NAME

       dlarfg.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dlarfg (N, ALPHA, X, INCX, TAU)
           DLARFG generates an elementary reflector (Householder matrix).

Function/Subroutine Documentation

   subroutine dlarfg (integer N, double precision ALPHA, double precision, dimension( * ) X,
       integer INCX, double precision TAU)
       DLARFG generates an elementary reflector (Householder matrix).

       Purpose:

            DLARFG generates a real elementary reflector H of order n, such
            that

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

       Parameters:
           N

                     N is INTEGER
                     The order of the elementary reflector.

           ALPHA

                     ALPHA is DOUBLE PRECISION
                     On entry, the value alpha.
                     On exit, it is overwritten with the value beta.

           X

                     X is DOUBLE PRECISION array, dimension
                                    (1+(N-2)*abs(INCX))
                     On entry, the vector x.
                     On exit, it is overwritten with the vector v.

           INCX

                     INCX is INTEGER
                     The increment between elements of X. INCX > 0.

           TAU

                     TAU is DOUBLE PRECISION
                     The value tau.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

Author

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