1SLAED0(1) LAPACK routine (version 3.2) SLAED0(1)
2
6 SLAED0 - computes all eigenvalues and corresponding eigenvectors of a
7 symmetric 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( * )
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21 SLAED0 computes all eigenvalues and corresponding eigenvectors of a
22 symmetric tridiagonal matrix using the divide and conquer method.
23
25 ICOMPQ (input) INTEGER
26 = 0: Compute eigenvalues only.
27 = 1: Compute eigenvectors of original dense symmetric matrix
28 also. On entry, Q contains the orthogonal matrix used to
29 reduce the original matrix to tridiagonal form. = 2: Compute
30 eigenvalues and eigenvectors of tridiagonal matrix.
31 QSIZ (input) INTEGER
33 The dimension of the orthogonal matrix used to reduce the full
34 matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
35 N (input) INTEGER
37 The dimension of the symmetric tridiagonal matrix. N >= 0.
38 D (input/output) REAL array, dimension (N)
40 On entry, the main diagonal of the tridiagonal matrix. On exit,
41 its eigenvalues.
42 E (input) REAL array, dimension (N-1)
44 The off-diagonal elements of the tridiagonal matrix. On exit, E
45 has been destroyed.
46 Q (input/output) REAL array, dimension (LDQ, N)
48 On entry, Q must contain an N-by-N orthogonal matrix. If ICOMPQ
49 = 0 Q is not referenced. If ICOMPQ = 1 On entry, Q is a
50 subset of the columns of the orthogonal matrix used to reduce
51 the full matrix to tridiagonal form corresponding to the subset
52 of the full matrix which is being decomposed at this time. If
53 ICOMPQ = 2 On entry, Q will be the identity matrix. On exit,
54 Q contains the eigenvectors of the tridiagonal matrix.
55 LDQ (input) INTEGER
57 The leading dimension of the array Q. If eigenvectors are
58 desired, then LDQ >= max(1,N). In any case, LDQ >= 1. QSTORE
59 (workspace) REAL array, dimension (LDQS, N) Referenced only when
60 ICOMPQ = 1. Used to store parts of the eigenvector matrix when
61 the updating matrix multiplies take place.
62 LDQS (input) INTEGER
64 The leading dimension of the array QSTORE. If ICOMPQ = 1, then
65 LDQS >= max(1,N). In any case, LDQS >= 1.
66 WORK (workspace) REAL array,
68 If ICOMPQ = 0 or 1, the dimension of WORK must be at least 1 +
69 3*N + 2*N*lg N + 2*N**2 ( lg( N ) = smallest integer k such that
70 2^k >= N ) If ICOMPQ = 2, the dimension of WORK must be at least
71 4*N + N**2.
72 IWORK (workspace) INTEGER array,
74 If ICOMPQ = 0 or 1, the dimension of IWORK must be at least 6 +
75 6*N + 5*N*lg N. ( lg( N ) = smallest integer k such that 2^k >=
76 N ) If ICOMPQ = 2, the dimension of IWORK must be at least 3 +
77 5*N.
78 INFO (output) INTEGER
80 = 0: successful exit.
81 < 0: if INFO = -i, the i-th argument had an illegal value.
82 > 0: The algorithm failed to compute an eigenvalue while work‐
83 ing on the submatrix lying in rows and columns INFO/(N+1)
84 through mod(INFO,N+1).
85
87 Based on contributions by
88 Jeff Rutter, Computer Science Division, University of California
89 at Berkeley, USA
90 LAPACK routine (version 3.2) November 2008 SLAED0(1)