n-1)-element real
       vector. 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 x are all zero, then tau = 0 and H is taken to be
       the unit matrix.

       Otherwise  1 <= tau <= 2.


ARGUMENTS
       N       (input) INTEGER
               The order of the elementary reflector.

       ALPHA   (input/output) REAL
               On entry, the value alpha.  On exit, it is overwritten with the
               value beta.

       X       (input/output) REAL array, dimension
               (1+(N-2)*abs(INCX)) On entry, the vector x.  On exit, it is
               overwritten with the vector v.

       INCX    (input) INTEGER
               The increment between elements of X. INCX > 0.

       TAU     (output) REAL
               The value tau.



 LAPACK auxiliary routine (versioNovember 2006                      SLARFG(3f)
