# dlarfg.f - Man Page

SRC/dlarfg.f

## Synopsis

### Functions/Subroutines

subroutine dlarfg (n, alpha, x, incx, tau)
DLARFG generates an elementary reflector (Householder matrix).

## Function/Subroutine Documentation

### subroutine dlarfg (integer n, double precision alpha, double precision, dimension( * ) x, integer incx, double precision tau)

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

NAG Ltd.

Definition at line 105 of file dlarfg.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK