1SSBEVD(1) LAPACK driver routine (version 3.2) SSBEVD(1)
2
6 SSBEVD - computes all the eigenvalues and, optionally, eigenvectors of
7 a real symmetric band matrix A
8
10 SUBROUTINE SSBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, LWORK,
11 IWORK, LIWORK, INFO )
12 CHARACTER JOBZ, UPLO
14 INTEGER INFO, KD, LDAB, LDZ, LIWORK, LWORK, N
16 INTEGER IWORK( * )
18 REAL AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
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22 SSBEVD computes all the eigenvalues and, optionally, eigenvectors of a
23 real symmetric band matrix A. If eigenvectors are desired, it uses a
24 divide and conquer algorithm.
25 The divide and conquer algorithm makes very mild assumptions about
26 floating point arithmetic. It will work on machines with a guard digit
27 in add/subtract, or on those binary machines without guard digits which
28 subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
29 conceivably fail on hexadecimal or decimal machines without guard dig‐
30 its, but we know of none.
31
33 JOBZ (input) CHARACTER*1
34 = 'N': Compute eigenvalues only;
35 = 'V': Compute eigenvalues and eigenvectors.
36 UPLO (input) CHARACTER*1
38 = 'U': Upper triangle of A is stored;
39 = 'L': Lower triangle of A is stored.
40 N (input) INTEGER
42 The order of the matrix A. N >= 0.
43 KD (input) INTEGER
45 The number of superdiagonals of the matrix A if UPLO = 'U', or
46 the number of subdiagonals if UPLO = 'L'. KD >= 0.
47 AB (input/output) REAL array, dimension (LDAB, N)
49 On entry, the upper or lower triangle of the symmetric band
50 matrix A, stored in the first KD+1 rows of the array. The j-th
51 column of A is stored in the j-th column of the array AB as
52 follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-
53 kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for
54 j<=i<=min(n,j+kd). On exit, AB is overwritten by values gener‐
55 ated during the reduction to tridiagonal form. If UPLO = 'U',
56 the first superdiagonal and the diagonal of the tridiagonal
57 matrix T are returned in rows KD and KD+1 of AB, and if UPLO =
58 'L', the diagonal and first subdiagonal of T are returned in
59 the first two rows of AB.
60 LDAB (input) INTEGER
62 The leading dimension of the array AB. LDAB >= KD + 1.
63 W (output) REAL array, dimension (N)
65 If INFO = 0, the eigenvalues in ascending order.
66 Z (output) REAL array, dimension (LDZ, N)
68 If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
69 eigenvectors of the matrix A, with the i-th column of Z holding
70 the eigenvector associated with W(i). If JOBZ = 'N', then Z is
71 not referenced.
72 LDZ (input) INTEGER
74 The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
75 'V', LDZ >= max(1,N).
76 WORK (workspace/output) REAL array,
78 dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the
79 optimal LWORK.
80 LWORK (input) INTEGER
82 The dimension of the array WORK. IF N <= 1,
83 LWORK must be at least 1. If JOBZ = 'N' and N > 2, LWORK must
84 be at least 2*N. If JOBZ = 'V' and N > 2, LWORK must be at
85 least ( 1 + 5*N + 2*N**2 ). If LWORK = -1, then a workspace
86 query is assumed; the routine only calculates the optimal sizes
87 of the WORK and IWORK arrays, returns these values as the first
88 entries of the WORK and IWORK arrays, and no error message
89 related to LWORK or LIWORK is issued by XERBLA.
90 IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
92 On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
93 LIWORK (input) INTEGER
95 The dimension of the array LIWORK. If JOBZ = 'N' or N <= 1,
96 LIWORK must be at least 1. If JOBZ = 'V' and N > 2, LIWORK
97 must be at least 3 + 5*N. If LIWORK = -1, then a workspace
98 query is assumed; the routine only calculates the optimal sizes
99 of the WORK and IWORK arrays, returns these values as the first
100 entries of the WORK and IWORK arrays, and no error message
101 related to LWORK or LIWORK is issued by XERBLA.
102 INFO (output) INTEGER
104 = 0: successful exit
105 < 0: if INFO = -i, the i-th argument had an illegal value
106 > 0: if INFO = i, the algorithm failed to converge; i off-
107 diagonal elements of an intermediate tridiagonal form did not
108 converge to zero.
109 LAPACK driver routine (version 3.N2o)vember 2008 SSBEVD(1)