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dlarfg

 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 overwrit-
              ten 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.