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.

KNITER

          KNITER is INTEGER


               Refer to DLAED4 for its significance.

ORGATI

          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


               DLAED4 for further details.

RHO

          RHO is DOUBLE PRECISION


               Refer to the equation f(x) above.

D

          D is DOUBLE PRECISION array, dimension (3)


               D satisfies d(1) < d(2) < d(3).

Z

          Z is DOUBLE PRECISION array, dimension (3)


               Each of the elements in z must be positive.

FINIT

          FINIT is 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).

TAU

          TAU is DOUBLE PRECISION


               The root of the equation f(x).

INFO

          INFO is INTEGER


               = 0: successful exit


               > 0: if INFO = 1, failure to converge

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

  10/02/03: This version has a few statements commented out for thread


  safety (machine parameters are computed on each entry). SJH.


  05/10/06: Modified from a new version of Ren-Cang Li, use


     Gragg-Thornton-Warner cubic convergent scheme for better stability.

Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA