1SLAED6(1) LAPACK routine (version 3.2) SLAED6(1)
2
6 SLAED6 - 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
9
11 SUBROUTINE SLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO )
12 LOGICAL ORGATI
14 INTEGER INFO, KNITER
16 REAL FINIT, RHO, TAU
18 REAL D( 3 ), Z( 3 )
20
22 SLAED6 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 SLAED4 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.
31
33 KNITER (input) INTEGER
34 Refer to SLAED4 for its significance.
35 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 SLAED4
39 for further details.
40 RHO (input) REAL
42 Refer to the equation f(x) above.
43 D (input) REAL array, dimension (3)
45 D satisfies d(1) < d(2) < d(3).
46 Z (input) REAL array, dimension (3)
48 Each of the elements in z must be positive.
49 FINIT (input) REAL
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).
53 TAU (output) REAL
55 The root of the equation f(x).
56 INFO (output) INTEGER
58 = 0: successful exit
59 > 0: if INFO = 1, failure to converge
60
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
67 (machine parameters are computed on each entry). SJH.
68 05/10/06: Modified from a new version of Ren-Cang Li, use
69 Gragg-Thornton-Warner cubic convergent scheme for better stability.
70 LAPACK routine (version 3.2) November 2008 SLAED6(1)