1SSTEDC(1) LAPACK driver routine (version 3.2) SSTEDC(1)
2
6 SSTEDC - computes all eigenvalues and, optionally, eigenvectors of a
7 symmetric 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.
28 It will work on machines with a guard digit in add/subtract, or on
29 those binary machines without guard digits which subtract like the Cray
30 X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on
31 hexadecimal or decimal machines without guard digits, but we know of
32 none. See SLAED3 for details.
33
35 COMPZ (input) CHARACTER*1
36 = 'N': Compute eigenvalues only.
37 = 'I': Compute eigenvectors of tridiagonal matrix also.
38 = 'V': Compute eigenvectors of original dense symmetric matrix
39 also. On entry, Z contains the orthogonal matrix used to
40 reduce the original matrix to tridiagonal form.
41 N (input) INTEGER
43 The dimension of the symmetric tridiagonal matrix. N >= 0.
44 D (input/output) REAL array, dimension (N)
46 On entry, the diagonal elements of the tridiagonal matrix. On
47 exit, if INFO = 0, the eigenvalues in ascending order.
48 E (input/output) REAL array, dimension (N-1)
50 On entry, the subdiagonal elements of the tridiagonal matrix.
51 On exit, E has been destroyed.
52 Z (input/output) REAL array, dimension (LDZ,N)
54 On entry, if COMPZ = 'V', then Z contains the orthogonal matrix
55 used in the reduction to tridiagonal form. On exit, if INFO =
56 0, then if COMPZ = 'V', Z contains the orthonormal eigenvectors
57 of the original symmetric matrix, and if COMPZ = 'I', Z con‐
58 tains the orthonormal eigenvectors of the symmetric tridiagonal
59 matrix. If COMPZ = 'N', then Z is not referenced.
60 LDZ (input) INTEGER
62 The leading dimension of the array Z. LDZ >= 1. If eigenvec‐
63 tors are desired, then LDZ >= max(1,N).
64 WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
66 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
67 LWORK (input) INTEGER
69 The dimension of the array WORK. If COMPZ = 'N' or N <= 1 then
70 LWORK must be at least 1. If COMPZ = 'V' and N > 1 then LWORK
71 must be at least ( 1 + 3*N + 2*N*lg N + 3*N**2 ), where lg( N )
72 = smallest integer k such that 2**k >= N. If COMPZ = 'I' and N
73 > 1 then LWORK must be at least ( 1 + 4*N + N**2 ). Note that
74 for COMPZ = 'I' or 'V', then if N is less than or equal to the
75 minimum divide size, usually 25, then LWORK need only be
76 max(1,2*(N-1)). If LWORK = -1, then a workspace query is
77 assumed; the routine only calculates the optimal size of the
78 WORK array, returns this value as the first entry of the WORK
79 array, and no error message related to LWORK is issued by
80 XERBLA.
81 IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
83 On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
84 LIWORK (input) INTEGER
86 The dimension of the array IWORK. If COMPZ = 'N' or N <= 1
87 then LIWORK must be at least 1. If COMPZ = 'V' and N > 1 then
88 LIWORK must be at least ( 6 + 6*N + 5*N*lg N ). If COMPZ = 'I'
89 and N > 1 then LIWORK must be at least ( 3 + 5*N ). Note that
90 for COMPZ = 'I' or 'V', then if N is less than or equal to the
91 minimum divide size, usually 25, then LIWORK need only be 1.
92 If LIWORK = -1, then a workspace query is assumed; the routine
93 only calculates the optimal size of the IWORK array, returns
94 this value as the first entry of the IWORK array, and no error
95 message related to LIWORK is issued by XERBLA.
96 INFO (output) INTEGER
98 = 0: successful exit.
99 < 0: if INFO = -i, the i-th argument had an illegal value.
100 > 0: The algorithm failed to compute an eigenvalue while work‐
101 ing on the submatrix lying in rows and columns INFO/(N+1)
102 through mod(INFO,N+1).
103
105 Based on contributions by
106 Jeff Rutter, Computer Science Division, University of California
107 at Berkeley, USA
108 Modified by Francoise Tisseur, University of Tennessee.
109 LAPACK driver routine (version 3.N2o)vember 2008 SSTEDC(1)