1DLAED6(1)                LAPACK routine (version 3.2)                DLAED6(1)
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NAME

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

11       SUBROUTINE DLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO )
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13           LOGICAL        ORGATI
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15           INTEGER        INFO, KNITER
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17           DOUBLE         PRECISION FINIT, RHO, TAU
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19           DOUBLE         PRECISION D( 3 ), Z( 3 )
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PURPOSE

22       DLAED6  computes  the positive or negative root (closest to the origin)
23       of
24                        z(1)        z(2)        z(3) f(x) =   rho +  ---------
25       + ---------- + ---------
26                       d(1)-x      d(2)-x      d(3)-x
27             otherwise it is between d(1) and d(2)
28       This  routine  will  be called by DLAED4 when necessary. In most cases,
29       the root sought is the smallest in magnitude, though it might not be in
30       some extremely rare situations.
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ARGUMENTS

33       KNITER       (input) INTEGER
34                    Refer to DLAED4 for its significance.
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36       ORGATI       (input) LOGICAL
37                    If  ORGATI  is  true,  the needed root is between d(2) and
38                    d(3); otherwise it is between d(1) and d(2).   See  DLAED4
39                    for further details.
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41       RHO          (input) DOUBLE PRECISION
42                    Refer to the equation f(x) above.
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44       D            (input) DOUBLE PRECISION array, dimension (3)
45                    D satisfies d(1) < d(2) < d(3).
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47       Z            (input) DOUBLE PRECISION array, dimension (3)
48                    Each of the elements in z must be positive.
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50       FINIT        (input) DOUBLE PRECISION
51                    The  value  of  f  at  0. It is more accurate than the one
52                    evaluated inside this routine (if someone wants to do so).
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54       TAU          (output) DOUBLE PRECISION
55                    The root of the equation f(x).
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57       INFO         (output) INTEGER
58                    = 0: successful exit
59                    > 0: if INFO = 1, failure to converge
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FURTHER DETAILS

62       30/06/99: Based on contributions by
63          Ren-Cang Li, Computer Science Division, University of California
64          at Berkeley, USA
65       10/02/03: This version has a few statements commented  out  for  thread
66       safety (machine parameters are computed on each entry). SJH.  05/10/06:
67       Modified from a new version of Ren-Cang Li, use
68          Gragg-Thornton-Warner cubic convergent scheme for better stability.
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72 LAPACK routine (version 3.2)    November 2008                       DLAED6(1)
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