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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.
```