ZLARFG(3)

NAME
ZLARFG - 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.