DSBGV(3)
computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x
SYNOPSIS
- SUBROUTINE DSBGV(
-
JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
LDZ, WORK, INFO )
-
CHARACTER
JOBZ, UPLO
-
INTEGER
INFO, KA, KB, LDAB, LDBB, LDZ, N
-
DOUBLE
PRECISION AB( LDAB, * ), BB( LDBB, * ), W( * ),
WORK( * ), Z( LDZ, * )
PURPOSE
DSBGV computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite banded eigenproblem, of
the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
and banded, and B is also positive definite.
ARGUMENTS
- JOBZ (input) CHARACTER*1
-
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
- UPLO (input) CHARACTER*1
-
= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.
- N (input) INTEGER
-
The order of the matrices A and B. N >= 0.
- KA (input) INTEGER
-
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KA >= 0.
- KB (input) INTEGER
-
The number of superdiagonals of the matrix B if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KB >= 0.
- AB (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
-
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first ka+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
On exit, the contents of AB are destroyed.
- LDAB (input) INTEGER
-
The leading dimension of the array AB. LDAB >= KA+1.
- BB (input/output) DOUBLE PRECISION array, dimension (LDBB, N)
-
On entry, the upper or lower triangle of the symmetric band
matrix B, stored in the first kb+1 rows of the array. The
j-th column of B is stored in the j-th column of the array BB
as follows:
if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
On exit, the factor S from the split Cholesky factorization
B = S**T*S, as returned by DPBSTF.
- LDBB (input) INTEGER
-
The leading dimension of the array BB. LDBB >= KB+1.
- W (output) DOUBLE PRECISION array, dimension (N)
-
If INFO = 0, the eigenvalues in ascending order.
- Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
-
If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
eigenvectors, with the i-th column of Z holding the
eigenvector associated with W(i). The eigenvectors are
normalized so that Z**T*B*Z = I.
If JOBZ = 'N', then Z is not referenced.
- LDZ (input) INTEGER
-
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', LDZ >= N.
- WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
-
- INFO (output) INTEGER
-
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, and i is:
<= N: the algorithm failed to converge:
i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
> N: if INFO = N + i, for 1 <= i <= N, then DPBSTF
returned INFO = i: B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.