Purpose

LA_SYEV and LA_SYEVD compute all eigenvalues and, optionally, all eigenvectors of a real symmetric matrix $A$.
LA_HEEV and LA_HEEVD compute all eigenvalues and, optionally, all eigenvectors of a complex Hermitian matrix $A$.
LA_SYEVD and LA_HEEVD use a divide and conquer algorithm. If eigenvectors are desired, they can be much faster than LA_SYEV and LA_HEEV for large matrices but use more workspace.