1SSBGV(1) LAPACK driver routine (version 3.1) SSBGV(1)
2
6 SSBGV - all the eigenvalues, and optionally, the eigenvectors of a real
7 generalized symmetric-definite banded eigenproblem, of the form
8 A*x=(lambda)*B*x
9
11 SUBROUTINE SSBGV( 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 REAL AB( LDAB, * ), BB( LDBB, * ), W( * ), WORK( * ), Z(
19 LDZ, * )
20
22 SSBGV 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
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) REAL array, dimension (LDAB, N)
49 On entry, the upper or lower triangle of the symmetric 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).
55 On exit, the contents of AB are destroyed.
57 LDAB (input) INTEGER
59 The leading dimension of the array AB. LDAB >= KA+1.
60 BB (input/output) REAL array, dimension (LDBB, N)
62 On entry, the upper or lower triangle of the symmetric band
63 matrix B, stored in the first kb+1 rows of the array. The j-th
64 column of B is stored in the j-th column of the array BB as
65 follows: if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-
66 kb)<=i<=j; if UPLO = 'L', BB(1+i-j,j) = B(i,j) for
67 j<=i<=min(n,j+kb).
68 On exit, the factor S from the split Cholesky factorization B =
70 S**T*S, as returned by SPBSTF.
71 LDBB (input) INTEGER
73 The leading dimension of the array BB. LDBB >= KB+1.
74 W (output) REAL array, dimension (N)
76 If INFO = 0, the eigenvalues in ascending order.
77 Z (output) REAL array, dimension (LDZ, N)
79 If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
80 eigenvectors, with the i-th column of Z holding the eigenvector
81 associated with W(i). The eigenvectors are normalized so that
82 Z**T*B*Z = I. If JOBZ = 'N', then Z is not referenced.
83 LDZ (input) INTEGER
85 The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
86 'V', LDZ >= N.
87 WORK (workspace) REAL array, dimension (3*N)
89 INFO (output) INTEGER
91 = 0: successful exit
92 < 0: if INFO = -i, the i-th argument had an illegal value
93 > 0: if INFO = i, and i is:
94 <= N: the algorithm failed to converge: i off-diagonal ele‐
95 ments of an intermediate tridiagonal form did not converge to
96 zero; > N: if INFO = N + i, for 1 <= i <= N, then SPBSTF
97 returned INFO = i: B is not positive definite. The factoriza‐
98 tion of B could not be completed and no eigenvalues or eigen‐
99 vectors were computed.
100 LAPACK driver routine (version 3.N1o)vember 2006 SSBGV(1)