# zlarfg.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **zlarfg** (**N**, ALPHA, X, INCX, TAU)**ZLARFG** generates an elementary reflector (Householder matrix).

## Function/Subroutine Documentation

### subroutine zlarfg (integer N, complex*16 ALPHA, complex*16, dimension( * ) X, integer INCX, complex*16 TAU)

**ZLARFG** generates an elementary reflector (Householder matrix).

**Purpose:**

ZLARFG generates a complex elementary reflector H of order n, such that H**H * ( alpha ) = ( beta ), H**H * H = I. ( x ) ( 0 ) where alpha and beta are scalars, with beta real, and x is an (n-1)-element complex vector. H is represented in the form H = I - tau * ( 1 ) * ( 1 v**H ) , ( v ) where tau is a complex scalar and v is a complex (n-1)-element vector. Note that H is not hermitian. If the elements of x are all zero and alpha is real, then tau = 0 and H is taken to be the unit matrix. Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 .

**Parameters:***N*N is INTEGER The order of the elementary reflector.

*ALPHA*ALPHA is COMPLEX*16 On entry, the value alpha. On exit, it is overwritten with the value beta.

*X*X is COMPLEX*16 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 COMPLEX*16 The value tau.

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**November 2017

Definition at line 108 of file zlarfg.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 14 2017 Version 3.8.0 LAPACK