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dlarfg examples
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Man Page Details
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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

        H * ( alpha ) = ( beta ),   H' * 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' ) ,
                      ( 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.

