dlarfg(3)

NAME

DLARFG - generate 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 H * ( alpha ) = ( beta ), H' * H = I. ( x

) ( 0 )

where alpha and beta are scalars, and x is an (n-1)-ele

ment 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 over

written 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.

LAPACK version 3.0 15 June 2000

DLARFG(3)