LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
zlarfg.f File Reference

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## Functions/Subroutines

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

## Function/Subroutine Documentation

 subroutine zlarfg ( integer N, complex*16 ALPHA, complex*16, dimension( * ) X, integer INCX, complex*16 TAU )

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:
 [in] N ``` N is INTEGER The order of the elementary reflector.``` [in,out] ALPHA ``` ALPHA is COMPLEX*16 On entry, the value alpha. On exit, it is overwritten with the value beta.``` [in,out] 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.``` [in] INCX ``` INCX is INTEGER The increment between elements of X. INCX > 0.``` [out] TAU ``` TAU is COMPLEX*16 The value tau.```
Date:
September 2012

Definition at line 107 of file zlarfg.f.

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