dlarfg(3F)

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

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

         INTEGER        INCX, N

         DOUBLE         PRECISION ALPHA, TAU

         DOUBLE         PRECISION X( * )

PURPOSE
     DLARFG 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) DOUBLE PRECISION
             On entry, the value alpha.  On exit, it is overwritten with the
             value beta.

     X       (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION
             The value tau.