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LAPACK95 is a Fortran 95 interface to the Fortran 77 LAPACK library. It improves upon the original user-interface to the LAPACK package, taking advantage of the considerable simplifications which Fortran 95 allows. The design of LAPACK95 exploits assumed-shape arrays, optional arguments, and generic interfaces. The Fortran 95 interface has been implemented by writing Fortran 95 ``wrappers'' to call existing routines from the LAPACK package. This interface can persist unchanged even if the underlying Fortran 77 LAPACK code is rewritten to take advantage of the new features of Fortran 95.