1ZHBGV(1) LAPACK driver routine (version 3.2) ZHBGV(1)
2
6 ZHBGV - computes all the eigenvalues, and optionally, the eigenvectors
7 of a complex generalized Hermitian-definite banded eigenproblem, of the
8 form A*x=(lambda)*B*x
9
11 SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ,
12 WORK, RWORK, INFO )
13 CHARACTER JOBZ, UPLO
15 INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
17 DOUBLE PRECISION RWORK( * ), W( * )
19 COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ), Z( LDZ, * )
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23 ZHBGV computes all the eigenvalues, and optionally, the eigenvectors of
24 a complex generalized Hermitian-definite banded eigenproblem, of the
25 form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian and
26 banded, and B is also positive definite.
27
29 JOBZ (input) CHARACTER*1
30 = 'N': Compute eigenvalues only;
31 = 'V': Compute eigenvalues and eigenvectors.
32 UPLO (input) CHARACTER*1
34 = 'U': Upper triangles of A and B are stored;
35 = 'L': Lower triangles of A and B are stored.
36 N (input) INTEGER
38 The order of the matrices A and B. N >= 0.
39 KA (input) INTEGER
41 The number of superdiagonals of the matrix A if UPLO = 'U', or
42 the number of subdiagonals if UPLO = 'L'. KA >= 0.
43 KB (input) INTEGER
45 The number of superdiagonals of the matrix B if UPLO = 'U', or
46 the number of subdiagonals if UPLO = 'L'. KB >= 0.
47 AB (input/output) COMPLEX*16 array, dimension (LDAB, N)
49 On entry, the upper or lower triangle of the Hermitian band
50 matrix A, stored in the first ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-
53 ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for
54 j<=i<=min(n,j+ka). On exit, the contents of AB are destroyed.
55 LDAB (input) INTEGER
57 The leading dimension of the array AB. LDAB >= KA+1.
58 BB (input/output) COMPLEX*16 array, dimension (LDBB, N)
60 On entry, the upper or lower triangle of the Hermitian band
61 matrix B, stored in the first kb+1 rows of the array. The j-th
62 column of B is stored in the j-th column of the array BB as
63 follows: if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-
64 kb)<=i<=j; if UPLO = 'L', BB(1+i-j,j) = B(i,j) for
65 j<=i<=min(n,j+kb). On exit, the factor S from the split
66 Cholesky factorization B = S**H*S, as returned by ZPBSTF.
67 LDBB (input) INTEGER
69 The leading dimension of the array BB. LDBB >= KB+1.
70 W (output) DOUBLE PRECISION array, dimension (N)
72 If INFO = 0, the eigenvalues in ascending order.
73 Z (output) COMPLEX*16 array, dimension (LDZ, N)
75 If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
76 eigenvectors, with the i-th column of Z holding the eigenvector
77 associated with W(i). The eigenvectors are normalized so that
78 Z**H*B*Z = I. If JOBZ = 'N', then Z is not referenced.
79 LDZ (input) INTEGER
81 The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
82 'V', LDZ >= N.
83 WORK (workspace) COMPLEX*16 array, dimension (N)
85 RWORK (workspace) DOUBLE PRECISION array, dimension (3*N)
87 INFO (output) INTEGER
89 = 0: successful exit
90 < 0: if INFO = -i, the i-th argument had an illegal value
91 > 0: if INFO = i, and i is:
92 <= N: the algorithm failed to converge: i off-diagonal ele‐
93 ments of an intermediate tridiagonal form did not converge to
94 zero; > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF
95 returned INFO = i: B is not positive definite. The factoriza‐
96 tion of B could not be completed and no eigenvalues or eigen‐
97 vectors were computed.
98 LAPACK driver routine (version 3.N2o)vember 2008 ZHBGV(1)