dsbgv(3F)

NAME
     DSBGV - compute 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.