# dlarfg.f man page

dlarfg.f —

## Synopsis

### Functions/Subroutines

subroutinedlarfg(N, ALPHA, X, INCX, TAU)DLARFGgenerates 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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

Definition at line 107 of file dlarfg.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

dlarfg(3) is an alias of dlarfg.f(3).