1SLAED3(1) LAPACK routine (version 3.2) SLAED3(1)
2
6 SLAED3 - finds the roots of the secular equation, as defined by the
7 values in D, W, and RHO, between 1 and K
8
10 SUBROUTINE SLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, CTOT, W,
11 S, INFO )
12 INTEGER INFO, K, LDQ, N, N1
14 REAL RHO
16 INTEGER CTOT( * ), INDX( * )
18 REAL D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), S( * ),
20 W( * )
21
23 SLAED3 finds the roots of the secular equation, as defined by the val‐
24 ues in D, W, and RHO, between 1 and K. It makes the appropriate calls
25 to SLAED4 and then updates the eigenvectors by multiplying the matrix
26 of eigenvectors of the pair of eigensystems being combined by the
27 matrix of eigenvectors of the K-by-K system which is solved here.
28 This code makes very mild assumptions about floating point arithmetic.
29 It will work on machines with a guard digit in add/subtract, or on
30 those binary machines without guard digits which subtract like the Cray
31 X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on
32 hexadecimal or decimal machines without guard digits, but we know of
33 none.
34
36 K (input) INTEGER
37 The number of terms in the rational function to be solved by
38 SLAED4. K >= 0.
39 N (input) INTEGER
41 The number of rows and columns in the Q matrix. N >= K (defla‐
42 tion may result in N>K).
43 N1 (input) INTEGER
45 The location of the last eigenvalue in the leading submatrix.
46 min(1,N) <= N1 <= N/2.
47 D (output) REAL array, dimension (N)
49 D(I) contains the updated eigenvalues for 1 <= I <= K.
50 Q (output) REAL array, dimension (LDQ,N)
52 Initially the first K columns are used as workspace. On output
53 the columns 1 to K contain the updated eigenvectors.
54 LDQ (input) INTEGER
56 The leading dimension of the array Q. LDQ >= max(1,N).
57 RHO (input) REAL
59 The value of the parameter in the rank one update equation.
60 RHO >= 0 required.
61 DLAMDA (input/output) REAL array, dimension (K)
63 The first K elements of this array contain the old roots of the
64 deflated updating problem. These are the poles of the secular
65 equation. May be changed on output by having lowest order bit
66 set to zero on Cray X-MP, Cray Y-MP, Cray-2, or Cray C-90, as
67 described above.
68 Q2 (input) REAL array, dimension (LDQ2, N)
70 The first K columns of this matrix contain the non-deflated
71 eigenvectors for the split problem.
72 INDX (input) INTEGER array, dimension (N)
74 The permutation used to arrange the columns of the deflated Q
75 matrix into three groups (see SLAED2). The rows of the eigen‐
76 vectors found by SLAED4 must be likewise permuted before the
77 matrix multiply can take place.
78 CTOT (input) INTEGER array, dimension (4)
80 A count of the total number of the various types of columns in
81 Q, as described in INDX. The fourth column type is any column
82 which has been deflated.
83 W (input/output) REAL array, dimension (K)
85 The first K elements of this array contain the components of
86 the deflation-adjusted updating vector. Destroyed on output.
87 S (workspace) REAL array, dimension (N1 + 1)*K
89 Will contain the eigenvectors of the repaired matrix which will
90 be multiplied by the previously accumulated eigenvectors to
91 update the system.
92 LDS (input) INTEGER
94 The leading dimension of S. LDS >= max(1,K).
95 INFO (output) INTEGER
97 = 0: successful exit.
98 < 0: if INFO = -i, the i-th argument had an illegal value.
99 > 0: if INFO = 1, an eigenvalue did not converge
100
102 Based on contributions by
103 Jeff Rutter, Computer Science Division, University of California
104 at Berkeley, USA
105 Modified by Francoise Tisseur, University of Tennessee.
106 LAPACK routine (version 3.2) November 2008 SLAED3(1)