1SLAED2(1) LAPACK routine (version 3.2) SLAED2(1)
2
6 SLAED2 - merges the two sets of eigenvalues together into a single
7 sorted set
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10 SUBROUTINE SLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2,
11 INDX, INDXC, INDXP, COLTYP, INFO )
12 INTEGER INFO, K, LDQ, N, N1
14 REAL RHO
16 INTEGER COLTYP( * ), INDX( * ), INDXC( * ), INDXP( * ),
18 INDXQ( * )
19 REAL D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), W( * ),
21 Z( * )
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24 SLAED2 merges the two sets of eigenvalues together into a single sorted
25 set. Then it tries to deflate the size of the problem. There are two
26 ways in which deflation can occur: when two or more eigenvalues are
27 close together or if there is a tiny entry in the Z vector. For each
28 such occurrence the order of the related secular equation problem is
29 reduced by one.
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32 K (output) INTEGER
33 The number of non-deflated eigenvalues, and the order of the
34 related secular equation. 0 <= K <=N.
35 N (input) INTEGER
37 The dimension of the symmetric tridiagonal matrix. N >= 0.
38 N1 (input) INTEGER
40 The location of the last eigenvalue in the leading sub-matrix.
41 min(1,N) <= N1 <= N/2.
42 D (input/output) REAL array, dimension (N)
44 On entry, D contains the eigenvalues of the two submatrices to
45 be combined. On exit, D contains the trailing (N-K) updated ei‐
46 genvalues (those which were deflated) sorted into increasing
47 order.
48 Q (input/output) REAL array, dimension (LDQ, N)
50 On entry, Q contains the eigenvectors of two submatrices in the
51 two square blocks with corners at (1,1), (N1,N1) and (N1+1,
52 N1+1), (N,N). On exit, Q contains the trailing (N-K) updated
53 eigenvectors (those which were deflated) in its last N-K col‐
54 umns.
55 LDQ (input) INTEGER
57 The leading dimension of the array Q. LDQ >= max(1,N).
58 INDXQ (input/output) INTEGER array, dimension (N)
60 The permutation which separately sorts the two sub-problems in D
61 into ascending order. Note that elements in the second half of
62 this permutation must first have N1 added to their values.
63 Destroyed on exit.
64 RHO (input/output) REAL
66 On entry, the off-diagonal element associated with the rank-1
67 cut which originally split the two submatrices which are now
68 being recombined. On exit, RHO has been modified to the value
69 required by SLAED3.
70 Z (input) REAL array, dimension (N)
72 On entry, Z contains the updating vector (the last row of the
73 first sub-eigenvector matrix and the first row of the second
74 sub-eigenvector matrix). On exit, the contents of Z have been
75 destroyed by the updating process. DLAMDA (output) REAL array,
76 dimension (N) A copy of the first K eigenvalues which will be
77 used by SLAED3 to form the secular equation.
78 W (output) REAL array, dimension (N)
80 The first k values of the final deflation-altered z-vector which
81 will be passed to SLAED3.
82 Q2 (output) REAL array, dimension (N1**2+(N-N1)**2)
84 A copy of the first K eigenvectors which will be used by SLAED3
85 in a matrix multiply (SGEMM) to solve for the new eigenvectors.
86 INDX (workspace) INTEGER array, dimension (N)
88 The permutation used to sort the contents of DLAMDA into ascend‐
89 ing order.
90 INDXC (output) INTEGER array, dimension (N)
92 The permutation used to arrange the columns of the deflated Q
93 matrix into three groups: the first group contains non-zero
94 elements only at and above N1, the second contains non-zero ele‐
95 ments only below N1, and the third is dense.
96 INDXP (workspace) INTEGER array, dimension (N)
98 The permutation used to place deflated values of D at the end of
99 the array. INDXP(1:K) points to the nondeflated D-values
100 and INDXP(K+1:N) points to the deflated eigenvalues. COLTYP
101 (workspace/output) INTEGER array, dimension (N) During execu‐
102 tion, a label which will indicate which of the following types a
103 column in the Q2 matrix is:
104 1 : non-zero in the upper half only;
105 2 : dense;
106 3 : non-zero in the lower half only;
107 4 : deflated. On exit, COLTYP(i) is the number of columns of
108 type i, for i=1 to 4 only.
109 INFO (output) INTEGER
111 = 0: successful exit.
112 < 0: if INFO = -i, the i-th argument had an illegal value.
113
115 Based on contributions by
116 Jeff Rutter, Computer Science Division, University of California
117 at Berkeley, USA
118 Modified by Francoise Tisseur, University of Tennessee.
119 LAPACK routine (version 3.2) November 2008 SLAED2(1)