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zlarfg.f(3) LAPACK zlarfg.f(3)

NAME

zlarfg.f -

SYNOPSIS

Functions/Subroutines


subroutine zlarfg (N, ALPHA, X, INCX, TAU)
ZLARFG generates an elementary reflector (Householder matrix).

Function/Subroutine Documentation

subroutine zlarfg (integerN, complex*16ALPHA, complex*16, dimension( * )X, integerINCX, complex*16TAU)

ZLARFG generates an elementary reflector (Householder matrix).

Purpose:


ZLARFG generates a complex elementary reflector H of order n, such
that
H**H * ( alpha ) = ( beta ), H**H * H = I.
( 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**H ) ,
( 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 .

Parameters:

N


N is INTEGER
The order of the elementary reflector.

ALPHA


ALPHA is COMPLEX*16
On entry, the value alpha.
On exit, it is overwritten with the value beta.

X


X is COMPLEX*16 array, dimension
(1+(N-2)*abs(INCX))
On entry, the vector x.
On exit, it is overwritten with the vector v.

INCX


INCX is INTEGER
The increment between elements of X. INCX > 0.

TAU


TAU is COMPLEX*16
The value tau.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 107 of file zlarfg.f.

Author

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Tue Sep 25 2012 Version 3.4.2