DLARFG(3)

NAME
DLARFG - 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.