DLAED6 - compute the positive or negative root (closest to
       the origin) of z(1) z(2) z(3) f(x) =  rho  +  ---------  +
       ---------- + --------- d(1)-x d(2)-x d(3)-x  It is assumed
       that  if ORGATI = .true


SYNOPSIS

       SUBROUTINE DLAED6( KNITER, ORGATI, RHO, D, Z, FINIT,  TAU,
                          INFO )

           LOGICAL        ORGATI

           INTEGER        INFO, KNITER

           DOUBLE         PRECISION FINIT, RHO, TAU

           DOUBLE         PRECISION D( 3 ), Z( 3 )


PURPOSE

       DLAED6  computes the positive or negative root (closest to
       the origin) of z(1) z(2) z(3) f(x) =  rho  +  ---------  +
       ----------  + --------- d(1)-x d(2)-x d(3)-x It is assumed
       that if ORGATI = .true. the root is between d(2) and d(3);
       otherwise it is between d(1) and d(2)

       This  routine  will be called by DLAED4 when necessary. In
       most cases, the root sought is the smallest in  magnitude,
       though  it might not be in some extremely rare situations.


ARGUMENTS

       KNITER       (input) INTEGER
                    Refer to DLAED4 for its significance.

       ORGATI       (input) LOGICAL
                    If ORGATI is true, the needed root is between
                    d(2)  and  d(3); otherwise it is between d(1)
                    and d(2).  See DLAED4 for further details.

       RHO          (input) DOUBLE PRECISION
                    Refer to the equation f(x) above.

       D            (input) DOUBLE PRECISION array, dimension (3)
                    D satisfies d(1) < d(2) < d(3).

       Z            (input) DOUBLE PRECISION array, dimension (3)
                    Each of the elements in z must be positive.

       FINIT        (input) DOUBLE PRECISION
                    The value of f at 0. It is more accurate than
                    the  one  evaluated  inside  this routine (if
                    someone wants to do so).

                    The root of the equation f(x).

       INFO         (output) INTEGER
                    = 0: successful exit
                    > 0: if INFO = 1, failure to converge


FURTHER DETAILS

       Based on contributions by
          Ren-Cang Li, Computer Science Division,  University  of
       California
          at Berkeley, USA


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