# clarfg.f - Man Page

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine clarfg (integer N, complex ALPHA, complex, dimension( * ) X, integer INCX, complex TAU)

CLARFG generates an elementary reflector (Householder matrix).

Purpose:

``` CLARFG 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
On entry, the value alpha.
On exit, it is overwritten with the value beta.```

X

```          X is COMPLEX 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
The value tau.```
Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

November 2017

Definition at line 108 of file clarfg.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page clarfg(3) is an alias of clarfg.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK