SLARFG (3lapack)

generate 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.