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
          (   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.

  —  LAPACK version 2.0  —  08 October 1994