---
name: "dlarfg"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dlarfg/3lapack"
---

# dlarfg(3lapack)

generates a real elementary reflector H of order n, such that H \* ( alpha ) = ( beta ), H' \* H = I

## NAME

DLARFG - generates a real elementary reflector H of order n, such that   H \* ( alpha ) = ( beta ), H' \* H = I

## SYNOPSIS

- SUBROUTINE DLARFG(

  N, ALPHA, X, INCX, TAU )

- INTEGER

  INCX, N

- DOUBLE

  PRECISION ALPHA, TAU

- DOUBLE

  PRECISION X( \* )

## PURPOSE

DLARFG generates a real elementary reflector H of order n, such that\
           (   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' ) ,\
\
                     ( 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.\

## ARGUMENTS

- N (input) INTEGER

  The order of the elementary reflector.

- ALPHA (input/output) DOUBLE PRECISION

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

- X (input/output) DOUBLE PRECISION array, dimension

  (1+(N-2)\*abs(INCX)) On entry, the vector x. On exit, it is overwritten with the vector v.

- INCX (input) INTEGER

  The increment between elements of X. INCX \> 0.

- TAU (output) DOUBLE PRECISION

  The value tau.