1DLAED3(1) LAPACK routine (version 3.1) DLAED3(1)
2
6 DLAED3 - the roots of the secular equation, as defined by the values in
7 D, W, and RHO, between 1 and K
8
10 SUBROUTINE DLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, CTOT, W,
11 S, INFO )
12 INTEGER INFO, K, LDQ, N, N1
14 DOUBLE PRECISION RHO
16 INTEGER CTOT( * ), INDX( * )
18 DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ),
20 S( * ), W( * )
21
23 DLAED3 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 DLAED4 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.
30 It will work on machines with a guard digit in add/subtract, or on
31 those binary machines without guard digits which subtract like the Cray
32 X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on
33 hexadecimal or decimal machines without guard digits, but we know of
34 none.
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38 K (input) INTEGER
39 The number of terms in the rational function to be solved by
40 DLAED4. K >= 0.
41 N (input) INTEGER
43 The number of rows and columns in the Q matrix. N >= K (defla‐
44 tion may result in N>K).
45 N1 (input) INTEGER
47 The location of the last eigenvalue in the leading submatrix.
48 min(1,N) <= N1 <= N/2.
49 D (output) DOUBLE PRECISION array, dimension (N)
51 D(I) contains the updated eigenvalues for 1 <= I <= K.
52 Q (output) DOUBLE PRECISION array, dimension (LDQ,N)
54 Initially the first K columns are used as workspace. On output
55 the columns 1 to K contain the updated eigenvectors.
56 LDQ (input) INTEGER
58 The leading dimension of the array Q. LDQ >= max(1,N).
59 RHO (input) DOUBLE PRECISION
61 The value of the parameter in the rank one update equation.
62 RHO >= 0 required.
63 DLAMDA (input/output) DOUBLE PRECISION array, dimension (K)
65 The first K elements of this array contain the old roots of the
66 deflated updating problem. These are the poles of the secular
67 equation. May be changed on output by having lowest order bit
68 set to zero on Cray X-MP, Cray Y-MP, Cray-2, or Cray C-90, as
69 described above.
70 Q2 (input) DOUBLE PRECISION array, dimension (LDQ2, N)
72 The first K columns of this matrix contain the non-deflated
73 eigenvectors for the split problem.
74 INDX (input) INTEGER array, dimension (N)
76 The permutation used to arrange the columns of the deflated Q
77 matrix into three groups (see DLAED2). The rows of the eigen‐
78 vectors found by DLAED4 must be likewise permuted before the
79 matrix multiply can take place.
80 CTOT (input) INTEGER array, dimension (4)
82 A count of the total number of the various types of columns in
83 Q, as described in INDX. The fourth column type is any column
84 which has been deflated.
85 W (input/output) DOUBLE PRECISION array, dimension (K)
87 The first K elements of this array contain the components of
88 the deflation-adjusted updating vector. Destroyed on output.
89 S (workspace) DOUBLE PRECISION array, dimension (N1 + 1)*K
91 Will contain the eigenvectors of the repaired matrix which will
92 be multiplied by the previously accumulated eigenvectors to
93 update the system.
94 LDS (input) INTEGER
96 The leading dimension of S. LDS >= max(1,K).
97 INFO (output) INTEGER
99 = 0: successful exit.
100 < 0: if INFO = -i, the i-th argument had an illegal value.
101 > 0: if INFO = 1, an eigenvalue did not converge
102
104 Based on contributions by
105 Jeff Rutter, Computer Science Division, University of California
106 at Berkeley, USA
107 Modified by Francoise Tisseur, University of Tennessee.
108 LAPACK routine (version 3.1) November 2006 DLAED3(1)