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 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.

SunSoft, Inc.  —  Last change: 27 Jun 1995