1SSTEDC(1) LAPACK driver routine (version 3.1) SSTEDC(1)
2
6 SSTEDC - all eigenvalues and, optionally, eigenvectors of a symmetric
7 tridiagonal matrix using the divide and conquer method
8
10 SUBROUTINE SSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
11 INFO )
12 CHARACTER COMPZ
14 INTEGER INFO, LDZ, LIWORK, LWORK, N
16 INTEGER IWORK( * )
18 REAL D( * ), E( * ), WORK( * ), Z( LDZ, * )
20
22 SSTEDC computes all eigenvalues and, optionally, eigenvectors of a sym‐
23 metric tridiagonal matrix using the divide and conquer method. The
24 eigenvectors of a full or band real symmetric matrix can also be found
25 if SSYTRD or SSPTRD or SSBTRD has been used to reduce this matrix to
26 tridiagonal form.
27 This code makes very mild assumptions about floating point arithmetic.
29 It will work on machines with a guard digit in add/subtract, or on
30 those binary machines without guard digits which subtract like the Cray
31 X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on
32 hexadecimal or decimal machines without guard digits, but we know of
33 none. See SLAED3 for details.
34
37 COMPZ (input) CHARACTER*1
38 = 'N': Compute eigenvalues only.
39 = 'I': Compute eigenvectors of tridiagonal matrix also.
40 = 'V': Compute eigenvectors of original dense symmetric matrix
41 also. On entry, Z contains the orthogonal matrix used to
42 reduce the original matrix to tridiagonal form.
43 N (input) INTEGER
45 The dimension of the symmetric tridiagonal matrix. N >= 0.
46 D (input/output) REAL array, dimension (N)
48 On entry, the diagonal elements of the tridiagonal matrix. On
49 exit, if INFO = 0, the eigenvalues in ascending order.
50 E (input/output) REAL array, dimension (N-1)
52 On entry, the subdiagonal elements of the tridiagonal matrix.
53 On exit, E has been destroyed.
54 Z (input/output) REAL array, dimension (LDZ,N)
56 On entry, if COMPZ = 'V', then Z contains the orthogonal matrix
57 used in the reduction to tridiagonal form. On exit, if INFO =
58 0, then if COMPZ = 'V', Z contains the orthonormal eigenvectors
59 of the original symmetric matrix, and if COMPZ = 'I', Z con‐
60 tains the orthonormal eigenvectors of the symmetric tridiagonal
61 matrix. If COMPZ = 'N', then Z is not referenced.
62 LDZ (input) INTEGER
64 The leading dimension of the array Z. LDZ >= 1. If eigenvec‐
65 tors are desired, then LDZ >= max(1,N).
66 WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
68 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
69 LWORK (input) INTEGER
71 The dimension of the array WORK. If COMPZ = 'N' or N <= 1 then
72 LWORK must be at least 1. If COMPZ = 'V' and N > 1 then LWORK
73 must be at least ( 1 + 3*N + 2*N*lg N + 3*N**2 ), where lg( N )
74 = smallest integer k such that 2**k >= N. If COMPZ = 'I' and N
75 > 1 then LWORK must be at least ( 1 + 4*N + N**2 ). Note that
76 for COMPZ = 'I' or 'V', then if N is less than or equal to the
77 minimum divide size, usually 25, then LWORK need only be
78 max(1,2*(N-1)).
79 If LWORK = -1, then a workspace query is assumed; the routine
81 only calculates the optimal size of the WORK array, returns
82 this value as the first entry of the WORK array, and no error
83 message related to LWORK is issued by XERBLA.
84 IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
86 On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
87 LIWORK (input) INTEGER
89 The dimension of the array IWORK. If COMPZ = 'N' or N <= 1
90 then LIWORK must be at least 1. If COMPZ = 'V' and N > 1 then
91 LIWORK must be at least ( 6 + 6*N + 5*N*lg N ). If COMPZ = 'I'
92 and N > 1 then LIWORK must be at least ( 3 + 5*N ). Note that
93 for COMPZ = 'I' or 'V', then if N is less than or equal to the
94 minimum divide size, usually 25, then LIWORK need only be 1.
95 If LIWORK = -1, then a workspace query is assumed; the routine
97 only calculates the optimal size of the IWORK array, returns
98 this value as the first entry of the IWORK array, and no error
99 message related to LIWORK is issued by XERBLA.
100 INFO (output) INTEGER
102 = 0: successful exit.
103 < 0: if INFO = -i, the i-th argument had an illegal value.
104 > 0: The algorithm failed to compute an eigenvalue while work‐
105 ing on the submatrix lying in rows and columns INFO/(N+1)
106 through mod(INFO,N+1).
107
109 Based on contributions by
110 Jeff Rutter, Computer Science Division, University of California
111 at Berkeley, USA
112 Modified by Francoise Tisseur, University of Tennessee.
113 LAPACK driver routine (version 3.N1o)vember 2006 SSTEDC(1)