1SLAED0(1) LAPACK routine (version 3.1) SLAED0(1)
2
6 SLAED0 - all eigenvalues and corresponding eigenvectors of a symmetric
7 tridiagonal matrix using the divide and conquer method
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10 SUBROUTINE SLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK,
11 IWORK, INFO )
12 INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ
14 INTEGER IWORK( * )
16 REAL D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ),
18 WORK( * )
19
21 SLAED0 computes all eigenvalues and corresponding eigenvectors of a
22 symmetric tridiagonal matrix using the divide and conquer method.
23
26 ICOMPQ (input) INTEGER
27 = 0: Compute eigenvalues only.
28 = 1: Compute eigenvectors of original dense symmetric matrix
29 also. On entry, Q contains the orthogonal matrix used to
30 reduce the original matrix to tridiagonal form. = 2: Compute
31 eigenvalues and eigenvectors of tridiagonal matrix.
32 QSIZ (input) INTEGER
34 The dimension of the orthogonal matrix used to reduce the full
35 matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
36 N (input) INTEGER
38 The dimension of the symmetric tridiagonal matrix. N >= 0.
39 D (input/output) REAL array, dimension (N)
41 On entry, the main diagonal of the tridiagonal matrix. On exit,
42 its eigenvalues.
43 E (input) REAL array, dimension (N-1)
45 The off-diagonal elements of the tridiagonal matrix. On exit, E
46 has been destroyed.
47 Q (input/output) REAL array, dimension (LDQ, N)
49 On entry, Q must contain an N-by-N orthogonal matrix. If ICOMPQ
50 = 0 Q is not referenced. If ICOMPQ = 1 On entry, Q is a
51 subset of the columns of the orthogonal matrix used to reduce
52 the full matrix to tridiagonal form corresponding to the subset
53 of the full matrix which is being decomposed at this time. If
54 ICOMPQ = 2 On entry, Q will be the identity matrix. On exit,
55 Q contains the eigenvectors of the tridiagonal matrix.
56 LDQ (input) INTEGER
58 The leading dimension of the array Q. If eigenvectors are
59 desired, then LDQ >= max(1,N). In any case, LDQ >= 1.
60 QSTORE (workspace) REAL array, dimension (LDQS, N) Referenced
62 only when ICOMPQ = 1. Used to store parts of the eigenvector
63 matrix when the updating matrix multiplies take place.
64 LDQS (input) INTEGER
66 The leading dimension of the array QSTORE. If ICOMPQ = 1, then
67 LDQS >= max(1,N). In any case, LDQS >= 1.
68 WORK (workspace) REAL array,
70 If ICOMPQ = 0 or 1, the dimension of WORK must be at least 1 +
71 3*N + 2*N*lg N + 2*N**2 ( lg( N ) = smallest integer k such that
72 2^k >= N ) If ICOMPQ = 2, the dimension of WORK must be at least
73 4*N + N**2.
74 IWORK (workspace) INTEGER array,
76 If ICOMPQ = 0 or 1, the dimension of IWORK must be at least 6 +
77 6*N + 5*N*lg N. ( lg( N ) = smallest integer k such that 2^k >=
78 N ) If ICOMPQ = 2, the dimension of IWORK must be at least 3 +
79 5*N.
80 INFO (output) INTEGER
82 = 0: successful exit.
83 < 0: if INFO = -i, the i-th argument had an illegal value.
84 > 0: The algorithm failed to compute an eigenvalue while work‐
85 ing on the submatrix lying in rows and columns INFO/(N+1)
86 through mod(INFO,N+1).
87
89 Based on contributions by
90 Jeff Rutter, Computer Science Division, University of California
91 at Berkeley, USA
92 LAPACK routine (version 3.1) November 2006 SLAED0(1)