ZLARFG(3F)ZLARFG(3F)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.
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