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

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
NAG Ltd.
Date:
September 2012
Definition at line 107 of file zlarfg.f.

# Author

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