1SSYEVX(1) LAPACK driver routine (version 3.2) SSYEVX(1)
2
6 SSYEVX - computes selected eigenvalues and, optionally, eigenvectors of
7 a real symmetric matrix A
8
10 SUBROUTINE SSYEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
11 ABSTOL, M, W, Z, LDZ, WORK, LWORK, IWORK, IFAIL,
12 INFO )
13 CHARACTER JOBZ, RANGE, UPLO
15 INTEGER IL, INFO, IU, LDA, LDZ, LWORK, M, N
17 REAL ABSTOL, VL, VU
19 INTEGER IFAIL( * ), IWORK( * )
21 REAL A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )
23
25 SSYEVX computes selected eigenvalues and, optionally, eigenvectors of a
26 real symmetric matrix A. Eigenvalues and eigenvectors can be selected
27 by specifying either a range of values or a range of indices for the
28 desired eigenvalues.
29
31 JOBZ (input) CHARACTER*1
32 = 'N': Compute eigenvalues only;
33 = 'V': Compute eigenvalues and eigenvectors.
34 RANGE (input) CHARACTER*1
36 = 'A': all eigenvalues will be found.
37 = 'V': all eigenvalues in the half-open interval (VL,VU] will
38 be found. = 'I': the IL-th through IU-th eigenvalues will be
39 found.
40 UPLO (input) CHARACTER*1
42 = 'U': Upper triangle of A is stored;
43 = 'L': Lower triangle of A is stored.
44 N (input) INTEGER
46 The order of the matrix A. N >= 0.
47 A (input/output) REAL array, dimension (LDA, N)
49 On entry, the symmetric matrix A. If UPLO = 'U', the leading
50 N-by-N upper triangular part of A contains the upper triangular
51 part of the matrix A. If UPLO = 'L', the leading N-by-N lower
52 triangular part of A contains the lower triangular part of the
53 matrix A. On exit, the lower triangle (if UPLO='L') or the
54 upper triangle (if UPLO='U') of A, including the diagonal, is
55 destroyed.
56 LDA (input) INTEGER
58 The leading dimension of the array A. LDA >= max(1,N).
59 VL (input) REAL
61 VU (input) REAL If RANGE='V', the lower and upper bounds
62 of the interval to be searched for eigenvalues. VL < VU. Not
63 referenced if RANGE = 'A' or 'I'.
64 IL (input) INTEGER
66 IU (input) INTEGER If RANGE='I', the indices (in ascending
67 order) of the smallest and largest eigenvalues to be returned.
68 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not
69 referenced if RANGE = 'A' or 'V'.
70 ABSTOL (input) REAL
72 The absolute error tolerance for the eigenvalues. An approxi‐
73 mate eigenvalue is accepted as converged when it is determined
74 to lie in an interval [a,b] of width less than or equal to
75 ABSTOL + EPS * max( |a|,|b| ) , where EPS is the machine pre‐
76 cision. If ABSTOL is less than or equal to zero, then EPS*|T|
77 will be used in its place, where |T| is the 1-norm of the
78 tridiagonal matrix obtained by reducing A to tridiagonal form.
79 Eigenvalues will be computed most accurately when ABSTOL is set
80 to twice the underflow threshold 2*SLAMCH('S'), not zero. If
81 this routine returns with INFO>0, indicating that some eigen‐
82 vectors did not converge, try setting ABSTOL to 2*SLAMCH('S').
83 See "Computing Small Singular Values of Bidiagonal Matrices
84 with Guaranteed High Relative Accuracy," by Demmel and Kahan,
85 LAPACK Working Note #3.
86 M (output) INTEGER
88 The total number of eigenvalues found. 0 <= M <= N. If RANGE
89 = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
90 W (output) REAL array, dimension (N)
92 On normal exit, the first M elements contain the selected ei‐
93 genvalues in ascending order.
94 Z (output) REAL array, dimension (LDZ, max(1,M))
96 If JOBZ = 'V', then if INFO = 0, the first M columns of Z con‐
97 tain the orthonormal eigenvectors of the matrix A corresponding
98 to the selected eigenvalues, with the i-th column of Z holding
99 the eigenvector associated with W(i). If an eigenvector fails
100 to converge, then that column of Z contains the latest approxi‐
101 mation to the eigenvector, and the index of the eigenvector is
102 returned in IFAIL. If JOBZ = 'N', then Z is not referenced.
103 Note: the user must ensure that at least max(1,M) columns are
104 supplied in the array Z; if RANGE = 'V', the exact value of M
105 is not known in advance and an upper bound must be used.
106 LDZ (input) INTEGER
108 The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
109 'V', LDZ >= max(1,N).
110 WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
112 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
113 LWORK (input) INTEGER
115 The length of the array WORK. LWORK >= 1, when N <= 1; other‐
116 wise 8*N. For optimal efficiency, LWORK >= (NB+3)*N, where NB
117 is the max of the blocksize for SSYTRD and SORMTR returned by
118 ILAENV. If LWORK = -1, then a workspace query is assumed; the
119 routine only calculates the optimal size of the WORK array,
120 returns this value as the first entry of the WORK array, and no
121 error message related to LWORK is issued by XERBLA.
122 IWORK (workspace) INTEGER array, dimension (5*N)
124 IFAIL (output) INTEGER array, dimension (N)
126 If JOBZ = 'V', then if INFO = 0, the first M elements of IFAIL
127 are zero. If INFO > 0, then IFAIL contains the indices of the
128 eigenvectors that failed to converge. If JOBZ = 'N', then
129 IFAIL is not referenced.
130 INFO (output) INTEGER
132 = 0: successful exit
133 < 0: if INFO = -i, the i-th argument had an illegal value
134 > 0: if INFO = i, then i eigenvectors failed to converge.
135 Their indices are stored in array IFAIL.
136 LAPACK driver routine (version 3.N2o)vember 2008 SSYEVX(1)