1ZHBGV(1) LAPACK driver routine (version 3.1) ZHBGV(1)
2
6 ZHBGV - all the eigenvalues, and optionally, the eigenvectors of a com‐
7 plex generalized Hermitian-definite banded eigenproblem, of the form
8 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, * )
21
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
30 JOBZ (input) CHARACTER*1
31 = 'N': Compute eigenvalues only;
32 = 'V': Compute eigenvalues and eigenvectors.
33 UPLO (input) CHARACTER*1
35 = 'U': Upper triangles of A and B are stored;
36 = 'L': Lower triangles of A and B are stored.
37 N (input) INTEGER
39 The order of the matrices A and B. N >= 0.
40 KA (input) INTEGER
42 The number of superdiagonals of the matrix A if UPLO = 'U', or
43 the number of subdiagonals if UPLO = 'L'. KA >= 0.
44 KB (input) INTEGER
46 The number of superdiagonals of the matrix B if UPLO = 'U', or
47 the number of subdiagonals if UPLO = 'L'. KB >= 0.
48 AB (input/output) COMPLEX*16 array, dimension (LDAB, N)
50 On entry, the upper or lower triangle of the Hermitian band
51 matrix A, stored in the first ka+1 rows of the array. The j-th
52 column of A is stored in the j-th column of the array AB as
53 follows: if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-
54 ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for
55 j<=i<=min(n,j+ka).
56 On exit, the contents of AB are destroyed.
58 LDAB (input) INTEGER
60 The leading dimension of the array AB. LDAB >= KA+1.
61 BB (input/output) COMPLEX*16 array, dimension (LDBB, N)
63 On entry, the upper or lower triangle of the Hermitian band
64 matrix B, stored in the first kb+1 rows of the array. The j-th
65 column of B is stored in the j-th column of the array BB as
66 follows: if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-
67 kb)<=i<=j; if UPLO = 'L', BB(1+i-j,j) = B(i,j) for
68 j<=i<=min(n,j+kb).
69 On exit, the factor S from the split Cholesky factorization B =
71 S**H*S, as returned by ZPBSTF.
72 LDBB (input) INTEGER
74 The leading dimension of the array BB. LDBB >= KB+1.
75 W (output) DOUBLE PRECISION array, dimension (N)
77 If INFO = 0, the eigenvalues in ascending order.
78 Z (output) COMPLEX*16 array, dimension (LDZ, N)
80 If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
81 eigenvectors, with the i-th column of Z holding the eigenvector
82 associated with W(i). The eigenvectors are normalized so that
83 Z**H*B*Z = I. If JOBZ = 'N', then Z is not referenced.
84 LDZ (input) INTEGER
86 The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
87 'V', LDZ >= N.
88 WORK (workspace) COMPLEX*16 array, dimension (N)
90 RWORK (workspace) DOUBLE PRECISION array, dimension (3*N)
92 INFO (output) INTEGER
94 = 0: successful exit
95 < 0: if INFO = -i, the i-th argument had an illegal value
96 > 0: if INFO = i, and i is:
97 <= N: the algorithm failed to converge: i off-diagonal ele‐
98 ments of an intermediate tridiagonal form did not converge to
99 zero; > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF
100 returned INFO = i: B is not positive definite. The factoriza‐
101 tion of B could not be completed and no eigenvalues or eigen‐
102 vectors were computed.
103 LAPACK driver routine (version 3.N1o)vember 2006 ZHBGV(1)