SLAED6(3)      LAPACK routine of NEC Numeric Library Collection      SLAED6(3)



NAME
       SLAED6

SYNOPSIS
       SUBROUTINE SLAED6 (KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO)



PURPOSE
            SLAED6 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 SLAED4 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)
                     KNITER is INTEGER
                          Refer to SLAED4 for its significance.

           ORGATI    (input)
                     ORGATI is 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
                          SLAED4 for further details.

           RHO       (input)
                     RHO is REAL
                          Refer to the equation f(x) above.

           D         (input)
                     D is REAL array, dimension (3)
                          D satisfies d(1) < d(2) < d(3).

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

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

           TAU       (output)
                     TAU is REAL
                          The root of the equation f(x).

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



LAPACK routine                  31 October 2017                      SLAED6(3)