dlarfg.f -

## SYNOPSIS

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine dlarfg (integerN, double precisionALPHA, double precision, dimension( * )X, integerINCX, double precisionTAU)

DLARFG generates an elementary reflector (Householder matrix).

Purpose:

``` DLARFG generates a real elementary reflector H of order n, such
that

H * ( alpha ) = ( beta ),   H**T * H = I.
(   x   )   (   0  )

where alpha and beta are scalars, and x is an (n-1)-element real
vector. H is represented in the form

H = I - tau * ( 1 ) * ( 1 v**T ) ,
( v )

where tau is a real scalar and v is a real (n-1)-element
vector.

If the elements of x are all zero, then tau = 0 and H is taken to be
the unit matrix.

Otherwise  1 <= tau <= 2.
```

Parameters:

N

```          N is INTEGER
The order of the elementary reflector.
```

ALPHA

```          ALPHA is DOUBLE PRECISION
On entry, the value alpha.
On exit, it is overwritten with the value beta.
```

X

```          X is DOUBLE PRECISION 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 DOUBLE PRECISION
The value tau.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley