1SLAED9(1)                LAPACK routine (version 3.1)                SLAED9(1)
2
3
4

NAME

6       SLAED9 - the roots of the secular equation, as defined by the values in
7       D, Z, and RHO, between KSTART and KSTOP
8

SYNOPSIS

10       SUBROUTINE SLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA,  W,  S,
11                          LDS, INFO )
12
13           INTEGER        INFO, K, KSTART, KSTOP, LDQ, LDS, N
14
15           REAL           RHO
16
17           REAL           D(  * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, * ), W( *
18                          )
19

PURPOSE

21       SLAED9 finds the roots of the secular equation, as defined by the  val‐
22       ues in D, Z, and RHO, between KSTART and KSTOP.  It makes the appropri‐
23       ate calls to SLAED4 and then stores the new matrix of eigenvectors  for
24       use in calculating the next level of Z vectors.
25
26

ARGUMENTS

28       K       (input) INTEGER
29               The  number  of  terms in the rational function to be solved by
30               SLAED4.  K >= 0.
31
32       KSTART  (input) INTEGER
33               KSTOP   (input)  INTEGER  The  updated  eigenvalues  Lambda(I),
34               KSTART  <= I <= KSTOP are to be computed.  1 <= KSTART <= KSTOP
35               <= K.
36
37       N       (input) INTEGER
38               The number of rows and columns in the Q matrix.  N >= K  (dela‐
39               tion may result in N > K).
40
41       D       (output) REAL array, dimension (N)
42               D(I) contains the updated eigenvalues for KSTART <= I <= KSTOP.
43
44       Q       (workspace) REAL array, dimension (LDQ,N)
45
46       LDQ     (input) INTEGER
47               The leading dimension of the array Q.  LDQ >= max( 1, N ).
48
49       RHO     (input) REAL
50               The  value  of  the  parameter in the rank one update equation.
51               RHO >= 0 required.
52
53       DLAMDA  (input) REAL array, dimension (K)
54               The first K elements of this array contain the old roots of the
55               deflated  updating problem.  These are the poles of the secular
56               equation.
57
58       W       (input) REAL array, dimension (K)
59               The first K elements of this array contain  the  components  of
60               the deflation-adjusted updating vector.
61
62       S       (output) REAL array, dimension (LDS, K)
63               Will contain the eigenvectors of the repaired matrix which will
64               be stored for subsequent Z vector calculation and multiplied by
65               the previously accumulated eigenvectors to update the system.
66
67       LDS     (input) INTEGER
68               The leading dimension of S.  LDS >= max( 1, K ).
69
70       INFO    (output) INTEGER
71               = 0:  successful exit.
72               < 0:  if INFO = -i, the i-th argument had an illegal value.
73               > 0:  if INFO = 1, an eigenvalue did not converge
74

FURTHER DETAILS

76       Based on contributions by
77          Jeff Rutter, Computer Science Division, University of California
78          at Berkeley, USA
79
80
81
82
83 LAPACK routine (version 3.1)    November 2006                       SLAED9(1)