DSBGV(3)
computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite 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 symmetricdefinite 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
jth column of A is stored in the jth column of the array AB
as follows:
if UPLO = 'U', AB(ka+1+ij,j) = A(i,j) for max(1,jka)<=i<=j;
if UPLO = 'L', AB(1+ij,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
jth column of B is stored in the jth column of the array BB
as follows:
if UPLO = 'U', BB(kb+1+ij,j) = B(i,j) for max(1,jkb)<=i<=j;
if UPLO = 'L', BB(1+ij,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 ith 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 ith argument had an illegal value
> 0: if INFO = i, and i is:
<= N: the algorithm failed to converge:
i offdiagonal 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.