Purpose

LA_SYGV, LA_SYGVD, LA_HEGV and LA_HEGVD 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_SYGV and LA_SYGVD and complex Hermitian in the cases of LA_HEGV and LA_HEGVD. In all four cases $B$ is positive definite.
LA_SYGVD and LA_HEGVD use a divide and conquer algorithm. If eigenvectors are desired, they can be much faster than LA_SYGV and LA_HEGV for large matrices but use more workspace.