Purpose

LA_SPGV, LA_SPGVD, LA_HPGV and LA_HPGVD compute all eigenvalues and, optionally, all eigenvectors of generalized eigenvalue problems of the form

$$A\,z=\lambda\,B\,z, \;\;\; A\,Bz=\lambda\,z, \;\;\; \mbox{and} \;\;\; B\,A\,z=\lambda\,z,$$

where $A$ and $B$ are real symmetric in the cases of LA_SPGV and LA_SPGVD and complex Hermitian in the cases of LA_HPGV and LA_HPGVD. In all four cases $B$ is positive definite. Matrices $A$ and $B$ are stored in a packed format.
LA_SPGVD and LA_HPGVD use a divide and conquer algorithm. If eigenvectors are desired, they can be much faster than LA_SPGV and LA_HPGV for large matrices but use more workspace.