NAME¶

ZLARFG - generates 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.