1DSBGV(1) LAPACK driver routine (version 3.2) DSBGV(1)
2
6 DSBGV - computes all the eigenvalues, and optionally, the eigenvectors
7 of a real generalized symmetric-definite banded eigenproblem, of the
8 form A*x=(lambda)*B*x
9
11 SUBROUTINE DSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ,
12 WORK, INFO )
13 CHARACTER JOBZ, UPLO
15 INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
17 DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), W( * ), WORK(
19 * ), Z( LDZ, * )
20
22 DSBGV computes all the eigenvalues, and optionally, the eigenvectors of
23 a real generalized symmetric-definite banded eigenproblem, of the form
24 A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and banded,
25 and B is also positive definite.
26
28 JOBZ (input) CHARACTER*1
29 = 'N': Compute eigenvalues only;
30 = 'V': Compute eigenvalues and eigenvectors.
31 UPLO (input) CHARACTER*1
33 = 'U': Upper triangles of A and B are stored;
34 = 'L': Lower triangles of A and B are stored.
35 N (input) INTEGER
37 The order of the matrices A and B. N >= 0.
38 KA (input) INTEGER
40 The number of superdiagonals of the matrix A if UPLO = 'U', or
41 the number of subdiagonals if UPLO = 'L'. KA >= 0.
42 KB (input) INTEGER
44 The number of superdiagonals of the matrix B if UPLO = 'U', or
45 the number of subdiagonals if UPLO = 'L'. KB >= 0.
46 AB (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
48 On entry, the upper or lower triangle of the symmetric band
49 matrix A, stored in the first ka+1 rows of the array. The j-th
50 column of A is stored in the j-th column of the array AB as
51 follows: if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-
52 ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for
53 j<=i<=min(n,j+ka). On exit, the contents of AB are destroyed.
54 LDAB (input) INTEGER
56 The leading dimension of the array AB. LDAB >= KA+1.
57 BB (input/output) DOUBLE PRECISION array, dimension (LDBB, N)
59 On entry, the upper or lower triangle of the symmetric band
60 matrix B, stored in the first kb+1 rows of the array. The j-th
61 column of B is stored in the j-th column of the array BB as
62 follows: if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-
63 kb)<=i<=j; if UPLO = 'L', BB(1+i-j,j) = B(i,j) for
64 j<=i<=min(n,j+kb). On exit, the factor S from the split
65 Cholesky factorization B = S**T*S, as returned by DPBSTF.
66 LDBB (input) INTEGER
68 The leading dimension of the array BB. LDBB >= KB+1.
69 W (output) DOUBLE PRECISION array, dimension (N)
71 If INFO = 0, the eigenvalues in ascending order.
72 Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
74 If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
75 eigenvectors, with the i-th column of Z holding the eigenvector
76 associated with W(i). The eigenvectors are normalized so that
77 Z**T*B*Z = I. If JOBZ = 'N', then Z is not referenced.
78 LDZ (input) INTEGER
80 The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
81 'V', LDZ >= N.
82 WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
84 INFO (output) INTEGER
86 = 0: successful exit
87 < 0: if INFO = -i, the i-th argument had an illegal value
88 > 0: if INFO = i, and i is:
89 <= N: the algorithm failed to converge: i off-diagonal ele‐
90 ments of an intermediate tridiagonal form did not converge to
91 zero; > N: if INFO = N + i, for 1 <= i <= N, then DPBSTF
92 returned INFO = i: B is not positive definite. The factoriza‐
93 tion of B could not be completed and no eigenvalues or eigen‐
94 vectors were computed.
95 LAPACK driver routine (version 3.N2o)vember 2008 DSBGV(1)