1SLAED2(1) LAPACK routine (version 3.1) SLAED2(1)
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6 SLAED2 - the two sets of eigenvalues together into a single sorted set
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9 SUBROUTINE SLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2,
10 INDX, INDXC, INDXP, COLTYP, INFO )
11 INTEGER INFO, K, LDQ, N, N1
13 REAL RHO
15 INTEGER COLTYP( * ), INDX( * ), INDXC( * ), INDXP( * ),
17 INDXQ( * )
18 REAL D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), W( * ),
20 Z( * )
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23 SLAED2 merges the two sets of eigenvalues together into a single sorted
24 set. Then it tries to deflate the size of the problem. There are two
25 ways in which deflation can occur: when two or more eigenvalues are
26 close together or if there is a tiny entry in the Z vector. For each
27 such occurrence the order of the related secular equation problem is
28 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.
76 DLAMDA (output) REAL array, dimension (N) A copy of the first K
78 eigenvalues which will be used by SLAED3 to form the secular
79 equation.
80 W (output) REAL array, dimension (N)
82 The first k values of the final deflation-altered z-vector which
83 will be passed to SLAED3.
84 Q2 (output) REAL array, dimension (N1**2+(N-N1)**2)
86 A copy of the first K eigenvectors which will be used by SLAED3
87 in a matrix multiply (SGEMM) to solve for the new eigenvectors.
88 INDX (workspace) INTEGER array, dimension (N)
90 The permutation used to sort the contents of DLAMDA into ascend‐
91 ing order.
92 INDXC (output) INTEGER array, dimension (N)
94 The permutation used to arrange the columns of the deflated Q
95 matrix into three groups: the first group contains non-zero
96 elements only at and above N1, the second contains non-zero ele‐
97 ments only below N1, and the third is dense.
98 INDXP (workspace) INTEGER array, dimension (N)
100 The permutation used to place deflated values of D at the end of
101 the array. INDXP(1:K) points to the nondeflated D-values
102 and INDXP(K+1:N) points to the deflated eigenvalues.
103 COLTYP (workspace/output) INTEGER array, dimension (N) During
105 execution, a label which will indicate which of the following
106 types a column in the Q2 matrix is:
107 1 : non-zero in the upper half only;
108 2 : dense;
109 3 : non-zero in the lower half only;
110 4 : deflated. On exit, COLTYP(i) is the number of columns of
111 type i, for i=1 to 4 only.
112 INFO (output) INTEGER
114 = 0: successful exit.
115 < 0: if INFO = -i, the i-th argument had an illegal value.
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118 Based on contributions by
119 Jeff Rutter, Computer Science Division, University of California
120 at Berkeley, USA
121 Modified by Francoise Tisseur, University of Tennessee.
122 LAPACK routine (version 3.1) November 2006 SLAED2(1)