NAME

       zlarfg.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zlarfg (N, ALPHA, X, INCX, TAU)
           ZLARFG generates an elementary reflector (Householder matrix).

Function/Subroutine Documentation

   subroutine zlarfg (integer N, complex*16 ALPHA, complex*16, dimension( * ) X, integer INCX,
       complex*16 TAU)
       ZLARFG generates an elementary reflector (Householder matrix).

       Purpose:

            ZLARFG generates a complex elementary reflector H of order n, such
            that

                  H**H * ( alpha ) = ( beta ),   H**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**H ) ,
                                ( 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 .

       Parameters:
           N

                     N is INTEGER
                     The order of the elementary reflector.

           ALPHA

                     ALPHA is COMPLEX*16
                     On entry, the value alpha.
                     On exit, it is overwritten with the value beta.

           X

                     X is COMPLEX*16 array, dimension
                                    (1+(N-2)*abs(INCX))
                     On entry, the vector x.
                     On exit, it is overwritten with the vector v.

           INCX

                     INCX is INTEGER
                     The increment between elements of X. INCX > 0.

           TAU

                     TAU is COMPLEX*16
                     The value tau.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

Author

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