1DSBGVD(1) LAPACK driver routine (version 3.1) DSBGVD(1)
2
6 DSBGVD - all the eigenvalues, and optionally, the eigenvectors of a
7 real generalized symmetric-definite banded eigenproblem, of the form
8 A*x=(lambda)*B*x
9
11 SUBROUTINE DSBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
12 LDZ, WORK, LWORK, IWORK, LIWORK, INFO )
13 CHARACTER JOBZ, UPLO
15 INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LWORK, N
17 INTEGER IWORK( * )
19 DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), W( * ),
21 WORK( * ), Z( LDZ, * )
22
24 DSBGVD computes all the eigenvalues, and optionally, the eigenvectors
25 of a real generalized symmetric-definite banded eigenproblem, of the
26 form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and
27 banded, and B is also positive definite. If eigenvectors are desired,
28 it uses a divide and conquer algorithm.
29 The divide and conquer algorithm makes very mild assumptions about
31 floating point arithmetic. It will work on machines with a guard digit
32 in add/subtract, or on those binary machines without guard digits which
33 subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
34 conceivably fail on hexadecimal or decimal machines without guard dig‐
35 its, but we know of none.
36
39 JOBZ (input) CHARACTER*1
40 = 'N': Compute eigenvalues only;
41 = 'V': Compute eigenvalues and eigenvectors.
42 UPLO (input) CHARACTER*1
44 = 'U': Upper triangles of A and B are stored;
45 = 'L': Lower triangles of A and B are stored.
46 N (input) INTEGER
48 The order of the matrices A and B. N >= 0.
49 KA (input) INTEGER
51 The number of superdiagonals of the matrix A if UPLO = 'U', or
52 the number of subdiagonals if UPLO = 'L'. KA >= 0.
53 KB (input) INTEGER
55 The number of superdiagonals of the matrix B if UPLO = 'U', or
56 the number of subdiagonals if UPLO = 'L'. KB >= 0.
57 AB (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
59 On entry, the upper or lower triangle of the symmetric band
60 matrix A, stored in the first ka+1 rows of the array. The j-th
61 column of A is stored in the j-th column of the array AB as
62 follows: if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-
63 ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for
64 j<=i<=min(n,j+ka).
65 On exit, the contents of AB are destroyed.
67 LDAB (input) INTEGER
69 The leading dimension of the array AB. LDAB >= KA+1.
70 BB (input/output) DOUBLE PRECISION array, dimension (LDBB, N)
72 On entry, the upper or lower triangle of the symmetric band
73 matrix B, stored in the first kb+1 rows of the array. The j-th
74 column of B is stored in the j-th column of the array BB as
75 follows: if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-
76 kb)<=i<=j; if UPLO = 'L', BB(1+i-j,j) = B(i,j) for
77 j<=i<=min(n,j+kb).
78 On exit, the factor S from the split Cholesky factorization B =
80 S**T*S, as returned by DPBSTF.
81 LDBB (input) INTEGER
83 The leading dimension of the array BB. LDBB >= KB+1.
84 W (output) DOUBLE PRECISION array, dimension (N)
86 If INFO = 0, the eigenvalues in ascending order.
87 Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
89 If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
90 eigenvectors, with the i-th column of Z holding the eigenvector
91 associated with W(i). The eigenvectors are normalized so
92 Z**T*B*Z = I. If JOBZ = 'N', then Z is not referenced.
93 LDZ (input) INTEGER
95 The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
96 'V', LDZ >= max(1,N).
97 WORK (workspace/output) DOUBLE PRECISION array, dimension
99 (MAX(1,LWORK))
100 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
101 LWORK (input) INTEGER
103 The dimension of the array WORK. If N <= 1,
104 LWORK >= 1. If JOBZ = 'N' and N > 1, LWORK >= 3*N. If JOBZ =
105 'V' and N > 1, LWORK >= 1 + 5*N + 2*N**2.
106 If LWORK = -1, then a workspace query is assumed; the routine
108 only calculates the optimal sizes of the WORK and IWORK arrays,
109 returns these values as the first entries of the WORK and IWORK
110 arrays, and no error message related to LWORK or LIWORK is
111 issued by XERBLA.
112 IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
114 On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
115 LIWORK (input) INTEGER
117 The dimension of the array IWORK. If JOBZ = 'N' or N <= 1,
118 LIWORK >= 1. If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
119 If LIWORK = -1, then a workspace query is assumed; the routine
121 only calculates the optimal sizes of the WORK and IWORK arrays,
122 returns these values as the first entries of the WORK and IWORK
123 arrays, and no error message related to LWORK or LIWORK is
124 issued by XERBLA.
125 INFO (output) INTEGER
127 = 0: successful exit
128 < 0: if INFO = -i, the i-th argument had an illegal value
129 > 0: if INFO = i, and i is:
130 <= N: the algorithm failed to converge: i off-diagonal ele‐
131 ments of an intermediate tridiagonal form did not converge to
132 zero; > N: if INFO = N + i, for 1 <= i <= N, then DPBSTF
133 returned INFO = i: B is not positive definite. The factoriza‐
134 tion of B could not be completed and no eigenvalues or eigen‐
135 vectors were computed.
136
138 Based on contributions by
139 Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
140 LAPACK driver routine (version 3.N1o)vember 2006 DSBGVD(1)