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zlarfg

 NAME
      ZLARFG - 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 overwrit-
              ten 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.