Purpose

LA_SBGV, LA_SBGVD, LA_HBGV and LA_HBGVD compute all eigenvalues and, optionally, all eigenvectors of the generalized eigenvalue problem

$$A\,z=\lambda\,B\,z,$$

where $A$ and $B$ are real symmetric in the cases of LA_SBGV and LA_SBGVD and complex Hermitian in the cases of LA_HBGV and LA_HBGVD. Matrix $B$ is positive definite. Matrices $A$ and $B$ are stored in a band format.
LA_SBGVD and LA_HBGVD use a divide and conquer algorithm. If eigenvectors are desired, they can be much faster than LA_SBGV and LA_HBGV for large matrices but use more workspace.