# dlarfgp.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dlarfgp.f

## SYNOPSIS

### Functions/Subroutines

subroutine dlarfgp (N, ALPHA, X, INCX, TAU)
DLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.

## Function/Subroutine Documentation

### subroutine dlarfgp (integer N, double precision ALPHA, double precision, dimension( * ) X, integer INCX, double precision TAU)

DLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.

Purpose:

``` DLARFGP 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, beta is non-negative, 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.
```

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