ZLARFG (3lapack)

generate a complex elementary reflector H of order n, such that H' * ( alpha ) = ( beta ), H' * H = I

SYNOPSIS

  SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU )

      INTEGER        INCX, N

      COMPLEX*16     ALPHA, TAU

      COMPLEX*16     X( * )

PURPOSE

  ZLARFG generates a complex elementary reflector H of order n, such that
             (   x   )   (   0  )

  where alpha and beta are scalars, with beta real, and x is an (n-1)-element
  complex vector. H is represented in the form

        H = I - tau * ( 1 ) * ( 1 v' ) ,
                      ( v )

  where tau is a complex scalar and v is a complex (n-1)-element vector. Note
  that H is not hermitian.

  If the elements of x are all zero and alpha is real, then tau = 0 and H is
  taken to be the unit matrix.

  Otherwise  1 <= real(tau) <= 2  and  abs(tau-1) <= 1 .

ARGUMENTS

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

  ALPHA   (input/output) COMPLEX*16
          On entry, the value alpha.  On exit, it is overwritten with the
          value beta.

  X       (input/output) COMPLEX*16 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) COMPLEX*16
          The value tau.