# 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

Univ. of Colorado Denver

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