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.


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