# zlarfg (3) - Linux Manuals

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