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LAPACK version 3.0
zlarfg(3)

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

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

      INTEGER	     INCX, N

      COMPLEX*16     ALPHA, TAU

      COMPLEX*16     X( * )

DESCRIPTION
  ZLARFG generates a complex elementary reflector H of order n, such that H'
  * ( alpha ) = ( beta ), H' * H = I.		 (   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.